Finite Group Databasebeta

← #7590874

Subgroups — #7590874

Order 512.

1235 conjugacy classes of subgroups.

The subgroup lattice has 1101 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45304C211yesmaximal, characteristic
2#45123C211yesmaximal, characteristic
3#31631C211yesmaximal, characteristic
4#31631C211yesmaximal, characteristic
5#31628C211yesmaximal, characteristic
6#31627C211yesmaximal, characteristic
7#28839C211yesmaximal, characteristic, complemented
8#28278C211yesmaximal, characteristic, complemented
9#28006C211yesmaximal, characteristic, complemented
10#28002C211yesmaximal, characteristic, complemented
11#27848C211yesmaximal, characteristic
12#27836C211yesmaximal, characteristic
13#27643C211yesmaximal, characteristic
14#27638C211yesmaximal, characteristic
15#27373C211yesmaximal, characteristic, complemented
16#27368C211yesmaximal, characteristic, complemented
17#27366C211yesmaximal, characteristic, complemented
18#27361C211yesmaximal, characteristic, complemented
19#26114C211yesmaximal, characteristic, complemented
20#26113C211yesmaximal, characteristic, complemented
21#25043C211yesmaximal, characteristic
22#25033C211yesmaximal, characteristic
23#25000C211yesmaximal, characteristic, complemented
24#24995C211yesmaximal, characteristic, complemented
25#22818C211yesmaximal, characteristic, complemented
26#22815C211yesmaximal, characteristic, complemented
27#22730C211yesmaximal, characteristic, complemented
28#22679C211yesmaximal, characteristic, complemented
29#21605C211yesmaximal, characteristic
30#21530C211yesmaximal, characteristic
31#20822C211yesmaximal, characteristic
32C2×#467C2211yescharacteristic
33C2×#446C2211yescharacteristic
34C2×#441C2211yescharacteristic
35C2×#441C2211yescharacteristic
36C2×C4×Q16C2211yescharacteristic
37C2×#405C2211yescharacteristic
38#2794—21no—
39#2793—21no—
40#2777—21no—
41#2775—21no—
42#2774—21no—
43#2773—21no—
44#2766—21no—
45#2762—21no—
46#2606—21no—
47#2596—21no—
48#2582C2211yescharacteristic
49#2581C2211yescharacteristic
50#2571C2211yescharacteristic
51#2570C2211yescharacteristic
52#2533—21no—
53#2533—21no—
54#2532—21no—
55#2529—21no—
56#2529—21no—
57#2524—21no—
58#2509C2211yescharacteristic
59#2509C2211yescharacteristic
60#2508C2211yescharacteristic
61#2507C2211yescharacteristic
62#2497C2211yescharacteristic
63#2495C2211yescharacteristic
64#2495C2211yescharacteristic
65#2494C2211yescharacteristic
66#2423C2211yescharacteristic
67#2421C2211yescharacteristic
68#2421C2211yescharacteristic
69#2421C2211yescharacteristic
70#2396C2211yescharacteristic
71#2356C2211yescharacteristic
72#2356C2211yescharacteristic
73#2356C2211yescharacteristic
74#2355C2211yescharacteristic
75#2355C2211yescharacteristic
76#2355C2211yescharacteristic
77#2351C2211yescharacteristic
78Q8×C4⋊C4C2211yescharacteristic
79#2323C2211yescharacteristic
80#2323C2211yescharacteristic
81#2314C2211yescharacteristic
82#2314C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2087C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2083C2211yescharacteristic
99#2077C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2075C2211yescharacteristic
103#2074C2211yescharacteristic
104#2074C2211yescharacteristic
105#2074C2211yescharacteristic
106#2072C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2036C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#1984C2211yescharacteristic
116#1971C2211yescharacteristic
117#1971C2211yescharacteristic
118#1969C2211yescharacteristic
119#1949C2211yescharacteristic
120#1949C2211yescharacteristic
121#1949C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1948C2211yescharacteristic
125#1948C2211yescharacteristic
126#1947C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1943C2211yescharacteristic
130#1943C2211yescharacteristic
131#1942C2211yescharacteristic
132#1941C2211yescharacteristic
133#1941C2211yescharacteristic
134#1939C2211yescharacteristic
135#1933C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1921C2211yescharacteristic
146#1920C2211yescharacteristic
147#1920C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1918C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1916C2211yescharacteristic
154#1916C2211yescharacteristic
155#1894C2211yescharacteristic
156#1894C2211yescharacteristic
157#1865C2211yescharacteristic
