Finite Group Databasebeta

← #62612

Subgroups — #62612

Order 256.

835 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#3563C211yesmaximal, characteristic, complemented
2#3562C211yesmaximal, characteristic
3#3377C211yesmaximal, characteristic, complemented
4#3371C211yesmaximal, characteristic, complemented
5#3365C211yesmaximal, characteristic, complemented
6#3364C211yesmaximal, characteristic, complemented
7#3333C211yesmaximal, characteristic, complemented
8#3331C211yesmaximal, characteristic, complemented
9#3327C211yesmaximal, characteristic, complemented
10#3327C211yesmaximal, characteristic, complemented
11#3323C211yesmaximal, characteristic, complemented
12#3323C211yesmaximal, characteristic, complemented
13#3317C211yesmaximal, characteristic, complemented
14#3316C211yesmaximal, characteristic, complemented
15#3315C211yesmaximal, characteristic, complemented
16#3314C211yesmaximal, characteristic, complemented
17#3300C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3242C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3232C211yesmaximal, characteristic, complemented
22#3223C211yesmaximal, characteristic, complemented
23#3222C211yesmaximal, characteristic, complemented
24#3210C211yesmaximal, characteristic, complemented
25#3177C211yesmaximal, characteristic, complemented
26#3174C211yesmaximal, characteristic, complemented
27#3172C211yesmaximal, characteristic, complemented
28#3142C211yesmaximal, characteristic, complemented
29#3137C211yesmaximal, characteristic, complemented
30#3136C211yesmaximal, characteristic, complemented
31#2969C211yesmaximal, characteristic, complemented
32#564—21no—
33#563—21no—
34#562—21no—
35#560—21no—
36#559C2211yescharacteristic
37#557C2211yescharacteristic, complemented
38#557C2211yescharacteristic, complemented
39#556C2211yescharacteristic
40#554C2211yescharacteristic
41#554C2211yescharacteristic, complemented
42#553—21no—
43#552—21no—
44#552—21no—
45#552C2211yescharacteristic
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic, complemented
49#551—21no—
50#550C2211yescharacteristic
51#548C2211yescharacteristic
52#548C2211yescharacteristic
53#547C2211yescharacteristic
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#544—21no—
57#544C2211yescharacteristic
58#544C2211yescharacteristic, complemented
59#541—21no—
60#541—21no—
61#541C2211yescharacteristic
62#541C2211yescharacteristic
63#541C2211yescharacteristic, complemented
64#540—21no—
65#540C2211yescharacteristic
66#539—21no—
67#539—21no—
68#538—21no—
69#538—21no—
70#536C2211yescharacteristic
71#535C2211yescharacteristic
72#533C2211yescharacteristic, complemented
73#532C2211yescharacteristic
74#529C2211yescharacteristic
75#529C2211yescharacteristic
76C2×#125C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#499C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#497C2211yescharacteristic
81#494C2211yescharacteristic, complemented
82#492C2211yescharacteristic
83#491C2211yescharacteristic, complemented
84#491C2211yescharacteristic, complemented
85#491C2211yescharacteristic, complemented
86#491C2211yescharacteristic, complemented
87#490C2211yescharacteristic
88#490C2211yescharacteristic
89#490C2211yescharacteristic
90#489C2211yescharacteristic
91#489C2211yescharacteristic
92#489C2211yescharacteristic
93#488C2211yescharacteristic
94#488C2211yescharacteristic
95#488C2211yescharacteristic
96#488C2211yescharacteristic
97#488C2211yescharacteristic
98#488C2211yescharacteristic
99#488C2211yescharacteristic, complemented
100#488C2211yescharacteristic, complemented
101#487C2211yescharacteristic, complemented
102#487C2211yescharacteristic, complemented
103#486C2211yescharacteristic
104#486C2211yescharacteristic
105#485C2211yescharacteristic
106#485C2211yescharacteristic
107#484C2211yescharacteristic
108#484C2211yescharacteristic, complemented
109#483C2211yescharacteristic
110#483C2211yescharacteristic, complemented
111#482C2211yescharacteristic
112#482C2211yescharacteristic, complemented
113#481C2211yescharacteristic
114#481C2211yescharacteristic
115#480C2211yescharacteristic
116#480C2211yescharacteristic, complemented
117#479C2211yescharacteristic, complemented
118#479C2211yescharacteristic, complemented
119#479C2211yescharacteristic, complemented
120#479C2211yescharacteristic, complemented
121#478C2211yescharacteristic
122#478C2211yescharacteristic
