Finite Group Databasebeta

← #33967917

Subgroups — #33967917

Order 18688.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623545C211yesmaximal, characteristic, complemented
2D4×#11924027C211yesmaximal, characteristic, complemented
3#22622946C211yesmaximal, characteristic, complemented
4#22622847C211yesmaximal, characteristic, complemented
5#22622657C211yesmaximal, characteristic, complemented
6#22622650C211yesmaximal, characteristic, complemented
7#22622371C211yesmaximal, characteristic, complemented
8#22622364C211yesmaximal, characteristic, complemented
9#22622273C211yesmaximal, characteristic, complemented
10#22621953C211yesmaximal, characteristic, complemented
11#22621924C211yesmaximal, characteristic, complemented
12#22621917C211yesmaximal, characteristic, complemented
13#22621791C211yesmaximal, characteristic, complemented
14#22621740C211yesmaximal, characteristic, complemented
15#22621625C211yesmaximal, characteristic, complemented
16#22621424C211yesmaximal, characteristic, complemented
17#22621422C211yesmaximal, characteristic, complemented
18#22620644C211yesmaximal, characteristic, complemented
19#22620628C211yesmaximal, characteristic, complemented
20#22620622C211yesmaximal, characteristic, complemented
21#22620077C211yesmaximal, characteristic, complemented
22#22620074C211yesmaximal, characteristic, complemented
23#22620070C211yesmaximal, characteristic, complemented
24#22620052C211yesmaximal, characteristic, complemented
25#22620050C211yesmaximal, characteristic, complemented
26#22620025C211yesmaximal, characteristic, complemented
27#22618941C211yesmaximal, characteristic, complemented
28#22618735C211yesmaximal, characteristic, complemented
29C2×#17988684C211yesmaximal, characteristic, complemented
30#440×D73C211yesmaximal, characteristic, complemented
31C73×#3310C211yesmaximal, characteristic, complemented
32C22×#11924027—21no—
33C2×#14556617C2211yescharacteristic
34C22×#11924016C2211yescharacteristic
35C2×SD16×D73C2211yescharacteristic
36#17989314C2211yescharacteristic, complemented
37#17989309C2211yescharacteristic, complemented
38#17989304—21no—
39#17989276C2211yescharacteristic, complemented
40#17989270—21no—
41#17989269—21no—
42#17989257C2211yescharacteristic
43D4×Dic146C2211yescharacteristic
44#17989250C2211yescharacteristic, complemented
45#17989247C2211yescharacteristic, complemented
46#17989246C2211yescharacteristic, complemented
47#17989243—21no—
48#17989241C2211yescharacteristic
49#17989238C2211yescharacteristic, complemented
50#17989237C2211yescharacteristic
51#17989237C2211yescharacteristic
52#17989235—21no—
53#17989231—21no—
54#17989224—21no—
55#17989224—21no—
56D4×C22⋊D73C2211yescharacteristic
57D4×C22⋊D73C2211yescharacteristic
58#17989143—21no—
59#17989139C2211yescharacteristic, complemented
60#17989135C2211yescharacteristic
61#17989132C2211yescharacteristic
62#17989132C2211yescharacteristic
63#17989123C2211yescharacteristic, complemented
64#17989122C2211yescharacteristic, complemented
65#17989120—21no—
66#17989114—21no—
67#17989097—21no—
68#17989093—21no—
69#17989093—21no—
70#17989055—21no—
71#17989055C2211yescharacteristic, complemented
72C4×#11924027C2211yescharacteristic
73C2×#14556556C2211yescharacteristic, complemented
74C4×Q8×D73C2211yescharacteristic, complemented
75C2×D4×Dic73C2211yescharacteristic
76C2×D4×Dic73C2211yescharacteristic
77C4×D4×D73C2211yescharacteristic
78#17988997C2211yescharacteristic, complemented
79#17988994C2211yescharacteristic, complemented
80#17988991C2211yescharacteristic, complemented
81#17988974C2211yescharacteristic, complemented
82#17988973C2211yescharacteristic, complemented
83#17988958C2211yescharacteristic, complemented
84#17988950C2211yescharacteristic, complemented
85#17988948C2211yescharacteristic, complemented
86#17988947C2211yescharacteristic, complemented
87#17988936C2211yescharacteristic, complemented
88#17988932C2211yescharacteristic, complemented
89#17988923C2211yescharacteristic, complemented
90#17988920C2211yescharacteristic, complemented
91#17988919C2211yescharacteristic, complemented
92#17988915C2211yescharacteristic, complemented
93#17988911C2211yescharacteristic, complemented
94#17988902C2211yescharacteristic, complemented
95#17988901C2211yescharacteristic, complemented
96#17988900C2211yescharacteristic, complemented
97#17988899C2211yescharacteristic, complemented
98#17988899C2211yescharacteristic, complemented
99#17988885C2211yescharacteristic
100#17988885C2211yescharacteristic, complemented
101#17988884C2211yescharacteristic, complemented
102#17988883C2211yescharacteristic, complemented
103#17988882C2211yescharacteristic, complemented
104#17988881C2211yescharacteristic, complemented
105#17988881C2211yescharacteristic, complemented
106#17988871C2211yescharacteristic, complemented
107#17988866C2211yescharacteristic, complemented
108#17988865C2211yescharacteristic
109#17988865C2211yescharacteristic, complemented
110#17988835C2211yescharacteristic, complemented
111#17988833C2211yescharacteristic, complemented
112#17988831C2211yescharacteristic, complemented
113#17988823C2211yescharacteristic, complemented
114#17988822C2211yescharacteristic, complemented
115#17988822C2211yescharacteristic, complemented
116#17988821C2211yescharacteristic, complemented
117#17988818C2211yescharacteristic, complemented
118#17988815C2211yescharacteristic, complemented
119#17988815C2211yescharacteristic, complemented
120#17988804C2211yescharacteristic
121#17988804C2211yescharacteristic, complemented
122#17988803C2211yescharacteristic, complemented
123#17988802C2211yescharacteristic
124#17988790C2211yescharacteristic
125#17988790C2211yescharacteristic, complemented
126#17988786C2211yescharacteristic, complemented
127#17988786C2211yescharacteristic, complemented
128#17988786C2211yescharacteristic, complemented
129#17988784C2211yescharacteristic, complemented
130#17988781C2211yescharacteristic, complemented
131#17988739C2211yescharacteristic