158#1865C2211yescharacteristic
159#1865C2211yescharacteristic
160#1865C2211yescharacteristic
161#1865C2211yescharacteristic
162#1863C2211yescharacteristic
163#1863C2211yescharacteristic
164#1863C2211yescharacteristic
165#1851C2211yescharacteristic
166#1851C2211yescharacteristic
167#1847C2211yescharacteristic
168#1847C2211yescharacteristic
169#1847C2211yescharacteristic
170#1847C2211yescharacteristic
171#1846C2211yescharacteristic
172#1846C2211yescharacteristic
173#1835C2211yescharacteristic
174#1834C2211yescharacteristic
175#1809C2211yescharacteristic
176#1809C2211yescharacteristic
177#1808C2211yescharacteristic
178#1807C2211yescharacteristic
179#1807C2211yescharacteristic
180#1805C2211yescharacteristic
181#1805C2211yescharacteristic
182#1805C2211yescharacteristic
183#1805C2211yescharacteristic
184#1805C2211yescharacteristic
185#1803C2211yescharacteristic
186#1803C2211yescharacteristic
187#1803C2211yescharacteristic
188#1798C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193C4×#107C2211yescharacteristic
194C4×#106C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1770C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C22⋊Q8C2311yescharacteristic
207C2×C22⋊Q8C2311yescharacteristic
208C2×C4×Q8C2311yescharacteristic
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×#117C2311yescharacteristic
216#467—24no—
217#446—24no—
218#441—24no—
219#441—24no—
220C4×Q16—24no—
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×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262#405—24no—
263C2×#97C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271#401—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400D411yescharacteristic
288#399—21no—
289#399D411yescharacteristic
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398D411yescharacteristic
298#398D411yescharacteristic
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#396—21no—
306#396D411yescharacteristic
307#396D411yescharacteristic
308#395—21no—
309#395D411yescharacteristic
310#393D411yescharacteristic
311#391—21no—
312#391—21no—
313#391—21no—
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
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#389—21no—
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#388—21no—
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#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—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#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#384—21no—
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#383—21no—
399#383—21no—
400#383—21no—
401#383—21no—
402#383—21no—
403#382—21no—
404#382—21no—
405#382—21no—
406#382—21no—
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376—21no—
442#376—21no—
443#376—21no—
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#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8C2×D411yescharacteristic
485C22×Q8C2411yescharacteristic
486C22×Q8C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C2×Q16—22no—
489C2×Q16—22no—
490C2×Q16#4114yes—
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C22×C8—22no—
495C22×C8—22no—
496C22×C8—22no—
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—41no—
508C22⋊Q8—41no—
509C4×Q8—22no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×Q8—22no—
513C4×Q8—22no—
514C4×Q8—22no—
515C4×Q8—22no—
516C4×Q8—22no—
517C4×Q8—22no—
518C4×Q8—22no—
519C4×Q8—41no—
520C4×Q8—41no—
521C4×Q8—41no—
522C4×Q8—41no—
523#117—22no—
524#117—22no—
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⋊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⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
588C2×C22⋊C4C2×D411yescharacteristic
589C2×C22⋊C4C2×D411yescharacteristic
590C2×C22⋊C4C2×D411yescharacteristic
591C2×C22⋊C4C2×D411yescharacteristic
592C2×C22⋊C4C2×D411yescharacteristic
593C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616#107—22no—
617#107—22no—
618#107—22no—
619#107—41no—
620#107—41no—
621#107—41no—
622#107—41no—
623#107—41no—
624#107—41no—
625#106—22no—
626#106—22no—
627#106—22no—
628#106—22no—
629#106—41no—
630#106—41no—
631#106—41no—
632#106—41no—
633#106—41no—
634#106—41no—
635C4⋊C8—22no—
636C4⋊C8—22no—
637C4⋊C8—22no—
638C4⋊C8—22no—
639C4⋊C8—41no—
640C4⋊C8—41no—
641#103—22no—
642#103—22no—
643#103—22no—
644#103—22no—
645#103—22no—
646#103—22no—
