Finite Group Databasebeta

← #7712230

Subgroups — #7712230

Order 512.

6328 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3555C212yesmaximal
2#59667C214yesmaximal, complemented
3#59428C214yesmaximal, complemented
4#45488C218yesmaximal, complemented
5#39619C212yesmaximal, complemented
6#39490C212yesmaximal, complemented
7#39407C218yesmaximal, complemented
8#39353C214yesmaximal, complemented
9#39350C214yesmaximal
10#37868C214yesmaximal, complemented
11#37635C212yesmaximal, complemented
12#37392C214yesmaximal, complemented
13#36645C211yesmaximal, characteristic, complemented
14#36645C211yesmaximal, characteristic, complemented
15#36560C211yesmaximal, characteristic, complemented
16Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
17#36188C211yesmaximal, characteristic, complemented
18#36188C212yesmaximal, complemented
19#36181C212yesmaximal, complemented
20#36180C211yesmaximal, characteristic, complemented
21#35319C212yesmaximal, complemented
22#35275C212yesmaximal, complemented
23C4×#529C211yesmaximal, characteristic
24#3555—232no—
25C2×#563C2218yes—
26C2×Q82C2212yes—
27C2×#557C2214yes—
28C2×#557C2212yes—
29C2×#556C2214yes—
30C2×#556C2212yes—
31C2×#556C2214yes—
32C2×#554C2212yes—
33C2×#552C2214yes—
34C2×#544C2214yes—
35C2×#542C2214yes—
36C2×#541C2214yes—
37C2×#541C2214yes—
38C2×#541C2218yes—
39C2×#533C2212yes—
40C2×#533C2212yes—
41C2×#529C2211yescharacteristic
42#2868C2211yescharacteristic
43#2868C2211yescharacteristic
44#2868C2211yescharacteristic
45#2868C2211yescharacteristic
46#2868C2212yes—
47#2862C2212yes—
48#2862C2212yes—
49#2859C2212yes—
50#2859C2212yes—
51#2859C2214yes—
52#2859C2212yes—
53#2857C2211yescharacteristic
54#2857C2211yescharacteristic
55#2857C2214yes—
56#2857C2214yes—
57#2857C2214yes—
58#2857C2212yes—
59#2857C2212yes—
60#2857C2212yes—
61#2817C2218yes—
62#2722C22116yes—
63#2719C22116yes—
64#2717C22116yes—
65#2713C22116yes—
66#2713C22116yes—
67#2698C22116yes—
68#2689C22116yes—
69#2689C22116yes—
70#2660C2214yes—
71#2660C2214yes—
72#2642C2214yes—
73#2634C2218yes—
74#2625C2218yes—
75#2621C2214yes—
76#2581C2218yes—
77#2568C2212yes—
78#2568C2212yes—
79#2568C2214yes—
80#2567C2212yes—
81#2567C2212yes—
82#2567C2214yes—
83#2565C2214yes—
84#2565C2214yes—
85#2552C2214yes—
86#2552C2218yes—
87#2551C2218yes—
88#2551C2214yes—
89#2551C2218yes—
90#2547C2214yes—
91#2547C2218yes—
92#2546C2214yes—
93#2506C2218yes—
94#2506C2218yes—
95#2506C2218yes—
96#2506C2218yes—
97#2503C2214yes—
98#2502C2214yes—
99#2499C2214yes—
100#2499C2214yes—
101#2499C2214yes—
102#2499C2214yes—
103#2496C2218yes—
104#2496C2218yes—
105#2496C2218yes—
106#2496C2218yes—
107#2496C2218yes—
108#2496C2218yes—
109#2486C2218yes—
110#2478C22116yes—
111#2462C22116yes—
112#2453C2218yes—
113#2451C2218yes—
114#2447C2218yes—
115#2446C2218yes—
116#2440C2218yes—
117#2440C2218yes—
118#2440C2218yes—
119#2365C2214yes—
120#2365C2218yes—
121#2365C2214yes—
122Q8×C4⋊C4C2214yes—
123D4×C4⋊C4C2214yes—
124#2344C2218yes—
125#2327C2214yes—
126#2317C2214yes—
127C4×C4⋊Q8C2214yes—
128C4×C4⋊Q8C2214yes—
129C4×C4⋊Q8C2212yes—
130C4×C4⋊Q8C2211yescharacteristic
131C4×C4⋊Q8C2211yescharacteristic
132C4×C4⋊Q8C2214yes—
133C4×C4⋊Q8C2212yes—
134C4×C4⋊Q8C2212yes—
135C4×#125C2212yes—
136C4×#126C2214yes—
