Finite Group Databasebeta

← #62138

Subgroups — #62138

Order 256.

866 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3515C211yesmaximal, characteristic, complemented
2#3475C211yesmaximal, characteristic, complemented
3#3389C211yesmaximal, characteristic, complemented
4#3388C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3376C211yesmaximal, characteristic, complemented
7#3348C211yesmaximal, characteristic, complemented
8#3347C211yesmaximal, characteristic, complemented
9#3344C211yesmaximal, characteristic, complemented
10#3343C211yesmaximal, characteristic, complemented
11#3337C211yesmaximal, characteristic, complemented
12#3336C211yesmaximal, characteristic, complemented
13#3315C211yesmaximal, characteristic, complemented
14#3314C211yesmaximal, characteristic, complemented
15#3307C211yesmaximal, characteristic, complemented
16#3306C211yesmaximal, characteristic, complemented
17#3297C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3256C211yesmaximal, characteristic, complemented
20#3250C211yesmaximal, characteristic, complemented
21#3248C211yesmaximal, characteristic, complemented
22#3240C211yesmaximal, characteristic, complemented
23#3236C211yesmaximal, characteristic, complemented
24#3232C211yesmaximal, characteristic, complemented
25#3114C211yesmaximal, characteristic, complemented
26#3111C211yesmaximal, characteristic, complemented
27#3102C211yesmaximal, characteristic, complemented
28#3080C211yesmaximal, characteristic, complemented
29#3076C211yesmaximal, characteristic, complemented
30C2×#478C211yesmaximal, characteristic, complemented
31#2990C211yesmaximal, characteristic, complemented
32#557C2211yescharacteristic, complemented
33#556C2211yescharacteristic
34#555C2211yescharacteristic
35#554C2211yescharacteristic
36#554C2211yescharacteristic
37#554C2211yescharacteristic, complemented
38#553—21no—
39#553C2211yescharacteristic
40#553C2211yescharacteristic, complemented
41#552—21no—
42#552—21no—
43#552—21no—
44#552—21no—
45#552C2211yescharacteristic
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic, complemented
49#551—21no—
50#551—21no—
51#547—21no—
52#547C2211yescharacteristic
53#547C2211yescharacteristic
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#541—21no—
57#539—21no—
58#539—21no—
59#533C2211yescharacteristic
60#533C2211yescharacteristic, complemented
61#529—21no—
62#529—21no—
63#529C2211yescharacteristic
64#529C2211yescharacteristic
65#529C2211yescharacteristic
66#529C2211yescharacteristic, complemented
67#529C2211yescharacteristic, complemented
68C2×#125C2211yescharacteristic
69C2×#125C2211yescharacteristic, complemented
70#525—21no—
71#520—21no—
72C4×#41C2211yescharacteristic
73C4×#41C2211yescharacteristic
74C4×#41C2211yescharacteristic
75C2×C4×D4C2211yescharacteristic
76C2×#117—21no—
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#501C2211yescharacteristic, complemented
80#501C2211yescharacteristic, complemented
81#499C2211yescharacteristic, complemented
82#499C2211yescharacteristic, complemented
83#491C2211yescharacteristic, complemented
84#491C2211yescharacteristic, complemented
85#489C2211yescharacteristic
86#489C2211yescharacteristic
87#488C2211yescharacteristic
88#488C2211yescharacteristic
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#484C2211yescharacteristic
94#484C2211yescharacteristic
95#484C2211yescharacteristic, complemented
96#483C2211yescharacteristic
97#483C2211yescharacteristic
98#483C2211yescharacteristic
99#483C2211yescharacteristic, complemented
100#482C2211yescharacteristic
101#482C2211yescharacteristic
102#482C2211yescharacteristic, complemented
103#482C2211yescharacteristic, complemented
104#481C2211yescharacteristic
105#480C2211yescharacteristic
106#480C2211yescharacteristic
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
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
118#478C2211yescharacteristic
