Finite Group Databasebeta

← #61741

Subgroups — #61741

Order 256.

888 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505C211yesmaximal, characteristic, complemented
2#3475C211yesmaximal, characteristic, complemented
3#3352C211yesmaximal, characteristic, complemented
4#3351C211yesmaximal, characteristic, complemented
5#3349C211yesmaximal, characteristic, complemented
6#3348C211yesmaximal, characteristic, complemented
7#3346C211yesmaximal, characteristic, complemented
8#3345C211yesmaximal, characteristic, complemented
9#3339C211yesmaximal, characteristic, complemented
10#3337C211yesmaximal, characteristic, complemented
11#3323C211yesmaximal, characteristic, complemented
12#3322C211yesmaximal, characteristic, complemented
13#3319C211yesmaximal, characteristic, complemented
14#3316C211yesmaximal, characteristic, complemented
15#3311C211yesmaximal, characteristic, complemented
16#3308C211yesmaximal, characteristic, complemented
17#3301C211yesmaximal, characteristic, complemented
18#3300C211yesmaximal, characteristic, complemented
19#3240C211yesmaximal, characteristic, complemented
20#3233C211yesmaximal, characteristic, complemented
21#3197C211yesmaximal, characteristic, complemented
22#3196C211yesmaximal, characteristic, complemented
23#3191C211yesmaximal, characteristic, complemented
24#3188C211yesmaximal, characteristic, complemented
25#3111C211yesmaximal, characteristic, complemented
26#3102C211yesmaximal, characteristic, complemented
27#3094C211yesmaximal, characteristic, complemented
28#3093C211yesmaximal, characteristic, complemented
29#3091C211yesmaximal, characteristic, complemented
30C2×#485C211yesmaximal, characteristic, complemented
31#2974C211yesmaximal, characteristic, complemented
32#556C2211yescharacteristic
33#555C2211yescharacteristic
34#554C2211yescharacteristic, complemented
35#553—21no—
36#553—21no—
37#553C2211yescharacteristic
38#553C2211yescharacteristic
39#553C2211yescharacteristic
40#553C2211yescharacteristic, complemented
41#552—21no—
42#552C2211yescharacteristic
43#552C2211yescharacteristic
44#552C2211yescharacteristic
45#552C2211yescharacteristic, complemented
46#551—21no—
47#551—21no—
48#551—21no—
49#551—21no—
50#548C2211yescharacteristic
51#548C2211yescharacteristic
52#547C2211yescharacteristic, complemented
53#546—21no—
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#539—21no—
57#538—21no—
58#534—21no—
59#533C2211yescharacteristic, complemented
60#529—21no—
61#529—21no—
62#529—21no—
63#529C2211yescharacteristic
64#529C2211yescharacteristic
65#525C2211yescharacteristic
66#525C2211yescharacteristic
67#525C2211yescharacteristic
68#525C2211yescharacteristic, complemented
69C2×C22⋊Q8C2211yescharacteristic
70C2×#121C2211yescharacteristic
71#518—21no—
72C4×#41—21no—
73C4×#41C2211yescharacteristic, complemented
74C2×C4×D4C2211yescharacteristic
75C2×#117C2211yescharacteristic
76C2×#117C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#489C2211yescharacteristic, complemented
82#489C2211yescharacteristic, complemented
83#488C2211yescharacteristic, complemented
84#488C2211yescharacteristic, complemented
85#485C2211yescharacteristic, complemented
86#485C2211yescharacteristic, complemented
87#485C2211yescharacteristic, complemented
88#485C2211yescharacteristic, complemented
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#485C2211yescharacteristic, complemented
98#485C2211yescharacteristic, complemented
99#484C2211yescharacteristic, complemented
100#484C2211yescharacteristic, complemented
101#484C2211yescharacteristic, complemented
102#483C2211yescharacteristic, complemented
103#482C2211yescharacteristic
104#482C2211yescharacteristic
105#482C2211yescharacteristic
106#482C2211yescharacteristic
107#482C2211yescharacteristic
108#482C2211yescharacteristic
109#482C2211yescharacteristic, complemented
110#482C2211yescharacteristic, complemented
111#482C2211yescharacteristic, complemented
112#482C2211yescharacteristic, complemented
113#481C2211yescharacteristic, complemented
114#481C2211yescharacteristic, complemented
115#481C2211yescharacteristic, complemented
116#481C2211yescharacteristic, complemented
117#481C2211yescharacteristic, complemented
