Finite Group Databasebeta

← #62614

Subgroups — #62614

Order 256.

867 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic, complemented
2#3558C211yesmaximal, characteristic, complemented
3#3371C211yesmaximal, characteristic, complemented
4#3370C211yesmaximal, characteristic, complemented
5#3365C211yesmaximal, characteristic, complemented
6#3361C211yesmaximal, characteristic, complemented
7#3327C211yesmaximal, characteristic, complemented
8#3326C211yesmaximal, characteristic, complemented
9#3325C211yesmaximal, characteristic, complemented
10#3324C211yesmaximal, characteristic, complemented
11#3323C211yesmaximal, characteristic, complemented
12#3322C211yesmaximal, characteristic, complemented
13#3321C211yesmaximal, characteristic, complemented
14#3318C211yesmaximal, characteristic, complemented
15#3313C211yesmaximal, characteristic, complemented
16#3310C211yesmaximal, characteristic, complemented
17#3297C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3243C211yesmaximal, characteristic, complemented
21#3228C211yesmaximal, characteristic, complemented
22#3224C211yesmaximal, characteristic, complemented
23#3224C211yesmaximal, characteristic, complemented
24#3211C211yesmaximal, characteristic, complemented
25#3175C211yesmaximal, characteristic, complemented
26#3173C211yesmaximal, characteristic, complemented
27#3171C211yesmaximal, characteristic, complemented
28#3140C211yesmaximal, characteristic, complemented
29#3136C211yesmaximal, characteristic, complemented
30#3136C211yesmaximal, characteristic, complemented
31#2969C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#562—21no—
35H(3,𝔽4)—21no—
36#559C2211yescharacteristic
37#559C2211yescharacteristic
38#557C2211yescharacteristic, complemented
39#556—21no—
40#556C2211yescharacteristic, complemented
41#555C2211yescharacteristic, complemented
42#554C2211yescharacteristic, complemented
43#553C2211yescharacteristic, complemented
44#553C2211yescharacteristic, complemented
45#552—21no—
46#552C2211yescharacteristic, complemented
47#552C2211yescharacteristic, complemented
48#548C2211yescharacteristic
49#548C2211yescharacteristic
50#546—21no—
51#546—21no—
52#546C2211yescharacteristic
53#546C2211yescharacteristic
54D42C2211yescharacteristic
55D42C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#544C2211yescharacteristic, complemented
58#542—21no—
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic
62#542C2211yescharacteristic, complemented
63#542C2211yescharacteristic, complemented
64#541—21no—
65#539—21no—
66#538—21no—
67#538—21no—
68#538—21no—
69#535C2211yescharacteristic
70#535C2211yescharacteristic
71#534—21no—
72#533C2211yescharacteristic, complemented
73#532C2211yescharacteristic
74#529C2211yescharacteristic
75#529C2211yescharacteristic, complemented
76C2×#124C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#500C2211yescharacteristic, complemented
79#498C2211yescharacteristic, complemented
80#496C2211yescharacteristic, complemented
81#495C2211yescharacteristic, complemented
82#495C2211yescharacteristic, complemented
83#490C2211yescharacteristic
84#490C2211yescharacteristic
85#490C2211yescharacteristic, complemented
86#489C2211yescharacteristic, complemented
87#489C2211yescharacteristic, complemented
88#489C2211yescharacteristic, complemented
89#489C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#489C2211yescharacteristic, complemented
92#489C2211yescharacteristic, complemented
93#488C2211yescharacteristic, complemented
94#488C2211yescharacteristic, complemented
95#488C2211yescharacteristic, complemented
96#488C2211yescharacteristic, complemented
97#488C2211yescharacteristic, complemented
98#488C2211yescharacteristic, complemented
99#488C2211yescharacteristic, complemented
100#488C2211yescharacteristic, complemented
101#486C2211yescharacteristic
102#486C2211yescharacteristic
103#486C2211yescharacteristic, complemented
104#486C2211yescharacteristic, complemented
105#485C2211yescharacteristic, complemented
106#485C2211yescharacteristic, complemented
107#484C2211yescharacteristic, complemented
108#483C2211yescharacteristic, complemented
109#482C2211yescharacteristic
110#482C2211yescharacteristic
111#482C2211yescharacteristic, complemented
