Finite Group Databasebeta

← #7234134

Subgroups — #7234134

Order 512.

1549 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53137C211yesmaximal, characteristic, complemented
2#53103C211yesmaximal, characteristic
3#33274C211yesmaximal, characteristic, complemented
4#33274C211yesmaximal, characteristic, complemented
5#32868C211yesmaximal, characteristic, complemented
6#32865C211yesmaximal, characteristic, complemented
7#31735C211yesmaximal, characteristic, complemented
8#31734C211yesmaximal, characteristic, complemented
9#31726C211yesmaximal, characteristic, complemented
10#31725C211yesmaximal, characteristic, complemented
11#31721C211yesmaximal, characteristic, complemented
12#31721C211yesmaximal, characteristic, complemented
13#31677C211yesmaximal, characteristic, complemented
14#31676C211yesmaximal, characteristic, complemented
15#31673C211yesmaximal, characteristic, complemented
16#31672C211yesmaximal, characteristic, complemented
17#31668C211yesmaximal, characteristic, complemented
18#31667C211yesmaximal, characteristic, complemented
19#27669C211yesmaximal, characteristic, complemented
20#27668C211yesmaximal, characteristic, complemented
21#27660C211yesmaximal, characteristic, complemented
22#24795C211yesmaximal, characteristic, complemented
23#24794C211yesmaximal, characteristic, complemented
24#24789C211yesmaximal, characteristic, complemented
25#24788C211yesmaximal, characteristic, complemented
26#24786C211yesmaximal, characteristic, complemented
27#24786C211yesmaximal, characteristic, complemented
28#24269C211yesmaximal, characteristic, complemented
29#24269C211yesmaximal, characteristic, complemented
30#24264C211yesmaximal, characteristic, complemented
31#21685C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#468C2211yescharacteristic
34C2×#468C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#436C2211yescharacteristic, complemented
40C2×#435C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×#435C2211yescharacteristic, complemented
43C2×#435C2211yescharacteristic, complemented
44C2×C8×D4C2211yescharacteristic
45C2×#428C2211yescharacteristic, complemented
46C2×#428C2211yescharacteristic, complemented
47C2×#427C2211yescharacteristic, complemented
48#2838—21no—
49#2838—21no—
50#2829—21no—
51#2829—21no—
52#2826—21no—
53#2824—21no—
54#2815—21no—
55#2812—21no—
56#2807—21no—
57#2778—21no—
58#2778—21no—
59#2752—21no—
60#2742—21no—
61#2735—21no—
62#2678—21no—
63#2678—21no—
64#2645C2211yescharacteristic, complemented
65#2645C2211yescharacteristic, complemented
66#2644C2211yescharacteristic
67#2644C2211yescharacteristic
68#2487C2211yescharacteristic
69#2486C2211yescharacteristic
70#2485C2211yescharacteristic
71#2485C2211yescharacteristic
72#2485C2211yescharacteristic
73#2485C2211yescharacteristic
74#2417C2211yescharacteristic, complemented
75#2417C2211yescharacteristic, complemented
76#2416C2211yescharacteristic
77#2416C2211yescharacteristic
78#2415C2211yescharacteristic, complemented
79#2415C2211yescharacteristic, complemented
80#2415C2211yescharacteristic, complemented
81#2415C2211yescharacteristic, complemented
82#2414C2211yescharacteristic
83#2414C2211yescharacteristic
84#2414C2211yescharacteristic
85#2414C2211yescharacteristic
86#2409C2211yescharacteristic
87#2409C2211yescharacteristic
88#2409C2211yescharacteristic
89#2408C2211yescharacteristic
90#2408C2211yescharacteristic
91#2408C2211yescharacteristic
92#2397C2211yescharacteristic
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2087C2211yescharacteristic, complemented
98#2086C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2076C2211yescharacteristic
104#2075C2211yescharacteristic
105#2068C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic, complemented
110#2066C2211yescharacteristic, complemented
111#2066C2211yescharacteristic, complemented
112#2066C2211yescharacteristic, complemented
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2055C2211yescharacteristic
121#2055C2211yescharacteristic
122#2055C2211yescharacteristic
123#2036C2211yescharacteristic, complemented
124#2036C2211yescharacteristic, complemented
125#2035C2211yescharacteristic, complemented
126#2035C2211yescharacteristic, complemented
127#2035C2211yescharacteristic, complemented
128#2035C2211yescharacteristic, complemented
129#2034C2211yescharacteristic
130#2034C2211yescharacteristic
131#2034C2211yescharacteristic
132#2034C2211yescharacteristic
133#2033C2211yescharacteristic
134#2033C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic
143#1973C2211yescharacteristic
144#1973C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1955C2211yescharacteristic
148#1955C2211yescharacteristic, complemented
