Finite Group Databasebeta

← #62547

Subgroups — #62547

Order 256.

875 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3515C211yesmaximal, characteristic, complemented
2#3514C211yesmaximal, characteristic, complemented
3#3377C211yesmaximal, characteristic, complemented
4#3376C211yesmaximal, characteristic, complemented
5#3371C211yesmaximal, characteristic, complemented
6#3370C211yesmaximal, characteristic, complemented
7#3327C211yesmaximal, characteristic, complemented
8#3326C211yesmaximal, characteristic, complemented
9#3323C211yesmaximal, characteristic, complemented
10#3322C211yesmaximal, characteristic, complemented
11#3320C211yesmaximal, characteristic, complemented
12#3318C211yesmaximal, characteristic, complemented
13#3316C211yesmaximal, characteristic, complemented
14#3314C211yesmaximal, characteristic, complemented
15#3312C211yesmaximal, characteristic, complemented
16#3310C211yesmaximal, characteristic, complemented
17#3308C211yesmaximal, characteristic, complemented
18#3306C211yesmaximal, characteristic, complemented
19#3233C211yesmaximal, characteristic, complemented
20#3232C211yesmaximal, characteristic, complemented
21#3232C211yesmaximal, characteristic, complemented
22#3212C211yesmaximal, characteristic, complemented
23#3211C211yesmaximal, characteristic, complemented
24#3211C211yesmaximal, characteristic, complemented
25#3183C211yesmaximal, characteristic, complemented
26#3183C211yesmaximal, characteristic, complemented
27#3168C211yesmaximal, characteristic, complemented
28#3142C211yesmaximal, characteristic, complemented
29#3140C211yesmaximal, characteristic, complemented
30C2×#488C211yesmaximal, characteristic, complemented
31#2965C211yesmaximal, characteristic, complemented
32#559C2211yescharacteristic
33#557C2211yescharacteristic, complemented
34#556C2211yescharacteristic
35#555—21no—
36#554C2211yescharacteristic, complemented
37#554C2211yescharacteristic, complemented
38#553C2211yescharacteristic
39#553C2211yescharacteristic, complemented
40#552—21no—
41#552—21no—
42#552—21no—
43#552C2211yescharacteristic
44#552C2211yescharacteristic, complemented
45#551—21no—
46#551—21no—
47D4×Q8C2211yescharacteristic
48#548C2211yescharacteristic
49#548C2211yescharacteristic
50#547—21no—
51#547C2211yescharacteristic, complemented
52#546—21no—
53#546C2211yescharacteristic
54#546C2211yescharacteristic
55D42C2211yescharacteristic
56#542—21no—
57#541—21no—
58#539—21no—
59#539—21no—
60#538—21no—
61#538—21no—
62#533C2211yescharacteristic, complemented
63#532C2211yescharacteristic
64#529C2211yescharacteristic
65#529C2211yescharacteristic
66#529C2211yescharacteristic
67#529C2211yescharacteristic, complemented
68#529C2211yescharacteristic, complemented
69#529C2211yescharacteristic, complemented
70C2×#125C2211yescharacteristic, complemented
71C2×#125C2211yescharacteristic, complemented
72C2×#124C2211yescharacteristic
73C2×#124C2211yescharacteristic
74#520—21no—
75#518—21no—
76C4×#41C2211yescharacteristic
77#499C2211yescharacteristic, complemented
78#499C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#495C2211yescharacteristic
81#495C2211yescharacteristic, complemented
82#495C2211yescharacteristic, complemented
83#491C2211yescharacteristic, complemented
84#491C2211yescharacteristic, complemented
85#490C2211yescharacteristic
86#490C2211yescharacteristic
87#489C2211yescharacteristic
88#489C2211yescharacteristic
89#489C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#488C2211yescharacteristic
92#488C2211yescharacteristic
93#488C2211yescharacteristic
94#488C2211yescharacteristic
95#488C2211yescharacteristic
96#488C2211yescharacteristic, complemented
97#488C2211yescharacteristic, complemented
98#488C2211yescharacteristic, complemented
99#488C2211yescharacteristic, complemented
100#488C2211yescharacteristic, complemented
101#488C2211yescharacteristic, complemented
102#488C2211yescharacteristic, complemented
103#488C2211yescharacteristic, complemented
104#488C2211yescharacteristic, complemented
105#485C2211yescharacteristic, complemented
106#485C2211yescharacteristic, complemented
107#484C2211yescharacteristic, complemented
108#484C2211yescharacteristic, complemented
109#483C2211yescharacteristic, complemented
110#483C2211yescharacteristic, complemented
111#482C2211yescharacteristic
112#482C2211yescharacteristic
113#481C2211yescharacteristic
114#481C2211yescharacteristic
115#480C2211yescharacteristic
116#480C2211yescharacteristic
117#479C2211yescharacteristic, complemented
118#479C2211yescharacteristic, complemented
119#479C2211yescharacteristic, complemented
120#479C2211yescharacteristic, complemented
121#478C2211yescharacteristic
