Finite Group Databasebeta

← #62159

Subgroups — #62159

Order 256.

856 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic, complemented
2#3514C211yesmaximal, characteristic, complemented
3#3386C211yesmaximal, characteristic, complemented
4#3384C211yesmaximal, characteristic, complemented
5#3371C211yesmaximal, characteristic, complemented
6#3370C211yesmaximal, characteristic, complemented
7#3350C211yesmaximal, characteristic, complemented
8#3349C211yesmaximal, characteristic, complemented
9#3348C211yesmaximal, characteristic, complemented
10#3347C211yesmaximal, characteristic, complemented
11#3341C211yesmaximal, characteristic, complemented
12#3340C211yesmaximal, characteristic, complemented
13#3319C211yesmaximal, characteristic, complemented
14#3318C211yesmaximal, characteristic, complemented
15#3311C211yesmaximal, characteristic, complemented
16#3310C211yesmaximal, characteristic, complemented
17#3297C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3263C211yesmaximal, characteristic, complemented
20#3262C211yesmaximal, characteristic, complemented
21#3247C211yesmaximal, characteristic, complemented
22#3244C211yesmaximal, characteristic, complemented
23#3243C211yesmaximal, characteristic, complemented
24#3235C211yesmaximal, characteristic, complemented
25#3118C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3111C211yesmaximal, characteristic, complemented
28#3081C211yesmaximal, characteristic, complemented
29#3081C211yesmaximal, characteristic, complemented
30#3076C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#559C2211yescharacteristic
35#557C2211yescharacteristic, complemented
36#556—21no—
37#556C2211yescharacteristic
38#556C2211yescharacteristic, complemented
39#555C2211yescharacteristic
40#555C2211yescharacteristic
41#555C2211yescharacteristic, complemented
42#554C2211yescharacteristic, complemented
43#553C2211yescharacteristic
44#553C2211yescharacteristic, complemented
45#552—21no—
46#552C2211yescharacteristic
47#552C2211yescharacteristic, complemented
48#551—21no—
49#551—21no—
50D4×Q8C2211yescharacteristic
51#548—21no—
52#546—21no—
53#546C2211yescharacteristic
54#546C2211yescharacteristic
55D42C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#544C2211yescharacteristic, complemented
58#542—21no—
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic
62#542C2211yescharacteristic, complemented
63#542C2211yescharacteristic, complemented
64#541—21no—
65#539—21no—
66#538—21no—
67#538—21no—
68#533C2211yescharacteristic, complemented
69#532C2211yescharacteristic
70#529—21no—
71#529C2211yescharacteristic
72#529C2211yescharacteristic, complemented
73C2×#124—21no—
74#518C2211yescharacteristic
75#518C2211yescharacteristic
76C4×#41C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#501C2211yescharacteristic, complemented
80#501C2211yescharacteristic, complemented
81#500C2211yescharacteristic, complemented
82#498C2211yescharacteristic, complemented
83#490C2211yescharacteristic
84#490C2211yescharacteristic
85#489C2211yescharacteristic, complemented
86#489C2211yescharacteristic, complemented
87#488C2211yescharacteristic, complemented
88#488C2211yescharacteristic, complemented
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#484C2211yescharacteristic, complemented
95#483C2211yescharacteristic, complemented
96#482C2211yescharacteristic
97#482C2211yescharacteristic
98#482C2211yescharacteristic, complemented
99#482C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#482C2211yescharacteristic, complemented
104#482C2211yescharacteristic, complemented
105#481C2211yescharacteristic
106#480C2211yescharacteristic
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#478C2211yescharacteristic
111#478C2211yescharacteristic
112#478C2211yescharacteristic
113#478C2211yescharacteristic
114#478C2211yescharacteristic
115#478C2211yescharacteristic, complemented
116#478C2211yescharacteristic, complemented
117#478C2211yescharacteristic, complemented
118#478C2211yescharacteristic, complemented
119#477C2211yescharacteristic, complemented
120#477C2211yescharacteristic, complemented
121#477C2211yescharacteristic, complemented
122#476C2211yescharacteristic
123#476C2211yescharacteristic
124#476C2211yescharacteristic, complemented
125#476C2211yescharacteristic, complemented
126#476C2211yescharacteristic, complemented
127#476C2211yescharacteristic, complemented
128#476C2211yescharacteristic, complemented
129#475C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#474C2211yescharacteristic
132#474C2211yescharacteristic
133#474C2211yescharacteristic, complemented
134#474C2211yescharacteristic, complemented
135#474C2211yescharacteristic, complemented
136#474C2211yescharacteristic, complemented
137#470C2211yescharacteristic, complemented
138#469C2211yescharacteristic
139#468C2211yescharacteristic
140#468C2211yescharacteristic, complemented
141#467C2211yescharacteristic, complemented
142#466C2211yescharacteristic
143#466C2211yescharacteristic, complemented
144#466C2211yescharacteristic, complemented
145#465C2211yescharacteristic
146#465C2211yescharacteristic, complemented
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#464C2211yescharacteristic, complemented
