Finite Group Databasebeta

← #6854224

Subgroups — #6854224

Order 512.

1399 conjugacy classes of subgroups.

The subgroup lattice has 1185 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39591C211yesmaximal, characteristic
2#39591C211yesmaximal, characteristic
3#33219C211yesmaximal, characteristic
4#32692C211yesmaximal, characteristic, complemented
5#32689C211yesmaximal, characteristic, complemented
6#32664C211yesmaximal, characteristic, complemented
7#32660C211yesmaximal, characteristic, complemented
8#32575C211yesmaximal, characteristic, complemented
9#32574C211yesmaximal, characteristic, complemented
10#32571C211yesmaximal, characteristic, complemented
11#32567C211yesmaximal, characteristic, complemented
12#30299C211yesmaximal, characteristic
13#30297C211yesmaximal, characteristic
14#29173C211yesmaximal, characteristic
15#29170C211yesmaximal, characteristic
16#29158C211yesmaximal, characteristic
17#29158C211yesmaximal, characteristic
18#26286C211yesmaximal, characteristic, complemented
19#26279C211yesmaximal, characteristic, complemented
20#25848C211yesmaximal, characteristic, complemented
21#25846C211yesmaximal, characteristic, complemented
22#25075C211yesmaximal, characteristic, complemented
23#25071C211yesmaximal, characteristic, complemented
24#24853C211yesmaximal, characteristic
25#24850C211yesmaximal, characteristic
26#24336C211yesmaximal, characteristic, complemented
27#24332C211yesmaximal, characteristic, complemented
28#22203C211yesmaximal, characteristic
29#22189C211yesmaximal, characteristic
30#21537C211yesmaximal, characteristic
31#21304C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#470C2211yescharacteristic
39C2×C4×Q16C2211yescharacteristic
40C2×#424C2211yescharacteristic
41C2×#405C2211yescharacteristic
42#2851C2211yescharacteristic
43#2851C2211yescharacteristic
44#2734—21no—
45#2734—21no—
46#2729—21no—
47#2729—21no—
48#2720—21no—
49#2720—21no—
50#2713—21no—
51#2713—21no—
52#2629C2211yescharacteristic
53#2629C2211yescharacteristic
54#2628C2211yescharacteristic
55#2628C2211yescharacteristic
56#2584C2211yescharacteristic
57#2584C2211yescharacteristic
58#2584C2211yescharacteristic
59#2584C2211yescharacteristic
60#2582C2211yescharacteristic
61#2582C2211yescharacteristic
62#2581C2211yescharacteristic
63#2581C2211yescharacteristic
64#2581C2211yescharacteristic
65#2581C2211yescharacteristic
66#2567C2211yescharacteristic
67#2567C2211yescharacteristic
68#2556—21no—
69#2556—21no—
70#2506—21no—
71#2506—21no—
72#2465—21no—
73#2465—21no—
74#2462—21no—
75#2462—21no—
76#2355C2211yescharacteristic
77#2355C2211yescharacteristic
78#2323C2211yescharacteristic
79#2323C2211yescharacteristic
80#2323C2211yescharacteristic
81#2323C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×C22⋊Q8C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2099C2211yescharacteristic
88#2097C2211yescharacteristic
89#2097C2211yescharacteristic
90#2097C2211yescharacteristic
91#2095C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2086C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2084C2211yescharacteristic
103#2083C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2066C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2057C2211yescharacteristic
120#2026C2211yescharacteristic
121#2026C2211yescharacteristic
122#2026C2211yescharacteristic
123#2024C2211yescharacteristic
124#1991C2211yescharacteristic
125#1990C2211yescharacteristic
126#1989C2211yescharacteristic
127#1987C2211yescharacteristic
128#1985C2211yescharacteristic
129#1985C2211yescharacteristic
130#1985C2211yescharacteristic
131#1985C2211yescharacteristic
132#1984C2211yescharacteristic
133#1984C2211yescharacteristic
134#1984C2211yescharacteristic
135#1984C2211yescharacteristic
136#1971C2211yescharacteristic
137#1949C2211yescharacteristic
138#1947C2211yescharacteristic
139#1944C2211yescharacteristic
140#1944C2211yescharacteristic
141#1943C2211yescharacteristic
142#1942C2211yescharacteristic
143#1941C2211yescharacteristic
144#1933C2211yescharacteristic
145#1933C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1927C2211yescharacteristic
149#1927C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1894C2211yescharacteristic
163#1894C2211yescharacteristic
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1847C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1808C2211yescharacteristic
191#1808C2211yescharacteristic
192#1807C2211yescharacteristic
193#1807C2211yescharacteristic
194#1805C2211yescharacteristic
195#1803C2211yescharacteristic
196C4×#106C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1729C2211yescharacteristic
200#1729C2211yescharacteristic
201#1728C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#557—42no—
209#557—42no—
210#557—42no—
211#557—42no—
212#533—42no—
213#533—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8D411yescharacteristic
217C2×C4⋊Q8D411yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#125—21no—
221C2×#125—21no—
222C2×#125—21no—
223C2×#125—21no—
224C2×#125D411yescharacteristic
225C2×#125D411yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×C22⋊Q8D411yescharacteristic
231C2×C22⋊Q8D411yescharacteristic
232C2×C22⋊Q8D411yescharacteristic
233C2×C22⋊Q8D411yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C4×Q8—21no—
237C2×C4×Q8—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C42C2311yescharacteristic
251#501—42no—
252#479—42no—
253#475—42no—
254#470Q818yescomplemented
255C4×Q16—42no—
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275#424—42no—
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
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
294#405—42no—
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#399—21no—
306#399—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#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#395—21no—