118#480C2211yescharacteristic, complemented
119#480C2211yescharacteristic, complemented
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#479C2211yescharacteristic, complemented
124#479C2211yescharacteristic, complemented
125#478C2211yescharacteristic, complemented
126#478C2211yescharacteristic, complemented
127#478C2211yescharacteristic, complemented
128#478C2211yescharacteristic, complemented
129#477C2211yescharacteristic, complemented
130#476C2211yescharacteristic, complemented
131#475C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#470C2211yescharacteristic, complemented
134#470C2211yescharacteristic, complemented
135#470C2211yescharacteristic, complemented
136#469C2211yescharacteristic, complemented
137#468C2211yescharacteristic, complemented
138#468C2211yescharacteristic, complemented
139#468C2211yescharacteristic, complemented
140#468C2211yescharacteristic, complemented
141#467C2211yescharacteristic, complemented
142#466C2211yescharacteristic, complemented
143#466C2211yescharacteristic, complemented
144#466C2211yescharacteristic, complemented
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#464C2211yescharacteristic, complemented
151#463C2211yescharacteristic, complemented
152#463C2211yescharacteristic, complemented
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#451C2211yescharacteristic, complemented
158#450C2211yescharacteristic, complemented
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic, complemented
162#449C2211yescharacteristic, complemented
163#448C2211yescharacteristic, complemented
164#447C2211yescharacteristic, complemented
165#442C2211yescharacteristic, complemented
166#441C2211yescharacteristic, complemented
167#440C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×Q16C2211yescharacteristic, complemented
170C4×SD16C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic, complemented
172C4×D8C2211yescharacteristic, complemented
173#436C2211yescharacteristic
174#436C2211yescharacteristic
175#435C2211yescharacteristic
176#435C2211yescharacteristic
177#435C2211yescharacteristic, complemented
178#435C2211yescharacteristic, complemented
179C8×D4C2211yescharacteristic, complemented
180C8×D4C2211yescharacteristic, complemented
181#432C2211yescharacteristic, complemented
182#431C2211yescharacteristic, complemented
183#428C2211yescharacteristic, complemented
184#428C2211yescharacteristic, complemented
185#428C2211yescharacteristic, complemented
186#428C2211yescharacteristic, complemented
187#427C2211yescharacteristic, complemented
188#427C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#418C2211yescharacteristic, complemented
192#418C2211yescharacteristic, complemented
193#417C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199#407C2211yescharacteristic
200#407C2211yescharacteristic, complemented
201C2×C22⋊C8C2211yescharacteristic
202C2×C22⋊C8C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4—21no—
209C22×D4D411yescharacteristic
210C22×D4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×D8C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C2×M16C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231#126—21no—
232#126—21no—
233#126—21no—
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#125—21no—
244#125—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125C2311yescharacteristic
249#125C2311yescharacteristic
250#125C2311yescharacteristic
251#125C2311yescharacteristic
252#124—21no—
253#124—21no—
254#124—21no—
255#124—21no—
256#124—21no—
257#124C2311yescharacteristic
258#124C2311yescharacteristic
259#123—21no—
260#123—21no—
261#123—21no—
262#123—21no—
263#123—21no—
264#123—21no—
265#123—21no—
266#123—21no—
267#123—21no—
268#123—21no—
269#123—21no—
270#123—21no—
271#123—21no—
272#123—21no—
273#123—21no—
274#123—21no—
275#123—21no—
276#123—21no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8C2311yescharacteristic
287C22⋊Q8C2311yescharacteristic
288C22⋊Q8C2311yescharacteristic
289C22⋊Q8C2311yescharacteristic
290C22⋊Q8C2311yescharacteristic
291C22⋊Q8C2311yescharacteristic
292C22⋊Q8C2311yescharacteristic
293C22⋊Q8C2311yescharacteristic
294C22⋊Q8C2311yescharacteristic
295C22⋊Q8C2311yescharacteristic
