Finite Group Databasebeta

← #7677887

Subgroups — #7677887

Order 512.

6780 conjugacy classes of subgroups.

The subgroup lattice has 1089 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3502C211yesmaximal, characteristic, complemented
2C22×#544C211yesmaximal, characteristic
3#59154C214yesmaximal, complemented
4#59154C214yesmaximal, complemented
5#59151C214yesmaximal, complemented
6#59144C214yesmaximal, complemented
7#45274C214yesmaximal, complemented
8#45272C214yesmaximal, complemented
9#45099C214yesmaximal, complemented
10#44894C214yesmaximal, complemented
11#39368C214yesmaximal, complemented
12#37689C214yesmaximal, complemented
13#37685C214yesmaximal
14#36130C214yesmaximal
15#35668C212yesmaximal, complemented
16#35566C212yesmaximal, complemented
17#35224C211yesmaximal, characteristic
18#35167C211yesmaximal, characteristic, complemented
19#35154C211yesmaximal, characteristic, complemented
20#34739C212yesmaximal
21#34271C211yesmaximal, characteristic, complemented
22#34203C212yesmaximal
23C2×#2360C211yesmaximal, characteristic
24#3502—216no—
25C2×Q82C2214yescomplemented
26C2×#557C2214yescomplemented
27C2×#557C2214yescomplemented
28C2×#557C2214yescomplemented
29C2×#544—216no—
30C2×#544C2214yes—
31C2×#544C2214yes—
32C2×#544C2214yes—
33C2×#544C2211yescharacteristic
34C2×#544C2211yescharacteristic
35C2×#544C2212yes—
36C2×#544C2214yes—
37C2×#544C2211yescharacteristic
38C2×#533C2214yes—
39C2×#533C2212yes—
40C22×C4⋊Q8C2214yes—
41C22×#125C2214yes—
42C22×C22⋊Q8C2214yes—
43C22×C22⋊Q8C2211yescharacteristic
44C2×#519C2212yes—
45C22×C4×Q8C2211yescharacteristic
46C22×#117C2212yes—
47C23×C4⋊C4C2211yescharacteristic
48#2857C2214yes—
49#2855C2214yes—
50#2848C2214yes—
51#2734C2218yescomplemented
52#2734C2218yescomplemented
53#2729C2218yes—
54#2726C2218yescomplemented
55#2726C2218yescomplemented
56#2720C2218yes—
57#2713C2218yescomplemented
58#2713C2218yescomplemented
59#2713C2218yescomplemented
60#2713C2218yescomplemented
61#2704C2218yes—
62#2677C2218yes—
63#2659C2214yes—
64#2627C2214yes—
65#2627C2214yes—
66#2584C2214yescomplemented
67#2584C2214yescomplemented
68#2568C2214yescomplemented
69#2567C2214yescomplemented
70#2567C2214yescomplemented
71#2565C2214yescomplemented
72#2565C2214yescomplemented
73#2556C2218yes—
74#2552C2214yescomplemented
75#2552C2214yescomplemented
76#2551C2214yescomplemented
77#2551C2214yescomplemented
78#2551C2218yescomplemented
79#2550C2214yescomplemented
80#2550C2214yescomplemented
81#2550C2214yescomplemented
82#2550C2214yescomplemented
83#2549C2218yes—
84#2546C2218yescomplemented
85#2546C2214yescomplemented
86#2506C2218yescomplemented
87#2506C2218yescomplemented
88#2492C2214yes—
89#2473C2218yes—
90#2473C2218yes—
91#2473C2218yes—
92#2465C2218yes—
93#2462C2218yescomplemented
94#2462C2218yescomplemented
95#2453C2214yescomplemented
96#2453C2214yescomplemented
97#2453C2214yescomplemented
98#2453C2214yescomplemented
99#2451C2214yescomplemented
100#2451C2214yescomplemented
101#2451C2214yescomplemented
102#2451C2218yescomplemented
103#2451C2214yescomplemented
104#2446C2218yescomplemented
105#2442C2212yes—
106#2442C2214yes—
107#2442C2212yes—
108#2442C2214yes—
109#2441C2212yes—
110#2441C2212yes—
111#2440C2212yes—
112#2440C2218yes—
113#2440C2214yes—
114#2440C2214yes—
115#2440C2212yes—
116#2440C2218yes—
117#2440C2214yes—
118#2439C2212yes—
119#2439C2212yes—
120#2438C2218yes—
121#2438C2218yes—
122#2438C2214yes—
123#2438C2214yes—
124#2437C2214yes—
125#2437C2214yes—
126#2434C2218yes—
127#2434C2214yes—
128#2429C2214yes—
129#2429C2214yes—
130#2423C2214yes—
131#2396C2214yes—
132#2396C2214yes—
