Finite Group Databasebeta

← #7672369

Subgroups — #7672369

Order 512.

6826 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C212yesmaximal
2#59667C214yesmaximal, complemented
3#59428C214yesmaximal, complemented
4#59290C218yesmaximal, complemented
5#39407C218yesmaximal, complemented
6#39170C212yesmaximal, complemented
7#38954C212yesmaximal, complemented
8#38081C214yesmaximal, complemented
9#36645C211yesmaximal, characteristic, complemented
10#36593C211yesmaximal, characteristic, complemented
11#36560C211yesmaximal, characteristic, complemented
12#36188C211yesmaximal, characteristic, complemented
13#36181C212yesmaximal, complemented
14#36133C214yesmaximal, complemented
15D4×C4⋊Q8C212yesmaximal, complemented
16D4×C4⋊Q8C211yesmaximal, characteristic, complemented
17#36116C214yesmaximal
18#35670C214yesmaximal, complemented
19#35319C212yesmaximal, complemented
20#35248C212yesmaximal, complemented
21#34209C212yesmaximal, complemented
22C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
23C4×#529C211yesmaximal, characteristic
24#3523—232no—
25C2×#557C2212yes—
26C2×#557C2212yes—
27C2×#557C2214yes—
28C2×#556C2214yes—
29C2×#556C2212yes—
30C2×#552C2214yes—
31C2×#552C2218yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2214yes—
34C2×#541C2214yes—
35C2×#541C2218yes—
36C2×#533C2214yes—
37C2×#533C2212yes—
38C22×C4⋊Q8C2212yes—
39C22×C4⋊Q8C2211yescharacteristic
40C2×#529C2214yes—
41C2×#529C2211yescharacteristic
42C2×#519C2214yes—
43C22×C4×Q8C2212yes—
44#2868C2211yescharacteristic
45#2868C2212yes—
46#2868C2211yescharacteristic
47#2862C2212yes—
48#2859C2214yes—
49#2859C2212yes—
50#2857C2214yes—
51#2857C2212yes—
52#2857C2212yes—
53#2857C2212yes—
54#2857C2212yes—
55#2855C2218yes—
56#2719C22116yes—
57#2713C22116yes—
58#2698C22116yes—
59#2689C22116yes—
60#2642C2214yes—
61#2634C2218yes—
62#2621C2214yes—
63#2581C2218yes—
64#2568C2212yes—
65#2568C2212yes—
66#2565C2214yes—
67#2565C2214yes—
68#2552C2214yes—
69#2552C2218yes—
70#2551C2214yes—
71#2551C2218yes—
72#2547C2214yes—
73#2546C2214yes—
74#2546C2212yes—
75#2546C2214yes—
76#2546C2212yes—
77#2546C2214yes—
78#2506C2218yes—
79#2506C2218yes—
80#2506C2218yes—
81#2506C2218yes—
82#2503C2214yes—
83#2499C2214yes—
84#2499C2214yes—
85#2496C2218yes—
86#2496C2218yes—
87#2496C2218yes—
88#2496C2218yes—
89#2486C2218yes—
90#2484C2218yes—
91#2478C22116yes—
92#2478C22116yes—
93#2462C22116yes—
94#2462C22116yes—
95#2453C2218yes—
96#2451C2218yes—
97#2447C2218yes—
98#2446C2218yes—
99#2440C2218yes—
100#2440C2218yes—
101#2440C2218yes—
102#2438C22116yes—
103#2434C2214yes—
104#2434C2214yes—
105#2434C2214yes—
106#2419C22116yes—
107#2365C2214yes—
108#2365C2214yes—
109#2365C2218yes—
110#2365C2218yes—
111Q8×C4⋊C4C2214yes—
112D4×C4⋊C4C2214yes—
113D4×C4⋊C4C2218yes—
114#2344C2218yes—
