Finite Group Databasebeta

← #7671974

Subgroups — #7671974

Order 512.

8370 conjugacy classes of subgroups.

The subgroup lattice has 997 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C23×C4⋊Q8C211yesmaximal, characteristic, complemented
3#59151C214yesmaximal, complemented
4#59144C214yesmaximal, complemented
5#59136C214yesmaximal, complemented
6#59127C214yesmaximal, complemented
7#39593C214yesmaximal, complemented
8#39592C214yesmaximal, complemented
9#37686C218yesmaximal, complemented
10#36625C211yesmaximal, characteristic, complemented
11#36546C214yesmaximal, complemented
12Q8×#120C214yesmaximal, complemented
13#36129C214yesmaximal, complemented
14D4×C4⋊Q8C214yesmaximal, complemented
15#35576C212yesmaximal, complemented
16#35574C212yesmaximal, complemented
17#35281C211yesmaximal, characteristic, complemented
18#35279C211yesmaximal, characteristic, complemented
19#35224C212yesmaximal, complemented
20#34216C211yesmaximal, characteristic, complemented
21#34200C212yesmaximal
22C4×#525C211yesmaximal, characteristic
23C24×Q8C2212yes—
24#3503—216no—
25C2×Q82C2212yescomplemented
26C2×#557C2212yescomplemented
27C2×#554C2214yes—
28C2×#554C2212yescomplemented
29C2×D4×Q8C2214yes—
30C2×D4×Q8C2218yes—
31C2×D4×Q8C2212yescomplemented
32C2×#544C2212yes—
33C2×#544C2214yescomplemented
34C2×#533C2211yescharacteristic
35C2×#533C2212yescomplemented
36C22×C4⋊Q8—216no—
37C22×C4⋊Q8C2214yes—
38C22×C4⋊Q8C2214yes—
39C22×C4⋊Q8C2214yes—
40C22×C4⋊Q8C2214yes—
41C22×C4⋊Q8C2212yes—
42C22×C4⋊Q8C2212yes—
43C22×C4⋊Q8C2211yescharacteristic
44C22×C4⋊Q8C2212yes—
45C22×C4⋊Q8C2211yescharacteristic
46C22×C4⋊Q8C2212yescomplemented
47C2×#525C2211yescharacteristic
48C2×#520C2212yes—
49C2×C4×#41C2211yescharacteristic
50C23×C4⋊C4C2212yes—
51C23×C4⋊C4C2212yes—
52C23×C42C2211yescharacteristic
53#2868C2212yescomplemented
54#2862C2212yescomplemented
55#2857C2212yes—
56#2857C2212yes—
57#2857C2214yescomplemented
58#2855C2212yes—
59#2855C2212yes—
60#2851C2214yes—
61#2848C2212yes—
62#2848C2212yes—
63#2848C2218yes—
64#2734C22116yescomplemented
65#2729C22116yescomplemented
66#2713C22116yescomplemented
67#2677C22116yescomplemented
68#2660C2214yescomplemented
69#2628C2214yescomplemented
70#2627C2218yes—
71#2583C2218yes—
72#2579C2218yes—
73#2568C2212yescomplemented
74#2567C2214yescomplemented
75#2567C2212yescomplemented
76#2563C2212yescomplemented
77#2551C2218yescomplemented
78#2551C2218yescomplemented
79#2551C2218yescomplemented
80#2550C2218yescomplemented
81#2550C2218yescomplemented
82#2546C2218yescomplemented
83#2546C2214yescomplemented
84#2542C2212yescomplemented
85#2502C2214yes—
86#2492C2218yescomplemented
87#2487C2214yes—
88#2473C22116yes—
89#2452C2218yescomplemented
90#2451C2218yescomplemented
91#2451C2218yescomplemented
92#2449C22116yes—
93#2446C2218yescomplemented
94#2442C2218yes—
