Finite Group Databasebeta

← #33967945

Subgroups — #33967945

Order 18688.

1888 conjugacy classes of subgroups.

The subgroup lattice has 1716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623535C211yesmaximal, characteristic
2Q8×#11924028C211yesmaximal, characteristic, complemented
3#22622985C211yesmaximal, characteristic, complemented
4#22622842C211yesmaximal, characteristic, complemented
5#22622746C211yesmaximal, characteristic, complemented
6#22622713C211yesmaximal, characteristic, complemented
7#22622421C211yesmaximal, characteristic, complemented
8#22622412C211yesmaximal, characteristic, complemented
9#22622321C211yesmaximal, characteristic, complemented
10#22622107C211yesmaximal, characteristic, complemented
11#22622098C211yesmaximal, characteristic, complemented
12#22622017C211yesmaximal, characteristic, complemented
13#22622008C211yesmaximal, characteristic, complemented
14#22621803C211yesmaximal, characteristic, complemented
15#22621751C211yesmaximal, characteristic, complemented
16SD16×C22⋊D73C211yesmaximal, characteristic, complemented
17#22621443C211yesmaximal, characteristic, complemented
18#22621441C211yesmaximal, characteristic, complemented
19#22620646C211yesmaximal, characteristic, complemented
20#22620640C211yesmaximal, characteristic, complemented
21#22620636C211yesmaximal, characteristic, complemented
22#22620102C211yesmaximal, characteristic, complemented
23#22620100C211yesmaximal, characteristic, complemented
24#22620089C211yesmaximal, characteristic, complemented
25#22620051C211yesmaximal, characteristic, complemented
26#22620030C211yesmaximal, characteristic, complemented
27#22620028C211yesmaximal, characteristic, complemented
28#22618942C211yesmaximal, characteristic, complemented
29#22618753C211yesmaximal, characteristic, complemented
30#440×D73C211yesmaximal, characteristic, complemented
31C2×#440×C73C211yesmaximal, characteristic, complemented
32C2×#14556620C2211yescharacteristic
33C2×SD16×D73C2211yescharacteristic
34#17989320C2211yescharacteristic
35Q8×Dic146C2211yescharacteristic, complemented
36#17989315—21no—
37#17989315C2211yescharacteristic, complemented
38#17989297—21no—
39#17989297C2211yescharacteristic, complemented
40#17989296C2211yescharacteristic
41#17989292—21no—
42#17989292—21no—
43#17989292C2211yescharacteristic
44#17989292C2211yescharacteristic
45#17989292C2211yescharacteristic, complemented
46#17989287C2211yescharacteristic
47#17989286—21no—
48#17989285C2211yescharacteristic
49#17989266—21no—
50#17989263—21no—
51Q8×D292C2211yescharacteristic, complemented
52Q8×C22⋊D73C2211yescharacteristic
53Q8×C22⋊D73C2211yescharacteristic, complemented
54#17989232C2211yescharacteristic
55#17989231C2211yescharacteristic
56#17989227—21no—
57D4×C22⋊D73C2211yescharacteristic
58#17989144—21no—
59#17989144C2211yescharacteristic, complemented
60#17989141—21no—
61#17989141—21no—
62#17989141C2211yescharacteristic, complemented
63#17989141C2211yescharacteristic, complemented
64#17989134C2211yescharacteristic
65#17989121C2211yescharacteristic
66#17989119C2211yescharacteristic
67#17989117—21no—
68#17989098—21no—
69#17989096—21no—
70C4×#11924028—21no—
71C4×#11924028C2211yescharacteristic
72C4×#11924027C2211yescharacteristic
73C4×Q8×D73C2211yescharacteristic, complemented
74C4×Q8×D73C2211yescharacteristic, complemented
75C2×C4×C22⋊D73—21no—
76C4×D4×D73C2211yescharacteristic
77#17988996C2211yescharacteristic, complemented
78#17988995C2211yescharacteristic, complemented
79#17988991C2211yescharacteristic, complemented
80#17988981C2211yescharacteristic, complemented
81#17988978C2211yescharacteristic, complemented
82#17988958C2211yescharacteristic
83#17988956C2211yescharacteristic, complemented
84#17988954C2211yescharacteristic, complemented
85#17988947C2211yescharacteristic, complemented
86#17988945C2211yescharacteristic, complemented
87#17988936C2211yescharacteristic, complemented
88#17988932C2211yescharacteristic
89#17988930C2211yescharacteristic, complemented
90#17988926C2211yescharacteristic, complemented
91#17988924C2211yescharacteristic, complemented
92#17988924C2211yescharacteristic, complemented
93#17988922C2211yescharacteristic, complemented
94#17988922C2211yescharacteristic, complemented
95#17988922C2211yescharacteristic, complemented
96#17988921C2211yescharacteristic, complemented
97#17988905C2211yescharacteristic
98#17988904C2211yescharacteristic
99#17988902C2211yescharacteristic, complemented
100#17988899C2211yescharacteristic, complemented
101#17988894C2211yescharacteristic, complemented
102#17988894C2211yescharacteristic, complemented
103#17988893C2211yescharacteristic, complemented
104#17988892C2211yescharacteristic, complemented
105#17988881C2211yescharacteristic, complemented
106#17988881C2211yescharacteristic, complemented
107#17988880C2211yescharacteristic, complemented
108#17988875C2211yescharacteristic
109#17988867C2211yescharacteristic
110#17988867C2211yescharacteristic, complemented
111#17988866C2211yescharacteristic, complemented
112#17988865C2211yescharacteristic
113#17988836C2211yescharacteristic, complemented
114#17988834C2211yescharacteristic, complemented
115#17988832C2211yescharacteristic, complemented
116#17988830C2211yescharacteristic, complemented
117#17988829C2211yescharacteristic, complemented
118#17988828C2211yescharacteristic, complemented
119#17988828C2211yescharacteristic, complemented
120#17988827C2211yescharacteristic, complemented
121#17988816C2211yescharacteristic
122#17988816C2211yescharacteristic
123#17988815C2211yescharacteristic
124#17988813C2211yescharacteristic
125#17988809C2211yescharacteristic, complemented
126#17988809C2211yescharacteristic, complemented
127#17988808C2211yescharacteristic, complemented