133#2370C2214yescomplemented
134#2370C2214yescomplemented
135#2369C2214yescomplemented
136#2365C2214yescomplemented
137#2362C2214yes—
138#2362C2214yes—
139#2360C2214yes—
140#2360C2214yes—
141#2360C2218yes—
142#2360C2214yes—
143#2360C2214yes—
144#2360C2214yes—
145#2360C2214yes—
146#2360C2214yes—
147#2344C2218yes—
148#2342C2218yes—
149Q8×C22⋊C4C2214yes—
150#2329C2214yes—
151#2323C2214yes—
152#2323C2214yes—
153#2317C2212yes—
154#2316C2211yescharacteristic
155#2316C2212yes—
156#2310C2212yes—
157C4×C22⋊Q8C2214yes—
158C4×C22⋊Q8C2214yes—
159C4×C22⋊Q8C2214yes—
160C4×C22⋊Q8C2214yes—
161C4×C22⋊Q8C2214yes—
162#2296C2212yes—
163#2296C2212yes—
164C2×#391C2211yescharacteristic
165C2×#389C2212yes—
166C2×#389C2211yescharacteristic
167C2×#387C2212yes—
168C2×#385C2212yes—
169#2285C2212yes—
170#2280C2212yes—
171#2274C2212yes—
172C2×C4×C4⋊C4C2211yescharacteristic
173C2×C4×C22⋊C4C2212yes—
174C2×C4×C22⋊C4C2211yescharacteristic
175C23×Q8C2311yescharacteristic
176C23×Q8C2314yes—
177C24×C4C2311yescharacteristic
178C24×C4C2312yes—
179Q82—232no—
180#557—232no—
181#557—232no—
182#557—232no—
183#544—232no—
184#544—232no—
185#544—232no—
186#544—232no—
187#544—216no—
188#544—28no—
189#544—28no—
190#544D4116yes—
191#533—232no—
192#533—216no—
193C2×C4⋊Q8—232no—
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2318yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2318yes—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2318yes—
204C2×C4⋊Q8C2318yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2318yes—
208C2×C4⋊Q8C2314yes—
209C2×#125—232no—
210C2×#125C2314yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×#125C2318yes—
214C2×#125C2318yes—
215C2×#125C2312yes—
216C2×#125C2312yes—
217C2×#125C2318yes—
218C2×#125C2314yes—
219C2×#125C2318yes—
220C2×#125C2318yes—
221C2×#125C2314yes—
222C2×C22⋊Q8—232no—
223C2×C22⋊Q8Q8116yescomplemented
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239#519—216no—
240C2×C4×Q8—28no—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2318yes—
252C2×C4×Q8C2314yes—
253C2×#117—216no—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2314yes—
258C2×#117C2318yes—
259C2×#117C2314yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2312yes—
263C22×C4⋊C4—28no—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2318yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2312yes—
277C22×C22⋊C4C2314yes—
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2312yes—
281C22×C42C2312yes—
282C22×C42C2314yes—
283C22×C42C2311yescharacteristic
284C22×C42C2311yescharacteristic
285C22×C42C2312yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2314yes—
291#400C2314yes—
292#399C2314yes—
293#399C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#396C2314yes—
313#396C2314yes—
314#396C2314yes—
315#396C2314yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2318yes—
320#395C2318yes—
321#395C2318yes—
322#395C2318yes—
323#395C2318yes—
324#395C2314yes—
325#395C2314yes—
326#395C2318yes—
327#395C2318yes—
328#393C2314yes—
329#393C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2318yes—
337#391C2318yes—
338#391C2318yes—
339#391C2318yes—
340#391C2314yes—
341#391C2314yes—
342#391C2318yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#391C2314yes—
348#389C2312yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2318yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#389C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2312yes—
380#389C2312yes—
381#389C2314yes—
382#389C2314yes—
383#389C2312yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#385C2318yes—