95#2442C2218yes—
96#2440C2218yes—
97#2440C2218yes—
98#2440C2218yes—
99#2440C2218yescomplemented
100#2440C2218yescomplemented
101#2439C2218yescomplemented
102#2434C2218yes—
103#2434C22116yes—
104#2434C2218yes—
105#2434C2214yes—
106#2434C2218yescomplemented
107#2429C2218yescomplemented
108#2417C2218yes—
109#2409C22116yes—
110#2409C2218yes—
111#2409C2218yes—
112#2409C2214yes—
113#2369C2214yescomplemented
114#2365C2214yescomplemented
115#2361C2218yes—
116#2360C2218yes—
117#2360C2218yes—
118#2352C2218yes—
119D4×C4⋊C4C2218yes—
120D4×C4⋊C4C2218yes—
121#2345C2214yes—
122Q8×C22⋊C4C2218yes—
123Q8×C22⋊C4C2214yes—
124#2331C2214yescomplemented
125#2322C2218yes—
126#2317C2212yes—
127#2317C2212yes—
128#2317C2212yes—
129#2316C2212yes—
130#2311C2212yes—
131C4×C4⋊Q8C2214yescomplemented
132C4×C22⋊Q8C2214yes—
133C4×C22⋊Q8C2212yes—
134C4×C22⋊Q8C2214yes—
135C4×C22⋊Q8C2212yes—
136C4×#123C2212yes—
137C4×#123C2212yes—
138C4×#121C2212yes—
139C4×#121C2212yes—
140C4×#120C2218yes—
141C4×#120C2212yes—
142C4×#120C2212yes—
143#2297C2211yescharacteristic
144#2296C2212yes—
145#2296C2211yescharacteristic
146#2290C2214yes—
147#2285C2211yescharacteristic
148#2280C2212yes—
149#2280C2211yescharacteristic
150#2274C2212yes—
151C42×D4C2214yes—
152C4×#117C2211yescharacteristic
153C22×#41C2311yescharacteristic
154C23×Q8—216no—
155C23×Q8—416no—
156C23×Q8C2318yes—
157C23×Q8C2318yes—
158C23×Q8C2314yes—
159C23×Q8C2312yes—
160C23×Q8C2314yes—
161C23×Q8C2312yes—
162C24×C4C2311yescharacteristic
163C24×C4C2311yescharacteristic
164C24×C4C2311yescharacteristic
165C24×C4C2314yes—
166Q82—216no—
167#557—216no—
168#554—216no—
169#554—232no—
170D4×Q8—232no—
171D4×Q8—216no—
172D4×Q8—432no—
173#544—232no—
174#544—216no—
175#533—216no—
176#533—28no—
177C2×C4⋊Q8—216no—
178C2×C4⋊Q8—232no—
179C2×C4⋊Q8—232no—
180C2×C4⋊Q8—232no—
181C2×C4⋊Q8—232no—
182C2×C4⋊Q8—216no—
183C2×C4⋊Q8—216no—
184C2×C4⋊Q8—216no—
185C2×C4⋊Q8—28no—
186C2×C4⋊Q8D4116yescomplemented
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2318yes—
194C2×C4⋊Q8C2318yes—
195C2×C4⋊Q8C2318yes—
196C2×C4⋊Q8C2318yes—
197C2×C4⋊Q8C2318yes—
198C2×C4⋊Q8C2318yes—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2318yes—
204C2×C4⋊Q8C2318yes—
205C2×C4⋊Q8C23116yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×#125C2312yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×#125C2318yes—
214#525Q8116yescomplemented
215C2×#123C2312yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C23116yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C23116yes—
228C2×C22⋊Q8C2312yes—
229C2×#121C2312yes—
230C2×#120C2312yes—
231#520—216no—
232C4×#41—28no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2318yes—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2318yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C23116yes—
250C2×C4×D4C2314yes—