115#2344C2218yes—
116#2344C2218yes—
117#2327C2214yes—
118#2327C2214yes—
119#2327C2214yes—
120#2310C2214yes—
121C4×C4⋊Q8C2212yes—
122C4×C4⋊Q8C2214yes—
123C4×C4⋊Q8C2214yes—
124C4×C4⋊Q8C2212yes—
125C4×C4⋊Q8C2211yescharacteristic
126C4×C4⋊Q8C2212yes—
127C4×C4⋊Q8C2212yes—
128C4×C4⋊Q8C2212yes—
129C4×C4⋊Q8C2212yes—
130C4×C4⋊Q8C2211yescharacteristic
131C4×C4⋊Q8C2211yescharacteristic
132C4×C4⋊Q8C2214yes—
133C4×C4⋊Q8C2211yescharacteristic
134C4×#125C2212yes—
135C4×#126C2214yes—
136C4×#124C2212yes—
137C4×C22⋊Q8C2212yes—
138C4×#123C2214yes—
139C4×#121C2212yes—
140#2298C2212yes—
141#2295C2211yescharacteristic
142C2×#391C2212yes—
143#2293C2211yescharacteristic
144C2×#389C2214yes—
145#2290C2212yes—
146#2285C2214yes—
147#2285C2212yes—
148C2×#384C2211yescharacteristic
149#2283C2211yescharacteristic
150C42×Q8C2211yescharacteristic
151C42×D4C2212yes—
152C42×D4C2211yescharacteristic
153C4×#117C2212yes—
154C2×C4×C4⋊C4C2214yes—
155C2×C43C2211yescharacteristic
156C23×Q8C2314yes—
157C23×Q8C2312yes—
158#557—232no—
159#557—216no—
160#557—216no—
161#556—232no—
162#556—216no—
163#552—264no—
164#552—232no—
165D4×Q8—232no—
166D4×Q8—216no—
167#541—264no—
168#541—232no—
169#533—232no—
170#533—216no—
171C2×C4⋊Q8—216no—
172C2×C4⋊Q8—28no—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2311yescharacteristic
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2318yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2318yes—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2314yes—
188C2×C4⋊Q8C2311yescharacteristic
189#529—232no—
190#529D4116yes—
191C2×#126C2318yes—
192C2×#126C2318yes—
193C2×#126C2318yes—
194C2×#126C2318yes—
195C2×#126C2312yes—
196C2×#125C2314yes—
197C2×#125C2314yes—
198C2×#125C2314yes—
199C2×#125C2318yes—
200C2×#125C2318yes—
201C2×#125C2318yes—
202C2×#125C2318yes—
203C2×#125C2318yes—
204C2×#125C2311yescharacteristic
205C2×#124C2314yes—
206C2×#124C2311yescharacteristic
207C2×#123C2318yes—
208C2×#123C2312yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2311yescharacteristic
217C2×#121C2311yescharacteristic
218#519—232no—
219C2×C4×Q8—216no—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2318yes—
233C2×C4×Q8C2318yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4C2318yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×#117C2314yes—
244C2×#117C2318yes—
245C2×#117C2318yes—
246C2×#117C2318yes—
247C2×#117C2314yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C22×C4⋊C4C2318yes—
251C22×C4⋊C4C2314yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2312yes—
255C22×C42C2314yes—
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258C22×C42C2312yes—
259C22×C42C2312yes—
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262#400C2318yes—
263#400C2318yes—
264#400C23116yes—