408#385C2314yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2314yes—
414#385C2318yes—
415#385C2314yes—
416#385C2318yes—
417#385C2314yes—
418#385C2314yes—
419#385C2314yes—
420#385C2314yes—
421#385C2314yes—
422#384C2312yes—
423#384C2314yes—
424#384C2312yes—
425#384C2318yes—
426#384C2314yes—
427#382C2312yes—
428#382C2314yes—
429#382C2312yes—
430#381C2318yes—
431#381C2314yes—
432#380C2314yes—
433#380C2318yes—
434#380C2312yes—
435#380C2312yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2312yes—
443#380C2312yes—
444#379C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2318yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2318yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2318yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2318yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2312yes—
473C4×C22⋊C4C2314yes—
474C2×#95C2312yes—
475C2×#95C2311yescharacteristic
476C2×#95C2311yescharacteristic
477C2×#95C2312yes—
478C2×#95C2312yes—
479C2×#95C2312yes—
480C25C2411yescharacteristic
481C22×Q8—216no—
482C22×Q8—24no—
483C22×Q8—24no—
484C22×Q8—48no—
485C22×Q8—84no—
486C22×Q8C2×Q818yescomplemented
487C22×Q8C2414yes—
488C22×Q8C2414yes—
489C22×Q8C2414yes—
490C22×Q8C2414yes—
491C22×Q8C2414yes—
492C22×Q8C2418yes—
493C22×Q8C2414yes—
494C23×C4—24no—
495C23×C4—24no—
496C23×C4—28no—
497C23×C4—44no—
498C23×C4—82no—
499C23×C4C2×Q818yes—
500C23×C4C2414yes—
501C23×C4C2414yes—
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C23×C4C2414yes—
505C23×C4C2412yes—
506C23×C4C2411yescharacteristic
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2412yes—
512C23×C4C2414yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2411yescharacteristic
516C4⋊Q8—232no—
517C4⋊Q8—216no—
518C4⋊Q8—232no—
519C4⋊Q8—232no—
520C4⋊Q8—216no—
521C4⋊Q8—216no—
522C4⋊Q8—216no—
523C4⋊Q8—28no—
524C4⋊Q8—28no—
525C4⋊Q8—232no—
526C4⋊Q8—216no—
527C4⋊Q8—216no—
528C4⋊Q8—84no—
529C4⋊Q8—88no—
530C4⋊Q8C2×D4132yes—
531#125—232no—
532#125—232no—
533#125—216no—
534#125—216no—
535#125—232no—
536#125—28no—
537#125—28no—
538#125—232no—
539#125—232no—
540#125—216no—
541#125—216no—
542#125C2×D4132yes—
543C22⋊Q8—216no—
544C22⋊Q8—216no—
545C22⋊Q8—216no—
546C22⋊Q8—232no—
547C22⋊Q8—216no—
548C22⋊Q8—232no—
549C22⋊Q8—216no—
550C22⋊Q8—216no—
551C22⋊Q8—216no—
552C22⋊Q8—48no—
553C22⋊Q8—48no—
554C22⋊Q8—84no—
555C22⋊Q8C2×D4132yes—
556C22⋊Q8C2×Q8132yes—
557C22⋊Q8C2×Q8132yescomplemented
558C4×Q8—216no—
559C4×Q8—216no—
560C4×Q8—216no—
561C4×Q8—216no—
562C4×Q8—216no—
563C4×Q8—216no—
564C4×Q8—232no—
565C4×Q8—216no—
566C4×Q8—216no—
567C4×Q8—216no—
568C4×Q8—216no—
569C4×Q8—84no—
570#117—28no—
571#117—28no—
572#117—28no—
573#117—28no—
574#117—28no—
575#117—216no—
576#117—232no—
577#117—216no—
578#117C2×D4116yes—
579C2×C4⋊C4—28no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—216no—
583C2×C4⋊C4—216no—
584C2×C4⋊C4—28no—
585C2×C4⋊C4—28no—
586C2×C4⋊C4—216no—
587C2×C4⋊C4—232no—
588C2×C4⋊C4—82no—
589C2×C4⋊C4C2×D418yes—
590C2×C4⋊C4C2×Q8116yescomplemented
591C2×C4⋊C4C2×Q818yescomplemented
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C22⋊C4—216no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—42no—
647C2×C22⋊C4C2×Q8116yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2411yescharacteristic
653C2×C22⋊C4C2411yescharacteristic
654C2×C22⋊C4C2411yescharacteristic
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2411yescharacteristic
666C2×C42—28no—
667C2×C42—24no—
668C2×C42—24no—
669C2×C42—216no—
670C2×C42—82no—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2418yes—