112#482C2211yescharacteristic, complemented
113#482C2211yescharacteristic, complemented
114#482C2211yescharacteristic, complemented
115#481C2211yescharacteristic
116#480C2211yescharacteristic
117#479C2211yescharacteristic, complemented
118#479C2211yescharacteristic, complemented
119#478C2211yescharacteristic, complemented
120#478C2211yescharacteristic, complemented
121#478C2211yescharacteristic, complemented
122#478C2211yescharacteristic, complemented
123#478C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#476C2211yescharacteristic, complemented
127#475C2211yescharacteristic, complemented
128#474C2211yescharacteristic, complemented
129#470C2211yescharacteristic, complemented
130#469C2211yescharacteristic
131#469C2211yescharacteristic, complemented
132#469C2211yescharacteristic, complemented
133#468C2211yescharacteristic
134#468C2211yescharacteristic, complemented
135#468C2211yescharacteristic, complemented
136#468C2211yescharacteristic, complemented
137#467C2211yescharacteristic, complemented
138#466C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic, complemented
141#464C2211yescharacteristic, complemented
142#464C2211yescharacteristic, complemented
143#464C2211yescharacteristic, complemented
144#464C2211yescharacteristic, complemented
145#463C2211yescharacteristic, complemented
146#463C2211yescharacteristic, complemented
147#463C2211yescharacteristic, complemented
148#463C2211yescharacteristic, complemented
149#460C2211yescharacteristic
150#460C2211yescharacteristic
151#459C2211yescharacteristic
152#459C2211yescharacteristic
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#451C2211yescharacteristic, complemented
156#450C2211yescharacteristic
157#450C2211yescharacteristic, complemented
158#450C2211yescharacteristic, complemented
159#449C2211yescharacteristic, complemented
160#449C2211yescharacteristic, complemented
161#448C2211yescharacteristic, complemented
162#447C2211yescharacteristic
163#447C2211yescharacteristic, complemented
164#447C2211yescharacteristic, complemented
165#446C2211yescharacteristic, complemented
166C8×Q8C2211yescharacteristic, complemented
167#442C2211yescharacteristic, complemented
168#441C2211yescharacteristic, complemented
169#440C2211yescharacteristic, complemented
170#440C2211yescharacteristic, complemented
171C4×Q16C2211yescharacteristic, complemented
172C4×SD16C2211yescharacteristic, complemented
173C4×SD16C2211yescharacteristic, complemented
174C4×SD16C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic, complemented
176C4×D8C2211yescharacteristic, complemented
177C4×D8C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic, complemented
180#436C2211yescharacteristic, complemented
181#436C2211yescharacteristic, complemented
182#435C2211yescharacteristic, complemented
183#435C2211yescharacteristic, complemented
184C8×D4C2211yescharacteristic, complemented
185#433C2211yescharacteristic, complemented
186#433C2211yescharacteristic, complemented
187#431C2211yescharacteristic, complemented
188#419C2211yescharacteristic, complemented
189#419C2211yescharacteristic, complemented
190#418C2211yescharacteristic
191#418C2211yescharacteristic
192#418C2211yescharacteristic, complemented
193#418C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic, complemented
200#405C2211yescharacteristic, complemented
201#405C2211yescharacteristic, complemented
202C4×M16C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C22×Q8C2311yescharacteristic
207C22×D4—21no—
208C22×D4—21no—
209C22×D4C2311yescharacteristic
210C22×D4C2311yescharacteristic
211C22×D4C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×D8C2311yescharacteristic
222C2×D8C2311yescharacteristic
223C2×D8C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C2×M16C2311yescharacteristic
226C2×M16C2311yescharacteristic
227C2×M16C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C22×C8C2311yescharacteristic
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238#127C2311yescharacteristic
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#126D411yescharacteristic
253#126D411yescharacteristic
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125D411yescharacteristic
261#125C2311yescharacteristic
262#125C2311yescharacteristic
