Finite Group Databasebeta

← #60973

Subgroups — #60973

Order 256.

866 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3461C211yesmaximal, characteristic, complemented
2#3460C211yesmaximal, characteristic, complemented
3#3262C211yesmaximal, characteristic, complemented
4#3260C211yesmaximal, characteristic, complemented
5#3258C211yesmaximal, characteristic, complemented
6#3257C211yesmaximal, characteristic, complemented
7#3243C211yesmaximal, characteristic, complemented
8#3243C211yesmaximal, characteristic, complemented
9#3242C211yesmaximal, characteristic, complemented
10#3241C211yesmaximal, characteristic, complemented
11#3225C211yesmaximal, characteristic, complemented
12#3224C211yesmaximal, characteristic, complemented
13#3222C211yesmaximal, characteristic, complemented
14#3221C211yesmaximal, characteristic, complemented
15#3203C211yesmaximal, characteristic, complemented
16#3201C211yesmaximal, characteristic, complemented
17#3200C211yesmaximal, characteristic, complemented
18#3198C211yesmaximal, characteristic, complemented
19#3183C211yesmaximal, characteristic, complemented
20#3182C211yesmaximal, characteristic, complemented
21#3181C211yesmaximal, characteristic, complemented
22#3180C211yesmaximal, characteristic, complemented
23#3117C211yesmaximal, characteristic, complemented
24#3116C211yesmaximal, characteristic, complemented
25#3115C211yesmaximal, characteristic, complemented
26#3114C211yesmaximal, characteristic, complemented
27#3112C211yesmaximal, characteristic, complemented
28#3111C211yesmaximal, characteristic, complemented
29#3111C211yesmaximal, characteristic, complemented
30#3110C211yesmaximal, characteristic, complemented
31#2923C211yesmaximal, characteristic, complemented
32#544C2211yescharacteristic
33#544C2211yescharacteristic, complemented
34#542—21no—
35#542—21no—
36#542C2211yescharacteristic
37#542C2211yescharacteristic
38#542C2211yescharacteristic
39#542C2211yescharacteristic, complemented
40#541—21no—
41#541C2211yescharacteristic
42#541C2211yescharacteristic, complemented
43#540—21no—
44#540C2211yescharacteristic
45#540C2211yescharacteristic
46#539—21no—
47#539—21no—
48#538—21no—
49#538—21no—
50#537C2211yescharacteristic
51#537C2211yescharacteristic
52#536C2211yescharacteristic
53#536C2211yescharacteristic, complemented
54#535C2211yescharacteristic
55#535C2211yescharacteristic
56#533—21no—
57#533C2211yescharacteristic
58#533C2211yescharacteristic, complemented
59#532—21no—
60#532C2211yescharacteristic
61#532C2211yescharacteristic
62#529—21no—
63#529—21no—
64#529—21no—
65#529—21no—
66#529C2211yescharacteristic
67#529C2211yescharacteristic
68#529C2211yescharacteristic
69#529C2211yescharacteristic, complemented
70#525—21no—
71#525—21no—
72C4×#41C2211yescharacteristic
73C4×#41C2211yescharacteristic
74C4×#41C2211yescharacteristic, complemented
75C2×C4×Q8C2211yescharacteristic, complemented
76C2×C4×D4C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#497C2211yescharacteristic
82#496C2211yescharacteristic
83#495C2211yescharacteristic
84#492C2211yescharacteristic
85#491C2211yescharacteristic, complemented
86#490C2211yescharacteristic
87#489C2211yescharacteristic
88#489C2211yescharacteristic, complemented
89#488C2211yescharacteristic
90#488C2211yescharacteristic, complemented
91#487C2211yescharacteristic, complemented
92#486C2211yescharacteristic
93#485C2211yescharacteristic
94#485C2211yescharacteristic
95#485C2211yescharacteristic
96#485C2211yescharacteristic, complemented
97#484C2211yescharacteristic
98#484C2211yescharacteristic
99#484C2211yescharacteristic, complemented
100#483C2211yescharacteristic
101#482C2211yescharacteristic
102#482C2211yescharacteristic
103#482C2211yescharacteristic
104#482C2211yescharacteristic, complemented
105#481C2211yescharacteristic
106#480C2211yescharacteristic
107#480C2211yescharacteristic
108#480C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#479C2211yescharacteristic, complemented
112#479C2211yescharacteristic, complemented
113#478C2211yescharacteristic
114#478C2211yescharacteristic
115#478C2211yescharacteristic, complemented
116#478C2211yescharacteristic, complemented
117#477C2211yescharacteristic, complemented
118#477C2211yescharacteristic, complemented
119#477C2211yescharacteristic, complemented
120#476C2211yescharacteristic, complemented
121#475C2211yescharacteristic, complemented
122#474C2211yescharacteristic
123#474C2211yescharacteristic
124#474C2211yescharacteristic, complemented
125#470C2211yescharacteristic, complemented
126#469C2211yescharacteristic
127#468C2211yescharacteristic
128#468C2211yescharacteristic
129#468C2211yescharacteristic
130#468C2211yescharacteristic, complemented
131#468C2211yescharacteristic, complemented
132#468C2211yescharacteristic, complemented
133#467C2211yescharacteristic, complemented
134#467C2211yescharacteristic, complemented
135#466C2211yescharacteristic
136#466C2211yescharacteristic, complemented
137#465C2211yescharacteristic
