Finite Group Databasebeta

← #6851877

Subgroups — #6851877

Order 512.

1198 conjugacy classes of subgroups.

The subgroup lattice has 1071 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39681C211yesmaximal, characteristic
2#35582C211yesmaximal, characteristic
3#33077C211yesmaximal, characteristic
4#32687C211yesmaximal, characteristic
5#32685C211yesmaximal, characteristic
6#32578C211yesmaximal, characteristic
7#32570C211yesmaximal, characteristic
8#32372C211yesmaximal, characteristic
9#32350C211yesmaximal, characteristic
10#32152C211yesmaximal, characteristic
11#32134C211yesmaximal, characteristic
12#30001C211yesmaximal, characteristic
13#29992C211yesmaximal, characteristic
14#29324C211yesmaximal, characteristic
15#29315C211yesmaximal, characteristic
16#29290C211yesmaximal, characteristic
17#29282C211yesmaximal, characteristic
18#29281C211yesmaximal, characteristic
19#29217C211yesmaximal, characteristic
20#28956C211yesmaximal, characteristic
21#28945C211yesmaximal, characteristic
22#28009C211yesmaximal, characteristic
23#27991C211yesmaximal, characteristic
24#27028C211yesmaximal, characteristic
25#27000C211yesmaximal, characteristic
26#26873C211yesmaximal, characteristic
27#26869C211yesmaximal, characteristic
28#22822C211yesmaximal, characteristic
29#22129C211yesmaximal, characteristic
30#22112C211yesmaximal, characteristic
31#21626C211yesmaximal, characteristic
32C2×#475C2211yescharacteristic
33#2864C2211yescharacteristic
34#2806—21no—
35#2799—21no—
36#2791—21no—
37#2774—21no—
38#2660C2211yescharacteristic
39#2647C2211yescharacteristic
40#2612—21no—
41#2606—21no—
42#2605—21no—
43#2590—21no—
44#2586—21no—
45#2584C2211yescharacteristic
46#2584C2211yescharacteristic
47#2582C2211yescharacteristic
48#2581—21no—
49#2567C2211yescharacteristic
50#2565—21no—
51#2565C2211yescharacteristic
52#2551C2211yescharacteristic
53#2550—21no—
54#2520—21no—
55#2509C2211yescharacteristic
56#2508C2211yescharacteristic
57#2508C2211yescharacteristic
58#2507C2211yescharacteristic
59#2506C2211yescharacteristic
60#2506C2211yescharacteristic
61#2462—21no—
62#2462—21no—
63#2451C2211yescharacteristic
64#2451C2211yescharacteristic
65#2446—21no—
66#2370C2211yescharacteristic
67#2365C2211yescharacteristic
68#2331C2211yescharacteristic
69#2331C2211yescharacteristic
70#2331C2211yescharacteristic
71#2330C2211yescharacteristic
72#2320C2211yescharacteristic
73C4×C4⋊Q8C2211yescharacteristic
74C4×C4⋊Q8C2211yescharacteristic
75#2295C2211yescharacteristic
76#2295C2211yescharacteristic
77#2276C2211yescharacteristic
78#2101C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2100C2211yescharacteristic
82#2099C2211yescharacteristic
83#2099C2211yescharacteristic
84#2097C2211yescharacteristic
85#2095C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2087C2211yescharacteristic
89#2087C2211yescharacteristic
90#2087C2211yescharacteristic
91#2087C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2084C2211yescharacteristic
95#2084C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2058C2211yescharacteristic
112#2057C2211yescharacteristic
113#2057C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2026C2211yescharacteristic
117#2024C2211yescharacteristic
118#1993C2211yescharacteristic
119#1990C2211yescharacteristic
120#1988C2211yescharacteristic
121#1987C2211yescharacteristic
122#1987C2211yescharacteristic
123#1987C2211yescharacteristic
124#1987C2211yescharacteristic
125#1984C2211yescharacteristic
126#1984C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1948C2211yescharacteristic
134#1947C2211yescharacteristic
135#1947C2211yescharacteristic
136#1947C2211yescharacteristic
137#1947C2211yescharacteristic
138#1944C2211yescharacteristic
139#1944C2211yescharacteristic
140#1943C2211yescharacteristic
141#1942C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1941C2211yescharacteristic
150#1935C2211yescharacteristic
151#1933C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1928C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1919C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1919C2211yescharacteristic
