Finite Group Databasebeta

← #7278010

Subgroups — #7278010

Order 512.

1595 conjugacy classes of subgroups.

The subgroup lattice has 1401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42581C211yesmaximal, characteristic, complemented
2#42552C211yesmaximal, characteristic, complemented
3#32865C211yesmaximal, characteristic, complemented
4#32623C211yesmaximal, characteristic, complemented
5#32621C211yesmaximal, characteristic, complemented
6#31934C211yesmaximal, characteristic, complemented
7#31931C211yesmaximal, characteristic, complemented
8#31730C211yesmaximal, characteristic, complemented
9#31501C211yesmaximal, characteristic, complemented
10#31486C211yesmaximal, characteristic, complemented
11#31063C211yesmaximal, characteristic, complemented
12#30595C211yesmaximal, characteristic, complemented
13#30592C211yesmaximal, characteristic, complemented
14#30456C211yesmaximal, characteristic, complemented
15#30454C211yesmaximal, characteristic, complemented
16#29510C211yesmaximal, characteristic, complemented
17#29504C211yesmaximal, characteristic, complemented
18#28738C211yesmaximal, characteristic, complemented
19#28257C211yesmaximal, characteristic, complemented
20#28185C211yesmaximal, characteristic, complemented
21#27107C211yesmaximal, characteristic, complemented
22#27097C211yesmaximal, characteristic, complemented
23#25162C211yesmaximal, characteristic, complemented
24#25160C211yesmaximal, characteristic, complemented
25#25112C211yesmaximal, characteristic, complemented
26#25109C211yesmaximal, characteristic, complemented
27#25085C211yesmaximal, characteristic, complemented
28#25076C211yesmaximal, characteristic, complemented
29#24537C211yesmaximal, characteristic, complemented
30#24530C211yesmaximal, characteristic, complemented
31#22209C211yesmaximal, characteristic, complemented
32C2×#492C2211yescharacteristic
33C2×#466C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#460C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#463C2211yescharacteristic, complemented
38C2×#459C2211yescharacteristic
39C2×#449C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#449C2211yescharacteristic, complemented
42C2×#450C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×C8×Q8C2211yescharacteristic, complemented
46C2×C4×D8C2211yescharacteristic
47C2×C8×D4C2211yescharacteristic
48C2×#416C2211yescharacteristic, complemented
49C22×#102C2211yescharacteristic
50#2827—21no—
51#2825—21no—
52#2778—21no—
53#2778—21no—
54#2765—21no—
55#2750—21no—
56#2702—21no—
57#2697—21no—
58#2678—21no—
59#2676—21no—
60#2648—21no—
61#2646—21no—
62#2645C2211yescharacteristic, complemented
63#2644C2211yescharacteristic
64#2636—21no—
65#2617—21no—
66#2568C2211yescharacteristic, complemented
67#2548C2211yescharacteristic
68#2538C2211yescharacteristic
69#2538C2211yescharacteristic, complemented
70#2502C2211yescharacteristic
71#2500C2211yescharacteristic
72#2496C2211yescharacteristic, complemented
73#2494C2211yescharacteristic
74#2472—21no—
75#2450—21no—
76#2433C2211yescharacteristic
77#2432C2211yescharacteristic, complemented
78#2429C2211yescharacteristic
79#2428C2211yescharacteristic
80#2428C2211yescharacteristic
81#2427C2211yescharacteristic
82#2423C2211yescharacteristic, complemented
83#2422C2211yescharacteristic
84#2417C2211yescharacteristic
85#2414C2211yescharacteristic
86#2408C2211yescharacteristic
87#2407C2211yescharacteristic
88#2398C2211yescharacteristic
89#2363C2211yescharacteristic
90#2361C2211yescharacteristic
91#2339C2211yescharacteristic, complemented
92D4×C22⋊C4C2211yescharacteristic
93#2328C2211yescharacteristic
94#2326C2211yescharacteristic, complemented
95#2095C2211yescharacteristic, complemented
96#2094C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2087C2211yescharacteristic, complemented
99#2086C2211yescharacteristic, complemented
100#2086C2211yescharacteristic, complemented
101#2085C2211yescharacteristic, complemented
102#2084C2211yescharacteristic, complemented
103#2074C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2068C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2066C2211yescharacteristic, complemented
112#2065C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic, complemented
119#2055C2211yescharacteristic, complemented
120#2054C2211yescharacteristic
121#2054C2211yescharacteristic
122#2054C2211yescharacteristic, complemented
123#2043C2211yescharacteristic, complemented
124#2042C2211yescharacteristic, complemented
125#2041C2211yescharacteristic
126#2041C2211yescharacteristic
127#2036C2211yescharacteristic
128#2035C2211yescharacteristic
129#2034C2211yescharacteristic
130#2034C2211yescharacteristic
131#2034C2211yescharacteristic
132#2033C2211yescharacteristic
133#2033C2211yescharacteristic
134#2033C2211yescharacteristic, complemented
135#2014C2211yescharacteristic
136#2013C2211yescharacteristic
137#2012C2211yescharacteristic
138#2011C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#2000C2211yescharacteristic
142#2000C2211yescharacteristic, complemented
143#1985C2211yescharacteristic, complemented
144#1982C2211yescharacteristic
145#1981C2211yescharacteristic, complemented
146#1973C2211yescharacteristic
147#1972C2211yescharacteristic
148#1968C2211yescharacteristic
149#1968C2211yescharacteristic
