Finite Group Databasebeta

← #7333390

Subgroups — #7333390

Order 512.

1296 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52965C211yesmaximal, characteristic
2#45099C211yesmaximal, characteristic
3#32690C211yesmaximal, characteristic, complemented
4#32587C211yesmaximal, characteristic, complemented
5#32429C211yesmaximal, characteristic, complemented
6#32352C211yesmaximal, characteristic, complemented
7#32233C211yesmaximal, characteristic, complemented
8#31687C211yesmaximal, characteristic
9#31460C211yesmaximal, characteristic, complemented
10#31442C211yesmaximal, characteristic
11#31079C211yesmaximal, characteristic
12#30961C211yesmaximal, characteristic, complemented
13#30960C211yesmaximal, characteristic, complemented
14#30792C211yesmaximal, characteristic
15#30184C211yesmaximal, characteristic
16#29649C211yesmaximal, characteristic
17#29487C211yesmaximal, characteristic
18#29082C211yesmaximal, characteristic, complemented
19#28818C211yesmaximal, characteristic, complemented
20#28798C211yesmaximal, characteristic, complemented
21#27132C211yesmaximal, characteristic, complemented
22#27103C211yesmaximal, characteristic
23#27053C211yesmaximal, characteristic
24#26863C211yesmaximal, characteristic, complemented
25#26790C211yesmaximal, characteristic
26#26576C211yesmaximal, characteristic
27#26497C211yesmaximal, characteristic, complemented
28#25849C211yesmaximal, characteristic, complemented
29#25822C211yesmaximal, characteristic
30#24348C211yesmaximal, characteristic, complemented
31#22328C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#499C2211yescharacteristic
37C2×#484C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#479C2211yescharacteristic
40C2×#477C2211yescharacteristic
41C2×#441C2211yescharacteristic
42#2839—21no—
43#2839—21no—
44#2836—21no—
45#2831—21no—
46#2809—21no—
47#2734—21no—
48#2729—21no—
49#2726—21no—
50#2725—21no—
51#2716—21no—
52#2713—21no—
53#2704—21no—
54#2629C2211yescharacteristic
55#2625C2211yescharacteristic
56#2584C2211yescharacteristic
57#2582C2211yescharacteristic
58#2565C2211yescharacteristic
59#2556—21no—
60#2552C2211yescharacteristic
61#2552C2211yescharacteristic
62#2550C2211yescharacteristic
63#2550C2211yescharacteristic
64#2546C2211yescharacteristic
65#2511C2211yescharacteristic
66#2511C2211yescharacteristic
67#2509C2211yescharacteristic
68#2506—21no—
69#2497C2211yescharacteristic
70#2496C2211yescharacteristic
71#2492C2211yescharacteristic
72#2453C2211yescharacteristic
73#2453C2211yescharacteristic
74#2451C2211yescharacteristic
75#2446—21no—
76#2442C2211yescharacteristic
77#2441C2211yescharacteristic
78#2423—21no—
79#2421C2211yescharacteristic
80#2396C2211yescharacteristic
81#2369C2211yescharacteristic
82#2362C2211yescharacteristic
83#2360C2211yescharacteristic
84#2323C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2085C2211yescharacteristic
95#2083C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2075C2211yescharacteristic
101#2074C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2066C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2057C2211yescharacteristic
118#2057C2211yescharacteristic
119#2057C2211yescharacteristic
120#2057C2211yescharacteristic
121#2056C2211yescharacteristic
122#2036C2211yescharacteristic
123#2036C2211yescharacteristic
124#2036C2211yescharacteristic
125#2035C2211yescharacteristic
126#2026C2211yescharacteristic
127#2026C2211yescharacteristic
128#2026C2211yescharacteristic
129#2026C2211yescharacteristic
130#2024C2211yescharacteristic
131#2024C2211yescharacteristic
132#2001C2211yescharacteristic
133#1992C2211yescharacteristic
134#1992C2211yescharacteristic
135#1990C2211yescharacteristic
136#1989C2211yescharacteristic
137#1985C2211yescharacteristic
138#1985C2211yescharacteristic
139#1971C2211yescharacteristic
140#1969C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1948C2211yescharacteristic
144#1947C2211yescharacteristic
145#1944C2211yescharacteristic
146#1943C2211yescharacteristic
147#1943C2211yescharacteristic
148#1943C2211yescharacteristic
149#1941C2211yescharacteristic
150#1935C2211yescharacteristic
151#1933C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1933C2211yescharacteristic
155#1928C2211yescharacteristic
156#1928C2211yescharacteristic
157#1928C2211yescharacteristic
158#1928C2211yescharacteristic
159#1927C2211yescharacteristic
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1921C2211yescharacteristic
165#1921C2211yescharacteristic
166#1921C2211yescharacteristic
167#1920C2211yescharacteristic
168#1920C2211yescharacteristic
169#1919C2211yescharacteristic
170#1918C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1916C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1916C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1854C2211yescharacteristic
188#1854C2211yescharacteristic
189#1853C2211yescharacteristic
190#1852C2211yescharacteristic
191#1846C2211yescharacteristic
192#1834C2211yescharacteristic
193#1825C2211yescharacteristic
194#1823C2211yescharacteristic
195#1818C2211yescharacteristic
196#1803C2211yescharacteristic
197C4×#107C2211yescharacteristic
198C4×#107C2211yescharacteristic
199#1770C2211yescharacteristic
200#1770C2211yescharacteristic
201#1763C2211yescharacteristic
202#1750C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204#557—42no—
205#557—42no—
206#544—42no—
207#544—42no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C4×Q8—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237#501—42no—