132#17988738C2211yescharacteristic
133#17988734C2211yescharacteristic, complemented
134#17988730C2211yescharacteristic, complemented
135#17988728C2211yescharacteristic, complemented
136#17988725C2211yescharacteristic, complemented
137#17988724C2211yescharacteristic, complemented
138#17988724C2211yescharacteristic, complemented
139#17988722C2211yescharacteristic
140#17988721C2211yescharacteristic
141#17988716C2211yescharacteristic, complemented
142#17988715C2211yescharacteristic, complemented
143#17988698C2211yescharacteristic, complemented
144#17988696C2211yescharacteristic
145#17988696C2211yescharacteristic, complemented
146#17988696C2211yescharacteristic, complemented
147#17988690C2211yescharacteristic, complemented
148#17988689C2211yescharacteristic, complemented
149#17988688C2211yescharacteristic
150#17988688C2211yescharacteristic, complemented
151#17988688C2211yescharacteristic, complemented
152#17988687C2211yescharacteristic
153#17988686C2211yescharacteristic, complemented
154#17988686C2211yescharacteristic, complemented
155#17988685C2211yescharacteristic, complemented
156#17988684C2211yescharacteristic
157#17988684C2211yescharacteristic
158#17988684C2211yescharacteristic
159#17988684C2211yescharacteristic
160#17988684C2211yescharacteristic, complemented
161#17988684C2211yescharacteristic, complemented
162#17988684C2211yescharacteristic, complemented
163#17988684C2211yescharacteristic, complemented
164#17988684C2211yescharacteristic, complemented
165#17988684C2211yescharacteristic, complemented
166#17988678C2211yescharacteristic
167#17988678C2211yescharacteristic, complemented
168#17988667C2211yescharacteristic
169#17988667C2211yescharacteristic, complemented
170#17988661C2211yescharacteristic, complemented
171#17988659C2211yescharacteristic, complemented
172#17988656C2211yescharacteristic, complemented
173C8×C22⋊D73C2211yescharacteristic, complemented
174#17988650C2211yescharacteristic, complemented
175#17988643C2211yescharacteristic, complemented
176#17988641C2211yescharacteristic, complemented
177#17988641C2211yescharacteristic, complemented
178#17988630C2211yescharacteristic, complemented
179C2×#14556524C2211yescharacteristic, complemented
180#107×D73C2211yescharacteristic, complemented
181#17988589C2211yescharacteristic, complemented
182C2×#14556516C2211yescharacteristic, complemented
183#103×D73C2211yescharacteristic, complemented
184#102×D73C2211yescharacteristic
185M16×Dic73C2211yescharacteristic, complemented
186C2×#14556501C2211yescharacteristic, complemented
187#97×D73C2211yescharacteristic, complemented
188#552×C73C2211yescharacteristic, complemented
189D42×C73C2211yescharacteristic
190#490×C73C2211yescharacteristic, complemented
191#482×C73C2211yescharacteristic, complemented
192#480×C73C2211yescharacteristic, complemented
193#478×C73C2211yescharacteristic
194#468×C73C2211yescharacteristic, complemented
195#465×C73C2211yescharacteristic, complemented
196#460×C73C2211yescharacteristic, complemented
197#450×C73C2211yescharacteristic
198#450×C73C2211yescharacteristic
199#440×C73C2211yescharacteristic
200#435×C73C2211yescharacteristic, complemented
201#418×C73C2211yescharacteristic
202C2×#102×C73C2211yescharacteristic
203C2×#11924028—21no—
204C2×#11924028C2311yescharacteristic
205C2×#11924027—21no—
206C2×#11924027—21no—
207C2×#11924027—21no—
208C2×#11924027—21no—
209C2×#11924027—21no—
210C2×#11924027—21no—
211C2×#11924027—21no—
212C2×#11924027—48no—
213C2×#11924027D411yescharacteristic
214C22×Dic146—21no—
215C22×Dic146C2311yescharacteristic
216C2×Q8×D73C2311yescharacteristic
217C22×C22⋊D73—21no—
218C22×C22⋊D73—21no—
219C2×D4×D73C2311yescharacteristic
220C23×Dic73—21no—
221C23×Dic73—21no—
222C22×C4×D73—21no—
223#14556617—24no—
224C2×#11924017C2311yescharacteristic
225C2×#11924017C2311yescharacteristic
226C2×#11924016—24no—
227C2×#11924016C2311yescharacteristic
228C2×#11924016C2311yescharacteristic
229C2×#11924016C2311yescharacteristic
230C2×#11924016C2311yescharacteristic
231C2×#11924016C2311yescharacteristic
232C2×#11924016C2311yescharacteristic
233C2×#11924015C2311yescharacteristic
234SD16×D73—24no—
235C2×D584C2311yescharacteristic
236C2×#11924013C2311yescharacteristic
237C2×#11924013C2311yescharacteristic
238C2×#11924013C2311yescharacteristic
239C2×#11924012C2311yescharacteristic
240C22×#10596831C2311yescharacteristic
241C2×C8×D73C2311yescharacteristic
242C2×C8×D73C2311yescharacteristic
243#14556591C2311yescharacteristic
244#14556590—21no—
245#14556590—21no—
246#14556590C2311yescharacteristic
247#14556590C2311yescharacteristic
248#14556590C2311yescharacteristic
249#14556589C2311yescharacteristic
250#14556587C2311yescharacteristic
251#14556587C2311yescharacteristic
252#14556586—21no—
253#14556586—21no—
254#14556586—21no—
255#14556585—21no—
256#14556584—21no—
257#14556583—21no—
258#14556582C2311yescharacteristic
259#14556581—21no—
260#14556581—21no—
261#14556581—21no—
262#14556580C2311yescharacteristic
263#14556579C2311yescharacteristic
264#14556578—21no—
265#14556577—21no—
266#14556577—21no—
267#14556577—21no—
268#14556577—21no—
269#14556576—21no—
270#14556576—21no—
271#14556575—21no—
272#14556575—21no—
273#14556575—21no—
274#14556574—21no—
275#14556573—21no—
276#14556573—21no—
277#14556573—21no—
278#14556572—21no—
279#14556572—21no—
280#14556571—21no—
281#14556571C2311yescharacteristic
282#14556570—21no—
283#14556570C2311yescharacteristic
284#14556569—21no—
285#14556569—21no—
286#14556569—21no—
287#14556569—21no—
288#14556569—21no—
289#14556568—21no—
290#14556568—21no—
291#14556568—21no—
292#14556568—21no—
293#14556568—21no—
294#14556568—21no—
295#14556566C2311yescharacteristic
296#14556565C2311yescharacteristic
297#14556565C2311yescharacteristic
298#14556565C2311yescharacteristic
299#14556564—21no—
300#14556563—21no—
301#14556563—21no—
302#14556563—21no—
303#14556563—21no—
304#14556563—21no—
305#14556563—21no—
306#14556563—21no—
307#14556562—21no—
308#14556562—21no—
