Finite Group Databasebeta

← #62023

Subgroups — #62023

Order 256.

896 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3554C211yesmaximal, characteristic, complemented
2#3521C211yesmaximal, characteristic, complemented
3#3401C211yesmaximal, characteristic, complemented
4#3398C211yesmaximal, characteristic, complemented
5#3372C211yesmaximal, characteristic, complemented
6#3370C211yesmaximal, characteristic, complemented
7#3317C211yesmaximal, characteristic, complemented
8#3313C211yesmaximal, characteristic, complemented
9#3312C211yesmaximal, characteristic, complemented
10#3307C211yesmaximal, characteristic, complemented
11#3302C211yesmaximal, characteristic, complemented
12#3301C211yesmaximal, characteristic, complemented
13#3283C211yesmaximal, characteristic, complemented
14#3282C211yesmaximal, characteristic, complemented
15#3269C211yesmaximal, characteristic, complemented
16#3268C211yesmaximal, characteristic, complemented
17#3267C211yesmaximal, characteristic, complemented
18#3266C211yesmaximal, characteristic, complemented
19#3262C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3248C211yesmaximal, characteristic, complemented
22#3225C211yesmaximal, characteristic, complemented
23#3223C211yesmaximal, characteristic, complemented
24#3219C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3116C211yesmaximal, characteristic, complemented
28#3046C211yesmaximal, characteristic, complemented
29#3042C211yesmaximal, characteristic, complemented
30#3035C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic
35C2×#135C2211yescharacteristic
36C2×#135C2211yescharacteristic
37C22×SD16C2211yescharacteristic
38#562—21no—
39#562—21no—
40#559—21no—
41#559C2211yescharacteristic, complemented
42#557C2211yescharacteristic, complemented
43#556C2211yescharacteristic
44#556C2211yescharacteristic
45#554—21no—
46#554C2211yescharacteristic
47#553—21no—
48#553C2211yescharacteristic
49#552—21no—
50#552C2211yescharacteristic
51#551—21no—
52#551—21no—
53#550C2211yescharacteristic
54D4×Q8C2211yescharacteristic
55#548C2211yescharacteristic
56#548C2211yescharacteristic, complemented
57#547C2211yescharacteristic
58#547C2211yescharacteristic
59#547C2211yescharacteristic, complemented
60#546C2211yescharacteristic
61#546C2211yescharacteristic
62#542—21no—
63#542C2211yescharacteristic
64#542C2211yescharacteristic
65#542C2211yescharacteristic, complemented
66#541C2211yescharacteristic
67#540—21no—
68#539—21no—
69#539—21no—
70#539—21no—
71#538—21no—
72#536C2211yescharacteristic
73#536C2211yescharacteristic, complemented
74#533C2211yescharacteristic, complemented
75#532C2211yescharacteristic, complemented
76#529—21no—
77#529C2211yescharacteristic
78#529C2211yescharacteristic
79C2×#126—21no—
80#520C2211yescharacteristic
81#518C2211yescharacteristic
82C4×#41C2211yescharacteristic
83#497C2211yescharacteristic
84#497C2211yescharacteristic
85#497C2211yescharacteristic, complemented
86#496C2211yescharacteristic
87#495C2211yescharacteristic
88#494C2211yescharacteristic, complemented
89#491C2211yescharacteristic, complemented
90#491C2211yescharacteristic, complemented
91#490C2211yescharacteristic, complemented
92#489C2211yescharacteristic, complemented
93#488C2211yescharacteristic, complemented
94#487C2211yescharacteristic, complemented
95#485C2211yescharacteristic
96#485C2211yescharacteristic, complemented
97#485C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#482C2211yescharacteristic
100#481C2211yescharacteristic, complemented
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#478C2211yescharacteristic, complemented
105#477C2211yescharacteristic, complemented
106#477C2211yescharacteristic, complemented
107#476C2211yescharacteristic
108#475C2211yescharacteristic, complemented
109#474C2211yescharacteristic
110#474C2211yescharacteristic, complemented
111#470C2211yescharacteristic
112#468C2211yescharacteristic
113#468C2211yescharacteristic
114#468C2211yescharacteristic, complemented
115#467C2211yescharacteristic
116#467C2211yescharacteristic, complemented
117#467C2211yescharacteristic, complemented
118#467C2211yescharacteristic, complemented
119#466C2211yescharacteristic
120#465C2211yescharacteristic
121#465C2211yescharacteristic
122#465C2211yescharacteristic
123#464C2211yescharacteristic
124#464C2211yescharacteristic
125#464C2211yescharacteristic
