Finite Group Databasebeta

← #7563686

Subgroups — #7563686

Order 512.

1670 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
1C2×#3390C211yesmaximal, characteristic
2C2×#3387C211yesmaximal, characteristic
3#45389C211yesmaximal, characteristic
4#35957C211yesmaximal, characteristic
5#30977C211yesmaximal, characteristic
6#30968C211yesmaximal, characteristic
7#30964C211yesmaximal, characteristic
8#30952C211yesmaximal, characteristic
9#28822C211yesmaximal, characteristic
10#28818C211yesmaximal, characteristic
11#28696C211yesmaximal, characteristic
12#28526C211yesmaximal, characteristic
13#26474C211yesmaximal, characteristic
14#26461C211yesmaximal, characteristic
15#26395C211yesmaximal, characteristic
16#26391C211yesmaximal, characteristic
17#26389C211yesmaximal, characteristic
18#26369C211yesmaximal, characteristic
19#26054C211yesmaximal, characteristic
20#26048C211yesmaximal, characteristic
21#25847C211yesmaximal, characteristic
22#25836C211yesmaximal, characteristic
23#25487C211yesmaximal, characteristic
24#25476C211yesmaximal, characteristic
25#24344C211yesmaximal, characteristic
26#24336C211yesmaximal, characteristic
27#23155C211yesmaximal, characteristic
28#23014C211yesmaximal, characteristic
29#23004C211yesmaximal, characteristic
30#21625C211yesmaximal, characteristic
31#21516C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36#3390—28no—
37#3387—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#501C2211yescharacteristic
41C2×#501C2211yescharacteristic
42C2×#499C2211yescharacteristic
43C2×#498C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#479C2211yescharacteristic
48C2×#479C2211yescharacteristic
49C2×#479C2211yescharacteristic
50C2×#479C2211yescharacteristic
51C2×#477C2211yescharacteristic
52C2×#477C2211yescharacteristic
53C2×#477C2211yescharacteristic
54C2×#475C2211yescharacteristic
55C2×#475C2211yescharacteristic
56C2×#475C2211yescharacteristic
57C2×#462C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×#446C2211yescharacteristic
60C2×#441C2211yescharacteristic
61C2×#441C2211yescharacteristic
62C2×#441C2211yescharacteristic
63C2×#441C2211yescharacteristic
64C2×C4×Q16C2211yescharacteristic
65C2×C4×Q16C2211yescharacteristic
66#2734—21no—
67#2734—21no—
68#2713—21no—
69#2713—21no—
70#2660—21no—
71#2660C2211yescharacteristic
72#2584—21no—
73#2584C2211yescharacteristic
74#2581C2211yescharacteristic
75#2581C2211yescharacteristic
76#2567—21no—
77#2567C2211yescharacteristic
78#2552—21no—
79#2552—21no—
80#2552C2211yescharacteristic
81#2552C2211yescharacteristic
82#2550—21no—
83#2550—21no—
84#2550C2211yescharacteristic
85#2550C2211yescharacteristic
86#2550C2211yescharacteristic
87#2550C2211yescharacteristic
88#2462—21no—
89#2462—21no—
90#2453C2211yescharacteristic
91#2453C2211yescharacteristic
92#2451C2211yescharacteristic
93#2451C2211yescharacteristic
94#2446—21no—
95#2446—21no—
96#2399—21no—
97#2399C2211yescharacteristic
98#2365C2211yescharacteristic
99#2365C2211yescharacteristic
100#2351C2211yescharacteristic
101#2351C2211yescharacteristic
102Q8×C4⋊C4C2211yescharacteristic
103Q8×C4⋊C4C2211yescharacteristic
104#2331C2211yescharacteristic
105#2327C2211yescharacteristic
106#2276C2211yescharacteristic
107#2097C2211yescharacteristic
108#2097C2211yescharacteristic
109#2096C2211yescharacteristic
110#2095C2211yescharacteristic
111#2088C2211yescharacteristic
112#2088C2211yescharacteristic
113#2088C2211yescharacteristic
114#2087C2211yescharacteristic
115#2085C2211yescharacteristic
116#2085C2211yescharacteristic
117#2084C2211yescharacteristic
118#2084C2211yescharacteristic
119#2068C2211yescharacteristic
120#2068C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2059C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2059C2211yescharacteristic
129#2059C2211yescharacteristic
130#2058C2211yescharacteristic
131#2058C2211yescharacteristic
132#2057C2211yescharacteristic
133#2057C2211yescharacteristic
134#2057C2211yescharacteristic
135#2026C2211yescharacteristic
136#2026C2211yescharacteristic
137#2026C2211yescharacteristic
138#2024C2211yescharacteristic
139#1993C2211yescharacteristic
140#1991C2211yescharacteristic
141#1988C2211yescharacteristic
142#1985C2211yescharacteristic
143#1984C2211yescharacteristic
144#1981C2211yescharacteristic
145#1960C2211yescharacteristic
146#1956C2211yescharacteristic
147#1949C2211yescharacteristic