171#1919C2211yescharacteristic
172#1918C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1918C2211yescharacteristic
176#1917C2211yescharacteristic
177#1917C2211yescharacteristic
178#1916C2211yescharacteristic
179#1916C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1847C2211yescharacteristic
187#1846C2211yescharacteristic
188#1842C2211yescharacteristic
189#1832C2211yescharacteristic
190#1832C2211yescharacteristic
191#1805C2211yescharacteristic
192#1805C2211yescharacteristic
193#1803C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1770C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198#1768C2211yescharacteristic
199#1768C2211yescharacteristic
200C4×C4⋊C8C2211yescharacteristic
201#1763C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125—21no—
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×C4×Q8—21no—
213C2×C4×Q8—21no—
214C2×C4×Q8—21no—
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219#475Q818yescomplemented
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#97C2311yescharacteristic
257C2×#97C2311yescharacteristic
258C2×C4×C8C2311yescharacteristic
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262#400—21no—
263#400—21no—
264#400—21no—
265#400—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#398—21no—
271#398—21no—
272#398—21no—
273#398—21no—
274#398—21no—
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#395—21no—
289#395—21no—
290#395—21no—
291#395—21no—
292#395—21no—
293#395—21no—
294#395—21no—
295#395—21no—
296#395—21no—
297#395—21no—
298#391—21no—
299#391—21no—
300#391—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#391—21no—
311#391D411yescharacteristic
312#391D411yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389D411yescharacteristic
331#389D411yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387D411yescharacteristic
387#387D411yescharacteristic
388#387D411yescharacteristic
389#387D411yescharacteristic
390#384—21no—
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#383—21no—
396#382—21no—
397#382—21no—
398#382—21no—
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424#376—21no—
425#376—21no—
426#376C2311yescharacteristic
427#376C2311yescharacteristic
428C43C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
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#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479C22×Q8—21no—
480C22×Q8—21no—
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8C2×D411yescharacteristic
484C22×Q8C2411yescharacteristic
485C22×C8C2411yescharacteristic
486C22×C8C2411yescharacteristic
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C4⋊Q8—22no—
494C4⋊Q8—22no—
495C4⋊Q8—22no—
496C4⋊Q8—41no—
497C4⋊Q8—41no—
498C4⋊Q8—41no—
499C4⋊Q8—41no—
500C4⋊Q8—82no—
501C4⋊Q8C2×Q814yes—
502#125—41no—
503#125—41no—
504#125—41no—
505#125—41no—
506#125—82no—
507#125—82no—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—41no—
511C4×Q8—41no—
512C4×Q8—41no—
513C4×Q8—41no—
514C4×Q8—41no—
515C4×Q8—82no—
516C4×Q8—82no—
517C4×Q8—82no—
518C4×Q8C2×Q814yes—
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⋊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⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C42—21no—
587C2×C42—21no—
588C2×C42—21no—
589C2×C42—21no—
590C2×C42—21no—
591C2×C42—21no—
592C2×C42—21no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42C2×D411yescharacteristic
601C2×C42C2×D411yescharacteristic
602C2×C42C2×D411yescharacteristic
603C2×C42C2×D411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611#107—22no—
612#107—41no—
613#107—41no—
614#107—41no—
615#107—41no—
616#107—41no—
617#107—41no—
618#107—41no—
619#107—41no—
620#107—41no—
621#106—22no—
622#106—41no—
623#106—41no—
624#106—41no—
625#106—41no—
626#106—41no—
627#106—41no—
628#106—41no—
629#106C2×Q814yes—
630#106C2×Q814yes—
631C4⋊C8—22no—
632C4⋊C8—22no—
633C4⋊C8—22no—
634C4⋊C8—41no—
635C4⋊C8—41no—
636C4⋊C8—41no—
637C4⋊C8—41no—
638C4⋊C8C2×Q814yes—
639#103—41no—
640#103—41no—
641#103—41no—
642#103—41no—
643#103—41no—
644#103—41no—
645#103C2×Q814yes—