647#103—22no—
648#103—22no—
649#103—41no—
650#103—41no—
651#103—41no—
652#103—41no—
653#103—41no—
654#103—41no—
655C22⋊C8—41no—
656C22⋊C8—41no—
657#97—22no—
658#97—22no—
659#97—22no—
660#97#4114yes—
661C4×C8—22no—
662C4×C8—22no—
663C4×C8—22no—
664C4×C8—22no—
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#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#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733C24C22×D411yescharacteristic
734C2×Q8—22no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—41no—
746C2×Q8—41no—
747C2×Q8C2×#4112yes—
748C2×Q8C2×#4112yes—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C2511yescharacteristic
785Q16—28no—
786M16—44no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—44no—
808C2×C8C2×#4112yes—
809C2×C8C2×#4112yes—
810C2×C8C2×#4112yes—
811C2×C82−1+412yes—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—22no—
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—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
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—41no—
846C4⋊C4—41no—
847C4⋊C4—41no—
848C4⋊C4—41no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
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⋊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—
881C22⋊C4—22no—
882C22⋊C4—22no—
883C22⋊C4—41no—
884C22⋊C4—41no—
885C22⋊C4—41no—
886C22⋊C4—41no—
887C22⋊C4—42no—
888C22⋊C4—42no—
889C22⋊C4—81no—
890C22⋊C4—81no—
891C22⋊C4—81no—
892C22⋊C4—81no—
893C22⋊C4—81no—
894C22⋊C4—81no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—42no—
906C42—42no—
907C42—42no—
908C42—42no—
909C42—42no—
910C42—42no—
911C42—42no—
912C42—81no—
913C42—81no—
914C42—81no—
915C42—81no—
916C42—81no—
917C42—81no—
918C42—81no—
919C42—81no—
920C42—81no—
921C42C2×#4112yes—
922C422−1+412yes—
923C23—21no—
924C23—21no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23C23×D411yescharacteristic
931Q8—22no—
932Q8—22no—
933Q8—22no—
934Q8—22no—
935Q8—41no—
936Q8—41no—
937Q8—41no—
938Q8—41no—
939Q8—82no—
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—21no—
950C2×C4—21no—
951C2×C4—21no—
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—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—22no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—21no—
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×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#54712yes—
1030C2×C4#54712yes—
1031C2×C4C22×#4111yescharacteristic
1032C2×C4C22×#4111yescharacteristic
1033C2×C4C2×2−1+411yescharacteristic
1034C2×C4C2×2−1+411yescharacteristic
1035C2×C4#58511yescharacteristic
1036C2×C4#58511yescharacteristic
1037C8—22no—
1038C8—41no—
1039C8—41no—
1040C8—41no—
1041C8—41no—
1042C8—41no—
1043C8—41no—
1044C8#55214yes—
1045C22—41no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22C2×#54711yescharacteristic
1053C22D4×#4111yescharacteristic
1054C22#349711yescharacteristic
1055C22#358411yescharacteristic
1056C22#358411yescharacteristic
1057C22#358611yescharacteristic
1058C22#358611yescharacteristic
1059C4—22no—
1060C4—22no—
1061C4—41no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—41no—
1072C4—42no—
1073C4—42no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4C2×#55211yescharacteristic
1089C4#349311yescharacteristic
1090C4#351511yescharacteristic
1091C4#355511yescharacteristic
1092C2—81no—
1093C2#5925811yescharacteristic
1094C2#6127711yescharacteristic
1095C2#6128011yescharacteristic
1096C2#6153311yescharacteristic
1097C2#6153711yescharacteristic
1098C2#6238311yescharacteristic
1099C2#6239111yescharacteristic
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
7. #28839C2semidirect
8. #28278C2semidirect
9. #28006C2semidirect
10. #28002C2semidirect
15. #27373C2semidirect
16. #27368C2semidirect
17. #27366C2semidirect
18. #27361C2semidirect
19. #26114C2semidirect
20. #26113C2semidirect
23. #25000C2semidirect
24. #24995C2semidirect
25. #22818C2semidirect
26. #22815C2semidirect
27. #22730C2semidirect
28. #22679C2semidirect

Maximal subgroups

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

subgroupindex
#453042
#451232
#316312
#316282
#316272
#288392
#282782
#280062
#280022
#278482
#278362
#276432
#276382
#273732
#273682
#273662
#273612
#261142
#261132
#250432
#250332
#250002
#249952
#228182
#228152
#227302
#226792
#216052
#215302
#208222