Finite Group Databasebeta

← #33978972

Subgroups — #33978972

Order 18688.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623880C211yesmaximal, characteristic
2#22623509C211yesmaximal, characteristic, complemented
3#22622979C211yesmaximal, characteristic, complemented
4#22622957C211yesmaximal, characteristic, complemented
5#22622748C211yesmaximal, characteristic, complemented
6#22622674C211yesmaximal, characteristic, complemented
7#22622048C211yesmaximal, characteristic, complemented
8#22622039C211yesmaximal, characteristic, complemented
9#22622018C211yesmaximal, characteristic, complemented
10#22622009C211yesmaximal, characteristic, complemented
11#22621802C211yesmaximal, characteristic, complemented
12#22621750C211yesmaximal, characteristic, complemented
13#22621680C211yesmaximal, characteristic, complemented
14#22621624C211yesmaximal, characteristic, complemented
15#22621507C211yesmaximal, characteristic, complemented
16#22621498C211yesmaximal, characteristic, complemented
17#22621447C211yesmaximal, characteristic, complemented
18#22621438C211yesmaximal, characteristic, complemented
19#22621303C211yesmaximal, characteristic, complemented
20#22621267C211yesmaximal, characteristic, complemented
21#22620932C211yesmaximal, characteristic, complemented
22#22620930C211yesmaximal, characteristic, complemented
23#22620886C211yesmaximal, characteristic, complemented
24#22620107C211yesmaximal, characteristic, complemented
25#22620098C211yesmaximal, characteristic, complemented
26#22620016C211yesmaximal, characteristic, complemented
27#22619401C211yesmaximal, characteristic, complemented
28C2×#17988810C211yesmaximal, characteristic, complemented
29#464×D73C211yesmaximal, characteristic, complemented
30#22619053C211yesmaximal, characteristic, complemented
31C73×#3248C211yesmaximal, characteristic, complemented
32C2×#14556623C2211yescharacteristic, complemented
33C2×#14556620C2211yescharacteristic, complemented
34C22×Dic292C2211yescharacteristic, complemented
35C2×Q16×D73C2211yescharacteristic, complemented
36C22×#11924017C2211yescharacteristic
37C2×SD16×D73C2211yescharacteristic
38#17989320C2211yescharacteristic
39#17989317C2211yescharacteristic, complemented
40#17989314—21no—
41#17989312C2211yescharacteristic, complemented
42#17989309C2211yescharacteristic
43#17989300—21no—
44#17989298C2211yescharacteristic, complemented
45#17989295C2211yescharacteristic
46#17989295C2211yescharacteristic, complemented
47#17989293—21no—
48#17989291—21no—
49#17989291—21no—
50#17989261—21no—
51#17989260—21no—
52#17989252C2211yescharacteristic, complemented
53#17989250C2211yescharacteristic
54#17989250C2211yescharacteristic
55#17989250C2211yescharacteristic, complemented
56#17989249C2211yescharacteristic
57#17989243C2211yescharacteristic
58#17989232C2211yescharacteristic
59#17989229—21no—
60#17989228C2211yescharacteristic
61#17989221C2211yescharacteristic
62#17989203—21no—
63#17989176—21no—
64#17989170—21no—
65#17989141—21no—
66#17989141—21no—
67#17989141C2211yescharacteristic, complemented
68#17989141C2211yescharacteristic, complemented
69#17989140—21no—
70#17989136C2211yescharacteristic
71#17989122C2211yescharacteristic
72#17989122C2211yescharacteristic
73C2×#14556579C2211yescharacteristic
74#124×D73C2211yescharacteristic
75#17989059—21no—
76C4×#11924028C2211yescharacteristic
77#17989055—21no—
78C2×C4×Dic146C2211yescharacteristic, complemented
79C4×Q8×D73C2211yescharacteristic, complemented
80C4×Q8×D73C2211yescharacteristic, complemented
81#17988980C2211yescharacteristic
82#17988979C2211yescharacteristic
83#17988979C2211yescharacteristic, complemented
84#17988978C2211yescharacteristic, complemented
85#17988965C2211yescharacteristic, complemented
86#17988958C2211yescharacteristic
87#17988949C2211yescharacteristic
88#17988949C2211yescharacteristic, complemented
89#17988948C2211yescharacteristic
90#17988945C2211yescharacteristic, complemented
91#17988936C2211yescharacteristic, complemented
92#17988932C2211yescharacteristic
93#17988924C2211yescharacteristic, complemented
94#17988920C2211yescharacteristic, complemented
95#17988919C2211yescharacteristic, complemented
96#17988907C2211yescharacteristic
97#17988903C2211yescharacteristic
98#17988902C2211yescharacteristic
99#17988891C2211yescharacteristic, complemented
100#17988891C2211yescharacteristic, complemented
101#17988881C2211yescharacteristic, complemented
102#17988876C2211yescharacteristic
103#17988871C2211yescharacteristic, complemented
104#17988866C2211yescharacteristic, complemented
105#17988846C2211yescharacteristic, complemented
106#17988844C2211yescharacteristic, complemented
107#17988836C2211yescharacteristic
108#17988834C2211yescharacteristic
109#17988829C2211yescharacteristic, complemented
110#17988827C2211yescharacteristic, complemented
111#17988819C2211yescharacteristic
112#17988817C2211yescharacteristic
113#17988812C2211yescharacteristic
114#17988811C2211yescharacteristic
115#17988810C2211yescharacteristic
116#17988810C2211yescharacteristic
117#17988810C2211yescharacteristic
118#17988810C2211yescharacteristic
119#17988810C2211yescharacteristic, complemented
120#17988810C2211yescharacteristic, complemented
121#17988810C2211yescharacteristic, complemented
122#17988810C2211yescharacteristic, complemented
123#17988809C2211yescharacteristic
124#17988809C2211yescharacteristic
125#17988809C2211yescharacteristic, complemented
126#17988809C2211yescharacteristic, complemented
127#17988808C2211yescharacteristic, complemented
128#17988807C2211yescharacteristic, complemented
129#17988806C2211yescharacteristic, complemented
130#17988806C2211yescharacteristic, complemented
