Finite Group Databasebeta

← #6814229

Subgroups — #6814229

Order 512.

1186 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#42670C211yesmaximal, characteristic
2#42470C211yesmaximal, characteristic
3#33213C211yesmaximal, characteristic
4#32419C211yesmaximal, characteristic
5#32418C211yesmaximal, characteristic
6#32417C211yesmaximal, characteristic
7#32416C211yesmaximal, characteristic
8#32332C211yesmaximal, characteristic, complemented
9#32331C211yesmaximal, characteristic, complemented
10#32329C211yesmaximal, characteristic, complemented
11#32326C211yesmaximal, characteristic, complemented
12#29945C211yesmaximal, characteristic
13#29945C211yesmaximal, characteristic
14#28831C211yesmaximal, characteristic, complemented
15#28831C211yesmaximal, characteristic, complemented
16#28829C211yesmaximal, characteristic, complemented
17#28677C211yesmaximal, characteristic, complemented
18#27991C211yesmaximal, characteristic, complemented
19#27991C211yesmaximal, characteristic, complemented
20#27836C211yesmaximal, characteristic
21#27836C211yesmaximal, characteristic
22#27835C211yesmaximal, characteristic
23#27835C211yesmaximal, characteristic
24#26521C211yesmaximal, characteristic, complemented
25#26520C211yesmaximal, characteristic, complemented
26#26295C211yesmaximal, characteristic, complemented
27#26294C211yesmaximal, characteristic, complemented
28#23156C211yesmaximal, characteristic, complemented
29#22725C211yesmaximal, characteristic, complemented
30#21601C211yesmaximal, characteristic
31#20820C211yesmaximal, characteristic
32C2×#498C2211yescharacteristic
33C2×C8×Q8C2211yescharacteristic
34C2×#405C2211yescharacteristic
35#2836—21no—
36#2831—21no—
37#2798—21no—
38#2794—21no—
39#2789—21no—
40#2758—21no—
41#2754—21no—
42#2721—21no—
43#2716—21no—
44#2713—21no—
45#2666—21no—
46#2655—21no—
47#2655—21no—
48#2634—21no—
49#2628C2211yescharacteristic
50#2628C2211yescharacteristic
51#2570C2211yescharacteristic
52#2570C2211yescharacteristic
53#2570C2211yescharacteristic
54#2570C2211yescharacteristic
55#2567C2211yescharacteristic
56#2552C2211yescharacteristic
57#2552C2211yescharacteristic
58#2546C2211yescharacteristic
59#2519—21no—
60#2509C2211yescharacteristic
61#2509C2211yescharacteristic
62#2508C2211yescharacteristic
63#2508C2211yescharacteristic
64#2497C2211yescharacteristic
65#2497C2211yescharacteristic
66#2496C2211yescharacteristic
67#2496C2211yescharacteristic
68#2495C2211yescharacteristic
69#2495C2211yescharacteristic
70#2494C2211yescharacteristic
71#2494C2211yescharacteristic
72#2469—21no—
73#2396C2211yescharacteristic
74#2369C2211yescharacteristic
75#2365C2211yescharacteristic
76#2355C2211yescharacteristic
77#2355C2211yescharacteristic
78#2314C2211yescharacteristic
79#2314C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2087C2211yescharacteristic
97#2087C2211yescharacteristic
98#2086C2211yescharacteristic
99#2086C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2084C2211yescharacteristic
107#2084C2211yescharacteristic
108#2083C2211yescharacteristic
109#2083C2211yescharacteristic
110#2083C2211yescharacteristic
111#2083C2211yescharacteristic
112#2077C2211yescharacteristic
113#2077C2211yescharacteristic
114#2077C2211yescharacteristic
115#2077C2211yescharacteristic
116#2076C2211yescharacteristic
117#2076C2211yescharacteristic
118#2075C2211yescharacteristic
119#2075C2211yescharacteristic
120#1993C2211yescharacteristic
121#1993C2211yescharacteristic
122#1988C2211yescharacteristic
123#1988C2211yescharacteristic
124#1987C2211yescharacteristic
125#1987C2211yescharacteristic
126#1985C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1948C2211yescharacteristic
137#1947C2211yescharacteristic
138#1947C2211yescharacteristic
139#1943C2211yescharacteristic
140#1943C2211yescharacteristic
141#1941C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1941C2211yescharacteristic
150#1941C2211yescharacteristic
151#1940C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1917C2211yescharacteristic
169#1917C2211yescharacteristic
170#1851C2211yescharacteristic
171#1851C2211yescharacteristic
172#1846C2211yescharacteristic
173#1846C2211yescharacteristic
174#1846C2211yescharacteristic
175#1846C2211yescharacteristic
176#1844C2211yescharacteristic
177#1844C2211yescharacteristic