122#478C2211yescharacteristic
123#478C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#476C2211yescharacteristic, complemented
127#475C2211yescharacteristic, complemented
128#474C2211yescharacteristic, complemented
129#470C2211yescharacteristic, complemented
130#470C2211yescharacteristic, complemented
131#469C2211yescharacteristic
132#469C2211yescharacteristic
133#468C2211yescharacteristic
134#468C2211yescharacteristic
135#468C2211yescharacteristic, complemented
136#468C2211yescharacteristic, complemented
137#467C2211yescharacteristic, complemented
138#466C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic, complemented
141#464C2211yescharacteristic
142#464C2211yescharacteristic
143#464C2211yescharacteristic, complemented
144#464C2211yescharacteristic, complemented
145#463C2211yescharacteristic
146#463C2211yescharacteristic
147#463C2211yescharacteristic, complemented
148#463C2211yescharacteristic, complemented
149#462C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#460C2211yescharacteristic
152#459C2211yescharacteristic
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#451C2211yescharacteristic, complemented
156#451C2211yescharacteristic, complemented
157#450C2211yescharacteristic
158#450C2211yescharacteristic
159#449C2211yescharacteristic, complemented
160#449C2211yescharacteristic, complemented
161#448C2211yescharacteristic, complemented
162#448C2211yescharacteristic, complemented
163#447C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#442C2211yescharacteristic
168#442C2211yescharacteristic, complemented
169#441C2211yescharacteristic, complemented
170#441C2211yescharacteristic, complemented
171#440C2211yescharacteristic
172#440C2211yescharacteristic, complemented
173#440C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic, complemented
177C4×SD16C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic, complemented
180#436C2211yescharacteristic, complemented
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185#431C2211yescharacteristic, complemented
186#431C2211yescharacteristic, complemented
187#431C2211yescharacteristic, complemented
188#419C2211yescharacteristic, complemented
189#419C2211yescharacteristic, complemented
190#418C2211yescharacteristic
191#418C2211yescharacteristic
192#417C2211yescharacteristic, complemented
193#417C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196C2×#103C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic
199C2×#102C2211yescharacteristic
200C4×M16C2211yescharacteristic, complemented
201C4×M16C2211yescharacteristic, complemented
202C2×C4×C8C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41D411yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×D4—21no—
210C22×D4C2311yescharacteristic
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⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235#127C2311yescharacteristic
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#125C2311yescharacteristic
260#125C2311yescharacteristic
261#125C2311yescharacteristic
262#125C2311yescharacteristic
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#124—21no—
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#124—21no—
272#124C2311yescharacteristic
273#124C2311yescharacteristic
274#124C2311yescharacteristic
275#124C2311yescharacteristic
276#124C2311yescharacteristic
277#124C2311yescharacteristic
278#124C2311yescharacteristic
279#124C2311yescharacteristic
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—
295#123—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
315#121—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121C2311yescharacteristic
325#121C2311yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#120—21no—
331#120—21no—
332#120—21no—
333#120—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8D411yescharacteristic
338C4×Q8C2311yescharacteristic
339C4×Q8C2311yescharacteristic
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4D411yescharacteristic
361C4×D4D411yescharacteristic
362C4×D4D411yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117D411yescharacteristic
382#117D411yescharacteristic
383#117D411yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42C2311yescharacteristic
402C2×C42C2311yescharacteristic
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
472C4×C8C2311yescharacteristic
473C4×C8C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24—21no—
480#41—42no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—44no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—41no—
491C2×Q8—41no—
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—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—44no—
