Finite Group Databasebeta

← #60998

Subgroups — #60998

Order 256.

875 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3510C211yesmaximal, characteristic, complemented
2#3460C211yesmaximal, characteristic, complemented
3#3256C211yesmaximal, characteristic, complemented
4#3251C211yesmaximal, characteristic, complemented
5#3250C211yesmaximal, characteristic, complemented
6#3247C211yesmaximal, characteristic, complemented
7#3244C211yesmaximal, characteristic, complemented
8#3243C211yesmaximal, characteristic, complemented
9#3240C211yesmaximal, characteristic, complemented
10#3228C211yesmaximal, characteristic, complemented
11#3224C211yesmaximal, characteristic, complemented
12#3224C211yesmaximal, characteristic, complemented
13#3213C211yesmaximal, characteristic, complemented
14#3211C211yesmaximal, characteristic, complemented
15#3201C211yesmaximal, characteristic, complemented
16#3200C211yesmaximal, characteristic, complemented
17#3199C211yesmaximal, characteristic, complemented
18#3198C211yesmaximal, characteristic, complemented
19#3179C211yesmaximal, characteristic, complemented
20#3179C211yesmaximal, characteristic, complemented
21#3175C211yesmaximal, characteristic, complemented
22#3173C211yesmaximal, characteristic, complemented
23#3126C211yesmaximal, characteristic, complemented
24#3122C211yesmaximal, characteristic, complemented
25#3121C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3114C211yesmaximal, characteristic, complemented
28#3111C211yesmaximal, characteristic, complemented
29#3105C211yesmaximal, characteristic, complemented
30#3102C211yesmaximal, characteristic, complemented
31#2925C211yesmaximal, characteristic, complemented
32#559—21no—
33#559—21no—
34#556—21no—
35#556—21no—
36#551—21no—
37#551—21no—
38#551—21no—
39#551—21no—
40#544C2211yescharacteristic, complemented
41#542—21no—
42#542C2211yescharacteristic
43#542C2211yescharacteristic
44#542C2211yescharacteristic
45#542C2211yescharacteristic, complemented
46#542C2211yescharacteristic, complemented
47#542C2211yescharacteristic, complemented
48#540—21no—
49#540C2211yescharacteristic
50#540C2211yescharacteristic, complemented
51#538—21no—
52#538—21no—
53#537C2211yescharacteristic
54#536C2211yescharacteristic
55#535C2211yescharacteristic
56#535C2211yescharacteristic
57#535C2211yescharacteristic, complemented
58#533C2211yescharacteristic, complemented
59#532—21no—
60#532C2211yescharacteristic
61#532C2211yescharacteristic, complemented
62#529—21no—
63#529C2211yescharacteristic
64#529C2211yescharacteristic
65#529C2211yescharacteristic
66#529C2211yescharacteristic, complemented
67#529C2211yescharacteristic, complemented
68#529C2211yescharacteristic, complemented
69C2×#124C2211yescharacteristic, complemented
70#525—21no—
71#525—21no—
72#519C2211yescharacteristic, complemented
73#518C2211yescharacteristic, complemented
74C4×#41C2211yescharacteristic
75C4×#41C2211yescharacteristic, complemented
76C2×C4×D4C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#498C2211yescharacteristic, complemented
81#496C2211yescharacteristic
82#496C2211yescharacteristic
83#495C2211yescharacteristic
84#495C2211yescharacteristic
85#489C2211yescharacteristic, complemented
86#489C2211yescharacteristic, complemented
87#489C2211yescharacteristic, complemented
88#489C2211yescharacteristic, complemented
89#488C2211yescharacteristic, complemented
90#488C2211yescharacteristic, complemented
91#486C2211yescharacteristic, complemented
92#486C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#482C2211yescharacteristic
100#482C2211yescharacteristic
101#482C2211yescharacteristic
102#482C2211yescharacteristic
103#482C2211yescharacteristic
104#482C2211yescharacteristic
105#482C2211yescharacteristic, complemented
106#482C2211yescharacteristic, complemented
107#481C2211yescharacteristic
108#480C2211yescharacteristic
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#479C2211yescharacteristic, complemented
112#479C2211yescharacteristic, complemented
113#478C2211yescharacteristic, complemented