119#478C2211yescharacteristic
120#478C2211yescharacteristic
121#478C2211yescharacteristic
122#478C2211yescharacteristic
123#478C2211yescharacteristic
124#478C2211yescharacteristic
125#478C2211yescharacteristic
126#478C2211yescharacteristic
127#478C2211yescharacteristic
128#478C2211yescharacteristic
129#478C2211yescharacteristic, complemented
130#478C2211yescharacteristic, complemented
131#477C2211yescharacteristic, complemented
132#476C2211yescharacteristic
133#475C2211yescharacteristic, complemented
134#475C2211yescharacteristic, complemented
135#474C2211yescharacteristic
136#474C2211yescharacteristic, complemented
137#470C2211yescharacteristic, complemented
138#469C2211yescharacteristic
139#468C2211yescharacteristic
140#468C2211yescharacteristic, complemented
141#467C2211yescharacteristic
142#467C2211yescharacteristic
143#467C2211yescharacteristic, complemented
144#466C2211yescharacteristic
145#465C2211yescharacteristic
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#464C2211yescharacteristic, complemented
152#464C2211yescharacteristic, complemented
153#463C2211yescharacteristic
154#463C2211yescharacteristic
155#463C2211yescharacteristic
156#463C2211yescharacteristic
157#462C2211yescharacteristic, complemented
158#461C2211yescharacteristic, complemented
159#452C2211yescharacteristic
160#452C2211yescharacteristic
161#450C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#442C2211yescharacteristic
168#442C2211yescharacteristic
169#442C2211yescharacteristic
170#441C2211yescharacteristic, complemented
171#440C2211yescharacteristic
172#440C2211yescharacteristic
173#440C2211yescharacteristic
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic
179#435C2211yescharacteristic
180#435C2211yescharacteristic
181#435C2211yescharacteristic, complemented
182#435C2211yescharacteristic, complemented
183C8×D4C2211yescharacteristic
184C8×D4C2211yescharacteristic
185#432C2211yescharacteristic
186#432C2211yescharacteristic, complemented
187#431C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189#428C2211yescharacteristic, complemented
190#427C2211yescharacteristic, complemented
191#427C2211yescharacteristic, complemented
192C2×#107C2211yescharacteristic
193C2×#106C2211yescharacteristic
194#423C2211yescharacteristic, complemented
195C2×C4⋊C8C2211yescharacteristic
196C2×C4⋊C8C2211yescharacteristic, complemented
197#417C2211yescharacteristic
198#417C2211yescharacteristic
199#416C2211yescharacteristic
200#416C2211yescharacteristic
201C2×#102C2211yescharacteristic
202C2×#102C2211yescharacteristic
203C2×#41—21no—
204C2×#41D411yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×D4C2311yescharacteristic
208C23×C4—21no—
209C2×Q16C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×D8C2311yescharacteristic
216C2×D8C2311yescharacteristic
217C2×M16C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C22×C8C2311yescharacteristic
220C22×C8C2311yescharacteristic
221C22×C8C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C4⋊Q8—21no—
224C4⋊Q8C2311yescharacteristic
225C4⋊Q8C2311yescharacteristic
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228#126—21no—
229#126—21no—
230#126—21no—
231#126—21no—
232#126—21no—
233#126—21no—
234#126—21no—
235#126—21no—
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#125—21no—
242#125—21no—
243#125—21no—
244#125—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125C2311yescharacteristic
254#125C2311yescharacteristic
255#125C2311yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#125C2311yescharacteristic
260#125C2311yescharacteristic
261#125C2311yescharacteristic
262#124—21no—
263#124—21no—
264#124C2311yescharacteristic
265#124C2311yescharacteristic
266#124C2311yescharacteristic
267#123—21no—
268#123—21no—
269#123—21no—
270#123—21no—
271#123—21no—
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—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