131#17988796C2211yescharacteristic, complemented
132#17988796C2211yescharacteristic, complemented
133#17988796C2211yescharacteristic, complemented
134#17988795C2211yescharacteristic, complemented
135#17988791C2211yescharacteristic
136#17988791C2211yescharacteristic, complemented
137#17988786C2211yescharacteristic
138#17988785C2211yescharacteristic
139#17988752C2211yescharacteristic, complemented
140#17988750C2211yescharacteristic, complemented
141#17988748C2211yescharacteristic, complemented
142#17988746C2211yescharacteristic, complemented
143#17988744C2211yescharacteristic, complemented
144#17988744C2211yescharacteristic, complemented
145#17988744C2211yescharacteristic, complemented
146#17988742C2211yescharacteristic, complemented
147#17988742C2211yescharacteristic, complemented
148#17988742C2211yescharacteristic, complemented
149#17988741C2211yescharacteristic, complemented
150#17988739C2211yescharacteristic
151#17988737C2211yescharacteristic
152#17988737C2211yescharacteristic
153#17988736C2211yescharacteristic
154#17988727C2211yescharacteristic
155#17988727C2211yescharacteristic
156#17988725C2211yescharacteristic
157#17988716C2211yescharacteristic, complemented
158#17988716C2211yescharacteristic, complemented
159#17988693C2211yescharacteristic, complemented
160#17988692C2211yescharacteristic, complemented
161#17988692C2211yescharacteristic, complemented
162#17988691C2211yescharacteristic, complemented
163#17988690C2211yescharacteristic, complemented
164#17988687C2211yescharacteristic, complemented
165#17988687C2211yescharacteristic, complemented
166#17988686C2211yescharacteristic, complemented
167#17988681C2211yescharacteristic, complemented
168#17988679C2211yescharacteristic, complemented
169#17988674C2211yescharacteristic
170#17988672C2211yescharacteristic
171#17988658C2211yescharacteristic, complemented
172#17988658C2211yescharacteristic, complemented
173#17988657C2211yescharacteristic, complemented
174#17988657C2211yescharacteristic, complemented
175C8×C22⋊D73C2211yescharacteristic
176C8×C22⋊D73C2211yescharacteristic
177#17988644C2211yescharacteristic, complemented
178#17988643C2211yescharacteristic, complemented
179#17988639C2211yescharacteristic, complemented
180#17988609C2211yescharacteristic, complemented
181C4⋊C8×D73C2211yescharacteristic, complemented
182#17988587C2211yescharacteristic, complemented
183#17988585C2211yescharacteristic, complemented
184C2×#14556516C2211yescharacteristic, complemented
185#103×D73C2211yescharacteristic, complemented
186C2×#14556513C2211yescharacteristic
187#102×D73C2211yescharacteristic
188#533×C73C2211yescharacteristic, complemented
189#529×C73C2211yescharacteristic
190#479×C73C2211yescharacteristic, complemented
191#479×C73C2211yescharacteristic, complemented
192#475×C73C2211yescharacteristic, complemented
193#474×C73C2211yescharacteristic, complemented
194#467×C73C2211yescharacteristic, complemented
195#467×C73C2211yescharacteristic, complemented
196#465×C73C2211yescharacteristic
197#465×C73C2211yescharacteristic
198#464×C73C2211yescharacteristic, complemented
199#464×C73C2211yescharacteristic, complemented
200#462×C73C2211yescharacteristic, complemented
201#461×C73C2211yescharacteristic, complemented
202C2×C4⋊C8×C73C2211yescharacteristic, complemented
203C2×#11924029C2311yescharacteristic
204C2×#11924028D411yescharacteristic
205C2×#11924027C2311yescharacteristic
206C22×Dic146C2311yescharacteristic
207C22×Dic146C2311yescharacteristic
208C2×Q8×D73C2311yescharacteristic
209C2×Q8×D73C2311yescharacteristic
210C2×Q8×D73C2311yescharacteristic
211C22×D292C2311yescharacteristic
212C2×D4×D73—21no—
213C2×D4×D73C2311yescharacteristic
214#14556623—42no—
215#14556620—42no—
216C2×Dic292—42no—
217C2×Dic292C2311yescharacteristic
218C2×Dic292C2311yescharacteristic
219C2×Dic292C2311yescharacteristic
220C2×Dic292C2311yescharacteristic
221C2×#11924018C2311yescharacteristic
222C2×#11924018C2311yescharacteristic
223C2×#11924018C2311yescharacteristic
224C2×#11924018C2311yescharacteristic
225C2×#11924018C2311yescharacteristic
226C2×#11924018C2311yescharacteristic
227Q16×D73—42no—
228C2×#11924017—42no—
229C2×#11924017C2311yescharacteristic
230C2×#11924017C2311yescharacteristic
231C2×#11924017C2311yescharacteristic
232C2×#11924017C2311yescharacteristic
233C2×#11924016C2311yescharacteristic
234C2×#11924016C2311yescharacteristic
235C2×#11924015C2311yescharacteristic
236C2×#11924015C2311yescharacteristic
237C2×#11924015C2311yescharacteristic
238C2×#11924015C2311yescharacteristic
239SD16×D73—42no—
240C2×#11924011C2311yescharacteristic
241C2×#11924011C2311yescharacteristic
242C2×C8×D73C2311yescharacteristic
243C2×C8×D73C2311yescharacteristic
244#14556590—21no—
245#14556590—21no—
246#14556590—21no—
247#14556590—21no—
248#14556590—21no—
249#14556590C2311yescharacteristic
250#14556590C2311yescharacteristic
251#14556589—21no—
252#14556589—21no—
253#14556589C2311yescharacteristic
254#14556589C2311yescharacteristic
255#14556589C2311yescharacteristic
256#14556587C2311yescharacteristic
257#14556586—21no—
258#14556586—21no—
259#14556586—21no—
260#14556585—21no—
261#14556582—21no—
262#14556582—21no—
263#14556581—21no—
264#14556581—21no—
265#14556581—21no—
266#14556581—21no—
267#14556581—21no—
268#14556581—21no—
269#14556580C2311yescharacteristic
270#14556579—21no—
271#14556579—21no—
272#14556579—21no—
273#14556579C2311yescharacteristic
274#14556579C2311yescharacteristic
275#14556579C2311yescharacteristic
276#14556579C2311yescharacteristic
277#14556578C2311yescharacteristic
278#14556577—21no—
279#14556577—21no—
280#14556577—21no—
281#14556577—21no—
282#14556576—21no—
283#14556576—21no—
284#14556576—21no—
285#14556575—21no—
286#14556574—21no—
