Finite Group Databasebeta

← #7230218

Subgroups — #7230218

Order 512.

1123 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53131C211yesmaximal, characteristic, complemented
2#52998C211yesmaximal, characteristic
3#33283C211yesmaximal, characteristic
4#33262C211yesmaximal, characteristic, complemented
5#32854C211yesmaximal, characteristic, complemented
6#32830C211yesmaximal, characteristic
7#32485C211yesmaximal, characteristic
8#32476C211yesmaximal, characteristic, complemented
9#32400C211yesmaximal, characteristic
10#32398C211yesmaximal, characteristic, complemented
11#32369C211yesmaximal, characteristic, complemented
12#32368C211yesmaximal, characteristic
13#32135C211yesmaximal, characteristic, complemented
14#32134C211yesmaximal, characteristic, complemented
15#31879C211yesmaximal, characteristic
16#31869C211yesmaximal, characteristic, complemented
17#31581C211yesmaximal, characteristic
18#31579C211yesmaximal, characteristic
19#29023C211yesmaximal, characteristic
20#29022C211yesmaximal, characteristic
21#28971C211yesmaximal, characteristic, complemented
22#28965C211yesmaximal, characteristic
23#28808C211yesmaximal, characteristic, complemented
24#28799C211yesmaximal, characteristic, complemented
25#28048C211yesmaximal, characteristic, complemented
26#28046C211yesmaximal, characteristic
27#28043C211yesmaximal, characteristic
28#28030C211yesmaximal, characteristic, complemented
29#27742C211yesmaximal, characteristic, complemented
30#27731C211yesmaximal, characteristic
31#21678C211yesmaximal, characteristic, complemented
32#2839—21no—
33#2839—21no—
34#2839—21no—
35#2836—21no—
36#2835—21no—
37#2831—21no—
38#2831—21no—
39#2822—21no—
40#2771—21no—
41#2767—21no—
42#2767—21no—
43#2729—21no—
44#2726—21no—
45#2719—21no—
46#2716—21no—
47#2689—21no—
48#2647C2211yescharacteristic
49#2647C2211yescharacteristic
50#2647C2211yescharacteristic
51#2640C2211yescharacteristic
52#2571C2211yescharacteristic
53#2571C2211yescharacteristic
54#2570C2211yescharacteristic
55#2570C2211yescharacteristic
56#2568C2211yescharacteristic
57#2566C2211yescharacteristic
58#2551C2211yescharacteristic
59#2550C2211yescharacteristic
60#2513C2211yescharacteristic
61#2512C2211yescharacteristic
62#2511C2211yescharacteristic
63#2511C2211yescharacteristic
64#2509C2211yescharacteristic
65#2508C2211yescharacteristic
66#2507C2211yescharacteristic
67#2507C2211yescharacteristic
68#2507C2211yescharacteristic
69#2506C2211yescharacteristic
70#2506C2211yescharacteristic
71#2506C2211yescharacteristic
72#2453C2211yescharacteristic
73#2452C2211yescharacteristic
74#2448C2211yescharacteristic
75#2447C2211yescharacteristic
76#2402C2211yescharacteristic
77#2101C2211yescharacteristic
78#2101C2211yescharacteristic
79#2101C2211yescharacteristic
80#2100C2211yescharacteristic
81#2100C2211yescharacteristic
82#2099C2211yescharacteristic
83#2097C2211yescharacteristic
84#2096C2211yescharacteristic
85#2095C2211yescharacteristic
86#2094C2211yescharacteristic
87#2094C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2084C2211yescharacteristic
101#2084C2211yescharacteristic
102#2083C2211yescharacteristic
103#2074C2211yescharacteristic
104#2073C2211yescharacteristic
105#2072C2211yescharacteristic
106#2071C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2066C2211yescharacteristic
114#2066C2211yescharacteristic
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2058C2211yescharacteristic
120#2058C2211yescharacteristic
121#2058C2211yescharacteristic
