Finite Group Databasebeta

← #61771

Subgroups — #61771

Order 256.

844 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3541C211yesmaximal, characteristic
2#3495C211yesmaximal, characteristic, complemented
3#3349C211yesmaximal, characteristic, complemented
4#3349C211yesmaximal, characteristic, complemented
5#3346C211yesmaximal, characteristic, complemented
6#3344C211yesmaximal, characteristic, complemented
7#3342C211yesmaximal, characteristic, complemented
8#3338C211yesmaximal, characteristic, complemented
9#3337C211yesmaximal, characteristic, complemented
10#3336C211yesmaximal, characteristic, complemented
11#3316C211yesmaximal, characteristic, complemented
12#3315C211yesmaximal, characteristic, complemented
13#3313C211yesmaximal, characteristic, complemented
14#3312C211yesmaximal, characteristic, complemented
15#3302C211yesmaximal, characteristic, complemented
16#3300C211yesmaximal, characteristic, complemented
17#3300C211yesmaximal, characteristic, complemented
18#3299C211yesmaximal, characteristic, complemented
19#3243C211yesmaximal, characteristic, complemented
20#3242C211yesmaximal, characteristic, complemented
21#3202C211yesmaximal, characteristic, complemented
22#3201C211yesmaximal, characteristic, complemented
23#3190C211yesmaximal, characteristic, complemented
24#3189C211yesmaximal, characteristic, complemented
25#3127C211yesmaximal, characteristic, complemented
26#3121C211yesmaximal, characteristic, complemented
27#3098C211yesmaximal, characteristic, complemented
28#3097C211yesmaximal, characteristic, complemented
29#3091C211yesmaximal, characteristic, complemented
30C2×#485C211yesmaximal, characteristic, complemented
31#2977C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#556C2211yescharacteristic
35#556C2211yescharacteristic
36#556C2211yescharacteristic
37#554—21no—
38#554C2211yescharacteristic
39#554C2211yescharacteristic
40#554C2211yescharacteristic
41#553—21no—
42#553C2211yescharacteristic
43#552—21no—
44#552—21no—
45#552C2211yescharacteristic
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic
49#552C2211yescharacteristic
50#551—21no—
51#551—21no—
52D4×Q8C2211yescharacteristic
53#548C2211yescharacteristic
54#548C2211yescharacteristic
55#547C2211yescharacteristic
56#544C2211yescharacteristic
57#542—21no—
58#542—21no—
59#542C2211yescharacteristic
60#541—21no—
61#541C2211yescharacteristic
62#539—21no—
63#538—21no—
64#538—21no—
65#537C2211yescharacteristic
66#536C2211yescharacteristic
67#536C2211yescharacteristic
68#533—21no—
69#529—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72C2×C22⋊Q8C2211yescharacteristic
73C2×C22⋊Q8C2211yescharacteristic
74#520C2211yescharacteristic
75#519C2211yescharacteristic
76C2×#117C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#491C2211yescharacteristic, complemented
82#489C2211yescharacteristic, complemented
83#488C2211yescharacteristic, complemented
84#487C2211yescharacteristic, complemented
85#485C2211yescharacteristic
86#485C2211yescharacteristic
87#485C2211yescharacteristic
88#485C2211yescharacteristic
89#485C2211yescharacteristic
90#485C2211yescharacteristic
91#485C2211yescharacteristic
92#485C2211yescharacteristic
93#485C2211yescharacteristic
94#485C2211yescharacteristic
95#485C2211yescharacteristic
96#485C2211yescharacteristic
97#485C2211yescharacteristic, complemented
98#485C2211yescharacteristic, complemented
99#485C2211yescharacteristic, complemented
100#485C2211yescharacteristic, complemented
101#485C2211yescharacteristic, complemented
102#484C2211yescharacteristic
103#484C2211yescharacteristic
104#484C2211yescharacteristic
105#484C2211yescharacteristic
106#484C2211yescharacteristic
107#484C2211yescharacteristic, complemented
108#484C2211yescharacteristic, complemented
109#484C2211yescharacteristic, complemented
110#483C2211yescharacteristic
111#483C2211yescharacteristic
112#483C2211yescharacteristic, complemented
113#483C2211yescharacteristic, complemented
114#482C2211yescharacteristic
115#482C2211yescharacteristic
116#482C2211yescharacteristic, complemented
117#481C2211yescharacteristic
118#480C2211yescharacteristic
119#480C2211yescharacteristic
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#479C2211yescharacteristic, complemented
124#479C2211yescharacteristic, complemented
125#479C2211yescharacteristic, complemented
126#478C2211yescharacteristic, complemented
127#477C2211yescharacteristic, complemented
128#477C2211yescharacteristic, complemented
129#477C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#475C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#470C2211yescharacteristic, complemented