149#1954C2211yescharacteristic
150#1954C2211yescharacteristic
151#1954C2211yescharacteristic, complemented
152#1954C2211yescharacteristic, complemented
153#1944C2211yescharacteristic, complemented
154#1944C2211yescharacteristic, complemented
155#1943C2211yescharacteristic, complemented
156#1943C2211yescharacteristic, complemented
157#1942C2211yescharacteristic, complemented
158#1942C2211yescharacteristic, complemented
159#1936C2211yescharacteristic
160#1936C2211yescharacteristic
161#1935C2211yescharacteristic, complemented
162#1935C2211yescharacteristic, complemented
163#1934C2211yescharacteristic
164#1934C2211yescharacteristic
165#1934C2211yescharacteristic
166#1934C2211yescharacteristic
167#1933C2211yescharacteristic, complemented
168#1933C2211yescharacteristic, complemented
169#1933C2211yescharacteristic, complemented
170#1933C2211yescharacteristic, complemented
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic
173#1875C2211yescharacteristic
174#1875C2211yescharacteristic
175#1874C2211yescharacteristic
176#1874C2211yescharacteristic
177#1873C2211yescharacteristic, complemented
178#1873C2211yescharacteristic, complemented
179#1873C2211yescharacteristic, complemented
180#1873C2211yescharacteristic, complemented
181#1872C2211yescharacteristic, complemented
182#1872C2211yescharacteristic, complemented
183#1843C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1825C2211yescharacteristic, complemented
187#1825C2211yescharacteristic, complemented
188#1824C2211yescharacteristic, complemented
189#1823C2211yescharacteristic, complemented
190#1809C2211yescharacteristic, complemented
191#1809C2211yescharacteristic, complemented
192#1808C2211yescharacteristic
193#1808C2211yescharacteristic
194#1808C2211yescharacteristic, complemented
195#1807C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic
198#1787C2211yescharacteristic
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201#1786C2211yescharacteristic
202#1726C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16—42no—
206C22×SD16—42no—
207C22×SD16—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121—21no—
224C2×#121—21no—
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×#120—21no—
233C2×#120—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246#468—42no—
247#468—42no—
248#468—42no—
249#468—42no—
250#465—42no—
251#465—42no—
252#436—42no—
253#435—42no—
254#435—42no—
255#435—42no—
256#435—42no—
257C8×D4—42no—
258#428—42no—
259#428—42no—
260#427—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321#401—21no—
322#401—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#399—21no—
331#399D411yescharacteristic
332#399D411yescharacteristic
333#399D411yescharacteristic
334#399D411yescharacteristic
335#398—21no—
336#398—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#395—21no—
360#395—21no—
361#395—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#393—21no—
380#393—21no—
381#393—21no—
382#392—21no—
383#392—21no—
384#392—21no—
385#392—21no—
386#392—21no—
387#392—21no—
388#392—21no—
389#392D411yescharacteristic
390#392D411yescharacteristic
391#392D411yescharacteristic
392#392D411yescharacteristic
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#390—21no—
400#390—21no—
401#390—21no—
402#390—21no—
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#381—21no—
454#380—21no—
455#380—21no—
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#379—21no—
469#379—21no—
470#379—21no—
471#376C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2×D411yescharacteristic
524C22×D4C2×D411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—416no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—22no—
553C22×C8—22no—
554C22×C8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567#123—82no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—82no—
593#121—82no—
594#120—82no—
595#120—82no—
596#120—82no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609#117—41no—
610#117—41no—
611#117—41no—
612#117—41no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—41no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—22no—
719#107—22no—
720#107—22no—
721#107—22no—
722#107—41no—
723#107—41no—
724#106—22no—
725#106—22no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772#97—22no—
773#97—22no—
774#97—41no—
775C4×C8—22no—
776C4×C8—41no—
777C4×C8—41no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818C24—21no—
819C24—21no—
820C24—42no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24C22×D411yescharacteristic
828C24C22×D411yescharacteristic
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—44no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×Q8—82no—
848C2×Q8—82no—