122#2058C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#1993C2211yescharacteristic
126#1993C2211yescharacteristic
127#1991C2211yescharacteristic
128#1990C2211yescharacteristic
129#1989C2211yescharacteristic
130#1987C2211yescharacteristic
131#1959C2211yescharacteristic
132#1958C2211yescharacteristic
133#1949C2211yescharacteristic
134#1948C2211yescharacteristic
135#1948C2211yescharacteristic
136#1947C2211yescharacteristic
137#1944C2211yescharacteristic
138#1944C2211yescharacteristic
139#1943C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1939C2211yescharacteristic
148#1939C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1936C2211yescharacteristic
153#1935C2211yescharacteristic
154#1935C2211yescharacteristic
155#1935C2211yescharacteristic
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1933C2211yescharacteristic
160#1933C2211yescharacteristic
161#1933C2211yescharacteristic
162#1933C2211yescharacteristic
163#1928C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1926C2211yescharacteristic
167#1925C2211yescharacteristic
168#1925C2211yescharacteristic
169#1920C2211yescharacteristic
170#1919C2211yescharacteristic
171#1919C2211yescharacteristic
172#1919C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1917C2211yescharacteristic
176#1917C2211yescharacteristic
177#1916C2211yescharacteristic
178#1916C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1847C2211yescharacteristic
184#1847C2211yescharacteristic
185#1836C2211yescharacteristic
186#1835C2211yescharacteristic
187#1834C2211yescharacteristic
188#1834C2211yescharacteristic
189#1832C2211yescharacteristic
190#1805C2211yescharacteristic
191#1804C2211yescharacteristic
192#1776C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1771C2211yescharacteristic
195#1771C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1770C2211yescharacteristic
199C8×C4⋊C4C2211yescharacteristic
200#1763C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1726C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#126—21no—
207C2×#125—21no—
208C2×#125—21no—
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×C4×Q8C2311yescharacteristic
214C2×C4×D4C2311yescharacteristic
215C2×#107C2311yescharacteristic
216C2×#107C2311yescharacteristic
217C2×#107C2311yescharacteristic
218C2×#107C2311yescharacteristic
219C2×#107C2311yescharacteristic
220C2×#107C2311yescharacteristic
221C2×#106C2311yescharacteristic
222C2×#106C2311yescharacteristic
223C2×#106C2311yescharacteristic
224C2×#106C2311yescharacteristic
225C2×#106C2311yescharacteristic
226C2×#106C2311yescharacteristic
227C2×#106C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×C4⋊C8C2311yescharacteristic
232C2×C4⋊C8C2311yescharacteristic
233C2×C4⋊C8C2311yescharacteristic
234C2×C4⋊C8C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×#103C2311yescharacteristic
238C2×#103C2311yescharacteristic
239C2×#103C2311yescharacteristic
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#102C2311yescharacteristic
246C2×#102C2311yescharacteristic
247C2×#102C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#97C2311yescharacteristic
254C2×#97C2311yescharacteristic
255C2×#97C2311yescharacteristic
256C2×#97C2311yescharacteristic
257C2×#97C2311yescharacteristic
258C2×C4×C8C2311yescharacteristic
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263#400—21no—
264#400—21no—
265#400—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400D411yescharacteristic
289#400D411yescharacteristic