287#14556573—21no—
288#14556571—21no—
289#14556571—21no—
290#14556571—21no—
291#14556571C2311yescharacteristic
292#14556571C2311yescharacteristic
293#14556571C2311yescharacteristic
294#14556571C2311yescharacteristic
295#14556569—21no—
296#14556569—21no—
297#14556569—21no—
298#14556569—21no—
299#14556569—21no—
300#14556569—21no—
301#14556569—21no—
302#14556569—21no—
303#14556568—21no—
304#14556568—21no—
305#14556568—21no—
306#14556568—21no—
307#14556568—21no—
308#14556568—21no—
309#14556567—21no—
310#14556567—21no—
311#14556567C2311yescharacteristic
312#14556567C2311yescharacteristic
313#14556566—21no—
314#14556566—21no—
315#14556566C2311yescharacteristic
316#14556566C2311yescharacteristic
317#14556565—21no—
318#14556564—21no—
319#14556564—21no—
320#14556564—21no—
321#14556563—21no—
322#14556561—21no—
323#14556561—21no—
324#14556561—21no—
325#14556559—21no—
326Q8×Dic73C2311yescharacteristic
327Q8×Dic73C2311yescharacteristic
328C4×Dic146—21no—
329C4×Dic146—21no—
330C4×Dic146—21no—
331C4×Dic146—21no—
332C4×Dic146—21no—
333C4×Dic146—21no—
334C4×Dic146D411yescharacteristic
335C4×Dic146C2311yescharacteristic
336C4×Dic146C2311yescharacteristic
337C4×Dic146C2311yescharacteristic
338C4×Dic146C2311yescharacteristic
339C4×Dic146C2311yescharacteristic
340#14556556—21no—
341#14556556—21no—
342#14556556—21no—
343#14556556—21no—
344#14556556C2311yescharacteristic
345#14556556C2311yescharacteristic
346#14556556C2311yescharacteristic
347#14556556C2311yescharacteristic
348C4×D292—21no—
349C4×D292D411yescharacteristic
350C4×D292C2311yescharacteristic
351D4×Dic73—21no—
352#14556553—21no—
353#14556553—21no—
354#14556553—21no—
355#14556553—21no—
356#14556553C2311yescharacteristic
357#14556553C2311yescharacteristic
358C4×C22⋊D73—21no—
359C4×C22⋊D73D411yescharacteristic
360C4×C22⋊D73D411yescharacteristic
361C4×C22⋊D73C2311yescharacteristic
362C4×C22⋊D73C2311yescharacteristic
363#14556551—21no—
364#14556551—21no—
365#14556551—21no—
366#14556551—21no—
367#14556551—21no—
368#14556551—21no—
369#14556551—21no—
370#14556550D411yescharacteristic
371#14556549—21no—
372#14556549—21no—
373#14556548—21no—
374#14556548—21no—
375#14556548—21no—
376#14556548D411yescharacteristic
377#14556548D411yescharacteristic
378C2×C4⋊Dic73C2311yescharacteristic
379C2×#11924007—21no—
380C4⋊C4×D73—21no—
381C4⋊C4×D73—21no—
382C4⋊C4×D73C2311yescharacteristic
383C4⋊C4×D73C2311yescharacteristic
384C2×#11924005—21no—
385C2×#11924005—21no—
386C2×#11924005—21no—
387C22⋊C4×D73—21no—
388C22⋊C4×D73—21no—
389C22⋊C4×D73—21no—
390C2×C4×Dic73—21no—
391C42×D73—21no—
392C42×D73—21no—
393C42×D73C2311yescharacteristic
394C42×D73C2311yescharacteristic
395#14556524C2311yescharacteristic
396#14556524C2311yescharacteristic
397#14556522C2311yescharacteristic
398#14556522C2311yescharacteristic
399C4⋊#10596831C2311yescharacteristic
400C4⋊#10596831C2311yescharacteristic
401#14556520C2311yescharacteristic
402#14556520C2311yescharacteristic
403#14556520C2311yescharacteristic
404#14556520C2311yescharacteristic
405#14556516C2311yescharacteristic
406#14556516C2311yescharacteristic
407#14556516C2311yescharacteristic
408#14556516C2311yescharacteristic
409#14556515C2311yescharacteristic
410#14556515C2311yescharacteristic
411#14556514C2311yescharacteristic
412#14556514C2311yescharacteristic
413#14556514C2311yescharacteristic
414#14556514C2311yescharacteristic
415#14556514C2311yescharacteristic
416#14556514C2311yescharacteristic
417#14556514C2311yescharacteristic
418#14556514C2311yescharacteristic
419#14556513C2311yescharacteristic
420#14556513C2311yescharacteristic
421#14556513C2311yescharacteristic
422#14556513C2311yescharacteristic
423#14556512C2311yescharacteristic
424#14556512C2311yescharacteristic
425#14556511C2311yescharacteristic
426#14556511C2311yescharacteristic
427#14556511C2311yescharacteristic
428#14556511C2311yescharacteristic
429C22⋊#10596831C2311yescharacteristic
430C22⋊#10596831C2311yescharacteristic
431#14556503C2311yescharacteristic
432#14556503C2311yescharacteristic
433#14556503C2311yescharacteristic
434#14556503C2311yescharacteristic
435#14556502C2311yescharacteristic
436#14556502C2311yescharacteristic
437#14556501C2311yescharacteristic
438#14556501C2311yescharacteristic
439C8×Dic73C2311yescharacteristic
440C8×Dic73C2311yescharacteristic
441C2×Q16×C73C2311yescharacteristic
442C2×Q16×C73C2311yescharacteristic
443C2×SD16×C73C2311yescharacteristic
444C2×SD16×C73C2311yescharacteristic
445C22×C8×C73C2311yescharacteristic
446C22×C8×C73C2311yescharacteristic
447C4⋊Q8×C73C2311yescharacteristic
448C4⋊Q8×C73C2311yescharacteristic
449#126×C73—21no—
450#125×C73—21no—
451#125×C73C2311yescharacteristic
452#124×C73C2311yescharacteristic
453#123×C73—21no—
454C22⋊Q8×C73—21no—
455C22⋊Q8×C73C2311yescharacteristic
456C22⋊Q8×C73C2311yescharacteristic
457C22⋊Q8×C73C2311yescharacteristic
458#121×C73C2311yescharacteristic
459C4×Q8×C73—21no—
460C4×Q8×C73C2311yescharacteristic
461C4×Q8×C73C2311yescharacteristic
462C4×Q8×C73C2311yescharacteristic
463C4×D4×C73—21no—
464C4×D4×C73C2311yescharacteristic
465#117×C73—21no—
466#117×C73—21no—
467C2×C42×C73C2311yescharacteristic
468#107×C73C2311yescharacteristic
469#107×C73C2311yescharacteristic
470#106×C73C2311yescharacteristic
471#106×C73C2311yescharacteristic
472C4⋊C8×C73C2311yescharacteristic
473C4⋊C8×C73C2311yescharacteristic
474C4⋊C8×C73C2311yescharacteristic
475C4⋊C8×C73C2311yescharacteristic
476#103×C73C2311yescharacteristic
477#103×C73C2311yescharacteristic
478#103×C73C2311yescharacteristic
479#103×C73C2311yescharacteristic
480#103×C73C2311yescharacteristic
481#103×C73C2311yescharacteristic
482#102×C73C2311yescharacteristic
483#102×C73C2311yescharacteristic
