Finite Group Databasebeta

← #60984

Subgroups — #60984

Order 256.

843 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3495C211yesmaximal, characteristic, complemented
2#3455C211yesmaximal, characteristic, complemented
3#3261C211yesmaximal, characteristic, complemented
4#3260C211yesmaximal, characteristic, complemented
5#3258C211yesmaximal, characteristic, complemented
6#3257C211yesmaximal, characteristic, complemented
7#3244C211yesmaximal, characteristic, complemented
8#3243C211yesmaximal, characteristic, complemented
9#3240C211yesmaximal, characteristic, complemented
10#3231C211yesmaximal, characteristic, complemented
11#3225C211yesmaximal, characteristic, complemented
12#3225C211yesmaximal, characteristic, complemented
13#3216C211yesmaximal, characteristic, complemented
14#3212C211yesmaximal, characteristic, complemented
15#3197C211yesmaximal, characteristic, complemented
16#3196C211yesmaximal, characteristic, complemented
17#3191C211yesmaximal, characteristic, complemented
18#3190C211yesmaximal, characteristic, complemented
19#3178C211yesmaximal, characteristic, complemented
20#3178C211yesmaximal, characteristic, complemented
21#3175C211yesmaximal, characteristic, complemented
22#3173C211yesmaximal, characteristic, complemented
23#3127C211yesmaximal, characteristic, complemented
24#3126C211yesmaximal, characteristic, complemented
25#3120C211yesmaximal, characteristic, complemented
26#3119C211yesmaximal, characteristic, complemented
27#3116C211yesmaximal, characteristic, complemented
28#3111C211yesmaximal, characteristic, complemented
29#3107C211yesmaximal, characteristic, complemented
30#3102C211yesmaximal, characteristic, complemented
31#2924C211yesmaximal, characteristic, complemented
32#556—21no—
33#554—21no—
34#552—21no—
35#552—21no—
36#552—21no—
37#552—21no—
38#551—21no—
39#551—21no—
40#544C2211yescharacteristic
41#542C2211yescharacteristic
42#542C2211yescharacteristic
43#542C2211yescharacteristic
44#542C2211yescharacteristic
45#542C2211yescharacteristic
46#542C2211yescharacteristic
47#541C2211yescharacteristic
48#541C2211yescharacteristic
49#541C2211yescharacteristic
50#541C2211yescharacteristic
51#540C2211yescharacteristic
52#540C2211yescharacteristic
53#539—21no—
54#539—21no—
55#538—21no—
56#538—21no—
57#536C2211yescharacteristic
58#533C2211yescharacteristic
59#533C2211yescharacteristic
60#533C2211yescharacteristic
61#532C2211yescharacteristic
62#529—21no—
63#529—21no—
64#529—21no—
65#529—21no—
66#529C2211yescharacteristic
67#529C2211yescharacteristic
68#525C2211yescharacteristic
69#525C2211yescharacteristic
70#525C2211yescharacteristic
71C2×C22⋊Q8C2211yescharacteristic
72#520C2211yescharacteristic
73#519C2211yescharacteristic
74C4×#41C2211yescharacteristic
75C4×#41C2211yescharacteristic
76C2×#117C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#498C2211yescharacteristic, complemented
81#497C2211yescharacteristic, complemented
82#497C2211yescharacteristic, complemented
83#495C2211yescharacteristic, complemented
84#495C2211yescharacteristic, complemented
85#489C2211yescharacteristic, complemented
86#489C2211yescharacteristic, complemented
87#489C2211yescharacteristic, complemented
88#489C2211yescharacteristic, complemented
89#488C2211yescharacteristic, complemented
90#488C2211yescharacteristic, complemented
91#487C2211yescharacteristic, complemented
92#487C2211yescharacteristic, complemented
93#485C2211yescharacteristic
94#485C2211yescharacteristic
95#485C2211yescharacteristic
96#485C2211yescharacteristic
97#485C2211yescharacteristic
98#485C2211yescharacteristic
99#485C2211yescharacteristic
100#485C2211yescharacteristic
101#484C2211yescharacteristic
102#483C2211yescharacteristic
103#482C2211yescharacteristic
104#482C2211yescharacteristic
105#482C2211yescharacteristic
106#482C2211yescharacteristic
107#481C2211yescharacteristic
108#480C2211yescharacteristic
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#479C2211yescharacteristic, complemented
112#479C2211yescharacteristic, complemented
113#479C2211yescharacteristic, complemented
114#479C2211yescharacteristic, complemented
115#479C2211yescharacteristic, complemented
116#479C2211yescharacteristic, complemented
117#478C2211yescharacteristic, complemented
118#478C2211yescharacteristic, complemented
119#478C2211yescharacteristic, complemented
120#478C2211yescharacteristic, complemented
121#477C2211yescharacteristic, complemented
122#476C2211yescharacteristic, complemented
123#475C2211yescharacteristic, complemented
124#474C2211yescharacteristic, complemented
125#470C2211yescharacteristic
126#470C2211yescharacteristic
127#470C2211yescharacteristic
128#469C2211yescharacteristic
129#468C2211yescharacteristic
130#468C2211yescharacteristic
131#468C2211yescharacteristic
132#468C2211yescharacteristic
133#467C2211yescharacteristic
134#467C2211yescharacteristic
135#467C2211yescharacteristic