251C2×#117C2312yes—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2312yes—
257C2×#117C2311yescharacteristic
258C22×C4⋊C4—216no—
259C22×C4⋊C4—216no—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2318yes—
266C22×C4⋊C4C2318yes—
267C22×C4⋊C4C2318yes—
268C22×C4⋊C4C2318yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C42—28no—
273C22×C42C2312yes—
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2311yescharacteristic
279C22×C42C2312yes—
280C22×C42C2312yes—
281C22×C42C2311yescharacteristic
282#400C2318yes—
283#400C23116yes—
284#399C2318yes—
285#398C23116yes—
286#398C23116yes—
287#398C23116yes—
288#398C23116yes—
289#398C23116yes—
290#396C23116yes—
291#395C2318yes—
292#395C23116yes—
293#395C23116yes—
294#395C23116yes—
295#395C23116yes—
296#395C23116yes—
297#395C23116yes—
298#393C2318yes—
299#393C23116yes—
300#391C2318yes—
301#391C2314yes—
302#391C2318yes—
303#391C2318yes—
304#391C23116yes—
305#391C2318yes—
306#391C23116yes—
307#391C23116yes—
308#391C2314yes—
309#391C2314yes—
310#391C2312yes—
311#390C2314yes—
312#390C2312yes—
313#389C2318yes—
314#389C2318yes—
315#389C2318yes—
316#389C2318yes—
317#389C2318yes—
318#389C2318yes—
319#389C2318yes—
320#389C23116yes—
321#389C23116yes—
322#389C23116yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2312yes—
328#389C2312yes—
329#388C23116yes—
330#388C2314yes—
331#388C2314yes—
332#387C23116yes—
333#387C23116yes—
334#387C23116yes—
335#387C2318yes—
336#387C2318yes—
337#387C2314yes—
338#387C2314yes—
339#386C2318yes—
340#386C2312yes—
341#386C23116yes—
342#386C2314yes—
343#386C2312yes—
344#386C2314yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C23116yes—
349#385C2314yes—
350#385C23116yes—
351#385C2312yes—
352#385C2318yes—
353#385C2318yes—
354#385C2314yes—
355#385C23116yes—
356#385C23116yes—
357#385C23116yes—
358#385C2314yes—
359#385C2312yes—
360#385C2314yes—
361#384C2312yes—
362#384C2314yes—
363#384C2318yes—
364#384C2314yes—
365#384C2314yes—
366#382C2314yes—
367#382C2314yes—
368#382C2314yes—
369#382C2312yes—
370#381C2314yes—
371#381C2312yes—
372#380C2318yes—
373#380C2318yes—
374#380C2318yes—
375#380C2312yes—
376#380C2314yes—
377#380C23116yes—
378#380C2312yes—
379#380C2314yes—
380#380C2314yes—
381#380C2314yes—
382#380C2312yes—
383#380C2312yes—
384#379C2314yes—
385#379C2312yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2318yes—
388C4×C4⋊C4C2312yes—
389C4×C4⋊C4C2312yes—
390C4×C4⋊C4C2312yes—
391C4×C4⋊C4C2318yes—
392C4×C4⋊C4C2312yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2318yes—
396C4×C4⋊C4C2314yes—
397C4×C22⋊C4C2318yes—
398C4×C22⋊C4C2312yes—
399C4×C22⋊C4C2314yes—
400C4×C22⋊C4C23116yes—
401C4×C22⋊C4C2312yes—
402C4×C22⋊C4C2314yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2314yes—
405C4×C22⋊C4C2314yes—
406C4×C22⋊C4C2314yes—
407C4×C22⋊C4C2314yes—
