Finite Group Databasebeta

← #6814211

Subgroups — #6814211

Order 512.

1238 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39927C211yesmaximal, characteristic
2#39901C211yesmaximal, characteristic
3#33208C211yesmaximal, characteristic
4#32415C211yesmaximal, characteristic
5#32414C211yesmaximal, characteristic
6#32413C211yesmaximal, characteristic
7#32412C211yesmaximal, characteristic
8#32316C211yesmaximal, characteristic, complemented
9#32315C211yesmaximal, characteristic, complemented
10#32313C211yesmaximal, characteristic, complemented
11#32310C211yesmaximal, characteristic, complemented
12#29944C211yesmaximal, characteristic
13#29943C211yesmaximal, characteristic
14#28831C211yesmaximal, characteristic, complemented
15#28831C211yesmaximal, characteristic, complemented
16#28829C211yesmaximal, characteristic, complemented
17#28678C211yesmaximal, characteristic, complemented
18#27990C211yesmaximal, characteristic, complemented
19#27990C211yesmaximal, characteristic, complemented
20#27836C211yesmaximal, characteristic
21#27836C211yesmaximal, characteristic
22#27835C211yesmaximal, characteristic
23#27835C211yesmaximal, characteristic
24#26517C211yesmaximal, characteristic, complemented
25#26514C211yesmaximal, characteristic, complemented
26#26286C211yesmaximal, characteristic, complemented
27#26285C211yesmaximal, characteristic, complemented
28#23159C211yesmaximal, characteristic, complemented
29#22725C211yesmaximal, characteristic, complemented
30C8×C22⋊Q8C211yesmaximal, characteristic
31#20816C211yesmaximal, characteristic
32C2×#499C2211yescharacteristic
33C2×C8×Q8C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35#2851C2211yescharacteristic
36#2851C2211yescharacteristic
37#2766—21no—
38#2762—21no—
39#2755—21no—
40#2747—21no—
41#2722—21no—
42#2719—21no—
43#2704—21no—
44#2690—21no—
45#2655—21no—
46#2655—21no—
47#2584C2211yescharacteristic
48#2584C2211yescharacteristic
49#2570C2211yescharacteristic
50#2570C2211yescharacteristic
51#2570C2211yescharacteristic
52#2570C2211yescharacteristic
53#2552C2211yescharacteristic
54#2552C2211yescharacteristic
55#2507C2211yescharacteristic
56#2507C2211yescharacteristic
57#2506C2211yescharacteristic
58#2506C2211yescharacteristic
59#2497C2211yescharacteristic
60#2497C2211yescharacteristic
61#2496C2211yescharacteristic
62#2496C2211yescharacteristic
63#2495C2211yescharacteristic
64#2495C2211yescharacteristic
65#2494C2211yescharacteristic
66#2494C2211yescharacteristic
67#2478—21no—
68#2478—21no—
69#2475—21no—
70#2475—21no—
71#2370C2211yescharacteristic
72#2370C2211yescharacteristic
73#2355C2211yescharacteristic
74#2355C2211yescharacteristic
75#2336—21no—
76#2336—21no—
77C4×C22⋊Q8C2211yescharacteristic
78#2285C2211yescharacteristic
79#2285C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
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#1991C2211yescharacteristic
121#1991C2211yescharacteristic
122#1989C2211yescharacteristic
123#1989C2211yescharacteristic
124#1989C2211yescharacteristic
125#1989C2211yescharacteristic
126#1984C2211yescharacteristic
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#1942C2211yescharacteristic
140#1942C2211yescharacteristic
141#1941C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1941C2211yescharacteristic
150#1941C2211yescharacteristic
151#1939C2211yescharacteristic
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#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1850C2211yescharacteristic
171#1850C2211yescharacteristic
172#1846C2211yescharacteristic
173#1846C2211yescharacteristic
174#1846C2211yescharacteristic
175#1844C2211yescharacteristic
176#1844C2211yescharacteristic
177#1844C2211yescharacteristic
178#1844C2211yescharacteristic
179#1834C2211yescharacteristic
180#1834C2211yescharacteristic
181#1808C2211yescharacteristic
182#1808C2211yescharacteristic
183#1807C2211yescharacteristic
184#1807C2211yescharacteristic
185#1807C2211yescharacteristic
186#1807C2211yescharacteristic
187#1807C2211yescharacteristic
188#1807C2211yescharacteristic