128#17988807C2211yescharacteristic, complemented
129#17988796C2211yescharacteristic, complemented
130#17988792C2211yescharacteristic
131#17988792C2211yescharacteristic, complemented
132#17988791C2211yescharacteristic, complemented
133#17988790C2211yescharacteristic
134#17988790C2211yescharacteristic
135#17988786C2211yescharacteristic
136#17988785C2211yescharacteristic
137#17988750C2211yescharacteristic
138#17988746C2211yescharacteristic
139#17988744C2211yescharacteristic, complemented
140#17988743C2211yescharacteristic, complemented
141#17988739C2211yescharacteristic
142#17988738C2211yescharacteristic
143#17988738C2211yescharacteristic
144#17988736C2211yescharacteristic
145#17988727C2211yescharacteristic, complemented
146#17988726C2211yescharacteristic
147#17988724C2211yescharacteristic
148#17988724C2211yescharacteristic, complemented
149#17988715C2211yescharacteristic, complemented
150#17988715C2211yescharacteristic, complemented
151#17988695C2211yescharacteristic, complemented
152#17988695C2211yescharacteristic, complemented
153#17988692C2211yescharacteristic, complemented
154#17988692C2211yescharacteristic, complemented
155#17988690C2211yescharacteristic, complemented
156#17988689C2211yescharacteristic, complemented
157#17988689C2211yescharacteristic, complemented
158#17988688C2211yescharacteristic
159#17988687C2211yescharacteristic
160#17988687C2211yescharacteristic
161#17988687C2211yescharacteristic, complemented
162#17988687C2211yescharacteristic, complemented
163#17988686C2211yescharacteristic, complemented
164#17988685C2211yescharacteristic, complemented
165#17988685C2211yescharacteristic, complemented
166#17988684C2211yescharacteristic
167#17988681C2211yescharacteristic, complemented
168#17988679C2211yescharacteristic, complemented
169#17988678C2211yescharacteristic
170SD16×Dic73C2211yescharacteristic
171#17988660C2211yescharacteristic, complemented
172#17988660C2211yescharacteristic, complemented
173#17988658C2211yescharacteristic, complemented
174#17988658C2211yescharacteristic, complemented
175C8×C22⋊D73C2211yescharacteristic
176C8×C22⋊D73C2211yescharacteristic
177#17988644C2211yescharacteristic, complemented
178#17988642C2211yescharacteristic, complemented
179#17988642C2211yescharacteristic, complemented
180#17988628C2211yescharacteristic, complemented
181#107×D73C2211yescharacteristic, complemented
182#17988594C2211yescharacteristic, complemented
183#17988585C2211yescharacteristic
184#103×D73C2211yescharacteristic, complemented
185#102×D73C2211yescharacteristic
186#17988539C2211yescharacteristic, complemented
187#97×D73C2211yescharacteristic, complemented
188C22×SD16×C73C2211yescharacteristic
189C2×C4×Q8×C73C2211yescharacteristic, complemented
190C2×C4×D4×C73C2211yescharacteristic
191#440×C73C2211yescharacteristic
192#440×C73C2211yescharacteristic
193#440×C73C2211yescharacteristic
194#440×C73C2211yescharacteristic
195#440×C73C2211yescharacteristic, complemented
196#440×C73C2211yescharacteristic, complemented
197#440×C73C2211yescharacteristic, complemented
198#440×C73C2211yescharacteristic, complemented
199C2×#107×C73C2211yescharacteristic, complemented
200C2×#103×C73C2211yescharacteristic, complemented
201C2×#102×C73C2211yescharacteristic
202C2×#97×C73C2211yescharacteristic, complemented
203C2×#11924028—21no—
204C2×#11924028D411yescharacteristic
205C2×#11924027C2311yescharacteristic
206C2×Q8×D73C2311yescharacteristic
207C2×Q8×D73C2311yescharacteristic
208C22×C22⋊D73—21no—
209C2×D4×D73C2311yescharacteristic
210C22×C4×D73—21no—
211#14556620—24no—
212C2×Dic292C2311yescharacteristic
213C2×Dic292C2311yescharacteristic
214C2×#11924018C2311yescharacteristic
215C2×#11924018C2311yescharacteristic
216C2×#11924017C2311yescharacteristic
217C2×#11924017C2311yescharacteristic
218C2×#11924016C2311yescharacteristic
219C2×#11924016C2311yescharacteristic
220C2×#11924016C2311yescharacteristic
221C2×#11924016C2311yescharacteristic
222C2×#11924015C2311yescharacteristic
223C2×#11924015C2311yescharacteristic
224SD16×D73—24no—
225C2×#11924011C2311yescharacteristic
226C2×#11924011C2311yescharacteristic
227C2×C8×D73C2311yescharacteristic
228C2×C8×D73C2311yescharacteristic
229#14556591—21no—
230#14556591—21no—
231#14556591C2311yescharacteristic
232#14556591C2311yescharacteristic
233#14556590—21no—
234#14556590—21no—
235#14556590C2311yescharacteristic
236#14556590C2311yescharacteristic
237#14556590C2311yescharacteristic
238#14556589—21no—
239#14556589—21no—
240#14556589C2311yescharacteristic
241#14556589C2311yescharacteristic
242#14556587C2311yescharacteristic
243#14556586—21no—
244#14556585—21no—
245#14556584—21no—
246#14556584—21no—
247#14556583—21no—
248#14556583—21no—
249#14556583—21no—
250#14556583C2311yescharacteristic
251#14556582C2311yescharacteristic
252#14556581—21no—
253#14556581—21no—
254#14556581—21no—
255#14556581—21no—
256#14556581—21no—
257#14556581—21no—
258#14556581—21no—
259#14556579C2311yescharacteristic
260#14556578C2311yescharacteristic
261#14556577—21no—
262#14556577—21no—
263#14556576—21no—
264#14556575—21no—
265#14556574—21no—
266#14556574—21no—
267#14556574—21no—
268#14556573—21no—
269#14556573—21no—
270#14556572—21no—
271#14556571—21no—
272#14556571—21no—
273#14556571C2311yescharacteristic
274#14556571C2311yescharacteristic
275#14556571C2311yescharacteristic
276#14556570—21no—
277#14556570—21no—
278#14556570—21no—
279#14556570—21no—
280#14556570—21no—
281#14556570—21no—
282#14556570—21no—
283#14556570C2311yescharacteristic
284#14556570C2311yescharacteristic
285#14556570C2311yescharacteristic
286#14556569—21no—
287#14556569—21no—
288#14556569—21no—
289#14556569—21no—
290#14556569—21no—
291#14556569—21no—
292#14556569—21no—
293#14556568—21no—
294#14556568—21no—
295#14556567—21no—