265#400C23116yes—
266#400C23116yes—
267#398C23116yes—
268#398C23116yes—
269#398C23116yes—
270#398C2318yes—
271#398C2318yes—
272#398C23116yes—
273#398C23116yes—
274#397C23116yes—
275#397C23116yes—
276#397C23116yes—
277#395C23116yes—
278#395C23116yes—
279#395C23116yes—
280#391C2312yes—
281#391C2312yes—
282#391C2312yes—
283#391C2318yes—
284#391C2312yes—
285#391C2314yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2318yes—
290#391C2314yes—
291#391C23116yes—
292#391C2318yes—
293#391C2318yes—
294#391C2314yes—
295#391C2312yes—
296#390C2312yes—
297#389C2312yes—
298#389C2312yes—
299#389C2314yes—
300#389C2314yes—
301#389C2318yes—
302#389C2318yes—
303#389C2314yes—
304#389C2314yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#389C2318yes—
311#389C2318yes—
312#389C2318yes—
313#389C2318yes—
314#389C2318yes—
315#389C2318yes—
316#389C2318yes—
317#389C23116yes—
318#389C23116yes—
319#388C2314yes—
320#388C2314yes—
321#388C2314yes—
322#388C2314yes—
323#387C2314yes—
324#387C2314yes—
325#387C2314yes—
326#387C2314yes—
327#387C23116yes—
328#387C23116yes—
329#387C23116yes—
330#387C23116yes—
331#387C23116yes—
332#387C23116yes—
333#387C23116yes—
334#387C23116yes—
335#387C23116yes—
336#387C23116yes—
337#386C2314yes—
338#385C23116yes—
339#385C23116yes—
340#385C23116yes—
341#385C2314yes—
342#384C2311yescharacteristic
343#384C2312yes—
344#384C2311yescharacteristic
345#384C2312yes—
346#384C2314yes—
347#384C2312yes—
348#384C2314yes—
349#384C2314yes—
350#384C2314yes—
351#384C2318yes—
352#384C2318yes—
353#383C2312yes—
354#382C2312yes—
355#382C2314yes—
356#382C2314yes—
357#382C2318yes—
358#381C23116yes—
359#381C23116yes—
360#381C2312yes—
361#380C2312yes—
362#380C2318yes—
363#380C2318yes—
364#380C2318yes—
365#380C2318yes—
366#380C2318yes—
367C4×C4⋊C4C2314yes—
368C4×C4⋊C4C2314yes—
369C4×C4⋊C4C2314yes—
370C4×C4⋊C4C2314yes—
371C4×C4⋊C4C2312yes—
372C4×C4⋊C4C2312yes—
373C4×C4⋊C4C2314yes—
374C4×C4⋊C4C2318yes—
375C4×C4⋊C4C2314yes—
376C4×C4⋊C4C2314yes—
377C4×C4⋊C4C2318yes—
378C4×C4⋊C4C2318yes—
379C4×C4⋊C4C2318yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2318yes—
383C4×C4⋊C4C2312yes—
384C4×C4⋊C4C2312yes—
385C4×C4⋊C4C2311yescharacteristic
386C4×C4⋊C4C2311yescharacteristic
387C4×C4⋊C4C2318yes—
388C4×C22⋊C4C2314yes—
389C4×C22⋊C4C2314yes—
390C4×C22⋊C4C2314yes—
391C4×C22⋊C4C2314yes—
392C4×C22⋊C4C2314yes—
393C4×C22⋊C4C2312yes—
394C4×C22⋊C4C2312yes—
395C4×C22⋊C4C2312yes—
396#376C2312yes—
397#376C2312yes—
398C2×#95C2318yes—
399C43C2312yes—
400C43C2312yes—
401C43C2311yescharacteristic
402C43C2311yescharacteristic
403C43C2312yes—
404C43C2311yescharacteristic
405C43C2311yescharacteristic
406C22×Q8—216no—
407C22×Q8—28no—
408C22×Q8—28no—
409C22×Q8—216no—
410C22×Q8—44no—
411C22×Q8—48no—
412C22×Q8C2414yes—
413C22×Q8C2412yes—
