Finite Group Databasebeta

← #6697533

Subgroups — #6697533

Order 512.

1330 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40191C211yesmaximal, characteristic
2#36447C211yesmaximal, characteristic, complemented
3#33081C211yesmaximal, characteristic
4#32504C211yesmaximal, characteristic, complemented
5#32380C211yesmaximal, characteristic, complemented
6#32342C211yesmaximal, characteristic
7#32108C211yesmaximal, characteristic
8#31984C211yesmaximal, characteristic, complemented
9#31592C211yesmaximal, characteristic
10#31585C211yesmaximal, characteristic
11#31485C211yesmaximal, characteristic, complemented
12#30376C211yesmaximal, characteristic
13#30079C211yesmaximal, characteristic, complemented
14#29010C211yesmaximal, characteristic
15#28961C211yesmaximal, characteristic, complemented
16#27569C211yesmaximal, characteristic, complemented
17#27322C211yesmaximal, characteristic, complemented
18#27295C211yesmaximal, characteristic, complemented
19#26764C211yesmaximal, characteristic
20#26381C211yesmaximal, characteristic, complemented
21#26381C211yesmaximal, characteristic, complemented
22#26177C211yesmaximal, characteristic
23#26169C211yesmaximal, characteristic
24#26169C211yesmaximal, characteristic
25#26167C211yesmaximal, characteristic, complemented
26#24827C211yesmaximal, characteristic
27#24736C211yesmaximal, characteristic
28#23009C211yesmaximal, characteristic
29C4⋊C4×Q16C211yesmaximal, characteristic, complemented
30#22377C211yesmaximal, characteristic, complemented
31C4×#462C211yesmaximal, characteristic, complemented
32C2×#477C2211yescharacteristic
33C2×#464C2211yescharacteristic
34C2×#464C2211yescharacteristic
35C2×#462C2211yescharacteristic
36C2×#440C2211yescharacteristic
37C2×C4×Q16C2211yescharacteristic
38C2×C4×Q16C2211yescharacteristic
39C2×C4×Q16C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic
41#2860C2211yescharacteristic
42#2859—21no—
43#2859C2211yescharacteristic
44#2773—21no—
45#2721—21no—
46#2720—21no—
47#2689—21no—
48#2654—21no—
49#2596—21no—
50#2571—21no—
51#2571C2211yescharacteristic
52#2556—21no—
53#2552—21no—
54#2552C2211yescharacteristic
55#2545C2211yescharacteristic
56#2542C2211yescharacteristic
57#2511C2211yescharacteristic
58#2508—21no—
59#2508—21no—
60#2508C2211yescharacteristic
61#2508C2211yescharacteristic
62#2506—21no—
63#2506—21no—
64#2506C2211yescharacteristic
65#2506C2211yescharacteristic
66#2506C2211yescharacteristic
67#2451C2211yescharacteristic
68#2451C2211yescharacteristic
69#2448C2211yescharacteristic
70#2448C2211yescharacteristic
71#2447C2211yescharacteristic
72#2446C2211yescharacteristic
73#2367C2211yescharacteristic
74#2351C2211yescharacteristic
75#2351C2211yescharacteristic
76Q8×C4⋊C4C2211yescharacteristic
77Q8×C4⋊C4C2211yescharacteristic
78Q8×C4⋊C4C2211yescharacteristic
79Q8×C4⋊C4C2211yescharacteristic
80Q8×C4⋊C4C2211yescharacteristic
81#2332—21no—
82C4×C4⋊Q8C2211yescharacteristic
83C4×#125—21no—
84C4×#125C2211yescharacteristic
85C42×Q8C2211yescharacteristic
86#2101C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2097C2211yescharacteristic
90#2095C2211yescharacteristic
91#2095C2211yescharacteristic
92#2095C2211yescharacteristic
93#2093C2211yescharacteristic
94#2093C2211yescharacteristic
95#2086C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2086C2211yescharacteristic
99#2086C2211yescharacteristic
100#2085C2211yescharacteristic
101#2083C2211yescharacteristic
102#2083C2211yescharacteristic
103#2083C2211yescharacteristic
104#2083C2211yescharacteristic
105#2083C2211yescharacteristic
106#2074C2211yescharacteristic
107#2072C2211yescharacteristic
108#2072C2211yescharacteristic
109#2072C2211yescharacteristic
110#2071C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic
118#2057C2211yescharacteristic
119#2057C2211yescharacteristic
120#2043C2211yescharacteristic
121#2043C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic
126#1993C2211yescharacteristic
127#1981C2211yescharacteristic
128#1959C2211yescharacteristic
129#1958C2211yescharacteristic
130#1947C2211yescharacteristic
131#1947C2211yescharacteristic
132#1943C2211yescharacteristic
133#1942C2211yescharacteristic
134#1942C2211yescharacteristic
135#1942C2211yescharacteristic
136#1942C2211yescharacteristic
137#1940C2211yescharacteristic
138#1939C2211yescharacteristic
139#1935C2211yescharacteristic
140#1935C2211yescharacteristic
141#1935C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1933C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1926C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1921C2211yescharacteristic
152#1921C2211yescharacteristic
153#1920C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1917C2211yescharacteristic
157#1917C2211yescharacteristic
158#1917C2211yescharacteristic
159#1916C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1862C2211yescharacteristic
189#1862C2211yescharacteristic
190#1845C2211yescharacteristic
191#1839C2211yescharacteristic
192#1805C2211yescharacteristic
193#1804C2211yescharacteristic
194#1803C2211yescharacteristic
195#1803C2211yescharacteristic
196#1803C2211yescharacteristic
197#1771C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199C4×C4⋊C8C2211yescharacteristic
200#1763C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#125—21no—
214C2×#125D411yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231#477—42no—
