Finite Group Databasebeta

← #6997173

Subgroups — #6997173

Order 512.

1462 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59154C211yesmaximal, characteristic
2#39624C211yesmaximal, characteristic
3#32583C211yesmaximal, characteristic, complemented
4#32578C211yesmaximal, characteristic, complemented
5#31548C211yesmaximal, characteristic, complemented
6#31536C211yesmaximal, characteristic, complemented
7#31536C211yesmaximal, characteristic, complemented
8#31521C211yesmaximal, characteristic, complemented
9#30969C211yesmaximal, characteristic, complemented
10#30968C211yesmaximal, characteristic, complemented
11#29159C211yesmaximal, characteristic
12#28776C211yesmaximal, characteristic
13#28771C211yesmaximal, characteristic
14#27832C211yesmaximal, characteristic, complemented
15#27824C211yesmaximal, characteristic, complemented
16#27024C211yesmaximal, characteristic, complemented
17#27013C211yesmaximal, characteristic, complemented
18#26497C211yesmaximal, characteristic, complemented
19#26489C211yesmaximal, characteristic, complemented
20#26414C211yesmaximal, characteristic
21#26412C211yesmaximal, characteristic
22#25957C211yesmaximal, characteristic
23#25955C211yesmaximal, characteristic
24#25819C211yesmaximal, characteristic
25#24348C211yesmaximal, characteristic, complemented
26#24332C211yesmaximal, characteristic, complemented
27C2×#2026C211yesmaximal, characteristic
28#23238C211yesmaximal, characteristic
29#22871C211yesmaximal, characteristic
30#22859C211yesmaximal, characteristic
31#22050C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#451C2211yescharacteristic
39C2×#441C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43#2857C2211yescharacteristic
44#2811—21no—
45#2806—21no—
46#2806—21no—
47#2806—21no—
48#2726—21no—
49#2713—21no—
50#2659—21no—
51#2584C2211yescharacteristic
52#2582C2211yescharacteristic
53#2582C2211yescharacteristic
54#2567C2211yescharacteristic
55#2567C2211yescharacteristic
56#2565C2211yescharacteristic
57#2552C2211yescharacteristic
58#2550C2211yescharacteristic
59#2549—21no—
60#2549—21no—
61#2506—21no—
62#2473—21no—
63#2473—21no—
64#2462—21no—
65#2453C2211yescharacteristic
66#2453C2211yescharacteristic
67#2451C2211yescharacteristic
68#2451C2211yescharacteristic
69#2451C2211yescharacteristic
70#2451C2211yescharacteristic
71#2442C2211yescharacteristic
72#2440—21no—
73#2440C2211yescharacteristic
74#2440C2211yescharacteristic
75#2440C2211yescharacteristic
76#2370C2211yescharacteristic
77#2360—21no—
78#2360C2211yescharacteristic
79#2360C2211yescharacteristic
80Q8×C22⋊C4C2211yescharacteristic
81Q8×C22⋊C4C2211yescharacteristic
82#2329—21no—
83C4×C22⋊Q8C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C2×#391C2211yescharacteristic
86#2100C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2097C2211yescharacteristic
90#2096C2211yescharacteristic
91#2096C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2085C2211yescharacteristic
95#2084C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2058C2211yescharacteristic
112#2058C2211yescharacteristic
113#2026C2211yescharacteristic
114#2026C2211yescharacteristic
115#2026C2211yescharacteristic
116#2026C2211yescharacteristic
117#2026C2211yescharacteristic
118#2026C2211yescharacteristic
119#2026C2211yescharacteristic
120#2026C2211yescharacteristic
121#2026C2211yescharacteristic
122#2024C2211yescharacteristic
123#2024C2211yescharacteristic
124#2024C2211yescharacteristic
125#2024C2211yescharacteristic
126#1993C2211yescharacteristic
127#1992C2211yescharacteristic
128#1992C2211yescharacteristic
129#1992C2211yescharacteristic
130#1990C2211yescharacteristic
131#1990C2211yescharacteristic
132#1988C2211yescharacteristic
133#1987C2211yescharacteristic
134#1985C2211yescharacteristic
135#1984C2211yescharacteristic
136#1971C2211yescharacteristic
137#1971C2211yescharacteristic
138#1971C2211yescharacteristic
139#1969C2211yescharacteristic
140#1944C2211yescharacteristic
141#1943C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1933C2211yescharacteristic
148#1928C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1921C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1917C2211yescharacteristic
157#1917C2211yescharacteristic
158#1917C2211yescharacteristic
159#1916C2211yescharacteristic
160#1892C2211yescharacteristic
161#1892C2211yescharacteristic
162#1878C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1872C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic
186#1807C2211yescharacteristic
187#1807C2211yescharacteristic
188#1805C2211yescharacteristic
189#1803C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1787C2211yescharacteristic
193#1771C2211yescharacteristic
194#1770C2211yescharacteristic
195#1763C2211yescharacteristic
196C4×#103C2211yescharacteristic
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1749C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#557—42no—
209#557—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#125—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125—42no—
220C2×#125—42no—
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8D411yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C4×Q8—21no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C22×C4⋊C4—21no—
242C22×C4⋊C4—21no—
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C42C2311yescharacteristic
247#501—42no—
248#501—42no—
249#479—42no—
250#475—42no—
251#451Q818yescomplemented
252#441—42no—
253C4×Q16—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×#103—42no—
273C2×#103—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#400—21no—
303#400—21no—
304#400—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#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#395—21no—
337#395—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391D411yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389D411yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387D411yescharacteristic