138#465C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic, complemented
141#464C2211yescharacteristic
142#464C2211yescharacteristic
143#464C2211yescharacteristic
144#464C2211yescharacteristic, complemented
145#463C2211yescharacteristic
146#463C2211yescharacteristic
147#463C2211yescharacteristic
148#463C2211yescharacteristic, complemented
149#462C2211yescharacteristic, complemented
150#461C2211yescharacteristic
151#461C2211yescharacteristic
152#461C2211yescharacteristic, complemented
153#460C2211yescharacteristic
154#460C2211yescharacteristic
155#460C2211yescharacteristic
156#459C2211yescharacteristic
157#452C2211yescharacteristic
158#452C2211yescharacteristic
159#452C2211yescharacteristic
160#452C2211yescharacteristic, complemented
161#451C2211yescharacteristic, complemented
162#450C2211yescharacteristic
163#450C2211yescharacteristic
164#450C2211yescharacteristic
165#449C2211yescharacteristic
166#449C2211yescharacteristic
167#449C2211yescharacteristic
168#449C2211yescharacteristic, complemented
169#448C2211yescharacteristic
170#448C2211yescharacteristic
171#448C2211yescharacteristic, complemented
172#447C2211yescharacteristic
173#442C2211yescharacteristic
174#442C2211yescharacteristic
175#442C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#441C2211yescharacteristic, complemented
178#441C2211yescharacteristic, complemented
179#440C2211yescharacteristic
180#440C2211yescharacteristic
181#440C2211yescharacteristic
182#440C2211yescharacteristic
183#440C2211yescharacteristic
184#440C2211yescharacteristic
185#440C2211yescharacteristic, complemented
186#440C2211yescharacteristic, complemented
187#440C2211yescharacteristic, complemented
188#440C2211yescharacteristic, complemented
189#433C2211yescharacteristic
190#433C2211yescharacteristic
191#433C2211yescharacteristic, complemented
192#433C2211yescharacteristic, complemented
193#432C2211yescharacteristic
194#432C2211yescharacteristic
195#432C2211yescharacteristic, complemented
196#432C2211yescharacteristic, complemented
197#424C2211yescharacteristic, complemented
198#424C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201C4×M16C2211yescharacteristic, complemented
202C2×#97C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×D4C2311yescharacteristic
210C23×C4—21no—
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×D8C2311yescharacteristic
225C2×D8C2311yescharacteristic
226C2×D8C2311yescharacteristic
227C2×M16C2311yescharacteristic
228C2×M16C2311yescharacteristic
229C22×C8C2311yescharacteristic
230C22×C8C2311yescharacteristic
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
239C4⋊Q8C2311yescharacteristic
240#127—21no—
241#127C2311yescharacteristic
242#127C2311yescharacteristic
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#126—21no—
254#126—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#125C2311yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#125C2311yescharacteristic
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124C2311yescharacteristic
276#124C2311yescharacteristic
277#124C2311yescharacteristic
278#124C2311yescharacteristic
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⋊Q8C2311yescharacteristic
310C22⋊Q8C2311yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#121C2311yescharacteristic
338#121C2311yescharacteristic
339#120—21no—
340#120—21no—
341#120—21no—
342#120—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8D411yescharacteristic
348C4×Q8D411yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
354C4×Q8C2311yescharacteristic
355C4×Q8C2311yescharacteristic
356C4×Q8C2311yescharacteristic
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×D4—21no—
369C4×D4D411yescharacteristic
370C4×D4D411yescharacteristic
371C4×D4D411yescharacteristic
372C4×D4D411yescharacteristic
373C4×D4D411yescharacteristic
374C4×D4D411yescharacteristic
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117C2311yescharacteristic
392#117C2311yescharacteristic
393#117C2311yescharacteristic
394#117C2311yescharacteristic
395#117C2311yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4C2311yescharacteristic
398C2×C4⋊C4C2311yescharacteristic
399C2×C22⋊C4—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42C2311yescharacteristic
404C2×C42C2311yescharacteristic
405C2×C42C2311yescharacteristic
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
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#102C2311yescharacteristic
447#102C2311yescharacteristic
448#102C2311yescharacteristic
449#102C2311yescharacteristic
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
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—82no—
486#41—82no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8C2×D411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
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×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4C2×D411yescharacteristic
517C2×D4C2×D411yescharacteristic
518C2×D4C2×D411yescharacteristic
519C2×D4C2411yescharacteristic
520C2×D4C2411yescharacteristic
521C2×D4C2411yescharacteristic
