Finite Group Databasebeta

← #7241012

Subgroups — #7241012

Order 512.

1694 conjugacy classes of subgroups.

The subgroup lattice has 1410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40196C211yesmaximal, characteristic, complemented
2#39881C211yesmaximal, characteristic
3#32728C211yesmaximal, characteristic, complemented
4#32201C211yesmaximal, characteristic, complemented
5#32174C211yesmaximal, characteristic, complemented
6#32118C211yesmaximal, characteristic, complemented
7#32001C211yesmaximal, characteristic, complemented
8#31298C211yesmaximal, characteristic, complemented
9#31260C211yesmaximal, characteristic, complemented
10#30881C211yesmaximal, characteristic, complemented
11#30706C211yesmaximal, characteristic, complemented
12#30520C211yesmaximal, characteristic, complemented
13#30507C211yesmaximal, characteristic, complemented
14#30411C211yesmaximal, characteristic, complemented
15#30405C211yesmaximal, characteristic, complemented
16#28600C211yesmaximal, characteristic, complemented
17#28576C211yesmaximal, characteristic, complemented
18#27498C211yesmaximal, characteristic, complemented
19#27433C211yesmaximal, characteristic, complemented
20#27223C211yesmaximal, characteristic, complemented
21#26794C211yesmaximal, characteristic, complemented
22#25499C211yesmaximal, characteristic, complemented
23#25389C211yesmaximal, characteristic, complemented
24#25113C211yesmaximal, characteristic, complemented
25#25089C211yesmaximal, characteristic, complemented
26#24357C211yesmaximal, characteristic, complemented
27#24264C211yesmaximal, characteristic, complemented
28#24160C211yesmaximal, characteristic, complemented
29#24037C211yesmaximal, characteristic, complemented
30#23852C211yesmaximal, characteristic, complemented
31#22168C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#487C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#479C2211yescharacteristic, complemented
38C2×#467C2211yescharacteristic, complemented
39C2×#467C2211yescharacteristic, complemented
40C2×#467C2211yescharacteristic, complemented
41C2×#465C2211yescharacteristic
42C2×#465C2211yescharacteristic
43C2×#464C2211yescharacteristic
44C2×#464C2211yescharacteristic
45C2×#452C2211yescharacteristic
46C2×#452C2211yescharacteristic
47C2×#451C2211yescharacteristic
48C2×#451C2211yescharacteristic
49C2×C8×D4C2211yescharacteristic
50C2×C8×D4C2211yescharacteristic, complemented
51C2×#416C2211yescharacteristic
52#2855C2211yescharacteristic, complemented
53#2850C2211yescharacteristic
54#2787—21no—
55#2759—21no—
56#2745—21no—
57#2718—21no—
58#2706—21no—
59#2686—21no—
60#2685—21no—
61#2678—21no—
62#2653—21no—
63#2635—21no—
64#2595—21no—
65#2586—21no—
66#2547C2211yescharacteristic
67#2545C2211yescharacteristic
68#2542C2211yescharacteristic
69#2540C2211yescharacteristic
70#2536C2211yescharacteristic
71#2536C2211yescharacteristic, complemented
72#2514C2211yescharacteristic, complemented
73#2500—21no—
74#2494C2211yescharacteristic
75#2492C2211yescharacteristic, complemented
76#2490C2211yescharacteristic
77#2489C2211yescharacteristic
78#2485C2211yescharacteristic
79#2482—21no—
80#2451C2211yescharacteristic, complemented
81#2435C2211yescharacteristic
82#2432C2211yescharacteristic
83#2415C2211yescharacteristic, complemented
84#2409C2211yescharacteristic
85#2409C2211yescharacteristic
86#2408C2211yescharacteristic
87#2407C2211yescharacteristic
88#2362C2211yescharacteristic, complemented
89#2357C2211yescharacteristic
90Q8×C22⋊C4C2211yescharacteristic
91#2337—21no—
92#2321—21no—
93C4×C22⋊Q8C2211yescharacteristic, complemented
94C4×#121C2211yescharacteristic
95#2101C2211yescharacteristic, complemented
96#2097C2211yescharacteristic, complemented
97#2092C2211yescharacteristic
98#2085C2211yescharacteristic, complemented
99#2076C2211yescharacteristic, complemented
100#2075C2211yescharacteristic
101#2075C2211yescharacteristic
102#2074C2211yescharacteristic, complemented
103#2074C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic, complemented
108#2056C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic, complemented
122#2035C2211yescharacteristic, complemented
123#2035C2211yescharacteristic, complemented
124#2035C2211yescharacteristic, complemented
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2026C2211yescharacteristic, complemented
128#2023C2211yescharacteristic
