Finite Group Databasebeta

← #7716047

Subgroups — #7716047

Order 512.

4808 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48846C218yesmaximal, complemented
2#47972C218yesmaximal, complemented
3#45025C214yesmaximal, complemented
4#44997C214yesmaximal, complemented
5#44923C214yesmaximal, complemented
6#44894C214yesmaximal, complemented
7#39752C212yesmaximal, complemented
8#39496C212yesmaximal, complemented
9#39492C214yesmaximal
10#37688C214yesmaximal
11#36752C214yesmaximal, complemented
12Q8×C22⋊Q8C212yesmaximal, complemented
13#36133C212yesmaximal, complemented
14#35253C212yesmaximal
15#35173C212yesmaximal, complemented
16#35013C212yesmaximal, complemented
17#35002C211yesmaximal, characteristic
18#34578C211yesmaximal, characteristic
19#34380C212yesmaximal
20C2×#2362C211yesmaximal, characteristic
21C2×Q82C2212yescomplemented
22C2×#544C2212yes—
23C2×#543C2212yes—
24C2×#533C2214yes—
25C22×C22⋊Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×#117C2211yescharacteristic
28#2857C2212yes—
29#2857C2214yes—
30#2857C2212yes—
31#2857C2214yes—
32#2855C2214yes—
33#2851C2214yes—
34#2809C2214yescomplemented
35#2807C2218yes—
36#2806C2214yescomplemented
37#2806C2214yescomplemented
38#2805C2214yescomplemented
39#2805C2218yescomplemented
40#2802C2218yescomplemented
41#2802C2218yescomplemented
42#2799C2218yescomplemented
43#2792C2218yescomplemented
44#2791C2218yescomplemented
45#2791C2218yescomplemented
46#2790C2218yes—
47#2788C2218yes—
48#2755C2218yescomplemented
49#2734C2218yescomplemented
50#2729C2218yes—
51#2729C2218yes—
52#2720C2218yes—
53#2713C2218yescomplemented
54#2704C2218yes—
55#2677C2218yes—
56#2667C2214yes—
57#2665C2214yes—
58#2659C2211yescharacteristic
59#2659C2211yescharacteristic
60#2659C2214yes—
61#2659C2212yes—
62#2659C2212yes—
63#2646C2212yes—
64#2629C2214yes—
65#2628C2214yes—
66#2627C2214yes—
67#2626C2212yes—
68#2626C2212yes—
69#2589C2218yes—
70#2587C2218yes—
71#2586C2218yescomplemented
72#2585C2218yescomplemented
73#2584C2214yescomplemented
74#2584C2218yescomplemented
75#2584C2218yescomplemented
76#2582C2214yescomplemented
77#2582C2212yescomplemented
78#2581C2214yescomplemented
79#2569C2218yes—
80#2567C2218yescomplemented
81#2567C2212yescomplemented
82#2567C2214yescomplemented
83#2565C2214yescomplemented
84#2551C2212yescomplemented
85#2550C2214yescomplemented
86#2549C2218yes—
87#2546C2212yescomplemented
88#2546C2218yescomplemented
89#2522C2218yes—
90#2520C2218yescomplemented
91#2509C2214yescomplemented
92#2507C2214yescomplemented
93#2506C2214yescomplemented
94#2465C2218yes—
95#2465C2218yes—
96#2465C2218yes—
97#2462C2218yescomplemented
98#2462C2218yescomplemented
99#2453C2214yescomplemented
100#2451C2214yescomplemented
101#2451C2214yescomplemented
102#2451C2214yescomplemented
103#2451C2218yescomplemented
104#2446C2214yescomplemented
105#2442C2214yes—
106#2441C2214yes—
107#2440C2214yes—
108#2440C2218yes—
109#2440C2214yes—
110#2440C2214yes—
111#2439C2214yes—
112#2438C2218yes—
113#2438C2218yes—
114#2438C2218yes—
115#2437C2218yes—
116#2429C2218yes—
117#2423C2218yes—
118#2396C2214yes—
119#2396C2214yes—
120#2378C2218yes—