324#395—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#393—21no—
338#393—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#387—21no—
392#387—21no—
393#387—21no—
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#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#384—21no—
420#384—21no—
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
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#340C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
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×Q8C2×D411yescharacteristic
494C22×Q8C2×D411yescharacteristic
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C23×C4C2×D411yescharacteristic
500C23×C4C2×D411yescharacteristic
501C23×C4C2411yescharacteristic
502C2×Q16—41no—
503C2×Q16—41no—
504C2×Q16C2×Q814yes—
505C2×M16—22no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16—41no—
509C2×M16—41no—
510C2×M16C2×Q814yes—
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8—41no—
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—42no—
530C4⋊Q8—42no—
531C4⋊Q8—44no—
532C4⋊Q8—44no—
533#125—22no—
534#125—22no—
535#125—41no—
536#125—41no—
537#125—41no—
538#125—41no—
539#125—41no—
540#125—41no—
541#125—42no—
542#125—42no—
543#125—44no—
544#125—44no—
545#125—44no—
546#125—44no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—42no—
550C22⋊Q8—42no—
551C22⋊Q8—42no—
552C22⋊Q8—42no—
553C22⋊Q8C2×Q814yes—
554C22⋊Q8C2×Q814yes—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—41no—
564C4×Q8—41no—
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—44no—
576C4×Q8—44no—
577#117—22no—
578#117—22no—
579#117—41no—
580#117—41no—
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⋊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⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C42—21no—
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—21no—
675C2×C42—41no—
676C2×C42—41no—
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#107—22no—
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#107—41no—
694#106—22no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106C2×Q814yes—
704C4⋊C8—22no—
705C4⋊C8—22no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708#103—22no—
709#103—22no—
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—
722#97—22no—
723#97—41no—
724C4×C8—22no—
725C4×C8—41no—
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#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#95—21no—
774#95—21no—
775#95—21no—
776C24C22×D411yescharacteristic
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—41no—
790C2×Q8—41no—
791C2×Q8—41no—
792C2×Q8—41no—
793C2×Q8—41no—
794C2×Q8—41no—
795C2×Q8—41no—
796C2×Q8—41no—
797C2×Q8—41no—
798C2×Q8—41no—
799C2×Q8—42no—
800C2×Q8—42no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×Q8—81no—
804C2×Q8—81no—
805C2×Q8C22×Q812yes—
806C2×Q8C22×Q812yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×Q812yes—
847C22×C42−1+412yes—
848C22×C4C2511yescharacteristic
849Q16—44no—
850M16—44no—
851M16—82no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—44no—
874C2×C8—82no—
875C2×C8C22×Q812yes—
876C2×C8C22×Q812yes—
877C2×C82−1+412yes—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4C22×Q812yes—
961C4⋊C4C22×Q812yes—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—41no—
985C42—41no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—42no—
990C42—42no—
991C42—42no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42H(5,𝔽2)12yes—
999C42H(5,𝔽2)12yes—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23D4×Q812yes—
1007C23C23×D411yescharacteristic
1008Q8—22no—
1009Q8—22no—
1010Q8—22no—
1011Q8—22no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—82no—
1017Q8—82no—
1018Q8—84no—
1019Q8—82no—
1020Q8—82no—
1021Q8—84no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
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—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
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—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
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—82no—
1111C2×C4—82no—
1112C2×C4#53412yes—
1113C2×C4#53412yes—
1114C2×C4D4×Q812yes—
1115C2×C4C23×Q811yescharacteristic
1116C2×C4C2×H(5,𝔽2)11yescharacteristic
1117C2×C4C2×H(5,𝔽2)11yescharacteristic
1118C2×C4C2×2−1+411yescharacteristic
1119C2×C4C2×2−1+411yescharacteristic
1120C2×C4#58511yescharacteristic
1121C8—22no—
1122C8—22no—
1123C8—22no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22C2×#53411yescharacteristic
1137C22C2×D4×Q811yescharacteristic
1138C22#349711yescharacteristic
1139C22#358411yescharacteristic
1140C22#358411yescharacteristic
1141C22#358611yescharacteristic
1142C22#358611yescharacteristic
1143C4—22no—
1144C4—22no—
1145C4—22no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4#350111yescharacteristic
1173C4#350311yescharacteristic
1174C4#353811yescharacteristic
1175C4#356111yescharacteristic
1176C2—42no—
1177C2#3961511yescharacteristic
1178C2#6076111yescharacteristic
1179C2#6076611yescharacteristic
1180C2#6138611yescharacteristic
1181C2#6138611yescharacteristic
1182C2#6238311yescharacteristic
1183C2#6239111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #32692C2semidirect
5. #32689C2semidirect
6. #32664C2semidirect
7. #32660C2semidirect
8. #32575C2semidirect
9. #32574C2semidirect
10. #32571C2semidirect
11. #32567C2semidirect
18. #26286C2semidirect
19. #26279C2semidirect
20. #25848C2semidirect
21. #25846C2semidirect
22. #25075C2semidirect
23. #25071C2semidirect
26. #24336C2semidirect
27. #24332C2semidirect
254. #470Q8semidirect

Maximal subgroups

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

subgroupindex
#395912
#332192
#326922
#326892
#326642
#326602
#325752
#325742
#325712
#325672
#302992
#302972
#291732
#291702
#291582
#262862
#262792
#258482
#258462
#250752
#250712
#248532
#248502
#243362
#243322
#222032
#221892
#215372
#213042