137C4×#124C2212yes—
138C4×C22⋊Q8C2212yes—
139C4×#123C2214yes—
140C4×#121C2212yes—
141#2298C2212yes—
142#2295C2211yescharacteristic
143#2293C2211yescharacteristic
144#2290C2212yes—
145#2285C2212yes—
146#2285C2214yes—
147#2285C2212yes—
148#2285C2212yes—
149C2×#384C2212yes—
150#2283C2211yescharacteristic
151C42×Q8C2211yescharacteristic
152C42×D4C2211yescharacteristic
153C42×D4C2212yes—
154C4×#117C2212yes—
155C2×C43C2211yescharacteristic
156#563—264no—
157Q82—216no—
158#557—232no—
159#557—216no—
160#556—232no—
161#556—232no—
162#556—216no—
163#554—216no—
164#552—232no—
165#544—232no—
166#542—232no—
167#541—264no—
168#541—232no—
169#541—232no—
170#533—216no—
171#533—216no—
172C2×C4⋊Q8C2311yescharacteristic
173C2×C4⋊Q8C2311yescharacteristic
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2312yes—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2318yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2318yes—
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2314yes—
187C2×C4⋊Q8C2318yes—
188#529D4116yes—
189C2×#126C2318yes—
190C2×#126C2318yes—
191C2×#126C2318yes—
192C2×#126C2318yes—
193C2×#126C2318yes—
194C2×#126C2318yes—
195C2×#126C2312yes—
196C2×#125C2314yes—
197C2×#125C2314yes—
198C2×#125C2314yes—
199C2×#125C2318yes—
200C2×#125C2318yes—
201C2×#125C2318yes—
202C2×#125C2314yes—
203C2×#125C2318yes—
204C2×#125C2318yes—
205C2×#125C2311yescharacteristic
206C2×#124C2314yes—
207C2×#124C2318yes—
208C2×#124C2311yescharacteristic
209C2×#123C2318yes—
210C2×#123C2312yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2318yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2314yes—
243C2×#117C2318yes—
244C2×#117C2314yes—
245C2×#117C2314yes—
246C2×#117C2312yes—
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2318yes—
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2312yes—
252C22×C42C2312yes—
253C22×C42C2312yes—
254C22×C42C2311yescharacteristic
255#400C2318yes—
256#400C2318yes—
257#400C23116yes—
258#400C23116yes—
259#400C23116yes—
260#400C23116yes—
261#398C23116yes—
262#398C23116yes—
263#398C23116yes—
264#398C23116yes—
265#398C23116yes—
266#398C23116yes—
267#397C23116yes—
268#397C23116yes—
269#397C23116yes—
270#397C23116yes—
271#397C23116yes—
272#395C2318yes—
273#395C2318yes—
274#395C23116yes—
275#395C23116yes—
276#395C23116yes—
277#391C2312yes—
278#391C2312yes—
279#391C2314yes—
280#391C2312yes—
281#391C2314yes—
282#391C2312yes—
283#391C2318yes—
284#391C2318yes—
285#391C2318yes—
286#391C2314yes—
287#391C2314yes—
288#391C2318yes—
289#391C2318yes—
290#391C23116yes—
291#391C2312yes—
292#390C2312yes—
293#389C2312yes—
294#389C2312yes—
295#389C2314yes—
296#389C2314yes—
297#389C2318yes—
298#389C2318yes—
299#389C2314yes—
300#389C2318yes—
301#389C2318yes—
302#389C2318yes—
303#389C2318yes—
304#389C2314yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C23116yes—
310#389C23116yes—
311#389C2318yes—
312#389C2318yes—
313#389C2318yes—
314#389C2318yes—
315#388C2314yes—
316#388C2314yes—
317#388C2314yes—
318#388C2314yes—
319#387C2314yes—
320#387C2314yes—
321#387C2314yes—
322#387C2314yes—
323#387C23116yes—
324#387C23116yes—
325#387C23116yes—
326#387C23116yes—
327#387C23116yes—
328#387C23116yes—
329#387C23116yes—
330#387C23116yes—
331#386C2314yes—