129#2023C2211yescharacteristic
130#2016C2211yescharacteristic, complemented
131#2016C2211yescharacteristic, complemented
132#2015C2211yescharacteristic
133#2015C2211yescharacteristic
134#2015C2211yescharacteristic
135#2015C2211yescharacteristic
136#2001C2211yescharacteristic, complemented
137#2001C2211yescharacteristic, complemented
138#2001C2211yescharacteristic, complemented
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#2000C2211yescharacteristic
142#2000C2211yescharacteristic
143#1989C2211yescharacteristic, complemented
144#1988C2211yescharacteristic, complemented
145#1983C2211yescharacteristic
146#1981C2211yescharacteristic, complemented
147#1969C2211yescharacteristic, complemented
148#1968C2211yescharacteristic
149#1968C2211yescharacteristic
150#1958C2211yescharacteristic
151#1949C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1928C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic, complemented
162#1921C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic, complemented
171#1892C2211yescharacteristic, complemented
172#1892C2211yescharacteristic, complemented
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1878C2211yescharacteristic, complemented
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1873C2211yescharacteristic, complemented
182#1869C2211yescharacteristic
183#1869C2211yescharacteristic
184#1869C2211yescharacteristic
185#1869C2211yescharacteristic, complemented
186#1865C2211yescharacteristic, complemented
187#1864C2211yescharacteristic
188#1863C2211yescharacteristic, complemented
189#1862C2211yescharacteristic
190#1854C2211yescharacteristic, complemented
191#1850C2211yescharacteristic
192#1850C2211yescharacteristic, complemented
193#1807C2211yescharacteristic
194#1797C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1787C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1786C2211yescharacteristic
200C4×#106C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202C2×#336C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16—42no—
211C22×SD16—42no—
212C22×SD16—42no—
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C23×C8C2311yescharacteristic
220C23×C8C2311yescharacteristic
221#546—42no—
222#546—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225#529—42no—
226#529—42no—
227C2×#126—21no—
228C2×#125C2311yescharacteristic
229C2×#124—21no—
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121—21no—
245C2×#121D411yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×#120—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×#117—21no—
260C2×#117C2311yescharacteristic
261C22×C22⋊C4—21no—
262C22×C42C2311yescharacteristic
263#487—42no—
264#482—42no—
265#479—42no—
266#467—42no—
267#467—42no—
268#467—42no—
269#465—42no—
270#465—42no—
271#464—42no—
272#464—42no—
273#452—42no—
274#452—42no—
275#451—42no—
276#451—42no—
277C8×D4—42no—
278C8×D4—42no—
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291#416—42no—
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334#401—21no—
335#401—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#399—21no—
340#399—21no—
341#399—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#396—21no—
353#396—21no—
354#395—21no—
355#395—21no—
356#395—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#393—21no—
369#393—21no—
370#393—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#391—21no—
375#391—21no—
376#391—21no—
377#391—21no—
378#391—21no—
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390D411yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389D411yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#388—21no—
403#388—21no—
404#388—21no—
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#388D411yescharacteristic
421#388D411yescharacteristic
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386D411yescharacteristic
436#386D411yescharacteristic
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#384—21no—
445#383—21no—
446#382—21no—
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#381—21no—
450#381—21no—
451#380—21no—
452#380D411yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#379—21no—
462#379—21no—
463#379—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8—22no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×D411yescharacteristic
533C22×D4C2×D411yescharacteristic