150#1968C2211yescharacteristic, complemented
151#1968C2211yescharacteristic, complemented
152#1955C2211yescharacteristic
153#1936C2211yescharacteristic, complemented
154#1935C2211yescharacteristic, complemented
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic, complemented
158#1934C2211yescharacteristic, complemented
159#1926C2211yescharacteristic, complemented
160#1925C2211yescharacteristic
161#1923C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic, complemented
164#1923C2211yescharacteristic, complemented
165#1919C2211yescharacteristic, complemented
166#1918C2211yescharacteristic, complemented
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic, complemented
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1880C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic, complemented
179#1874C2211yescharacteristic
180#1873C2211yescharacteristic, complemented
181#1865C2211yescharacteristic, complemented
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1854C2211yescharacteristic, complemented
186#1853C2211yescharacteristic
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic
189#1850C2211yescharacteristic, complemented
190#1850C2211yescharacteristic, complemented
191#1843C2211yescharacteristic, complemented
192#1834C2211yescharacteristic, complemented
193#1825C2211yescharacteristic, complemented
194#1824C2211yescharacteristic
195#1805C2211yescharacteristic, complemented
196#1804C2211yescharacteristic, complemented
197#1802C2211yescharacteristic
198#1802C2211yescharacteristic
199#1802C2211yescharacteristic, complemented
200#1802C2211yescharacteristic, complemented
201C4×#106C2211yescharacteristic, complemented
202#1746C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#126—21no—
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×#120—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250#492—42no—
251#466—42no—
252#465—42no—
253#463—42no—
254#463—42no—
255#460—42no—
256#459—42no—
257#450—42no—
258#450—42no—
259#449—42no—
260#449—42no—
261#449—42no—
262#447—42no—
263C8×Q8—42no—
264C4×D8—42no—
265C8×D4—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
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×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281#416—42no—
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#102—42no—
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#401—21no—
324#401—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400D411yescharacteristic
332#400D411yescharacteristic
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397D411yescharacteristic
347#397D411yescharacteristic
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394D411yescharacteristic
369#394D411yescharacteristic
370#393D411yescharacteristic
371#393D411yescharacteristic
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#391—21no—
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#390—21no—
387#390—21no—
388#390—21no—
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#389—21no—
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#382—21no—
449#382C2311yescharacteristic
450#381—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460#379—21no—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468#376C2311yescharacteristic
469C2×#95—21no—
470#340C2311yescharacteristic
471#340C2311yescharacteristic
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#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2×D411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C22×C8—41no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8—41no—
569C22×C8—41no—
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580#127—22no—
581#127—41no—
582#127—41no—
583#127—41no—
584#126—82no—
585#124—22no—
586#124—41no—
587#124—82no—
588#123—82no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—82no—
596C22⋊Q8—82no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—41no—
606#121—41no—
607#121—82no—
608#121—82no—
609#120—82no—
610#120—82no—
611#120—82no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—82no—
629#117—41no—
630#117—41no—
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—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—82no—
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#107—41no—
729#107—41no—
730#107—41no—
731#106—41no—
732#106—41no—
733#106—41no—
734#106—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779#97—41no—
780C4×C8—22no—
781C4×C8—22no—
782C4×C8—22no—
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#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—42no—
828C24—42no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24C22×D411yescharacteristic
835C24C22×D411yescharacteristic
836#41—44no—
837#41—82no—
838#41—82no—
839#41—82no—
840C2×Q8—22no—
841C2×Q8—22no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×D4—22no—
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—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—44no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
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—82no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4H(5,𝔽2)12yes—
918C2×D4H(5,𝔽2)12yes—
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—42no—