309#14556562C2311yescharacteristic
310#14556562C2311yescharacteristic
311#14556560—21no—
312#14556560—21no—
313#14556559—21no—
314#14556559—21no—
315Q8×Dic73C2311yescharacteristic
316C4×Dic146—21no—
317C4×Dic146C2311yescharacteristic
318C4×Dic146C2311yescharacteristic
319#14556556—21no—
320#14556556—21no—
321#14556556—21no—
322#14556556—21no—
323#14556556—21no—
324#14556556D411yescharacteristic
325#14556556C2311yescharacteristic
326#14556556C2311yescharacteristic
327#14556556C2311yescharacteristic
328#14556556C2311yescharacteristic
329#14556556C2311yescharacteristic
330C4×D292C2311yescharacteristic
331D4×Dic73—21no—
332D4×Dic73—21no—
333D4×Dic73—21no—
334D4×Dic73—21no—
335D4×Dic73—21no—
336D4×Dic73D411yescharacteristic
337D4×Dic73C2311yescharacteristic
338D4×Dic73C2311yescharacteristic
339D4×Dic73C2311yescharacteristic
340D4×Dic73C2311yescharacteristic
341D4×Dic73C2311yescharacteristic
342D4×Dic73C2311yescharacteristic
343D4×Dic73C2311yescharacteristic
344#14556553—21no—
345#14556553—21no—
346#14556553C2311yescharacteristic
347#14556553C2311yescharacteristic
348#14556553C2311yescharacteristic
349C4×C22⋊D73—21no—
350C4×C22⋊D73C2311yescharacteristic
351C4×C22⋊D73C2311yescharacteristic
352#14556551—21no—
353#14556551—21no—
354#14556551—21no—
355#14556551—21no—
356#14556551—21no—
357#14556551—21no—
358#14556551—21no—
359#14556551—21no—
360#14556551D411yescharacteristic
361#14556551D411yescharacteristic
362#14556549—21no—
363#14556549—21no—
364#14556549D411yescharacteristic
365#14556548—21no—
366#14556548—21no—
367#14556548—21no—
368#14556547—21no—
369#14556547D411yescharacteristic
370#14556547D411yescharacteristic
371C2×C4⋊Dic73C2311yescharacteristic
372C2×C4⋊Dic73C2311yescharacteristic
373C2×#11924007—21no—
374C4⋊C4×D73—21no—
375C4⋊C4×D73C2311yescharacteristic
376C4⋊C4×D73C2311yescharacteristic
377C2×C22⋊Dic73—21no—
378C2×C22⋊Dic73—21no—
379C22⋊C4×D73—21no—
380C2×C4×Dic73—21no—
381C2×C4×Dic73C2311yescharacteristic
382C2×C4×Dic73C2311yescharacteristic
383C42×D73—21no—
384C42×D73—21no—
385C42×D73C2311yescharacteristic
386#14556525C2311yescharacteristic
387#14556525C2311yescharacteristic
388#14556525C2311yescharacteristic
389#14556524C2311yescharacteristic
390#14556524C2311yescharacteristic
391#14556524C2311yescharacteristic
392#14556524C2311yescharacteristic
393#14556524C2311yescharacteristic
394#14556524C2311yescharacteristic
395#14556524C2311yescharacteristic
396#14556522C2311yescharacteristic
397#14556522C2311yescharacteristic
398#14556522C2311yescharacteristic
399C4⋊#10596831C2311yescharacteristic
400#14556520C2311yescharacteristic
401#14556520C2311yescharacteristic
402#14556520C2311yescharacteristic
403#14556520C2311yescharacteristic
404#14556516C2311yescharacteristic
405#14556516C2311yescharacteristic
406#14556516C2311yescharacteristic
407#14556516C2311yescharacteristic
408#14556516C2311yescharacteristic
409#14556516C2311yescharacteristic
410#14556515C2311yescharacteristic
411#14556515C2311yescharacteristic
412#14556515C2311yescharacteristic
413#14556514C2311yescharacteristic
414#14556514C2311yescharacteristic
415#14556513C2311yescharacteristic
416#14556513C2311yescharacteristic
417#14556513C2311yescharacteristic
418#14556513C2311yescharacteristic
419#14556512C2311yescharacteristic
420#14556512C2311yescharacteristic
421#14556512C2311yescharacteristic
422#14556511C2311yescharacteristic
423#14556511C2311yescharacteristic
424#14556511C2311yescharacteristic
425#14556511C2311yescharacteristic
426C22⋊#10596831C2311yescharacteristic
427C22⋊#10596831C2311yescharacteristic
428#14556503C2311yescharacteristic
429#14556503C2311yescharacteristic
430#14556502C2311yescharacteristic
431#14556501C2311yescharacteristic
432#14556501C2311yescharacteristic
433#14556501C2311yescharacteristic
434#14556501C2311yescharacteristic
435#14556501C2311yescharacteristic
436#14556501C2311yescharacteristic
437C8×Dic73C2311yescharacteristic
438C8×Dic73C2311yescharacteristic
439C22×D4×C73—21no—
440C22×D4×C73C2311yescharacteristic
441C22×D4×C73C2311yescharacteristic
442C2×SD16×C73C2311yescharacteristic
443C2×SD16×C73C2311yescharacteristic
444C2×SD16×C73C2311yescharacteristic
445C2×M16×C73C2311yescharacteristic
446C22×C8×C73C2311yescharacteristic
447#127×C73C2311yescharacteristic
448#126×C73—21no—
449#125×C73—21no—
450#125×C73C2311yescharacteristic
451#123×C73—21no—
452C22⋊Q8×C73C2311yescharacteristic
453C22⋊Q8×C73C2311yescharacteristic
454#121×C73—21no—
455#121×C73C2311yescharacteristic
456#121×C73C2311yescharacteristic
457#120×C73—21no—
458#120×C73—21no—
459C4×Q8×C73C2311yescharacteristic
460C4×D4×C73C2311yescharacteristic
461C4×D4×C73C2311yescharacteristic
462#117×C73—21no—
463#117×C73C2311yescharacteristic
464C2×C4⋊C4×C73C2311yescharacteristic
465#107×C73C2311yescharacteristic
466#107×C73C2311yescharacteristic
467#106×C73C2311yescharacteristic
468C4⋊C8×C73C2311yescharacteristic
469#103×C73C2311yescharacteristic
470#102×C73C2311yescharacteristic
471#102×C73C2311yescharacteristic
472#102×C73C2311yescharacteristic
473#102×C73C2311yescharacteristic
474#102×C73C2311yescharacteristic
475#102×C73C2311yescharacteristic
476#102×C73C2311yescharacteristic
477#102×C73C2311yescharacteristic
478#102×C73C2311yescharacteristic
479C22⋊C8×C73C2311yescharacteristic
480C22⋊C8×C73C2311yescharacteristic
481#97×C73C2311yescharacteristic
482C23×D73—21no—
483#11924028—22no—
484#11924028—41no—
485#11924028—44no—
486#11924027—24no—
487#11924027—44no—
488#11924027—44no—
489#11924027—44no—
490#11924027—44no—
491#11924027—44no—
492#11924027—44no—
493#11924027—44no—
494C2×Dic146—22no—
495C2×Dic146—21no—
496C2×Dic146—21no—
497C2×Dic146—21no—
498C2×Dic146—21no—
499C2×Dic146—21no—
500C2×Dic146—21no—
501C2×Dic146—41no—
502C2×Dic146—44no—
503C2×Dic146C2×D411yescharacteristic
504C2×Dic146C2411yescharacteristic
505C2×Dic146C2411yescharacteristic
506Q8×D73—22no—
507Q8×D73—41no—
508C2×D292—21no—
509C2×D292C2411yescharacteristic
510C2×D292C2411yescharacteristic
511C2×C22⋊D73—21no—