290#400D411yescharacteristic
291#400D411yescharacteristic
292#399—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398D411yescharacteristic
314#398D411yescharacteristic
315#398D411yescharacteristic
316#398D411yescharacteristic
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#393—21no—
333#393—21no—
334#393—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#382—21no—
412#382—21no—
413#382—21no—
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433#376C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478C22×Q8—21no—
479C22×Q8—21no—
480C22×Q8C2411yescharacteristic
481C22×D4C2411yescharacteristic
482C23×C4—21no—
483C22×C8C2411yescharacteristic
484C22×C8C2411yescharacteristic
485C22×C8C2411yescharacteristic
486C22×C8C2411yescharacteristic
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C4⋊Q8—41no—
492C4⋊Q8—41no—
493C4⋊Q8—41no—
494C4⋊Q8—41no—
495C4⋊Q8—82no—
496#126—82no—
497#125—41no—
498#125—41no—
499#125—82no—
500#125—82no—
501#125—82no—
502#124—41no—
503#124—41no—
504C22⋊Q8—82no—
505C4×Q8—41no—
506C4×Q8—41no—
507C4×D4—41no—
508C4×D4—41no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4C2×D411yescharacteristic
549C2×C4⋊C4C2×D411yescharacteristic
550C2×C4⋊C4C2×D411yescharacteristic
551C2×C4⋊C4C2×D411yescharacteristic
552C2×C4⋊C4C2×D411yescharacteristic
553C2×C4⋊C4C2×D411yescharacteristic
554C2×C4⋊C4C2×D411yescharacteristic
555C2×C4⋊C4C2×D411yescharacteristic
556C2×C4⋊C4C2×D411yescharacteristic
557C2×C4⋊C4C2×D411yescharacteristic
558C2×C4⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C42—21no—
588C2×C42—21no—
589C2×C42—21no—
590C2×C42—21no—
591C2×C42—21no—
592C2×C42—21no—
593C2×C42—21no—
594C2×C42C2411yescharacteristic
595C2×C42C2411yescharacteristic
596C2×C42C2411yescharacteristic
597C2×C42C2411yescharacteristic
598C2×C42C2411yescharacteristic
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601#107—22no—
602#107—41no—
603#107—41no—
604#107—41no—
605#107—41no—
606#107—41no—
607#106—22no—
608#106—41no—
609#106—41no—
610#106—41no—
611#106—41no—
612#106—41no—
613#106—41no—
614#106—41no—
615#106—41no—
616#106—41no—
617C4⋊C8—22no—
618C4⋊C8—22no—
619C4⋊C8—41no—
620C4⋊C8—41no—
621C4⋊C8—41no—
622C4⋊C8—41no—
623#103—22no—
624#103—22no—
625#103—22no—
626#103—41no—
627#103—41no—
628#103—41no—
629#103—41no—
630#103—41no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—41no—
635#102—41no—
636#102—41no—
637#102—41no—
638#102—41no—
639#97—22no—
640#97—22no—
641#97—22no—
642#97—41no—
643#97—41no—
644C4×C8—22no—
645C4×C8—22no—
646C4×C8—41no—
647C4×C8—41no—
648C4×C8—41no—
649#95—21no—
650#95—21no—
651#95—21no—
652#95—21no—
653#95—21no—
654#95—21no—
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95C2×D411yescharacteristic
700#95C2×D411yescharacteristic
701#95C2×D411yescharacteristic
702#95C2×D411yescharacteristic
703#95C2×D411yescharacteristic
704#95C2×D411yescharacteristic
705#95C2×D411yescharacteristic
706#95C2×D411yescharacteristic
707#95C2×D411yescharacteristic
708#95C2×D411yescharacteristic
709#95C2×D411yescharacteristic
710#95C2×D411yescharacteristic
711#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715C24—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8—21no—
720C2×Q8—21no—
721C2×Q8—21no—
722C2×Q8—42no—
723C2×Q8—81no—
724C2×Q8—81no—
725C2×Q8—81no—
726C2×Q8—81no—
727C2×Q8—81no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—81no—
750C22×C4—81no—
751C22×C4—81no—
752C22×C4C22×D411yescharacteristic
753C22×C4C22×D411yescharacteristic