189#1797C2211yescharacteristic
190C4×#106C2211yescharacteristic
191C4×#106C2211yescharacteristic
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
203C23×C8C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C2×#126—21no—
206C2×#126—21no—
207C2×#125—21no—
208C2×#125—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×C22⋊Q8D411yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×#117—21no—
216C2×#117—21no—
217C22×C42C2311yescharacteristic
218#499—24no—
219C8×Q8—24no—
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
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×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C22⋊C8C2311yescharacteristic
251C2×C22⋊C8C2311yescharacteristic
252C2×C4×C8—24no—
253C2×C4×C8C2311yescharacteristic
254C2×C4×C8C2311yescharacteristic
255C2×C4×C8C2311yescharacteristic
256C2×C4×C8C2311yescharacteristic
257C2×C4×C8C2311yescharacteristic
258C2×C4×C8C2311yescharacteristic
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261#401—21no—
262#401—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#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#398—21no—
289#398—21no—
290#398—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#396—21no—
298#396—21no—
299#395—21no—
300#395—21no—
301#391—21no—
302#391—21no—
303#391D411yescharacteristic
304#389—21no—
305#389—21no—
306#389—21no—
307#389—21no—
308#389—21no—
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389D411yescharacteristic
315#389C2311yescharacteristic
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—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#387D411yescharacteristic
372#387D411yescharacteristic
373#385—21no—
374#385—21no—
375#385—21no—
376#385—21no—
377#385D411yescharacteristic
378#385D411yescharacteristic
379#384C2311yescharacteristic
380#384C2311yescharacteristic
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#384C2311yescharacteristic
384#384C2311yescharacteristic
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#383—21no—
388#383—21no—
389#382—21no—
390#382—21no—
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#380—21no—
398#380—21no—
399#380D411yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
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×Q8C2×D411yescharacteristic
482C23×C4C2×D411yescharacteristic
483C23×C4C2×D411yescharacteristic
484C23×C4C2411yescharacteristic
485C22×C8—22no—
486C22×C8—22no—
487C22×C8—22no—
488C22×C8—22no—
489C22×C8—22no—
490C22×C8—41no—
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499#126—82no—
500#126—82no—
501#125—22no—
502#125—22no—
503#125—22no—
504#125—22no—
505#125—44no—
506#125—44no—
507#125—82no—
508#125—82no—
509C22⋊Q8—24no—
510C4×Q8—22no—
511C4×Q8—22no—
512#117—82no—
513#117—82no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4C2×D411yescharacteristic
555C2×C4⋊C4C2×D411yescharacteristic
556C2×C4⋊C4C2×D411yescharacteristic
557C2×C4⋊C4C2×D411yescharacteristic
558C2×C4⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2×D411yescharacteristic
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4C2×D411yescharacteristic
588C2×C22⋊C4C2×D411yescharacteristic
589C2×C22⋊C4C2×D411yescharacteristic
590C2×C22⋊C4C2×D411yescharacteristic
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42C2×D411yescharacteristic
606C2×C42C2×D411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613#107—22no—
614#107—22no—
615#107—41no—
616#107—41no—
617#107—41no—
618#107—41no—
619#107—41no—
620#107—41no—
621#106—22no—
622#106—22no—
623#106—22no—
624#106—22no—
625#106—22no—
626#106—22no—
627#106—22no—
628#106—22no—
629#106—22no—
630#106—22no—
631#106—41no—
632#106—41no—
633#106—41no—
634#106—41no—
635#106—41no—
636#106—41no—
637C4⋊C8—22no—
638C4⋊C8—22no—
639C4⋊C8—22no—
640C4⋊C8—22no—
641C4⋊C8—22no—
642C4⋊C8—22no—
643C22⋊C8—41no—
644C22⋊C8—41no—
645C4×C8—22no—
646C4×C8—22no—
647C4×C8—22no—
648C4×C8—22no—
649C4×C8—22no—
650C4×C8—22no—
651C4×C8—22no—
652C4×C8#4114yes—
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#95—21no—