296#14556567—21no—
297#14556567C2311yescharacteristic
298#14556567C2311yescharacteristic
299#14556566C2311yescharacteristic
300#14556565—21no—
301#14556565—21no—
302#14556565C2311yescharacteristic
303#14556564—21no—
304#14556564—21no—
305#14556563—21no—
306#14556563—21no—
307#14556562C2311yescharacteristic
308#14556562C2311yescharacteristic
309#14556561—21no—
310#14556560—21no—
311#14556560—21no—
312#14556559—21no—
313Q8×Dic73C2311yescharacteristic
314Q8×Dic73C2311yescharacteristic
315C4×Dic146—21no—
316C4×Dic146—21no—
317C4×Dic146—21no—
318C4×Dic146—21no—
319C4×Dic146—21no—
320C4×Dic146—21no—
321C4×Dic146—21no—
322C4×Dic146D411yescharacteristic
323C4×Dic146C2311yescharacteristic
324C4×Dic146C2311yescharacteristic
325C4×Dic146C2311yescharacteristic
326C4×Dic146C2311yescharacteristic
327#14556556—21no—
328#14556556—21no—
329#14556556C2311yescharacteristic
330#14556556C2311yescharacteristic
331#14556556C2311yescharacteristic
332C4×D292—21no—
333C4×D292—21no—
334C4×D292D411yescharacteristic
335C4×D292C2311yescharacteristic
336C4×D292C2311yescharacteristic
337D4×Dic73C2311yescharacteristic
338D4×Dic73C2311yescharacteristic
339#14556553C2311yescharacteristic
340C4×C22⋊D73—21no—
341C4×C22⋊D73—21no—
342C4×C22⋊D73—21no—
343C4×C22⋊D73—21no—
344C4×C22⋊D73—21no—
345C4×C22⋊D73—21no—
346C4×C22⋊D73—21no—
347C4×C22⋊D73—21no—
348C4×C22⋊D73—21no—
349C4×C22⋊D73—21no—
350C4×C22⋊D73—21no—
351C4×C22⋊D73—21no—
352C4×C22⋊D73—21no—
353C4×C22⋊D73D411yescharacteristic
354C4×C22⋊D73D411yescharacteristic
355C4×C22⋊D73C2311yescharacteristic
356C4×C22⋊D73C2311yescharacteristic
357#14556551—21no—
358#14556551—21no—
359#14556550—21no—
360#14556550—21no—
361#14556550D411yescharacteristic
362#14556549C2311yescharacteristic
363#14556548—21no—
364#14556548—21no—
365#14556548—21no—
366#14556548D411yescharacteristic
367#14556548D411yescharacteristic
368#14556547—21no—
369C2×#11924007—21no—
370C4⋊C4×D73—21no—
371C4⋊C4×D73—21no—
372C4⋊C4×D73C2311yescharacteristic
373C4⋊C4×D73C2311yescharacteristic
374C4⋊C4×D73C2311yescharacteristic
375C2×C22⋊Dic73—21no—
376C2×#11924005—21no—
377C22⋊C4×D73—21no—
378C2×C4×Dic73—21no—
379C42×D73—21no—
380C42×D73—21no—
381C42×D73C2311yescharacteristic
382C42×D73C2311yescharacteristic
383#14556525C2311yescharacteristic
384#14556525C2311yescharacteristic
385#14556524C2311yescharacteristic
386#14556524C2311yescharacteristic
387#14556524C2311yescharacteristic
388#14556524C2311yescharacteristic
389#14556524C2311yescharacteristic
390#14556524C2311yescharacteristic
391#14556523C2311yescharacteristic
392#14556523C2311yescharacteristic
393#14556522C2311yescharacteristic
394#14556522C2311yescharacteristic
395C4⋊#10596831C2311yescharacteristic
396C4⋊#10596831C2311yescharacteristic
397#14556520C2311yescharacteristic
398#14556520C2311yescharacteristic
399#14556520C2311yescharacteristic
400#14556520C2311yescharacteristic
401#14556516C2311yescharacteristic
402#14556516C2311yescharacteristic
403#14556516C2311yescharacteristic
404#14556516C2311yescharacteristic
405#14556516C2311yescharacteristic
406#14556516C2311yescharacteristic
407#14556515C2311yescharacteristic
408#14556515C2311yescharacteristic
409#14556515C2311yescharacteristic
410#14556515C2311yescharacteristic
411#14556514C2311yescharacteristic
412#14556514C2311yescharacteristic
413#14556514C2311yescharacteristic
414#14556514C2311yescharacteristic
415#14556514C2311yescharacteristic
416#14556514C2311yescharacteristic
417#14556513C2311yescharacteristic
418#14556513C2311yescharacteristic
419#14556512C2311yescharacteristic
420#14556512C2311yescharacteristic
421#14556512C2311yescharacteristic
422#14556512C2311yescharacteristic
423#14556511C2311yescharacteristic
424#14556511C2311yescharacteristic
425C22⋊#10596831C2311yescharacteristic
426C22⋊#10596831C2311yescharacteristic
427#14556503C2311yescharacteristic
428#14556503C2311yescharacteristic
429#14556503C2311yescharacteristic
430#14556503C2311yescharacteristic
431#14556502C2311yescharacteristic
432#14556502C2311yescharacteristic
433#14556501C2311yescharacteristic
434#14556501C2311yescharacteristic
435C8×Dic73C2311yescharacteristic
436C8×Dic73C2311yescharacteristic
437C22×Q8×C73C2311yescharacteristic
438C22×D4×C73C2311yescharacteristic
439C23×C4×C73—21no—
440C2×SD16×C73—24no—
441C2×SD16×C73C2311yescharacteristic
442C2×SD16×C73C2311yescharacteristic
443C2×SD16×C73C2311yescharacteristic
444C2×SD16×C73C2311yescharacteristic
445C22×C8×C73C2311yescharacteristic
446C22×C8×C73C2311yescharacteristic
447C4×Q8×C73—21no—
448C4×Q8×C73—21no—
449C4×Q8×C73C2311yescharacteristic
450C4×Q8×C73C2311yescharacteristic
451C4×Q8×C73C2311yescharacteristic
452C4×Q8×C73C2311yescharacteristic
453C4×D4×C73—21no—
454C4×D4×C73—21no—
455C4×D4×C73C2311yescharacteristic
456C4×D4×C73C2311yescharacteristic
457C4×D4×C73C2311yescharacteristic
458C4×D4×C73C2311yescharacteristic
459C2×C4⋊C4×C73—21no—
460C2×C4⋊C4×C73C2311yescharacteristic
461C2×C4⋊C4×C73C2311yescharacteristic
462C2×C22⋊C4×C73—21no—
463C2×C42×C73—21no—
464C2×C42×C73C2311yescharacteristic
465#107×C73C2311yescharacteristic
466#107×C73C2311yescharacteristic
467#107×C73C2311yescharacteristic
468#107×C73C2311yescharacteristic
469#103×C73C2311yescharacteristic
470#103×C73C2311yescharacteristic
471#103×C73C2311yescharacteristic
472#103×C73C2311yescharacteristic
473#102×C73C2311yescharacteristic
474#102×C73C2311yescharacteristic
475#102×C73C2311yescharacteristic
476#102×C73C2311yescharacteristic
477#97×C73C2311yescharacteristic
478#97×C73C2311yescharacteristic
479#97×C73C2311yescharacteristic
480#97×C73C2311yescharacteristic
481C23×D73—21no—
482#11924028—24no—
483#11924028—82no—
484#11924027—22no—
485#11924027—41no—
486C2×Dic146—21no—
487C2×Dic146—21no—
488C2×Dic146—21no—
