Finite Group Databasebeta

← #61508

Subgroups — #61508

Order 256.

913 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3524C211yesmaximal, characteristic, complemented
2#3520C211yesmaximal, characteristic, complemented
3#3401C211yesmaximal, characteristic, complemented
4#3386C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3373C211yesmaximal, characteristic, complemented
7#3357C211yesmaximal, characteristic, complemented
8#3345C211yesmaximal, characteristic, complemented
9#3344C211yesmaximal, characteristic, complemented
10#3333C211yesmaximal, characteristic, complemented
11#3323C211yesmaximal, characteristic, complemented
12#3319C211yesmaximal, characteristic, complemented
13#3316C211yesmaximal, characteristic, complemented
14#3308C211yesmaximal, characteristic, complemented
15#3307C211yesmaximal, characteristic, complemented
16#3275C211yesmaximal, characteristic, complemented
17#3269C211yesmaximal, characteristic, complemented
18#3268C211yesmaximal, characteristic, complemented
19#3179C211yesmaximal, characteristic, complemented
20#3175C211yesmaximal, characteristic, complemented
21#3172C211yesmaximal, characteristic, complemented
22#3125C211yesmaximal, characteristic, complemented
23#3124C211yesmaximal, characteristic, complemented
24#3121C211yesmaximal, characteristic, complemented
25#3119C211yesmaximal, characteristic, complemented
26#3116C211yesmaximal, characteristic, complemented
27#3114C211yesmaximal, characteristic, complemented
28#2967C211yesmaximal, characteristic, complemented
29#2952C211yesmaximal, characteristic, complemented
30#2947C211yesmaximal, characteristic, complemented
31C4×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic
35#559—21no—
36#559C2211yescharacteristic, complemented
37#557C2211yescharacteristic, complemented
38#556C2211yescharacteristic
39#555—21no—
40#555C2211yescharacteristic
41#554C2211yescharacteristic
42#554C2211yescharacteristic
43#553—21no—
44#553C2211yescharacteristic, complemented
45#552—21no—
46#552—21no—
47#552C2211yescharacteristic
48#551—21no—
49#551—21no—
50#550C2211yescharacteristic
51D4×Q8C2211yescharacteristic
52#548—21no—
53#548C2211yescharacteristic
54#548C2211yescharacteristic, complemented
55#547C2211yescharacteristic
56#547C2211yescharacteristic
57#546C2211yescharacteristic
58#546C2211yescharacteristic
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic
62#542C2211yescharacteristic, complemented
63#540—21no—
64#540C2211yescharacteristic, complemented
65#539—21no—
66#539—21no—
67#533C2211yescharacteristic
68#529—21no—
69#529—21no—
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72#525—21no—
73C2×C22⋊Q8—21no—
74#520C2211yescharacteristic
75#520C2211yescharacteristic
76#520C2211yescharacteristic, complemented
77#519C2211yescharacteristic, complemented
78C4×#41C2211yescharacteristic
79C2×C4×D4C2211yescharacteristic
80#501C2211yescharacteristic, complemented
81#501C2211yescharacteristic, complemented
82#500C2211yescharacteristic, complemented
83#497C2211yescharacteristic, complemented
84#496C2211yescharacteristic
85#495C2211yescharacteristic
86#491C2211yescharacteristic, complemented
87#489C2211yescharacteristic
88#489C2211yescharacteristic, complemented
89#489C2211yescharacteristic, complemented
90#488C2211yescharacteristic
91#486C2211yescharacteristic, complemented
92#485C2211yescharacteristic
93#485C2211yescharacteristic
94#485C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#483C2211yescharacteristic
97#483C2211yescharacteristic, complemented
98#482C2211yescharacteristic
99#481C2211yescharacteristic
100#481C2211yescharacteristic, complemented
101#480C2211yescharacteristic
102#480C2211yescharacteristic, complemented
103#480C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#478C2211yescharacteristic
106#478C2211yescharacteristic
107#478C2211yescharacteristic
108#477C2211yescharacteristic, complemented
109#477C2211yescharacteristic, complemented
110#477C2211yescharacteristic, complemented
111#476C2211yescharacteristic, complemented