151#464C2211yescharacteristic, complemented
152#463C2211yescharacteristic
153#463C2211yescharacteristic, complemented
154#463C2211yescharacteristic, complemented
155#463C2211yescharacteristic, complemented
156#463C2211yescharacteristic, complemented
157#460C2211yescharacteristic
158#459C2211yescharacteristic
159#452C2211yescharacteristic
160#450C2211yescharacteristic
161#450C2211yescharacteristic
162#449C2211yescharacteristic
163#447C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#442C2211yescharacteristic
168#442C2211yescharacteristic
169#442C2211yescharacteristic, complemented
170#441C2211yescharacteristic, complemented
171#440C2211yescharacteristic
172#440C2211yescharacteristic
173#440C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic
176C4×SD16C2211yescharacteristic, complemented
177C4×D8C2211yescharacteristic
178C4×D8C2211yescharacteristic, complemented
179#435C2211yescharacteristic
180#435C2211yescharacteristic
181#435C2211yescharacteristic, complemented
182#435C2211yescharacteristic, complemented
183C8×D4C2211yescharacteristic, complemented
184C8×D4C2211yescharacteristic, complemented
185#433C2211yescharacteristic, complemented
186#433C2211yescharacteristic, complemented
187#432C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189#428C2211yescharacteristic, complemented
190#427C2211yescharacteristic, complemented
191#427C2211yescharacteristic, complemented
192#427C2211yescharacteristic, complemented
193#427C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#418C2211yescharacteristic
198#418C2211yescharacteristic
199#416C2211yescharacteristic
200#416C2211yescharacteristic
201C2×#102C2211yescharacteristic
202C2×#102C2211yescharacteristic
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C22×Q8—21no—
206C22×D4—21no—
207C22×D4C2311yescharacteristic
208C22×D4C2311yescharacteristic
209C2×Q16C2311yescharacteristic
210C2×SD16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×D8C2311yescharacteristic
215C2×D8C2311yescharacteristic
216C2×D8C2311yescharacteristic
217C2×M16C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C22×C8C2311yescharacteristic
220C22×C8C2311yescharacteristic
221C22×C8C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233#127C2311yescharacteristic
234#126—21no—
235#126—21no—
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#126D411yescharacteristic
248#126D411yescharacteristic
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125—21no—
255#125D411yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#125C2311yescharacteristic
260#125C2311yescharacteristic
261#124—21no—
262#124—21no—
263#124—21no—
264#124—21no—
265#124—21no—
266#124—21no—
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#124D411yescharacteristic
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#123D411yescharacteristic
293#123D411yescharacteristic
294C22⋊Q8—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⋊Q8—21no—
310C22⋊Q8D411yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
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#121—21no—
325#121D411yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#120—21no—
334#120—21no—
335#120—21no—
336#120—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
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×D4C2311yescharacteristic
360C4×D4C2311yescharacteristic
361C4×D4C2311yescharacteristic
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C42—21no—
399C2×C42C2311yescharacteristic
400#107C2311yescharacteristic
401#107C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#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
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24—21no—
480#41—22no—
481#41—41no—
482#41—82no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—82no—
491C2×Q8C2×D411yescharacteristic
492C2×Q8C2411yescharacteristic
493C2×Q8C2411yescharacteristic
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
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—41no—
509C2×D4—41no—
510C2×D4—82no—
511C2×D4C2×D411yescharacteristic
512C2×D4C2×D411yescharacteristic
513C2×D4C2×D411yescharacteristic
514C2×D4C2411yescharacteristic
515C2×D4C2411yescharacteristic
516C2×D4C2411yescharacteristic
517C2×D4C2411yescharacteristic
518C22×C4—21no—
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×C4—21no—
532C22×C4C2×D411yescharacteristic
533C22×C4C2×D411yescharacteristic
534C22×C4C2411yescharacteristic
535C22×C4C2411yescharacteristic
536C22×C4C2411yescharacteristic
537Q16—41no—
538SD16—22no—
539SD16—41no—
540SD16—41no—
541SD16—41no—
542D8—22no—
543D8—41no—
544D8—41no—
545M16—41no—
546M16—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8C2411yescharacteristic
552C2×C8C2411yescharacteristic
553C2×C8C2411yescharacteristic
554C2×C8C2411yescharacteristic
555C2×C8C2411yescharacteristic
556C2×C8C2411yescharacteristic
557C2×C8C2411yescharacteristic
558C2×C8C2411yescharacteristic
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4C2×D411yescharacteristic
589C4⋊C4C2×D411yescharacteristic
590C4⋊C4C2×D411yescharacteristic
591C4⋊C4C2×D411yescharacteristic
592C4⋊C4C2×D411yescharacteristic
593C4⋊C4C2×D411yescharacteristic