296#121—21no—
297#121—21no—
298#121—21no—
299#121—21no—
300#121—21no—
301#121—21no—
302#121—21no—
303#121—21no—
304#121—21no—
305#121—21no—
306#121—21no—
307#121C2311yescharacteristic
308#121C2311yescharacteristic
309#121C2311yescharacteristic
310#121C2311yescharacteristic
311#121C2311yescharacteristic
312#121C2311yescharacteristic
313#121C2311yescharacteristic
314#121C2311yescharacteristic
315#121C2311yescharacteristic
316#121C2311yescharacteristic
317#120—21no—
318#120—21no—
319#120—21no—
320#120—21no—
321#120—21no—
322#120—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8C2311yescharacteristic
327C4×Q8C2311yescharacteristic
328C4×Q8C2311yescharacteristic
329C4×Q8C2311yescharacteristic
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4D411yescharacteristic
350C4×D4D411yescharacteristic
351C4×D4D411yescharacteristic
352C4×D4D411yescharacteristic
353C4×D4C2311yescharacteristic
354C4×D4C2311yescharacteristic
355C4×D4C2311yescharacteristic
356C4×D4C2311yescharacteristic
357C4×D4C2311yescharacteristic
358C4×D4C2311yescharacteristic
359C4×D4C2311yescharacteristic
360C4×D4C2311yescharacteristic
361#117—21no—
362#117—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117C2311yescharacteristic
374#117C2311yescharacteristic
375#117C2311yescharacteristic
376#117C2311yescharacteristic
377#117C2311yescharacteristic
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382C2×C4⋊C4—21no—
383C2×C4⋊C4D411yescharacteristic
384C2×C4⋊C4C2311yescharacteristic
385C2×C4⋊C4C2311yescharacteristic
386C2×C4⋊C4C2311yescharacteristic
387C2×C4⋊C4C2311yescharacteristic
388C2×C4⋊C4C2311yescharacteristic
389C2×C4⋊C4C2311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4D411yescharacteristic
397C2×C22⋊C4D411yescharacteristic
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
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
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
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#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
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
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24C2×D411yescharacteristic
480C24C2×D411yescharacteristic
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487#41—44no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8C2411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×Q8C2411yescharacteristic
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—21no—
509C2×D4—21no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—42no—
513C2×D4—44no—
514C2×D4C2×D411yescharacteristic
515C2×D4C2×D411yescharacteristic
516C2×D4C2×D411yescharacteristic
517C2×D4C2×D411yescharacteristic
518C2×D4C2411yescharacteristic
519C2×D4C2411yescharacteristic
520C2×D4C2411yescharacteristic
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×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4C2×D411yescharacteristic
540C22×C4C2×D411yescharacteristic
541C22×C4C2×D411yescharacteristic
542C22×C4C2×D411yescharacteristic
543C22×C4C2×D411yescharacteristic
544C22×C4C2×D411yescharacteristic
545C22×C4C2×D411yescharacteristic
546C22×C4C2×D411yescharacteristic
547C22×C4C2411yescharacteristic
548C22×C4C2411yescharacteristic
549C22×C4C2411yescharacteristic
550C22×C4C2411yescharacteristic
551C22×C4C2411yescharacteristic
552Q16—41no—
553Q16—41no—
554SD16—41no—
555SD16—41no—
556SD16—41no—
557SD16—41no—
558D8—41no—
559D8—41no—
560M16—41no—
561M16—41no—
562M16—41no—
563M16—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
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
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42C2×D411yescharacteristic
679C42C2×D411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—22no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—81no—
693C23—81no—
694C23C22×D411yescharacteristic
695C23C22×D411yescharacteristic
696C23C22×D411yescharacteristic
697C23C22×D411yescharacteristic
698C23C22×D411yescharacteristic
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—42no—
706Q8—81no—
707Q8—81no—
708D4—22no—
709D4—22no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—41no—
717D4—41no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