408#376C2312yes—
409C43C2312yes—
410C25C2411yescharacteristic
411C2×#41—24no—
412C2×#41—24no—
413C2×#41C2×Q818yescomplemented
414C22×Q8—232no—
415C22×Q8—232no—
416C22×Q8—216no—
417C22×Q8—216no—
418C22×Q8—28no—
419C22×Q8—232no—
420C22×Q8—416no—
421C22×Q8—48no—
422C22×Q8—416no—
423C22×Q8—416no—
424C22×Q8—416no—
425C22×Q8—48no—
426C22×Q8—416no—
427C22×Q8—4128no—
428C22×Q8C2×D4116yes—
429C22×Q8C2412yes—
430C22×Q8C2412yes—
431C22×Q8C2414yes—
432C22×Q8C24116yes—
433C22×Q8C2414yes—
434C22×Q8C2411yescharacteristic
435C22×Q8C2418yes—
436C22×Q8C2414yes—
437C22×Q8C2414yes—
438C22×D4C2414yes—
439C22×D4C2412yes—
440C22×D4C2411yescharacteristic
441C23×C4—24no—
442C23×C4—24no—
443C23×C4—24no—
444C23×C4—28no—
445C23×C4—28no—
446C23×C4—24no—
447C23×C4—216no—
448C23×C4—416no—
449C23×C4C2×Q818yescomplemented
450C23×C4C2411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2412yes—
456C23×C4C24116yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2411yescharacteristic
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2412yes—
465C23×C4C2414yes—
466C23×C4C2418yes—
467C23×C4C2414yes—
468C23×C4C2411yescharacteristic
469C4⋊Q8—232no—
470C4⋊Q8—232no—
471C4⋊Q8—216no—
472C4⋊Q8—232no—
473C4⋊Q8—232no—
474C4⋊Q8—232no—
475C4⋊Q8—232no—
476C4⋊Q8—232no—
477C4⋊Q8—216no—
478C4⋊Q8—216no—
479C4⋊Q8—216no—
480C4⋊Q8—28no—
481C4⋊Q8—28no—
482C4⋊Q8—28no—
483C4⋊Q8—28no—
484C4⋊Q8—24no—
485C4⋊Q8—24no—
486C4⋊Q8—416no—
487C4⋊Q8—432no—
488C4⋊Q8C2×D4116yes—
489C4⋊Q8C2×D4116yes—
490C4⋊Q8C2×D4116yes—
491C4⋊Q8C2×D4116yes—
492#125—216no—
493#125—232no—
494#125—216no—
495#125—28no—
496#123C2×Q8116yescomplemented
497C22⋊Q8—216no—
498C22⋊Q8—232no—
499C22⋊Q8—28no—
500C22⋊Q8—28no—
501C22⋊Q8—232no—
502C22⋊Q8—216no—
503C22⋊Q8—216no—
504C22⋊Q8—216no—
505C22⋊Q8—232no—
506C22⋊Q8—432no—
507C22⋊Q8—432no—
508C22⋊Q8—416no—
509C22⋊Q8C2×Q8116yescomplemented
510#121C2×Q8116yescomplemented
511#120C2×Q8116yescomplemented
512C4×Q8—216no—
513C4×Q8—216no—
514C4×Q8—216no—
515C4×Q8—24no—
516C4×Q8—24no—
517C4×Q8—28no—
518C4×Q8—28no—
519C4×Q8—416no—
520C4×D4—28no—
521C4×D4—28no—
522C4×D4—232no—
523C4×D4—216no—
524C4×D4—216no—
525C4×D4—216no—
526C4×D4—24no—
527C4×D4—24no—
528C4×D4—432no—
529C4×D4C2×Q8132yescomplemented
530#117—24no—
531#117—28no—
532#117—28no—
533#117—24no—
534#117—216no—
535#117—28no—
536#117C2×Q818yescomplemented
537C2×C4⋊C4—216no—
538C2×C4⋊C4—216no—
539C2×C4⋊C4—28no—
540C2×C4⋊C4—28no—
541C2×C4⋊C4—232no—
542C2×C4⋊C4—232no—
543C2×C4⋊C4—232no—
544C2×C4⋊C4—232no—
545C2×C4⋊C4—216no—
546C2×C4⋊C4—216no—
547C2×C4⋊C4C2×D4116yes—
548C2×C4⋊C4C2×D4116yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C24116yes—
553C2×C4⋊C4C24116yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C24116yes—
578C2×C4⋊C4C24116yes—
579C2×C4⋊C4C24116yes—