484C23×D73—21no—
485C23×D73—21no—
486#11924029—41no—
487#11924029—41no—
488#11924028—24no—
489#11924027—41no—
490#11924027—41no—
491C2×Dic146—22no—
492C2×Dic146—21no—
493C2×Dic146—21no—
494C2×Dic146—21no—
495C2×Dic146—21no—
496C2×Dic146—21no—
497C2×Dic146—21no—
498C2×Dic146—21no—
499C2×Dic146—41no—
500C2×Dic146—41no—
501C2×Dic146—41no—
502C2×Dic146C2×D411yescharacteristic
503C2×Dic146C2411yescharacteristic
504C2×Dic146C2411yescharacteristic
505C2×Dic146C2411yescharacteristic
506C2×Dic146C2411yescharacteristic
507Q8×D73—22no—
508Q8×D73—22no—
509Q8×D73—41no—
510Q8×D73—41no—
511Q8×D73—41no—
512Q8×D73—41no—
513C2×D292—21no—
514C2×D292—21no—
515C2×D292—21no—
516C2×D292—21no—
517C2×D292—41no—
518C2×D292—41no—
519C2×D292C2×D411yescharacteristic
520C2×D292C2411yescharacteristic
521C2×D292C2411yescharacteristic
522C2×C22⋊D73—21no—
523C2×C22⋊D73—21no—
524C2×C22⋊D73—21no—
525C2×C22⋊D73—21no—
526C2×C22⋊D73C2×D411yescharacteristic
527C2×C22⋊D73C2×D411yescharacteristic
528D4×D73—41no—
529D4×D73—41no—
530D4×D73—44no—
531C22×Dic73—21no—
532C22×Dic73—21no—
533C22×Dic73—21no—
534C22×Dic73—21no—
535C2×C4×D73—21no—
536C2×C4×D73—21no—
537C2×C4×D73—21no—
538C2×C4×D73—21no—
539C2×C4×D73—21no—
540C2×C4×D73—21no—
541C2×C4×D73—21no—
542C2×C4×D73—21no—
543C2×C4×D73C2×D411yescharacteristic
544C2×C4×D73C2×D411yescharacteristic
545C2×C4×D73C2×D411yescharacteristic
546C2×C4×D73C2×D411yescharacteristic
547C2×C4×D73C2411yescharacteristic
548C2×C4×D73C2411yescharacteristic
549Dic292—22no—
550Dic292—22no—
551Dic292—41no—
552Dic292—41no—
553#11924018—22no—
554#11924018—41no—
555#11924018—41no—
556#11924018—41no—
557#11924018—41no—
558#11924018—41no—
559#11924017—22no—
560#11924017—22no—
561#11924017—41no—
562#11924017—41no—
563#11924016—22no—
564#11924016—41no—
565#11924015—41no—
566#11924015—41no—
567#11924015—41no—
568#11924015—41no—
569#11924011—41no—
570#11924011—41no—
571C2×#10596831C2411yescharacteristic
572C2×#10596831C2411yescharacteristic
573C2×#10596831C2411yescharacteristic
574C2×#10596831C2411yescharacteristic
575C8×D73—41no—
576C8×D73—41no—
577C4⋊Dic73—21no—
578C4⋊Dic73—21no—
579C4⋊Dic73—21no—
580C4⋊Dic73—21no—
581C4⋊Dic73—21no—
582C4⋊Dic73—21no—
583C4⋊Dic73—21no—
584C4⋊Dic73C2×D411yescharacteristic
585C4⋊Dic73C2×D411yescharacteristic
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#11924007—21no—
604#11924007—21no—
605#11924007—21no—
606#11924007—21no—
607#11924007—21no—
608#11924007C2×D411yescharacteristic
609#11924007C2×D411yescharacteristic
610#11924007C2×D411yescharacteristic
611#11924007C2×D411yescharacteristic
612C22⋊Dic73—21no—
613C22⋊Dic73—21no—
614C22⋊Dic73C2×D411yescharacteristic
615C22⋊Dic73C2×D411yescharacteristic
616#11924005—21no—
617#11924005—21no—
618#11924005—21no—
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#11924005—21no—
633#11924005—21no—
634#11924005—21no—
635#11924005—21no—
636#11924005C2×D411yescharacteristic
637#11924005C2×D411yescharacteristic
638#11924005C2×D411yescharacteristic
639#11924005C2×D411yescharacteristic
640C4×Dic73—21no—
641C4×Dic73—21no—
642C4×Dic73—21no—
643C4×Dic73—21no—
644C4×Dic73—21no—
645C4×Dic73—21no—
646C4×Dic73—21no—
647C4×Dic73—21no—
648C4×Dic73—21no—
649C4×Dic73—21no—
650C4×Dic73C2×D411yescharacteristic
651C4×Dic73C2×D411yescharacteristic
652C4×Dic73C2×D411yescharacteristic
653C4×Dic73C2×D411yescharacteristic
654C4×Dic73C2411yescharacteristic
655C4×Dic73C2411yescharacteristic
656C2×Q8×C73—21no—
657C2×Q8×C73C2411yescharacteristic
658C2×Q8×C73C2411yescharacteristic
659C2×Q8×C73C2411yescharacteristic
660C2×D4×C73—21no—
661C2×D4×C73C2411yescharacteristic
662C22×C4×C73—21no—
663C22×C4×C73C2×D411yescharacteristic
664C22×C4×C73C2×D411yescharacteristic
665C22×C4×C73C2411yescharacteristic
666Q16×C73—41no—
667Q16×C73—41no—
668SD16×C73—41no—
669SD16×C73—41no—
670C2×C8×C73—41no—
671C2×C8×C73—41no—
672C2×C8×C73C2411yescharacteristic
673C2×C8×C73C2411yescharacteristic
674C2×C8×C73C2411yescharacteristic
675C2×C8×C73C2411yescharacteristic
676C4⋊C4×C73—21no—
677C4⋊C4×C73—21no—
678C4⋊C4×C73—21no—
679C4⋊C4×C73—21no—
680C4⋊C4×C73—21no—
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×C73C2411yescharacteristic
688C4⋊C4×C73C2411yescharacteristic
689C4⋊C4×C73C2411yescharacteristic
690C4⋊C4×C73C2411yescharacteristic
691C22⋊C4×C73—21no—
692C22⋊C4×C73—21no—
693C22⋊C4×C73—21no—
694C22⋊C4×C73—21no—
695C22⋊C4×C73—21no—
696C22⋊C4×C73—21no—
697C22⋊C4×C73—21no—
698C42×C73—21no—
699C42×C73—21no—
700C42×C73—21no—
701C42×C73C2×D411yescharacteristic
702C42×C73C2×D411yescharacteristic
703C42×C73C2411yescharacteristic
704C42×C73C2411yescharacteristic
705C23×C73—21no—
706C23×C73C22×D411yescharacteristic
707C22×D73—21no—
708C22×D73—21no—
709C22×D73—42no—
710C22×D73—42no—
711C22×D73—81no—
712C22×D73—81no—
713C22×D73—81no—
714C22×D73—81no—
715C22×D73C22×D411yescharacteristic
716C22×D73C22×D411yescharacteristic
717Q8×C73—21no—
718Q8×C73—21no—
719Q8×C73—21no—
720Q8×C73—21no—
721Q8×C73—21no—
722Q8×C73—21no—
723Q8×C73—81no—
724D4×C73—21no—
725D4×C73—21no—
726D4×C73—42no—
727C2×C4×C73—22no—
728C2×C4×C73—21no—
729C2×C4×C73—21no—
730C2×C4×C73—21no—
731C2×C4×C73—21no—
732C2×C4×C73—21no—
733C2×C4×C73—21no—
734C2×C4×C73—21no—
735C2×C4×C73—21no—
736C2×C4×C73—21no—
737C2×C4×C73—41no—
738C2×C4×C73—81no—
739C2×C4×C73C22×D411yescharacteristic
740C2×C4×C73C22×D411yescharacteristic
741C2×C4×C73C22×D411yescharacteristic
742C2×C4×C73C22×D411yescharacteristic
743C2×C4×C73C22×D411yescharacteristic
744C2×C4×C73C2511yescharacteristic
745C22⋊D73—22no—
746C22⋊D73—42no—
747C22⋊D73—81no—
748C22⋊D73—81no—
749C22⋊D73—81no—
750C22⋊D73#13714yescomplemented
751C2×Dic73—21no—
752C2×Dic73—21no—
753C2×Dic73—21no—
754C2×Dic73—21no—
755C2×Dic73—21no—