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124D411yescharacteristic
281#124C2311yescharacteristic
282#124C2311yescharacteristic
283#124C2311yescharacteristic
284#124C2311yescharacteristic
285#124C2311yescharacteristic
286#124C2311yescharacteristic
287#124C2311yescharacteristic
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#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123D411yescharacteristic
304#123D411yescharacteristic
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8D411yescharacteristic
321C22⋊Q8C2311yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325C22⋊Q8C2311yescharacteristic
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121D411yescharacteristic
341#121C2311yescharacteristic
342#121C2311yescharacteristic
343#121C2311yescharacteristic
344#121C2311yescharacteristic
345#121C2311yescharacteristic
346#121C2311yescharacteristic
347#121C2311yescharacteristic
348#120—21no—
349#120—21no—
350#120—21no—
351#120—21no—
352#120—21no—
353#120—21no—
354#120—21no—
355#120—21no—
356#120—21no—
357#120—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8C2311yescharacteristic
363C4×Q8C2311yescharacteristic
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384C4×D4C2311yescharacteristic
385C4×D4C2311yescharacteristic
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⋊C4—21no—
397C2×C4⋊C4C2311yescharacteristic
398C2×C4⋊C4C2311yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#106C2311yescharacteristic
411#106C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416C4⋊C8C2311yescharacteristic
417C4⋊C8C2311yescharacteristic
418C4⋊C8C2311yescharacteristic
419C4⋊C8C2311yescharacteristic
420C4⋊C8C2311yescharacteristic
421C4⋊C8C2311yescharacteristic
422#103C2311yescharacteristic
423#103C2311yescharacteristic
424#103C2311yescharacteristic
425#103C2311yescharacteristic
426#103C2311yescharacteristic
427#103C2311yescharacteristic
428#103C2311yescharacteristic
429#103C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#102C2311yescharacteristic
437#102C2311yescharacteristic
438#102C2311yescharacteristic
439#102C2311yescharacteristic
440#102C2311yescharacteristic
441#102C2311yescharacteristic
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
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472C4×C8C2311yescharacteristic
473C4×C8C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24—21no—
480C24—21no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—82no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8C2×D411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×Q8C2411yescharacteristic
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—21no—
515C2×D4—21no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—82no—
523C2×D4—82no—
524C2×D4C2×D411yescharacteristic
525C2×D4C2×D411yescharacteristic
526C2×D4C2×D411yescharacteristic
527C2×D4C2411yescharacteristic
528C2×D4C2411yescharacteristic
529C2×D4C2411yescharacteristic
530C2×D4C2411yescharacteristic
531C2×D4C2411yescharacteristic
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×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—
557D8—41no—
558D8—41no—
559D8—41no—
560D8—41no—
561M16—41no—
562M16—41no—
563M16—41no—
564M16—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
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⋊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
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42C2×D411yescharacteristic
677C42C2×D411yescharacteristic
678C42C2411yescharacteristic
679C42C2411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—42no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23—81no—
694C23—81no—
695C23—81no—
696C23C22×D411yescharacteristic
697C23C22×D411yescharacteristic
698C23C22×D411yescharacteristic
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—41no—
706Q8—81no—
707Q8—81no—
708Q8—81no—
709Q8—81no—
710Q8—81no—
711Q8—81no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—21no—
721D4—21no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—42no—
726D4—42no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
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—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—81no—
763C2×C4—81no—