148#1949C2211yescharacteristic
149#1949C2211yescharacteristic
150#1949C2211yescharacteristic
151#1948C2211yescharacteristic
152#1948C2211yescharacteristic
153#1944C2211yescharacteristic
154#1943C2211yescharacteristic
155#1943C2211yescharacteristic
156#1941C2211yescharacteristic
157#1940C2211yescharacteristic
158#1939C2211yescharacteristic
159#1935C2211yescharacteristic
160#1935C2211yescharacteristic
161#1935C2211yescharacteristic
162#1933C2211yescharacteristic
163#1928C2211yescharacteristic
164#1927C2211yescharacteristic
165#1921C2211yescharacteristic
166#1918C2211yescharacteristic
167#1917C2211yescharacteristic
168#1917C2211yescharacteristic
169#1917C2211yescharacteristic
170#1916C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1863C2211yescharacteristic
190#1863C2211yescharacteristic
191#1847C2211yescharacteristic
192#1846C2211yescharacteristic
193#1805C2211yescharacteristic
194#1805C2211yescharacteristic
195#1776C2211yescharacteristic
196C4×#107C2211yescharacteristic
197#1771C2211yescharacteristic
198#1770C2211yescharacteristic
199#1768C2211yescharacteristic
200#1768C2211yescharacteristic
201#1763C2211yescharacteristic
202#1763C2211yescharacteristic
203C4×#103C2211yescharacteristic
204C4×#103C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207Q82—24no—
208Q82—42no—
209#557—24no—
210#557—24no—
211#557—24no—
212#557—42no—
213#557—42no—
214#557—42no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#125—21no—
228C2×#125—21no—
229C2×#125—21no—
230C2×#125—21no—
231C2×#125—21no—
232C2×#125—21no—
233C2×#125C2311yescharacteristic
234C2×#125C2311yescharacteristic
235C2×#125C2311yescharacteristic
236C2×#125C2311yescharacteristic
237C2×#125C2311yescharacteristic
238C2×#125C2311yescharacteristic
239C2×C4×Q8—21no—
240C2×C4×Q8—21no—
241C2×C4×Q8—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258#501—24no—
259#501—24no—
260#501—24no—
261#501—24no—
262#499—24no—
263#498—24no—
264#479—24no—
265#479—24no—
266#479—24no—
267#479—24no—
268#479—24no—
269#479—24no—
270#479—42no—
271#477—24no—
272#477—42no—
273#477D418yes—
274#475—24no—
275#475—24no—
276#475—24no—
277#462Q818yescomplemented
278#446—24no—
279#446—24no—
280#441—24no—
281#441—24no—
282#441—24no—
283#441—24no—
284C4×Q16—24no—
285C4×Q16—24no—
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×#97C2311yescharacteristic
340C2×#97C2311yescharacteristic
341C2×C4×C8C2311yescharacteristic
342C2×C4×C8C2311yescharacteristic
343C2×C4×C8C2311yescharacteristic
344#400—21no—
345#400—21no—
346#400—21no—
347#400—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#398—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398D411yescharacteristic
364#398D411yescharacteristic
365#398D411yescharacteristic
366#398D411yescharacteristic
367#395—21no—
368#395—21no—
369#395—21no—
370#395—21no—
371#395—21no—
372#395—21no—
373#395—21no—
374#395—21no—
375#395—21no—
376#395—21no—
377#395—21no—
378#395—21no—
379#395—21no—
380#395D411yescharacteristic
381#395D411yescharacteristic
382#395D411yescharacteristic
383#395D411yescharacteristic
384#391—21no—
385#391—21no—
386#391—21no—
387#391—21no—
388#391—21no—
389#391—21no—
390#391—21no—
391#391—21no—
392#391—21no—
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#384—21no—
452#384—21no—
453#384—21no—
454#384—21no—
455#384—21no—
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#382—21no—
459#382—21no—
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#382C2311yescharacteristic
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4—21no—
468C4×C4⋊C4—21no—
469C4×C4⋊C4—21no—
470C4×C4⋊C4—21no—
471C4×C4⋊C4—21no—
472C4×C4⋊C4—21no—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482#376—21no—
483#376C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8C2×D411yescharacteristic
522C22×Q8C2×D411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C2×Q16—22no—
527C2×Q16—22no—
528C2×Q16—22no—
529C2×Q16—22no—
530C2×Q16C2×Q814yes—
531C2×Q16C2×Q814yes—
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C4⋊Q8—22no—
541C4⋊Q8—22no—
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—22no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552C4⋊Q8—44no—
553C4⋊Q8—44no—
554C4⋊Q8—44no—
555C4⋊Q8—44no—
556C4⋊Q8C2×D414yes—
557C4⋊Q8C2×Q814yes—
558#125—22no—
559#125—22no—
560#125—22no—
561#125—22no—
562#125—22no—
563#125—22no—
564#125—22no—
565#125—41no—
566#125—41no—
567#125—41no—