414C22×Q8C2414yes—
415C22×Q8C2414yes—
416C22×Q8C2418yes—
417C22×Q8C2411yescharacteristic
418C22×Q8C2412yes—
419C22×D4C2412yes—
420C22×D4C2411yescharacteristic
421C23×C4C2414yes—
422C23×C4C2414yes—
423C23×C4C2414yes—
424C23×C4C2418yes—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C4⋊Q8—216no—
432C4⋊Q8—28no—
433C4⋊Q8—216no—
434C4⋊Q8—216no—
435C4⋊Q8—232no—
436C4⋊Q8—216no—
437C4⋊Q8—232no—
438C4⋊Q8—28no—
439C4⋊Q8—28no—
440C4⋊Q8—216no—
441C4⋊Q8—28no—
442C4⋊Q8—24no—
443C4⋊Q8—216no—
444C4⋊Q8—44no—
445C4⋊Q8—48no—
446C4⋊Q8#4118yes—
447#126—232no—
448#126—232no—
449#126—232no—
450#126—232no—
451#126C2×D4116yes—
452#125—216no—
453#125—232no—
454#125—232no—
455#125—232no—
456#125—232no—
457#125—232no—
458#125—216no—
459#125—216no—
460#125C2×D418yes—
461#124—216no—
462#124C2×D418yes—
463#123—232no—
464#123C2×D4116yes—
465C22⋊Q8—216no—
466C22⋊Q8—216no—
467C22⋊Q8—216no—
468C22⋊Q8—216no—
469C22⋊Q8—232no—
470C22⋊Q8—232no—
471C22⋊Q8—232no—
472C22⋊Q8C2×D418yes—
473#121C2×D418yes—
474C4×Q8—216no—
475C4×Q8—232no—
476C4×Q8—232no—
477C4×Q8—216no—
478C4×Q8—216no—
479C4×Q8—28no—
480C4×Q8—216no—
481C4×Q8—28no—
482C4×Q8—28no—
483C4×Q8—216no—
484C4×Q8—28no—
485C4×Q8—216no—
486C4×Q8—216no—
487C4×Q8—216no—
488C4×Q8—216no—
489C4×Q8—28no—
490C4×Q8C2×D418yes—
491C4×D4—232no—
492C4×D4—216no—
493C4×D4—216no—
494C4×D4—28no—
495C4×D4C2×D4116yes—
496C4×D4C2×D418yes—
497#117—216no—
498#117—216no—
499#117—232no—
500#117—232no—
501#117—232no—
502#117—44no—
503#117C2×D4116yes—
504C2×C4⋊C4—28no—
505C2×C4⋊C4—216no—
506C2×C4⋊C4—216no—
507C2×C4⋊C4—216no—
508C2×C4⋊C4—232no—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C24116yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C24116yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2411yescharacteristic
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2412yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C42—216no—
567C2×C42—28no—
568C2×C42—24no—
569C2×C42—28no—
570C2×C42—28no—
571C2×C42—42no—
572C2×C42C2×D418yes—
573C2×C42C2414yes—
574C2×C42C2418yes—
575C2×C42C2418yes—
576C2×C42C2418yes—
577C2×C42C2411yescharacteristic
578C2×C42C2418yes—
579C2×C42C2412yes—
580C2×C42C2414yes—
581C2×C42C2414yes—
582C2×C42C2414yes—
583C2×C42C2414yes—
584C2×C42C2414yes—
585C2×C42C2412yes—
586C2×C42C2411yescharacteristic
587C2×C42C2411yescharacteristic
588C2×C42C2412yes—
589C2×C42C2414yes—
590C2×C42C2412yes—
591C2×C42C2412yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2412yes—
598C2×C42C2411yescharacteristic
599C2×C42C2412yes—
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2412yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2412yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2412yes—
619#95C2414yes—
620#95C24116yes—
621#95C24116yes—
622#95C24116yes—
