Finite Group Databasebeta

← #7670542

Subgroups — #7670542

Order 512.

5128 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59663C214yesmaximal, complemented
2#59425C214yesmaximal, complemented
3#59285C214yesmaximal
4#59262C211yesmaximal, characteristic, complemented
5#59248C211yesmaximal, characteristic, complemented
6#59071C212yesmaximal, complemented
7#39223C214yesmaximal, complemented
8#39007C214yesmaximal, complemented
9#38143C218yesmaximal, complemented
10#36625C211yesmaximal, characteristic
11#36577C212yesmaximal, complemented
12#36545C212yesmaximal, complemented
13#36177C212yesmaximal, complemented
14#36167C214yesmaximal
15#36133C212yesmaximal, complemented
16#36130C214yesmaximal
17#35434C214yesmaximal, complemented
18#35087C214yesmaximal, complemented
19#34235C214yesmaximal, complemented
20C2×C4×C22⋊Q8C212yesmaximal
21C2×#557C2212yescomplemented
22C2×#533C2214yes—
23C2×#533C2211yescharacteristic
24C22×C22⋊Q8C2212yes—
25C22×C4×Q8C2212yes—
26C23×C42C2211yescharacteristic
27#2857C2214yes—
28#2857C2212yes—
29#2857C2212yes—
30#2855C2214yes—
31#2855C2214yes—
32#2855C2214yes—
33#2851C2214yes—
34#2851C2214yes—
35#2848C2214yes—
36#2802C2218yescomplemented
37#2789C2218yescomplemented
38#2789C2214yescomplemented
39#2771C2214yes—
40#2769C2214yescomplemented
41#2765C2218yes—
42#2764C2214yes—
43#2758C2218yescomplemented
44#2755C2218yescomplemented
45#2719C2218yescomplemented
46#2655C2218yescomplemented
47#2655C2218yescomplemented
48#2611C2214yes—
49#2605C2214yescomplemented
50#2599C2214yes—
51#2588C2218yescomplemented
52#2584C2214yescomplemented
53#2584C2214yescomplemented
54#2582C2214yescomplemented
55#2582C2211yescharacteristic, complemented
56#2582C2211yescharacteristic, complemented
57#2581C2214yescomplemented
58#2577C2218yes—
59#2571C2211yescharacteristic, complemented
60#2568C2214yescomplemented
61#2568C2212yescomplemented
62#2556C2218yes—
63#2551C2211yescharacteristic, complemented
64#2549C2218yes—
65#2546C2212yescomplemented
66#2533C2218yescomplemented
67#2530C2218yes—
68#2514C2214yescomplemented
69#2514C2214yescomplemented
70#2514C2214yescomplemented
71#2509C2214yescomplemented
72#2506C2214yescomplemented
73#2506C2214yescomplemented
74#2505C2218yes—
75#2503C2214yes—
76#2495C2214yes—
77#2494C2214yes—
78#2493C2218yes—
79#2493C2218yes—
80#2493C2218yes—
81#2493C2218yes—
82#2492C2214yes—
83#2489C2214yes—
84#2483C2214yes—
85#2475C2218yes—
86#2473C2218yes—
87#2473C2218yes—
88#2473C2218yes—
89#2465C2218yes—
90#2462C2218yescomplemented
91#2462C2218yescomplemented
92#2453C2214yescomplemented
93#2453C2214yescomplemented
94#2453C2218yescomplemented
95#2451C2214yescomplemented
96#2446C2214yescomplemented
97#2446C2214yescomplemented
98#2446C2214yescomplemented
99#2442C2214yes—
100#2442C2218yes—
101#2440C2214yes—
102#2438C2218yes—
103#2438C2218yes—
104#2437C2214yes—
105#2434C2214yes—
106#2429C2214yes—
107#2429C2214yes—
108#2423C2214yes—
109#2421C2214yes—
110#2365C2214yescomplemented
111#2365C2214yescomplemented
112#2365C2212yescomplemented
113#2365C2214yescomplemented
114#2365C2214yescomplemented
115#2360C2214yes—