512C2×C22⋊D73—21no—
513C2×C22⋊D73—21no—
514C2×C22⋊D73—21no—
515C2×C22⋊D73—21no—
516C2×C22⋊D73—21no—
517C2×C22⋊D73—21no—
518C2×C22⋊D73—21no—
519C2×C22⋊D73—21no—
520C2×C22⋊D73—21no—
521C2×C22⋊D73—21no—
522C2×C22⋊D73—44no—
523C2×C22⋊D73—44no—
524C2×C22⋊D73C2×D411yescharacteristic
525C2×C22⋊D73C2×D411yescharacteristic
526D4×D73—22no—
527D4×D73—41no—
528C22×Dic73—21no—
529C22×Dic73—21no—
530C22×Dic73—21no—
531C22×Dic73—21no—
532C22×Dic73—21no—
533C22×Dic73—21no—
534C22×Dic73—21no—
535C22×Dic73—21no—
536C22×Dic73—21no—
537C22×Dic73—21no—
538C22×Dic73—44no—
539C22×Dic73—44no—
540C22×Dic73C2×D411yescharacteristic
541C22×Dic73C2×D411yescharacteristic
542C22×Dic73C2×D411yescharacteristic
543C22×Dic73C2×D411yescharacteristic
544C2×C4×D73—21no—
545C2×C4×D73—21no—
546C2×C4×D73—21no—
547C2×C4×D73—21no—
548C2×C4×D73—21no—
549C2×C4×D73—21no—
550C2×C4×D73—21no—
551C2×C4×D73—21no—
552C2×C4×D73—44no—
553C2×C4×D73C2×D411yescharacteristic
554C2×C4×D73C2×D411yescharacteristic
555C2×C4×D73C2411yescharacteristic
556#11924017—22no—
557#11924017—41no—
558#11924016—22no—
559#11924016—22no—
560#11924016—22no—
561#11924016—22no—
562#11924016—41no—
563#11924016#4114yescomplemented
564#11924015—22no—
565D584—41no—
566#11924013—22no—
567#11924013—22no—
568#11924013—41no—
569#11924012—22no—
570C2×#10596831—22no—
571C2×#10596831C2411yescharacteristic
572C2×#10596831C2411yescharacteristic
573C2×#10596831C2411yescharacteristic
574C2×#10596831C2411yescharacteristic
575C8×D73—22no—
576C8×D73—41no—
577C4⋊Dic73—21no—
578C4⋊Dic73—21no—
579C4⋊Dic73—21no—
580C4⋊Dic73—21no—
581C4⋊Dic73—21no—
582C4⋊Dic73—21no—
583C4⋊Dic73C2×D411yescharacteristic
584C4⋊Dic73C2411yescharacteristic
585C4⋊Dic73C2411yescharacteristic
586C4⋊Dic73C2411yescharacteristic
587C4⋊Dic73C2411yescharacteristic
588#11924007—21no—
589#11924007—21no—
590#11924007—21no—
591#11924007—21no—
592#11924007—21no—
593#11924007—21no—
594#11924007—21no—
595#11924007—21no—
596#11924007—21no—
597#11924007—21no—
598#11924007—21no—
599#11924007—21no—
600#11924007—21no—
601#11924007—21no—
602#11924007—21no—
603#11924007C2×D411yescharacteristic
604#11924007C2×D411yescharacteristic
605#11924007C2×D411yescharacteristic
606#11924007C2×D411yescharacteristic
607C22⋊Dic73—21no—
608C22⋊Dic73—21no—
609C22⋊Dic73—21no—
610C22⋊Dic73—21no—
611C22⋊Dic73—21no—
612C22⋊Dic73—21no—
613C22⋊Dic73—21no—
614C22⋊Dic73—21no—
615C22⋊Dic73—21no—
616C22⋊Dic73—21no—
617C22⋊Dic73C2×D411yescharacteristic
618C22⋊Dic73C2×D411yescharacteristic
619#11924005—21no—
620#11924005—21no—
621#11924005—21no—
622#11924005—21no—
623#11924005—21no—
624#11924005—21no—
625#11924005—21no—
626#11924005—21no—
627#11924005—21no—
628#11924005—21no—
629#11924005—21no—
630#11924005—21no—
631#11924005—21no—
632#11924005C2×D411yescharacteristic
633#11924005C2×D411yescharacteristic
634C4×Dic73—21no—
635C4×Dic73—21no—
636C4×Dic73—21no—
637C4×Dic73—21no—
638C4×Dic73—21no—
639C4×Dic73—21no—
640C4×Dic73—21no—
641C4×Dic73C2×D411yescharacteristic
642C4×Dic73C2×D411yescharacteristic
643C4×Dic73C2×D411yescharacteristic
644C4×Dic73C2×D411yescharacteristic
645C4×Dic73C2×D411yescharacteristic
646C4×Dic73C2×D411yescharacteristic
647C4×Dic73C2411yescharacteristic
648C4×Dic73C2411yescharacteristic
649C4×Dic73C2411yescharacteristic
650C24×C73—21no—
651C24×C73—21no—
652C2×Q8×C73C2411yescharacteristic
653C2×D4×C73—22no—
654C2×D4×C73—22no—
655C2×D4×C73—21no—
656C2×D4×C73—21no—
657C2×D4×C73—21no—
658C2×D4×C73—21no—
659C2×D4×C73—21no—
660C2×D4×C73—21no—
661C2×D4×C73—41no—
662C2×D4×C73—41no—
663C2×D4×C73—44no—
664C2×D4×C73C2×D411yescharacteristic
665C2×D4×C73C2411yescharacteristic
666C2×D4×C73C2411yescharacteristic
667C2×D4×C73C2411yescharacteristic
668C22×C4×C73—21no—
669C22×C4×C73—21no—
670C22×C4×C73C2411yescharacteristic
671C22×C4×C73C2411yescharacteristic
672SD16×C73—22no—
673SD16×C73—41no—
674SD16×C73—41no—
675M16×C73—41no—
676C2×C8×C73—41no—
677C2×C8×C73C2411yescharacteristic
678C2×C8×C73C2411yescharacteristic
679C2×C8×C73C2411yescharacteristic
680C2×C8×C73C2411yescharacteristic
681C4⋊C4×C73—21no—
682C4⋊C4×C73—21no—
683C4⋊C4×C73—21no—
684C4⋊C4×C73—21no—
685C4⋊C4×C73—21no—
686C4⋊C4×C73—21no—
687C4⋊C4×C73C2×D411yescharacteristic
688C4⋊C4×C73C2411yescharacteristic
689C4⋊C4×C73C2411yescharacteristic
690C4⋊C4×C73C2411yescharacteristic
691C4⋊C4×C73C2411yescharacteristic
692C22⋊C4×C73—21no—
693C22⋊C4×C73—21no—
694C22⋊C4×C73—21no—
695C22⋊C4×C73—21no—
696C22⋊C4×C73—21no—
697C22⋊C4×C73—21no—
698C22⋊C4×C73C2×D411yescharacteristic
699C22⋊C4×C73C2×D411yescharacteristic
700C42×C73—21no—
701C42×C73—21no—
702C42×C73C2411yescharacteristic
703C23×C73—21no—
704C23×C73—21no—
705C23×C73—21no—
706C23×C73—42no—
707C23×C73—42no—
708C23×C73—42no—
709C23×C73—42no—
710C23×C73—81no—
711C23×C73—81no—
712C23×C73C22×D411yescharacteristic
713C23×C73C22×D411yescharacteristic
714C22×D73—21no—
715C22×D73—21no—
716C22×D73—42no—
717C22×D73—42no—
718C22×D73—81no—
719C22×D73C22×D411yescharacteristic
720Q8×C73—21no—
721Q8×C73—21no—
722D4×C73—22no—
723D4×C73—21no—
724D4×C73—21no—
725D4×C73—21no—
726D4×C73—21no—
727D4×C73—21no—
728D4×C73—42no—
729D4×C73—42no—
730D4×C73—42no—
731D4×C73—42no—
732D4×C73—42no—
733D4×C73—81no—
734D4×C73C2×#4112yes—
735C2×C4×C73—21no—
736C2×C4×C73—21no—
737C2×C4×C73—21no—
738C2×C4×C73—21no—
739C2×C4×C73—21no—
740C2×C4×C73—21no—
741C2×C4×C73—21no—
742C2×C4×C73—21no—
743C2×C4×C73—21no—
744C2×C4×C73—42no—
745C2×C4×C73—42no—
746C2×C4×C73C22×D411yescharacteristic
747C2×C4×C73C22×D411yescharacteristic
748C2×C4×C73C22×D411yescharacteristic
749C2×C4×C73C22×D411yescharacteristic
750C2×C4×C73C2511yescharacteristic
751C22⋊D73—22no—
752C22⋊D73—42no—
753C22⋊D73—42no—
754C22⋊D73—42no—
755C22⋊D73—42no—
756C22⋊D73—42no—
757C22⋊D73—42no—
758C22⋊D73—42no—
759C22⋊D73—42no—
760C22⋊D73—42no—
761C22⋊D73—81no—
762C22⋊D73—81no—
763C22⋊D73AGL(1,ℤ/8)14yescomplemented
764C2×Dic73—22no—
765C2×Dic73—21no—
766C2×Dic73—22no—
767C2×Dic73—21no—
768C2×Dic73—21no—
769C2×Dic73—21no—
770C2×Dic73—21no—