534C22×D4C2×D411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C2×D411yescharacteristic
541C23×C4C2×D411yescharacteristic
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—416no—
570C22×C8—22no—
571C22×C8—22no—
572C22×C8—41no—
573C22×C8—41no—
574C22×C8—41no—
575C22×C8—41no—
576C22×C8—41no—
577C22×C8—41no—
578C22×C8—41no—
579C22×C8—41no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C4⋊Q8—41no—
591C4⋊Q8—41no—
592C4⋊Q8—41no—
593C4⋊Q8—41no—
594#126—44no—
595#125—22no—
596#125—41no—
597#124—22no—
598#124—41no—
599#124—41no—
600#124—41no—
601#124—41no—
602#124—41no—
603#124—44no—
604#123—44no—
605#123—44no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624#121—24no—
625#121—22no—
626#121—22no—
627#121—41no—
628#121—41no—
629#121—44no—
630#121—41no—
631#121—41no—
632#120—44no—
633#120—44no—
634C4×Q8—41no—
635C4×Q8—41no—
636C4×Q8—41no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×Q8—41no—
640C4×D4—22no—
641C4×D4—22no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648C4×D4—44no—
649#117—44no—
650#117—41no—
651#117—41no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
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—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—44no—
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—41no—
744C2×C42—41no—
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751#107—22no—
752#107—41no—
753#107—41no—
754#107—41no—
755#106—22no—
756#106—41no—
757#106—41no—
758#106—41no—
759C4⋊C8—22no—
760C4⋊C8—41no—
761C4⋊C8—41no—
762C4⋊C8—41no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#102—22no—
784#102—22no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795C22⋊C8—22no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C4×C8—22no—
804C4×C8—41no—
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#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847C24—21no—
848C24—21no—
849C24—42no—
850C24—42no—
851C24—81no—
852C24—81no—
853C24—81no—
854C24—81no—
855C24—81no—
856C24C22×D411yescharacteristic
857C24C22×D411yescharacteristic
858C24C22×D411yescharacteristic
859#41—44no—
860#41—82no—
861#41—82no—
862#41—82no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—44no—
889C2×Q8—81no—
890C2×Q8—81no—
891C2×Q8—81no—
892C2×Q8—81no—
893C2×Q8—82no—
894C2×Q8—82no—
895C2×Q8—82no—
896C2×Q8H(5,𝔽2)12yes—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—41no—
911C2×D4—41no—
912C2×D4—41no—
913C2×D4—41no—
914C2×D4—41no—
915C2×D4—41no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—82no—
926C2×D4—82no—
927C2×D4—82no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4#13514yes—
936C2×D4H(5,𝔽2)12yes—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—24no—
940C22×C4—22no—
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—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—41no—
972C22×C4—41no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—41no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C2511yescharacteristic
996Q16—82no—
997Q16—82no—
998Q16—82no—
999Q16—82no—
1000SD16—44no—
1001SD16—44no—
1002SD16—44no—
1003SD16—44no—
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—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—44no—
1028C2×C8—82no—
1029C2×C8—82no—
1030C2×C8—82no—
1031C2×C8H(5,𝔽2)12yes—
1032C4⋊C4—22no—
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—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4H(5,𝔽2)12yes—
1078C22⋊C4—24no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
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—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—41no—
1133C42—41no—
1134C42—42no—
1135C42—42no—
1136C42—81no—
1137C42—81no—
1138C42—81no—
1139C42—81no—
1140C42—81no—
1141C42—81no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—22no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
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—84no—
1176C23—84no—
1177C23—162no—
1178C23—162no—
1179C23—162no—
1180C23—162no—
1181C23—162no—
1182C23C2×#13512yes—
1183C23C2×#13512yes—
1184C23C23×D411yescharacteristic
1185Q8—22no—
1186Q8—22no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—84no—
1202Q8—162no—
1203D4—22no—
1204D4—22no—
1205D4—44no—
1206D4—44no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—82no—
1214D4—84no—
1215D4—84no—
1216D4—84no—
1217D4—162no—
1218D4—162no—