116#2360C2214yes—
117#2360C2218yes—
118#2360C2218yes—
119#2356C2214yescomplemented
120#2356C2214yescomplemented
121#2355C2212yescomplemented
122#2351C2214yescomplemented
123#2351C2214yescomplemented
124Q8×C4⋊C4C2212yescomplemented
125#2344C2214yes—
126#2343C2218yes—
127#2343C2218yes—
128#2342C2218yes—
129Q8×C22⋊C4C2214yes—
130#2336C2214yescomplemented
131#2336C2218yescomplemented
132#2336C2218yescomplemented
133#2320C2218yescomplemented
134C4×C22⋊Q8C2212yes—
135C4×C22⋊Q8C2214yes—
136C4×C22⋊Q8C2214yes—
137C4×C22⋊Q8C2214yes—
138C4×C22⋊Q8C2214yes—
139C4×C22⋊Q8C2212yes—
140C4×C22⋊Q8C2212yes—
141C4×C22⋊Q8C2214yes—
142C4×C22⋊Q8C2214yes—
143C4×C22⋊Q8C2212yes—
144C4×C22⋊Q8C2212yes—
145C4×C22⋊Q8C2214yes—
146C4×C22⋊Q8C2212yes—
147C4×C22⋊Q8C2212yes—
148C4×C22⋊Q8C2212yes—
149C4×C22⋊Q8C2214yes—
150#2296C2212yes—
151C2×#391C2212yes—
152C2×#389C2212yes—
153C2×#387C2214yes—
154C2×#385C2214yes—
155#2285C2211yescharacteristic
156#2283C2214yes—
157#2280C2212yes—
158C2×#380C2212yes—
159#2276C2214yescomplemented
160C2×C4×C4⋊C4C2214yes—
161C2×C4×C4⋊C4C2212yes—
162C2×C4×C22⋊C4C2214yes—
163C23×Q8C2312yes—
164C24×C4C2312yes—
165C24×C4C2311yescharacteristic
166#557—48no—
167#533—232no—
168#533—44no—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2314yes—
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2314yes—
173C2×#125C2318yes—
174C2×#125C2314yes—
175C2×#125C2314yes—
176C2×#125C2312yes—
177C2×#125C2318yes—
178C2×C22⋊Q8—216no—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2312yes—
182C2×C22⋊Q8C2318yes—
183C2×C22⋊Q8C2312yes—
184C2×C22⋊Q8C2312yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2312yes—
189C2×C4×Q8—48no—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2318yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2314yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2314yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2314yes—
203C2×#117C2318yes—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2314yes—
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2314yes—
211C22×C4⋊C4C2314yes—
212C22×C22⋊C4C2314yes—
213C22×C22⋊C4C2314yes—
214C22×C42—44no—
215C22×C42C2314yes—
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2314yes—
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224#401C2318yes—
225#401C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2314yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#399C2314yes—
240#398C2318yes—
241#398C2314yes—
242#398C2314yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#397C2314yes—
252#397C2318yes—
253#397C2314yes—
254#396C2318yes—
255#395C2318yes—
256#395C2318yes—
257#395C2318yes—
258#395C2314yes—
259#393C2314yes—
260#391C2314yes—
261#391C2312yes—
262#391C2314yes—
263#391C2314yes—
264#391C2314yes—
265#391C2314yes—
266#391C2318yes—
267#391C2318yes—
268#391C2318yes—
269#391C2312yes—
270#391C2314yes—
271#391C2318yes—
272#391C2314yes—
273#391C2314yes—
274#391C2314yes—
275#391C2314yes—
276#391C2314yes—
277#391C2312yes—
278#391C2312yes—
279#391C2314yes—
280#389C2314yes—
281#389C2318yes—
282#389C2318yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2312yes—