121#2365C2214yescomplemented
122#2365C2212yescomplemented
123#2362C2214yes—
124#2362C2218yes—
125#2362C2214yes—
126#2360C2214yes—
127#2360C2214yes—
128Q8×C4⋊C4C2212yescomplemented
129Q8×C4⋊C4C2214yescomplemented
130Q8×C4⋊C4C2212yescomplemented
131#2344C2214yes—
132#2342C2218yes—
133Q8×C22⋊C4C2214yes—
134#2329C2214yes—
135#2329C2214yes—
136#2329C2214yes—
137#2323C2214yes—
138#2323C2214yes—
139#2317C2212yes—
140#2317C2212yes—
141#2316C2214yes—
142#2316C2214yes—
143#2316C2212yes—
144#2315C2212yes—
145#2313C2214yes—
146C4×C22⋊Q8C2212yes—
147C4×C22⋊Q8C2212yes—
148C4×C22⋊Q8C2214yes—
149C2×#391C2211yescharacteristic
150C2×#389C2211yescharacteristic
151C2×#388C2212yes—
152C2×#388C2212yes—
153C2×#387C2212yes—
154#2280C2212yes—
155C2×#380C2212yes—
156C2×C4×C4⋊C4C2211yescharacteristic
157C2×C4×C4⋊C4C2212yes—
158C2×C4×C22⋊C4C2211yescharacteristic
159C23×Q8C2311yescharacteristic
160C24×C4C2311yescharacteristic
161Q82—48no—
162#544—48no—
163#543—48no—
164#533—416no—
165C2×C4⋊Q8C2314yes—
166C2×C4⋊Q8C2314yes—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2314yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2314yes—
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2318yes—
173C2×#125C2314yes—
174C2×#125C2318yes—
175C2×#125C2314yes—
176C2×C22⋊Q8Q8116yescomplemented
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2312yes—
179C2×C22⋊Q8C2312yes—
180C2×C22⋊Q8C2318yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2318yes—
183C2×C22⋊Q8C2318yes—
184C2×C22⋊Q8C2318yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2314yes—
187C2×C4×Q8—44no—
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2314yes—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2314yes—
192C2×C4×Q8C2318yes—
193C2×C4×Q8C2314yes—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×#117—44no—
200C2×#117C2312yes—
201C2×#117C2318yes—
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2314yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2314yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C42C2312yes—
220C22×C42C2312yes—
221C22×C42C2311yescharacteristic
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2314yes—
230#400C2314yes—
231#400C2318yes—
232#399C2314yes—
233#399C2314yes—
234#399C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2314yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2314yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2314yes—
251#398C2314yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#396C2314yes—
256#396C2318yes—
257#396C2314yes—
258#396C2314yes—
259#396C2314yes—
260#396C2318yes—
261#395C2314yes—
262#395C2318yes—
263#395C2318yes—
264#395C2318yes—
265#395C2318yes—
266#395C2318yes—
267#395C2318yes—
268#395C2318yes—
269#395C2314yes—
270#395C2318yes—
271#395C2318yes—
272#395C2318yes—
273#393C2318yes—
274#393C2314yes—
275#393C2314yes—
276#391C2314yes—
277#391C2314yes—
278#391C2318yes—
279#391C2318yes—
280#391C2318yes—
281#391C2314yes—
282#391C2314yes—
283#391C2312yes—
284#391C2318yes—
285#391C2318yes—
286#391C2314yes—
287#391C2318yes—
288#391C2314yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2312yes—