754C22×C4C22×D411yescharacteristic
755C22×C4C22×D411yescharacteristic
756C22×C4C22×D411yescharacteristic
757C22×C4C22×D411yescharacteristic
758C22×C4C22×D411yescharacteristic
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C2511yescharacteristic
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C82−1+412yes—
789C2×C82−1+412yes—
790C2×C82−1+412yes—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—41no—
823C4⋊C4—41no—
824C4⋊C4—41no—
825C4⋊C4—41no—
826C4⋊C4—41no—
827C4⋊C4—41no—
828C4⋊C4—41no—
829C4⋊C4—41no—
830C4⋊C4—41no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—81no—
836C4⋊C4—81no—
837C4⋊C4—81no—
838C4⋊C4—81no—
839C4⋊C4—81no—
840C4⋊C4—81no—
841C4⋊C4—81no—
842C4⋊C4—81no—
843C4⋊C4—81no—
844C4⋊C4—81no—
845C4⋊C4—81no—
846C4⋊C4—81no—
847C4⋊C4—81no—
848C4⋊C4—81no—
849C4⋊C4—81no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—81no—
873C22⋊C4—81no—
874C22⋊C4—81no—
875C22⋊C4—81no—
876C22⋊C4—81no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C22⋊C4—81no—
880C22⋊C4—81no—
881C22⋊C4—81no—
882C22⋊C4—81no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—21no—
890C42—21no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42—81no—
899C42—81no—
900C42—81no—
901C42—81no—
902C42—81no—
903C42—81no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23C23×D411yescharacteristic
912Q8—41no—
913Q8—41no—
914Q8—41no—
915Q8—41no—
916Q8—162no—
917Q8—162no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—162no—
1009C2×C4#57712yes—
1010C2×C4C2×2−1+411yescharacteristic
1011C2×C4C2×2−1+411yescharacteristic
1012C2×C4C2×2−1+411yescharacteristic
1013C2×C4#58511yescharacteristic
1014C2×C4#58511yescharacteristic
1015C2×C4#58511yescharacteristic
1016C8—22no—
1017C8—22no—
1018C8—22no—
1019C8—41no—
1020C8—41no—
1021C8—41no—
1022C8—41no—
1023C8—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22#349711yescharacteristic
1032C22#349911yescharacteristic
1033C22#350011yescharacteristic
1034C22C2×#57711yescharacteristic
1035C22#358411yescharacteristic
1036C22#358511yescharacteristic
1037C22#358611yescharacteristic
1038C4—22no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—41no—
1048C4—41no—
1049C4—41no—
1050C4—41no—
1051C4—41no—
1052C4—81no—
1053C4—81no—
1054C4—81no—
1055C4—81no—
1056C4—81no—
1057C4—81no—
1058C4—81no—
1059C4—81no—
1060C4—81no—
1061C4—81no—
1062C4—81no—
1063C4—81no—
1064C4—81no—
1065C4—81no—
1066C4—81no—
1067C4#353111yescharacteristic
1068C4#355311yescharacteristic
1069C4#356311yescharacteristic
1070C4#356311yescharacteristic
1071C2—161no—
1072C2#4615011yescharacteristic
1073C2#6240711yescharacteristic
1074C2#6241011yescharacteristic
1075C2#6251411yescharacteristic
1076C2#6252311yescharacteristic
1077C2#6256211yescharacteristic
1078C2#6256811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53131C2semidirect
4. #33262C2semidirect
5. #32854C2semidirect
8. #32476C2semidirect
10. #32398C2semidirect
11. #32369C2semidirect
13. #32135C2semidirect
14. #32134C2semidirect
16. #31869C2semidirect
21. #28971C2semidirect
23. #28808C2semidirect
24. #28799C2semidirect
25. #28048C2semidirect
28. #28030C2semidirect
29. #27742C2semidirect
31. #21678C2semidirect

Maximal subgroups

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

subgroupindex
#531312
#529982
#332832
#332622
#328542
#328302
#324852
#324762
#324002
#323982
#323692
#323682
#321352
#321342
#318792
#318692
#315812
#315792
#290232
#290222
#289712
#289652
#288082
#287992
#280482
#280462
#280432
#280302
#277422
#277312
#216782