Finite Group Databasebeta

← #61486

Subgroups — #61486

Order 256.

897 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3524C211yesmaximal, characteristic, complemented
2#3521C211yesmaximal, characteristic, complemented
3#3394C211yesmaximal, characteristic, complemented
4#3381C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3370C211yesmaximal, characteristic, complemented
7#3340C211yesmaximal, characteristic, complemented
8#3337C211yesmaximal, characteristic, complemented
9#3337C211yesmaximal, characteristic, complemented
10#3327C211yesmaximal, characteristic, complemented
11#3322C211yesmaximal, characteristic, complemented
12#3319C211yesmaximal, characteristic, complemented
13#3315C211yesmaximal, characteristic, complemented
14#3313C211yesmaximal, characteristic, complemented
15#3309C211yesmaximal, characteristic, complemented
16#3284C211yesmaximal, characteristic, complemented
17#3282C211yesmaximal, characteristic, complemented
18#3282C211yesmaximal, characteristic, complemented
19#3174C211yesmaximal, characteristic, complemented
20#3173C211yesmaximal, characteristic, complemented
21#3168C211yesmaximal, characteristic, complemented
22#3127C211yesmaximal, characteristic, complemented
23#3124C211yesmaximal, characteristic, complemented
24#3124C211yesmaximal, characteristic, complemented
25#3122C211yesmaximal, characteristic, complemented
26#3111C211yesmaximal, characteristic, complemented
27#3111C211yesmaximal, characteristic, complemented
28#2966C211yesmaximal, characteristic, complemented
29#2952C211yesmaximal, characteristic, complemented
30#2949C211yesmaximal, characteristic, complemented
31C4×#135C211yesmaximal, characteristic, complemented
32C2×#135C2211yescharacteristic
33C2×#135C2211yescharacteristic
34C22×SD16C2211yescharacteristic
35#559—21no—
36#559C2211yescharacteristic, complemented
37#557C2211yescharacteristic, complemented
38#556C2211yescharacteristic
39#556C2211yescharacteristic
40#555—21no—
41#555C2211yescharacteristic
42#554C2211yescharacteristic
43#553—21no—
44#553—21no—
45#553C2211yescharacteristic
46#553C2211yescharacteristic
47#552—21no—
48#552—21no—
49#552C2211yescharacteristic
50#552C2211yescharacteristic, complemented
51#551—21no—
52#551—21no—
53#550C2211yescharacteristic, complemented
54#548C2211yescharacteristic
55#548C2211yescharacteristic
56#547C2211yescharacteristic
57#546C2211yescharacteristic
58#546C2211yescharacteristic
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic, complemented
62#541C2211yescharacteristic
63#540—21no—
64#540C2211yescharacteristic
65#539—21no—
66#538—21no—
67#529—21no—
68#529—21no—
69#529—21no—
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72#529C2211yescharacteristic, complemented
73C2×#126—21no—
74#520C2211yescharacteristic
75#520C2211yescharacteristic, complemented
76#519C2211yescharacteristic
77#518C2211yescharacteristic
78C4×#41C2211yescharacteristic
79C4×#41C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#499C2211yescharacteristic, complemented
82#498C2211yescharacteristic, complemented
83#495C2211yescharacteristic
84#495C2211yescharacteristic
85#492C2211yescharacteristic, complemented
86#491C2211yescharacteristic, complemented
87#490C2211yescharacteristic, complemented
88#489C2211yescharacteristic
89#489C2211yescharacteristic, complemented
90#488C2211yescharacteristic
91#488C2211yescharacteristic, complemented
92#485C2211yescharacteristic
93#485C2211yescharacteristic
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#482C2211yescharacteristic
99#482C2211yescharacteristic
100#482C2211yescharacteristic
101#482C2211yescharacteristic, complemented
102#480C2211yescharacteristic
103#480C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#478C2211yescharacteristic
109#478C2211yescharacteristic
110#478C2211yescharacteristic
111#478C2211yescharacteristic, complemented
112#477C2211yescharacteristic, complemented
113#477C2211yescharacteristic, complemented
114#474C2211yescharacteristic
115#474C2211yescharacteristic, complemented
116#470C2211yescharacteristic, complemented
117#469C2211yescharacteristic
118#468C2211yescharacteristic
119#468C2211yescharacteristic
120#467C2211yescharacteristic, complemented
121#466C2211yescharacteristic
122#465C2211yescharacteristic
123#465C2211yescharacteristic
124#465C2211yescharacteristic
125#465C2211yescharacteristic
126#465C2211yescharacteristic, complemented
127#465C2211yescharacteristic, complemented
128#464C2211yescharacteristic
129#464C2211yescharacteristic
130#464C2211yescharacteristic, complemented
131#464C2211yescharacteristic, complemented
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic
135#463C2211yescharacteristic
136#462C2211yescharacteristic, complemented