287#389C2314yes—
288#389C2318yes—
289#389C2314yes—
290#389C2318yes—
291#389C2312yes—
292#389C2318yes—
293#389C2314yes—
294#389C2318yes—
295#389C2318yes—
296#389C2318yes—
297#389C2318yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2318yes—
305#389C2312yes—
306#389C2312yes—
307#389C2314yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#387C2314yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2314yes—
340#387C2314yes—
341#387C2314yes—
342#387C2314yes—
343#387C2314yes—
344#387C2314yes—
345#387C2314yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2314yes—
353#385C2318yes—
354#385C2318yes—
355#385C2314yes—
356#385C2318yes—
357#385C2314yes—
358#385C2314yes—
359#385C2314yes—
360#385C2314yes—
361#385C2314yes—
362#385C2314yes—
363#384C2311yescharacteristic
364#384C2311yescharacteristic
365#384C2314yes—
366#383C2318yes—
367#383C2318yes—
368#383C2318yes—
369#383C2314yes—
370#382C2318yes—
371#382C2314yes—
372#382C2314yes—
373#382C2318yes—
374#382C2314yes—
375#382C2312yes—
376#381C2318yes—
377#381C2318yes—
378#381C2314yes—
379#381C2318yes—
380#380C2314yes—
381#380C2314yes—
382#380C2314yes—
383#380C2314yes—
384#380C2312yes—
385#380C2314yes—
386#380C2314yes—
387#380C2318yes—
388#380C2318yes—
389#380C2312yes—
390#380C2312yes—
391#380C2314yes—
392#380C2312yes—
393#379C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430#376C2318yes—
431#376C2314yes—
432C2×#95C2314yes—
433C2×#95C2314yes—
434C2×#95C2314yes—
435C2×#95C2314yes—
436C2×#95C2314yes—
437C25C2411yescharacteristic
438C22×Q8—28no—
439C22×Q8—28no—
440C22×Q8—44no—
441C22×Q8C2414yes—
442C22×Q8C2412yes—
443C22×Q8C2414yes—
444C22×Q8C2414yes—
445C22×Q8C2412yes—
446C23×C4—24no—
447C23×C4—28no—
448C23×C4—28no—
449C23×C4—42no—
450C23×C4—44no—
451C23×C4—42no—
452C23×C4C2414yes—
453C23×C4C2411yescharacteristic
454C23×C4C2412yes—
455C23×C4C2414yes—
456C23×C4C2414yes—
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2414yes—
465C23×C4C2411yescharacteristic
466C4⋊Q8—216no—
467C4⋊Q8—216no—
468C4⋊Q8—28no—
469C4⋊Q8—48no—
470#125—232no—
471#125—48no—
472#125—44no—
473#125—48no—
474#125—416no—
475C22⋊Q8—28no—
476C22⋊Q8—28no—
477C22⋊Q8—216no—
478C22⋊Q8—216no—
479C22⋊Q8—216no—
480C22⋊Q8—28no—
481C22⋊Q8—216no—
482C22⋊Q8—232no—
483C22⋊Q8—48no—
484C22⋊Q8#41116yes—
485C4×Q8—216no—
486C4×Q8—216no—
487C4×Q8—232no—
488C4×Q8—28no—
489C4×Q8—28no—
490C4×Q8—48no—
491C4×Q8—48no—
492C4×Q8—48no—
493C4×Q8—44no—
494C4×Q8—44no—
495C4×Q8—48no—
496C4×Q8—48no—
497C4×Q8—48no—
498#117—232no—
499#117—44no—
500#117—44no—
501C2×C4⋊C4—28no—
502C2×C4⋊C4—216no—
503C2×C4⋊C4—28no—
504C2×C4⋊C4—48no—
505C2×C4⋊C4—44no—
506C2×C4⋊C4—48no—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2412yes—
549C2×C22⋊C4—216no—
550C2×C22⋊C4—216no—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C42—216no—
564C2×C42—28no—
565C2×C42—24no—
566C2×C42—48no—
567C2×C42—44no—
568C2×C42—44no—
569C2×C42—42no—
570C2×C42—44no—
571C2×C42—44no—
572C2×C42C2418yes—
573C2×C42C2418yes—
574C2×C42C2414yes—
575C2×C42C2414yes—
576C2×C42C2414yes—
577C2×C42C2414yes—
578C2×C42C2414yes—