594C4⋊C4C2×D411yescharacteristic
595C4⋊C4C2×D411yescharacteristic
596C4⋊C4C2×D411yescharacteristic
597C4⋊C4C2×D411yescharacteristic
598C4⋊C4C2411yescharacteristic
599C4⋊C4C2411yescharacteristic
600C4⋊C4C2411yescharacteristic
601C4⋊C4C2411yescharacteristic
602C4⋊C4C2411yescharacteristic
603C4⋊C4C2411yescharacteristic
604C4⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4C2×D411yescharacteristic
645C22⋊C4C2×D411yescharacteristic
646C22⋊C4C2×D411yescharacteristic
647C22⋊C4C2×D411yescharacteristic
648C22⋊C4C2×D411yescharacteristic
649C22⋊C4C2×D411yescharacteristic
650C22⋊C4C2×D411yescharacteristic
651C22⋊C4C2×D411yescharacteristic
652C22⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42C2×D411yescharacteristic
667C42C2×D411yescharacteristic
668C42C2411yescharacteristic
669C42C2411yescharacteristic
670C42C2411yescharacteristic
671C42C2411yescharacteristic
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—42no—
677C23—42no—
678C23—81no—
679C23—81no—
680C23—81no—
681C23—81no—
682C23C22×D411yescharacteristic
683C23C22×D411yescharacteristic
684C23C22×D411yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—41no—
690Q8—42no—
691Q8—81no—
692Q8—81no—
693Q8—81no—
694Q8—81no—
695Q8—81no—
696Q8—81no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—81no—
712D4—81no—
713D4—81no—
714D4—81no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—81no—
719D42−1+412yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—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—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
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×C4C22×D411yescharacteristic
755C2×C4C22×D411yescharacteristic
756C2×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
766C8—21no—
767C8—21no—
768C8—21no—
769C8—21no—
770C8—21no—
771C8—21no—
772C8—21no—
773C8—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—162no—
796C22—162no—
797C22C23×D411yescharacteristic
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4C2×2−1+411yescharacteristic
822C4#58511yescharacteristic
823C2—41no—
824C2—41no—
825C2—41no—
826C2—42no—
827C2—81no—
828C2—81no—
829C2—81no—
830C2#348911yescharacteristic
831C2#358411yescharacteristic
832C2#358511yescharacteristic
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. #3565C2semidirect
2. #3514C2semidirect
3. #3386C2semidirect
4. #3384C2semidirect
5. #3371C2semidirect
6. #3370C2semidirect
7. #3350C2semidirect
8. #3349C2semidirect
9. #3348C2semidirect
10. #3347C2semidirect
11. #3341C2semidirect
12. #3340C2semidirect
13. #3319C2semidirect
14. #3318C2semidirect
15. #3311C2semidirect
16. #3310C2semidirect
17. #3297C2semidirect
18. #3296C2semidirect
19. #3263C2semidirect
20. #3262C2semidirect
21. #3247C2semidirect
22. #3244C2semidirect
23. #3243C2semidirect
24. #3235C2semidirect
25. #3118C2semidirect
26. #3118C2semidirect
27. #3111C2semidirect
28. #3081C2semidirect
29. #3081C2semidirect
30. #3076C2semidirect
31. #2992C2semidirect
35. #557C22semidirect
38. #556C22semidirect
41. #555C22semidirect
42. #554C22semidirect
44. #553C22semidirect
47. #552C22semidirect
56. #544C22semidirect
57. #544C22semidirect
62. #542C22semidirect
63. #542C22semidirect
68. #533C22semidirect
72. #529C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #501C22semidirect
80. #501C22semidirect
81. #500C22semidirect
82. #498C22semidirect
85. #489C22semidirect
86. #489C22semidirect
87. #488C22semidirect
88. #488C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #484C22semidirect
95. #483C22semidirect
98. #482C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #482C22semidirect
102. #482C22semidirect
103. #482C22semidirect
104. #482C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
115. #478C22semidirect
116. #478C22semidirect
117. #478C22semidirect
118. #478C22semidirect
119. #477C22semidirect
120. #477C22semidirect
121. #477C22semidirect
124. #476C22semidirect
125. #476C22semidirect
126. #476C22semidirect
127. #476C22semidirect
128. #476C22semidirect
129. #475C22semidirect
130. #475C22semidirect
133. #474C22semidirect
134. #474C22semidirect
135. #474C22semidirect
136. #474C22semidirect
137. #470C22semidirect
140. #468C22semidirect
141. #467C22semidirect
143. #466C22semidirect
144. #466C22semidirect
146. #465C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #464C22semidirect
151. #464C22semidirect
153. #463C22semidirect
154. #463C22semidirect
155. #463C22semidirect
156. #463C22semidirect
165. #446C22semidirect
166. #446C22semidirect
169. #442C22semidirect
170. #441C22semidirect
173. #440C22semidirect
174. #440C22semidirect
176. C4×SD16C22semidirect
178. C4×D8C22semidirect
181. #435C22semidirect
182. #435C22semidirect
183. C8×D4C22semidirect
184. C8×D4C22semidirect
185. #433C22semidirect
186. #433C22semidirect
187. #432C22semidirect
188. #428C22semidirect
189. #428C22semidirect
190. #427C22semidirect
191. #427C22semidirect
192. #427C22semidirect
193. #427C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#35652
#35142
#33862
#33842
#33712
#33702
#33502
#33492
#33482
#33472
#33412
#33402
#33192
#33182
#33112
#33102
#32972
#32962
#32632
#32622
#32472
#32442
#32432
#32352
#31182
#31112
#30812
#30762
#29922