568#125—41no—
569#125—41no—
570#125—44no—
571#125—44no—
572#125—44no—
573#125—44no—
574#125—44no—
575#125—44no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—44no—
605C4×Q8—44no—
606C4×Q8—44no—
607C4×Q8—44no—
608C4×Q8C2×D414yes—
609C4×Q8C2×Q814yes—
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—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#107—22no—
713#107—22no—
714#107—22no—
715#107—22no—
716#107—22no—
717#107—41no—
718#107—41no—
719#107—41no—
720#107C2×D414yes—
721#107C2×D414yes—
722#106—22no—
723#106—22no—
724#106—22no—
725#106—22no—
726#106—22no—
727#106—22no—
728#106—22no—
729#106—22no—
730#106—22no—
731#106—22no—
732#106—22no—
733#106—41no—
734C4⋊C8—22no—
735C4⋊C8—22no—
736C4⋊C8—22no—
737C4⋊C8—22no—
738C4⋊C8—22no—
739C4⋊C8—22no—
740C4⋊C8C2×D414yes—
741C4⋊C8C2×Q814yes—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103C2×D414yes—
759#103C2×D414yes—
760#103C2×Q814yes—
761#103C2×Q814yes—
762#97—22no—
763#97—22no—
764#97—22no—
765#97—22no—
766#97—22no—
767C4×C8—22no—
768C4×C8—22no—
769C4×C8—22no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821C2×Q8—22no—
822C2×Q8—22no—
823C2×Q8—24no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—41no—
838C2×Q8—41no—
839C2×Q8—41no—
840C2×Q8—41no—
841C2×Q8—42no—
842C2×Q8—42no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×Q8—81no—
855C2×Q8C22×D412yes—
856C2×Q8C22×Q812yes—
857C2×Q8C22×Q812yes—
858C2×Q8C22×Q812yes—
859C2×Q82−1+412yes—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C2511yescharacteristic
891Q16—28no—
892Q16—28no—
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—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8C22×D412yes—
914C2×C8C22×D412yes—
915C2×C8C22×Q812yes—
916C2×C8C22×Q812yes—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4C22×D412yes—
1003C4⋊C4C22×D412yes—
1004C4⋊C4C22×D412yes—
1005C4⋊C4C22×Q812yes—
1006C4⋊C42−1+412yes—
1007C42—24no—
1008C42—24no—
1009C42—24no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—42no—
1021C42—42no—
1022C42—42no—
1023C42—42no—
1024C42—42no—
1025C42—42no—
1026C42—42no—
1027C42—42no—
1028C42—42no—
1029C42—42no—
1030C42—81no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42C22×D412yes—
1036C42C22×Q812yes—
1037C42H(5,𝔽2)12yes—
1038C422−1+412yes—
1039C23C23×D411yescharacteristic
1040Q8—22no—
1041Q8—22no—
1042Q8—22no—
1043Q8—22no—
1044Q8—22no—
1045Q8—22no—
1046Q8—22no—
1047Q8—44no—
1048Q8—41no—
1049Q8—41no—
1050Q8—41no—
1051Q8—41no—
1052Q8—82no—
1053Q8—84no—
1054Q8—84no—
1055Q8—84no—
1056Q8—162no—
1057Q8—162no—
1058Q8D4×Q814yes—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
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—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—22no—
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—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4D4212yes—
1146C2×C4D4212yes—
1147C2×C4D4×Q812yes—
1148C2×C4D4×Q812yes—
1149C2×C4C23×D411yescharacteristic
1150C2×C4C23×Q811yescharacteristic
1151C2×C4C2×H(5,𝔽2)11yescharacteristic
1152C2×C4C2×2−1+411yescharacteristic
1153C2×C4C2×2−1+411yescharacteristic
1154C2×C4C2×2−1+411yescharacteristic
1155C8—22no—
1156C8—22no—
1157C8—22no—
1158C8—22no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C22C2×D4211yescharacteristic
1164C22C2×D4×Q811yescharacteristic
1165C22#348611yescharacteristic
1166C22#358411yescharacteristic
1167C22#358611yescharacteristic
1168C22#358611yescharacteristic
1169C22#358611yescharacteristic
1170C4—22no—
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—24no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—41no—
1187C4—42no—
1188C4—41no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4C2×D4×Q811yescharacteristic
1201C4#349911yescharacteristic
1202C4#350311yescharacteristic
1203C4#355211yescharacteristic
1204C2#5912711yescharacteristic
1205C2#6106111yescharacteristic
1206C2#6107311yescharacteristic
1207C2#6137911yescharacteristic
1208C2#6138611yescharacteristic
1209C2#6186211yescharacteristic
1210C2#6187511yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
277. #462Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#33902
C2×#33872
#453892
#359572
#309772
#309682
#309642
#309522
#288222
#288182
#286962
#285262
#264742
#264612
#263952
#263912
#263892
#263692
#260542
#260482
#258472
#258362
#254872
#254762
#243442
#243362
#231552
#230142
#230042
#216252
#215162