580C2×C4⋊C4C24116yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C24116yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C42—24no—
605C2×C42—24no—
606C2×C42—24no—
607C2×C42—28no—
608C2×C42—28no—
609C2×C42—28no—
610C2×C42—28no—
611C2×C42—28no—
612C2×C42C2×D418yes—
613C2×C42C2412yes—
614C2×C42C2414yes—
615C2×C42C2418yes—
616C2×C42C2412yes—
617C2×C42C2414yes—
618C2×C42C2412yes—
619C2×C42C2412yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C24116yes—
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2412yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C24116yes—
643#95C2418yes—
644#95C2418yes—
645#95C24116yes—
646#95C24116yes—
647#95C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C24116yes—
651#95C2418yes—
652#95C24116yes—
653#95C24116yes—
654C24—22no—
655C24—24no—
656C24—24no—
657C24—22no—
658C24C22×Q814yes—
659C24C2512yes—
660C24C2511yescharacteristic
661C24C2512yes—
662#41—232no—
663C2×Q8—22no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—232no—
667C2×Q8—28no—
668C2×Q8—28no—
669C2×Q8—216no—
670C2×Q8—216no—
671C2×Q8—28no—
672C2×Q8—232no—
673C2×Q8—216no—
674C2×Q8—22no—
675C2×Q8—28no—
676C2×Q8—48no—
677C2×Q8—416no—
678C2×Q8—48no—
679C2×Q8—416no—
680C2×Q8—432no—
681C2×Q8—4128no—
682C2×Q8—464no—
683C2×Q8—4128no—
684C2×Q8—432no—
685C2×Q8—832no—
686C2×Q8C22×D4116yes—
687C2×Q8C22×D4116yes—
688C2×Q8C22×Q814yescomplemented
689C2×D4—24no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—24no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4C22×Q8116yes—
696C2×D4C22×Q818yes—
697C2×D4C22×Q814yescomplemented
698C22×C4—232no—
699C22×C4—232no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—22no—
706C22×C4—232no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—28no—
726C22×C4—232no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—232no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—216no—
733C22×C4—48no—
734C22×C4—416no—
735C22×C4—48no—
736C22×C4—416no—
737C22×C4—464no—
738C22×C4C22×D414yes—
739C22×C4C22×D414yes—
740C22×C4C22×D4116yes—
741C22×C4C22×D414yes—
742C22×C4C22×Q818yes—
743C22×C4C22×Q818yes—
744C22×C4C22×Q814yes—
745C22×C4C22×Q814yes—
746C22×C4C22×Q818yescomplemented
747C22×C4H(5,𝔽2)18yes—
748C22×C42−1+418yes—
749C22×C42−1+414yes—
750C22×C4C2514yes—
751C22×C4C2518yes—
752C22×C4C2514yes—
753C22×C4C2512yes—
754C22×C4C2518yes—
755C22×C4C2512yes—
756C22×C4C2514yes—
757C22×C4C2511yescharacteristic
758C22×C4C2511yescharacteristic
759C22×C4C2518yes—
760C22×C4C2514yes—
761C22×C4C2512yes—
762C22×C4C2512yes—
763C22×C4C2512yes—
764C22×C4C2512yes—
765C22×C4C2511yescharacteristic
766C22×C4C2511yescharacteristic
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C4⋊C4—232no—
770C4⋊C4—232no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—216no—
778C4⋊C4—216no—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—22no—
782C4⋊C4—24no—
783C4⋊C4—22no—
