Finite Group Databasebeta

← #6854447

Subgroups — #6854447

Order 512.

1246 conjugacy classes of subgroups.

The subgroup lattice has 1111 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39673C211yesmaximal, characteristic
2#39622C211yesmaximal, characteristic
3#33318C211yesmaximal, characteristic
4#30977C211yesmaximal, characteristic
5#30976C211yesmaximal, characteristic
6#30972C211yesmaximal, characteristic
7#30964C211yesmaximal, characteristic
8#30960C211yesmaximal, characteristic
9#30956C211yesmaximal, characteristic
10#30956C211yesmaximal, characteristic
11#30953C211yesmaximal, characteristic
12#30313C211yesmaximal, characteristic
13#30311C211yesmaximal, characteristic
14#29216C211yesmaximal, characteristic
15#29185C211yesmaximal, characteristic
16#29180C211yesmaximal, characteristic
17#29153C211yesmaximal, characteristic
18#28526C211yesmaximal, characteristic
19#28515C211yesmaximal, characteristic
20#26057C211yesmaximal, characteristic
21#26055C211yesmaximal, characteristic
22#26048C211yesmaximal, characteristic
23#26043C211yesmaximal, characteristic
24#25075C211yesmaximal, characteristic
25#25071C211yesmaximal, characteristic
26#25066C211yesmaximal, characteristic
27#25061C211yesmaximal, characteristic
28#22231C211yesmaximal, characteristic
29#22225C211yesmaximal, characteristic
30#21653C211yesmaximal, characteristic
31#21348C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#498C2211yescharacteristic
36C2×#491C2211yescharacteristic
37C2×#479C2211yescharacteristic
38C2×#479C2211yescharacteristic
39C2×#479C2211yescharacteristic
40C2×#479C2211yescharacteristic
41C2×#479C2211yescharacteristic
42C2×#479C2211yescharacteristic
43C2×#477C2211yescharacteristic
44C2×#475C2211yescharacteristic
45#2864C2211yescharacteristic
46#2859C2211yescharacteristic
47#2806—21no—
48#2806—21no—
49#2792—21no—
50#2792—21no—
51#2792—21no—
52#2791—21no—
53#2774—21no—
54#2755—21no—
55#2660C2211yescharacteristic
56#2660C2211yescharacteristic
57#2660C2211yescharacteristic
58#2647C2211yescharacteristic
59#2590—21no—
60#2588—21no—
61#2586—21no—
62#2586—21no—
63#2586—21no—
64#2585—21no—
65#2582C2211yescharacteristic
66#2581C2211yescharacteristic
67#2552C2211yescharacteristic
68#2552C2211yescharacteristic
69#2550C2211yescharacteristic
70#2550C2211yescharacteristic
71#2550C2211yescharacteristic
72#2550C2211yescharacteristic
73#2507—21no—
74#2507—21no—
75#2453C2211yescharacteristic
76#2453C2211yescharacteristic
77#2451C2211yescharacteristic
78#2451C2211yescharacteristic
79#2355C2211yescharacteristic
80#2355C2211yescharacteristic
81#2351C2211yescharacteristic
82Q8×C4⋊C4C2211yescharacteristic
83#2330C2211yescharacteristic
84#2330C2211yescharacteristic
85#2327C2211yescharacteristic
86#2327C2211yescharacteristic
87C4×C4⋊Q8C2211yescharacteristic
88C4×#125C2211yescharacteristic
89#2295C2211yescharacteristic
90#2097C2211yescharacteristic
91#2097C2211yescharacteristic
92#2097C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2096C2211yescharacteristic
97#2095C2211yescharacteristic
98#2088C2211yescharacteristic
99#2088C2211yescharacteristic
100#2088C2211yescharacteristic
101#2088C2211yescharacteristic
102#2088C2211yescharacteristic
103#2088C2211yescharacteristic
104#2087C2211yescharacteristic
105#2086C2211yescharacteristic
106#2085C2211yescharacteristic
107#2085C2211yescharacteristic
108#2085C2211yescharacteristic
109#2085C2211yescharacteristic
110#2085C2211yescharacteristic
111#2085C2211yescharacteristic
112#2083C2211yescharacteristic
113#2083C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2059C2211yescharacteristic
122#2057C2211yescharacteristic
123#2057C2211yescharacteristic
124#2057C2211yescharacteristic
125#2057C2211yescharacteristic
126#2026C2211yescharacteristic
127#2026C2211yescharacteristic
128#2024C2211yescharacteristic
129#2024C2211yescharacteristic
130#1992C2211yescharacteristic
131#1991C2211yescharacteristic
132#1991C2211yescharacteristic
133#1985C2211yescharacteristic
134#1984C2211yescharacteristic
135#1960C2211yescharacteristic
136#1956C2211yescharacteristic
137#1956C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1947C2211yescharacteristic
141#1947C2211yescharacteristic
142#1940C2211yescharacteristic
143#1939C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1933C2211yescharacteristic
147#1933C2211yescharacteristic
148#1928C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1928C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1918C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1865C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1847C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1847C2211yescharacteristic
180#1847C2211yescharacteristic
181#1846C2211yescharacteristic
182#1846C2211yescharacteristic
183#1845C2211yescharacteristic
184#1844C2211yescharacteristic
185#1844C2211yescharacteristic
186#1836C2211yescharacteristic
187#1836C2211yescharacteristic
188#1835C2211yescharacteristic
189#1805C2211yescharacteristic
190#1805C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1768C2211yescharacteristic
194#1768C2211yescharacteristic
195C4×C4⋊C8C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1746C2211yescharacteristic
201#1745C2211yescharacteristic
202#1726C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220#501—42no—
221#501—42no—
222#499—42no—
223#498—42no—
224#491Q818yescomplemented
225#479—42no—
226#479—42no—
227#479—42no—
228#479—42no—
229#479—42no—
230#479—42no—
231#477—42no—
232#475—42no—
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#398—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#398—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#395—21no—
