Finite Group Databasebeta

← #7325862

Subgroups — #7325862

Order 512.

1615 conjugacy classes of subgroups.

The subgroup lattice has 1425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53064C211yesmaximal, characteristic, complemented
2#44887C211yesmaximal, characteristic, complemented
3#32210C211yesmaximal, characteristic, complemented
4#31961C211yesmaximal, characteristic, complemented
5#31944C211yesmaximal, characteristic, complemented
6#31786C211yesmaximal, characteristic, complemented
7#31697C211yesmaximal, characteristic, complemented
8#31399C211yesmaximal, characteristic, complemented
9#31036C211yesmaximal, characteristic, complemented
10#30711C211yesmaximal, characteristic, complemented
11#30654C211yesmaximal, characteristic, complemented
12#30615C211yesmaximal, characteristic, complemented
13#30576C211yesmaximal, characteristic, complemented
14#30408C211yesmaximal, characteristic, complemented
15#29901C211yesmaximal, characteristic, complemented
16#29602C211yesmaximal, characteristic, complemented
17#28933C211yesmaximal, characteristic, complemented
18#28853C211yesmaximal, characteristic, complemented
19#28143C211yesmaximal, characteristic, complemented
20#27534C211yesmaximal, characteristic, complemented
21#26674C211yesmaximal, characteristic, complemented
22#26547C211yesmaximal, characteristic, complemented
23#26137C211yesmaximal, characteristic, complemented
24#25578C211yesmaximal, characteristic, complemented
25#25160C211yesmaximal, characteristic, complemented
26#24980C211yesmaximal, characteristic, complemented
27#24777C211yesmaximal, characteristic, complemented
28#24568C211yesmaximal, characteristic, complemented
29#24394C211yesmaximal, characteristic, complemented
30#24093C211yesmaximal, characteristic, complemented
31#22031C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#489C2211yescharacteristic, complemented
35C2×#481C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic
45C2×C8×D4C2211yescharacteristic, complemented
46C2×#427C2211yescharacteristic, complemented
47C2×#408C2211yescharacteristic
48#2838—21no—
49#2828—21no—
50#2828—21no—
51#2825—21no—
52#2803—21no—
53#2756—21no—
54#2752—21no—
55#2737—21no—
56#2712—21no—
57#2684—21no—
58#2673—21no—
59#2670—21no—
60#2616C2211yescharacteristic
61#2615C2211yescharacteristic
62#2544—21no—
63#2540C2211yescharacteristic, complemented
64#2536C2211yescharacteristic
65#2535C2211yescharacteristic
66#2535C2211yescharacteristic, complemented
67#2500C2211yescharacteristic
68#2495C2211yescharacteristic
69#2494C2211yescharacteristic, complemented
70#2491C2211yescharacteristic
71#2485C2211yescharacteristic, complemented
72#2474—21no—
73#2439C2211yescharacteristic
74#2427C2211yescharacteristic
75#2426C2211yescharacteristic, complemented
76#2424—21no—
77#2422C2211yescharacteristic
78#2421C2211yescharacteristic, complemented
79#2420C2211yescharacteristic, complemented
80#2416C2211yescharacteristic
81#2415C2211yescharacteristic, complemented
82#2414C2211yescharacteristic
83#2414C2211yescharacteristic
84#2411—21no—
85#2408C2211yescharacteristic
86#2388C2211yescharacteristic
87#2361C2211yescharacteristic
88#2354C2211yescharacteristic
89D4×C22⋊C4C2211yescharacteristic
90#2311C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2093C2211yescharacteristic, complemented
94#2092C2211yescharacteristic
95#2087C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2076C2211yescharacteristic, complemented
102#2076C2211yescharacteristic, complemented
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic, complemented
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2068C2211yescharacteristic, complemented
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2058C2211yescharacteristic, complemented
112#2057C2211yescharacteristic, complemented
113#2054C2211yescharacteristic
114#2042C2211yescharacteristic, complemented
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2035C2211yescharacteristic, complemented
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2012C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#1999C2211yescharacteristic
134#1999C2211yescharacteristic
135#1999C2211yescharacteristic
136#1999C2211yescharacteristic
137#1999C2211yescharacteristic
138#1999C2211yescharacteristic
139#1988C2211yescharacteristic, complemented
140#1972C2211yescharacteristic
141#1968C2211yescharacteristic
142#1955C2211yescharacteristic
143#1955C2211yescharacteristic, complemented
144#1949C2211yescharacteristic, complemented
145#1943C2211yescharacteristic, complemented
146#1941C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic, complemented
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic, complemented
153#1923C2211yescharacteristic
154#1923C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic, complemented
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic, complemented
162#1893C2211yescharacteristic, complemented
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1879C2211yescharacteristic
166#1877C2211yescharacteristic
167#1875C2211yescharacteristic
168#1875C2211yescharacteristic, complemented
169#1875C2211yescharacteristic, complemented
170#1873C2211yescharacteristic
171#1873C2211yescharacteristic, complemented
172#1873C2211yescharacteristic, complemented
173#1872C2211yescharacteristic, complemented
174#1870C2211yescharacteristic, complemented
175#1869C2211yescharacteristic
176#1869C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic, complemented
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1854C2211yescharacteristic, complemented