112#476C2211yescharacteristic, complemented
113#475C2211yescharacteristic, complemented
114#475C2211yescharacteristic, complemented
115#474C2211yescharacteristic
116#470C2211yescharacteristic
117#470C2211yescharacteristic
118#469C2211yescharacteristic
119#468C2211yescharacteristic
120#468C2211yescharacteristic
121#468C2211yescharacteristic
122#468C2211yescharacteristic, complemented
123#468C2211yescharacteristic, complemented
124#467C2211yescharacteristic, complemented
125#466C2211yescharacteristic
126#466C2211yescharacteristic
127#465C2211yescharacteristic, complemented
128#464C2211yescharacteristic
129#464C2211yescharacteristic
130#464C2211yescharacteristic
131#464C2211yescharacteristic, complemented
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic
135#463C2211yescharacteristic
136#462C2211yescharacteristic, complemented
137#461C2211yescharacteristic, complemented
138#460C2211yescharacteristic, complemented
139#459C2211yescharacteristic
140#452C2211yescharacteristic
141#452C2211yescharacteristic
142#452C2211yescharacteristic
143#452C2211yescharacteristic, complemented
144#451C2211yescharacteristic, complemented
145#450C2211yescharacteristic
146#449C2211yescharacteristic
147#449C2211yescharacteristic
148#449C2211yescharacteristic
149#449C2211yescharacteristic
150#448C2211yescharacteristic
151#447C2211yescharacteristic
152#446C2211yescharacteristic, complemented
153#446C2211yescharacteristic, complemented
154#442C2211yescharacteristic
155#442C2211yescharacteristic
156#442C2211yescharacteristic
157#442C2211yescharacteristic
158#442C2211yescharacteristic
159#441C2211yescharacteristic, complemented
160#441C2211yescharacteristic, complemented
161#441C2211yescharacteristic, complemented
162#441C2211yescharacteristic, complemented
163#440C2211yescharacteristic
164#440C2211yescharacteristic
165#440C2211yescharacteristic
166#440C2211yescharacteristic
167#440C2211yescharacteristic
168#440C2211yescharacteristic, complemented
169#440C2211yescharacteristic, complemented
170C4×Q16C2211yescharacteristic, complemented
171C4×Q16C2211yescharacteristic, complemented
172C4×Q16C2211yescharacteristic, complemented
173C4×SD16C2211yescharacteristic
174C4×SD16C2211yescharacteristic
175C4×SD16C2211yescharacteristic
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic, complemented
178C4×SD16C2211yescharacteristic, complemented
179C4×SD16C2211yescharacteristic, complemented
180C4×D8C2211yescharacteristic
181C4×D8C2211yescharacteristic
182#436C2211yescharacteristic
183#436C2211yescharacteristic
184#435C2211yescharacteristic
185#435C2211yescharacteristic
186#435C2211yescharacteristic, complemented
187#435C2211yescharacteristic, complemented
188#433C2211yescharacteristic, complemented
189#433C2211yescharacteristic, complemented
190#432C2211yescharacteristic
191#428C2211yescharacteristic
192#428C2211yescharacteristic, complemented
193C2×#106C2211yescharacteristic, complemented
194#418C2211yescharacteristic
195#417C2211yescharacteristic
196#417C2211yescharacteristic
197#417C2211yescharacteristic, complemented
198#416C2211yescharacteristic
199C2×#103C2211yescharacteristic, complemented
200#405C2211yescharacteristic, complemented
201#405C2211yescharacteristic, complemented
202C4×M16C2211yescharacteristic
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8—21no—
209C22×Q8C2311yescharacteristic
210C22×D4C2311yescharacteristic
211C23×C4—21no—
212#137—24no—
213AGL(1,ℤ/8)—24no—
214#135—24no—
215C2×Q16C2311yescharacteristic
216C2×Q16C2311yescharacteristic
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×D8C2311yescharacteristic
228C2×D8C2311yescharacteristic
229C2×D8C2311yescharacteristic
230C2×D8C2311yescharacteristic
231C2×M16C2311yescharacteristic
232C2×M16C2311yescharacteristic
233C2×M16C2311yescharacteristic
234C2×M16C2311yescharacteristic
235C22×C8C2311yescharacteristic
236C22×C8C2311yescharacteristic
237C4⋊Q8—21no—
238C4⋊Q8C2311yescharacteristic
239C4⋊Q8C2311yescharacteristic
240C4⋊Q8C2311yescharacteristic
241C4⋊Q8C2311yescharacteristic
242C4⋊Q8C2311yescharacteristic