238#501—42no—
239#499—42no—
240#485—42no—
241#484—42no—
242#479—42no—
243#477—42no—
244#441—42no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400D411yescharacteristic
307#399—21no—
308#399D411yescharacteristic
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398D411yescharacteristic
330#398D411yescharacteristic
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396D411yescharacteristic
340#396D411yescharacteristic
341#395—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#395D411yescharacteristic
346#393—21no—
347#393D411yescharacteristic
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#385—21no—
419#385—21no—
420#384—21no—
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#380—21no—
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2×D411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C23×C4—21no—
497C23×C4C2411yescharacteristic
498C2×Q16—22no—
499C2×Q16—22no—
500C2×Q16—41no—
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511C4⋊Q8—22no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514C4⋊Q8—41no—
515C4⋊Q8—44no—
516C4⋊Q8—44no—
517C4⋊Q8—82no—
518#126—82no—
519#125—22no—
520#125—22no—
521#125—22no—
522#125—41no—
523#125—41no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528#125—41no—
529#125—44no—
530#125—44no—
531#125—44no—
532#125—82no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—44no—
536C22⋊Q8—44no—
537C22⋊Q8—41no—
538C22⋊Q8—41no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—44no—
550#117—22no—
551#117—41no—
552#117—41no—
553#117—41no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655#107—22no—
656#107—22no—
657#107—22no—
658#107—22no—
659#107—22no—
660#107—22no—
661#107—22no—
662#107—41no—
663#107—41no—
664#107—41no—
665#107—41no—
666#106—22no—
667#106—22no—
668#106—22no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106—41no—
674C4⋊C8—22no—
675C4⋊C8—22no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692C22⋊C8—22no—
693C22⋊C8—22no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696#97—41no—
697#97—41no—
698#97—41no—
699C4×C8—22no—
700C4×C8—22no—
701C4×C8—41no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758C24C22×D411yescharacteristic
759C2×Q8—24no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—41no—
772C2×Q8—41no—
773C2×Q8—41no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—81no—
777C2×Q8—81no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q82−1+412yes—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—42no—
806C22×C4—81no—
807C22×C4—81no—
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C2511yescharacteristic
822Q16—44no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C82−1+412yes—
846C2×C82−1+412yes—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—41no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—41no—
882C4⋊C4—41no—
883C4⋊C4—41no—
884C4⋊C4—41no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4H(5,𝔽2)12yes—
928C4⋊C4H(5,𝔽2)12yes—
929C4⋊C42−1+412yes—
930C22⋊C4—24no—
931C22⋊C4—22no—
932C22⋊C4—41no—
933C22⋊C4—41no—
934C22⋊C4—41no—
935C22⋊C4—41no—
936C22⋊C4—41no—
937C22⋊C4—42no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—42no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—81no—
960C42—81no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23C23×D411yescharacteristic
974Q8—22no—
975Q8—22no—
976Q8—41no—
977Q8—41no—
978Q8—41no—
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—84no—
983Q8—82no—
984Q8—162no—
985Q8—162no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—162no—
1077C2×C4#57812yes—
1078C2×C4C2×H(5,𝔽2)11yescharacteristic
1079C2×C4C2×H(5,𝔽2)11yescharacteristic
1080C2×C4C2×2−1+411yescharacteristic
1081C2×C4C2×2−1+411yescharacteristic
1082C2×C4C2×2−1+411yescharacteristic
1083C2×C4C2×2−1+411yescharacteristic
1084C8—22no—
1085C8—22no—
1086C8—41no—
1087C8—41no—
1088C8—41no—
1089C8—41no—
1090C8—41no—
1091C8—41no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22#348411yescharacteristic
1100C22#348611yescharacteristic
1101C22#349911yescharacteristic
1102C22C2×#57811yescharacteristic
1103C22#358411yescharacteristic
1104C22#358511yescharacteristic
1105C22#358611yescharacteristic
1106C4—22no—
1107C4—41no—
1108C4—41no—
1109C4—41no—
1110C4—41no—
1111C4—42no—
1112C4—42no—
1113C4—41no—
1114C4—41no—
1115C4—41no—
1116C4—41no—
1117C4—42no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4#353811yescharacteristic
1136C4#355011yescharacteristic
1137C4#355211yescharacteristic
1138C4#355211yescharacteristic
1139C2—81no—
1140C2#4794511yescharacteristic
1141C2#6164711yescharacteristic
1142C2#6166011yescharacteristic
1143C2#6185211yescharacteristic
1144C2#6186111yescharacteristic
1145C2#6251611yescharacteristic
1146C2#6251711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32690C2semidirect
4. #32587C2semidirect
5. #32429C2semidirect
6. #32352C2semidirect
7. #32233C2semidirect
9. #31460C2semidirect
12. #30961C2semidirect
13. #30960C2semidirect
18. #29082C2semidirect
19. #28818C2semidirect
20. #28798C2semidirect
21. #27132C2semidirect
24. #26863C2semidirect
27. #26497C2semidirect
28. #25849C2semidirect
30. #24348C2semidirect

Maximal subgroups

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

subgroupindex
#529652
#450992
#326902
#325872
#324292
#323522
#322332
#316872
#314602
#314422
#310792
#309612
#309602
#307922
#301842
#296492
#294872
#290822
#288182
#287982
#271322
#271032
#270532
#268632
#267902
#265762
#264972
#258492
#258222
#243482
#223282