185#1852C2211yescharacteristic, complemented
186#1851C2211yescharacteristic, complemented
187#1836C2211yescharacteristic, complemented
188#1835C2211yescharacteristic, complemented
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic, complemented
191#1823C2211yescharacteristic, complemented
192#1809C2211yescharacteristic, complemented
193#1807C2211yescharacteristic, complemented
194#1804C2211yescharacteristic
195#1804C2211yescharacteristic, complemented
196#1803C2211yescharacteristic, complemented
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1780C2211yescharacteristic
200#1763C2211yescharacteristic, complemented
201#1762C2211yescharacteristic
202#1752C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#555—42no—
213#555—42no—
214#535—42no—
215#535—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127—21no—
218C2×#124—21no—
219C2×#124—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×C22⋊Q8C2311yescharacteristic
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×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×#120—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258#489—42no—
259#482—42no—
260#482—42no—
261#481—42no—
262#468—42no—
263#465—42no—
264#465—42no—
265#463—42no—
266#450—42no—
267#447—42no—
268C4×D8—42no—
269C8×D4—42no—
270#427—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#102C2311yescharacteristic
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
310#408—42no—
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#401—21no—
328#400—21no—
329#400—21no—
330#399—21no—
331#398—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#395—21no—
346#395D411yescharacteristic
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—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#394D411yescharacteristic
365#394D411yescharacteristic
366#394D411yescharacteristic
367#393—21no—
368#393—21no—
369#393—21no—
370#393D411yescharacteristic
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#392—21no—
380#392D411yescharacteristic
381#392D411yescharacteristic
382#392D411yescharacteristic
383#391—21no—
384#391—21no—
385#391C2311yescharacteristic
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390—21no—
392#390—21no—
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#389—21no—
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#388—21no—
406#388—21no—
407#388—21no—
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#388—21no—
419#388—21no—
420#388—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—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#386—21no—
437#385—21no—
438#385—21no—
439#384C2311yescharacteristic
440#383—21no—
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#381—21no—
445#380—21no—
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
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#340C2311yescharacteristic
489#340C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8C2×D411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—22no—
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×D4C2×D411yescharacteristic
525C22×D4C2×D411yescharacteristic
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×D8—22no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C4⋊Q8—22no—
570C4⋊Q8—41no—
571#127—44no—
572#124—41no—
573#124—41no—
574#124—44no—
575#124—44no—
576#124—44no—
577#124—82no—
578#123—82no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—44no—
598#121—41no—
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—41no—
608#121—82no—
609#120—44no—
610#120—44no—
611#120—82no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×D4—22no—
615C4×D4—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—82no—
627#117—22no—
628#117—22no—
629#117—44no—
630#117—41no—
631#117—41no—
632#117—41no—
633#117—41no—
634#117—41no—
635#117—41no—
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—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
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—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—82no—
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—22no—
737#107—41no—
738#107—41no—
739#107—41no—
740#107—41no—
741#107—41no—
742#106—22no—
743#106—22no—
744#106—41no—
745#106—41no—
746#106—41no—
747#106—41no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750C4⋊C8—41no—
751#103—22no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
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—
773#102—41no—
774#102—41no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788#97—41no—
789#97—41no—
790C4×C8—22no—
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#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—21no—
828C24—42no—
829C24—42no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837C24C22×D411yescharacteristic
838C24C22×D411yescharacteristic
839#41—82no—
840#41—82no—
841#41—82no—
842#41—82no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—41no—
850C2×Q8—41no—
851C2×Q8—41no—
852C2×Q8—42no—
853C2×Q8—81no—
854C2×Q8—81no—
855C2×D4—24no—
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—41no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—41no—
890C2×D4—41no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—81no—
898C2×D4—82no—
899C2×D4—82no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—81no—
903C2×D4—81no—
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×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4H(5,𝔽2)12yes—