756C2×Dic73—21no—
757C2×Dic73—42no—
758C2×Dic73—81no—
759C2×Dic73—81no—
760C2×Dic73—81no—
761C2×Dic73C22×D411yescharacteristic
762C2×Dic73C22×D411yescharacteristic
763C2×Dic73C22×D411yescharacteristic
764C2×Dic73C22×D411yescharacteristic
765C2×Dic73C22×D411yescharacteristic
766C2×Dic73C22×D411yescharacteristic
767D292—22no—
768D292—21no—
769D292—21no—
770D292—21no—
771D292—21no—
772D292—42no—
773D292—81no—
774D292—81no—
775D292—81no—
776C4×D73—22no—
777C4×D73—21no—
778C4×D73—21no—
779C4×D73—21no—
780C4×D73—21no—
781C4×D73—22no—
782C4×D73—41no—
783C4×D73—41no—
784C4×D73—42no—
785C4×D73—42no—
786C4×D73—42no—
787C4×D73—81no—
788C4×D73—81no—
789C4×D73—81no—
790C4×D73—81no—
791C4×D73—81no—
792Dic146—21no—
793Dic146—22no—
794Dic146—21no—
795Dic146—21no—
796Dic146—21no—
797Dic146—21no—
798Dic146—21no—
799Dic146—21no—
800Dic146—42no—
801Dic146—42no—
802Dic146—42no—
803Dic146—81no—
804Dic146—81no—
805Dic146—81no—
806Dic146—81no—
807Dic146H(5,𝔽2)12yes—
808C8×C73—21no—
809C8×C73—21no—
810C8×C73—21no—
811C8×C73—21no—
812#10596831—21no—
813#10596831—21no—
814#10596831—21no—
815#10596831—21no—
816C22×C73—21no—
817C22×C73—21no—
818C22×C73—41no—
819C22×C73—41no—
820C22×C73—41no—
821C22×C73C2×#13712yes—
822C22×C73C23×D411yescharacteristic
823C2×D73—21no—
824C2×D73—21no—
825C2×D73—21no—
826C2×D73—21no—
827C2×D73—21no—
828C2×D73—41no—
829C2×D73—41no—
830C2×D73—41no—
831C2×D73—41no—
832C2×D73—41no—
833C2×D73—41no—
834C2×D73—162no—
835C2×D73—162no—
836C2×D73C2×#13712yes—
837C4×C73—21no—
838C4×C73—21no—
839C4×C73—21no—
840C4×C73—21no—
841C4×C73—21no—
842C4×C73—41no—
843C4×C73—41no—
844C4×C73—41no—
845C4×C73—41no—
846C4×C73—41no—
847C4×C73—41no—
848C4×C73—41no—
849C4×C73C2×H(5,𝔽2)11yescharacteristic
850C4×C73#58511yescharacteristic
851Dic73—21no—
852Dic73—21no—
853Dic73—22no—
854Dic73—21no—
855Dic73—21no—
856Dic73—21no—
857Dic73—41no—
858Dic73—41no—
859Dic73—41no—
860Dic73—41no—
861Dic73—41no—
862Dic73C2×#13712yes—
863#61991—731nomaximal, Sylow
864C2×C73—22no—
865C2×C73—81no—
866C2×C73#348811yescharacteristic
867C2×C73C22×#13711yescharacteristic
868C2×C73#358411yescharacteristic
869D73—22no—
870D73—41no—
871D73—81no—
872D73—81no—
873#3514—731no—
874Q8×#41—731no—
875#3400—731no—
876#3398—731no—
877#3375—731no—
878#3369—731no—
879#3316—731no—
880#3316—731no—
881#3314—731no—
882#3314—731no—
883#3299—731no—
884#3295—731no—
885D4×Q16—731no—
886D4×SD16—731no—
887#3270—731no—
888#3270—731no—
889#3266—731no—
890#3266—731no—
891#3252—731no—
892#3248—731no—
893#3248D7311yescharacteristic, complemented
894#3215—731no—
895#3215—731no—
896#3210—731no—
897#3117—731no—
898#3117—731no—
899#3108—731no—
900#3037—731no—
901C2×#464—731no—
902C2×#464—731no—
903#2990—731no—
904C73#6199111yescharacteristic, complemented, Sylow
905C2×#137—731no—
906C2×#137—731no—
907C22×Q16—731no—
908C22×Q16—731no—
909C22×SD16—731no—
910C22×SD16—731no—
911#559—731no—
912Q82—731no—
913#557—731no—
914#557—1461no—
915#556—731no—
916#555—1461no—
917#554—731no—
918#554—731no—
919#554—731no—
920#554—1461no—
921#554—1461no—
922#554—1461no—
923#551—1461no—
924#551—1461no—
925D4×Q8—731no—
926D4×Q8—731no—
927D4×Q8—731no—
928D4×Q8—731no—
929#548—731no—
930#548—731no—
931#546—731no—
932#546—731no—
933#546—1461no—
934D42—731no—
935#542—1461no—
936#538—1461no—
937#538—1461no—
938#533—731no—
939#533—731no—
940#533—1461no—
941#533—1461no—
942#533—1461no—
943#533C2×D7311yescharacteristic, complemented
944#532—731no—
945#529—731no—
946#529—731no—
947#529C2×D7311yescharacteristic
948C2×#124—731no—
949C2×#124—731no—
950#518—1461no—
951C4×#41—731no—
952C4×#41—1461no—
953C2×C4×Q8—731no—
954C2×C4×Q8—731no—
955C2×C4×Q8—731no—
956#497—731no—
957#497—731no—
958#497—731no—
959#497—731no—
960#494—731no—
961#492—731no—
962#489—731no—
963#489—731no—
964#489—731no—
965#489—731no—
966#487—731no—
967#486—731no—
968#484—731no—
969#484—731no—
970#483—731no—
971#481—731no—
972#481—731no—
973#480—731no—
974#479—731no—
975#479—731no—
976#479C2×D7311yescharacteristic, complemented
977#479C2×D7311yescharacteristic, complemented
978#477—731no—
979#476—731no—
980#475—731no—
981#475C2×D7311yescharacteristic, complemented
982#474—731no—
983#474C2×D7311yescharacteristic, complemented
984#470—731no—
985#470—731no—
986#468—731no—
987#468—731no—
988#467—731no—
989#467—731no—
990#467C2×D7311yescharacteristic, complemented
991#467C2×D7311yescharacteristic, complemented
992#465—731no—
993#465—731no—
994#465C2×D7311yescharacteristic
995#465C2×D7311yescharacteristic
996#464—731no—
997#464—731no—
998#464—731no—
999#464—731no—
1000#464—731no—
1001#464—731no—
1002#464—731no—
1003#464—731no—
1004#464—731no—
1005#464—731no—
1006#464—731no—
1007#464—731no—
1008#464—731no—
1009#464—731no—
1010#464—731no—
1011#464—731no—
1012#464—731no—
1013#464—731no—
1014#464C2×D7311yescharacteristic, complemented
1015#464C2×D7311yescharacteristic, complemented
1016#462—731no—
1017#462—731no—
1018#462—731no—
1019#462—731no—
1020#462C2×D7311yescharacteristic, complemented
1021#461—731no—
1022#461—731no—
1023#461C2×D7311yescharacteristic, complemented
1024#460—731no—
1025#460—731no—
1026#452—731no—
1027#452—731no—
1028#452—731no—
1029#452—731no—
1030#451—731no—
1031#451—731no—
1032#451—731no—
1033#451—731no—
1034#451—731no—
1035#451—731no—
1036#451—731no—
1037#450—731no—
1038#450—731no—
1039#450—731no—
1040#450—731no—
1041#448—731no—
1042#448—731no—
1043#448—731no—
1044#446—731no—
1045#446—731no—
1046#441—731no—
1047#441—731no—
1048#441—731no—
1049#441—731no—
1050#440—731no—
1051#440—731no—
1052#440—731no—
1053#440—731no—
1054C4×Q16—731no—
1055C4×Q16—731no—
1056C4×SD16—731no—
1057C4×SD16—731no—
1058#435—731no—
1059#435—731no—
1060#435—731no—
1061#435—731no—