319#395—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391D411yescharacteristic
337#391D411yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
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#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389D411yescharacteristic
368#389D411yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#387—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#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#387D411yescharacteristic
412#387D411yescharacteristic
413#387D411yescharacteristic
414#387D411yescharacteristic
415#384—21no—
416#384—21no—
417#384—21no—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#382—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450#376C2311yescharacteristic
451#376C2311yescharacteristic
452C43C2311yescharacteristic
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#340C2311yescharacteristic
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
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8C2×D411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8—41no—
507C4⋊Q8—41no—
508C4⋊Q8—41no—
509C4⋊Q8—41no—
510C4⋊Q8—41no—
511C4⋊Q8—41no—
512C4⋊Q8C2×Q814yes—
513#125—22no—
514#125—41no—
515#125—41no—
516#125—41no—
517#125—41no—
518#125—41no—
519#125—41no—
520#125—41no—
521#125—41no—
522#125—41no—
523#125—41no—
524#125C2×Q814yes—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
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⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42C2×D411yescharacteristic
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634#107—22no—
635#107—22no—
636#107—41no—
637#107—41no—
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#107—41no—
643#107—41no—
644#107—41no—
645#107—41no—
646#106—22no—
647#106—22no—
648#106—22no—
649#106—22no—
650#106—22no—
651#106—22no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103—41no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103C2×Q814yes—
677#103C2×Q814yes—
678#103C2×Q814yes—
679#103C2×Q814yes—
680#97—22no—
681#97—22no—
682#97—22no—
683#97C2×Q814yes—
684C4×C8—22no—
685C4×C8—22no—
686C4×C8—22no—
687C4×C8—22no—
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#95—21no—
700#95—21no—
701#95—21no—
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#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750C2×Q8—22no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—41no—
762C2×Q8—41no—
763C2×Q8—81no—
764C2×Q8—81no—
765C2×Q8—81no—
766C2×Q8—81no—
767C2×Q8—81no—
768C2×Q8—81no—
769C2×Q8—81no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8C22×Q812yes—
773C2×Q8C22×Q812yes—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C2511yescharacteristic
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8C22×Q812yes—
826C2×C8C22×Q812yes—
827C2×C8H(5,𝔽2)12yes—
828C2×C8H(5,𝔽2)12yes—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
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—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—41no—
866C4⋊C4—41no—
867C4⋊C4—41no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
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⋊C4C22×Q812yes—
914C4⋊C4C22×Q812yes—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—41no—
926C42—41no—
927C42—41no—
928C42—41no—
929C42—42no—
930C42—42no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42—81no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42—81no—
941C42C22×Q812yes—
942C422−1+412yes—
943C422−1+412yes—
944C422−1+412yes—
945C23C23×D411yescharacteristic
946Q8—22no—
947Q8—22no—
948Q8—22no—
949Q8—22no—
950Q8—41no—
951Q8—41no—
952Q8—41no—
953Q8—41no—
954Q8—82no—
955Q8—162no—
956Q8—162no—
957Q8—162no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
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—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
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#53612yes—
1045C2×C4#53612yes—
1046C2×C4D4×Q812yes—
1047C2×C4D4×Q812yes—
1048C2×C4C23×Q811yescharacteristic
1049C2×C4C2×H(5,𝔽2)11yescharacteristic
1050C2×C4C2×H(5,𝔽2)11yescharacteristic
1051C2×C4C2×2−1+411yescharacteristic
1052C2×C4C2×2−1+411yescharacteristic
1053C2×C4C2×2−1+411yescharacteristic
1054C8—22no—
1055C8—22no—
1056C8—22no—
1057C8—22no—
1058C8—41no—
1059C8—41no—
1060C8—41no—
1061C8—41no—
1062C22C2×#53611yescharacteristic
1063C22C2×D4×Q811yescharacteristic
1064C22#349811yescharacteristic
1065C22#358411yescharacteristic
1066C22#358411yescharacteristic
1067C22#358611yescharacteristic
1068C22#358611yescharacteristic
1069C4—22no—
1070C4—22no—
1071C4—22no—
1072C4—22no—
1073C4—42no—
1074C4—42no—
1075C4—42no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—41no—
1081C4—41no—
1082C4—41no—
1083C4—41no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4#350311yescharacteristic
1100C4#350311yescharacteristic
1101C4#354411yescharacteristic
1102C4#354411yescharacteristic
1103C2#3961711yescharacteristic
1104C2#6087611yescharacteristic
1105C2#6089111yescharacteristic
1106C2#6138611yescharacteristic
1107C2#6138611yescharacteristic
1108C2#6243311yescharacteristic
1109C2#6244211yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
224. #491Q8semidirect

Maximal subgroups

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

subgroupindex
#396732
#396222
#333182
#309772
#309762
#309722
#309642
#309602
#309562
#309532
#303132
#303112
#292162
#291852
#291802
#291532
#285262
#285152
#260572
#260552
#260482
#260432
#250752
#250712
#250662
#250612
#222312
#222252
#216532
#213482