489C2×Dic146—21no—
490C2×Dic146—21no—
491C2×Dic146—21no—
492C2×Dic146C2×D411yescharacteristic
493C2×Dic146C2411yescharacteristic
494C2×Dic146C2411yescharacteristic
495C2×Dic146C2411yescharacteristic
496Q8×D73—22no—
497Q8×D73—22no—
498Q8×D73—41no—
499Q8×D73—41no—
500C2×D292—21no—
501C2×D292C2×D411yescharacteristic
502C2×D292C2411yescharacteristic
503C2×C22⋊D73—21no—
504C2×C22⋊D73—21no—
505C2×C22⋊D73—21no—
506C2×C22⋊D73—21no—
507C2×C22⋊D73—21no—
508C2×C22⋊D73—21no—
509C2×C22⋊D73—21no—
510C2×C22⋊D73—44no—
511C2×C22⋊D73C2×D411yescharacteristic
512C2×C22⋊D73C2×D411yescharacteristic
513D4×D73—22no—
514D4×D73—41no—
515C22×Dic73—21no—
516C22×Dic73—21no—
517C22×Dic73—21no—
518C2×C4×D73—21no—
519C2×C4×D73—21no—
520C2×C4×D73—21no—
521C2×C4×D73—21no—
522C2×C4×D73—21no—
523C2×C4×D73—21no—
524C2×C4×D73—21no—
525C2×C4×D73—82no—
526C2×C4×D73C2×D411yescharacteristic
527C2×C4×D73C2×D411yescharacteristic
528C2×C4×D73C2×D411yescharacteristic
529C2×C4×D73C2×D411yescharacteristic
530C2×C4×D73C2411yescharacteristic
531C2×C4×D73C2411yescharacteristic
532Dic292—22no—
533Dic292—41no—
534#11924018—22no—
535#11924018—41no—
536#11924017—22no—
537#11924017—41no—
538#11924016—22no—
539#11924016—22no—
540#11924016—41no—
541#11924016—41no—
542#11924015—22no—
543#11924015—41no—
544#11924011—22no—
545#11924011—41no—
546C2×#10596831C2411yescharacteristic
547C2×#10596831C2411yescharacteristic
548C2×#10596831C2411yescharacteristic
549C2×#10596831C2411yescharacteristic
550C8×D73—22no—
551C8×D73—41no—
552C4⋊Dic73—21no—
553C4⋊Dic73—21no—
554C4⋊Dic73—21no—
555C4⋊Dic73—21no—
556C4⋊Dic73—21no—
557C4⋊Dic73—21no—
558C4⋊Dic73—21no—
559C4⋊Dic73—21no—
560C4⋊Dic73—21no—
561C4⋊Dic73C2×D411yescharacteristic
562C4⋊Dic73C2×D411yescharacteristic
563C4⋊Dic73C2411yescharacteristic
564C4⋊Dic73C2411yescharacteristic
565C4⋊Dic73C2411yescharacteristic
566C4⋊Dic73C2411yescharacteristic
567#11924007—21no—
568#11924007—21no—
569#11924007—21no—
570#11924007—21no—
571#11924007—21no—
572#11924007—21no—
573#11924007—21no—
574#11924007—21no—
575#11924007—21no—
576#11924007—21no—
577#11924007—21no—
578#11924007—21no—
579#11924007—21no—
580#11924007—21no—
581#11924007—21no—
582#11924007—21no—
583#11924007—21no—
584#11924007—21no—
585#11924007—21no—
586#11924007—21no—
587#11924007—21no—
588#11924007—21no—
589#11924007—21no—
590#11924007—21no—
591#11924007C2×D411yescharacteristic
592#11924007C2×D411yescharacteristic
593#11924007C2×D411yescharacteristic
594#11924007C2×D411yescharacteristic
595C22⋊Dic73—21no—
596C22⋊Dic73—21no—
597C22⋊Dic73—21no—
598C22⋊Dic73—21no—
599C22⋊Dic73—21no—
600C22⋊Dic73—21no—
601C22⋊Dic73—21no—
602C22⋊Dic73—21no—
603C22⋊Dic73—21no—
604C22⋊Dic73C2×D411yescharacteristic
605C22⋊Dic73C2×D411yescharacteristic
606#11924005—21no—
607#11924005—21no—
608#11924005—21no—
609#11924005—21no—
610#11924005—21no—
611#11924005—21no—
612#11924005—21no—
613#11924005—21no—
614#11924005—21no—
615#11924005—21no—
616#11924005—21no—
617#11924005—21no—
618#11924005C2×D411yescharacteristic
619#11924005C2×D411yescharacteristic
620#11924005C2×D411yescharacteristic
621#11924005C2×D411yescharacteristic
622C4×Dic73—21no—
623C4×Dic73—21no—
624C4×Dic73—21no—
625C4×Dic73—21no—
626C4×Dic73—21no—
627C4×Dic73—21no—
628C4×Dic73—21no—
629C4×Dic73—21no—
630C4×Dic73—21no—
631C4×Dic73C2×D411yescharacteristic
632C4×Dic73C2×D411yescharacteristic
633C4×Dic73C2×D411yescharacteristic
634C4×Dic73C2×D411yescharacteristic
635C4×Dic73C2411yescharacteristic
636C4×Dic73C2411yescharacteristic
637C24×C73—21no—
638C2×Q8×C73—21no—
639C2×Q8×C73—22no—
640C2×Q8×C73—41no—
641C2×Q8×C73C2411yescharacteristic
642C2×Q8×C73C2411yescharacteristic
643C2×D4×C73—22no—
644C2×D4×C73—21no—
645C2×D4×C73—41no—
646C2×D4×C73C2411yescharacteristic
647C2×D4×C73C2411yescharacteristic
648C22×C4×C73—21no—
649C22×C4×C73—21no—
650C22×C4×C73—21no—
651C22×C4×C73—21no—
652C22×C4×C73—21no—
653C22×C4×C73—21no—
654C22×C4×C73—21no—
655C22×C4×C73—82no—
656C22×C4×C73C2×D411yescharacteristic
657C22×C4×C73C2×D411yescharacteristic
658C22×C4×C73C2411yescharacteristic
659SD16×C73—22no—
660SD16×C73—22no—
661SD16×C73—22no—
662SD16×C73#4114yescomplemented
663C2×C8×C73—22no—
664C2×C8×C73—41no—
665C2×C8×C73C2411yescharacteristic
666C2×C8×C73C2411yescharacteristic
667C2×C8×C73C2411yescharacteristic
668C2×C8×C73C2411yescharacteristic
669C4⋊C4×C73—21no—
670C4⋊C4×C73—21no—
671C4⋊C4×C73—21no—
672C4⋊C4×C73—21no—
673C4⋊C4×C73—21no—
674C4⋊C4×C73—21no—
675C4⋊C4×C73C2411yescharacteristic
676C4⋊C4×C73C2411yescharacteristic
677C4⋊C4×C73C2411yescharacteristic
678C4⋊C4×C73C2411yescharacteristic
679C22⋊C4×C73—21no—
680C22⋊C4×C73—21no—
681C22⋊C4×C73—21no—
682C22⋊C4×C73—21no—
683C42×C73—21no—
684C42×C73—21no—
685C42×C73—21no—
686C42×C73—21no—
687C42×C73C2×D411yescharacteristic
688C42×C73C2×D411yescharacteristic
689C42×C73C2411yescharacteristic
690C42×C73C2411yescharacteristic
691C23×C73—21no—
692C23×C73—21no—
693C23×C73—42no—
694C23×C73—42no—
695C23×C73—81no—
696C23×C73C22×D411yescharacteristic
697C22×D73—21no—
698C22×D73—42no—
699C22×D73—42no—
700C22×D73—81no—
701C22×D73C22×D411yescharacteristic
702C22×D73C22×D411yescharacteristic
703Q8×C73—21no—
704Q8×C73—21no—
705Q8×C73—21no—
706Q8×C73—42no—
707Q8×C73C2×#4112yes—
708D4×C73—21no—
709D4×C73—21no—
710D4×C73—21no—
711D4×C73—42no—
712D4×C73C2×#4112yes—
713C2×C4×C73—22no—
714C2×C4×C73—21no—
715C2×C4×C73—21no—
716C2×C4×C73—21no—
717C2×C4×C73—21no—
718C2×C4×C73—21no—
719C2×C4×C73—21no—
720C2×C4×C73—21no—
721C2×C4×C73—21no—
722C2×C4×C73—41no—
723C2×C4×C73—42no—
724C2×C4×C73—42no—
725C2×C4×C73—42no—
726C2×C4×C73—81no—
727C2×C4×C73—81no—
728C2×C4×C73—81no—
729C2×C4×C73—81no—
730C2×C4×C73C22×D411yescharacteristic
731C2×C4×C73C22×D411yescharacteristic
732C2×C4×C73C22×D411yescharacteristic
733C2×C4×C73C22×D411yescharacteristic