1062C8×D4—731no—
1063C8×D4—731no—
1064#432—731no—
1065#432—731no—
1066#431—731no—
1067#423—731no—
1068C2×C4⋊C8—731no—
1069C2×C4⋊C8C2×D7311yescharacteristic, complemented
1070#417—731no—
1071#417—731no—
1072C2×#103—731no—
1073C2×#103—731no—
1074C2×#102—731no—
1075C2×#102—731no—
1076C2×#41—731no—
1077C2×#41—731no—
1078C2×#41—731no—
1079C22×Q8—731no—
1080C22×Q8—731no—
1081C22×Q8—731no—
1082C22×Q8—731no—
1083C22×Q8—731no—
1084C22×D4—731no—
1085C22×D4—731no—
1086C22×D4—1461no—
1087#137—2922no—
1088#137—2922no—
1089C2×Q16—2922no—
1090C2×Q16—2922no—
1091C2×Q16—731no—
1092C2×Q16—731no—
1093C2×Q16—731no—
1094C2×Q16—731no—
1095C2×Q16—731no—
1096C2×Q16—731no—
1097C2×Q16—731no—
1098C2×Q16—731no—
1099C2×Q16—731no—
1100C2×Q16—731no—
1101C2×Q16C22×D7311yescharacteristic
1102C2×Q16C22×D7311yescharacteristic
1103C2×SD16—2922no—
1104C2×SD16—2922no—
1105C2×SD16—731no—
1106C2×SD16—731no—
1107C2×SD16—731no—
1108C2×SD16—731no—
1109C2×SD16—731no—
1110C2×SD16—731no—
1111C2×SD16—731no—
1112C2×SD16—731no—
1113C2×SD16—731no—
1114C2×SD16—731no—
1115C2×SD16C22×D7311yescharacteristic
1116C2×SD16C22×D7311yescharacteristic
1117C2×M16—731no—
1118C2×M16—731no—
1119C22×C8—731no—
1120C22×C8—731no—
1121C22×C8C22×D7311yescharacteristic
1122C22×C8C22×D7311yescharacteristic
1123C4⋊Q8—731no—
1124C4⋊Q8—731no—
1125C4⋊Q8—731no—
1126C4⋊Q8—731no—
1127C4⋊Q8—731no—
1128C4⋊Q8—1461no—
1129C4⋊Q8—1461no—
1130C4⋊Q8—1461no—
1131C4⋊Q8—1461no—
1132C4⋊Q8—1461no—
1133C4⋊Q8—1461no—
1134C4⋊Q8—1461no—
1135C4⋊Q8C22×D7311yescharacteristic
1136C4⋊Q8C22×D7311yescharacteristic
1137#127—731no—
1138#126—21no—
1139#126—1461no—
1140#126—1461no—
1141#126—1461no—
1142#126—1461no—
1143#125—21no—
1144#125—1461no—
1145#125—1461no—
1146#125—1461no—
1147#125—1461no—
1148#125—1461no—
1149#125—1461no—
1150#125—1461no—
1151#125—1461no—
1152#125C22×D7311yescharacteristic
1153#124—731no—
1154#124—731no—
1155#124—731no—
1156#124—731no—
1157#124—731no—
1158#124—731no—
1159#124—1461no—
1160#124—1461no—
1161#124—1461no—
1162#124—1461no—
1163#124—1461no—
1164#124—1461no—
1165#124—1461no—
1166#124C22×D7311yescharacteristic
1167#123—21no—
1168#123—1461no—
1169#123—1461no—
1170#123—1461no—
1171#123—1461no—
1172#123—1461no—
1173#123—1461no—
1174C22⋊Q8—21no—
1175C22⋊Q8—731no—
1176C22⋊Q8—731no—
1177C22⋊Q8—731no—
1178C22⋊Q8—731no—
1179C22⋊Q8—731no—
1180C22⋊Q8—731no—
1181C22⋊Q8—1461no—
1182C22⋊Q8—1461no—
1183C22⋊Q8—1461no—
1184C22⋊Q8—1461no—
1185C22⋊Q8—1461no—
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⋊Q8—1461no—
1200C22⋊Q8C22×D7311yescharacteristic
1201C22⋊Q8C22×D7311yescharacteristic
1202C22⋊Q8C22×D7311yescharacteristic
1203#121—731no—
1204#121—731no—
1205#121—1461no—
1206#121—1461no—
1207#121—1461no—
1208#121—1461no—
1209#121—1461no—
1210#121—1461no—
1211#121—1461no—
1212#121C22×D7311yescharacteristic
1213#120—1461no—
1214#120—1461no—
1215#120—1461no—
1216#120—1461no—
1217C4×Q8—21no—
1218C4×Q8—731no—
1219C4×Q8—731no—
1220C4×Q8—731no—
1221C4×Q8—731no—
1222C4×Q8—731no—
1223C4×Q8—731no—
1224C4×Q8—731no—
1225C4×Q8—731no—
1226C4×Q8—731no—
1227C4×Q8—731no—
1228C4×Q8—731no—
1229C4×Q8—731no—
1230C4×Q8—1461no—
1231C4×Q8—1461no—
1232C4×Q8—1461no—
1233C4×Q8—1461no—
1234C4×Q8—1461no—
1235C4×Q8—1461no—
1236C4×Q8—1461no—
1237C4×Q8—1461no—
1238C4×Q8—1461no—
1239C4×Q8—1461no—
1240C4×Q8C22×D7311yescharacteristic
1241C4×Q8C22×D7311yescharacteristic
1242C4×Q8C22×D7311yescharacteristic
1243C4×D4—21no—
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—1461no—
1253C4×D4—1461no—
1254C4×D4—1461no—
1255C4×D4—1461no—
1256C4×D4—1461no—
1257C4×D4—1461no—
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×D4C22×D7311yescharacteristic
1267#117—21no—
1268#117—21no—
1269#117—731no—
1270#117—731no—
1271#117—731no—
1272#117—1461no—
1273#117—1461no—
1274#117—1461no—
1275#117—1461no—
1276#117—1461no—
1277C2×C4⋊C4—731no—
1278C2×C4⋊C4—731no—
1279C2×C4⋊C4—731no—
1280C2×C4⋊C4—1461no—
1281C2×C4⋊C4—1461no—
1282C2×C4⋊C4—1461no—
1283C2×C22⋊C4—1461no—
1284C2×C22⋊C4—1461no—
1285C2×C22⋊C4—1461no—
1286C2×C22⋊C4—1461no—
1287C2×C22⋊C4—1461no—
1288C2×C22⋊C4—1461no—
1289C2×C42—731no—
1290C2×C42—731no—
1291C2×C42—1461no—
1292C2×C42—1461no—
1293C2×C42—1461no—
1294C2×C42C22×D7311yescharacteristic
1295#107—731no—
1296#107—731no—
1297#107C22×D7311yescharacteristic
1298#107C22×D7311yescharacteristic
1299#106—731no—
1300#106—731no—
1301#106C22×D7311yescharacteristic
1302#106C22×D7311yescharacteristic
1303C4⋊C8—731no—
1304C4⋊C8—731no—
1305C4⋊C8—731no—
1306C4⋊C8—731no—
1307C4⋊C8—731no—
1308C4⋊C8—731no—
1309C4⋊C8C22×D7311yescharacteristic
1310C4⋊C8C22×D7311yescharacteristic
1311C4⋊C8C22×D7311yescharacteristic
1312C4⋊C8C22×D7311yescharacteristic
1313#103—731no—
1314#103—731no—
1315#103—731no—
1316#103—731no—
1317#103—731no—
1318#103—731no—
1319#103—731no—
1320#103—731no—
1321#103—731no—
1322#103—731no—
1323#103—731no—
1324#103—731no—
1325#103—731no—
1326#103—731no—
1327#103C22×D7311yescharacteristic
1328#103C22×D7311yescharacteristic
1329#103C22×D7311yescharacteristic
1330#103C22×D7311yescharacteristic
1331#103C22×D7311yescharacteristic
1332#103C22×D7311yescharacteristic
1333#102—731no—
1334#102—731no—
1335#102—731no—
1336#102—731no—
1337#102—731no—
1338#102—731no—
1339#102—731no—
1340#102—731no—
1341#102—731no—
1342#102—731no—
1343#102C22×D7311yescharacteristic
1344#102C22×D7311yescharacteristic
1345C22⋊C8—731no—
1346C22⋊C8—731no—
1347C22⋊C8—731no—
1348C22⋊C8—731no—
1349C22⋊C8—731no—
1350C22⋊C8—731no—
1351#97—731no—
1352#97—731no—
1353#97—731no—
1354#97—731no—
1355C4×C8—731no—
1356C4×C8—731no—
1357C24—1461no—
1358C24—1461no—
1359#41—2921no—
1360#41—2921no—
1361#41—2921no—
1362#41—2921no—
1363#41—1464no—
1364C2×Q8—21no—
1365C2×Q8—2921no—
1366C2×Q8—2921no—