771C2×Dic73—21no—
772C2×Dic73—41no—
773C2×Dic73—41no—
774C2×Dic73—42no—
775C2×Dic73—42no—
776C2×Dic73—42no—
777C2×Dic73—42no—
778C2×Dic73—42no—
779C2×Dic73—42no—
780C2×Dic73—42no—
781C2×Dic73—42no—
782C2×Dic73—42no—
783C2×Dic73—42no—
784C2×Dic73C22×D411yescharacteristic
785C2×Dic73C22×D411yescharacteristic
786C2×Dic73C22×D411yescharacteristic
787C2×Dic73C22×D411yescharacteristic
788C2×Dic73C22×D411yescharacteristic
789C2×Dic73C22×D411yescharacteristic
790C2×Dic73C22×D411yescharacteristic
791D292—21no—
792D292—21no—
793D292—21no—
794D292—21no—
795D292—42no—
796C4×D73—22no—
797C4×D73—21no—
798C4×D73—21no—
799C4×D73—41no—
800C4×D73—42no—
801C4×D73—42no—
802C4×D73—42no—
803C4×D73—42no—
804C4×D73—42no—
805C4×D73—42no—
806C4×D73—42no—
807C4×D73—42no—
808Dic146—21no—
809Dic146—22no—
810Dic146—21no—
811Dic146—21no—
812Dic146—42no—
813Dic146—42no—
814Dic146—42no—
815Dic146—42no—
816Dic146—42no—
817Dic146—42no—
818Dic146C2×#4112yescomplemented
819C8×C73—21no—
820C8×C73—21no—
821C8×C73—21no—
822C8×C73—21no—
823#10596831—21no—
824#10596831—21no—
825#10596831—21no—
826#10596831C2×#4112yescomplemented
827C22×C73—21no—
828C22×C73—21no—
829C22×C73—21no—
830C22×C73—21no—
831C22×C73—22no—
832C22×C73—21no—
833C22×C73—41no—
834C22×C73—41no—
835C22×C73—41no—
836C22×C73—41no—
837C22×C73—41no—
838C22×C73—41no—
839C22×C73—41no—
840C22×C73—41no—
841C22×C73—84no—
842C22×C73—84no—
843C22×C73C2×AGL(1,ℤ/8)12yes—
844C22×C73C23×D411yescharacteristic
845C2×D73—21no—
846C2×D73—21no—
847C2×D73—41no—
848C2×D73—41no—
849C2×D73—41no—
850C2×D73—41no—
851C2×D73—41no—
852C2×D73—41no—
853C2×D73—84no—
854C2×D73C2×AGL(1,ℤ/8)12yes—
855C4×C73—21no—
856C4×C73—21no—
857C4×C73—21no—
858C4×C73—21no—
859C4×C73—41no—
860C4×C73—41no—
861C4×C73—41no—
862C4×C73—41no—
863C4×C73—41no—
864C4×C73C22×#4111yescharacteristic
865C4×C73#58511yescharacteristic
866Dic73—21no—
867Dic73—21no—
868Dic73—21no—
869Dic73—22no—
870Dic73—21no—
871Dic73—21no—
872Dic73—21no—
873Dic73—41no—
874Dic73—41no—
875Dic73—41no—
876Dic73—41no—
877Dic73—41no—
878Dic73C2×AGL(1,ℤ/8)12yes—
879#61452—731nomaximal, Sylow
880C2×C73—22no—
881C2×C73—42no—
882C2×C73—41no—
883C2×C73—81no—
884C2×C73—81no—
885C2×C73D4×#4111yescharacteristic
886C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
887C2×C73#358611yescharacteristic
888D73—22no—
889D73—81no—
890D73—81no—
891#3482—731no—
892D4×#41—731no—
893#3397—731no—
894#3386—731no—
895#3368—731no—
896#3367—731no—
897#3343—731no—
898#3343—731no—
899#3334—731no—
900#3310—731no—
901#3310D7311yescharacteristic, complemented
902#3308—731no—
903#3308—731no—
904#3298—731no—
905#3294—731no—
906D4×SD16—731no—
907#3265—731no—
908#3265—731no—
909#3182—731no—
910#3180—731no—
911#3180—731no—
912#3115—731no—
913#3114—731no—
914#3114—731no—
915#3112—731no—
916#3112—731no—
917#3110—731no—
918#2970—731no—
919C4×AGL(1,ℤ/8)—731no—
920C2×#440—731no—
921C2×#440—731no—
922C73#6145211yescharacteristic, complemented, Sylow
923C22×#41—1461no—
924C2×AGL(1,ℤ/8)—731no—
925C22×SD16—731no—
926C22×SD16—731no—
927#557—731no—
928#556—731no—
929#556—1461no—
930#552—731no—
931#552—1461no—
932#552—1461no—
933#552C2×D7311yescharacteristic, complemented
934#550—731no—
935D4×Q8—731no—
936D4×Q8—731no—
937#548—731no—
938#548—731no—
939#548—1461no—
940#547—731no—
941#547—731no—
942#547—731no—
943#547—731no—
944#547—1461no—
945#546—1461no—
946#546—1461no—
947#546—1461no—
948D42—731no—
949D42—731no—
950D42C2×D7311yescharacteristic
951#533—731no—
952#533—1461no—
953#532—731no—
954#532—731no—
955#532—731no—
956#529—731no—
957#529—731no—
958#529—1461no—
959#529—1461no—
960#525—1461no—
961#525—1461no—
962#525—1461no—
963C4×#41—731no—
964C4×#41—731no—
965C4×#41—1461no—
966C2×C4×Q8—731no—
967C2×C4×Q8—731no—
968C2×C4×D4—731no—
969C2×C4×D4—731no—
970C2×C4×D4—731no—
971#501—731no—
972#501—731no—
973#500—731no—
974#496—731no—
975#496—731no—
976#492—731no—
977#490—731no—
978#490C2×D7311yescharacteristic, complemented
979#489—731no—
980#489—731no—
981#487—731no—
982#486—731no—
983#484—731no—
984#484—731no—
985#483—731no—
986#483—731no—
987#482—731no—
988#482C2×D7311yescharacteristic, complemented
989#480—731no—
990#480—731no—
991#480—731no—
992#480—731no—
993#480—731no—
994#480C2×D7311yescharacteristic, complemented
995#478—731no—
996#478—731no—
997#478—731no—
998#478C2×D7311yescharacteristic
999#477—731no—
1000#477—731no—
1001#477—731no—
1002#477—731no—
1003#475—731no—
1004#474—731no—
1005#474—731no—
1006#474—731no—
1007#468—731no—
1008#468—731no—
1009#468—731no—
1010#468C2×D7311yescharacteristic, complemented
1011#466—731no—
1012#466—731no—
1013#466—731no—
1014#466—731no—
1015#465—731no—
1016#465—731no—
1017#465—731no—
1018#465C2×D7311yescharacteristic, complemented
1019#463—731no—
1020#463—731no—
1021#463—731no—
1022#463—731no—
1023#461—731no—
1024#461—731no—
1025#460—731no—
1026#460—731no—
1027#460—731no—
1028#460—731no—
1029#460C2×D7311yescharacteristic, complemented
1030#459—731no—
1031#450—731no—
1032#450—731no—
1033#450C2×D7311yescharacteristic
1034#450C2×D7311yescharacteristic
1035#449—731no—
1036#449—731no—
1037#448—731no—
1038#448—731no—
1039#448—731no—
1040#448—731no—
1041#447—731no—
1042#447—731no—
1043#446—731no—
1044#446—731no—
1045#442—731no—
1046#442—731no—
1047#442—731no—
1048#442—731no—
1049#440—731no—
1050#440—731no—
1051#440—731no—
1052#440—731no—
1053#440—731no—
1054#440—731no—
1055#440—731no—
1056#440—731no—
1057#440—731no—
1058#440—731no—
1059#440—731no—
1060#440—731no—
1061#440—731no—
1062#440—731no—
1063#440—731no—
1064#440—731no—
1065#440—731no—
1066#440—731no—
1067#440—731no—
1068#440C2×D7311yescharacteristic
1069C4×SD16—731no—
1070C4×SD16—731no—
1071C4×D8—731no—
1072C4×D8—731no—
1073#435—731no—
1074#435—731no—
1075#435—731no—
1076#435C2×D7311yescharacteristic, complemented
1077C8×D4—731no—
1078C8×D4—731no—
1079#432—731no—
1080#432—731no—
1081#432—731no—
1082#428—731no—
1083C2×#107—731no—
1084C2×#107—731no—
1085#418C2×D7311yescharacteristic
1086#417—731no—