408#387D411yescharacteristic
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385D411yescharacteristic
417#385D411yescharacteristic
418#384—21no—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#382C2311yescharacteristic
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380D411yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447C2×#95—21no—
448C2×#95—21no—
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#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8C2×D411yescharacteristic
502C22×Q8C2×Q814yes—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16—41no—
516C2×Q16—41no—
517C2×Q16C2×Q814yes—
518C2×Q16C2×Q814yes—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C4⋊Q8—22no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—44no—
542#125—22no—
543#125—22no—
544#125—22no—
545#125—22no—
546#125—22no—
547#125—41no—
548#125—41no—
549#125—41no—
550#125—41no—
551#125—41no—
552#125—44no—
553#125—44no—
554#125—44no—
555#125—44no—
556C22⋊Q8—22no—
557C22⋊Q8—24no—
558C22⋊Q8—44no—
559C22⋊Q8—82no—
560C22⋊Q8—82no—
561C22⋊Q8—82no—
562C22⋊Q8C2×Q814yes—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×Q8—44no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
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⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—44no—
633C2×C4⋊C4—44no—
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—41no—
675C2×C42—41no—
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684#107—22no—
685#107—22no—
686#107—41no—
687#107—41no—
688#106—22no—
689#106—22no—
690#106—41no—
691#106—41no—
692#106—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698C4⋊C8—41no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702#103—22no—
703#103—22no—
704#103—22no—
705#103—22no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103C2×Q814yes—
721#103C2×Q814yes—
722C22⋊C8—22no—
723C22⋊C8C2×Q814yes—
724#97—41no—
725#97—41no—
726#97—41no—
727#97—41no—
728C4×C8—41no—
729C4×C8—41no—
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#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783C24C22×D411yescharacteristic
784C2×Q8—24no—
785C2×Q8—22no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—41no—
802C2×Q8—41no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—44no—
806C2×Q8—44no—
807C2×Q8—42no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×Q8—81no—
816C2×Q8—81no—
817C2×Q8—81no—
818C2×Q8—81no—
819C2×Q8—82no—
820C2×Q8—82no—
821C2×Q8C22×Q812yes—
822C2×Q8C22×Q812yes—
823C2×Q8C22×Q812yes—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—24no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×Q812yes—
876C22×C42−1+412yes—
877C22×C4C2511yescharacteristic
878Q16—44no—
879Q16—44no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—82no—
903C2×C8—82no—
904C2×C8C22×Q812yes—
905C2×C8C22×Q812yes—
906C4⋊C4—24no—
907C4⋊C4—24no—
908C4⋊C4—24no—
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4C22×Q812yes—
985C4⋊C4H(5,𝔽2)12yes—
986C4⋊C4H(5,𝔽2)12yes—
987C22⋊C4—24no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4#13714yes—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—41no—
1008C42—41no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C42—81no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23D4×Q812yes—
1024C23C2×#13712yes—
1025C23#57712yes—
1026C23C23×D411yescharacteristic
1027Q8—22no—
1028Q8—22no—
1029Q8—22no—
1030Q8—22no—
1031Q8—22no—
1032Q8—22no—
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—41no—
1037Q8—41no—
1038Q8—41no—
1039Q8—82no—
1040Q8—84no—
1041Q8—84no—
1042Q8—162no—
1043Q8—162no—
1044Q8—162no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—82no—
1134C2×C4—82no—
1135C2×C4—84no—
1136C2×C4—84no—
1137C2×C4—84no—
1138C2×C4—162no—
1139C2×C4D4×Q812yes—
1140C2×C4C2×#13712yes—
1141C2×C4C2×#13712yes—
1142C2×C4C23×Q811yescharacteristic
1143C2×C4C2×H(5,𝔽2)11yescharacteristic
1144C2×C4C2×H(5,𝔽2)11yescharacteristic
1145C2×C4C2×2−1+411yescharacteristic
1146C2×C4#58511yescharacteristic
1147C2×C4#58511yescharacteristic
1148C8—22no—
1149C8—22no—
1150C8—41no—
1151C8—41no—
1152C8—41no—
1153C8—41no—
1154C8—41no—
1155C8—41no—
1156C22—22no—
1157C22—22no—
1158C22—22no—
1159C22—22no—
1160C22—22no—
1161C22—22no—
1162C22#338714yes—
1163C22C2×D4×Q811yescharacteristic
1164C22#348411yescharacteristic
1165C22#350011yescharacteristic
1166C22C22×#13711yescharacteristic
1167C22C2×#57711yescharacteristic
1168C22#358411yescharacteristic
1169C22#358611yescharacteristic
1170C4—22no—
1171C4—22no—
1172C4—22no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—42no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4#350111yescharacteristic
1200C4#350111yescharacteristic
1201C4#356111yescharacteristic
1202C4#356111yescharacteristic
1203C2—24no—
1204C2#4300311yescharacteristic
1205C2C2×#338711yescharacteristic
1206C2#6138611yescharacteristic
1207C2#6160711yescharacteristic
1208C2#6162011yescharacteristic
1209C2#6255611yescharacteristic
1210C2#6257711yescharacteristic
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
3. #32583C2semidirect
4. #32578C2semidirect
5. #31548C2semidirect
6. #31536C2semidirect
7. #31536C2semidirect
8. #31521C2semidirect
9. #30969C2semidirect
10. #30968C2semidirect
14. #27832C2semidirect
15. #27824C2semidirect
16. #27024C2semidirect
17. #27013C2semidirect
18. #26497C2semidirect
19. #26489C2semidirect
25. #24348C2semidirect
26. #24332C2semidirect
251. #451Q8semidirect

Maximal subgroups

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

subgroupindex
#591542
#396242
#325832
#325782
#315482
#315362
#315212
#309692
#309682
#291592
#287762
#287712
#278322
#278242
#270242
#270132
#264972
#264892
#264142
#264122
#259572
#259552
#258192
#243482
#243322
C2×#20262
#232382
#228712
#228592
#220502