243#127—21no—
244#127C2311yescharacteristic
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126D411yescharacteristic
254#126D411yescharacteristic
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125D411yescharacteristic
262#125C2311yescharacteristic
263#125C2311yescharacteristic
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#124D411yescharacteristic
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#123D411yescharacteristic
294#123D411yescharacteristic
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
316C22⋊Q8C2311yescharacteristic
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#121—21no—
326#121—21no—
327#121—21no—
328#121D411yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#120—21no—
336#120—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
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×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117C2311yescharacteristic
395#117C2311yescharacteristic
396#117C2311yescharacteristic
397#117C2311yescharacteristic
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4C2311yescharacteristic
403C2×C4⋊C4C2311yescharacteristic
404C2×C4⋊C4C2311yescharacteristic
405C2×C4⋊C4C2311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C42—21no—
410C2×C42C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#107C2311yescharacteristic
415#107C2311yescharacteristic
416#107C2311yescharacteristic
417#107C2311yescharacteristic
418#107C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426#106C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
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#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
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
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476#97C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C4×C8C2311yescharacteristic
479C4×C8C2311yescharacteristic
480C4×C8C2311yescharacteristic
481C24—21no—
482#41—22no—
483#41—22no—
484#41—22no—
485#41—22no—
486#41—41no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—82no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—22no—
497C2×Q8—41no—
498C2×Q8—82no—
499C2×Q8C2×D411yescharacteristic
500C2×Q8C2411yescharacteristic
501C2×Q8C2411yescharacteristic
502C2×Q8C2411yescharacteristic
503C2×Q8C2411yescharacteristic
504C2×D4—22no—
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—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—41no—
519C2×D4C2×D411yescharacteristic
520C2×D4C2×D411yescharacteristic
521C2×D4C2×D411yescharacteristic
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—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—82no—
546C22×C4C2×D411yescharacteristic
547C22×C4C2×D411yescharacteristic
548C22×C4C2411yescharacteristic
549C22×C4C2411yescharacteristic
550C22×C4C2411yescharacteristic
551Q16—22no—
552Q16—22no—
553Q16—22no—
554Q16—41no—
555SD16—22no—
556SD16—22no—
557SD16—22no—
558SD16—41no—
559SD16—41no—
560SD16—41no—
561SD16—41no—
562SD16#4114yescomplemented
563D8—22no—
564D8—22no—
565D8—22no—
566D8—41no—
567M16—22no—
568M16—22no—
569M16—41no—
570M16—41no—
571C2×C8—22no—
572C2×C8—41no—
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
576C2×C8C2411yescharacteristic
577C2×C8C2411yescharacteristic
578C2×C8C2411yescharacteristic
579C2×C8C2411yescharacteristic
580C2×C8C2411yescharacteristic
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⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2×D411yescharacteristic
615C4⋊C4C2×D411yescharacteristic
616C4⋊C4C2×D411yescharacteristic
617C4⋊C4C2×D411yescharacteristic
618C4⋊C4C2×D411yescharacteristic
619C4⋊C4C2×D411yescharacteristic
620C4⋊C4C2×D411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
626C4⋊C4C2411yescharacteristic
627C4⋊C4C2411yescharacteristic
628C4⋊C4C2411yescharacteristic
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⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C22⋊C4C2×D411yescharacteristic
668C22⋊C4C2×D411yescharacteristic
669C22⋊C4C2×D411yescharacteristic
670C22⋊C4C2×D411yescharacteristic