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#464C2211yescharacteristic, complemented
131#463C2211yescharacteristic
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic
135#463C2211yescharacteristic
136#463C2211yescharacteristic
137#463C2211yescharacteristic
138#463C2211yescharacteristic
139#462C2211yescharacteristic, complemented
140#462C2211yescharacteristic, complemented
141#462C2211yescharacteristic, complemented
142#462C2211yescharacteristic, complemented
143#462C2211yescharacteristic, complemented
144#461C2211yescharacteristic
145#461C2211yescharacteristic
146#461C2211yescharacteristic
147#461C2211yescharacteristic
148#461C2211yescharacteristic
149#461C2211yescharacteristic
150#461C2211yescharacteristic, complemented
151#460C2211yescharacteristic, complemented
152#459C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic
158#452C2211yescharacteristic, complemented
159#452C2211yescharacteristic, complemented
160#452C2211yescharacteristic, complemented
161#451C2211yescharacteristic
162#451C2211yescharacteristic
163#451C2211yescharacteristic, complemented
164#450C2211yescharacteristic
165#449C2211yescharacteristic
166#449C2211yescharacteristic
167#449C2211yescharacteristic
168#449C2211yescharacteristic
169#448C2211yescharacteristic
170#447C2211yescharacteristic
171#446C2211yescharacteristic, complemented
172#446C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#442C2211yescharacteristic
175#441C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#441C2211yescharacteristic, complemented
178#440C2211yescharacteristic
179#440C2211yescharacteristic
180#440C2211yescharacteristic
181C4×SD16C2211yescharacteristic
182C4×SD16C2211yescharacteristic
183C4×SD16C2211yescharacteristic, complemented
184C4×D8C2211yescharacteristic
185#435C2211yescharacteristic
186#435C2211yescharacteristic
187#435C2211yescharacteristic
188#435C2211yescharacteristic, complemented
189C8×D4C2211yescharacteristic
190C8×D4C2211yescharacteristic, complemented
191#433C2211yescharacteristic
192#433C2211yescharacteristic, complemented
193#432C2211yescharacteristic, complemented
194#424C2211yescharacteristic
195#424C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#419C2211yescharacteristic
198#417C2211yescharacteristic, complemented
199#416C2211yescharacteristic
200#416C2211yescharacteristic, complemented
201#416C2211yescharacteristic, complemented
202C2×#103C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×D4C2311yescharacteristic
212#137—42no—
213AGL(1,ℤ/8)—42no—
214#135—42no—
215#135—42no—
216#135—42no—
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×Q16C2311yescharacteristic
225C2×SD16—42no—
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×SD16C2311yescharacteristic
233C2×SD16C2311yescharacteristic
234C2×SD16C2311yescharacteristic
235C2×SD16C2311yescharacteristic
236C2×SD16C2311yescharacteristic
237C2×SD16C2311yescharacteristic
238C2×D8C2311yescharacteristic
239C2×D8C2311yescharacteristic
240C2×D8C2311yescharacteristic
241C2×D8C2311yescharacteristic
242C2×M16C2311yescharacteristic
243C2×M16C2311yescharacteristic
244C22×C8C2311yescharacteristic
245C22×C8C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C4⋊Q8—21no—
249C4⋊Q8C2311yescharacteristic
250C4⋊Q8C2311yescharacteristic
251C4⋊Q8C2311yescharacteristic
252C4⋊Q8C2311yescharacteristic
253C4⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255C4⋊Q8C2311yescharacteristic
256#127—21no—
257#127C2311yescharacteristic
258#126—21no—
259#126—21no—
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126—21no—
266#126—21no—
267#126—21no—
268#126—21no—
269#126—21no—
270#126D411yescharacteristic
271#126D411yescharacteristic
272#125—21no—
273#125—21no—
274#125—21no—
275#125—21no—
276#125—21no—
277#125—21no—
278#125—21no—
279#125D411yescharacteristic
280#125C2311yescharacteristic
281#125C2311yescharacteristic
282#124—21no—
283#124—21no—
284#124—21no—
285#124—21no—
286#124—21no—
287#124—21no—
288#124—21no—
289#124D411yescharacteristic
290#124C2311yescharacteristic
291#124C2311yescharacteristic
292#124C2311yescharacteristic
293#124C2311yescharacteristic
294#124C2311yescharacteristic
295#124C2311yescharacteristic
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304#123—21no—
305#123—21no—
306#123—21no—
307#123—21no—
308#123—21no—
309#123—21no—
310#123—21no—
311#123—21no—
312#123—21no—
313#123—21no—
314#123—21no—
315#123—21no—