646#103C2×Q814yes—
647#97—41no—
648#97—41no—
649C4×C8—41no—
650C4×C8—41no—
651C4×C8—41no—
652C4×C8—41no—
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#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
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
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718C2×Q8—24no—
719C2×Q8—22no—
720C2×Q8—21no—
721C2×Q8—21no—
722C2×Q8—21no—
723C2×Q8—21no—
724C2×Q8—21no—
725C2×Q8—41no—
726C2×Q8—41no—
727C2×Q8—42no—
728C2×Q8—42no—
729C2×Q8—42no—
730C2×Q8—42no—
731C2×Q8—81no—
732C2×Q8—81no—
733C2×Q8—81no—
734C2×Q8—81no—
735C2×Q8—81no—
736C2×Q8—81no—
737C2×Q8—81no—
738C2×Q8C22×Q812yes—
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—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
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×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C2511yescharacteristic
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×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8C22×Q812yes—
793C2×C8C22×Q812yes—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—22no—
798C4⋊C4—22no—
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—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
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—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
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—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4C22×Q812yes—
873C4⋊C4C22×Q812yes—
874C4⋊C4C22×Q812yes—
875C4⋊C42−1+412yes—
876C42—24no—
877C42—22no—
878C42—22no—
879C42—21no—
880C42—21no—
881C42—21no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—21no—
890C42—21no—
891C42—41no—
892C42—41no—
893C42—42no—
894C42—42no—
895C42—42no—
896C42—42no—
897C42—81no—
898C42—81no—
899C42—81no—
900C42—81no—
901C42—81no—
902C42—81no—
903C42—81no—
904C42—81no—
905C42—81no—
906C42C22×Q812yes—
907C422−1+412yes—
908C23C23×D411yescharacteristic
909Q8—22no—
910Q8—22no—
911Q8—41no—
912Q8—41no—
913Q8—82no—
914Q8—84no—
915Q8—84no—
916Q8—84no—
917Q8—162no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
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—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—22no—
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—41no—
962C2×C4—41no—
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×C4D4×Q812yes—
1005C2×C4D4×Q812yes—
1006C2×C4#57712yes—
1007C2×C4#57812yes—
1008C2×C4C23×Q811yescharacteristic
1009C2×C4C2×2−1+411yescharacteristic
1010C2×C4C2×2−1+411yescharacteristic
1011C2×C4#58511yescharacteristic
1012C2×C4#58511yescharacteristic
1013C2×C4#58511yescharacteristic
1014C8—22no—
1015C8—22no—
1016C8—41no—
1017C8—41no—
1018C8—41no—
1019C8—41no—
1020C8—41no—
1021C8—41no—
1022C22#344911yescharacteristic
1023C22C2×D4×Q811yescharacteristic
1024C22#348911yescharacteristic
1025C22C2×#57711yescharacteristic
1026C22C2×#57811yescharacteristic
1027C22#358411yescharacteristic
1028C22#358511yescharacteristic
1029C4—22no—
1030C4—22no—
1031C4—22no—
1032C4—22no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—41no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—42no—
1046C4—41no—
1047C4—41no—
1048C4—81no—
1049C4—81no—
1050C4—81no—
1051C4—81no—
1052C4—81no—
1053C4—81no—
1054C4—81no—
1055C4—81no—
1056C4—81no—
1057C4—81no—
1058C4—81no—
1059C4#350211yescharacteristic
1060C4#350411yescharacteristic
1061C4#355511yescharacteristic
1062C4#355711yescharacteristic
1063C2#3959111yescharacteristic
1064C2#6098911yescharacteristic
1065C2#6100211yescharacteristic
1066C2#6137111yescharacteristic
1067C2#6138411yescharacteristic
1068C2#6217611yescharacteristic
1069C2#6220411yescharacteristic
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
219. #475Q8semidirect

Maximal subgroups

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

subgroupindex
#396812
#355822
#330772
#326872
#326852
#325782
#325702
#323722
#323502
#321522
#321342
#300012
#299922
#293242
#293152
#292902
#292822
#292812
#292172
#289562
#289452
#280092
#279912
#270282
#270002
#268732
#268692
#228222
#221292
#221122
#216262