232#464—24no—
233#464—42no—
234#462—24no—
235#440—42no—
236C4×Q16—24no—
237C4×Q16—42no—
238C4×Q16—42no—
239C4×Q16—42no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#399—21no—
302#399—21no—
303#399—21no—
304#399—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#396—21no—
321#395—21no—
322#395—21no—
323#391—21no—
324#391—21no—
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389D411yescharacteristic
356#389D411yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387D411yescharacteristic
398#387D411yescharacteristic
399#387D411yescharacteristic
400#387D411yescharacteristic
401#385—21no—
402#385—21no—
403#384—21no—
404#384—21no—
405#384—21no—
406#384—21no—
407#384—21no—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#382—21no—
415#382—21no—
416#382—21no—
417#382—21no—
418#382—21no—
419#382—21no—
420#382D411yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#381—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C43—21no—
448C43C2311yescharacteristic
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
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×D4C2411yescharacteristic
492C23×C4—21no—
493C2×Q16—22no—
494C2×Q16—22no—
495C2×Q16—22no—
496C2×Q16—22no—
497C2×Q16—22no—
498C2×Q16#4114yes—
499C2×SD16—22no—
500C2×SD16—22no—
501C2×SD16—22no—
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C4⋊Q8—22no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514#126—82no—
515#125—42no—
516#125—44no—
517#125—82no—
518#125—82no—
519#125—82no—
520#125—82no—
521#124—22no—
522#124—41no—
523#124—41no—
524#124—41no—
525C22⋊Q8—44no—
526C22⋊Q8—82no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×D4—41no—
550C4×D4—41no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658#107—22no—
659#107—22no—
660#107—41no—
661#107—41no—
662#107—41no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#106—41no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—41no—
674C4⋊C8—41no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#102—22no—
697#102—22no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#97—41no—
704#97—41no—
705C4×C8—22no—
706C4×C8—41no—
707C4×C8—41no—
708C4×C8—41no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759C24—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—42no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×Q8C2×#4112yes—
778C2×Q8C2×#4112yes—
779C2×Q8H(5,𝔽2)12yes—
780C2×Q82−1+412yes—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—42no—
803C22×C4—81no—
804C22×C4—81no—
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C2511yescharacteristic
820Q16—28no—
821Q16—44no—
822SD16—44no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8C2×#4112yes—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—41no—
881C4⋊C4—41no—
882C4⋊C4—41no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C42−1+412yes—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C42—24no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—41no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—42no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C23×D411yescharacteristic
981Q8—22no—
982Q8—22no—
983Q8—22no—
984Q8—22no—
985Q8—22no—
986Q8—41no—
987Q8—41no—
988Q8—41no—
989Q8—41no—
990Q8—41no—
991Q8—41no—
992Q8—162no—
993Q8#53914yes—
994D4—41no—
995D4—41no—
996D4—41no—
997D4—41no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—162no—
1082C2×C4#57512yes—
1083C2×C4#57612yes—
1084C2×C4#57812yes—
1085C2×C4#57812yes—
1086C2×C4C22×#4111yescharacteristic
1087C2×C4C2×H(5,𝔽2)11yescharacteristic
1088C2×C4C2×2−1+411yescharacteristic
1089C2×C4C2×2−1+411yescharacteristic
1090C2×C4#58511yescharacteristic
1091C2×C4#58511yescharacteristic
1092C8—22no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22D4×#4111yescharacteristic
1108C22#348611yescharacteristic
1109C22#348811yescharacteristic
1110C22C2×#57511yescharacteristic
1111C22C2×#57611yescharacteristic
1112C22C2×#57811yescharacteristic
1113C22C2×#57811yescharacteristic
1114C4—22no—
1115C4—22no—
1116C4—24no—
1117C4—22no—
1118C4—22no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—42no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—42no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4C2×#53911yescharacteristic
1144C4#351511yescharacteristic
1145C4#355311yescharacteristic
1146C4#355911yescharacteristic
1147C2—161no—
1148C2#3771711yescharacteristic
1149C2#6144611yescharacteristic
1150C2#6148511yescharacteristic
1151C2#6184211yescharacteristic
1152C2#6187011yescharacteristic
1153C2#6198811yescharacteristic
1154C2#6205611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36447C2semidirect
4. #32504C2semidirect
5. #32380C2semidirect
8. #31984C2semidirect
11. #31485C2semidirect
13. #30079C2semidirect
15. #28961C2semidirect
16. #27569C2semidirect
17. #27322C2semidirect
18. #27295C2semidirect
20. #26381C2semidirect
21. #26381C2semidirect
25. #26167C2semidirect
29. C4⋊C4×Q16C2semidirect
30. #22377C2semidirect
31. C4×#462C2semidirect

Maximal subgroups

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

subgroupindex
#401912
#364472
#330812
#325042
#323802
#323422
#321082
#319842
#315922
#315852
#314852
#303762
#300792
#290102
#289612
#275692
#273222
#272952
#267642
#263812
#261772
#261692
#261672
#248272
#247362
#230092
C4⋊C4×Q162
#223772
C4×#4622