316#123D411yescharacteristic
317#123D411yescharacteristic
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8D411yescharacteristic
335C22⋊Q8C2311yescharacteristic
336C22⋊Q8C2311yescharacteristic
337C22⋊Q8C2311yescharacteristic
338C22⋊Q8C2311yescharacteristic
339C22⋊Q8C2311yescharacteristic
340C22⋊Q8C2311yescharacteristic
341C22⋊Q8C2311yescharacteristic
342C22⋊Q8C2311yescharacteristic
343#121—21no—
344#121—21no—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355#121D411yescharacteristic
356#121C2311yescharacteristic
357#121C2311yescharacteristic
358#121C2311yescharacteristic
359#121C2311yescharacteristic
360#120—21no—
361#120—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×Q8C2311yescharacteristic
371C4×Q8C2311yescharacteristic
372C4×Q8C2311yescharacteristic
373C4×Q8C2311yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399C4×D4C2311yescharacteristic
400#117—21no—
401#117—21no—
402#117—21no—
403#117—21no—
404#117—21no—
405#117—21no—
406#117C2311yescharacteristic
407#117C2311yescharacteristic
408#117C2311yescharacteristic
409#117C2311yescharacteristic
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4C2311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C42—21no—
421C2×C42C2311yescharacteristic
422#107C2311yescharacteristic
423#107C2311yescharacteristic
424#107C2311yescharacteristic
425#107C2311yescharacteristic
426#106C2311yescharacteristic
427#106C2311yescharacteristic
428#106C2311yescharacteristic
429#106C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434C4⋊C8C2311yescharacteristic
435C4⋊C8C2311yescharacteristic
436C4⋊C8C2311yescharacteristic
437C4⋊C8C2311yescharacteristic
438C4⋊C8C2311yescharacteristic
439C4⋊C8C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#103C2311yescharacteristic
457#103C2311yescharacteristic
458#103C2311yescharacteristic
459#103C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466#102C2311yescharacteristic
467#102C2311yescharacteristic
468#102C2311yescharacteristic
469#102C2311yescharacteristic
470#102C2311yescharacteristic
471#102C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474C22⋊C8C2311yescharacteristic
475C22⋊C8C2311yescharacteristic
476C22⋊C8C2311yescharacteristic
477C22⋊C8C2311yescharacteristic
478#97C2311yescharacteristic
479#97C2311yescharacteristic
480#97C2311yescharacteristic
481#97C2311yescharacteristic
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24—21no—
485#41—22no—
486#41—22no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496#41—41no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8C2×D411yescharacteristic
506C2×Q8C2411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×Q8C2411yescharacteristic
510C2×Q8C2411yescharacteristic
511C2×Q8C2411yescharacteristic
512C2×D4—22no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—41no—
527C2×D4C2×D411yescharacteristic
528C2×D4C2×D411yescharacteristic
529C2×D4C2×D411yescharacteristic
530C2×D4C2411yescharacteristic
531C2×D4C2411yescharacteristic
532C2×D4C2411yescharacteristic
533C2×D4C2411yescharacteristic
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—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4C2×D411yescharacteristic
552C22×C4C2×D411yescharacteristic
553C22×C4C2411yescharacteristic
554C22×C4C2411yescharacteristic
555C22×C4C2411yescharacteristic
556Q16—41no—
557Q16—41no—
558Q16—41no—
559Q16—41no—
560Q16—41no—
561Q16—41no—
562Q16—41no—
563Q16—41no—
564SD16—22no—
565SD16—22no—
566SD16—22no—
567SD16—22no—
568SD16—41no—
569SD16—41no—
570SD16—41no—
571SD16—41no—
572SD16—41no—
573SD16—41no—
574SD16—41no—
575SD16—41no—
576D8—22no—
577D8—22no—
578D8—41no—
579D8—41no—
580M16—41no—
581M16—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8C2411yescharacteristic
587C2×C8C2411yescharacteristic
588C2×C8C2411yescharacteristic
589C2×C8C2411yescharacteristic
590C2×C8C2411yescharacteristic
591C2×C8C2411yescharacteristic
592C2×C8C2411yescharacteristic
593C2×C8C2411yescharacteristic
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⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4C2×D411yescharacteristic
628C4⋊C4C2×D411yescharacteristic
629C4⋊C4C2×D411yescharacteristic
630C4⋊C4C2×D411yescharacteristic
631C4⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2×D411yescharacteristic
634C4⋊C4C2×D411yescharacteristic
635C4⋊C4C2×D411yescharacteristic
636C4⋊C4C2×D411yescharacteristic
637C4⋊C4C2411yescharacteristic
