Finite Group Databasebeta

← #62567

Subgroups — #62567

Order 256.

856 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#3562C211yesmaximal, characteristic, complemented
2#3544C211yesmaximal, characteristic, complemented
3#3376C211yesmaximal, characteristic, complemented
4#3375C211yesmaximal, characteristic, complemented
5#3370C211yesmaximal, characteristic, complemented
6#3369C211yesmaximal, characteristic, complemented
7#3332C211yesmaximal, characteristic, complemented
8#3330C211yesmaximal, characteristic, complemented
9#3327C211yesmaximal, characteristic, complemented
10#3323C211yesmaximal, characteristic, complemented
11#3321C211yesmaximal, characteristic, complemented
12#3319C211yesmaximal, characteristic, complemented
13#3317C211yesmaximal, characteristic, complemented
14#3316C211yesmaximal, characteristic, complemented
15#3315C211yesmaximal, characteristic, complemented
16#3314C211yesmaximal, characteristic, complemented
17#3308C211yesmaximal, characteristic, complemented
18#3306C211yesmaximal, characteristic, complemented
19#3242C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3239C211yesmaximal, characteristic, complemented
22#3225C211yesmaximal, characteristic, complemented
23#3224C211yesmaximal, characteristic, complemented
24#3219C211yesmaximal, characteristic, complemented
25#3183C211yesmaximal, characteristic, complemented
26#3179C211yesmaximal, characteristic, complemented
27#3178C211yesmaximal, characteristic, complemented
28#3141C211yesmaximal, characteristic, complemented
29#3137C211yesmaximal, characteristic, complemented
30#3136C211yesmaximal, characteristic, complemented
31#2967C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#562—21no—
35#560—21no—
36#559C2211yescharacteristic
37Q82C2211yescharacteristic, complemented
38#556C2211yescharacteristic
39#555C2211yescharacteristic
40#554C2211yescharacteristic
41#554C2211yescharacteristic, complemented
42#553—21no—
43#552—21no—
44#552C2211yescharacteristic
45#552C2211yescharacteristic, complemented
46#551—21no—
47#550C2211yescharacteristic
48#548C2211yescharacteristic
49#548C2211yescharacteristic
50#547—21no—
51#547C2211yescharacteristic
52#547C2211yescharacteristic
53#547C2211yescharacteristic, complemented
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#544—21no—
57#544C2211yescharacteristic
58#544C2211yescharacteristic, complemented
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic, complemented
62#541C2211yescharacteristic
63#540—21no—
64#540C2211yescharacteristic
65#539—21no—
66#538—21no—
67#538—21no—
68#536—21no—
69#536—21no—
70#536C2211yescharacteristic
71#535C2211yescharacteristic
72#532C2211yescharacteristic
73C2×C4⋊Q8C2211yescharacteristic, complemented
74#529C2211yescharacteristic
75#529C2211yescharacteristic
76#529C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#497C2211yescharacteristic, complemented
81#496C2211yescharacteristic
82#495C2211yescharacteristic
83#491C2211yescharacteristic, complemented
84#491C2211yescharacteristic, complemented
85#490C2211yescharacteristic
86#490C2211yescharacteristic
87#489C2211yescharacteristic
88#489C2211yescharacteristic
89#489C2211yescharacteristic
90#489C2211yescharacteristic
91#489C2211yescharacteristic
92#489C2211yescharacteristic
93#489C2211yescharacteristic, complemented
94#489C2211yescharacteristic, complemented
95#488C2211yescharacteristic
96#488C2211yescharacteristic
97#488C2211yescharacteristic
98#488C2211yescharacteristic, complemented
99#487C2211yescharacteristic, complemented
100#487C2211yescharacteristic, complemented
101#487C2211yescharacteristic, complemented
102#486C2211yescharacteristic
103#486C2211yescharacteristic
104#486C2211yescharacteristic
105#485C2211yescharacteristic
106#485C2211yescharacteristic
107#484C2211yescharacteristic
108#484C2211yescharacteristic, complemented
109#484C2211yescharacteristic, complemented
110#483C2211yescharacteristic
111#482C2211yescharacteristic
112#482C2211yescharacteristic, complemented
113#481C2211yescharacteristic
114#481C2211yescharacteristic
115#481C2211yescharacteristic, complemented
116#480C2211yescharacteristic
117#479C2211yescharacteristic, complemented
118#479C2211yescharacteristic, complemented
119#478C2211yescharacteristic
120#478C2211yescharacteristic, complemented
121#477C2211yescharacteristic, complemented
122#476C2211yescharacteristic
123#475C2211yescharacteristic, complemented
124#475C2211yescharacteristic, complemented
125#475C2211yescharacteristic, complemented
126#474C2211yescharacteristic
127#474C2211yescharacteristic
128#474C2211yescharacteristic, complemented
129#470C2211yescharacteristic
130#470C2211yescharacteristic, complemented
131#469C2211yescharacteristic
132#469C2211yescharacteristic, complemented
133#468C2211yescharacteristic
134#468C2211yescharacteristic
135#468C2211yescharacteristic
136#468C2211yescharacteristic, complemented