1087C2×#103—731no—
1088C2×#103—731no—
1089C2×#102—731no—
1090C2×#102C2×D7311yescharacteristic
1091C4×M16—731no—
1092C2×#97—731no—
1093C2×#97—731no—
1094C2×#41—2928no—
1095C2×#41—731no—
1096C2×#41—731no—
1097C2×#41—1461no—
1098C2×#41—1461no—
1099C2×#41—1461no—
1100C2×#41—1461no—
1101C2×#41—1461no—
1102C2×#41—1461no—
1103C2×#41—1461no—
1104C2×#41—1461no—
1105C22×Q8—731no—
1106C22×Q8—731no—
1107C22×Q8—1461no—
1108C22×D4—21no—
1109C22×D4—731no—
1110C22×D4—1461no—
1111C22×D4—1461no—
1112C22×D4C22×D7311yescharacteristic
1113C22×D4C22×D7311yescharacteristic
1114C23×C4—1461no—
1115C23×C4—1461no—
1116C23×C4—1461no—
1117AGL(1,ℤ/8)—1464no—
1118C2×SD16—731no—
1119C2×SD16—731no—
1120C2×SD16—731no—
1121C2×SD16—731no—
1122C2×SD16—731no—
1123C2×SD16—731no—
1124C2×SD16—731no—
1125C2×SD16—731no—
1126C2×SD16—731no—
1127C2×SD16—1464no—
1128C2×SD16—1464no—
1129C2×SD16C22×D7311yescharacteristic
1130C2×SD16C22×D7311yescharacteristic
1131C2×SD16C22×D7311yescharacteristic
1132C2×D8—731no—
1133C2×D8—731no—
1134C2×D8—731no—
1135C2×D8—731no—
1136C2×M16—731no—
1137C2×M16C22×D7311yescharacteristic
1138C22×C8—731no—
1139C22×C8—731no—
1140C22×C8—731no—
1141C22×C8C22×D7311yescharacteristic
1142C4⋊Q8—731no—
1143C4⋊Q8—731no—
1144C4⋊Q8—731no—
1145C4⋊Q8—731no—
1146C4⋊Q8—731no—
1147C4⋊Q8—1461no—
1148C4⋊Q8—1461no—
1149#127—731no—
1150#127—731no—
1151#127C22×D7311yescharacteristic
1152#126—21no—
1153#126—1461no—
1154#126—1461no—
1155#126—1461no—
1156#126—1461no—
1157#126—1461no—
1158#125—21no—
1159#125—731no—
1160#125—1461no—
1161#125—1461no—
1162#125—1461no—
1163#125—1461no—
1164#125C22×D7311yescharacteristic
1165#124—731no—
1166#124—731no—
1167#124—1461no—
1168#124—1461no—
1169#124—1461no—
1170#124—1461no—
1171#124—1461no—
1172#123—21no—
1173#123—1461no—
1174#123—1461no—
1175#123—1461no—
1176#123—1461no—
1177#123—1461no—
1178#123—1461no—
1179#123—1461no—
1180#123—1461no—
1181#123—1461no—
1182#123—1461no—
1183#123—1461no—
1184C22⋊Q8—731no—
1185C22⋊Q8—731no—
1186C22⋊Q8—1461no—
1187C22⋊Q8—1461no—
1188C22⋊Q8—1461no—
1189C22⋊Q8—1461no—
1190C22⋊Q8—1461no—
1191C22⋊Q8—1461no—
1192C22⋊Q8—1461no—
1193C22⋊Q8—1461no—
1194C22⋊Q8—1461no—
1195C22⋊Q8—1461no—
1196C22⋊Q8—1461no—
1197C22⋊Q8—1461no—
1198C22⋊Q8—1461no—
1199C22⋊Q8C22×D7311yescharacteristic
1200C22⋊Q8C22×D7311yescharacteristic
1201#121—21no—
1202#121—731no—
1203#121—731no—
1204#121—731no—
1205#121—731no—
1206#121—731no—
1207#121—731no—
1208#121—1461no—
1209#121—1461no—
1210#121—1461no—
1211#121—1461no—
1212#121—1461no—
1213#121—1461no—
1214#121—1461no—
1215#121—1461no—
1216#121—1461no—
1217#121—1461no—
1218#121C22×D7311yescharacteristic
1219#121C22×D7311yescharacteristic
1220#120—21no—
1221#120—21no—
1222#120—1461no—
1223#120—1461no—
1224#120—1461no—
1225#120—1461no—
1226C4×Q8—731no—
1227C4×Q8—731no—
1228C4×Q8—731no—
1229C4×Q8—731no—
1230C4×Q8—731no—
1231C4×Q8—731no—
1232C4×Q8—731no—
1233C4×Q8—731no—
1234C4×Q8—731no—
1235C4×Q8—1461no—
1236C4×Q8—1461no—
1237C4×Q8—1461no—
1238C4×Q8—1461no—
1239C4×Q8—1461no—
1240C4×Q8—1461no—
1241C4×Q8C22×D7311yescharacteristic
1242C4×D4—731no—
1243C4×D4—731no—
1244C4×D4—731no—
1245C4×D4—731no—
1246C4×D4—731no—
1247C4×D4—731no—
1248C4×D4—731no—
1249C4×D4—731no—
1250C4×D4—731no—
1251C4×D4—731no—
1252C4×D4—731no—
1253C4×D4—731no—
1254C4×D4—731no—
1255C4×D4—731no—
1256C4×D4—731no—
1257C4×D4—731no—
1258C4×D4—1461no—
1259C4×D4—1461no—
1260C4×D4—1461no—
1261C4×D4—1461no—
1262C4×D4—1461no—
1263C4×D4—1461no—
1264C4×D4—1461no—
1265C4×D4—1461no—
1266C4×D4—1461no—
1267C4×D4—1461no—
1268C4×D4—1461no—
1269C4×D4—1461no—
1270C4×D4—1461no—
1271C4×D4—1461no—
1272C4×D4—1461no—
1273C4×D4—1461no—
1274C4×D4C22×D7311yescharacteristic
1275C4×D4C22×D7311yescharacteristic
1276#117—21no—
1277#117—731no—
1278#117—731no—
1279#117—731no—
1280#117—1461no—
1281#117—1461no—
1282#117—1461no—
1283#117—1461no—
1284#117—1461no—
1285#117—1461no—
1286#117C22×D7311yescharacteristic
1287C2×C4⋊C4—731no—
1288C2×C4⋊C4—731no—
1289C2×C4⋊C4—731no—
1290C2×C4⋊C4—731no—
1291C2×C4⋊C4—1461no—
1292C2×C4⋊C4—1461no—
1293C2×C4⋊C4C22×D7311yescharacteristic
1294C2×C22⋊C4—1461no—
1295C2×C22⋊C4—1461no—
1296C2×C22⋊C4—1461no—
1297C2×C42—731no—
1298C2×C42—731no—
1299C2×C42—731no—
1300C2×C42—1461no—
1301C2×C42—1461no—
1302C2×C42—1461no—
1303#107—731no—
1304#107—731no—
1305#107—731no—
1306#107—731no—
1307#107—731no—
1308#107—731no—
1309#107—731no—
1310#107—731no—
1311#107—731no—
1312#107—731no—
1313#107C22×D7311yescharacteristic
1314#107C22×D7311yescharacteristic
1315#106—731no—
1316#106—731no—
1317#106—731no—
1318#106C22×D7311yescharacteristic
1319C4⋊C8—731no—
1320C4⋊C8—731no—
1321C4⋊C8—731no—
1322C4⋊C8—731no—
1323C4⋊C8—731no—
1324C4⋊C8C22×D7311yescharacteristic
1325#103—731no—
1326#103—731no—
1327#103—731no—
1328#103—731no—
1329#103—731no—
1330#103—731no—
1331#103—731no—
1332#103—731no—
1333#103—731no—
1334#103—731no—
1335#103—731no—
1336#103C22×D7311yescharacteristic
1337#102—731no—
1338#102—731no—
1339#102—731no—
1340#102—731no—
1341#102—731no—
1342#102—731no—
1343#102—731no—
1344#102—731no—
1345#102—731no—
1346#102—731no—
1347#102—731no—
1348#102C22×D7311yescharacteristic
1349#102C22×D7311yescharacteristic
1350#102C22×D7311yescharacteristic
1351#102C22×D7311yescharacteristic
1352#102C22×D7311yescharacteristic
1353#102C22×D7311yescharacteristic
1354#102C22×D7311yescharacteristic
1355#102C22×D7311yescharacteristic
1356#102C22×D7311yescharacteristic
1357C22⋊C8—731no—
1358C22⋊C8—731no—
1359C22⋊C8—731no—
1360C22⋊C8—731no—
1361C22⋊C8C22×D7311yescharacteristic
1362C22⋊C8C22×D7311yescharacteristic
1363#97—731no—
1364#97—731no—
1365#97—731no—
1366#97—731no—
1367#97—731no—
1368#97—731no—
1369#97—731no—
1370#97C22×D7311yescharacteristic
1371C4×C8—731no—
1372C4×C8—731no—
1373C24—21no—
1374C24—21no—
1375C24—1461no—
1376#41—2921no—
1377#41—2924no—
1378#41—2924no—
1379#41—2924no—
1380#41—2924no—
1381#41—2924no—
1382#41—2924no—
1383#41—2924no—
1384#41—2924no—
1385#41—1462no—
1386#41—1464no—
1387C2×Q8—2921no—
1388C2×Q8—2924no—
1389C2×Q8—2921no—