676C2×C42C2418yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679C2×C42C2414yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2418yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2418yes—
688C2×C42C2414yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2412yes—
696#95C2414yes—
697#95C2418yes—
698#95C2418yes—
699#95C2414yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2414yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2418yes—
716#95C2414yes—
717#95C2414yes—
718#95C2418yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726C24—22no—
727C24—22no—
728C24—22no—
729C24—22no—
730C24—41no—
731C24—41no—
732C24C22×Q814yes—
733C24C2511yescharacteristic
734C24C2511yescharacteristic
735C24C2511yescharacteristic
736C2×Q8—232no—
737C2×Q8—28no—
738C2×Q8—28no—
739C2×Q8—28no—
740C2×Q8—28no—
741C2×Q8—28no—
742C2×Q8—216no—
743C2×Q8—28no—
744C2×Q8—28no—
745C2×Q8—44no—
746C2×Q8—44no—
747C2×Q8—44no—
748C2×Q8—44no—
749C2×Q8—44no—
750C2×Q8—44no—
751C2×Q8—44no—
752C2×Q8—44no—
753C2×Q8—48no—
754C2×Q8—44no—
755C2×Q8—48no—
756C2×Q8—832no—
757C2×Q8C22×D4116yes—
758C2×Q8C22×Q8116yes—
759C22×C4—24no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—24no—
763C22×C4—232no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—22no—
774C22×C4—24no—
775C22×C4—22no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—41no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—44no—
787C22×C4—42no—
788C22×C4—44no—
789C22×C4—41no—
790C22×C4—44no—
791C22×C4—41no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—42no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—42no—
798C22×C4—41no—
799C22×C4—816no—
800C22×C4C22×D418yes—
801C22×C4C22×D414yes—
802C22×C4C22×Q818yes—
803C22×C4C22×Q814yes—
804C22×C4C22×Q818yes—
805C22×C4C22×Q818yes—
806C22×C4C22×Q818yes—
807C22×C4C22×Q814yes—
808C22×C42−1+414yes—
809C22×C4C2511yescharacteristic
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2511yescharacteristic
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2512yes—
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C22×C4C2512yes—
829C4⋊C4—216no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—216no—
836C4⋊C4—28no—
837C4⋊C4—216no—
838C4⋊C4—216no—
839C4⋊C4—216no—
840C4⋊C4—216no—
841C4⋊C4—216no—
842C4⋊C4—24no—
843C4⋊C4—216no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—216no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4C22×D4116yes—
875C4⋊C4C22×D418yes—
876C4⋊C4C22×D418yes—
877C4⋊C4C22×D4116yes—
878C4⋊C4C22×D4132yes—
879C4⋊C4C22×Q8116yes—
880C4⋊C4C22×Q8132yes—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—22no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—24no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—42no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4C22×D4116yes—
896C22⋊C4C22×Q8116yes—
897C22⋊C4C22×Q8116yes—
898C22⋊C42−1+414yes—
899C42—28no—
900C42—28no—
901C42—28no—
902C42—28no—
903C42—24no—
904C42—28no—
905C42—24no—
906C42—216no—
907C42—216no—
908C42—28no—
909C42—24no—
910C42—24no—
911C42—28no—
912C42—44no—
913C42—44no—
914C42—48no—
915C42—48no—
916C42C22×D4116yes—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—28no—
932C23—28no—
933C23—44no—
934C23—44no—
935C23—44no—
936C23—44no—
937C23—44no—
938C23C23×D412yes—
939C23C23×Q812yes—
940C23C23×Q812yes—
941C23C23×Q812yes—
942C23C2×2−1+412yes—
943C23C2×2−1+412yes—
944C23#58512yes—
945C23C2611yescharacteristic
946Q8—232no—
947Q8—416no—
948Q8—416no—
949Q8—88no—
950Q8—88no—
951Q8—88no—
952Q8—816no—
953C2×C4—24no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—21no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—21no—
969C2×C4—28no—
970C2×C4—216no—