332#385C23116yes—
333#385C23116yes—
334#385C2314yes—
335#384C2312yes—
336#384C2311yescharacteristic
337#384C2312yes—
338#384C2312yes—
339#384C2314yes—
340#384C2311yescharacteristic
341#384C2314yes—
342#384C2314yes—
343#384C2312yes—
344#384C2314yes—
345#384C2314yes—
346#384C2312yes—
347#384C2314yes—
348#384C2314yes—
349#384C2318yes—
350#384C2318yes—
351#383C2312yes—
352#382C2312yes—
353#382C2314yes—
354#382C2314yes—
355#382C2314yes—
356#382C2314yes—
357#382C2318yes—
358#381C2312yes—
359#381C23116yes—
360#380C2318yes—
361#380C2318yes—
362#380C2318yes—
363#380C2314yes—
364#380C2318yes—
365#380C2314yes—
366#380C2318yes—
367#380C2312yes—
368#380C2318yes—
369C4×C4⋊C4C2314yes—
370C4×C4⋊C4C2314yes—
371C4×C4⋊C4C2314yes—
372C4×C4⋊C4C2312yes—
373C4×C4⋊C4C2312yes—
374C4×C4⋊C4C2314yes—
375C4×C4⋊C4C2318yes—
376C4×C4⋊C4C2314yes—
377C4×C4⋊C4C2314yes—
378C4×C4⋊C4C2318yes—
379C4×C4⋊C4C2318yes—
380C4×C4⋊C4C2318yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2312yes—
383C4×C4⋊C4C2312yes—
384C4×C4⋊C4C2311yescharacteristic
385C4×C4⋊C4C2311yescharacteristic
386C4×C4⋊C4C2318yes—
387C4×C22⋊C4C2314yes—
388C4×C22⋊C4C2314yes—
389C4×C22⋊C4C2314yes—
390C4×C22⋊C4C2314yes—
391C4×C22⋊C4C2314yes—
392C4×C22⋊C4C2312yes—
393C4×C22⋊C4C2312yes—
394C4×C22⋊C4C2312yes—
395#376C2312yes—
396#376C2312yes—
397C43C2312yes—
398C43C2312yes—
399C43C2312yes—
400C43C2311yescharacteristic
401C43C2311yescharacteristic
402C43C2311yescharacteristic
403C43C2311yescharacteristic
404C22×Q8C2412yes—
405C22×Q8C2412yes—
406C22×Q8C2414yes—
407C22×Q8C2411yescharacteristic
408C22×Q8C2414yes—
409C22×Q8C2414yes—
410C22×Q8C2418yes—
411C22×D4C2411yescharacteristic
412C22×D4C2412yes—
413C23×C4C2414yes—
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2418yes—
420C23×C4C2411yescharacteristic
421C4⋊Q8—216no—
422C4⋊Q8—232no—
423C4⋊Q8—216no—
424C4⋊Q8—232no—
425C4⋊Q8—28no—
426C4⋊Q8—28no—
427C4⋊Q8—28no—
428C4⋊Q8—28no—
429C4⋊Q8—216no—
430C4⋊Q8—24no—
431C4⋊Q8—24no—
432C4⋊Q8—28no—
433C4⋊Q8—216no—
434C4⋊Q8—48no—
435C4⋊Q8—48no—
436C4⋊Q8—416no—
437#126—232no—
438#126—232no—
439#126—232no—
440#126—232no—
441#126—232no—
442#126—232no—
443#126C2×D4116yes—
444#125—232no—
445#125—232no—
446#125—232no—
447#125—216no—
448#125—232no—
449#125—232no—
450#125—216no—
451#125—216no—
452#125—216no—
453#125C2×D418yes—
454#124—216no—
455#124—232no—
456#124C2×D418yes—
457#123—232no—
458#123C2×D4116yes—
459C22⋊Q8—216no—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—216no—
463C22⋊Q8—216no—
464C22⋊Q8—216no—
465C22⋊Q8—216no—
466C22⋊Q8—232no—
467C22⋊Q8—232no—
468C22⋊Q8—232no—
469C22⋊Q8C2×D418yes—
470#121C2×D418yes—
471C4×Q8—216no—
472C4×Q8—232no—
473C4×Q8—216no—
474C4×Q8—216no—
475C4×Q8—216no—
476C4×Q8—28no—
477C4×Q8—216no—
478C4×Q8—216no—
479C4×Q8—28no—
480C4×Q8—216no—
481C4×Q8—216no—
482C4×Q8—28no—
483C4×Q8C2×D418yes—
484C4×D4—216no—
485C4×D4—28no—
486C4×D4—48no—
487C4×D4C2×D4116yes—
488C4×D4C2×D418yes—
489#117—216no—
490#117—216no—
491#117—216no—
492#117—232no—
493#117—28no—
494#117C2×D4116yes—
495C2×C4⋊C4—216no—
496C2×C4⋊C4—416no—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C24116yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C24116yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2411yescharacteristic