114#478C2211yescharacteristic, complemented
115#478C2211yescharacteristic, complemented
116#478C2211yescharacteristic, complemented
117#478C2211yescharacteristic, complemented
118#478C2211yescharacteristic, complemented
119#478C2211yescharacteristic, complemented
120#478C2211yescharacteristic, complemented
121#477C2211yescharacteristic, complemented
122#476C2211yescharacteristic, complemented
123#475C2211yescharacteristic, complemented
124#474C2211yescharacteristic, complemented
125#470C2211yescharacteristic, complemented
126#469C2211yescharacteristic
127#469C2211yescharacteristic
128#469C2211yescharacteristic, complemented
129#468C2211yescharacteristic, complemented
130#468C2211yescharacteristic, complemented
131#468C2211yescharacteristic, complemented
132#468C2211yescharacteristic, complemented
133#467C2211yescharacteristic, complemented
134#466C2211yescharacteristic
135#466C2211yescharacteristic
136#466C2211yescharacteristic, complemented
137#465C2211yescharacteristic, complemented
138#465C2211yescharacteristic, complemented
139#465C2211yescharacteristic, complemented
140#465C2211yescharacteristic, complemented
141#464C2211yescharacteristic, complemented
142#464C2211yescharacteristic, complemented
143#464C2211yescharacteristic, complemented
144#464C2211yescharacteristic, complemented
145#463C2211yescharacteristic
146#463C2211yescharacteristic
147#463C2211yescharacteristic
148#463C2211yescharacteristic
149#463C2211yescharacteristic
150#463C2211yescharacteristic
151#463C2211yescharacteristic, complemented
152#463C2211yescharacteristic, complemented
153#460C2211yescharacteristic, complemented
154#460C2211yescharacteristic, complemented
155#459C2211yescharacteristic
156#459C2211yescharacteristic
157#452C2211yescharacteristic, complemented
158#452C2211yescharacteristic, complemented
159#451C2211yescharacteristic, complemented
160#450C2211yescharacteristic, complemented
161#450C2211yescharacteristic, complemented
162#450C2211yescharacteristic, complemented
163#449C2211yescharacteristic
164#449C2211yescharacteristic
165#448C2211yescharacteristic
166#448C2211yescharacteristic
167#448C2211yescharacteristic, complemented
168#447C2211yescharacteristic
169#447C2211yescharacteristic
170#447C2211yescharacteristic
171#447C2211yescharacteristic
172#447C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#442C2211yescharacteristic
175#442C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#440C2211yescharacteristic, complemented
178#440C2211yescharacteristic, complemented
179#440C2211yescharacteristic, complemented
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic, complemented
183C4×SD16C2211yescharacteristic, complemented
184C4×SD16C2211yescharacteristic, complemented
185C4×SD16C2211yescharacteristic, complemented
186C4×D8C2211yescharacteristic
187C4×D8C2211yescharacteristic
188C4×D8C2211yescharacteristic, complemented
189#433C2211yescharacteristic, complemented
190#433C2211yescharacteristic, complemented
191#433C2211yescharacteristic, complemented
192#433C2211yescharacteristic, complemented
193#432C2211yescharacteristic, complemented
194#432C2211yescharacteristic, complemented
195#431C2211yescharacteristic, complemented
196#431C2211yescharacteristic, complemented
197#423C2211yescharacteristic, complemented
198C2×C4⋊C8C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#405C2211yescharacteristic, complemented
202#405C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4C2311yescharacteristic
209C22×D4C2311yescharacteristic
210C23×C4—21no—
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×D8C2311yescharacteristic
222C2×D8C2311yescharacteristic
223C2×D8C2311yescharacteristic
224C2×D8C2311yescharacteristic
225C2×D8C2311yescharacteristic
226C2×D8C2311yescharacteristic
227C2×M16C2311yescharacteristic
228C2×M16C2311yescharacteristic
229C22×C8C2311yescharacteristic
230C22×C8C2311yescharacteristic
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237#127—21no—
238#127—21no—
239#127C2311yescharacteristic