784C4⋊C4—24no—
785C4⋊C4—216no—
786C4⋊C4—28no—
787C4⋊C4—216no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—216no—
792C4⋊C4—24no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—216no—
797C4⋊C4—416no—
798C4⋊C4—416no—
799C4⋊C4—416no—
800C4⋊C4—416no—
801C4⋊C4C22×D4116yes—
802C4⋊C4C22×D4116yes—
803C4⋊C4C22×D4116yes—
804C4⋊C4C22×D4116yes—
805C4⋊C4C22×Q818yescomplemented
806C4⋊C4C22×Q8116yescomplemented
807C22⋊C4—28no—
808C22⋊C4—24no—
809C22⋊C4—28no—
810C22⋊C4—216no—
811C22⋊C4—28no—
812C22⋊C4—24no—
813C22⋊C4—28no—
814C22⋊C4—216no—
815C22⋊C4—216no—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—416no—
821C22⋊C4C22×Q818yes—
822C22⋊C4C22×Q8116yes—
823C22⋊C4C22×Q8116yescomplemented
824C42—24no—
825C42—24no—
826C42—24no—
827C42—24no—
828C42—24no—
829C42—24no—
830C42—24no—
831C42—24no—
832C42—24no—
833C42—216no—
834C42—28no—
835C42—28no—
836C42—28no—
837C42—24no—
838C42—28no—
839C42—416no—
840C42C22×D414yes—
841C42C22×D414yes—
842C42C22×D414yes—
843C42C22×D414yes—
844C42C22×Q818yescomplemented
845C23—28no—
846C23—28no—
847C23—216no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—28no—
855C23—216no—
856C23—22no—
857C23—24no—
858C23—24no—
859C23—22no—
860C23C23×D412yes—
861C23C23×Q814yes—
862C23C23×Q812yes—
863C23C23×Q814yes—
864C23C2×H(5,𝔽2)14yes—
865C23C2×2−1+412yes—
866C23C2×2−1+414yes—
867C23C2611yescharacteristic
868Q8—28no—
869Q8—232no—
870Q8—416no—
871Q8—464no—
872Q8—416no—
873Q8—416no—
874Q8—48no—
875Q8—48no—
876Q8—816no—
877D4—216no—
878D4—232no—
879D4—28no—
880C2×C4—216no—
881C2×C4—28no—
882C2×C4—216no—
883C2×C4—28no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—216no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—28no—
898C2×C4—216no—
899C2×C4—216no—
900C2×C4—216no—
901C2×C4—28no—
902C2×C4—216no—
903C2×C4—28no—
904C2×C4—216no—
905C2×C4—24no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—28no—
910C2×C4—24no—
911C2×C4—28no—
912C2×C4—24no—
913C2×C4—28no—
914C2×C4—216no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—28no—
921C2×C4—416no—
922C2×C4—464no—
923C2×C4—416no—
924C2×C4—48no—
925C2×C4—48no—
926C2×C4—816no—
927C2×C4D4×Q8116yescomplemented
928C2×C4C23×D412yes—
929C2×C4C23×D412yes—
930C2×C4C23×D4116yes—
931C2×C4C23×D412yes—
932C2×C4C23×D412yes—
933C2×C4C23×D412yes—
934C2×C4C23×D412yes—
935C2×C4C23×Q818yes—
936C2×C4C23×Q814yes—
937C2×C4C23×Q814yes—
938C2×C4C23×Q812yes—
939C2×C4C23×Q812yes—
940C2×C4C2×H(5,𝔽2)14yes—
941C2×C4C2×H(5,𝔽2)14yes—
942C2×C4C2×2−1+414yes—
943C2×C4C2×2−1+412yes—
944C2×C4C2×2−1+412yes—
945C2×C4C2×2−1+414yes—
946C22—232no—
947C22—22no—
948C22—24no—
949C22—22no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—28no—
958C22—24no—
959C22—42no—
960C22—42no—
961C22—44no—
962C22C2×D4×Q814yes—
963C22#350318yescomplemented
964C22C24×D411yescharacteristic
965C22C24×Q811yescharacteristic