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—22no—
1239C2×C4—21no—
1240C2×C4—22no—
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—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—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—82no—
1306C2×C4—84no—
1307C2×C4—82no—
1308C2×C4—84no—
1309C2×C4—84no—
1310C2×C4C2×#13512yes—
1311C2×C4C2×H(5,𝔽2)11yescharacteristic
1312C2×C4C2×H(5,𝔽2)11yescharacteristic
1313C2×C4C2×H(5,𝔽2)11yescharacteristic
1314C2×C4C2×H(5,𝔽2)11yescharacteristic
1315C2×C4#58511yescharacteristic
1316C2×C4#58511yescharacteristic
1317C8—22no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C8—41no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—42no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—42no—
1346C22—41no—
1347C22—42no—
1348C22—41no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—168no—
1361C22#348411yescharacteristic
1362C22#348811yescharacteristic
1363C22#349611yescharacteristic
1364C22C22×#13511yescharacteristic
1365C22#358411yescharacteristic
1366C22#358611yescharacteristic
1367C22#358611yescharacteristic
1368C4—22no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—42no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—42no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4#353211yescharacteristic
1394C4#353311yescharacteristic
1395C4#354611yescharacteristic
1396C4#355811yescharacteristic
1397C2—42no—
1398C2—42no—
1399C2—81no—
1400C2—82no—
1401C2—161no—
1402C2#4636711yescharacteristic
1403C2#6156811yescharacteristic
1404C2#6161311yescharacteristic
1405C2#6195611yescharacteristic
1406C2#6201311yescharacteristic
1407C2#6224411yescharacteristic
1408C2#6233711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39881C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40196C2semidirect
3. #32728C2semidirect
4. #32201C2semidirect
5. #32174C2semidirect
6. #32118C2semidirect
7. #32001C2semidirect
8. #31298C2semidirect
9. #31260C2semidirect
10. #30881C2semidirect
11. #30706C2semidirect
12. #30520C2semidirect
13. #30507C2semidirect
14. #30411C2semidirect
15. #30405C2semidirect
16. #28600C2semidirect
17. #28576C2semidirect
18. #27498C2semidirect
19. #27433C2semidirect
20. #27223C2semidirect
21. #26794C2semidirect
22. #25499C2semidirect
23. #25389C2semidirect
24. #25113C2semidirect
25. #25089C2semidirect
26. #24357C2semidirect
27. #24264C2semidirect
28. #24160C2semidirect
29. #24037C2semidirect
30. #23852C2semidirect
31. #22168C2semidirect
35. C2×#487C22semidirect
37. C2×#479C22semidirect
38. C2×#467C22semidirect
39. C2×#467C22semidirect
40. C2×#467C22semidirect
50. C2×C8×D4C22semidirect
52. #2855C22semidirect
71. #2536C22semidirect
72. #2514C22semidirect
75. #2492C22semidirect
80. #2451C22semidirect
83. #2415C22semidirect
88. #2362C22semidirect
93. C4×C22⋊Q8C22semidirect
95. #2101C22semidirect
96. #2097C22semidirect
98. #2085C22semidirect
99. #2076C22semidirect
102. #2074C22semidirect
103. #2074C22semidirect
104. #2068C22semidirect
105. #2066C22semidirect
107. #2059C22semidirect
108. #2056C22semidirect
121. #2035C22semidirect
122. #2035C22semidirect
123. #2035C22semidirect
124. #2035C22semidirect
127. #2026C22semidirect
130. #2016C22semidirect
131. #2016C22semidirect
136. #2001C22semidirect
137. #2001C22semidirect
138. #2001C22semidirect
143. #1989C22semidirect
144. #1988C22semidirect
146. #1981C22semidirect
147. #1969C22semidirect
151. #1949C22semidirect
153. #1928C22semidirect
154. #1928C22semidirect
155. #1927C22semidirect
156. #1927C22semidirect
161. #1923C22semidirect
162. #1921C22semidirect
163. #1916C22semidirect
164. #1916C22semidirect
170. #1892C22semidirect
171. #1892C22semidirect
172. #1892C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
177. #1878C22semidirect
178. #1878C22semidirect
181. #1873C22semidirect
185. #1869C22semidirect
186. #1865C22semidirect
188. #1863C22semidirect
190. #1854C22semidirect
192. #1850C22semidirect
194. #1797C22semidirect
200. C4×#106C22semidirect
201. C4×#103C22semidirect
202. C2×#336C22semidirect

Maximal subgroups

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

subgroupindex
#401962
#398812
#327282
#322012
#321742
#321182
#320012
#312982
#312602
#308812
#307062
#305202
#305072
#304112
#304052
#286002
#285762
#274982
#274332
#272232
#267942
#254992
#253892
#251132
#250892
#243572
#242642
#241602
#240372
#238522
#221682