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—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C2511yescharacteristic
988SD16—82no—
989SD16—82no—
990D8—44no—
991D8—82no—
992M16—82no—
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—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—44no—
1017C2×C8—82no—
1018C2×C8H(5,𝔽2)12yes—
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—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
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—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4H(5,𝔽2)12yes—
1061C22⋊C4—24no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
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—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—81no—
1129C42—81no—
1130C42—81no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—22no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—84no—
1181C23—84no—
1182C23—162no—
1183C23—162no—
1184C23—162no—
1185C23—162no—
1186C23—162no—
1187C23C23×D411yescharacteristic
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—82no—
1193Q8—162no—
1194D4—22no—
1195D4—22no—
1196D4—44no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—84no—
1208D4—82no—
1209D4—82no—
1210D4—82no—
1211D4—82no—
1212D4—82no—
1213D4—84no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217D4—162no—
1218D4—162no—
1219D4—162no—
1220D4—162no—
1221D4—162no—
1222D4—162no—
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—22no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
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—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—84no—
1309C2×C4—162no—
1310C2×C4—162no—
1311C2×C4—162no—
1312C2×C4C2×H(5,𝔽2)11yescharacteristic
1313C2×C4C2×H(5,𝔽2)11yescharacteristic
1314C2×C4C2×H(5,𝔽2)11yescharacteristic
1315C2×C4#58511yescharacteristic
1316C2×C4#58511yescharacteristic
1317C2×C4#58511yescharacteristic
1318C8—22no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C8—41no—
1325C8—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—42no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—42no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—42no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—168no—
1376C22#348411yescharacteristic
1377C22#348511yescharacteristic
1378C22#349611yescharacteristic
1379C22#358411yescharacteristic
1380C22#358411yescharacteristic
1381C22#358511yescharacteristic
1382C22#358511yescharacteristic
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—41no—
1393C4—42no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4#354211yescharacteristic
1407C4#354211yescharacteristic
1408C4#356011yescharacteristic
1409C4#356211yescharacteristic
1410C2—81no—
1411C2—81no—
1412C2—81no—
1413C2—81no—
1414C2—82no—
1415C2—161no—
1416C2—161no—
1417C2#4793011yescharacteristic
1418C2#6162811yescharacteristic
1419C2#6167811yescharacteristic
1420C2#6176211yescharacteristic
1421C2#6180411yescharacteristic
1422C2#6227311yescharacteristic
1423C2#6233611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53064C2semidirect
2. #44887C2semidirect
3. #32210C2semidirect
4. #31961C2semidirect
5. #31944C2semidirect
6. #31786C2semidirect
7. #31697C2semidirect
8. #31399C2semidirect
9. #31036C2semidirect
10. #30711C2semidirect
11. #30654C2semidirect
12. #30615C2semidirect
13. #30576C2semidirect
14. #30408C2semidirect
15. #29901C2semidirect
16. #29602C2semidirect
17. #28933C2semidirect
18. #28853C2semidirect
19. #28143C2semidirect
20. #27534C2semidirect
21. #26674C2semidirect
22. #26547C2semidirect
23. #26137C2semidirect
24. #25578C2semidirect
25. #25160C2semidirect
26. #24980C2semidirect
27. #24777C2semidirect
28. #24568C2semidirect
29. #24394C2semidirect
30. #24093C2semidirect
31. #22031C2semidirect
34. C2×#489C22semidirect
35. C2×#481C22semidirect
45. C2×C8×D4C22semidirect
46. C2×#427C22semidirect
63. #2540C22semidirect
66. #2535C22semidirect
69. #2494C22semidirect
71. #2485C22semidirect
75. #2426C22semidirect
78. #2421C22semidirect
79. #2420C22semidirect
81. #2415C22semidirect
91. #2101C22semidirect
92. #2097C22semidirect
93. #2093C22semidirect
95. #2087C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
101. #2076C22semidirect
102. #2076C22semidirect
104. #2075C22semidirect
107. #2068C22semidirect
111. #2058C22semidirect
112. #2057C22semidirect
114. #2042C22semidirect
117. #2036C22semidirect
118. #2035C22semidirect
119. #2035C22semidirect
139. #1988C22semidirect
143. #1955C22semidirect
144. #1949C22semidirect
145. #1943C22semidirect
146. #1941C22semidirect
150. #1926C22semidirect
152. #1924C22semidirect
154. #1923C22semidirect
155. #1921C22semidirect
156. #1920C22semidirect
158. #1895C22semidirect
161. #1893C22semidirect
162. #1893C22semidirect
168. #1875C22semidirect
169. #1875C22semidirect
171. #1873C22semidirect
172. #1873C22semidirect
173. #1872C22semidirect
174. #1870C22semidirect
176. #1869C22semidirect
180. #1862C22semidirect
182. #1854C22semidirect
183. #1854C22semidirect
184. #1854C22semidirect
185. #1852C22semidirect
186. #1851C22semidirect
187. #1836C22semidirect
188. #1835C22semidirect
190. #1825C22semidirect
191. #1823C22semidirect
192. #1809C22semidirect
193. #1807C22semidirect
195. #1804C22semidirect
196. #1803C22semidirect
200. #1763C22semidirect
202. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#530642
#448872
#322102
#319612
#319442
#317862
#316972
#313992
#310362
#307112
#306542
#306152
#305762
#304082
#299012
#296022
#289332
#288532
#281432
#275342
#266742
#265472
#261372
#255782
#251602
#249802
#247772
#245682
#243942
#240932
#220312