123#478C2211yescharacteristic
124#478C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#476C2211yescharacteristic, complemented
127#475C2211yescharacteristic, complemented
128#474C2211yescharacteristic
129#470C2211yescharacteristic
130#470C2211yescharacteristic
131#470C2211yescharacteristic, complemented
132#470C2211yescharacteristic, complemented
133#468C2211yescharacteristic
134#468C2211yescharacteristic
135#468C2211yescharacteristic
136#468C2211yescharacteristic, complemented
137#467C2211yescharacteristic
138#467C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic, complemented
141#464C2211yescharacteristic
142#464C2211yescharacteristic
143#464C2211yescharacteristic
144#464C2211yescharacteristic
145#464C2211yescharacteristic
146#464C2211yescharacteristic
147#464C2211yescharacteristic, complemented
148#464C2211yescharacteristic, complemented
149#462C2211yescharacteristic, complemented
150#462C2211yescharacteristic, complemented
151#460C2211yescharacteristic
152#460C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic
158#452C2211yescharacteristic
159#452C2211yescharacteristic, complemented
160#452C2211yescharacteristic, complemented
161#451C2211yescharacteristic, complemented
162#451C2211yescharacteristic, complemented
163#450C2211yescharacteristic
164#450C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166C8×Q8C2211yescharacteristic, complemented
167#441C2211yescharacteristic, complemented
168#441C2211yescharacteristic, complemented
169#440C2211yescharacteristic
170#440C2211yescharacteristic, complemented
171C4×Q16C2211yescharacteristic, complemented
172C4×Q16C2211yescharacteristic, complemented
173C4×Q16C2211yescharacteristic, complemented
174C4×Q16C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic
178C4×SD16C2211yescharacteristic, complemented
179#436C2211yescharacteristic
180#436C2211yescharacteristic
181#436C2211yescharacteristic, complemented
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184C8×D4C2211yescharacteristic
185#433C2211yescharacteristic
186#433C2211yescharacteristic, complemented
187#431C2211yescharacteristic, 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×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4C2311yescharacteristic
209C2×Q16C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C2×M16C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237#127—21no—
238#127C2311yescharacteristic
239#127C2311yescharacteristic
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#126D411yescharacteristic
254#126D411yescharacteristic
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#125—21no—
265#125—21no—
266#125—21no—
267#125—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125—21no—
272#125—21no—
273#125—21no—
274#125—21no—
275#125—21no—
276#125D411yescharacteristic
277#125C2311yescharacteristic
278#125C2311yescharacteristic
279#125C2311yescharacteristic
280#125C2311yescharacteristic
281#125C2311yescharacteristic
282#125C2311yescharacteristic
283#125C2311yescharacteristic
284#124—21no—
285#124—21no—
286#124—21no—
287#124D411yescharacteristic
288#124C2311yescharacteristic
289#124C2311yescharacteristic
290#124C2311yescharacteristic
291#124C2311yescharacteristic
292#124C2311yescharacteristic
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#123—21no—
307#123—21no—
308#123D411yescharacteristic
309#123D411yescharacteristic
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⋊Q8D411yescharacteristic
325C22⋊Q8C2311yescharacteristic
326C22⋊Q8C2311yescharacteristic
327C22⋊Q8C2311yescharacteristic
328C22⋊Q8C2311yescharacteristic
329C22⋊Q8C2311yescharacteristic
330C22⋊Q8C2311yescharacteristic
331C22⋊Q8C2311yescharacteristic
332C22⋊Q8C2311yescharacteristic
333C22⋊Q8C2311yescharacteristic
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#120—21no—
352#120—21no—
353#120—21no—
354#120—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8C2311yescharacteristic
359C4×Q8C2311yescharacteristic
360C4×Q8C2311yescharacteristic
361C4×Q8C2311yescharacteristic
362C4×Q8C2311yescharacteristic
363C4×Q8C2311yescharacteristic
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
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#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#103C2311yescharacteristic
443#103C2311yescharacteristic
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
472C4×C8C2311yescharacteristic