178#1844C2211yescharacteristic
179#1836C2211yescharacteristic
180#1836C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1807C2211yescharacteristic
186#1807C2211yescharacteristic
187#1807C2211yescharacteristic
188#1807C2211yescharacteristic
189#1798C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C4×#106C2211yescharacteristic
194C4×#106C2211yescharacteristic
195C4×#106C2211yescharacteristic
196C4×#106C2211yescharacteristic
197C4×#106C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199C8×C4⋊C4C2211yescharacteristic
200C8×C4⋊C4C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×C4×Q8—21no—
213C2×C4×Q8C2311yescharacteristic
214C2×#117C2311yescharacteristic
215#498—24no—
216C8×Q8—24no—
217C2×#107C2311yescharacteristic
218C2×#107C2311yescharacteristic
219C2×#107C2311yescharacteristic
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#106C2311yescharacteristic
226C2×#106C2311yescharacteristic
227C2×#106C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C22⋊C8C2311yescharacteristic
248C2×C22⋊C8C2311yescharacteristic
249#405—24no—
250C2×#97C2311yescharacteristic
251C2×#97C2311yescharacteristic
252C2×C4×C8C2311yescharacteristic
253C2×C4×C8C2311yescharacteristic
254C2×C4×C8C2311yescharacteristic
255C2×C4×C8C2311yescharacteristic
256C2×C4×C8C2311yescharacteristic
257C2×C4×C8C2311yescharacteristic
258#401—21no—
259#401—21no—
260#400—21no—
261#400—21no—
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#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400D411yescharacteristic
279#399—21no—
280#399—21no—
281#399D411yescharacteristic
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398D411yescharacteristic
295#398D411yescharacteristic
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#396—21no—
303#396—21no—
304#396D411yescharacteristic
305#396D411yescharacteristic
306#395—21no—
307#395—21no—
308#395—21no—
309#395—21no—
310#395D411yescharacteristic
311#393—21no—
312#393—21no—
313#393D411yescharacteristic
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
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#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
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#384—21no—
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#383—21no—
392#383—21no—
393#382—21no—
394#382—21no—
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
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
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C22⋊C4C2311yescharacteristic
430C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8C2×D411yescharacteristic
484C23×C4C2411yescharacteristic
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—41no—
488C22×C8—22no—
489C22×C8—22no—
490C22×C8—22no—
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C4⋊Q8—22no—
500C4⋊Q8—22no—
501C4⋊Q8—22no—
502C4⋊Q8—22no—
503C4⋊Q8—82no—
504#126—82no—
505#126—82no—
506#125—82no—
507#125—82no—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—82no—
511#117—22no—
512#117—22no—
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⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
559C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
583C2×C22⋊C4C2×D411yescharacteristic
584C2×C22⋊C4C2×D411yescharacteristic
585C2×C22⋊C4C2×D411yescharacteristic
586C2×C22⋊C4C2×D411yescharacteristic
587C2×C22⋊C4C2×D411yescharacteristic
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×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606#107—22no—
607#107—22no—
608#107—41no—
609#107—41no—
610#107—41no—
611#107—41no—
612#107—41no—
613#107—41no—
614#106—22no—
615#106—22no—
616#106—22no—
617#106—22no—
618#106—22no—
619#106—22no—
620#106—22no—
621#106—22no—
622#106—22no—
623#106—22no—
624#106—41no—
625#106—41no—
626#106—41no—
627#106—41no—
628#106—41no—
629#106—41no—
630C4⋊C8—22no—
631C4⋊C8—22no—
632C4⋊C8—22no—
633C4⋊C8—22no—
634C4⋊C8—22no—
635C4⋊C8—22no—
636C22⋊C8—41no—
637C22⋊C8—41no—
638#97—22no—
639#97—22no—
640C4×C8—22no—
641C4×C8—22no—
642C4×C8—22no—
643C4×C8—22no—
644C4×C8—22no—
645C4×C8#4114yes—
646#95—21no—
647#95—21no—
648#95—21no—
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#95—21no—
700#95—21no—
701#95—21no—
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
712C24C22×D411yescharacteristic
713C2×Q8—22no—
714C2×Q8—22no—
715C2×Q8—41no—