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2411yescharacteristic
542C2×C4⋊C4C2412yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2412yes—
558C2×C42—24no—
559C2×C42—28no—
560C2×C42—24no—
561C2×C42—28no—
562C2×C42—44no—
563C2×C42C2×D418yes—
564C2×C42C2418yes—
565C2×C42C2414yes—
566C2×C42C2414yes—
567C2×C42C2418yes—
568C2×C42C2418yes—
569C2×C42C2412yes—
570C2×C42C2414yes—
571C2×C42C2418yes—
572C2×C42C2414yes—
573C2×C42C2412yes—
574C2×C42C2412yes—
575C2×C42C2412yes—
576C2×C42C2411yescharacteristic
577C2×C42C2412yes—
578C2×C42C2411yescharacteristic
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2412yes—
582C2×C42C2412yes—
583C2×C42C2414yes—
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2411yescharacteristic
587C2×C42C2412yes—
588C2×C42C2411yescharacteristic
589C2×C42C2411yescharacteristic
590C2×C42C2411yescharacteristic
591C2×C42C2411yescharacteristic
592C2×C42C2412yes—
593C2×C42C2411yescharacteristic
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2414yes—
598#95C2412yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2412yes—
604#95C2414yes—
605#95C2418yes—
606#95C24116yes—
607#95C2418yes—
608#95C24116yes—
609#95C2418yes—
610#95C2418yes—
611#95C24116yes—
612#95C24116yes—
613#95C24116yes—
614#95C24116yes—
615#95C24116yes—
616#95C24116yes—
617C24C2512yes—
618C24C2511yescharacteristic
619C2×Q8—24no—
620C2×Q8—24no—
621C2×Q8—28no—
622C2×Q8—28no—
623C2×Q8—28no—
624C2×Q8—216no—
625C2×Q8—24no—
626C2×Q8—24no—
627C2×Q8—24no—
628C2×Q8—24no—
629C2×Q8—24no—
630C2×Q8—216no—
631C2×Q8—48no—
632C2×Q8—48no—
633C2×Q8—416no—
634C2×Q8C22×D414yes—
635C2×D4—24no—
636C2×D4—44no—
637C2×D4C22×D414yes—
638C2×D4C22×D418yes—
639C22×C4—24no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—216no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—28no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—28no—
651C22×C4—24no—
652C22×C4—28no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—416no—
656C22×C4C22×D414yes—
657C22×C4C22×D414yes—
658C22×C4C22×D418yes—
659C22×C4C22×D414yes—
660C22×C4C2512yes—
661C22×C4C2514yes—
662C22×C4C2514yes—
663C22×C4C2514yes—
664C22×C4C2518yes—
665C22×C4C2514yes—
666C22×C4C2514yes—
667C22×C4C2518yes—
668C22×C4C2514yes—
669C22×C4C2511yescharacteristic
670C22×C4C2512yes—
671C22×C4C2512yes—
672C22×C4C2511yescharacteristic
673C22×C4C2512yes—
674C22×C4C2511yescharacteristic
675C22×C4C2511yescharacteristic
676C22×C4C2512yes—
677C22×C4C2512yes—
678C22×C4C2511yescharacteristic
679C22×C4C2511yescharacteristic
680C22×C4C2512yes—
681C4⋊C4—24no—
682C4⋊C4—28no—
683C4⋊C4—216no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—24no—
687C4⋊C4—28no—
688C4⋊C4—216no—
689C4⋊C4—28no—
690C4⋊C4—28no—
691C4⋊C4—28no—
692C4⋊C4—28no—
693C4⋊C4—216no—
694C4⋊C4—216no—
695C4⋊C4—216no—
696C4⋊C4—216no—
697C4⋊C4—216no—
698C4⋊C4—28no—
699C4⋊C4—28no—
700C4⋊C4—28no—
701C4⋊C4—216no—
702C4⋊C4—216no—
703C4⋊C4—216no—
704C4⋊C4—28no—
705C4⋊C4—24no—
706C4⋊C4—28no—
707C4⋊C4—24no—
708C4⋊C4—216no—
709C4⋊C4—216no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—216no—
713C4⋊C4—28no—
714C4⋊C4—216no—
715C4⋊C4—28no—
716C4⋊C4—416no—
717C4⋊C4—44no—
718C4⋊C4—48no—
719C4⋊C4—48no—
720C4⋊C4—416no—
721C4⋊C4C22×D418yes—
722C4⋊C4C22×D418yes—