1367C2×Q8—2921no—
1368C2×Q8—2921no—
1369C2×Q8—2921no—
1370C2×Q8—2921no—
1371C2×Q8—2921no—
1372C2×Q8—731no—
1373C2×Q8—731no—
1374C2×Q8—731no—
1375C2×Q8—731no—
1376C2×Q8—731no—
1377C2×Q8—1462no—
1378C2×Q8—1461no—
1379C2×Q8—1461no—
1380C2×Q8—1461no—
1381C2×Q8—1461no—
1382C2×Q8—1461no—
1383C2×Q8—1462no—
1384C2×Q8—1462no—
1385C2×Q8—1461no—
1386C2×Q8—1461no—
1387C2×Q8C23×D7311yescharacteristic
1388C2×Q8C23×D7311yescharacteristic
1389C2×Q8C23×D7311yescharacteristic
1390C2×D4—21no—
1391C2×D4—2921no—
1392C2×D4—2921no—
1393C2×D4—2924no—
1394C2×D4—2921no—
1395C2×D4—2921no—
1396C2×D4—731no—
1397C2×D4—731no—
1398C2×D4—731no—
1399C2×D4—731no—
1400C2×D4—731no—
1401C2×D4—1461no—
1402C2×D4—1461no—
1403C2×D4—1461no—
1404C2×D4—1461no—
1405C2×D4—1461no—
1406C2×D4—1461no—
1407C2×D4—1461no—
1408C2×D4—1461no—
1409C2×D4C23×D7311yescharacteristic
1410C22×C4—21no—
1411C22×C4—731no—
1412C22×C4—731no—
1413C22×C4—731no—
1414C22×C4—731no—
1415C22×C4—731no—
1416C22×C4—731no—
1417C22×C4—1461no—
1418C22×C4—1461no—
1419C22×C4—1461no—
1420C22×C4—1461no—
1421C22×C4—1461no—
1422C22×C4—1461no—
1423C22×C4—1461no—
1424C22×C4—1461no—
1425C22×C4—1461no—
1426C22×C4—1461no—
1427C22×C4—1461no—
1428C22×C4—1461no—
1429C22×C4D4×D7311yescharacteristic
1430C22×C4D4×D7311yescharacteristic
1431C22×C4C23×D7311yescharacteristic
1432Q16—41no—
1433Q16—41no—
1434Q16—2921no—
1435Q16—2921no—
1436Q16—2921no—
1437Q16—2921no—
1438Q16—2921no—
1439Q16—2921no—
1440Q16—2921no—
1441Q16—1462no—
1442Q16—1462no—
1443Q16—1462no—
1444SD16—41no—
1445SD16—41no—
1446SD16—2921no—
1447SD16—2921no—
1448SD16—2921no—
1449SD16—2921no—
1450SD16—2921no—
1451SD16—2921no—
1452SD16—2921no—
1453SD16—1462no—
1454SD16—1462no—
1455SD16—1462no—
1456M16—2921no—
1457M16—2921no—
1458C2×C8—41no—
1459C2×C8—41no—
1460C2×C8—2921no—
1461C2×C8—2921no—
1462C2×C8—731no—
1463C2×C8—731no—
1464C2×C8—731no—
1465C2×C8—731no—
1466C2×C8C23×D7311yescharacteristic
1467C2×C8C23×D7311yescharacteristic
1468C2×C8C23×D7311yescharacteristic
1469C2×C8C23×D7311yescharacteristic
1470C4⋊C4—21no—
1471C4⋊C4—21no—
1472C4⋊C4—21no—
1473C4⋊C4—21no—
1474C4⋊C4—21no—
1475C4⋊C4—21no—
1476C4⋊C4—21no—
1477C4⋊C4—21no—
1478C4⋊C4—21no—
1479C4⋊C4—21no—
1480C4⋊C4—21no—
1481C4⋊C4—731no—
1482C4⋊C4—731no—
1483C4⋊C4—731no—
1484C4⋊C4—731no—
1485C4⋊C4—731no—
1486C4⋊C4—731no—
1487C4⋊C4—731no—
1488C4⋊C4—731no—
1489C4⋊C4—1461no—
1490C4⋊C4—1461no—
1491C4⋊C4—1461no—
1492C4⋊C4—1461no—
1493C4⋊C4—1461no—
1494C4⋊C4—1461no—
1495C4⋊C4—1461no—
1496C4⋊C4—1461no—
1497C4⋊C4—1461no—
1498C4⋊C4—1461no—
1499C4⋊C4—1461no—
1500C4⋊C4—1461no—
1501C4⋊C4—1461no—
1502C4⋊C4—1461no—
1503C4⋊C4—1461no—
1504C4⋊C4—1461no—
1505C4⋊C4—1461no—
1506C4⋊C4—1461no—
1507C4⋊C4—1461no—
1508C4⋊C4—1461no—
1509C4⋊C4—1461no—
1510C4⋊C4—1461no—
1511C4⋊C4—1461no—
1512C4⋊C4—1461no—
1513C4⋊C4—1461no—
1514C4⋊C4—1461no—
1515C4⋊C4—1461no—
1516C4⋊C4C23×D7311yescharacteristic
1517C4⋊C4C23×D7311yescharacteristic
1518C4⋊C4C23×D7311yescharacteristic
1519C4⋊C4C23×D7311yescharacteristic
1520C22⋊C4—21no—
1521C22⋊C4—21no—
1522C22⋊C4—21no—
1523C22⋊C4—21no—
1524C22⋊C4—21no—
1525C22⋊C4—21no—
1526C22⋊C4—21no—
1527C22⋊C4—731no—
1528C22⋊C4—731no—
1529C22⋊C4—731no—
1530C22⋊C4—731no—
1531C22⋊C4—731no—
1532C22⋊C4—731no—
1533C22⋊C4—1461no—
1534C22⋊C4—1461no—
1535C22⋊C4—1461no—
1536C22⋊C4—1461no—
1537C22⋊C4—1461no—
1538C22⋊C4—1461no—
1539C22⋊C4—1461no—
1540C22⋊C4—1461no—
1541C22⋊C4—1461no—
1542C22⋊C4—1461no—
1543C22⋊C4—1461no—
1544C22⋊C4—1461no—
1545C22⋊C4—1461no—
1546C22⋊C4—1461no—
1547C22⋊C4—1461no—
1548C22⋊C4—1461no—
1549C22⋊C4—1461no—
1550C22⋊C4—1461no—
1551C22⋊C4—1461no—
1552C22⋊C4—1461no—
1553C22⋊C4—1461no—
1554C22⋊C4—1461no—
1555C42—21no—
1556C42—21no—
1557C42—21no—
1558C42—731no—
1559C42—731no—
1560C42—731no—
1561C42—731no—
1562C42—731no—
1563C42—731no—
1564C42—1461no—
1565C42—1461no—
1566C42—1461no—
1567C42—1461no—
1568C42—1461no—
1569C42—1461no—
1570C42—1461no—
1571C42—1461no—
1572C42—1461no—
1573C42—1461no—
1574C42D4×D7311yescharacteristic
1575C42D4×D7311yescharacteristic
1576C42C23×D7311yescharacteristic
1577C42C23×D7311yescharacteristic
1578C23—21no—
1579C23—2922no—
1580C23—2922no—
1581C23—5841no—
1582C23—5841no—
1583C23—5841no—
1584C23—5841no—
1585C23—731no—
1586C23—731no—
1587C23—1461no—
1588C23—1461no—
1589C23C2×D4×D7311yescharacteristic
1590Q8—21no—
1591Q8—21no—
1592Q8—21no—
1593Q8—21no—
1594Q8—21no—
1595Q8—21no—
1596Q8—81no—
1597Q8—2922no—
1598Q8—2922no—
1599Q8—2922no—
1600Q8—5841no—
1601Q8—5841no—
1602Q8—5841no—
1603Q8—5841no—
1604Q8—732no—
1605Q8—1462no—
1606Q8—1461no—
1607Q8—1461no—
1608Q8—1461no—
1609Q8—1461no—
1610Q8—1461no—
1611Q8—1461no—
1612Q8—1461no—
1613D4—21no—
1614D4—21no—
1615D4—42no—
1616D4—2922no—
1617D4—2922no—
1618D4—5841no—
1619D4—5841no—
1620D4—5841no—
1621D4—5841no—
1622D4—5841no—
1623D4—5841no—
1624D4—734no—
1625D4—1462no—
1626D4—1462no—
1627D4—1461no—
1628D4—1461no—
1629D4—1461no—
1630D4—1461no—
1631C2×C4—22no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—41no—
1642C2×C4—81no—
1643C2×C4—2921no—
1644C2×C4—2921no—
1645C2×C4—2922no—
1646C2×C4—2922no—
1647C2×C4—2922no—
1648C2×C4—2922no—
1649C2×C4—5841no—
1650C2×C4—5841no—
1651C2×C4—5841no—
1652C2×C4—5841no—
1653C2×C4—5841no—
1654C2×C4—5841no—
1655C2×C4—5841no—
1656C2×C4—5841no—
1657C2×C4—731no—
1658C2×C4—731no—
1659C2×C4—731no—
1660C2×C4—731no—
1661C2×C4—731no—
1662C2×C4—731no—
1663C2×C4—1462no—
1664C2×C4—1462no—
1665C2×C4—1461no—
1666C2×C4—1461no—
1667C2×C4—1461no—
1668C2×C4—1461no—
1669C2×C4—1461no—
1670C2×C4—1461no—
1671C2×C4—1461no—
1672C2×C4—1461no—
1673C2×C4—1461no—
1674C2×C4—1461no—
1675C2×C4C2×D4×D7311yescharacteristic
1676C2×C4C2×D4×D7311yescharacteristic
1677C2×C4C2×D4×D7311yescharacteristic
1678C2×C4C2×D4×D7311yescharacteristic