849C2×Q8—82no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—44no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—82no—
887C2×D4—82no—
888C2×D4—82no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—42no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C2511yescharacteristic
963SD16—44no—
964SD16—44no—
965SD16—44no—
966SD16—44no—
967M16—44no—
968M16—44no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—44no—
991C2×C8—44no—
992C2×C8H(5,𝔽2)12yes—
993C2×C8H(5,𝔽2)12yes—
994C2×C8H(5,𝔽2)12yes—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—84no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23—162no—
1154C23—162no—
1155C23#57712yes—
1156C23C23×D411yescharacteristic
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—84no—
1166D4—44no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—82no—
1176D4—82no—
1177D4—82no—
1178D4—82no—
1179D4—82no—
1180D4—84no—
1181D4—162no—
1182D4—162no—
1183D4—162no—
1184D4—162no—
1185D4—162no—
1186D4—162no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—84no—
1276C2×C4—162no—
1277C2×C4—162no—
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4C2×H(5,𝔽2)11yescharacteristic
1280C2×C4C2×H(5,𝔽2)11yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C2×C4#58511yescharacteristic
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8#56014yes—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—168no—
1335C22#349611yescharacteristic
1336C22#349611yescharacteristic
1337C22#349611yescharacteristic
1338C22C2×#57711yescharacteristic
1339C22#358411yescharacteristic
1340C22#358511yescharacteristic
1341C22#358611yescharacteristic
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4C2×#56011yescharacteristic
1367C4#355111yescharacteristic
1368C4#355111yescharacteristic
1369C4#355111yescharacteristic
1370C2—42no—
1371C2—81no—
1372C2—81no—
1373C2—81no—
1374C2—161no—
1375C2—161no—
1376C2#4632811yescharacteristic
1377C2#6227711yescharacteristic
1378C2#6228511yescharacteristic
1379C2#6230711yescharacteristic
1380C2#6230811yescharacteristic
1381C2#6230911yescharacteristic
1382C2#6231011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#53103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2397 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53137C2semidirect
3. #33274C2semidirect
4. #33274C2semidirect
5. #32868C2semidirect
6. #32865C2semidirect
7. #31735C2semidirect
8. #31734C2semidirect
9. #31726C2semidirect
10. #31725C2semidirect
11. #31721C2semidirect
12. #31721C2semidirect
13. #31677C2semidirect
14. #31676C2semidirect
15. #31673C2semidirect
16. #31672C2semidirect
17. #31668C2semidirect
18. #31667C2semidirect
19. #27669C2semidirect
20. #27668C2semidirect
21. #27660C2semidirect
22. #24795C2semidirect
23. #24794C2semidirect
24. #24789C2semidirect
25. #24788C2semidirect
26. #24786C2semidirect
27. #24786C2semidirect
28. #24269C2semidirect
29. #24269C2semidirect
30. #24264C2semidirect
31. #21685C2semidirect
39. C2×#436C22semidirect
42. C2×#435C22semidirect
43. C2×#435C22semidirect
45. C2×#428C22semidirect
46. C2×#428C22semidirect
47. C2×#427C22semidirect
64. #2645C22semidirect
65. #2645C22semidirect
74. #2417C22semidirect
75. #2417C22semidirect
78. #2415C22semidirect
79. #2415C22semidirect
80. #2415C22semidirect
81. #2415C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2087C22semidirect
98. #2086C22semidirect
105. #2068C22semidirect
106. #2068C22semidirect
109. #2066C22semidirect
110. #2066C22semidirect
111. #2066C22semidirect
112. #2066C22semidirect
123. #2036C22semidirect
124. #2036C22semidirect
125. #2035C22semidirect
126. #2035C22semidirect
127. #2035C22semidirect
128. #2035C22semidirect
148. #1955C22semidirect
151. #1954C22semidirect
152. #1954C22semidirect
153. #1944C22semidirect
154. #1944C22semidirect
155. #1943C22semidirect
156. #1943C22semidirect
157. #1942C22semidirect
158. #1942C22semidirect
161. #1935C22semidirect
162. #1935C22semidirect
167. #1933C22semidirect
168. #1933C22semidirect
169. #1933C22semidirect
170. #1933C22semidirect
177. #1873C22semidirect
178. #1873C22semidirect
179. #1873C22semidirect
180. #1873C22semidirect
181. #1872C22semidirect
182. #1872C22semidirect
183. #1843C22semidirect
184. #1825C22semidirect
185. #1825C22semidirect
186. #1825C22semidirect
187. #1825C22semidirect
188. #1824C22semidirect
189. #1823C22semidirect
190. #1809C22semidirect
191. #1809C22semidirect
194. #1808C22semidirect
202. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#531372
#531032
#332742
#328682
#328652
#317352
#317342
#317262
#317252
#317212
#316772
#316762
#316732
#316722
#316682
#316672
#276692
#276682
#276602
#247952
#247942
#247892
#247882
#247862
#242692
#242642
#216852