136#466C2211yescharacteristic
137#465C2211yescharacteristic
138#465C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic
141#464C2211yescharacteristic, complemented
142#464C2211yescharacteristic, complemented
143#463C2211yescharacteristic, complemented
144#463C2211yescharacteristic, complemented
145#462C2211yescharacteristic, complemented
146#462C2211yescharacteristic, complemented
147#462C2211yescharacteristic, complemented
148#462C2211yescharacteristic, complemented
149#462C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#461C2211yescharacteristic, complemented
152#461C2211yescharacteristic, complemented
153#460C2211yescharacteristic, complemented
154#460C2211yescharacteristic, complemented
155#460C2211yescharacteristic, complemented
156#459C2211yescharacteristic, complemented
157#452C2211yescharacteristic
158#452C2211yescharacteristic
159#452C2211yescharacteristic
160#452C2211yescharacteristic
161#452C2211yescharacteristic
162#452C2211yescharacteristic
163#452C2211yescharacteristic
164#452C2211yescharacteristic
165#451C2211yescharacteristic
166#451C2211yescharacteristic
167#449C2211yescharacteristic
168#449C2211yescharacteristic
169#449C2211yescharacteristic
170#449C2211yescharacteristic
171#448C2211yescharacteristic
172#448C2211yescharacteristic
173#442C2211yescharacteristic, complemented
174#441C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#440C2211yescharacteristic, complemented
178#440C2211yescharacteristic, complemented
179#440C2211yescharacteristic, complemented
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×Q16C2211yescharacteristic, complemented
183C4×Q16C2211yescharacteristic, complemented
184C4×SD16C2211yescharacteristic, complemented
185C4×SD16C2211yescharacteristic, complemented
186C4×SD16C2211yescharacteristic, complemented
187C4×SD16C2211yescharacteristic, complemented
188C4×D8C2211yescharacteristic, complemented
189#433C2211yescharacteristic
190#433C2211yescharacteristic
191#433C2211yescharacteristic
192#433C2211yescharacteristic
193#432C2211yescharacteristic
194#432C2211yescharacteristic
195#431C2211yescharacteristic
196#431C2211yescharacteristic
197#424C2211yescharacteristic
198#424C2211yescharacteristic
199#407C2211yescharacteristic
200C2×C22⋊C8C2211yescharacteristic
201#405C2211yescharacteristic
202#405C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C22×Q8C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C2×Q16C2311yescharacteristic
209C2×Q16C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×D8C2311yescharacteristic
223C2×D8C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C2×M16C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C4⋊Q8—21no—
229C4⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236#127C2311yescharacteristic
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#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#125C2311yescharacteristic
267#125C2311yescharacteristic
268#124—21no—
269#124—21no—
270#124—21no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124C2311yescharacteristic
275#124C2311yescharacteristic
276#124C2311yescharacteristic
277#124C2311yescharacteristic
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#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—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⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#120—21no—
334#120—21no—
335#120—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×D4—21no—
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×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117D411yescharacteristic
384#117D411yescharacteristic
385#117D411yescharacteristic
386#117D411yescharacteristic
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389#117C2311yescharacteristic
390#117C2311yescharacteristic
391#117C2311yescharacteristic
392#117C2311yescharacteristic
393#117C2311yescharacteristic
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4D411yescharacteristic
397C2×C4⋊C4D411yescharacteristic
398C2×C4⋊C4C2311yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4D411yescharacteristic
401C2×C22⋊C4D411yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42C2311yescharacteristic
405C2×C42C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422C4⋊C8C2311yescharacteristic
423C4⋊C8C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
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#102C2311yescharacteristic
451#102C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
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
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
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—41no—
491C2×Q8—41no—
492C2×Q8C2411yescharacteristic
493C2×Q8C2411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C2411yescharacteristic
509C2×D4C2411yescharacteristic
510C2×D4C2411yescharacteristic
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4C2×D411yescharacteristic