1390C2×Q8—731no—
1391C2×Q8—731no—
1392C2×Q8—731no—
1393C2×Q8—1462no—
1394C2×Q8—1461no—
1395C2×Q8—1461no—
1396C2×Q8—1461no—
1397C2×Q8—1461no—
1398C2×Q8—1462no—
1399C2×Q8—1461no—
1400C2×Q8—1461no—
1401C2×Q8C23×D7311yescharacteristic
1402C2×D4—22no—
1403C2×D4—22no—
1404C2×D4—21no—
1405C2×D4—21no—
1406C2×D4—21no—
1407C2×D4—21no—
1408C2×D4—21no—
1409C2×D4—21no—
1410C2×D4—41no—
1411C2×D4—41no—
1412C2×D4—44no—
1413C2×D4—2924no—
1414C2×D4—2924no—
1415C2×D4—2921no—
1416C2×D4—731no—
1417C2×D4—731no—
1418C2×D4—731no—
1419C2×D4—731no—
1420C2×D4—1461no—
1421C2×D4—1461no—
1422C2×D4—1461no—
1423C2×D4—1461no—
1424C2×D4—1461no—
1425C2×D4—1461no—
1426C2×D4—1461no—
1427C2×D4—1461no—
1428C2×D4—1461no—
1429C2×D4—1461no—
1430C2×D4—1461no—
1431C2×D4—1461no—
1432C2×D4—1462no—
1433C2×D4D4×D7311yescharacteristic
1434C2×D4C23×D7311yescharacteristic
1435C2×D4C23×D7311yescharacteristic
1436C2×D4C23×D7311yescharacteristic
1437C22×C4—21no—
1438C22×C4—21no—
1439C22×C4—2924no—
1440C22×C4—2924no—
1441C22×C4—2924no—
1442C22×C4—731no—
1443C22×C4—731no—
1444C22×C4—731no—
1445C22×C4—731no—
1446C22×C4—731no—
1447C22×C4—731no—
1448C22×C4—731no—
1449C22×C4—1461no—
1450C22×C4—1461no—
1451C22×C4—1461no—
1452C22×C4—1461no—
1453C22×C4—1461no—
1454C22×C4—1461no—
1455C22×C4—1461no—
1456C22×C4—1461no—
1457C22×C4—1461no—
1458C22×C4—1461no—
1459C22×C4—1461no—
1460C22×C4—1461no—
1461C22×C4—1461no—
1462C22×C4—1461no—
1463C22×C4—1461no—
1464C22×C4—1461no—
1465C22×C4—1461no—
1466C22×C4—1461no—
1467C22×C4C23×D7311yescharacteristic
1468C22×C4C23×D7311yescharacteristic
1469SD16—22no—
1470SD16—41no—
1471SD16—41no—
1472SD16—2921no—
1473SD16—2921no—
1474SD16—734no—
1475SD16—1462no—
1476SD16—1462no—
1477SD16—1462no—
1478SD16—1462no—
1479SD16—1462no—
1480SD16—1462no—
1481D8—2921no—
1482D8—2921no—
1483D8—1462no—
1484D8—1462no—
1485M16—41no—
1486M16—1462no—
1487C2×C8—41no—
1488C2×C8—2921no—
1489C2×C8—731no—
1490C2×C8—731no—
1491C2×C8—731no—
1492C2×C8—731no—
1493C2×C8—1462no—
1494C2×C8—1462no—
1495C2×C8C23×D7311yescharacteristic
1496C2×C8C23×D7311yescharacteristic
1497C2×C8C23×D7311yescharacteristic
1498C2×C8C23×D7311yescharacteristic
1499C4⋊C4—21no—
1500C4⋊C4—21no—
1501C4⋊C4—21no—
1502C4⋊C4—21no—
1503C4⋊C4—21no—
1504C4⋊C4—21no—
1505C4⋊C4—731no—
1506C4⋊C4—731no—
1507C4⋊C4—731no—
1508C4⋊C4—731no—
1509C4⋊C4—731no—
1510C4⋊C4—731no—
1511C4⋊C4—731no—
1512C4⋊C4—731no—
1513C4⋊C4—731no—
1514C4⋊C4—1461no—
1515C4⋊C4—1461no—
1516C4⋊C4—1461no—
1517C4⋊C4—1461no—
1518C4⋊C4—1461no—
1519C4⋊C4—1461no—
1520C4⋊C4—1461no—
1521C4⋊C4—1461no—
1522C4⋊C4—1461no—
1523C4⋊C4—1461no—
1524C4⋊C4—1461no—
1525C4⋊C4—1461no—
1526C4⋊C4—1461no—
1527C4⋊C4—1461no—
1528C4⋊C4—1461no—
1529C4⋊C4—1461no—
1530C4⋊C4—1461no—
1531C4⋊C4—1461no—
1532C4⋊C4—1461no—
1533C4⋊C4—1461no—
1534C4⋊C4—1461no—
1535C4⋊C4D4×D7311yescharacteristic
1536C4⋊C4C23×D7311yescharacteristic
1537C4⋊C4C23×D7311yescharacteristic
1538C4⋊C4C23×D7311yescharacteristic
1539C4⋊C4C23×D7311yescharacteristic
1540C22⋊C4—21no—
1541C22⋊C4—21no—
1542C22⋊C4—21no—
1543C22⋊C4—21no—
1544C22⋊C4—21no—
1545C22⋊C4—21no—
1546C22⋊C4—731no—
1547C22⋊C4—731no—
1548C22⋊C4—731no—
1549C22⋊C4—731no—
1550C22⋊C4—1461no—
1551C22⋊C4—1461no—
1552C22⋊C4—1461no—
1553C22⋊C4—1461no—
1554C22⋊C4—1461no—
1555C22⋊C4—1461no—
1556C22⋊C4—1461no—
1557C22⋊C4—1461no—
1558C22⋊C4—1461no—
1559C22⋊C4—1461no—
1560C22⋊C4—1461no—
1561C22⋊C4—1461no—
1562C22⋊C4—1461no—
1563C22⋊C4—1461no—
1564C22⋊C4—1461no—
1565C22⋊C4—1461no—
1566C22⋊C4—1461no—
1567C22⋊C4—1461no—
1568C22⋊C4—1461no—
1569C22⋊C4—1461no—
1570C22⋊C4—1461no—
1571C22⋊C4—1461no—
1572C22⋊C4—1461no—
1573C22⋊C4D4×D7311yescharacteristic
1574C22⋊C4D4×D7311yescharacteristic
1575C42—21no—
1576C42—21no—
1577C42—731no—
1578C42—731no—
1579C42—731no—
1580C42—731no—
1581C42—731no—
1582C42—731no—
1583C42—731no—
1584C42—731no—
1585C42—731no—
1586C42—1461no—
1587C42—1461no—
1588C42—1461no—
1589C42—1461no—
1590C42—1461no—
1591C42—1461no—
1592C42—1461no—
1593C42C23×D7311yescharacteristic
1594C23—21no—
1595C23—21no—
1596C23—21no—
1597C23—42no—
1598C23—42no—
1599C23—42no—
1600C23—42no—
1601C23—81no—
1602C23—81no—
1603C23—2922no—
1604C23—2922no—
1605C23—5841no—
1606C23—731no—
1607C23—1461no—
1608C23—1461no—
1609C23C2×D4×D7311yescharacteristic
1610C23C2×D4×D7311yescharacteristic
1611Q8—21no—
1612Q8—21no—
1613Q8—2922no—
1614Q8—2922no—
1615Q8—2922no—
1616Q8—2922no—
1617Q8—2922no—
1618Q8—2922no—
1619Q8—732no—
1620Q8—1462no—
1621Q8—1461no—
1622Q8—1461no—
1623Q8—1461no—
1624D4—22no—
1625D4—21no—
1626D4—21no—
1627D4—21no—
1628D4—21no—
1629D4—21no—
1630D4—42no—
1631D4—42no—
1632D4—42no—
1633D4—42no—
1634D4—42no—
1635D4—81no—
1636D4—2922no—
1637D4—2922no—
1638D4—2922no—
1639D4—2922no—
1640D4—2922no—
1641D4—2922no—
1642D4—2922no—
1643D4—2922no—
1644D4—2922no—
1645D4—2922no—
1646D4—5841no—
1647D4—5841no—
1648D4—734no—
1649D4—1462no—
1650D4—1461no—
1651D4—1461no—
1652D4—1461no—
1653D4—1461no—
1654D4#41×D7312yes—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—21no—
1664C2×C4—42no—
1665C2×C4—42no—
1666C2×C4—2922no—
1667C2×C4—2922no—
1668C2×C4—2921no—
1669C2×C4—2922no—
1670C2×C4—2922no—
1671C2×C4—2922no—
1672C2×C4—2922no—
1673C2×C4—2922no—
1674C2×C4—2922no—
1675C2×C4—2922no—
1676C2×C4—2922no—
1677C2×C4—2922no—
1678C2×C4—2922no—
1679C2×C4—2922no—
1680C2×C4—2922no—
1681C2×C4—2922no—
1682C2×C4—2922no—
1683C2×C4—2922no—
1684C2×C4—2922no—
1685C2×C4—2921no—
1686C2×C4—2921no—
1687C2×C4—731no—
1688C2×C4—731no—
1689C2×C4—731no—
1690C2×C4—731no—
1691C2×C4—731no—
1692C2×C4—731no—
1693C2×C4—731no—
1694C2×C4—1462no—
1695C2×C4—1461no—
1696C2×C4—1461no—
1697C2×C4—1461no—
1698C2×C4—1461no—
1699C2×C4—1461no—
1700C2×C4—1462no—
1701C2×C4—1461no—
1702C2×C4—1462no—
1703C2×C4—1461no—
1704C2×C4—1461no—
1705C2×C4C2×D4×D7311yescharacteristic
1706C2×C4C2×D4×D7311yescharacteristic
1707C2×C4C2×D4×D7311yescharacteristic
1708C2×C4C2×D4×D7311yescharacteristic
1709C2×C4C24×D7311yescharacteristic
1710C8—21no—
1711C8—21no—
1712C8—21no—
1713C8—21no—
1714C8—732no—
1715C8—1461no—
1716C8—1461no—