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×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—162no—
819C22—162no—
820C22—162no—
821C22C23×D411yescharacteristic
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4#58511yescharacteristic
845C4#58511yescharacteristic
846C2—41no—
847C2—41no—
848C2—41no—
849C2—81no—
850C2—81no—
851C2—81no—
852C2—81no—
853C2—81no—
854C2#350011yescharacteristic
855C2#358411yescharacteristic
856C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3565C2semidirect
2. #3558C2semidirect
3. #3371C2semidirect
4. #3370C2semidirect
5. #3365C2semidirect
6. #3361C2semidirect
7. #3327C2semidirect
8. #3326C2semidirect
9. #3325C2semidirect
10. #3324C2semidirect
11. #3323C2semidirect
12. #3322C2semidirect
13. #3321C2semidirect
14. #3318C2semidirect
15. #3313C2semidirect
16. #3310C2semidirect
17. #3297C2semidirect
18. #3296C2semidirect
19. #3244C2semidirect
20. #3243C2semidirect
21. #3228C2semidirect
22. #3224C2semidirect
23. #3224C2semidirect
24. #3211C2semidirect
25. #3175C2semidirect
26. #3173C2semidirect
27. #3171C2semidirect
28. #3140C2semidirect
29. #3136C2semidirect
30. #3136C2semidirect
31. #2969C2semidirect
38. #557C22semidirect
40. #556C22semidirect
41. #555C22semidirect
42. #554C22semidirect
43. #553C22semidirect
44. #553C22semidirect
46. #552C22semidirect
47. #552C22semidirect
56. #544C22semidirect
57. #544C22semidirect
62. #542C22semidirect
63. #542C22semidirect
72. #533C22semidirect
75. #529C22semidirect
77. #501C22semidirect
78. #500C22semidirect
79. #498C22semidirect
80. #496C22semidirect
81. #495C22semidirect
82. #495C22semidirect
85. #490C22semidirect
86. #489C22semidirect
87. #489C22semidirect
88. #489C22semidirect
89. #489C22semidirect
90. #489C22semidirect
91. #489C22semidirect
92. #489C22semidirect
93. #488C22semidirect
94. #488C22semidirect
95. #488C22semidirect
96. #488C22semidirect
97. #488C22semidirect
98. #488C22semidirect
99. #488C22semidirect
100. #488C22semidirect
103. #486C22semidirect
104. #486C22semidirect
105. #485C22semidirect
106. #485C22semidirect
107. #484C22semidirect
108. #483C22semidirect
111. #482C22semidirect
112. #482C22semidirect
113. #482C22semidirect
114. #482C22semidirect
117. #479C22semidirect
118. #479C22semidirect
119. #478C22semidirect
120. #478C22semidirect
121. #478C22semidirect
122. #478C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #477C22semidirect
126. #476C22semidirect
127. #475C22semidirect
128. #474C22semidirect
129. #470C22semidirect
131. #469C22semidirect
132. #469C22semidirect
134. #468C22semidirect
135. #468C22semidirect
136. #468C22semidirect
137. #467C22semidirect
140. #465C22semidirect
141. #464C22semidirect
142. #464C22semidirect
143. #464C22semidirect
144. #464C22semidirect
145. #463C22semidirect
146. #463C22semidirect
147. #463C22semidirect
148. #463C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #451C22semidirect
157. #450C22semidirect
158. #450C22semidirect
159. #449C22semidirect
160. #449C22semidirect
161. #448C22semidirect
163. #447C22semidirect
164. #447C22semidirect
165. #446C22semidirect
166. C8×Q8C22semidirect
167. #442C22semidirect
168. #441C22semidirect
169. #440C22semidirect
170. #440C22semidirect
171. C4×Q16C22semidirect
172. C4×SD16C22semidirect
173. C4×SD16C22semidirect
174. C4×SD16C22semidirect
175. C4×SD16C22semidirect
176. C4×D8C22semidirect
177. C4×D8C22semidirect
178. C4×D8C22semidirect
179. #436C22semidirect
180. #436C22semidirect
181. #436C22semidirect
182. #435C22semidirect
183. #435C22semidirect
184. C8×D4C22semidirect
185. #433C22semidirect
186. #433C22semidirect
187. #431C22semidirect
188. #419C22semidirect
189. #419C22semidirect
192. #418C22semidirect
193. #418C22semidirect
194. #417C22semidirect
195. #417C22semidirect
196. #416C22semidirect
197. #416C22semidirect
198. C2×#102C22semidirect
199. C2×#102C22semidirect
200. #405C22semidirect
201. #405C22semidirect
202. C4×M16C22semidirect

Maximal subgroups

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

subgroupindex
#35652
#35582
#33712
#33702
#33652
#33612
#33272
#33262
#33252
#33242
#33232
#33222
#33212
#33182
#33132
#33102
#32972
#32962
#32442
#32432
#32282
#32242
#32112
#31752
#31732
#31712
#31402
#31362
#29692