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—21no—
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—
555D8—41no—
556D8—41no—
557D8—41no—
558M16—41no—
559M16—41no—
560M16—41no—
561M16—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8C2411yescharacteristic
565C2×C8C2411yescharacteristic
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
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⋊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⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
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—42no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23C22×D411yescharacteristic
693C23C22×D411yescharacteristic
694C23C22×D411yescharacteristic
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—41no—
704Q8—42no—
705Q8—81no—
706Q8—81no—
707Q8—81no—
708D4—22no—
709D4—22no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—41no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731C2×C4—22no—
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—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
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—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—162no—
810C22—162no—
811C22#57512yes—
812C22C23×D411yescharacteristic
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4#58511yescharacteristic
837C4#58511yescharacteristic
838C2—22no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2—81no—
845C2#350011yescharacteristic
846C2C2×#57511yescharacteristic
847C2#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. #3514C2semidirect
3. #3377C2semidirect
4. #3376C2semidirect
5. #3371C2semidirect
6. #3370C2semidirect
7. #3327C2semidirect
8. #3326C2semidirect
9. #3323C2semidirect
10. #3322C2semidirect
11. #3320C2semidirect
12. #3318C2semidirect
13. #3316C2semidirect
14. #3314C2semidirect
15. #3312C2semidirect
16. #3310C2semidirect
17. #3308C2semidirect
18. #3306C2semidirect
19. #3233C2semidirect
20. #3232C2semidirect
21. #3232C2semidirect
22. #3212C2semidirect
23. #3211C2semidirect
24. #3211C2semidirect
25. #3183C2semidirect
26. #3183C2semidirect
27. #3168C2semidirect
28. #3142C2semidirect
29. #3140C2semidirect
30. C2×#488C2semidirect
31. #2965C2semidirect
33. #557C22semidirect
36. #554C22semidirect
37. #554C22semidirect
39. #553C22semidirect
44. #552C22semidirect
51. #547C22semidirect
62. #533C22semidirect
67. #529C22semidirect
68. #529C22semidirect
69. #529C22semidirect
70. C2×#125C22semidirect
71. C2×#125C22semidirect
77. #499C22semidirect
78. #499C22semidirect
79. #499C22semidirect
81. #495C22semidirect
82. #495C22semidirect
83. #491C22semidirect
84. #491C22semidirect
89. #489C22semidirect
90. #489C22semidirect
96. #488C22semidirect
97. #488C22semidirect
98. #488C22semidirect
99. #488C22semidirect
100. #488C22semidirect
101. #488C22semidirect
102. #488C22semidirect
103. #488C22semidirect
104. #488C22semidirect
105. #485C22semidirect
106. #485C22semidirect
107. #484C22semidirect
108. #484C22semidirect
109. #483C22semidirect
110. #483C22semidirect
117. #479C22semidirect
118. #479C22semidirect
119. #479C22semidirect
120. #479C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #477C22semidirect
126. #476C22semidirect
127. #475C22semidirect
128. #474C22semidirect
129. #470C22semidirect
130. #470C22semidirect
135. #468C22semidirect
136. #468C22semidirect
137. #467C22semidirect
140. #465C22semidirect
143. #464C22semidirect
144. #464C22semidirect
147. #463C22semidirect
148. #463C22semidirect
149. #462C22semidirect
150. #461C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #451C22semidirect
156. #451C22semidirect
159. #449C22semidirect
160. #449C22semidirect
161. #448C22semidirect
162. #448C22semidirect
165. #446C22semidirect
166. #446C22semidirect
168. #442C22semidirect
169. #441C22semidirect
170. #441C22semidirect
172. #440C22semidirect
173. #440C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
176. C4×SD16C22semidirect
177. C4×SD16C22semidirect
178. C4×D8C22semidirect
179. #436C22semidirect
180. #436C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #431C22semidirect
186. #431C22semidirect
187. #431C22semidirect
188. #419C22semidirect
189. #419C22semidirect
192. #417C22semidirect
193. #417C22semidirect
194. #417C22semidirect
195. #417C22semidirect
196. C2×#103C22semidirect
197. C2×#103C22semidirect
200. C4×M16C22semidirect
201. C4×M16C22semidirect
202. C2×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#35152
#35142
#33772
#33762
#33712
#33702
#33272
#33262
#33232
#33222
#33202
#33182
#33162
#33142
#33122
#33102
#33082
#33062
#32332
#32322
#32122
#32112
#31832
#31682
#31422
#31402
C2×#4882
#29652