734C2×C4×C73C22×D411yescharacteristic
735C2×C4×C73C2511yescharacteristic
736C22⋊D73—22no—
737C22⋊D73—42no—
738C22⋊D73—42no—
739C22⋊D73—42no—
740C22⋊D73—42no—
741C22⋊D73—42no—
742C22⋊D73—81no—
743C22⋊D73—81no—
744C22⋊D73#13714yescomplemented
745C2×Dic73—21no—
746C2×Dic73—21no—
747C2×Dic73—21no—
748C2×Dic73—21no—
749C2×Dic73—21no—
750C2×Dic73—21no—
751C2×Dic73—21no—
752C2×Dic73—42no—
753C2×Dic73—42no—
754C2×Dic73—81no—
755C2×Dic73C22×D411yescharacteristic
756C2×Dic73C22×D411yescharacteristic
757C2×Dic73C22×D411yescharacteristic
758C2×Dic73C22×D411yescharacteristic
759C2×Dic73C22×D411yescharacteristic
760C2×Dic73C22×D411yescharacteristic
761D292—22no—
762D292—21no—
763D292—21no—
764D292—81no—
765C4×D73—22no—
766C4×D73—21no—
767C4×D73—21no—
768C4×D73—21no—
769C4×D73—21no—
770C4×D73—22no—
771C4×D73—41no—
772C4×D73—41no—
773C4×D73—42no—
774C4×D73—42no—
775C4×D73—42no—
776C4×D73—81no—
777C4×D73—81no—
778C4×D73—81no—
779C4×D73—81no—
780Dic146—22no—
781Dic146—21no—
782Dic146—21no—
783Dic146—21no—
784Dic146—21no—
785Dic146—21no—
786Dic146—21no—
787Dic146—42no—
788Dic146—42no—
789Dic146—81no—
790Dic146—81no—
791Dic146—81no—
792Dic146—81no—
793C8×C73—21no—
794C8×C73—21no—
795C8×C73—21no—
796C8×C73C2×#4112yes—
797#10596831—21no—
798#10596831—21no—
799#10596831—21no—
800#10596831—21no—
801C22×C73—21no—
802C22×C73—21no—
803C22×C73—22no—
804C22×C73—41no—
805C22×C73—41no—
806C22×C73—41no—
807C22×C73—41no—
808C22×C73—41no—
809C22×C73—84no—
810C22×C73C2×#13712yes—
811C22×C73C23×D411yescharacteristic
812C2×D73—21no—
813C2×D73—21no—
814C2×D73—21no—
815C2×D73—21no—
816C2×D73—21no—
817C2×D73—41no—
818C2×D73—41no—
819C2×D73—41no—
820C2×D73—84no—
821C2×D73C2×#13712yes—
822C4×C73—21no—
823C4×C73—21no—
824C4×C73—22no—
825C4×C73—21no—
826C4×C73—21no—
827C4×C73—21no—
828C4×C73—41no—
829C4×C73—41no—
830C4×C73—41no—
831C4×C73—41no—
832C4×C73—41no—
833C4×C73C22×#4111yescharacteristic
834C4×C73#58511yescharacteristic
835Dic73—21no—
836Dic73—21no—
837Dic73—21no—
838Dic73—21no—
839Dic73—21no—
840Dic73—41no—
841Dic73—41no—
842Dic73—41no—
843Dic73—41no—
844Dic73—41no—
845Dic73—41no—
846Dic73—41no—
847Dic73C2×#13712yes—
848#61453—731nomaximal, Sylow
849C2×C73—22no—
850C2×C73—42no—
851C2×C73—81no—
852C2×C73D4×#4111yescharacteristic
853C2×C73C22×#13711yescharacteristic
854C2×C73#358511yescharacteristic
855D73—22no—
856D73—41no—
857D73—81no—
858#3481—731no—
859Q8×#41—731no—
860#3400—731no—
861#3385—731no—
862#3375—731no—
863#3372—731no—
864#3346—731no—
865#3346—731no—
866#3338—731no—
867#3320—731no—
868#3320—731no—
869#3314—731no—
870#3314—731no—
871#3299—731no—
872#3295—731no—
873D4×SD16—731no—
874#3266—731no—
875#3266—731no—
876#3182—731no—
877#3181—731no—
878#3181—731no—
879#3117—731no—
880#3117—731no—
881#3116—731no—
882#3112—731no—
883#3110—731no—
884#3110—731no—
885#2970—731no—
886C4×#137—731no—
887C2×#440—731no—
888C2×#440D7311yescharacteristic, complemented
889C73#6145311yescharacteristic, complemented, Sylow
890C2×#137—731no—
891C22×SD16—731no—
892C22×SD16C2×D7311yescharacteristic
893#559—731no—
894Q82—731no—
895#557—731no—
896#557—1461no—
897#554—731no—
898#554—731no—
899#554—731no—
900#554—731no—
901#554—731no—
902#554—1461no—
903#554—1461no—
904#554—1461no—
905#553—731no—
906#553—731no—
907#553—1461no—
908#551—1461no—
909#551—1461no—
910D4×Q8—731no—
911D4×Q8—731no—
912D4×Q8—731no—
913#546—731no—
914#546—731no—
915#546—1461no—
916D42—731no—
917#533—731no—
918#533—731no—
919#533—731no—
920#533—1461no—
921#533—1461no—
922#533—1461no—
923#532—731no—
924#529—731no—
925#529—731no—
926#529—1461no—
927#525—1461no—
928#525—1461no—
929C4×#41—731no—
930C4×#41—731no—
931C4×#41—1461no—
932C2×C4×Q8—731no—
933C2×C4×Q8—731no—
934C2×C4×Q8C2×D7311yescharacteristic, complemented
935C2×C4×D4—731no—
936C2×C4×D4—1461no—
937C2×C4×D4C2×D7311yescharacteristic
938#501—731no—
939#501—731no—
940#500—731no—
941#497—731no—
942#497—731no—
943#492—731no—
944#491—731no—
945#491—731no—
946#489—731no—
947#489—731no—
948#487—731no—
949#486—731no—
950#485—731no—
951#485—731no—
952#484—731no—
953#484—731no—
954#484—731no—
955#484—731no—
956#484—731no—
957#484—731no—
958#481—731no—
959#481—731no—
960#480—731no—
961#480—731no—
962#479—731no—
963#479—731no—
964#479—731no—
965#479—731no—
966#477—731no—
967#477—731no—
968#477—731no—
969#476—731no—
970#474—731no—
971#474—731no—
972#474—731no—
973#474—731no—
974#468—731no—
975#468—731no—
976#468—731no—
977#468—731no—
978#467—731no—
979#467—731no—
980#467—731no—
981#467—731no—
982#465—731no—
983#465—731no—
984#465—731no—
985#465—731no—
986#464—731no—
987#464—731no—
988#464—731no—
989#464—731no—
990#462—731no—
991#461—731no—
992#461—731no—
993#461—731no—
994#461—731no—
995#461—731no—
996#460—731no—
997#460—731no—
998#452—731no—
999#452—731no—
1000#451—731no—
1001#451—731no—
1002#450—731no—
1003#450—731no—
1004#450—731no—
1005#450—731no—
1006#448—731no—
1007#448—731no—
1008#448—731no—
1009#448—731no—
1010#446—731no—
1011#446—731no—
1012#441—731no—
1013#441—731no—
1014#441—731no—
1015#441—731no—
1016#440—731no—
1017#440—731no—
1018#440—731no—
1019#440—731no—
1020#440—731no—
1021#440—731no—
1022#440—731no—
1023#440—731no—
1024#440—731no—
1025#440—731no—
1026#440—731no—
1027#440—731no—
1028#440C2×D7311yescharacteristic
1029#440C2×D7311yescharacteristic
1030#440C2×D7311yescharacteristic
1031#440C2×D7311yescharacteristic
1032#440C2×D7311yescharacteristic, complemented
1033#440C2×D7311yescharacteristic, complemented
1034#440C2×D7311yescharacteristic, complemented
1035#440C2×D7311yescharacteristic, complemented
1036C4×Q16—731no—
1037C4×Q16—731no—
1038C4×SD16—731no—
1039C4×SD16—731no—
1040#435—731no—
1041#435—731no—
1042#435—731no—
1043#435—731no—
1044C8×D4—731no—
1045C8×D4—731no—
1046#432—731no—