137#462C2211yescharacteristic, complemented
138#459C2211yescharacteristic
139#459C2211yescharacteristic
140#452C2211yescharacteristic
141#452C2211yescharacteristic
142#452C2211yescharacteristic, complemented
143#452C2211yescharacteristic, complemented
144#451C2211yescharacteristic
145#451C2211yescharacteristic
146#449C2211yescharacteristic
147#449C2211yescharacteristic
148#449C2211yescharacteristic
149#449C2211yescharacteristic
150#447C2211yescharacteristic
151#447C2211yescharacteristic
152#446C2211yescharacteristic, complemented
153C8×Q8C2211yescharacteristic, complemented
154#442C2211yescharacteristic
155#442C2211yescharacteristic
156#442C2211yescharacteristic
157#441C2211yescharacteristic, complemented
158#441C2211yescharacteristic, complemented
159#441C2211yescharacteristic, complemented
160#440C2211yescharacteristic
161#440C2211yescharacteristic
162#440C2211yescharacteristic
163#440C2211yescharacteristic
164#440C2211yescharacteristic, complemented
165#440C2211yescharacteristic, complemented
166C4×Q16C2211yescharacteristic, complemented
167C4×Q16C2211yescharacteristic, complemented
168C4×Q16C2211yescharacteristic, complemented
169C4×SD16C2211yescharacteristic
170C4×SD16C2211yescharacteristic
171C4×SD16C2211yescharacteristic
172C4×SD16C2211yescharacteristic
173C4×SD16C2211yescharacteristic
174C4×SD16C2211yescharacteristic
175C4×SD16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic, complemented
177C4×SD16C2211yescharacteristic, complemented
178C4×SD16C2211yescharacteristic, complemented
179C4×D8C2211yescharacteristic
180C4×D8C2211yescharacteristic
181C4×D8C2211yescharacteristic
182#436C2211yescharacteristic
183#435C2211yescharacteristic
184#435C2211yescharacteristic, complemented
185C8×D4C2211yescharacteristic
186C8×D4C2211yescharacteristic
187C8×D4C2211yescharacteristic, complemented
188#433C2211yescharacteristic
189#433C2211yescharacteristic, complemented
190#432C2211yescharacteristic, complemented
191#427C2211yescharacteristic
192#427C2211yescharacteristic, complemented
193C2×#106C2211yescharacteristic, complemented
194#419C2211yescharacteristic
195#418C2211yescharacteristic
196#417C2211yescharacteristic
197#417C2211yescharacteristic, complemented
198#416C2211yescharacteristic
199#416C2211yescharacteristic, complemented
200#405C2211yescharacteristic
201#405C2211yescharacteristic, complemented
202C2×C4×C8C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4C2311yescharacteristic
209#135—24no—
210#135—24no—
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×SD16—24no—
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×D8C2311yescharacteristic
225C2×D8C2311yescharacteristic
226C2×D8C2311yescharacteristic
227C2×D8C2311yescharacteristic
228C2×M16C2311yescharacteristic
229C2×M16C2311yescharacteristic
230C22×C8C2311yescharacteristic
231C22×C8C2311yescharacteristic
232C22×C8C2311yescharacteristic
233C22×C8C2311yescharacteristic
234C4⋊Q8—21no—
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238#127—21no—
239#127C2311yescharacteristic
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126—21no—
254#126D411yescharacteristic
255#126D411yescharacteristic
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#125D411yescharacteristic
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#125C2311yescharacteristic
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#124C2311yescharacteristic
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123D411yescharacteristic
297#123D411yescharacteristic
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⋊Q8D411yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309C22⋊Q8C2311yescharacteristic
310C22⋊Q8C2311yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
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#121—21no—
324#121—21no—
325#121D411yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#120—21no—
333#120—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8C2311yescharacteristic
339C4×Q8C2311yescharacteristic
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380#117—21no—
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#117—21no—
391#117—21no—
392#117C2311yescharacteristic
393#117C2311yescharacteristic
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×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—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
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
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—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—22no—
494C2×Q8—41no—
495C2×Q8C2×D411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×Q8C2411yescharacteristic
500C2×D4—22no—
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×D4C2×D411yescharacteristic