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42C2×D411yescharacteristic
684C42C2×D411yescharacteristic
685C42C2411yescharacteristic
686C42C2411yescharacteristic
687C42C2411yescharacteristic
688C42C2411yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—42no—
694C23—42no—
695C23—81no—
696C23C22×D411yescharacteristic
697C23C22×D411yescharacteristic
698C23C22×D411yescharacteristic
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—41no—
707Q8—42no—
708Q8—42no—
709Q8—81no—
710Q8—81no—
711Q8—81no—
712Q8C2×#4112yes—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4C2×#4112yes—
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—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—81no—
765C2×C4—81no—
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×C4—81no—
775C2×C4—81no—
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×C4C22×D411yescharacteristic
786C2×C4C22×D411yescharacteristic
787C2×C4C2511yescharacteristic
788C8—21no—
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8C2×#4112yes—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—84no—
818C22C23×D411yescharacteristic
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—22no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4C22×#4111yescharacteristic
843C4#58511yescharacteristic
844C2—41no—
845C2—41no—
846C2—41no—
847C2—42no—
848C2—81no—
849C2—81no—
850C2—81no—
851C2D4×#4111yescharacteristic
852C2#358511yescharacteristic
853C2#358611yescharacteristic
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. #3524C2semidirect
2. #3520C2semidirect
3. #3401C2semidirect
4. #3386C2semidirect
5. #3377C2semidirect
6. #3373C2semidirect
7. #3357C2semidirect
8. #3345C2semidirect
9. #3344C2semidirect
10. #3333C2semidirect
11. #3323C2semidirect
12. #3319C2semidirect
13. #3316C2semidirect
14. #3308C2semidirect
15. #3307C2semidirect
16. #3275C2semidirect
17. #3269C2semidirect
18. #3268C2semidirect
19. #3179C2semidirect
20. #3175C2semidirect
21. #3172C2semidirect
22. #3125C2semidirect
23. #3124C2semidirect
24. #3121C2semidirect
25. #3119C2semidirect
26. #3116C2semidirect
27. #3114C2semidirect
28. #2967C2semidirect
29. #2952C2semidirect
30. #2947C2semidirect
31. C4×AGL(1,ℤ/8)C2semidirect
36. #559C22semidirect
37. #557C22semidirect
44. #553C22semidirect
54. #548C22semidirect
62. #542C22semidirect
64. #540C22semidirect
76. #520C22semidirect
77. #519C22semidirect
80. #501C22semidirect
81. #501C22semidirect
82. #500C22semidirect
83. #497C22semidirect
86. #491C22semidirect
88. #489C22semidirect
89. #489C22semidirect
91. #486C22semidirect
94. #485C22semidirect
95. #484C22semidirect
97. #483C22semidirect
100. #481C22semidirect
102. #480C22semidirect
103. #480C22semidirect
104. #479C22semidirect
108. #477C22semidirect
109. #477C22semidirect
110. #477C22semidirect
111. #476C22semidirect
112. #476C22semidirect
113. #475C22semidirect
114. #475C22semidirect
122. #468C22semidirect
123. #468C22semidirect
124. #467C22semidirect
127. #465C22semidirect
131. #464C22semidirect
136. #462C22semidirect
137. #461C22semidirect
138. #460C22semidirect
143. #452C22semidirect
144. #451C22semidirect
152. #446C22semidirect
153. #446C22semidirect
159. #441C22semidirect
160. #441C22semidirect
161. #441C22semidirect
162. #441C22semidirect
168. #440C22semidirect
169. #440C22semidirect
170. C4×Q16C22semidirect
171. C4×Q16C22semidirect
172. C4×Q16C22semidirect
177. C4×SD16C22semidirect
178. C4×SD16C22semidirect
179. C4×SD16C22semidirect
186. #435C22semidirect
187. #435C22semidirect
188. #433C22semidirect
189. #433C22semidirect
192. #428C22semidirect
193. C2×#106C22semidirect
197. #417C22semidirect
199. C2×#103C22semidirect
200. #405C22semidirect
201. #405C22semidirect
562. SD16#41semidirect

Maximal subgroups

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

subgroupindex
#35242
#35202
#34012
#33862
#33772
#33732
#33572
#33452
#33442
#33332
#33232
#33192
#33162
#33082
#33072
#32752
#32692
#32682
#31792
#31752
#31722
#31252
#31242
#31212
#31192
#31162
#31142
#29672
#29522
#29472
C4×AGL(1,ℤ/8)2