240#127C2311yescharacteristic
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#125—21no—
254#125C2311yescharacteristic
255#125C2311yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#124—21no—
259#124—21no—
260#124—21no—
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#124C2311yescharacteristic
272#124C2311yescharacteristic
273#124C2311yescharacteristic
274#124C2311yescharacteristic
275#124C2311yescharacteristic
276#124C2311yescharacteristic
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8C2311yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309C22⋊Q8C2311yescharacteristic
310C22⋊Q8C2311yescharacteristic
311C22⋊Q8C2311yescharacteristic
312#121—21no—
313#121—21no—
314#121—21no—
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#121C2311yescharacteristic
324#121C2311yescharacteristic
325#121C2311yescharacteristic
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—
337#120—21no—
338#120—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8D411yescharacteristic
344C4×Q8D411yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
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×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4D411yescharacteristic
366C4×D4D411yescharacteristic
367C4×D4D411yescharacteristic
368C4×D4D411yescharacteristic
369C4×D4D411yescharacteristic
370C4×D4D411yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381#117—21no—
382#117—21no—
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
394#117C2311yescharacteristic
395#117C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C42—21no—
403C2×C42C2311yescharacteristic
404C2×C42C2311yescharacteristic
405C2×C42C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422C4⋊C8C2311yescharacteristic
423C4⋊C8C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#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
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24—21no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—82no—
485#41—82no—
486C2×Q8—21no—
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×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—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4C2×D411yescharacteristic
519C2×D4C2×D411yescharacteristic
520C2×D4C2×D411yescharacteristic
521C2×D4C2411yescharacteristic
522C2×D4C2411yescharacteristic
523C2×D4C2411yescharacteristic
524C2×D4C2411yescharacteristic
525C2×D4C2411yescharacteristic
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×C4—21no—
538C22×C4—21no—
539C22×C4—82no—
540C22×C4C2×D411yescharacteristic
541C22×C4C2×D411yescharacteristic
542C22×C4C2×D411yescharacteristic
543C22×C4C2×D411yescharacteristic
544C22×C4C2×D411yescharacteristic
545C22×C4C2×D411yescharacteristic
546C22×C4C2411yescharacteristic
547C22×C4C2411yescharacteristic
548C22×C4C2411yescharacteristic
549Q16—41no—
550Q16—41no—
551SD16—41no—
552SD16—41no—
553SD16—41no—
554SD16—41no—
555SD16—41no—
556SD16—41no—
557SD16—41no—
558SD16—41no—
559D8—41no—
560D8—41no—
561D8—41no—
562D8—41no—
563D8—41no—
564D8—41no—
565M16—41no—
566M16—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
576C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42C2×D411yescharacteristic
673C42C2×D411yescharacteristic
674C42C2×D411yescharacteristic
675C42C2×D411yescharacteristic
676C42C2×D411yescharacteristic
677C42C2×D411yescharacteristic
678C42C2411yescharacteristic
679C42C2411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—42no—
688C23—42no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23C22×D411yescharacteristic
694C23C22×D411yescharacteristic
695C23C22×D411yescharacteristic
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—41no—
703Q8—42no—
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—21no—
717D4—21no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
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—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4C22×D411yescharacteristic
775C2×C4C22×D411yescharacteristic
776C2×C4C22×D411yescharacteristic