516C2×D4C2×D411yescharacteristic
517C2×D4C2×D411yescharacteristic
518C2×D4C2411yescharacteristic
519C2×D4C2411yescharacteristic
520C2×D4C2411yescharacteristic
521C2×D4C2411yescharacteristic
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—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4C2×D411yescharacteristic
540C22×C4C2×D411yescharacteristic
541C22×C4C2411yescharacteristic
542C22×C4C2411yescharacteristic
543C22×C4C2411yescharacteristic
544Q16—22no—
545Q16—22no—
546Q16—41no—
547Q16—41no—
548SD16—22no—
549SD16—22no—
550SD16—22no—
551SD16—22no—
552SD16—22no—
553SD16—41no—
554SD16—41no—
555SD16#4114yes—
556D8—22no—
557D8—22no—
558D8—41no—
559D8—41no—
560M16—41no—
561M16—41no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—41no—
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42C2×D411yescharacteristic
681C42C2×D411yescharacteristic
682C42C2411yescharacteristic
683C42C2411yescharacteristic
684C42C2411yescharacteristic
685C42C2411yescharacteristic
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—42no—
691C23—81no—
692C23—81no—
693C23C22×D411yescharacteristic
694C23C22×D411yescharacteristic
695C23C22×D411yescharacteristic
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—41no—
704Q8—42no—
705Q8—81no—
706Q8—81no—
707Q8C2×#4112yes—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4C2×#4112yes—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4C22×D411yescharacteristic
770C2×C4C22×D411yescharacteristic
771C2×C4C22×D411yescharacteristic
772C2×C4C22×D411yescharacteristic
773C2×C4C22×D411yescharacteristic
774C2×C4C22×D411yescharacteristic
775C2×C4C22×D411yescharacteristic
776C2×C4C22×D411yescharacteristic
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C2511yescharacteristic
781C8—21no—
782C8—21no—
783C8—21no—
784C8—21no—
785C8—21no—
786C8—21no—
787C8—21no—
788C8C2×#4112yes—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—162no—
811C22C23×D411yescharacteristic
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—22no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4C22×#4111yescharacteristic
836C4#58511yescharacteristic
837C2—41no—
838C2—41no—
839C2—41no—
840C2—42no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2D4×#4111yescharacteristic
845C2#358411yescharacteristic
846C2#358411yescharacteristic
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. #3521C2semidirect
3. #3394C2semidirect
4. #3381C2semidirect
5. #3377C2semidirect
6. #3370C2semidirect
7. #3340C2semidirect
8. #3337C2semidirect
9. #3337C2semidirect
10. #3327C2semidirect
11. #3322C2semidirect
12. #3319C2semidirect
13. #3315C2semidirect
14. #3313C2semidirect
15. #3309C2semidirect
16. #3284C2semidirect
17. #3282C2semidirect
18. #3282C2semidirect
19. #3174C2semidirect
20. #3173C2semidirect
21. #3168C2semidirect
22. #3127C2semidirect
23. #3124C2semidirect
24. #3124C2semidirect
25. #3122C2semidirect
26. #3111C2semidirect
27. #3111C2semidirect
28. #2966C2semidirect
29. #2952C2semidirect
30. #2949C2semidirect
31. C4×#135C2semidirect
36. #559C22semidirect
37. #557C22semidirect
50. #552C22semidirect
53. #550C22semidirect
61. #542C22semidirect
72. #529C22semidirect
75. #520C22semidirect
79. C4×#41C22semidirect
80. #499C22semidirect
81. #499C22semidirect
82. #498C22semidirect
85. #492C22semidirect
86. #491C22semidirect
87. #490C22semidirect
89. #489C22semidirect
91. #488C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #484C22semidirect
97. #484C22semidirect
101. #482C22semidirect
103. #480C22semidirect
104. #479C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #479C22semidirect
111. #478C22semidirect
112. #477C22semidirect
113. #477C22semidirect
115. #474C22semidirect
116. #470C22semidirect
120. #467C22semidirect
126. #465C22semidirect
127. #465C22semidirect
130. #464C22semidirect
131. #464C22semidirect
136. #462C22semidirect
137. #462C22semidirect
142. #452C22semidirect
143. #452C22semidirect
152. #446C22semidirect
153. C8×Q8C22semidirect
157. #441C22semidirect
158. #441C22semidirect
159. #441C22semidirect
164. #440C22semidirect
165. #440C22semidirect
166. C4×Q16C22semidirect
167. C4×Q16C22semidirect
168. C4×Q16C22semidirect
175. C4×SD16C22semidirect
176. C4×SD16C22semidirect
177. C4×SD16C22semidirect
178. C4×SD16C22semidirect
184. #435C22semidirect
187. C8×D4C22semidirect
189. #433C22semidirect
190. #432C22semidirect
192. #427C22semidirect
193. C2×#106C22semidirect
197. #417C22semidirect
199. #416C22semidirect
201. #405C22semidirect
202. C2×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#35242
#35212
#33942
#33812
#33772
#33702
#33402
#33372
#33272
#33222
#33192
#33152
#33132
#33092
#32842
#32822
#31742
#31732
#31682
#31272
#31242
#31222
#31112
#29662
#29522
#29492
C4×#1352