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2412yes—
582C2×C42C2412yes—
583C2×C42C2414yes—
584C2×C42C2411yescharacteristic
585C2×C42C2414yes—
586C2×C42C2414yes—
587C2×C42C2418yes—
588C2×C42C2414yes—
589C2×C42C2414yes—
590C2×C42C2418yes—
591C2×C42C2411yescharacteristic
592C2×C42C2412yes—
593C2×C42C2411yescharacteristic
594C2×C42C2412yes—
595C2×C42C2411yescharacteristic
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2414yes—
635#95C2418yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640C24—24no—
641C24—24no—
642C24—41no—
643C24—41no—
644C242−1+414yes—
645C24C2511yescharacteristic
646C24C2512yes—
647C2×Q8—216no—
648C2×Q8—28no—
649C2×Q8—28no—
650C2×Q8—24no—
651C2×Q8—24no—
652C2×Q8—24no—
653C2×Q8—28no—
654C2×Q8—24no—
655C2×Q8—28no—
656C2×Q8—28no—
657C2×Q8—24no—
658C2×Q8—44no—
659C2×Q8—44no—
660C2×Q8—432no—
661C2×Q8C2×#4118yes—
662C22×C4—22no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—22no—
667C22×C4—24no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—28no—
671C22×C4—24no—
672C22×C4—28no—
673C22×C4—28no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—41no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—432no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—416no—
704C22×C4C2×#4118yes—
705C22×C42−1+418yes—
706C22×C4C2514yes—
707C22×C4C2514yes—
708C22×C4C2514yes—
709C22×C4C2512yes—
710C22×C4C2512yes—
711C22×C4C2514yes—
712C22×C4C2514yes—
713C22×C4C2514yes—
714C22×C4C2518yes—
715C22×C4C2514yes—
716C22×C4C2514yes—
717C22×C4C2512yes—
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2511yescharacteristic
721C22×C4C2512yes—
722C22×C4C2511yescharacteristic
723C22×C4C2512yes—
724C4⋊C4—28no—
725C4⋊C4—24no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—216no—
730C4⋊C4—216no—
731C4⋊C4—216no—
732C4⋊C4—216no—
733C4⋊C4—216no—
734C4⋊C4—216no—
735C4⋊C4—28no—
736C4⋊C4—24no—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—24no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—28no—
746C4⋊C4—216no—
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—42no—
755C4⋊C4—42no—
756C4⋊C4—44no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—48no—
763C4⋊C4—48no—
764C4⋊C4C2×#41116yes—
765C4⋊C4C2×#4118yes—
766C22⋊C4—28no—
767C22⋊C4—216no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—216no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4C2×#41116yes—
778C42—28no—
779C42—28no—
780C42—28no—
781C42—28no—
782C42—216no—
783C42—216no—
784C42—24no—
785C42—24no—
786C42—24no—
787C42—24no—
788C42—22no—
789C42—28no—
790C42—28no—
791C42—28no—
792C42—41no—
793C42—41no—
794C42—42no—
795C42—42no—
796C42—44no—
797C42—44no—
798C42—44no—
799C42—48no—
800C42—48no—
801C42H(5,𝔽2)14yes—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—21no—
808C23—22no—
809C23—21no—
810C23—216no—
811C23—44no—
812C23—48no—
813C23—44no—
814C23—44no—
815C23C22×#4114yes—
816C23C2×2−1+412yes—
817C23C2×2−1+414yes—
818C23C2×2−1+414yes—
819C23C2611yescharacteristic
820Q8—216no—
821Q8—416no—
822Q8—416no—
823Q8—416no—
824Q8—48no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—21no—
838C2×C4—216no—