716C2×Q8—42no—
717C2×Q8—42no—
718C2×Q8—81no—
719C2×Q8—81no—
720C2×Q8—81no—
721C2×Q8—81no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—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×C4C22×D411yescharacteristic
745C22×C4C22×D411yescharacteristic
746C22×C4C22×D411yescharacteristic
747C22×C4C22×D411yescharacteristic
748C22×C4C22×D411yescharacteristic
749C22×C4C22×D411yescharacteristic
750C22×C4C22×D411yescharacteristic
751C22×C4C22×D411yescharacteristic
752C22×C4C22×D411yescharacteristic
753C22×C4C22×D411yescharacteristic
754C22×C4C22×D411yescharacteristic
755C22×C4C22×D411yescharacteristic
756C22×C4C22×D411yescharacteristic
757C22×C4C2511yescharacteristic
758M16—44no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
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—44no—
779C2×C8C2×#4112yes—
780C2×C8C2×#4112yes—
781C2×C82−1+412yes—
782C2×C82−1+412yes—
783C2×C82−1+412yes—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—21no—
793C4⋊C4—21no—
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—21no—
823C4⋊C4—21no—
824C4⋊C4—41no—
825C4⋊C4—41no—
826C4⋊C4—41no—
827C4⋊C4—42no—
828C4⋊C4—42no—
829C4⋊C4—42no—
830C4⋊C4—42no—
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—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—41no—
866C22⋊C4—41no—
867C22⋊C4—81no—
868C22⋊C4—81no—
869C22⋊C4—81no—
870C22⋊C4—81no—
871C22⋊C4—81no—
872C22⋊C4—81no—
873C22⋊C4—81no—
874C22⋊C4—81no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—21no—
879C42—21no—
880C42—21no—
881C42—21no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—42no—
886C42—42no—
887C42—81no—
888C42—81no—
889C42—81no—
890C42—81no—
891C42—81no—
892C42—81no—
893C42—81no—
894C42—81no—
895C42—81no—
896C42—81no—
897C42C2×#4112yes—
898C422−1+412yes—
899C23—21no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—21no—
904C23—21no—
905C23—21no—
906C23C23×D411yescharacteristic
907Q8—44no—
908Q8—84no—
909Q8—162no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
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—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
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#54712yes—
998C2×C4#54712yes—
999C2×C4#57712yes—
1000C2×C4#57712yes—
1001C2×C4C22×#4111yescharacteristic
1002C2×C4C2×2−1+411yescharacteristic
1003C2×C4C2×2−1+411yescharacteristic
1004C2×C4C2×2−1+411yescharacteristic
1005C2×C4C2×2−1+411yescharacteristic
1006C2×C4#58511yescharacteristic
1007C8—22no—
1008C8—22no—
1009C8—41no—
1010C8—41no—
1011C8—41no—
1012C8—41no—
1013C8—41no—
1014C8#54114yes—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22C2×#54711yescharacteristic
1023C22#349711yescharacteristic
1024C22#349911yescharacteristic
1025C22C2×#57711yescharacteristic
1026C22C2×#57711yescharacteristic
1027C22#358411yescharacteristic
1028C22#358411yescharacteristic
1029C4—22no—
1030C4—22no—
1031C4—22no—
1032C4—22no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—41no—
1038C4—41no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—81no—
1043C4—81no—
1044C4—81no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4—81no—
1049C4—81no—
1050C4—81no—
1051C4—81no—
1052C4—81no—
1053C4—81no—
1054C4—81no—
1055C4—81no—
1056C4—81no—
1057C4—81no—
1058C4C2×#54111yescharacteristic
1059C4#349511yescharacteristic
1060C4#355511yescharacteristic
1061C4#355611yescharacteristic
1062C2—81no—
1063C2#3935311yescharacteristic
1064C2#6126311yescharacteristic
1065C2#6128511yescharacteristic
1066C2#6237811yescharacteristic
1067C2#6237811yescharacteristic
1068C2#6248611yescharacteristic
1069C2#6248911yescharacteristic
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
8. #32332C2semidirect
9. #32331C2semidirect
10. #32329C2semidirect
11. #32326C2semidirect
14. #28831C2semidirect
15. #28831C2semidirect
16. #28829C2semidirect
17. #28677C2semidirect
18. #27991C2semidirect
19. #27991C2semidirect
24. #26521C2semidirect
25. #26520C2semidirect
26. #26295C2semidirect
27. #26294C2semidirect
28. #23156C2semidirect
29. #22725C2semidirect

Maximal subgroups

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

subgroupindex
#426702
#424702
#332132
#324192
#324182
#324172
#324162
#323322
#323312
#323292
#323262
#299452
#288312
#288292
#286772
#279912
#278362
#278352
#265212
#265202
#262952
#262942
#231562
#227252
#216012
#208202