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C22×D411yescharacteristic
781C2×C4C22×D411yescharacteristic
782C2×C4C22×D411yescharacteristic
783C2×C4C22×D411yescharacteristic
784C2×C4C22×D411yescharacteristic
785C2×C4C2511yescharacteristic
786C8—21no—
787C8—21no—
788C8—21no—
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—84no—
819C22—162no—
820C22C23×D411yescharacteristic
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4#58511yescharacteristic
844C4#58511yescharacteristic
845C2—41no—
846C2—41no—
847C2—41no—
848C2—81no—
849C2—81no—
850C2—81no—
851C2—81no—
852C2—81no—
853C2#344911yescharacteristic
854C2#358411yescharacteristic
855C2#358511yescharacteristic
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. #3510C2semidirect
2. #3460C2semidirect
3. #3256C2semidirect
4. #3251C2semidirect
5. #3250C2semidirect
6. #3247C2semidirect
7. #3244C2semidirect
8. #3243C2semidirect
9. #3240C2semidirect
10. #3228C2semidirect
11. #3224C2semidirect
12. #3224C2semidirect
13. #3213C2semidirect
14. #3211C2semidirect
15. #3201C2semidirect
16. #3200C2semidirect
17. #3199C2semidirect
18. #3198C2semidirect
19. #3179C2semidirect
20. #3179C2semidirect
21. #3175C2semidirect
22. #3173C2semidirect
23. #3126C2semidirect
24. #3122C2semidirect
25. #3121C2semidirect
26. #3118C2semidirect
27. #3114C2semidirect
28. #3111C2semidirect
29. #3105C2semidirect
30. #3102C2semidirect
31. #2925C2semidirect
40. #544C22semidirect
45. #542C22semidirect
46. #542C22semidirect
47. #542C22semidirect
50. #540C22semidirect
57. #535C22semidirect
58. #533C22semidirect
61. #532C22semidirect
66. #529C22semidirect
67. #529C22semidirect
68. #529C22semidirect
69. C2×#124C22semidirect
72. #519C22semidirect
73. #518C22semidirect
75. C4×#41C22semidirect
76. C2×C4×D4C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #498C22semidirect
85. #489C22semidirect
86. #489C22semidirect
87. #489C22semidirect
88. #489C22semidirect
89. #488C22semidirect
90. #488C22semidirect
91. #486C22semidirect
92. #486C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #484C22semidirect
98. #483C22semidirect
105. #482C22semidirect
106. #482C22semidirect
109. #479C22semidirect
110. #479C22semidirect
111. #479C22semidirect
112. #479C22semidirect
113. #478C22semidirect
114. #478C22semidirect
115. #478C22semidirect
116. #478C22semidirect
117. #478C22semidirect
118. #478C22semidirect
119. #478C22semidirect
120. #478C22semidirect
121. #477C22semidirect
122. #476C22semidirect
123. #475C22semidirect
124. #474C22semidirect
125. #470C22semidirect
128. #469C22semidirect
129. #468C22semidirect
130. #468C22semidirect
131. #468C22semidirect
132. #468C22semidirect
133. #467C22semidirect
136. #466C22semidirect
137. #465C22semidirect
138. #465C22semidirect
139. #465C22semidirect
140. #465C22semidirect
141. #464C22semidirect
142. #464C22semidirect
143. #464C22semidirect
144. #464C22semidirect
151. #463C22semidirect
152. #463C22semidirect
153. #460C22semidirect
154. #460C22semidirect
157. #452C22semidirect
158. #452C22semidirect
159. #451C22semidirect
160. #450C22semidirect
161. #450C22semidirect
162. #450C22semidirect
167. #448C22semidirect
172. #447C22semidirect
175. #442C22semidirect
176. #441C22semidirect
177. #440C22semidirect
178. #440C22semidirect
179. #440C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
182. C4×SD16C22semidirect
183. C4×SD16C22semidirect
184. C4×SD16C22semidirect
185. C4×SD16C22semidirect
188. C4×D8C22semidirect
189. #433C22semidirect
190. #433C22semidirect
191. #433C22semidirect
192. #433C22semidirect
193. #432C22semidirect
194. #432C22semidirect
195. #431C22semidirect
196. #431C22semidirect
197. #423C22semidirect
198. C2×C4⋊C8C22semidirect
201. #405C22semidirect
202. #405C22semidirect

Maximal subgroups

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

subgroupindex
#35102
#34602
#32562
#32512
#32502
#32472
#32442
#32432
#32402
#32282
#32242
#32132
#32112
#32012
#32002
#31992
#31982
#31792
#31752
#31732
#31262
#31222
#31212
#31182
#31142
#31112
#31052
#31022
#29252