293#391C2318yes—
294#389C2314yes—
295#389C2312yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2318yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2318yes—
304#389C2314yes—
305#389C2314yes—
306#389C2318yes—
307#389C2318yes—
308#389C2314yes—
309#389C2318yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2318yes—
319#389C2318yes—
320#389C2318yes—
321#389C2314yes—
322#389C2314yes—
323#389C2318yes—
324#389C2318yes—
325#389C2314yes—
326#389C2318yes—
327#389C2314yes—
328#389C2314yes—
329#389C2318yes—
330#389C2314yes—
331#389C2312yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2314yes—
361#387C2314yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#385C2314yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2314yes—
375#384C2312yes—
376#384C2314yes—
377#384C2314yes—
378#384C2314yes—
379#384C2318yes—
380#384C2312yes—
381#382C2314yes—
382#382C2314yes—
383#381C2318yes—
384#381C2314yes—
385#380C2312yes—
386#380C2314yes—
387#380C2314yes—
388#380C2318yes—
389#380C2318yes—
390#380C2314yes—
391#380C2312yes—
392#380C2312yes—
393#380C2318yes—
394#380C2314yes—
395#380C2312yes—
396#380C2312yes—
397#380C2312yes—
398#380C2314yes—
399#380C2314yes—
400#379C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2312yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C2×#95C2312yes—
422C2×#95C2312yes—
423C2×#95C2314yes—
424C2×#95C2311yescharacteristic
425C2×#95C2311yescharacteristic
426C2×#95C2312yes—
427C2×#95C2312yes—
428C25C2411yescharacteristic
429C22×Q8—42no—
430C22×Q8—42no—
431C22×Q8C2×Q818yes—
432C22×Q8C2412yes—
433C22×Q8C2412yes—
434C22×Q8C2412yes—
435C22×Q8C2414yes—
436C22×Q8C2418yes—
437C22×Q8C2414yes—
438C22×Q8C2412yes—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4C2×Q818yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2411yescharacteristic
445C23×C4C2412yes—
446C23×C4C2411yescharacteristic
447C23×C4C2412yes—
448C23×C4C2411yescharacteristic
449C23×C4C2414yes—
450C23×C4C2414yes—
451C23×C4C2412yes—
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C4⋊Q8—216no—
457C4⋊Q8—44no—
458C4⋊Q8—48no—
459C4⋊Q8—44no—
460C4⋊Q8—48no—
461C4⋊Q8—48no—
462C4⋊Q8—48no—
463C4⋊Q8—416no—
464#125—416no—
465#125—48no—
466#125—48no—
467C22⋊Q8—28no—
468C22⋊Q8—216no—
469C22⋊Q8—28no—
470C22⋊Q8—416no—
471C22⋊Q8—48no—
472C22⋊Q8—416no—
473C22⋊Q8—416no—
474C22⋊Q8—416no—
475C22⋊Q8C2×Q8132yes—
476C22⋊Q8C2×Q8132yes—
477C4×Q8—28no—
478C4×Q8—44no—
479C4×Q8—44no—
480C4×Q8—48no—
481C4×Q8—416no—
482C4×Q8—48no—
483C4×Q8—44no—
484C4×Q8—48no—
485C4×Q8—48no—
486C4×Q8—48no—
487C4×Q8—48no—
488#117—28no—
489#117—44no—
490#117—44no—
491#117—48no—
492#117—416no—
493#117—44no—
494C2×C4⋊C4—28no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—44no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4—44no—
499C2×C4⋊C4—44no—
500C2×C4⋊C4C2×Q818yes—
501C2×C4⋊C4C2×Q8116yes—
502C2×C4⋊C4C2411yescharacteristic
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2411yescharacteristic
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—44no—
557C2×C22⋊C4—48no—
558C2×C22⋊C4C2×Q8116yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C42—28no—