134#470C2211yescharacteristic, complemented
135#470C2211yescharacteristic, complemented
136#468C2211yescharacteristic, complemented
137#467C2211yescharacteristic
138#467C2211yescharacteristic
139#467C2211yescharacteristic
140#467C2211yescharacteristic
141#467C2211yescharacteristic
142#467C2211yescharacteristic
143#467C2211yescharacteristic, complemented
144#467C2211yescharacteristic, complemented
145#467C2211yescharacteristic, complemented
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#464C2211yescharacteristic, complemented
151#462C2211yescharacteristic, complemented
152#462C2211yescharacteristic, complemented
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#451C2211yescharacteristic
158#451C2211yescharacteristic
159#451C2211yescharacteristic
160#451C2211yescharacteristic
161#451C2211yescharacteristic
162#451C2211yescharacteristic, complemented
163#451C2211yescharacteristic, complemented
164#448C2211yescharacteristic
165#441C2211yescharacteristic, complemented
166#441C2211yescharacteristic, complemented
167#441C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×Q16C2211yescharacteristic, complemented
170C4×Q16C2211yescharacteristic, complemented
171C4×Q16C2211yescharacteristic, complemented
172C4×SD16C2211yescharacteristic, complemented
173#435C2211yescharacteristic
174#435C2211yescharacteristic
175#435C2211yescharacteristic
176#435C2211yescharacteristic
177C8×D4C2211yescharacteristic
178C8×D4C2211yescharacteristic
179C8×D4C2211yescharacteristic
180C8×D4C2211yescharacteristic
181#433C2211yescharacteristic
182#433C2211yescharacteristic
183#428C2211yescharacteristic, complemented
184#428C2211yescharacteristic, complemented
185#427C2211yescharacteristic
186#427C2211yescharacteristic
187#427C2211yescharacteristic, complemented
188C2×#107C2211yescharacteristic
189C2×#107C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic
191#419C2211yescharacteristic, complemented
192#417C2211yescharacteristic, complemented
193#416C2211yescharacteristic
194#416C2211yescharacteristic
195#416C2211yescharacteristic, complemented
196C2×#103C2211yescharacteristic
197C2×#103C2211yescharacteristic
198C2×#103C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201C2×C22⋊C8C2211yescharacteristic
202C2×C22⋊C8C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C22×Q8C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×Q16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C2×M16C2311yescharacteristic
220C22×C8C2311yescharacteristic
221C22×C8C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C22×C8C2311yescharacteristic
224C22×C8C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234#126—21no—
235#126—21no—
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125C2311yescharacteristic
261#125C2311yescharacteristic
262#125C2311yescharacteristic
263#124—21no—
264#124—21no—
265#124—21no—
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#124C2311yescharacteristic
272#123—21no—
273#123—21no—
274#123—21no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123D411yescharacteristic
287#123D411yescharacteristic
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8D411yescharacteristic
307C22⋊Q8D411yescharacteristic
308C22⋊Q8C2311yescharacteristic
309C22⋊Q8C2311yescharacteristic
310C22⋊Q8C2311yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325#121—21no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121D411yescharacteristic
333#121D411yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#120—21no—
338#120D411yescharacteristic
339#120D411yescharacteristic
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#107C2311yescharacteristic
415#107C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24C2×D411yescharacteristic
479#41—41no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8C2×D411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×Q8C2411yescharacteristic
500C2×Q8C2411yescharacteristic
501C2×Q8C2411yescharacteristic
502C2×Q8C2411yescharacteristic
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C2×D411yescharacteristic
509C2×D4C2×D411yescharacteristic
510C2×D4C2×D411yescharacteristic
511C2×D4C2×D411yescharacteristic
512C2×D4C2×D411yescharacteristic
513C2×D4C2×D411yescharacteristic
514C2×D4C2×D411yescharacteristic
515C2×D4C2411yescharacteristic
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4C2×D411yescharacteristic
532C22×C4C2×D411yescharacteristic
533C22×C4C2×D411yescharacteristic
534C22×C4C2411yescharacteristic
535C22×C4C2411yescharacteristic