839C2×C4—216no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—28no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—28no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—48no—
872C2×C4—416no—
873C2×C4—48no—
874C2×C4—48no—
875C2×C4—48no—
876C2×C4—48no—
877C2×C4—416no—
878C2×C4—44no—
879C2×C4—416no—
880C2×C4—48no—
881C2×C4—88no—
882C2×C4C22×#4114yes—
883C2×C4C22×#4118yes—
884C2×C4C22×#4118yes—
885C2×C4C22×#4114yes—
886C2×C4C2×H(5,𝔽2)12yes—
887C2×C4C2×H(5,𝔽2)14yes—
888C2×C4C2×2−1+414yes—
889C2×C4C2×2−1+414yes—
890C2×C4#58512yes—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—24no—
897C22—24no—
898C22—22no—
899C22—416no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22#352318yes—
904C22C23×#4112yes—
905C22C22×H(5,𝔽2)11yescharacteristic
906C22C22×2−1+412yes—
907C22C22×2−1+411yescharacteristic
908C22C2×#58511yescharacteristic
909C4—24no—
910C4—24no—
911C4—28no—
912C4—22no—
913C4—22no—
914C4—28no—
915C4—42no—
916C4—44no—
917C4—48no—
918C4—44no—
919C4—44no—
920C4—42no—
921C4—44no—
922C4—44no—
923C4—44no—
924C4—44no—
925C4—44no—
926C4#352018yes—
927C2—28no—
928C2—42no—
929C2#41211yescharacteristic
930C2C2×#352012yes—
931C2C2×#352312yes—
932C2#6281911yescharacteristic
933C2#6283711yescharacteristic
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. #59663C2semidirect
2. #59425C2semidirect
4. #59262C2semidirect
5. #59248C2semidirect
6. #59071C2semidirect
7. #39223C2semidirect
8. #39007C2semidirect
9. #38143C2semidirect
11. #36577C2semidirect
12. #36545C2semidirect
13. #36177C2semidirect
15. #36133C2semidirect
17. #35434C2semidirect
18. #35087C2semidirect
19. #34235C2semidirect
21. C2×#557C22semidirect
36. #2802C22semidirect
37. #2789C22semidirect
38. #2789C22semidirect
40. #2769C22semidirect
43. #2758C22semidirect
44. #2755C22semidirect
45. #2719C22semidirect
46. #2655C22semidirect
47. #2655C22semidirect
49. #2605C22semidirect
51. #2588C22semidirect
52. #2584C22semidirect
53. #2584C22semidirect
54. #2582C22semidirect
55. #2582C22semidirect
56. #2582C22semidirect
57. #2581C22semidirect
59. #2571C22semidirect
60. #2568C22semidirect
61. #2568C22semidirect
63. #2551C22semidirect
65. #2546C22semidirect
66. #2533C22semidirect
68. #2514C22semidirect
69. #2514C22semidirect
70. #2514C22semidirect
71. #2509C22semidirect
72. #2506C22semidirect
73. #2506C22semidirect
90. #2462C22semidirect
91. #2462C22semidirect
92. #2453C22semidirect
93. #2453C22semidirect
94. #2453C22semidirect
95. #2451C22semidirect
96. #2446C22semidirect
97. #2446C22semidirect
98. #2446C22semidirect
110. #2365C22semidirect
111. #2365C22semidirect
112. #2365C22semidirect
113. #2365C22semidirect
114. #2365C22semidirect
119. #2356C22semidirect
120. #2356C22semidirect
121. #2355C22semidirect
122. #2351C22semidirect
123. #2351C22semidirect
124. Q8×C4⋊C4C22semidirect
130. #2336C22semidirect
131. #2336C22semidirect
132. #2336C22semidirect
133. #2320C22semidirect
159. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#596632
#594252
#592852
#592622
#592482
#590712
#392232
#390072
#381432
#366252
#365772
#365452
#361772
#361672
#361332
#361302
#354342
#350872
#342352
C2×C4×C22⋊Q82