971C2×C4—216no—
972C2×C4—216no—
973C2×C4—21no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—21no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—21no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—48no—
1007C2×C4—48no—
1008C2×C4—416no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—416no—
1012C2×C4—416no—
1013C2×C4—88no—
1014C2×C4—82no—
1015C2×C4—82no—
1016C2×C4—84no—
1017C2×C4D4×Q8116yes—
1018C2×C4C23×D418yes—
1019C2×C4C23×D418yes—
1020C2×C4C23×D418yes—
1021C2×C4C23×D414yes—
1022C2×C4C23×Q818yes—
1023C2×C4C23×Q818yes—
1024C2×C4C23×Q814yes—
1025C2×C4C23×Q814yes—
1026C2×C4C2×2−1+412yes—
1027C2×C4C2×2−1+412yes—
1028C2×C4C2×2−1+414yes—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—416no—
1045C22—41no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22C2×D4×Q814yes—
1050C22#350214yescomplemented
1051C22C24×D411yescharacteristic
1052C22C24×Q811yescharacteristic
1053C22C22×2−1+411yescharacteristic
1054C22C22×2−1+411yescharacteristic
1055C22C2×#58511yescharacteristic
1056C22H(7,𝔽2)11yescharacteristic
1057C222−1+611yescharacteristic
1058C4—28no—
1059C4—28no—
1060C4—28no—
1061C4—22no—
1062C4—28no—
1063C4—22no—
1064C4—24no—
1065C4—28no—
1066C4—44no—
1067C4—44no—
1068C4—42no—
1069C4—44no—
1070C4—41no—
1071C4—44no—
1072C4—44no—
1073C4—44no—
1074C4—42no—
1075C4—44no—
1076C4—41no—
1077C4C2×D4×Q818yes—
1078C2—24no—
1079C2—24no—
1080C2—42no—
1081C2C22×D4×Q811yescharacteristic
1082C2C2×#350211yescharacteristic
1083C2#6285411yescharacteristic
1084C2#6292811yescharacteristic
1085C2#6294511yescharacteristic
1086C2#6298711yescharacteristic
1087C2D4×2−1+411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3502C2semidirect
3. #59154C2semidirect
4. #59154C2semidirect
5. #59151C2semidirect
6. #59144C2semidirect
7. #45274C2semidirect
8. #45272C2semidirect
9. #45099C2semidirect
10. #44894C2semidirect
11. #39368C2semidirect
12. #37689C2semidirect
15. #35668C2semidirect
16. #35566C2semidirect
18. #35167C2semidirect
19. #35154C2semidirect
21. #34271C2semidirect
25. C2×Q82C22semidirect
26. C2×#557C22semidirect
27. C2×#557C22semidirect
28. C2×#557C22semidirect
51. #2734C22semidirect
52. #2734C22semidirect
54. #2726C22semidirect
55. #2726C22semidirect
57. #2713C22semidirect
58. #2713C22semidirect
59. #2713C22semidirect
60. #2713C22semidirect
66. #2584C22semidirect
67. #2584C22semidirect
68. #2568C22semidirect
69. #2567C22semidirect
70. #2567C22semidirect
71. #2565C22semidirect
72. #2565C22semidirect
74. #2552C22semidirect
75. #2552C22semidirect
76. #2551C22semidirect
77. #2551C22semidirect
78. #2551C22semidirect
79. #2550C22semidirect
80. #2550C22semidirect
81. #2550C22semidirect
82. #2550C22semidirect
84. #2546C22semidirect
85. #2546C22semidirect
86. #2506C22semidirect
87. #2506C22semidirect
93. #2462C22semidirect
94. #2462C22semidirect
95. #2453C22semidirect
96. #2453C22semidirect
97. #2453C22semidirect
98. #2453C22semidirect
99. #2451C22semidirect
100. #2451C22semidirect
101. #2451C22semidirect
102. #2451C22semidirect
103. #2451C22semidirect
104. #2446C22semidirect
133. #2370C22semidirect
134. #2370C22semidirect
135. #2369C22semidirect
136. #2365C22semidirect
223. C2×C22⋊Q8Q8semidirect
486. C22×Q8C2×Q8semidirect
557. C22⋊Q8C2×Q8semidirect
590. C2×C4⋊C4C2×Q8semidirect
591. C2×C4⋊C4C2×Q8semidirect
1050. C22#3502semidirect

Maximal subgroups

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

subgroupindex
C2×#35022
C22×#5442
#591542
#591512
#591442
#452742
#452722
#450992
#448942
#393682
#376892
#376852
#361302
#356682
#355662
#352242
#351672
#351542
#347392
#342712
#342032
C2×#23602