1679C2×C4C2×D4×D7311yescharacteristic
1680C2×C4C24×D7311yescharacteristic
1681C8—21no—
1682C8—21no—
1683C8—21no—
1684C8—21no—
1685C8—1461no—
1686C8—1461no—
1687C8—1461no—
1688C8—1461no—
1689C22—21no—
1690C22—21no—
1691C22—41no—
1692C22—41no—
1693C22—41no—
1694C22—2921no—
1695C22—2921no—
1696C22—2921no—
1697C22—2921no—
1698C22—2921no—
1699C22—2921no—
1700C22—732no—
1701C22—11682no—
1702C22—11682no—
1703C22—1461no—
1704C22—1461no—
1705C22—1461no—
1706C22—1461no—
1707C22—1461no—
1708C22#137×D7312yes—
1709C22C22×D4×D7311yescharacteristic
1710C4—21no—
1711C4—21no—
1712C4—21no—
1713C4—21no—
1714C4—21no—
1715C4—41no—
1716C4—41no—
1717C4—41no—
1718C4—41no—
1719C4—41no—
1720C4—41no—
1721C4—41no—
1722C4—2921no—
1723C4—2921no—
1724C4—2921no—
1725C4—2921no—
1726C4—2921no—
1727C4—732no—
1728C4—1462no—
1729C4—1461no—
1730C4—1461no—
1731C4—1461no—
1732C4—1461no—
1733C4—1461no—
1734C4H(5,𝔽2)×D7311yescharacteristic
1735C4#1798942411yescharacteristic
1736C2—22no—
1737C2—81no—
1738C2—2921no—
1739C2—5841no—
1740C2—5841no—
1741C2—1462no—
1742C2#2262359511yescharacteristic
1743C2C2×#137×D7311yescharacteristic
1744C2#2262470011yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3248C2
socleC22×C73C23×D4
prime radical#22623880C2
hypercenter#3248D73
hypocenterC73#61991
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3248

Complements

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

NH ≅ G/Ntype
2. #22623509C2semidirect
3. #22622979C2semidirect
4. #22622957C2semidirect
5. #22622748C2semidirect
6. #22622674C2semidirect
7. #22622048C2semidirect
8. #22622039C2semidirect
9. #22622018C2semidirect
10. #22622009C2semidirect
11. #22621802C2semidirect
12. #22621750C2semidirect
13. #22621680C2semidirect
14. #22621624C2semidirect
15. #22621507C2semidirect
16. #22621498C2semidirect
17. #22621447C2semidirect
18. #22621438C2semidirect
19. #22621303C2semidirect
20. #22621267C2semidirect
21. #22620932C2semidirect
22. #22620930C2semidirect
23. #22620886C2semidirect
24. #22620107C2semidirect
25. #22620098C2semidirect
26. #22620016C2semidirect
27. #22619401C2semidirect
28. C2×#17988810C2semidirect
29. #464×D73C2semidirect
30. #22619053C2semidirect
31. C73×#3248C2semidirect
32. C2×#14556623C22semidirect
33. C2×#14556620C22semidirect
34. C22×Dic292C22semidirect
35. C2×Q16×D73C22semidirect
39. #17989317C22semidirect
41. #17989312C22semidirect
44. #17989298C22semidirect
46. #17989295C22semidirect
52. #17989252C22semidirect
55. #17989250C22semidirect
67. #17989141C22semidirect
68. #17989141C22semidirect
78. C2×C4×Dic146C22semidirect
79. C4×Q8×D73C22semidirect
80. C4×Q8×D73C22semidirect
83. #17988979C22semidirect
84. #17988978C22semidirect
85. #17988965C22semidirect
88. #17988949C22semidirect
90. #17988945C22semidirect
91. #17988936C22semidirect
93. #17988924C22semidirect
94. #17988920C22semidirect
95. #17988919C22semidirect
99. #17988891C22semidirect
100. #17988891C22semidirect
101. #17988881C22semidirect
103. #17988871C22semidirect
104. #17988866C22semidirect
105. #17988846C22semidirect
106. #17988844C22semidirect
109. #17988829C22semidirect
110. #17988827C22semidirect
119. #17988810C22semidirect
120. #17988810C22semidirect
121. #17988810C22semidirect
122. #17988810C22semidirect
125. #17988809C22semidirect
126. #17988809C22semidirect
127. #17988808C22semidirect
128. #17988807C22semidirect
129. #17988806C22semidirect
130. #17988806C22semidirect
131. #17988796C22semidirect
132. #17988796C22semidirect
133. #17988796C22semidirect
134. #17988795C22semidirect
136. #17988791C22semidirect
139. #17988752C22semidirect
140. #17988750C22semidirect
141. #17988748C22semidirect
142. #17988746C22semidirect
143. #17988744C22semidirect
144. #17988744C22semidirect
145. #17988744C22semidirect
146. #17988742C22semidirect
147. #17988742C22semidirect
148. #17988742C22semidirect
149. #17988741C22semidirect
157. #17988716C22semidirect
158. #17988716C22semidirect
159. #17988693C22semidirect
160. #17988692C22semidirect
161. #17988692C22semidirect
162. #17988691C22semidirect
163. #17988690C22semidirect
164. #17988687C22semidirect
165. #17988687C22semidirect
166. #17988686C22semidirect
167. #17988681C22semidirect
168. #17988679C22semidirect
171. #17988658C22semidirect
172. #17988658C22semidirect
173. #17988657C22semidirect
174. #17988657C22semidirect
177. #17988644C22semidirect
178. #17988643C22semidirect
179. #17988639C22semidirect
180. #17988609C22semidirect
181. C4⋊C8×D73C22semidirect
182. #17988587C22semidirect
183. #17988585C22semidirect
184. C2×#14556516C22semidirect
185. #103×D73C22semidirect
188. #533×C73C22semidirect
190. #479×C73C22semidirect
191. #479×C73C22semidirect
192. #475×C73C22semidirect
193. #474×C73C22semidirect
194. #467×C73C22semidirect
195. #467×C73C22semidirect
198. #464×C73C22semidirect
199. #464×C73C22semidirect
200. #462×C73C22semidirect
201. #461×C73C22semidirect
202. C2×C4⋊C8×C73C22semidirect
750. C22⋊D73#137semidirect
893. #3248D73semidirect
904. C73#61991semidirect
943. #533C2×D73semidirect
976. #479C2×D73semidirect
977. #479C2×D73semidirect
981. #475C2×D73semidirect
983. #474C2×D73semidirect
990. #467C2×D73semidirect
991. #467C2×D73semidirect
1014. #464C2×D73semidirect
1015. #464C2×D73semidirect
1020. #462C2×D73semidirect
1023. #461C2×D73semidirect
1069. C2×C4⋊C8C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226238802
#226235092
#226229792
#226229572
#226227482
#226226742
#226220482
#226220392
#226220182
#226220092
#226218022
#226217502
#226216802
#226216242
#226215072
#226214982
#226214472
#226214382
#226213032
#226212672
#226209322
#226209302
#226208862
#226201072
#226200982
#226200162
#226194012
C2×#179888102
#464×D732
#226190532
C73×#32482
#6199173