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—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—41no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
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×C4C22×D411yescharacteristic
786C2×C4C2511yescharacteristic
787C8—21no—
788C8—21no—
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—82no—
819C22—82no—
820C22—162no—
821C22#57512yes—
822C22C23×D411yescharacteristic
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—41no—
844C4—41no—
845C4#58511yescharacteristic
846C4#58511yescharacteristic
847C2—22no—
848C2—41no—
849C2—41no—
850C2—41no—
851C2—41no—
852C2—81no—
853C2—81no—
854C2—81no—
855C2#348511yescharacteristic
856C2C2×#57511yescharacteristic
857C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3505C2semidirect
2. #3475C2semidirect
3. #3352C2semidirect
4. #3351C2semidirect
5. #3349C2semidirect
6. #3348C2semidirect
7. #3346C2semidirect
8. #3345C2semidirect
9. #3339C2semidirect
10. #3337C2semidirect
11. #3323C2semidirect
12. #3322C2semidirect
13. #3319C2semidirect
14. #3316C2semidirect
15. #3311C2semidirect
16. #3308C2semidirect
17. #3301C2semidirect
18. #3300C2semidirect
19. #3240C2semidirect
20. #3233C2semidirect
21. #3197C2semidirect
22. #3196C2semidirect
23. #3191C2semidirect
24. #3188C2semidirect
25. #3111C2semidirect
26. #3102C2semidirect
27. #3094C2semidirect
28. #3093C2semidirect
29. #3091C2semidirect
30. C2×#485C2semidirect
31. #2974C2semidirect
34. #554C22semidirect
40. #553C22semidirect
45. #552C22semidirect
52. #547C22semidirect
59. #533C22semidirect
68. #525C22semidirect
73. C4×#41C22semidirect
76. C2×#117C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #499C22semidirect
80. #499C22semidirect
81. #489C22semidirect
82. #489C22semidirect
83. #488C22semidirect
84. #488C22semidirect
85. #485C22semidirect
86. #485C22semidirect
87. #485C22semidirect
88. #485C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #485C22semidirect
98. #485C22semidirect
99. #484C22semidirect
100. #484C22semidirect
101. #484C22semidirect
102. #483C22semidirect
109. #482C22semidirect
110. #482C22semidirect
111. #482C22semidirect
112. #482C22semidirect
113. #481C22semidirect
114. #481C22semidirect
115. #481C22semidirect
116. #481C22semidirect
117. #481C22semidirect
118. #480C22semidirect
119. #480C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #479C22semidirect
124. #479C22semidirect
125. #478C22semidirect
126. #478C22semidirect
127. #478C22semidirect
128. #478C22semidirect
129. #477C22semidirect
130. #476C22semidirect
131. #475C22semidirect
132. #474C22semidirect
133. #470C22semidirect
134. #470C22semidirect
135. #470C22semidirect
136. #469C22semidirect
137. #468C22semidirect
138. #468C22semidirect
139. #468C22semidirect
140. #468C22semidirect
141. #467C22semidirect
142. #466C22semidirect
143. #466C22semidirect
144. #466C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #464C22semidirect
151. #463C22semidirect
152. #463C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #451C22semidirect
158. #450C22semidirect
161. #449C22semidirect
162. #449C22semidirect
163. #448C22semidirect
164. #447C22semidirect
165. #442C22semidirect
166. #441C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. C4×Q16C22semidirect
170. C4×SD16C22semidirect
171. C4×SD16C22semidirect
172. C4×D8C22semidirect
177. #435C22semidirect
178. #435C22semidirect
179. C8×D4C22semidirect
180. C8×D4C22semidirect
181. #432C22semidirect
182. #431C22semidirect
183. #428C22semidirect
184. #428C22semidirect
185. #428C22semidirect
186. #428C22semidirect
187. #427C22semidirect
188. #427C22semidirect
189. C2×#107C22semidirect
190. C2×#106C22semidirect
191. #418C22semidirect
192. #418C22semidirect
193. #417C22semidirect
194. #417C22semidirect
195. #416C22semidirect
196. #416C22semidirect
197. C2×#103C22semidirect
198. C2×#103C22semidirect
200. #407C22semidirect
202. C2×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#35052
#34752
#33522
#33512
#33492
#33482
#33462
#33452
#33392
#33372
#33232
#33222
#33192
#33162
#33112
#33082
#33012
#33002
#32402
#32332
#31972
#31962
#31912
#31882
#31112
#31022
#30942
#30932
#30912
C2×#4852
#29742