137#467C2211yescharacteristic
138#466C2211yescharacteristic
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, complemented
151#460C2211yescharacteristic
152#459C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic, complemented
157#451C2211yescharacteristic, complemented
158#450C2211yescharacteristic
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic, complemented
163#448C2211yescharacteristic, complemented
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#442C2211yescharacteristic
168#442C2211yescharacteristic
169#441C2211yescharacteristic, complemented
170#441C2211yescharacteristic, complemented
171#440C2211yescharacteristic
172#440C2211yescharacteristic, complemented
173#440C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic
180#436C2211yescharacteristic, complemented
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic
184#435C2211yescharacteristic, complemented
185#433C2211yescharacteristic
186#433C2211yescharacteristic, complemented
187#432C2211yescharacteristic, complemented
188#419C2211yescharacteristic, complemented
189#418C2211yescharacteristic
190#417C2211yescharacteristic
191#417C2211yescharacteristic
192#417C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic
197#416C2211yescharacteristic
198C2×#103C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic
200#405C2211yescharacteristic
201#405C2211yescharacteristic, complemented
202C4×M16C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C22×Q8—21no—
210C22×Q8C2311yescharacteristic
211C22×D4C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×D8C2311yescharacteristic
222C2×D8C2311yescharacteristic
223C2×D8C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C2×M16C2311yescharacteristic
226C2×M16C2311yescharacteristic
227C2×M16C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C22×C8C2311yescharacteristic
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
239C4⋊Q8C2311yescharacteristic
240C4⋊Q8C2311yescharacteristic
241C4⋊Q8C2311yescharacteristic
242C4⋊Q8C2311yescharacteristic
243C4⋊Q8C2311yescharacteristic
244C4⋊Q8C2311yescharacteristic
245#127—21no—
246#127C2311yescharacteristic
247#127C2311yescharacteristic
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126—21no—
254#126—21no—
255#126—21no—
256#126—21no—
257#126—21no—
258#126D411yescharacteristic
259#126D411yescharacteristic
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125D411yescharacteristic
268#125C2311yescharacteristic
269#125C2311yescharacteristic
270#125C2311yescharacteristic
271#125C2311yescharacteristic
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124D411yescharacteristic
280#124C2311yescharacteristic
281#124C2311yescharacteristic
282#124C2311yescharacteristic
283#124C2311yescharacteristic
284#124C2311yescharacteristic
285#124C2311yescharacteristic
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—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304#123—21no—
305#123—21no—
306#123D411yescharacteristic
307#123D411yescharacteristic
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8D411yescharacteristic
327C22⋊Q8C2311yescharacteristic
328C22⋊Q8C2311yescharacteristic
329C22⋊Q8C2311yescharacteristic
330C22⋊Q8C2311yescharacteristic
331C22⋊Q8C2311yescharacteristic
332C22⋊Q8C2311yescharacteristic
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—21no—
347#121D411yescharacteristic
348#121C2311yescharacteristic
349#121C2311yescharacteristic
350#121C2311yescharacteristic
351#121C2311yescharacteristic
352#121C2311yescharacteristic
353#121C2311yescharacteristic
354#120—21no—
355#120—21no—
356#120—21no—
357#120—21no—
358C4×Q8—21no—
359C4×Q8C2311yescharacteristic
360C4×Q8C2311yescharacteristic
361C4×Q8C2311yescharacteristic
362C4×Q8C2311yescharacteristic
363C4×Q8C2311yescharacteristic
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117C2311yescharacteristic
391#117C2311yescharacteristic
392#117C2311yescharacteristic
393#117C2311yescharacteristic
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4C2311yescharacteristic
398C2×C4⋊C4C2311yescharacteristic
399C2×C4⋊C4C2311yescharacteristic
400C2×C4⋊C4C2311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#106C2311yescharacteristic
411#106C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416C4⋊C8C2311yescharacteristic
417C4⋊C8C2311yescharacteristic
418C4⋊C8C2311yescharacteristic
419C4⋊C8C2311yescharacteristic
420C4⋊C8C2311yescharacteristic
421C4⋊C8C2311yescharacteristic
422#103C2311yescharacteristic
423#103C2311yescharacteristic
424#103C2311yescharacteristic
425#103C2311yescharacteristic
426#103C2311yescharacteristic
427#103C2311yescharacteristic
428#103C2311yescharacteristic
429#103C2311yescharacteristic
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#102C2311yescharacteristic
443#102C2311yescharacteristic
444#102C2311yescharacteristic
445#102C2311yescharacteristic