623#95C24116yes—
624#95C24116yes—
625#95C24116yes—
626#95C24116yes—
627#95C24116yes—
628C24C2512yes—
629C24C2511yescharacteristic
630C2×Q8—24no—
631C2×Q8—28no—
632C2×Q8—216no—
633C2×Q8—28no—
634C2×Q8—24no—
635C2×Q8—28no—
636C2×Q8—28no—
637C2×Q8—216no—
638C2×Q8—24no—
639C2×Q8—28no—
640C2×Q8—24no—
641C2×Q8—216no—
642C2×Q8—24no—
643C2×Q8—28no—
644C2×Q8—24no—
645C2×Q8—44no—
646C2×Q8—48no—
647C2×Q8—432no—
648C2×Q8—464no—
649C2×Q8C22×D414yes—
650C2×Q8C2×#4118yes—
651C2×D4—28no—
652C2×D4—24no—
653C2×D4C22×D418yes—
654C2×D4C22×D414yes—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—22no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—28no—
664C22×C4—28no—
665C22×C4—216no—
666C22×C4—24no—
667C22×C4—216no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—216no—
671C22×C4—24no—
672C22×C4—28no—
673C22×C4—28no—
674C22×C4—42no—
675C22×C4—44no—
676C22×C4—48no—
677C22×C4C22×D414yes—
678C22×C4C22×D414yes—
679C22×C4C22×D414yes—
680C22×C4C22×D418yes—
681C22×C42−1+418yes—
682C22×C4C2512yes—
683C22×C4C2514yes—
684C22×C4C2514yes—
685C22×C4C2514yes—
686C22×C4C2518yes—
687C22×C4C2514yes—
688C22×C4C2514yes—
689C22×C4C2518yes—
690C22×C4C2511yescharacteristic
691C22×C4C2511yescharacteristic
692C22×C4C2512yes—
693C22×C4C2512yes—
694C22×C4C2511yescharacteristic
695C22×C4C2511yescharacteristic
696C22×C4C2512yes—
697C22×C4C2514yes—
698C22×C4C2512yes—
699C22×C4C2512yes—
700C22×C4C2511yescharacteristic
701C22×C4C2511yescharacteristic
702C22×C4C2512yes—
703C4⋊C4—28no—
704C4⋊C4—24no—
705C4⋊C4—28no—
706C4⋊C4—24no—
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—216no—
711C4⋊C4—28no—
712C4⋊C4—216no—
713C4⋊C4—216no—
714C4⋊C4—216no—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—216no—
718C4⋊C4—28no—
719C4⋊C4—216no—
720C4⋊C4—216no—
721C4⋊C4—216no—
722C4⋊C4—216no—
723C4⋊C4—216no—
724C4⋊C4—216no—
725C4⋊C4—232no—
726C4⋊C4—28no—
727C4⋊C4—216no—
728C4⋊C4—216no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—24no—
733C4⋊C4—28no—
734C4⋊C4—24no—
735C4⋊C4—216no—
736C4⋊C4—216no—
737C4⋊C4—44no—
738C4⋊C4—48no—
739C4⋊C4—416no—
740C4⋊C4C22×D418yes—
741C4⋊C4C22×D418yes—
742C4⋊C4C22×D414yes—
743C4⋊C4C22×D418yes—
744C4⋊C4C22×D414yes—
745C4⋊C4C22×D418yes—
746C4⋊C4C2×#41116yes—
747C22⋊C4—216no—
748C22⋊C4—216no—
749C22⋊C4—216no—
750C22⋊C4—216no—
751C22⋊C4—28no—
752C22⋊C4—28no—
753C22⋊C4—28no—
754C22⋊C4—44no—
755C22⋊C4C22×D418yes—
756C22⋊C4C22×D418yes—
757C22⋊C4C22×D418yes—
758C22⋊C4C22×D418yes—
759C22⋊C4C22×D418yes—
760C42—28no—
761C42—28no—
762C42—28no—
763C42—28no—
764C42—216no—
765C42—216no—
766C42—216no—
767C42—216no—
768C42—22no—
769C42—24no—
770C42—28no—
771C42—24no—
772C42—24no—
773C42—24no—
774C42—24no—
775C42—24no—
776C42—24no—
777C42—24no—
778C42—24no—
779C42—28no—
780C42—28no—
781C42—22no—
782C42—22no—