525C22×C4C2×D411yescharacteristic
526C22×C4C2×D411yescharacteristic
527C22×C4C2×D411yescharacteristic
528C22×C4C2×D411yescharacteristic
529C22×C4C2×D411yescharacteristic
530C22×C4C2×D411yescharacteristic
531C22×C4C2411yescharacteristic
532C22×C4C2411yescharacteristic
533C22×C4C2411yescharacteristic
534Q16—41no—
535Q16—41no—
536Q16—41no—
537Q16—41no—
538Q16—41no—
539Q16—41no—
540SD16—41no—
541SD16—41no—
542SD16—41no—
543SD16—41no—
544SD16—41no—
545SD16—41no—
546SD16—41no—
547SD16—41no—
548D8—41no—
549D8—41no—
550M16—41no—
551M16—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8C2411yescharacteristic
555C2×C8C2411yescharacteristic
556C2×C8C2411yescharacteristic
557C2×C8C2411yescharacteristic
558C2×C8C2411yescharacteristic
559C2×C8C2411yescharacteristic
560C2×C8C2411yescharacteristic
561C2×C8C2411yescharacteristic
562C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
651C22⋊C4C2×D411yescharacteristic
652C22⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C22⋊C4C2×D411yescharacteristic
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42C2×D411yescharacteristic
672C42C2×D411yescharacteristic
673C42C2×D411yescharacteristic
674C42C2×D411yescharacteristic
675C42C2411yescharacteristic
676C42C2411yescharacteristic
677C42C2411yescharacteristic
678C42C2411yescharacteristic
679C23—21no—
680C23—21no—
681C23—21no—
682C23—41no—
683C23—41no—
684C23—41no—
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—42no—
699Q8—81no—
700Q8—81no—
701Q8—81no—
702Q8—81no—
703D4—21no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—81no—
714D4—81no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—81no—
719D4—81no—
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—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4C22×D411yescharacteristic
758C2×C4C22×D411yescharacteristic
759C2×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
769C8—21no—
770C8—21no—
771C8—21no—
772C8—21no—
773C8—21no—
774C8—21no—
775C8—21no—
776C8—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—82no—
796C22C23×D411yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
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#58511yescharacteristic
822C4#58511yescharacteristic
823C2—41no—
824C2—41no—
825C2—41no—
826C2—81no—
827C2—81no—
828C2—81no—
829C2#344911yescharacteristic
830C2#358411yescharacteristic
831C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#117 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3495C2semidirect
2. #3455C2semidirect
3. #3261C2semidirect
4. #3260C2semidirect
5. #3258C2semidirect
6. #3257C2semidirect
7. #3244C2semidirect
8. #3243C2semidirect
9. #3240C2semidirect
10. #3231C2semidirect
11. #3225C2semidirect
12. #3225C2semidirect
13. #3216C2semidirect
14. #3212C2semidirect
15. #3197C2semidirect
16. #3196C2semidirect
17. #3191C2semidirect
18. #3190C2semidirect
19. #3178C2semidirect
20. #3178C2semidirect
21. #3175C2semidirect
22. #3173C2semidirect
23. #3127C2semidirect
24. #3126C2semidirect
25. #3120C2semidirect
26. #3119C2semidirect
27. #3116C2semidirect
28. #3111C2semidirect
29. #3107C2semidirect
30. #3102C2semidirect
31. #2924C2semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #498C22semidirect
81. #497C22semidirect
82. #497C22semidirect
83. #495C22semidirect
84. #495C22semidirect
85. #489C22semidirect
86. #489C22semidirect
87. #489C22semidirect
88. #489C22semidirect
89. #488C22semidirect
90. #488C22semidirect
91. #487C22semidirect
92. #487C22semidirect
109. #479C22semidirect
110. #479C22semidirect
111. #479C22semidirect
112. #479C22semidirect
113. #479C22semidirect
114. #479C22semidirect
115. #479C22semidirect
116. #479C22semidirect
117. #478C22semidirect
118. #478C22semidirect
119. #478C22semidirect
120. #478C22semidirect
121. #477C22semidirect
122. #476C22semidirect
123. #475C22semidirect
124. #474C22semidirect
141. #464C22semidirect
142. #464C22semidirect
143. #463C22semidirect
144. #463C22semidirect
145. #462C22semidirect
146. #462C22semidirect
147. #462C22semidirect
148. #462C22semidirect
149. #462C22semidirect
150. #461C22semidirect
151. #461C22semidirect
152. #461C22semidirect
153. #460C22semidirect
154. #460C22semidirect
155. #460C22semidirect
156. #459C22semidirect
173. #442C22semidirect
174. #441C22semidirect
175. #441C22semidirect
176. #441C22semidirect
177. #440C22semidirect
178. #440C22semidirect
179. #440C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
182. C4×Q16C22semidirect
183. C4×Q16C22semidirect
184. C4×SD16C22semidirect
185. C4×SD16C22semidirect
186. C4×SD16C22semidirect
187. C4×SD16C22semidirect
188. C4×D8C22semidirect

Maximal subgroups

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

subgroupindex
#34952
#34552
#32612
#32602
#32582
#32572
#32442
#32432
#32402
#32312
#32252
#32162
#32122
#31972
#31962
#31912
#31902
#31782
#31752
#31732
#31272
#31262
#31202
#31192
#31162
#31112
#31072
#31022
#29242