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
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
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—41no—
486#41—41no—
487#41—82no—
488#41—82no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—82no—
499C2×Q8C2×D411yescharacteristic
500C2×Q8C2411yescharacteristic
501C2×Q8C2411yescharacteristic
502C2×Q8C2411yescharacteristic
503C2×Q8C2411yescharacteristic
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—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4C2×D411yescharacteristic
522C2×D4C2×D411yescharacteristic
523C2×D4C2×D411yescharacteristic
524C2×D4C2411yescharacteristic
525C2×D4C2411yescharacteristic
526C2×D4C2411yescharacteristic
527C2×D4C2411yescharacteristic
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—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4C2×D411yescharacteristic
544C22×C4C2×D411yescharacteristic
545C22×C4C2411yescharacteristic
546C22×C4C2411yescharacteristic
547C22×C4C2411yescharacteristic
548Q16—41no—
549Q16—41no—
550Q16—41no—
551SD16—41no—
552SD16—41no—
553SD16—41no—
554SD16—41no—
555SD16—41no—
556SD16—41no—
557D8—41no—
558D8—41no—
559D8—41no—
560M16—41no—
561M16—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⋊C4C2×D411yescharacteristic
615C4⋊C4C2×D411yescharacteristic
616C4⋊C4C2×D411yescharacteristic
617C4⋊C4C2×D411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
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⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C22⋊C4C2×D411yescharacteristic
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42C2×D411yescharacteristic
677C42C2×D411yescharacteristic
678C42C2411yescharacteristic
679C42C2411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—81no—
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—81no—
702Q8—81no—
703Q8—81no—
704Q8—81no—
705Q8—81no—
706Q8—81no—
707Q8—81no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—41no—
717D4—41no—
718D4—41no—
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—
732D4—81no—
733D4—81no—
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—21no—
751C2×C4—21no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
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—162no—
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#350011yescharacteristic
845C2#358511yescharacteristic
846C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3562C2semidirect
2. #3544C2semidirect
3. #3376C2semidirect
4. #3375C2semidirect
5. #3370C2semidirect
6. #3369C2semidirect
7. #3332C2semidirect
8. #3330C2semidirect
9. #3327C2semidirect
10. #3323C2semidirect
11. #3321C2semidirect
12. #3319C2semidirect
13. #3317C2semidirect
14. #3316C2semidirect
15. #3315C2semidirect
16. #3314C2semidirect
17. #3308C2semidirect
18. #3306C2semidirect
19. #3242C2semidirect
20. #3241C2semidirect
21. #3239C2semidirect
22. #3225C2semidirect
23. #3224C2semidirect
24. #3219C2semidirect
25. #3183C2semidirect
26. #3179C2semidirect
27. #3178C2semidirect
28. #3141C2semidirect
29. #3137C2semidirect
30. #3136C2semidirect
31. #2967C2semidirect
37. Q82C22semidirect
41. #554C22semidirect
45. #552C22semidirect
53. #547C22semidirect
58. #544C22semidirect
61. #542C22semidirect
73. C2×C4⋊Q8C22semidirect
76. #529C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #499C22semidirect
80. #497C22semidirect
83. #491C22semidirect
84. #491C22semidirect
93. #489C22semidirect
94. #489C22semidirect
98. #488C22semidirect
99. #487C22semidirect
100. #487C22semidirect
101. #487C22semidirect
108. #484C22semidirect
109. #484C22semidirect
112. #482C22semidirect
115. #481C22semidirect
117. #479C22semidirect
118. #479C22semidirect
120. #478C22semidirect
121. #477C22semidirect
123. #475C22semidirect
124. #475C22semidirect
125. #475C22semidirect
128. #474C22semidirect
130. #470C22semidirect
132. #469C22semidirect
136. #468C22semidirect
140. #465C22semidirect
144. #464C22semidirect
148. #463C22semidirect
149. #462C22semidirect
150. #461C22semidirect
156. #452C22semidirect
157. #451C22semidirect
162. #449C22semidirect
163. #448C22semidirect
165. #446C22semidirect
166. #446C22semidirect
169. #441C22semidirect
170. #441C22semidirect
172. #440C22semidirect
173. #440C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
177. C4×SD16C22semidirect
178. C4×D8C22semidirect
180. #436C22semidirect
184. #435C22semidirect
186. #433C22semidirect
187. #432C22semidirect
188. #419C22semidirect
194. #417C22semidirect
195. #417C22semidirect
198. C2×#103C22semidirect
201. #405C22semidirect
202. C4×M16C22semidirect

Maximal subgroups

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

subgroupindex
#35622
#35442
#33762
#33752
#33702
#33692
#33322
#33302
#33272
#33232
#33212
#33192
#33172
#33162
#33152
#33142
#33082
#33062
#32422
#32412
#32392
#32252
#32242
#32192
#31832
#31792
#31782
#31412
#31372
#31362
#29672