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⋊Q8C2311yescharacteristic
298C22⋊Q8C2311yescharacteristic
299C22⋊Q8C2311yescharacteristic
300C22⋊Q8C2311yescharacteristic
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
303C22⋊Q8C2311yescharacteristic
304#121—21no—
305#121—21no—
306#121—21no—
307#121—21no—
308#121—21no—
309#121—21no—
310#121C2311yescharacteristic
311#121C2311yescharacteristic
312#121C2311yescharacteristic
313#121C2311yescharacteristic
314#121C2311yescharacteristic
315#120—21no—
316#120—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8D411yescharacteristic
322C4×Q8C2311yescharacteristic
323C4×Q8C2311yescharacteristic
324C4×Q8C2311yescharacteristic
325C4×Q8C2311yescharacteristic
326C4×Q8C2311yescharacteristic
327C4×Q8C2311yescharacteristic
328C4×Q8C2311yescharacteristic
329C4×Q8C2311yescharacteristic
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4D411yescharacteristic
345C4×D4D411yescharacteristic
346C4×D4D411yescharacteristic
347C4×D4C2311yescharacteristic
348C4×D4C2311yescharacteristic
349C4×D4C2311yescharacteristic
350C4×D4C2311yescharacteristic
351C4×D4C2311yescharacteristic
352C4×D4C2311yescharacteristic
353C4×D4C2311yescharacteristic
354C4×D4C2311yescharacteristic
355C4×D4C2311yescharacteristic
356C4×D4C2311yescharacteristic
357C4×D4C2311yescharacteristic
358C4×D4C2311yescharacteristic
359#117—21no—
360#117—21no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117D411yescharacteristic
374#117D411yescharacteristic
375#117D411yescharacteristic
376#117C2311yescharacteristic
377#117C2311yescharacteristic
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4C2311yescharacteristic
388C2×C4⋊C4C2311yescharacteristic
389C2×C4⋊C4C2311yescharacteristic
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C2311yescharacteristic
398C2×C42C2311yescharacteristic
399C2×C42C2311yescharacteristic
400#107C2311yescharacteristic
401#107C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
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
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479#41—22no—
480#41—22no—
481#41—42no—
482#41—41no—
483#41—41no—
484#41—44no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8C2×D411yescharacteristic
489C2×Q8C2411yescharacteristic
490C2×Q8C2411yescharacteristic
491C2×Q8C2411yescharacteristic
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—41no—
502C2×D4C2×D411yescharacteristic
503C2×D4C2×D411yescharacteristic
504C2×D4C2×D411yescharacteristic
505C2×D4C2411yescharacteristic
506C2×D4C2411yescharacteristic
507C2×D4C2411yescharacteristic
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
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—21no—
523C22×C4—21no—
524C22×C4—44no—
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—
536SD16—22no—
537SD16—41no—
538SD16—41no—
539SD16—41no—
540D8—22no—
541D8—41no—
542M16—41no—
543M16—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8C2411yescharacteristic
549C2×C8C2411yescharacteristic
550C2×C8C2411yescharacteristic
551C2×C8C2411yescharacteristic
552C2×C8C2411yescharacteristic
553C2×C8C2411yescharacteristic
554C2×C8C2411yescharacteristic
555C2×C8C2411yescharacteristic
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
599C4⋊C4C2×D411yescharacteristic
600C4⋊C4C2×D411yescharacteristic
601C4⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
646C22⋊C4C2×D411yescharacteristic
647C22⋊C4C2×D411yescharacteristic
648C22⋊C4C2×D411yescharacteristic
649C22⋊C4C2×D411yescharacteristic
650C22⋊C4C2×D411yescharacteristic
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42C2×D411yescharacteristic
663C42C2×D411yescharacteristic
664C42C2×D411yescharacteristic
665C42C2×D411yescharacteristic
666C42C2×D411yescharacteristic
667C42C2×D411yescharacteristic
668C42C2411yescharacteristic
669C42C2411yescharacteristic
670C42C2411yescharacteristic
671C42C2411yescharacteristic