473C4×C8C2311yescharacteristic
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—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8C2×D411yescharacteristic
494C2×Q8C2411yescharacteristic
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—41no—
512C2×D4—41no—
513C2×D4C2×D411yescharacteristic
514C2×D4C2×D411yescharacteristic
515C2×D4C2×D411yescharacteristic
516C2×D4C2411yescharacteristic
517C2×D4C2411yescharacteristic
518C2×D4C2411yescharacteristic
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4C2×D411yescharacteristic
532C22×C4C2×D411yescharacteristic
533C22×C4C2411yescharacteristic
534C22×C4C2411yescharacteristic
535C22×C4C2411yescharacteristic
536Q16—41no—
537Q16—41no—
538Q16—41no—
539Q16—41no—
540Q16—41no—
541Q16—41no—
542SD16—41no—
543SD16—41no—
544SD16—41no—
545SD16—41no—
546SD16—41no—
547SD16—41no—
548M16—41no—
549M16—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⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C22⋊C4C2×D411yescharacteristic
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42C2×D411yescharacteristic
674C42C2×D411yescharacteristic
675C42C2411yescharacteristic
676C42C2411yescharacteristic
677C42C2411yescharacteristic
678C42C2411yescharacteristic
679C23—21no—
680C23—21no—
681C23—21no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23C22×D411yescharacteristic
686C23C22×D411yescharacteristic
687C23C22×D411yescharacteristic
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—21no—
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—41no—
699Q8—81no—
700Q8—81no—
701Q8—81no—
702Q8—81no—
703D4—21no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—81no—
713D4—81no—
714D4—81no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—81no—
722D4—81no—
723D4—81no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×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—162no—
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#350011yescharacteristic
830C2#358411yescharacteristic
831C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3562C2
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. #3563C2semidirect
3. #3377C2semidirect
4. #3371C2semidirect
5. #3365C2semidirect
6. #3364C2semidirect
7. #3333C2semidirect
8. #3331C2semidirect
9. #3327C2semidirect
10. #3327C2semidirect
11. #3323C2semidirect
12. #3323C2semidirect
13. #3317C2semidirect
14. #3316C2semidirect
15. #3315C2semidirect
16. #3314C2semidirect
17. #3300C2semidirect
18. #3296C2semidirect
19. #3242C2semidirect
20. #3241C2semidirect
21. #3232C2semidirect
22. #3223C2semidirect
23. #3222C2semidirect
24. #3210C2semidirect
25. #3177C2semidirect
26. #3174C2semidirect
27. #3172C2semidirect
28. #3142C2semidirect
29. #3137C2semidirect
30. #3136C2semidirect
31. #2969C2semidirect
37. #557C22semidirect
38. #557C22semidirect
41. #554C22semidirect
48. #552C22semidirect
58. #544C22semidirect
63. #541C22semidirect
72. #533C22semidirect
76. C2×#125C22semidirect
77. #501C22semidirect
78. #499C22semidirect
79. #499C22semidirect
81. #494C22semidirect
83. #491C22semidirect
84. #491C22semidirect
85. #491C22semidirect
86. #491C22semidirect
99. #488C22semidirect
100. #488C22semidirect
101. #487C22semidirect
102. #487C22semidirect
108. #484C22semidirect
110. #483C22semidirect
112. #482C22semidirect
116. #480C22semidirect
117. #479C22semidirect
118. #479C22semidirect
119. #479C22semidirect
120. #479C22semidirect
124. #478C22semidirect
125. #477C22semidirect
126. #476C22semidirect
127. #475C22semidirect
131. #470C22semidirect
132. #470C22semidirect
136. #468C22semidirect
140. #465C22semidirect
147. #464C22semidirect
148. #464C22semidirect
149. #462C22semidirect
150. #462C22semidirect
159. #452C22semidirect
160. #452C22semidirect
161. #451C22semidirect
162. #451C22semidirect
165. #446C22semidirect
166. C8×Q8C22semidirect
167. #441C22semidirect
168. #441C22semidirect
170. #440C22semidirect
171. C4×Q16C22semidirect
172. C4×Q16C22semidirect
173. C4×Q16C22semidirect
174. C4×Q16C22semidirect
178. C4×SD16C22semidirect
181. #436C22semidirect
183. #435C22semidirect
186. #433C22semidirect
187. #431C22semidirect
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
#35632
#35622
#33772
#33712
#33652
#33642
#33332
#33312
#33272
#33232
#33172
#33162
#33152
#33142
#33002
#32962
#32422
#32412
#32322
#32232
#32222
#32102
#31772
#31742
#31722
#31422
#31372
#31362
#29692