966C22C22×H(5,𝔽2)12yes—
967C22C22×2−1+412yes—
968C22C22×2−1+411yescharacteristic
969C4—22no—
970C4—24no—
971C4—216no—
972C4—22no—
973C4—24no—
974C4—28no—
975C4—24no—
976C4—24no—
977C4—48no—
978C4—42no—
979C4—44no—
980C4—42no—
981C4—44no—
982C4—44no—
983C4—48no—
984C4C2×D4×Q814yes—
985C4C2×D4×Q814yes—
986C4#348414yes—
987C4#348614yes—
988C2—24no—
989C2—28no—
990C2—44no—
991C2C22×D4×Q811yescharacteristic
992C2C2×#348411yescharacteristic
993C2C2×#348611yescharacteristic
994C2C2×#350312yes—
995C2#6283312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
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×#3503C2semidirect
2. C23×C4⋊Q8C2semidirect
3. #59151C2semidirect
4. #59144C2semidirect
5. #59136C2semidirect
6. #59127C2semidirect
7. #39593C2semidirect
8. #39592C2semidirect
9. #37686C2semidirect
10. #36625C2semidirect
11. #36546C2semidirect
12. Q8×#120C2semidirect
13. #36129C2semidirect
14. D4×C4⋊Q8C2semidirect
15. #35576C2semidirect
16. #35574C2semidirect
17. #35281C2semidirect
18. #35279C2semidirect
19. #35224C2semidirect
20. #34216C2semidirect
25. C2×Q82C22semidirect
26. C2×#557C22semidirect
28. C2×#554C22semidirect
31. C2×D4×Q8C22semidirect
33. C2×#544C22semidirect
35. C2×#533C22semidirect
46. C22×C4⋊Q8C22semidirect
53. #2868C22semidirect
54. #2862C22semidirect
57. #2857C22semidirect
64. #2734C22semidirect
65. #2729C22semidirect
66. #2713C22semidirect
67. #2677C22semidirect
68. #2660C22semidirect
69. #2628C22semidirect
73. #2568C22semidirect
74. #2567C22semidirect
75. #2567C22semidirect
76. #2563C22semidirect
77. #2551C22semidirect
78. #2551C22semidirect
79. #2551C22semidirect
80. #2550C22semidirect
81. #2550C22semidirect
82. #2546C22semidirect
83. #2546C22semidirect
84. #2542C22semidirect
86. #2492C22semidirect
89. #2452C22semidirect
90. #2451C22semidirect
91. #2451C22semidirect
93. #2446C22semidirect
99. #2440C22semidirect
100. #2440C22semidirect
101. #2439C22semidirect
106. #2434C22semidirect
107. #2429C22semidirect
113. #2369C22semidirect
114. #2365C22semidirect
124. #2331C22semidirect
131. C4×C4⋊Q8C22semidirect
186. C2×C4⋊Q8D4semidirect
214. #525Q8semidirect
413. C2×#41C2×Q8semidirect
449. C23×C4C2×Q8semidirect
496. #123C2×Q8semidirect
509. C22⋊Q8C2×Q8semidirect
510. #121C2×Q8semidirect
511. #120C2×Q8semidirect
529. C4×D4C2×Q8semidirect
536. #117C2×Q8semidirect
688. C2×Q8C22×Q8semidirect
697. C2×D4C22×Q8semidirect
746. C22×C4C22×Q8semidirect
805. C4⋊C4C22×Q8semidirect
806. C4⋊C4C22×Q8semidirect
823. C22⋊C4C22×Q8semidirect
844. C42C22×Q8semidirect
927. C2×C4D4×Q8semidirect
963. C22#3503semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C23×C4⋊Q82
#591512
#591442
#591362
#591272
#395932
#395922
#376862
#366252
#365462
Q8×#1202
#361292
D4×C4⋊Q82
#355762
#355742
#352812
#352792
#352242
#342162
#342002
C4×#5252