1047#432—731no—
1048#432—731no—
1049#428—731no—
1050C2×#107—731no—
1051C2×#107C2×D7311yescharacteristic, complemented
1052#419—731no—
1053#417—731no—
1054C2×#103—731no—
1055C2×#103C2×D7311yescharacteristic, complemented
1056C2×#102—731no—
1057C2×#102C2×D7311yescharacteristic
1058C4×M16—731no—
1059C2×#97—731no—
1060C2×#97C2×D7311yescharacteristic, complemented
1061C2×#41—731no—
1062C2×#41—731no—
1063C2×#41—1461no—
1064C22×Q8—731no—
1065C22×Q8—731no—
1066C22×Q8C22×D7311yescharacteristic
1067C22×D4—731no—
1068C22×D4—1461no—
1069C22×D4C22×D7311yescharacteristic
1070C23×C4—21no—
1071C23×C4—1461no—
1072#137—1464no—
1073C2×Q16—731no—
1074C2×Q16—731no—
1075C2×Q16—731no—
1076C2×Q16—731no—
1077C2×SD16—24no—
1078C2×SD16—731no—
1079C2×SD16—731no—
1080C2×SD16—731no—
1081C2×SD16—731no—
1082C2×SD16—731no—
1083C2×SD16—731no—
1084C2×SD16—731no—
1085C2×SD16—731no—
1086C2×SD16—1464no—
1087C2×SD16C22×D7311yescharacteristic
1088C2×SD16C22×D7311yescharacteristic
1089C2×SD16C22×D7311yescharacteristic
1090C2×SD16C22×D7311yescharacteristic
1091C2×M16—731no—
1092C2×M16—731no—
1093C22×C8—731no—
1094C22×C8—731no—
1095C22×C8C22×D7311yescharacteristic
1096C22×C8C22×D7311yescharacteristic
1097C4⋊Q8—731no—
1098C4⋊Q8—731no—
1099C4⋊Q8—731no—
1100C4⋊Q8—731no—
1101C4⋊Q8—731no—
1102C4⋊Q8—731no—
1103C4⋊Q8—731no—
1104C4⋊Q8—1461no—
1105C4⋊Q8—1461no—
1106C4⋊Q8—1461no—
1107C4⋊Q8—1461no—
1108C4⋊Q8—1461no—
1109C4⋊Q8—1461no—
1110#127—731no—
1111#126—1461no—
1112#126—1461no—
1113#126—1461no—
1114#126—1461no—
1115#125—731no—
1116#125—731no—
1117#125—1461no—
1118#125—1461no—
1119#125—1461no—
1120#125—1461no—
1121#125—1461no—
1122#125—1461no—
1123#125—1461no—
1124#125—1461no—
1125#125—1461no—
1126#125—1461no—
1127#124—731no—
1128#124—731no—
1129#124—1461no—
1130#124—1461no—
1131#123—1461no—
1132#123—1461no—
1133#123—1461no—
1134#123—1461no—
1135#123—1461no—
1136#123—1461no—
1137#123—1461no—
1138#123—1461no—
1139C22⋊Q8—731no—
1140C22⋊Q8—731no—
1141C22⋊Q8—731no—
1142C22⋊Q8—731no—
1143C22⋊Q8—731no—
1144C22⋊Q8—731no—
1145C22⋊Q8—731no—
1146C22⋊Q8—731no—
1147C22⋊Q8—1461no—
1148C22⋊Q8—1461no—
1149C22⋊Q8—1461no—
1150C22⋊Q8—1461no—
1151C22⋊Q8—1461no—
1152C22⋊Q8—1461no—
1153C22⋊Q8—1461no—
1154C22⋊Q8—1461no—
1155C22⋊Q8—1461no—
1156C22⋊Q8—1461no—
1157C22⋊Q8—1461no—
1158C22⋊Q8—1461no—
1159C22⋊Q8—1461no—
1160C22⋊Q8—1461no—
1161C22⋊Q8—1461no—
1162C22⋊Q8—1461no—
1163C22⋊Q8—1461no—
1164C22⋊Q8—1461no—
1165C22⋊Q8—1461no—
1166C22⋊Q8—1461no—
1167#121—731no—
1168#121—731no—
1169#121—731no—
1170#121—731no—
1171#121—1461no—
1172#121—1461no—
1173#121—1461no—
1174#121—1461no—
1175#121—1461no—
1176#121—1461no—
1177#120—1461no—
1178#120—1461no—
1179#120—1461no—
1180#120—1461no—
1181C4×Q8—21no—
1182C4×Q8—21no—
1183C4×Q8—731no—
1184C4×Q8—731no—
1185C4×Q8—731no—
1186C4×Q8—731no—
1187C4×Q8—731no—
1188C4×Q8—731no—
1189C4×Q8—731no—
1190C4×Q8—731no—
1191C4×Q8—731no—
1192C4×Q8—731no—
1193C4×Q8—1461no—
1194C4×Q8—1461no—
1195C4×Q8—1461no—
1196C4×Q8—1461no—
1197C4×Q8—1461no—
1198C4×Q8—1461no—
1199C4×Q8—1461no—
1200C4×Q8—1461no—
1201C4×Q8—1461no—
1202C4×Q8C22×D7311yescharacteristic
1203C4×Q8C22×D7311yescharacteristic
1204C4×Q8C22×D7311yescharacteristic
1205C4×Q8C22×D7311yescharacteristic
1206C4×D4—21no—
1207C4×D4—21no—
1208C4×D4—731no—
1209C4×D4—731no—
1210C4×D4—731no—
1211C4×D4—731no—
1212C4×D4—731no—
1213C4×D4—731no—
1214C4×D4—731no—
1215C4×D4—731no—
1216C4×D4—731no—
1217C4×D4—731no—
1218C4×D4—1461no—
1219C4×D4—1461no—
1220C4×D4—1461no—
1221C4×D4—1461no—
1222C4×D4—1461no—
1223C4×D4—1461no—
1224C4×D4—1461no—
1225C4×D4—1461no—
1226C4×D4—1461no—
1227C4×D4—1461no—
1228C4×D4—1461no—
1229C4×D4—1461no—
1230C4×D4—1461no—
1231C4×D4—1461no—
1232C4×D4—1461no—
1233C4×D4—1461no—
1234C4×D4—1461no—
1235C4×D4C22×D7311yescharacteristic
1236C4×D4C22×D7311yescharacteristic
1237C4×D4C22×D7311yescharacteristic
1238C4×D4C22×D7311yescharacteristic
1239#117—731no—
1240#117—731no—
1241#117—731no—
1242#117—731no—
1243#117—1461no—
1244#117—1461no—
1245#117—1461no—
1246#117—1461no—
1247#117—1461no—
1248#117—1461no—
1249C2×C4⋊C4—21no—
1250C2×C4⋊C4—731no—
1251C2×C4⋊C4—731no—
1252C2×C4⋊C4—731no—
1253C2×C4⋊C4—1461no—
1254C2×C4⋊C4—1461no—
1255C2×C4⋊C4—1461no—
1256C2×C4⋊C4C22×D7311yescharacteristic
1257C2×C4⋊C4C22×D7311yescharacteristic
1258C2×C22⋊C4—21no—
1259C2×C22⋊C4—1461no—
1260C2×C22⋊C4—1461no—
1261C2×C22⋊C4—1461no—
1262C2×C42—21no—
1263C2×C42—731no—
1264C2×C42—731no—
1265C2×C42—1461no—
1266C2×C42—1461no—
1267C2×C42—1461no—
1268C2×C42C22×D7311yescharacteristic
1269#107—731no—
1270#107—731no—
1271#107—731no—
1272#107—731no—
1273#107—731no—
1274#107—731no—
1275#107—731no—
1276#107—731no—
1277#107C22×D7311yescharacteristic
1278#107C22×D7311yescharacteristic
1279#107C22×D7311yescharacteristic
1280#107C22×D7311yescharacteristic
1281#106—731no—
1282#106—731no—
1283#106—731no—
1284#106—731no—
1285C4⋊C8—731no—
1286C4⋊C8—731no—
1287C4⋊C8—731no—
1288C4⋊C8—731no—
1289C4⋊C8—731no—
1290C4⋊C8—731no—
1291#103—731no—
1292#103—731no—
1293#103—731no—
1294#103—731no—
1295#103—731no—
1296#103—731no—
1297#103—731no—
1298#103—731no—
1299#103—731no—
1300#103—731no—
1301#103—731no—
1302#103—731no—
1303#103—731no—
1304#103—731no—
1305#103—731no—
1306#103—731no—
1307#103C22×D7311yescharacteristic
1308#103C22×D7311yescharacteristic
1309#103C22×D7311yescharacteristic
1310#103C22×D7311yescharacteristic
1311#102—731no—
1312#102—731no—
1313#102—731no—
1314#102—731no—
1315#102—731no—
1316#102—731no—
1317#102—731no—
1318#102—731no—
1319#102C22×D7311yescharacteristic
1320#102C22×D7311yescharacteristic
1321#102C22×D7311yescharacteristic
1322#102C22×D7311yescharacteristic
1323C22⋊C8—731no—
1324C22⋊C8—731no—
1325C22⋊C8—731no—
1326C22⋊C8—731no—
1327C22⋊C8—731no—
1328C22⋊C8—731no—
1329#97—731no—
1330#97—731no—
1331#97—731no—
1332#97—731no—