522C2×D4C2411yescharacteristic
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—82no—
537C22×C4C2×D411yescharacteristic
538C22×C4C2×D411yescharacteristic
539C22×C4C2×D411yescharacteristic
540C22×C4C2×D411yescharacteristic
541C22×C4C2×D411yescharacteristic
542C22×C4C2×D411yescharacteristic
543C22×C4C2411yescharacteristic
544C22×C4C2411yescharacteristic
545C22×C4C2411yescharacteristic
546Q16—41no—
547Q16—41no—
548Q16—41no—
549SD16—41no—
550SD16—41no—
551SD16—41no—
552SD16—41no—
553SD16—41no—
554SD16—41no—
555SD16—41no—
556SD16—41no—
557SD16—41no—
558SD16—41no—
559D8—41no—
560D8—41no—
561D8—41no—
562M16—41no—
563M16—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
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⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
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⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
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—
672C42C2×D411yescharacteristic
673C42C2×D411yescharacteristic
674C42C2×D411yescharacteristic
675C42C2×D411yescharacteristic
676C42C2×D411yescharacteristic
677C42C2×D411yescharacteristic
678C42C2411yescharacteristic
679C42C2411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—42no—
687C23—81no—
688C23—81no—
689C23C22×D411yescharacteristic
690C23C22×D411yescharacteristic
691C23C22×D411yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—41no—
701Q8—42no—
702Q8—81no—
703Q8—81no—
704Q8—81no—
705Q8—81no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—81no—
721D4—81no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
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—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4C22×D411yescharacteristic
770C2×C4C22×D411yescharacteristic
771C2×C4C22×D411yescharacteristic
772C2×C4C22×D411yescharacteristic
773C2×C4C22×D411yescharacteristic
774C2×C4C22×D411yescharacteristic
775C2×C4C22×D411yescharacteristic
776C2×C4C22×D411yescharacteristic
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C2511yescharacteristic
781C8—21no—
782C8—21no—
783C8—21no—
784C8—21no—
785C8—21no—
786C8—21no—
787C8—21no—
788C8—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—84no—
811C22C23×D411yescharacteristic
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4#58511yescharacteristic
836C4#58511yescharacteristic
837C2—41no—
838C2—41no—
839C2—41no—
840C2—81no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2#344911yescharacteristic
845C2#358511yescharacteristic
846C2#358611yescharacteristic
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. #3461C2semidirect
2. #3460C2semidirect
3. #3262C2semidirect
4. #3260C2semidirect
5. #3258C2semidirect
6. #3257C2semidirect
7. #3243C2semidirect
8. #3243C2semidirect
9. #3242C2semidirect
10. #3241C2semidirect
11. #3225C2semidirect
12. #3224C2semidirect
13. #3222C2semidirect
14. #3221C2semidirect
15. #3203C2semidirect
16. #3201C2semidirect
17. #3200C2semidirect
18. #3198C2semidirect
19. #3183C2semidirect
20. #3182C2semidirect
21. #3181C2semidirect
22. #3180C2semidirect
23. #3117C2semidirect
24. #3116C2semidirect
25. #3115C2semidirect
26. #3114C2semidirect
27. #3112C2semidirect
28. #3111C2semidirect
29. #3111C2semidirect
30. #3110C2semidirect
31. #2923C2semidirect
33. #544C22semidirect
39. #542C22semidirect
42. #541C22semidirect
53. #536C22semidirect
58. #533C22semidirect
69. #529C22semidirect
74. C4×#41C22semidirect
75. C2×C4×Q8C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #499C22semidirect
85. #491C22semidirect
88. #489C22semidirect
90. #488C22semidirect
91. #487C22semidirect
96. #485C22semidirect
99. #484C22semidirect
104. #482C22semidirect
108. #480C22semidirect
109. #479C22semidirect
110. #479C22semidirect
111. #479C22semidirect
112. #479C22semidirect
115. #478C22semidirect
116. #478C22semidirect
117. #477C22semidirect
118. #477C22semidirect
119. #477C22semidirect
120. #476C22semidirect
121. #475C22semidirect
124. #474C22semidirect
125. #470C22semidirect
130. #468C22semidirect
131. #468C22semidirect
132. #468C22semidirect
133. #467C22semidirect
134. #467C22semidirect
136. #466C22semidirect
140. #465C22semidirect
144. #464C22semidirect
148. #463C22semidirect
149. #462C22semidirect
152. #461C22semidirect
160. #452C22semidirect
161. #451C22semidirect
168. #449C22semidirect
171. #448C22semidirect
175. #442C22semidirect
176. #441C22semidirect
177. #441C22semidirect
178. #441C22semidirect
185. #440C22semidirect
186. #440C22semidirect
187. #440C22semidirect
188. #440C22semidirect
191. #433C22semidirect
192. #433C22semidirect
195. #432C22semidirect
196. #432C22semidirect
197. #424C22semidirect
198. #424C22semidirect
201. C4×M16C22semidirect
202. C2×#97C22semidirect

Maximal subgroups

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

subgroupindex
#34612
#34602
#32622
#32602
#32582
#32572
#32432
#32422
#32412
#32252
#32242
#32222
#32212
#32032
#32012
#32002
#31982
#31832
#31822
#31812
#31802
#31172
#31162
#31152
#31142
#31122
#31112
#31102
#29232