573C2×C42—44no—
574C2×C42—42no—
575C2×C42—44no—
576C2×C42—42no—
577C2×C42C2414yes—
578C2×C42C2414yes—
579C2×C42C2414yes—
580C2×C42C2412yes—
581C2×C42C2414yes—
582C2×C42C2414yes—
583C2×C42C2414yes—
584C2×C42C2412yes—
585C2×C42C2414yes—
586C2×C42C2418yes—
587C2×C42C2418yes—
588C2×C42C2418yes—
589C2×C42C2412yes—
590C2×C42C2414yes—
591C2×C42C2418yes—
592C2×C42C2412yes—
593#95C2414yes—
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2418yes—
598#95C2418yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2414yes—
615#95C2414yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628C24—22no—
629C24—22no—
630C24—41no—
631C24—41no—
632C24—41no—
633C24—41no—
634C24C22×Q814yes—
635C24C2512yes—
636C24C2511yescharacteristic
637C2×Q8—24no—
638C2×Q8—24no—
639C2×Q8—28no—
640C2×Q8—216no—
641C2×Q8—24no—
642C2×Q8—24no—
643C2×Q8—42no—
644C2×Q8—42no—
645C2×Q8—42no—
646C2×Q8—42no—
647C2×Q8—42no—
648C2×Q8—42no—
649C2×Q8—48no—
650C2×Q8—44no—
651C2×Q8—44no—
652C2×Q8—48no—
653C2×Q8—44no—
654C2×Q8—44no—
655C2×Q8—44no—
656C2×Q8—416no—
657C2×Q8C22×Q818yes—
658C2×Q8C22×Q818yes—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—22no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—416no—
671C22×C4—41no—
672C22×C4—41no—
673C22×C4—42no—
674C22×C4—41no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—42no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4C22×Q818yes—
695C22×C4C22×Q814yes—
696C22×C4C22×Q818yes—
697C22×C4C22×Q818yes—
698C22×C4C22×Q814yes—
699C22×C4C22×Q818yes—
700C22×C4H(5,𝔽2)14yes—
701C22×C42−1+414yes—
702C22×C4C2512yes—
703C22×C4C2514yes—
704C22×C4C2514yes—
705C22×C4C2514yes—
706C22×C4C2518yes—
707C22×C4C2514yes—
708C22×C4C2512yes—
709C22×C4C2518yes—
710C22×C4C2514yes—
711C22×C4C2512yes—
712C22×C4C2511yescharacteristic
713C22×C4C2514yes—
714C22×C4C2514yes—
715C22×C4C2512yes—
716C22×C4C2512yes—
717C22×C4C2512yes—
718C22×C4C2512yes—
719C22×C4C2511yescharacteristic
720C4⋊C4—24no—
721C4⋊C4—22no—
722C4⋊C4—24no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—28no—
726C4⋊C4—24no—
727C4⋊C4—216no—
728C4⋊C4—28no—
729C4⋊C4—216no—
730C4⋊C4—216no—
731C4⋊C4—24no—
732C4⋊C4—28no—
733C4⋊C4—28no—
734C4⋊C4—44no—
735C4⋊C4—42no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—42no—
739C4⋊C4—44no—
740C4⋊C4—42no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—44no—
747C4⋊C4—42no—
748C4⋊C4—42no—
749C4⋊C4—42no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—42no—
753C4⋊C4—42no—
754C4⋊C4—48no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—42no—
760C4⋊C4—44no—
761C4⋊C4—48no—
762C4⋊C4—44no—
763C4⋊C4—48no—
764C4⋊C4—44no—
765C4⋊C4—48no—
766C4⋊C4—48no—
767C4⋊C4—44no—
768C4⋊C4C22×Q818yes—
769C4⋊C4C22×Q818yes—
770C4⋊C4C22×Q8132yes—
771C4⋊C4H(5,𝔽2)14yes—
772C22⋊C4—216no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—28no—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—44no—
779C22⋊C4—48no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4C22×Q8132yes—
785C42—28no—
786C42—28no—
787C42—28no—
788C42—28no—
789C42—24no—
790C42—28no—
791C42—24no—
792C42—28no—
793C42—42no—
794C42—44no—
795C42—44no—
796C42—42no—
797C42—48no—