1333#97C22×D7311yescharacteristic
1334#97C22×D7311yescharacteristic
1335#97C22×D7311yescharacteristic
1336#97C22×D7311yescharacteristic
1337C4×C8—731no—
1338C4×C8—731no—
1339C24—21no—
1340C24—1461no—
1341#41—2921no—
1342#41—5842no—
1343#41—1464no—
1344#41—1462no—
1345C2×Q8—21no—
1346C2×Q8—22no—
1347C2×Q8—41no—
1348C2×Q8—2921no—
1349C2×Q8—2921no—
1350C2×Q8—731no—
1351C2×Q8—731no—
1352C2×Q8—731no—
1353C2×Q8—731no—
1354C2×Q8—1461no—
1355C2×Q8—1461no—
1356C2×Q8—1461no—
1357C2×Q8—1461no—
1358C2×Q8—1461no—
1359C2×Q8—1462no—
1360C2×Q8—1462no—
1361C2×Q8—1461no—
1362C2×Q8C23×D7311yescharacteristic
1363C2×Q8C23×D7311yescharacteristic
1364C2×D4—22no—
1365C2×D4—21no—
1366C2×D4—41no—
1367C2×D4—2924no—
1368C2×D4—2921no—
1369C2×D4—731no—
1370C2×D4—731no—
1371C2×D4—731no—
1372C2×D4—731no—
1373C2×D4—1461no—
1374C2×D4—1461no—
1375C2×D4—1461no—
1376C2×D4—1461no—
1377C2×D4—1461no—
1378C2×D4—1461no—
1379C2×D4—1461no—
1380C2×D4—1462no—
1381C2×D4—1461no—
1382C2×D4C23×D7311yescharacteristic
1383C2×D4C23×D7311yescharacteristic
1384C22×C4—21no—
1385C22×C4—21no—
1386C22×C4—21no—
1387C22×C4—21no—
1388C22×C4—21no—
1389C22×C4—21no—
1390C22×C4—21no—
1391C22×C4—82no—
1392C22×C4—5842no—
1393C22×C4—731no—
1394C22×C4—731no—
1395C22×C4—731no—
1396C22×C4—731no—
1397C22×C4—731no—
1398C22×C4—731no—
1399C22×C4—1461no—
1400C22×C4—1461no—
1401C22×C4—1461no—
1402C22×C4—1461no—
1403C22×C4—1461no—
1404C22×C4—1461no—
1405C22×C4—1461no—
1406C22×C4—1461no—
1407C22×C4—1461no—
1408C22×C4—1461no—
1409C22×C4D4×D7311yescharacteristic
1410C22×C4D4×D7311yescharacteristic
1411C22×C4C23×D7311yescharacteristic
1412Q16—2921no—
1413Q16—2921no—
1414Q16—1462no—
1415Q16—1462no—
1416SD16—22no—
1417SD16—22no—
1418SD16—22no—
1419SD16—2921no—
1420SD16—2921no—
1421SD16—2921no—
1422SD16—2921no—
1423SD16—1462no—
1424SD16—1462no—
1425SD16—1462no—
1426SD16—1462no—
1427SD16#1192402814yescomplemented
1428M16—2921no—
1429M16—1462no—
1430C2×C8—22no—
1431C2×C8—41no—
1432C2×C8—2921no—
1433C2×C8—731no—
1434C2×C8—731no—
1435C2×C8—731no—
1436C2×C8—731no—
1437C2×C8—1462no—
1438C2×C8C23×D7311yescharacteristic
1439C2×C8C23×D7311yescharacteristic
1440C2×C8C23×D7311yescharacteristic
1441C2×C8C23×D7311yescharacteristic
1442C4⋊C4—21no—
1443C4⋊C4—21no—
1444C4⋊C4—21no—
1445C4⋊C4—21no—
1446C4⋊C4—21no—
1447C4⋊C4—21no—
1448C4⋊C4—731no—
1449C4⋊C4—731no—
1450C4⋊C4—731no—
1451C4⋊C4—731no—
1452C4⋊C4—731no—
1453C4⋊C4—731no—
1454C4⋊C4—731no—
1455C4⋊C4—731no—
1456C4⋊C4—731no—
1457C4⋊C4—731no—
1458C4⋊C4—1461no—
1459C4⋊C4—1461no—
1460C4⋊C4—1461no—
1461C4⋊C4—1461no—
1462C4⋊C4—1461no—
1463C4⋊C4—1461no—
1464C4⋊C4—1461no—
1465C4⋊C4—1461no—
1466C4⋊C4—1461no—
1467C4⋊C4—1461no—
1468C4⋊C4—1461no—
1469C4⋊C4—1461no—
1470C4⋊C4—1461no—
1471C4⋊C4—1461no—
1472C4⋊C4—1461no—
1473C4⋊C4—1461no—
1474C4⋊C4—1461no—
1475C4⋊C4—1461no—
1476C4⋊C4—1461no—
1477C4⋊C4—1461no—
1478C4⋊C4—1461no—
1479C4⋊C4—1461no—
1480C4⋊C4—1461no—
1481C4⋊C4—1461no—
1482C4⋊C4—1461no—
1483C4⋊C4—1461no—
1484C4⋊C4—1461no—
1485C4⋊C4—1461no—
1486C4⋊C4—1461no—
1487C4⋊C4—1461no—
1488C4⋊C4—1461no—
1489C4⋊C4—1461no—
1490C4⋊C4—1461no—
1491C4⋊C4C23×D7311yescharacteristic
1492C4⋊C4C23×D7311yescharacteristic
1493C4⋊C4C23×D7311yescharacteristic
1494C4⋊C4C23×D7311yescharacteristic
1495C22⋊C4—21no—
1496C22⋊C4—21no—
1497C22⋊C4—21no—
1498C22⋊C4—21no—
1499C22⋊C4—731no—
1500C22⋊C4—731no—
1501C22⋊C4—731no—
1502C22⋊C4—731no—
1503C22⋊C4—731no—
1504C22⋊C4—731no—
1505C22⋊C4—1461no—
1506C22⋊C4—1461no—
1507C22⋊C4—1461no—
1508C22⋊C4—1461no—
1509C22⋊C4—1461no—
1510C22⋊C4—1461no—
1511C22⋊C4—1461no—
1512C22⋊C4—1461no—
1513C22⋊C4—1461no—
1514C22⋊C4—1461no—
1515C22⋊C4—1461no—
1516C22⋊C4—1461no—
1517C22⋊C4—1461no—
1518C22⋊C4—1461no—
1519C22⋊C4—1461no—
1520C22⋊C4—1461no—
1521C22⋊C4—1461no—
1522C22⋊C4—1461no—
1523C22⋊C4—1461no—
1524C22⋊C4—1461no—
1525C22⋊C4—1461no—
1526C42—21no—
1527C42—21no—
1528C42—21no—
1529C42—21no—
1530C42—731no—
1531C42—731no—
1532C42—731no—
1533C42—731no—
1534C42—731no—
1535C42—731no—
1536C42—1461no—
1537C42—1461no—
1538C42—1461no—
1539C42—1461no—
1540C42—1461no—
1541C42—1461no—
1542C42—1461no—
1543C42—1461no—
1544C42—1461no—
1545C42D4×D7311yescharacteristic
1546C42D4×D7311yescharacteristic
1547C42C23×D7311yescharacteristic
1548C42C23×D7311yescharacteristic
1549C23—21no—
1550C23—21no—
1551C23—42no—
1552C23—42no—
1553C23—81no—
1554C23—2922no—
1555C23—2922no—
1556C23—5841no—
1557C23—731no—
1558C23—731no—
1559C23—1461no—
1560C23C2×D4×D7311yescharacteristic
1561Q8—21no—
1562Q8—21no—
1563Q8—21no—
1564Q8—42no—
1565Q8—2922no—
1566Q8—2922no—
1567Q8—5841no—
1568Q8—5841no—
1569Q8—5841no—
1570Q8—5841no—
1571Q8—1462no—
1572Q8—1461no—
1573Q8—1461no—
1574Q8—1461no—
1575Q8—1461no—
1576Q8—1461no—
1577Q8—1461no—
1578Q8C2×#1192402812yes—
1579D4—21no—
1580D4—21no—
1581D4—21no—
1582D4—42no—
1583D4—2922no—
1584D4—2922no—
1585D4—2922no—
1586D4—2922no—
1587D4—2922no—
1588D4—5841no—
1589D4—5841no—
1590D4—5841no—
1591D4—734no—
1592D4—1462no—
1593D4—1462no—
1594D4—1461no—
1595D4—1461no—
1596D4C2×#1192402812yes—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—41no—
1607C2×C4—42no—
1608C2×C4—42no—
1609C2×C4—42no—
1610C2×C4—81no—
1611C2×C4—81no—
1612C2×C4—81no—
1613C2×C4—81no—
1614C2×C4—2922no—
1615C2×C4—2922no—
1616C2×C4—2922no—
1617C2×C4—2921no—
1618C2×C4—2921no—
1619C2×C4—2922no—
1620C2×C4—2922no—
1621C2×C4—5841no—
1622C2×C4—5841no—
1623C2×C4—5841no—
1624C2×C4—5841no—
1625C2×C4—5841no—
1626C2×C4—731no—
1627C2×C4—731no—
1628C2×C4—731no—
1629C2×C4—731no—
1630C2×C4—731no—
1631C2×C4—731no—
1632C2×C4—1462no—
1633C2×C4—1462no—
1634C2×C4—1461no—
1635C2×C4—1461no—
1636C2×C4—1461no—
1637C2×C4—1461no—
1638C2×C4—1461no—
1639C2×C4—1461no—
1640C2×C4—1461no—
1641C2×C4—1461no—
1642C2×C4—1461no—
1643C2×C4—1461no—
1644C2×C4—1461no—
1645C2×C4C2×D4×D7311yescharacteristic