1717C8—1461no—
1718C22—21no—
1719C22—21no—
1720C22—21no—
1721C22—21no—
1722C22—22no—
1723C22—21no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—84no—
1733C22—84no—
1734C22—2921no—
1735C22—2921no—
1736C22—2921no—
1737C22—2921no—
1738C22—2921no—
1739C22—2921no—
1740C22—5844no—
1741C22—732no—
1742C22—1461no—
1743C22—1461no—
1744C22AGL(1,ℤ/8)×D7312yes—
1745C22C22×D4×D7311yescharacteristic
1746C4—21no—
1747C4—21no—
1748C4—21no—
1749C4—21no—
1750C4—41no—
1751C4—41no—
1752C4—41no—
1753C4—41no—
1754C4—41no—
1755C4—2921no—
1756C4—2921no—
1757C4—2921no—
1758C4—2921no—
1759C4—2921no—
1760C4—732no—
1761C4—1461no—
1762C4—1461no—
1763C4—1462no—
1764C4—1461no—
1765C4—1461no—
1766C4—1461no—
1767C4—1461no—
1768C4C2×#41×D7311yescharacteristic
1769C4#1798942211yescharacteristic
1770C2—22no—
1771C2—41no—
1772C2—42no—
1773C2—81no—
1774C2—81no—
1775C2—5841no—
1776C2—5841no—
1777C2—1462no—
1778C2#2262341511yescharacteristic
1779C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
1780C2#2262471311yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3310C2
socleC22×C73C23×D4
hypercenter#3310D73
hypocenterC73#61452
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3310

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22623545C2semidirect
2. D4×#11924027C2semidirect
3. #22622946C2semidirect
4. #22622847C2semidirect
5. #22622657C2semidirect
6. #22622650C2semidirect
7. #22622371C2semidirect
8. #22622364C2semidirect
9. #22622273C2semidirect
10. #22621953C2semidirect
11. #22621924C2semidirect
12. #22621917C2semidirect
13. #22621791C2semidirect
14. #22621740C2semidirect
15. #22621625C2semidirect
16. #22621424C2semidirect
17. #22621422C2semidirect
18. #22620644C2semidirect
19. #22620628C2semidirect
20. #22620622C2semidirect
21. #22620077C2semidirect
22. #22620074C2semidirect
23. #22620070C2semidirect
24. #22620052C2semidirect
25. #22620050C2semidirect
26. #22620025C2semidirect
27. #22618941C2semidirect
28. #22618735C2semidirect
29. C2×#17988684C2semidirect
30. #440×D73C2semidirect
31. C73×#3310C2semidirect
36. #17989314C22semidirect
37. #17989309C22semidirect
39. #17989276C22semidirect
44. #17989250C22semidirect
45. #17989247C22semidirect
46. #17989246C22semidirect
49. #17989238C22semidirect
59. #17989139C22semidirect
63. #17989123C22semidirect
64. #17989122C22semidirect
71. #17989055C22semidirect
73. C2×#14556556C22semidirect
74. C4×Q8×D73C22semidirect
78. #17988997C22semidirect
79. #17988994C22semidirect
80. #17988991C22semidirect
81. #17988974C22semidirect
82. #17988973C22semidirect
83. #17988958C22semidirect
84. #17988950C22semidirect
85. #17988948C22semidirect
86. #17988947C22semidirect
87. #17988936C22semidirect
88. #17988932C22semidirect
89. #17988923C22semidirect
90. #17988920C22semidirect
91. #17988919C22semidirect
92. #17988915C22semidirect
93. #17988911C22semidirect
94. #17988902C22semidirect
95. #17988901C22semidirect
96. #17988900C22semidirect
97. #17988899C22semidirect
98. #17988899C22semidirect
100. #17988885C22semidirect
101. #17988884C22semidirect
102. #17988883C22semidirect
103. #17988882C22semidirect
104. #17988881C22semidirect
105. #17988881C22semidirect
106. #17988871C22semidirect
107. #17988866C22semidirect
109. #17988865C22semidirect
110. #17988835C22semidirect
111. #17988833C22semidirect
112. #17988831C22semidirect
113. #17988823C22semidirect
114. #17988822C22semidirect
115. #17988822C22semidirect
116. #17988821C22semidirect
117. #17988818C22semidirect
118. #17988815C22semidirect
119. #17988815C22semidirect
121. #17988804C22semidirect
122. #17988803C22semidirect
125. #17988790C22semidirect
126. #17988786C22semidirect
127. #17988786C22semidirect
128. #17988786C22semidirect
129. #17988784C22semidirect
130. #17988781C22semidirect
133. #17988734C22semidirect
134. #17988730C22semidirect
135. #17988728C22semidirect
136. #17988725C22semidirect
137. #17988724C22semidirect
138. #17988724C22semidirect
141. #17988716C22semidirect
142. #17988715C22semidirect
143. #17988698C22semidirect
145. #17988696C22semidirect
146. #17988696C22semidirect
147. #17988690C22semidirect
148. #17988689C22semidirect
150. #17988688C22semidirect
151. #17988688C22semidirect
153. #17988686C22semidirect
154. #17988686C22semidirect
155. #17988685C22semidirect
160. #17988684C22semidirect
161. #17988684C22semidirect
162. #17988684C22semidirect
163. #17988684C22semidirect
164. #17988684C22semidirect
165. #17988684C22semidirect
167. #17988678C22semidirect
169. #17988667C22semidirect
170. #17988661C22semidirect
171. #17988659C22semidirect
172. #17988656C22semidirect
173. C8×C22⋊D73C22semidirect
174. #17988650C22semidirect
175. #17988643C22semidirect
176. #17988641C22semidirect
177. #17988641C22semidirect
178. #17988630C22semidirect
179. C2×#14556524C22semidirect
180. #107×D73C22semidirect
181. #17988589C22semidirect
182. C2×#14556516C22semidirect
183. #103×D73C22semidirect
185. M16×Dic73C22semidirect
186. C2×#14556501C22semidirect
187. #97×D73C22semidirect
188. #552×C73C22semidirect
190. #490×C73C22semidirect
191. #482×C73C22semidirect
192. #480×C73C22semidirect
194. #468×C73C22semidirect
195. #465×C73C22semidirect
196. #460×C73C22semidirect
200. #435×C73C22semidirect
563. #11924016#41semidirect
763. C22⋊D73AGL(1,ℤ/8)semidirect
818. Dic146C2×#41semidirect
826. #10596831C2×#41semidirect
901. #3310D73semidirect
922. C73#61452semidirect
933. #552C2×D73semidirect
978. #490C2×D73semidirect
988. #482C2×D73semidirect
994. #480C2×D73semidirect
1010. #468C2×D73semidirect
1018. #465C2×D73semidirect
1029. #460C2×D73semidirect
1076. #435C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226235452
D4×#119240272
#226229462
#226228472
#226226572
#226226502
#226223712
#226223642
#226222732
#226219532
#226219242
#226219172
#226217912
#226217402
#226216252
#226214242
#226214222
#226206442
#226206282
#226206222
#226200772
#226200742
#226200702
#226200522
#226200502
#226200252
#226189412
#226187352
C2×#179886842
#440×D732
C73×#33102
#6145273