638C4⋊C4C2411yescharacteristic
639C4⋊C4C2411yescharacteristic
640C4⋊C4C2411yescharacteristic
641C4⋊C4C2411yescharacteristic
642C4⋊C4C2411yescharacteristic
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⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4C2×D411yescharacteristic
678C22⋊C4C2×D411yescharacteristic
679C22⋊C4C2×D411yescharacteristic
680C22⋊C4C2×D411yescharacteristic
681C22⋊C4C2×D411yescharacteristic
682C22⋊C4C2×D411yescharacteristic
683C22⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42C2×D411yescharacteristic
698C42C2×D411yescharacteristic
699C42C2411yescharacteristic
700C42C2411yescharacteristic
701C42C2411yescharacteristic
702C42C2411yescharacteristic
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—42no—
708C23—81no—
709C23—81no—
710C23C22×D411yescharacteristic
711C23C22×D411yescharacteristic
712C23C22×D411yescharacteristic
713Q8—21no—
714Q8—21no—
715Q8—21no—
716Q8—21no—
717Q8—21no—
718Q8—21no—
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—41no—
726Q8—81no—
727Q8—81no—
728Q8—81no—
729Q8—81no—
730D4—21no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4H(5,𝔽2)12yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4C22×D411yescharacteristic
792C2×C4C22×D411yescharacteristic
793C2×C4C22×D411yescharacteristic
794C2×C4C22×D411yescharacteristic
795C2×C4C22×D411yescharacteristic
796C2×C4C22×D411yescharacteristic
797C2×C4C22×D411yescharacteristic
798C2×C4C22×D411yescharacteristic
799C2×C4C22×D411yescharacteristic
800C2×C4C22×D411yescharacteristic
801C2×C4C22×D411yescharacteristic
802C2×C4C2511yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—21no—
810C8—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—162no—
833C22C23×D411yescharacteristic
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4C2×H(5,𝔽2)11yescharacteristic
858C4#58511yescharacteristic
859C2—41no—
860C2—41no—
861C2—41no—
862C2—42no—
863C2—81no—
864C2—81no—
865C2—81no—
866C2#348811yescharacteristic
867C2#358411yescharacteristic
868C2#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. #3554C2semidirect
2. #3521C2semidirect
3. #3401C2semidirect
4. #3398C2semidirect
5. #3372C2semidirect
6. #3370C2semidirect
7. #3317C2semidirect
8. #3313C2semidirect
9. #3312C2semidirect
10. #3307C2semidirect
11. #3302C2semidirect
12. #3301C2semidirect
13. #3283C2semidirect
14. #3282C2semidirect
15. #3269C2semidirect
16. #3268C2semidirect
17. #3267C2semidirect
18. #3266C2semidirect
19. #3262C2semidirect
20. #3258C2semidirect
21. #3248C2semidirect
22. #3225C2semidirect
23. #3223C2semidirect
24. #3219C2semidirect
25. #3125C2semidirect
26. #3118C2semidirect
27. #3116C2semidirect
28. #3046C2semidirect
29. #3042C2semidirect
30. #3035C2semidirect
31. #2992C2semidirect
41. #559C22semidirect
42. #557C22semidirect
56. #548C22semidirect
59. #547C22semidirect
65. #542C22semidirect
73. #536C22semidirect
74. #533C22semidirect
75. #532C22semidirect
85. #497C22semidirect
88. #494C22semidirect
89. #491C22semidirect
90. #491C22semidirect
91. #490C22semidirect
92. #489C22semidirect
93. #488C22semidirect
94. #487C22semidirect
96. #485C22semidirect
97. #485C22semidirect
98. #483C22semidirect
100. #481C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #478C22semidirect
105. #477C22semidirect
106. #477C22semidirect
108. #475C22semidirect
110. #474C22semidirect
114. #468C22semidirect
116. #467C22semidirect
117. #467C22semidirect
118. #467C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #464C22semidirect
139. #462C22semidirect
140. #462C22semidirect
141. #462C22semidirect
142. #462C22semidirect
143. #462C22semidirect
150. #461C22semidirect
151. #460C22semidirect
158. #452C22semidirect
159. #452C22semidirect
160. #452C22semidirect
163. #451C22semidirect
171. #446C22semidirect
172. #446C22semidirect
175. #441C22semidirect
176. #441C22semidirect
177. #441C22semidirect
183. C4×SD16C22semidirect
188. #435C22semidirect
190. C8×D4C22semidirect
192. #433C22semidirect
193. #432C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect
198. #417C22semidirect
200. #416C22semidirect
201. #416C22semidirect
202. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35542
#35212
#34012
#33982
#33722
#33702
#33172
#33132
#33122
#33072
#33022
#33012
#32832
#32822
#32692
#32682
#32672
#32662
#32622
#32582
#32482
#32252
#32232
#32192
#31252
#31182
#31162
#30462
#30422
#30352
#29922