723C4⋊C4C22×D414yes—
724C4⋊C4C22×D418yes—
725C4⋊C4C22×D414yes—
726C4⋊C4C22×D418yes—
727C22⋊C4—28no—
728C22⋊C4—216no—
729C22⋊C4—28no—
730C22⋊C4—216no—
731C22⋊C4—216no—
732C22⋊C4—216no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—44no—
736C22⋊C4—44no—
737C22⋊C4C22×D418yes—
738C22⋊C4C22×D418yes—
739C22⋊C4C22×D418yes—
740C22⋊C4C22×D418yes—
741C22⋊C4C22×D418yes—
742C42—216no—
743C42—28no—
744C42—28no—
745C42—216no—
746C42—216no—
747C42—216no—
748C42—24no—
749C42—22no—
750C42—24no—
751C42—24no—
752C42—24no—
753C42—24no—
754C42—28no—
755C42—22no—
756C42—24no—
757C42—24no—
758C42—28no—
759C42—24no—
760C42—24no—
761C42—28no—
762C42—42no—
763C42—42no—
764C42C22×D414yes—
765C42C22×D414yes—
766C42C22×D414yes—
767C42C22×D414yes—
768C42C22×D418yes—
769C422−1+414yes—
770C422−1+414yes—
771C422−1+418yes—
772C23—22no—
773C23—24no—
774C23—22no—
775C23—21no—
776C23—22no—
777C23—21no—
778C23—22no—
779C23—24no—
780C23C23×D412yes—
781C23C23×D414yes—
782C23C2611yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—48no—
786Q8—416no—
787Q8—88no—
788Q8—88no—
789Q8—816no—
790D4—28no—
791D4—48no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—28no—
806C2×C4—216no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—216no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—216no—
830C2×C4—28no—
831C2×C4—44no—
832C2×C4—48no—
833C2×C4—48no—
834C2×C4—416no—
835C2×C4—816no—
836C2×C4C23×D412yes—
837C2×C4C23×D414yes—
838C2×C4C23×D414yes—
839C2×C4C23×D414yes—
840C2×C4C23×D412yes—
841C2×C4C23×D412yes—
842C2×C4C23×D412yes—
843C2×C4C23×D412yes—
844C2×C4C23×D412yes—
845C2×C4C2×2−1+414yes—
846C2×C4C2×2−1+414yes—
847C2×C4C2×2−1+412yes—
848C2×C4C2×2−1+412yes—
849C2×C4C2×2−1+414yes—
850C2×C4C2×2−1+414yes—
851C2×C4C2×2−1+414yes—
852C2×C4#58514yes—
853C22—24no—
854C22—22no—
855C22—22no—
856C22—24no—
857C22—22no—
858C22—24no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—44no—
863C22C24×D411yescharacteristic
864C22C22×2−1+411yescharacteristic
865C22C22×2−1+412yes—
866C22C22×2−1+411yescharacteristic
867C22C2×#58512yes—
868C4—22no—
869C4—22no—
870C4—24no—
871C4—24no—
872C4—22no—
873C4—22no—
874C4—24no—
875C4—24no—
876C4—24no—
877C4—42no—
878C4—44no—
879C4—44no—
880C4—44no—
881C4—48no—
882C4—44no—
883C4—48no—
884C4—44no—
885C4—44no—
886C4#349914yes—
887C4#349914yes—
888C4#355518yescomplemented
889C2—42no—
890C2—44no—
891C2C2×#355512yes—
892C2C2×#349911yescharacteristic
893C2C2×#349911yescharacteristic
894C2#6281211yescharacteristic
895C2#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. #45488C2semidirect
5. #39619C2semidirect
6. #39490C2semidirect
7. #39407C2semidirect
8. #39353C2semidirect
10. #37868C2semidirect
11. #37635C2semidirect
12. #37392C2semidirect
13. #36645C2semidirect
14. #36645C2semidirect
15. #36560C2semidirect
16. Q8×C4⋊Q8C2semidirect
17. #36188C2semidirect
18. #36188C2semidirect
19. #36181C2semidirect
20. #36180C2semidirect
21. #35319C2semidirect
22. #35275C2semidirect
888. C4#3555semidirect

Maximal subgroups

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

subgroupindex
C2×#35552
#596672
#594282
#454882
#396192
#394902
#394072
#393532
#393502
#378682
#376352
#373922
#366452
#365602
Q8×C4⋊Q82
#361882
#361812
#361802
#353192
#352752
C4×#5292