783C42—24no—
784C42—42no—
785C42C22×D414yes—
786C42C22×D414yes—
787C42C22×D414yes—
788C42C22×D414yes—
789C42C22×D418yes—
790C42C2×#4114yes—
791C422−1+418yes—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—22no—
799C23C23×D414yes—
800C23C23×D412yes—
801C23C2×2−1+414yes—
802C23C2611yescharacteristic
803Q8—216no—
804Q8—28no—
805Q8—416no—
806Q8—432no—
807Q8—48no—
808Q8—416no—
809Q8—416no—
810D4—216no—
811D4—28no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—216no—
830C2×C4—28no—
831C2×C4—216no—
832C2×C4—24no—
833C2×C4—28no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—28no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—28no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—28no—
848C2×C4—216no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—28no—
852C2×C4—24no—
853C2×C4—48no—
854C2×C4—416no—
855C2×C4—432no—
856C2×C4—416no—
857C2×C4—416no—
858C2×C4C23×D412yes—
859C2×C4C23×D412yes—
860C2×C4C23×D414yes—
861C2×C4C23×D414yes—
862C2×C4C23×D414yes—
863C2×C4C23×D412yes—
864C2×C4C23×D412yes—
865C2×C4C23×D412yes—
866C2×C4C23×D412yes—
867C2×C4C22×#4118yes—
868C2×C4C22×#4112yes—
869C2×C4C22×#4114yes—
870C2×C4C2×2−1+414yes—
871C2×C4C2×2−1+414yes—
872C2×C4C2×2−1+414yes—
873C2×C4C2×2−1+414yes—
874C2×C4C2×2−1+414yes—
875C2×C4#58512yes—
876C22—24no—
877C22—22no—
878C22—24no—
879C22—22no—
880C22—24no—
881C22—24no—
882C22—24no—
883C22—44no—
884C22—44no—
885C22#349914yes—
886C22C24×D411yescharacteristic
887C22C23×#4111yescharacteristic
888C22C22×2−1+412yes—
889C22C22×2−1+412yes—
890C22C2×#58511yescharacteristic
891C4—24no—
892C4—22no—
893C4—22no—
894C4—22no—
895C4—24no—
896C4—24no—
897C4—24no—
898C4—22no—
899C4—24no—
900C4—28no—
901C4—44no—
902C4—44no—
903C4—44no—
904C4—48no—
905C4—44no—
906C4—42no—
907C4—44no—
908C4—48no—
909C4D4×#4114yes—
910C4#349914yes—
911C4#352318yescomplemented
912C2—24no—
913C2—44no—
914C2C2×D4×#4111yescharacteristic
915C2C2×#352312yes—
916C2C2×#349911yescharacteristic
917C2C2×#349911yescharacteristic
918C2#6283712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59667C2semidirect
3. #59428C2semidirect
4. #59290C2semidirect
5. #39407C2semidirect
6. #39170C2semidirect
7. #38954C2semidirect
8. #38081C2semidirect
9. #36645C2semidirect
10. #36593C2semidirect
11. #36560C2semidirect
12. #36188C2semidirect
13. #36181C2semidirect
14. #36133C2semidirect
15. D4×C4⋊Q8C2semidirect
16. D4×C4⋊Q8C2semidirect
18. #35670C2semidirect
19. #35319C2semidirect
20. #35248C2semidirect
21. #34209C2semidirect
22. C2×C4×C4⋊Q8C2semidirect
911. C4#3523semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
#596672
#594282
#592902
#394072
#391702
#389542
#380812
#366452
#365932
#365602
#361882
#361812
#361332
D4×C4⋊Q82
#361162
#356702
#353192
#352482
#342092
C2×C4×C4⋊Q82
C4×#5292