672C23—21no—
673C23—21no—
674C23—21no—
675C23—42no—
676C23—42no—
677C23—81no—
678C23C22×D411yescharacteristic
679C23C22×D411yescharacteristic
680C23C22×D411yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—21no—
687Q8—41no—
688Q8—42no—
689Q8—81no—
690Q8—81no—
691D4—22no—
692D4—22no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—41no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—81no—
705D4—81no—
706D4—81no—
707D42−1+412yes—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
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—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4C22×D411yescharacteristic
750C2×C4C22×D411yescharacteristic
751C2×C4C22×D411yescharacteristic
752C2×C4C22×D411yescharacteristic
753C2×C4C22×D411yescharacteristic
754C2×C4C22×D411yescharacteristic
755C2×C4C22×D411yescharacteristic
756C2×C4C22×D411yescharacteristic
757C2×C4C22×D411yescharacteristic
758C2×C4C22×D411yescharacteristic
759C2×C4C22×D411yescharacteristic
760C2×C4C2511yescharacteristic
761C8—21no—
762C8—21no—
763C8—21no—
764C8—21no—
765C8—21no—
766C8—21no—
767C8—21no—
768C8—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—21no—
777C22—21no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—84no—
787C22#57512yes—
788C22C23×D411yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4C2×2−1+411yescharacteristic
814C4#58511yescharacteristic
815C2—22no—
816C2—41no—
817C2—41no—
818C2—42no—
819C2—81no—
820C2—81no—
821C2#348911yescharacteristic
822C2C2×#57511yescharacteristic
823C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3515C2semidirect
2. #3475C2semidirect
3. #3389C2semidirect
4. #3388C2semidirect
5. #3377C2semidirect
6. #3376C2semidirect
7. #3348C2semidirect
8. #3347C2semidirect
9. #3344C2semidirect
10. #3343C2semidirect
11. #3337C2semidirect
12. #3336C2semidirect
13. #3315C2semidirect
14. #3314C2semidirect
15. #3307C2semidirect
16. #3306C2semidirect
17. #3297C2semidirect
18. #3296C2semidirect
19. #3256C2semidirect
20. #3250C2semidirect
21. #3248C2semidirect
22. #3240C2semidirect
23. #3236C2semidirect
24. #3232C2semidirect
25. #3114C2semidirect
26. #3111C2semidirect
27. #3102C2semidirect
28. #3080C2semidirect
29. #3076C2semidirect
30. C2×#478C2semidirect
31. #2990C2semidirect
32. #557C22semidirect
37. #554C22semidirect
40. #553C22semidirect
48. #552C22semidirect
60. #533C22semidirect
66. #529C22semidirect
67. #529C22semidirect
69. C2×#125C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #501C22semidirect
80. #501C22semidirect
81. #499C22semidirect
82. #499C22semidirect
83. #491C22semidirect
84. #491C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
95. #484C22semidirect
99. #483C22semidirect
102. #482C22semidirect
103. #482C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
110. #479C22semidirect
111. #479C22semidirect
112. #479C22semidirect
113. #479C22semidirect
114. #479C22semidirect
115. #479C22semidirect
116. #479C22semidirect
129. #478C22semidirect
130. #478C22semidirect
131. #477C22semidirect
133. #475C22semidirect
134. #475C22semidirect
136. #474C22semidirect
137. #470C22semidirect
140. #468C22semidirect
143. #467C22semidirect
148. #465C22semidirect
151. #464C22semidirect
152. #464C22semidirect
157. #462C22semidirect
158. #461C22semidirect
165. #446C22semidirect
166. #446C22semidirect
170. #441C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
177. C4×SD16C22semidirect
181. #435C22semidirect
182. #435C22semidirect
186. #432C22semidirect
187. #431C22semidirect
188. #428C22semidirect
189. #428C22semidirect
190. #427C22semidirect
191. #427C22semidirect
194. #423C22semidirect
196. C2×C4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#35152
#34752
#33892
#33882
#33772
#33762
#33482
#33472
#33442
#33432
#33372
#33362
#33152
#33142
#33072
#33062
#32972
#32962
#32562
#32502
#32482
#32402
#32362
#32322
#31142
#31112
#31022
#30802
#30762
C2×#4782
#29902