1646C2×C4C2×D4×D7311yescharacteristic
1647C2×C4C2×D4×D7311yescharacteristic
1648C2×C4C2×D4×D7311yescharacteristic
1649C2×C4C2×D4×D7311yescharacteristic
1650C2×C4C24×D7311yescharacteristic
1651C8—21no—
1652C8—21no—
1653C8—21no—
1654C8—1461no—
1655C8—1461no—
1656C8—1461no—
1657C8—1461no—
1658C8C2×#1192402812yes—
1659C22—21no—
1660C22—21no—
1661C22—22no—
1662C22—41no—
1663C22—41no—
1664C22—41no—
1665C22—41no—
1666C22—41no—
1667C22—84no—
1668C22—2921no—
1669C22—2921no—
1670C22—2921no—
1671C22—5844no—
1672C22—732no—
1673C22—1461no—
1674C22—1461no—
1675C22—1461no—
1676C22—1461no—
1677C22—1461no—
1678C22#137×D7312yes—
1679C22C22×D4×D7311yescharacteristic
1680C4—21no—
1681C4—21no—
1682C4—21no—
1683C4—22no—
1684C4—21no—
1685C4—21no—
1686C4—41no—
1687C4—41no—
1688C4—41no—
1689C4—41no—
1690C4—41no—
1691C4—2921no—
1692C4—2921no—
1693C4—2921no—
1694C4—2921no—
1695C4—2921no—
1696C4—2921no—
1697C4—2921no—
1698C4—732no—
1699C4—1461no—
1700C4—1461no—
1701C4—1461no—
1702C4—1461no—
1703C4—1461no—
1704C4C22×#1192402811yescharacteristic
1705C4#1798942311yescharacteristic
1706C2—22no—
1707C2—42no—
1708C2—81no—
1709C2—2921no—
1710C2—5841no—
1711C2—1462no—
1712C2D4×#1192402811yescharacteristic
1713C2C2×#137×D7311yescharacteristic
1714C2#2262470711yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#440×C73C2
socleC22×C73C23×D4
prime radical#22623535C2
hypercenterC2×#440D73
hypocenterC73#61453
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. Q8×#11924028C2semidirect
3. #22622985C2semidirect
4. #22622842C2semidirect
5. #22622746C2semidirect
6. #22622713C2semidirect
7. #22622421C2semidirect
8. #22622412C2semidirect
9. #22622321C2semidirect
10. #22622107C2semidirect
11. #22622098C2semidirect
12. #22622017C2semidirect
13. #22622008C2semidirect
14. #22621803C2semidirect
15. #22621751C2semidirect
16. SD16×C22⋊D73C2semidirect
17. #22621443C2semidirect
18. #22621441C2semidirect
19. #22620646C2semidirect
20. #22620640C2semidirect
21. #22620636C2semidirect
22. #22620102C2semidirect
23. #22620100C2semidirect
24. #22620089C2semidirect
25. #22620051C2semidirect
26. #22620030C2semidirect
27. #22620028C2semidirect
28. #22618942C2semidirect
29. #22618753C2semidirect
30. #440×D73C2semidirect
31. C2×#440×C73C2semidirect
35. Q8×Dic146C22semidirect
37. #17989315C22semidirect
39. #17989297C22semidirect
45. #17989292C22semidirect
51. Q8×D292C22semidirect
53. Q8×C22⋊D73C22semidirect
59. #17989144C22semidirect
62. #17989141C22semidirect
63. #17989141C22semidirect
73. C4×Q8×D73C22semidirect
74. C4×Q8×D73C22semidirect
77. #17988996C22semidirect
78. #17988995C22semidirect
79. #17988991C22semidirect
80. #17988981C22semidirect
81. #17988978C22semidirect
83. #17988956C22semidirect
84. #17988954C22semidirect
85. #17988947C22semidirect
86. #17988945C22semidirect
87. #17988936C22semidirect
89. #17988930C22semidirect
90. #17988926C22semidirect
91. #17988924C22semidirect
92. #17988924C22semidirect
93. #17988922C22semidirect
94. #17988922C22semidirect
95. #17988922C22semidirect
96. #17988921C22semidirect
99. #17988902C22semidirect
100. #17988899C22semidirect
101. #17988894C22semidirect
102. #17988894C22semidirect
103. #17988893C22semidirect
104. #17988892C22semidirect
105. #17988881C22semidirect
106. #17988881C22semidirect
107. #17988880C22semidirect
110. #17988867C22semidirect
111. #17988866C22semidirect
113. #17988836C22semidirect
114. #17988834C22semidirect
115. #17988832C22semidirect
116. #17988830C22semidirect
117. #17988829C22semidirect
118. #17988828C22semidirect
119. #17988828C22semidirect
120. #17988827C22semidirect
125. #17988809C22semidirect
126. #17988809C22semidirect
127. #17988808C22semidirect
128. #17988807C22semidirect
129. #17988796C22semidirect
131. #17988792C22semidirect
132. #17988791C22semidirect
139. #17988744C22semidirect
140. #17988743C22semidirect
145. #17988727C22semidirect
148. #17988724C22semidirect
149. #17988715C22semidirect
150. #17988715C22semidirect
151. #17988695C22semidirect
152. #17988695C22semidirect
153. #17988692C22semidirect
154. #17988692C22semidirect
155. #17988690C22semidirect
156. #17988689C22semidirect
157. #17988689C22semidirect
161. #17988687C22semidirect
162. #17988687C22semidirect
163. #17988686C22semidirect
164. #17988685C22semidirect
165. #17988685C22semidirect
167. #17988681C22semidirect
168. #17988679C22semidirect
171. #17988660C22semidirect
172. #17988660C22semidirect
173. #17988658C22semidirect
174. #17988658C22semidirect
177. #17988644C22semidirect
178. #17988642C22semidirect
179. #17988642C22semidirect
180. #17988628C22semidirect
181. #107×D73C22semidirect
182. #17988594C22semidirect
184. #103×D73C22semidirect
186. #17988539C22semidirect
187. #97×D73C22semidirect
189. C2×C4×Q8×C73C22semidirect
195. #440×C73C22semidirect
196. #440×C73C22semidirect
197. #440×C73C22semidirect
198. #440×C73C22semidirect
199. C2×#107×C73C22semidirect
200. C2×#103×C73C22semidirect
202. C2×#97×C73C22semidirect
662. SD16×C73#41semidirect
744. C22⋊D73#137semidirect
888. C2×#440D73semidirect
889. C73#61453semidirect
934. C2×C4×Q8C2×D73semidirect
1032. #440C2×D73semidirect
1033. #440C2×D73semidirect
1034. #440C2×D73semidirect
1035. #440C2×D73semidirect
1051. C2×#107C2×D73semidirect
1055. C2×#103C2×D73semidirect
1060. C2×#97C2×D73semidirect
1427. SD16#11924028semidirect

Maximal subgroups

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

subgroupindex
#226235352
Q8×#119240282
#226229852
#226228422
#226227462
#226227132
#226224212
#226224122
#226223212
#226221072
#226220982
#226220172
#226220082
#226218032
#226217512
SD16×C22⋊D732
#226214432
#226214412
#226206462
#226206402
#226206362
#226201022
#226201002
#226200892
#226200512
#226200302
#226200282
#226189422
#226187532
#440×D732
C2×#440×C732
#6145373