945C22×C4—42no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C2511yescharacteristic
977SD16—82no—
978SD16—82no—
979SD16—82no—
980SD16—82no—
981SD16—82no—
982SD16—82no—
983D8—44no—
984D8—82no—
985D8—82no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—82no—
1010C2×C8—82no—
1011C2×C8H(5,𝔽2)12yes—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
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—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—42no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—22no—
1129C23—22no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
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—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—84no—
1163C23—84no—
1164C23—162no—
1165C23—162no—
1166C23—162no—
1167C23—162no—
1168C23—162no—
1169C23#57712yes—
1170C23C23×D411yescharacteristic
1171Q8—44no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180D4—22no—
1181D4—22no—
1182D4—22no—
1183D4—22no—
1184D4—44no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—84no—
1198D4—84no—
1199D4—84no—
1200D4—162no—
1201D4—162no—
1202D4—162no—
1203D4—162no—
1204D4—162no—
1205D4—162no—
1206D4—162no—
1207D4—162no—
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—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
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—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—84no—
1287C2×C4—162no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4#57612yes—
1294C2×C4#57712yes—
1295C2×C4C2×H(5,𝔽2)11yescharacteristic
1296C2×C4C2×H(5,𝔽2)11yescharacteristic
1297C2×C4C2×H(5,𝔽2)11yescharacteristic
1298C2×C4#58511yescharacteristic
1299C2×C4#58511yescharacteristic
1300C2×C4#58511yescharacteristic
1301C8—22no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—42no—
1319C22—42no—
1320C22—41no—
1321C22—41no—
1322C22—42no—
1323C22—42no—
1324C22—41no—
1325C22—42no—
1326C22—41no—
1327C22—41no—
1328C22—42no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—168no—
1352C22#348811yescharacteristic
1353C22#348811yescharacteristic
1354C22#349611yescharacteristic
1355C22C2×#57611yescharacteristic
1356C22C2×#57711yescharacteristic
1357C22C2×#57711yescharacteristic
1358C22#358411yescharacteristic
1359C4—22no—
1360C4—22no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4#353311yescharacteristic
1384C4#353311yescharacteristic
1385C4#353711yescharacteristic
1386C4#354511yescharacteristic
1387C2—42no—
1388C2—81no—
1389C2—82no—
1390C2—82no—
1391C2—161no—
1392C2—161no—
1393C2#4767811yescharacteristic
1394C2#6205211yescharacteristic
1395C2#6205311yescharacteristic
1396C2#6206711yescharacteristic
1397C2#6207011yescharacteristic
1398C2#6226511yescharacteristic
1399C2#6228011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42581C2semidirect
2. #42552C2semidirect
3. #32865C2semidirect
4. #32623C2semidirect
5. #32621C2semidirect
6. #31934C2semidirect
7. #31931C2semidirect
8. #31730C2semidirect
9. #31501C2semidirect
10. #31486C2semidirect
11. #31063C2semidirect
12. #30595C2semidirect
13. #30592C2semidirect
14. #30456C2semidirect
15. #30454C2semidirect
16. #29510C2semidirect
17. #29504C2semidirect
18. #28738C2semidirect
19. #28257C2semidirect
20. #28185C2semidirect
21. #27107C2semidirect
22. #27097C2semidirect
23. #25162C2semidirect
24. #25160C2semidirect
25. #25112C2semidirect
26. #25109C2semidirect
27. #25085C2semidirect
28. #25076C2semidirect
29. #24537C2semidirect
30. #24530C2semidirect
31. #22209C2semidirect
37. C2×#463C22semidirect
41. C2×#449C22semidirect
45. C2×C8×Q8C22semidirect
48. C2×#416C22semidirect
62. #2645C22semidirect
66. #2568C22semidirect
69. #2538C22semidirect
72. #2496C22semidirect
77. #2432C22semidirect
82. #2423C22semidirect
91. #2339C22semidirect
94. #2326C22semidirect
95. #2095C22semidirect
96. #2094C22semidirect
97. #2088C22semidirect
98. #2087C22semidirect
99. #2086C22semidirect
100. #2086C22semidirect
101. #2085C22semidirect
102. #2084C22semidirect
103. #2074C22semidirect
104. #2072C22semidirect
107. #2068C22semidirect
108. #2068C22semidirect
111. #2066C22semidirect
118. #2055C22semidirect
119. #2055C22semidirect
122. #2054C22semidirect
123. #2043C22semidirect
124. #2042C22semidirect
134. #2033C22semidirect
142. #2000C22semidirect
143. #1985C22semidirect
145. #1981C22semidirect
150. #1968C22semidirect
151. #1968C22semidirect
153. #1936C22semidirect
154. #1935C22semidirect
157. #1934C22semidirect
158. #1934C22semidirect
159. #1926C22semidirect
163. #1923C22semidirect
164. #1923C22semidirect
165. #1919C22semidirect
166. #1918C22semidirect
168. #1893C22semidirect
174. #1879C22semidirect
178. #1877C22semidirect
180. #1873C22semidirect
181. #1865C22semidirect
183. #1864C22semidirect
184. #1862C22semidirect
185. #1854C22semidirect
189. #1850C22semidirect
190. #1850C22semidirect
191. #1843C22semidirect
192. #1834C22semidirect
193. #1825C22semidirect
195. #1805C22semidirect
196. #1804C22semidirect
199. #1802C22semidirect
200. #1802C22semidirect
201. C4×#106C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#425812
#425522
#328652
#326232
#326212
#319342
#319312
#317302
#315012
#314862
#310632
#305952
#305922
#304562
#304542
#295102
#295042
#287382
#282572
#281852
#271072
#270972
#251622
#251602
#251122
#251092
#250852
#250762
#245372
#245302
#222092