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
715C24C22×D411yescharacteristic
716C2×Q8—22no—
717C2×Q8—22no—
718C2×Q8—41no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
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×C4—21no—
745C22×C4—21no—
746C22×C4—41no—
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×C4C22×D411yescharacteristic
758C22×C4C22×D411yescharacteristic
759C22×C4C22×D411yescharacteristic
760C22×C4C2511yescharacteristic
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—21no—
779C2×C8—21no—
780C2×C8—44no—
781C2×C8—44no—
782C2×C8C2×#4112yes—
783C2×C8C2×#4112yes—
784C2×C82−1+412yes—
785C2×C82−1+412yes—
786C2×C82−1+412yes—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
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—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—81no—
846C4⋊C4—81no—
847C4⋊C4—81no—
848C4⋊C4—81no—
849C4⋊C4—81no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4#13514yes—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—42no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—81no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C22⋊C4—81no—
880C42—22no—
881C42—22no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—21no—
890C42—21no—
891C42—21no—
892C42—42no—
893C42—42no—
894C42—81no—
895C42—81no—
896C42—81no—
897C42—81no—
898C42—81no—
899C42—81no—
900C42—81no—
901C42—81no—
902C42—81no—
903C42—81no—
904C42C2×#4112yes—
905C422−1+412yes—
906C23—21no—
907C23—21no—
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23#57712yes—
913C23C23×D411yescharacteristic
914Q8—44no—
915C2×C4—28no—
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—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—44no—
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—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4#54712yes—
1003C2×C4#54712yes—
1004C2×C4C2×#13512yes—
1005C2×C4C2×#13512yes—
1006C2×C4C2×#13512yes—
1007C2×C4#57712yes—
1008C2×C4C22×#4111yescharacteristic
1009C2×C4C2×2−1+411yescharacteristic
1010C2×C4C2×2−1+411yescharacteristic
1011C2×C4C2×2−1+411yescharacteristic
1012C2×C4C2×2−1+411yescharacteristic
1013C2×C4#58511yescharacteristic
1014C8—22no—
1015C8—22no—
1016C8—41no—
1017C8—41no—
1018C8—41no—
1019C8—41no—
1020C8—41no—
1021C8#54114yes—
1022C22—22no—
1023C22—22no—
1024C22—22no—
1025C22—41no—
1026C22—41no—
1027C22—41no—
1028C22—41no—
1029C22C2×#54711yescharacteristic
1030C22#349711yescharacteristic
1031C22#349911yescharacteristic
1032C22C22×#13511yescharacteristic
1033C22C2×#57711yescharacteristic
1034C22C2×#57711yescharacteristic
1035C22#358411yescharacteristic
1036C4—22no—
1037C4—22no—
1038C4—22no—
1039C4—22no—
1040C4—22no—
1041C4—22no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—41no—
1048C4—41no—
1049C4—81no—
1050C4—81no—
1051C4—81no—
1052C4—81no—
1053C4—81no—
1054C4—81no—
1055C4—81no—
1056C4—81no—
1057C4—81no—
1058C4—81no—
1059C4—81no—
1060C4—81no—
1061C4—81no—
1062C4—81no—
1063C4—81no—
1064C4—81no—
1065C4C2×#54111yescharacteristic
1066C4#349511yescharacteristic
1067C4#355511yescharacteristic
1068C4#355611yescharacteristic
1069C2—42no—
1070C2#3935311yescharacteristic
1071C2#6123411yescharacteristic
1072C2#6125911yescharacteristic
1073C2#6236211yescharacteristic
1074C2#6237811yescharacteristic
1075C2#6247011yescharacteristic
1076C2#6249111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #32316C2semidirect
9. #32315C2semidirect
10. #32313C2semidirect
11. #32310C2semidirect
14. #28831C2semidirect
15. #28831C2semidirect
16. #28829C2semidirect
17. #28678C2semidirect
18. #27990C2semidirect
19. #27990C2semidirect
24. #26517C2semidirect
25. #26514C2semidirect
26. #26286C2semidirect
27. #26285C2semidirect
28. #23159C2semidirect
29. #22725C2semidirect

Maximal subgroups

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

subgroupindex
#399272
#399012
#332082
#324152
#324142
#324132
#324122
#323162
#323152
#323132
#323102
#299442
#299432
#288312
#288292
#286782
#279902
#278362
#278352
#265172
#265142
#262862
#262852
#231592
#227252
C8×C22⋊Q82
#208162