536C22×C4C2411yescharacteristic
537C22×C4C2411yescharacteristic
538C22×C4C2411yescharacteristic
539Q16—41no—
540Q16—41no—
541Q16—41no—
542Q16—41no—
543Q16—41no—
544Q16—41no—
545SD16—41no—
546SD16—41no—
547M16—41no—
548M16—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8C2411yescharacteristic
556C2×C8C2411yescharacteristic
557C2×C8C2411yescharacteristic
558C2×C8C2411yescharacteristic
559C2×C8C2411yescharacteristic
560C2×C8C2411yescharacteristic
561C2×C8C2411yescharacteristic
562C2×C8C2411yescharacteristic
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C22⋊C4C2×D411yescharacteristic
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42C2411yescharacteristic
678C42C2411yescharacteristic
679C23—22no—
680C23—21no—
681C23—41no—
682C23—41no—
683C23C22×D411yescharacteristic
684C23C22×D411yescharacteristic
685C23C22×D411yescharacteristic
686C23C22×D411yescharacteristic
687C23C22×D411yescharacteristic
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—21no—
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—41no—
699Q8—42no—
700Q8—81no—
701Q8—81no—
702Q8—81no—
703Q8—81no—
704Q8—81no—
705D4—22no—
706D4—22no—
707D4—21no—
708D4—21no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—42no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—81no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4C22×D411yescharacteristic
761C2×C4C22×D411yescharacteristic
762C2×C4C22×D411yescharacteristic
763C2×C4C22×D411yescharacteristic
764C2×C4C22×D411yescharacteristic
765C2×C4C22×D411yescharacteristic
766C2×C4C22×D411yescharacteristic
767C2×C4C22×D411yescharacteristic
768C2×C4C22×D411yescharacteristic
769C2×C4C2511yescharacteristic
770C8—21no—
771C8—21no—
772C8—21no—
773C8—21no—
774C8—21no—
775C8—21no—
776C8—21no—
777C8—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—82no—
796C22#57812yes—
797C22C23×D411yescharacteristic
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4#58511yescharacteristic
823C4#58511yescharacteristic
824C2—22no—
825C2—41no—
826C2—41no—
827C2—41no—
828C2—41no—
829C2—81no—
830C2#348511yescharacteristic
831C2C2×#57811yescharacteristic
832C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3541C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #3495C2semidirect
3. #3349C2semidirect
4. #3349C2semidirect
5. #3346C2semidirect
6. #3344C2semidirect
7. #3342C2semidirect
8. #3338C2semidirect
9. #3337C2semidirect
10. #3336C2semidirect
11. #3316C2semidirect
12. #3315C2semidirect
13. #3313C2semidirect
14. #3312C2semidirect
15. #3302C2semidirect
16. #3300C2semidirect
17. #3300C2semidirect
18. #3299C2semidirect
19. #3243C2semidirect
20. #3242C2semidirect
21. #3202C2semidirect
22. #3201C2semidirect
23. #3190C2semidirect
24. #3189C2semidirect
25. #3127C2semidirect
26. #3121C2semidirect
27. #3098C2semidirect
28. #3097C2semidirect
29. #3091C2semidirect
30. C2×#485C2semidirect
31. #2977C2semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #499C22semidirect
81. #491C22semidirect
82. #489C22semidirect
83. #488C22semidirect
84. #487C22semidirect
97. #485C22semidirect
98. #485C22semidirect
99. #485C22semidirect
100. #485C22semidirect
101. #485C22semidirect
107. #484C22semidirect
108. #484C22semidirect
109. #484C22semidirect
112. #483C22semidirect
113. #483C22semidirect
116. #482C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #479C22semidirect
124. #479C22semidirect
125. #479C22semidirect
126. #478C22semidirect
127. #477C22semidirect
128. #477C22semidirect
129. #477C22semidirect
130. #475C22semidirect
131. #475C22semidirect
132. #474C22semidirect
133. #470C22semidirect
134. #470C22semidirect
135. #470C22semidirect
136. #468C22semidirect
143. #467C22semidirect
144. #467C22semidirect
145. #467C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #464C22semidirect
151. #462C22semidirect
152. #462C22semidirect
155. #452C22semidirect
156. #452C22semidirect
162. #451C22semidirect
163. #451C22semidirect
165. #441C22semidirect
166. #441C22semidirect
167. #441C22semidirect
168. #440C22semidirect
169. C4×Q16C22semidirect
170. C4×Q16C22semidirect
171. C4×Q16C22semidirect
172. C4×SD16C22semidirect
183. #428C22semidirect
184. #428C22semidirect
187. #427C22semidirect
189. C2×#107C22semidirect
191. #419C22semidirect
192. #417C22semidirect
195. #416C22semidirect
198. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35412
#34952
#33492
#33462
#33442
#33422
#33382
#33372
#33362
#33162
#33152
#33132
#33122
#33022
#33002
#32992
#32432
#32422
#32022
#32012
#31902
#31892
#31272
#31212
#30982
#30972
#30912
C2×#4852
#29772