798C42—48no—
799C42—48no—
800C42—48no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—28no—
812C23—44no—
813C23—44no—
814C23—82no—
815C23—82no—
816C23—82no—
817C23—82no—
818C23C23×Q814yes—
819C23C23×Q812yes—
820C23C2×H(5,𝔽2)12yes—
821C23C2×2−1+412yes—
822C23C2611yescharacteristic
823Q8—216no—
824Q8—48no—
825Q8—48no—
826Q8—48no—
827Q8—88no—
828Q8—816no—
829Q8—164no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—21no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—216no—
845C2×C4—216no—
846C2×C4—28no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—28no—
857C2×C4—28no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—28no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—28no—
875C2×C4—22no—
876C2×C4—28no—
877C2×C4—44no—
878C2×C4—48no—
879C2×C4—48no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—48no—
883C2×C4—84no—
884C2×C4—82no—
885C2×C4—82no—
886C2×C4—164no—
887C2×C4—164no—
888C2×C4C23×Q818yes—
889C2×C4C23×Q818yes—
890C2×C4C23×Q814yes—
891C2×C4C23×Q812yes—
892C2×C4C23×Q812yes—
893C2×C4C2×H(5,𝔽2)14yes—
894C2×C4C2×H(5,𝔽2)14yes—
895C2×C4C2×H(5,𝔽2)12yes—
896C2×C4C2×2−1+414yes—
897C2×C4#58512yes—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—88no—
912C22#350314yes—
913C22C24×Q811yescharacteristic
914C22C22×H(5,𝔽2)11yescharacteristic
915C22C22×H(5,𝔽2)11yescharacteristic
916C22C22×2−1+411yescharacteristic
917C22C2×#58511yescharacteristic
918C222−1+611yescharacteristic
919C222−1+611yescharacteristic
920C4—24no—
921C4—22no—
922C4—28no—
923C4—28no—
924C4—24no—
925C4—24no—
926C4—24no—
927C4—44no—
928C4—44no—
929C4—48no—
930C4—44no—
931C4—42no—
932C4—42no—
933C4—48no—
934C4—44no—
935C4—44no—
936C4—42no—
937C4#350114yes—
938C2—24no—
939C2—44no—
940C2C2×#350111yescharacteristic
941C2C2×#350311yescharacteristic
942C2#6284911yescharacteristic
943C2#6289311yescharacteristic
944C2#6290111yescharacteristic
945C2#6291411yescharacteristic
946C2#6293211yescharacteristic
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. #48846C2semidirect
2. #47972C2semidirect
3. #45025C2semidirect
4. #44997C2semidirect
5. #44923C2semidirect
6. #44894C2semidirect
7. #39752C2semidirect
8. #39496C2semidirect
11. #36752C2semidirect
12. Q8×C22⋊Q8C2semidirect
13. #36133C2semidirect
15. #35173C2semidirect
16. #35013C2semidirect
21. C2×Q82C22semidirect
34. #2809C22semidirect
36. #2806C22semidirect
37. #2806C22semidirect
38. #2805C22semidirect
39. #2805C22semidirect
40. #2802C22semidirect
41. #2802C22semidirect
42. #2799C22semidirect
43. #2792C22semidirect
44. #2791C22semidirect
45. #2791C22semidirect
48. #2755C22semidirect
49. #2734C22semidirect
53. #2713C22semidirect
71. #2586C22semidirect
72. #2585C22semidirect
73. #2584C22semidirect
74. #2584C22semidirect
75. #2584C22semidirect
76. #2582C22semidirect
77. #2582C22semidirect
78. #2581C22semidirect
80. #2567C22semidirect
81. #2567C22semidirect
82. #2567C22semidirect
83. #2565C22semidirect
84. #2551C22semidirect
85. #2550C22semidirect
87. #2546C22semidirect
88. #2546C22semidirect
90. #2520C22semidirect
91. #2509C22semidirect
92. #2507C22semidirect
93. #2506C22semidirect
97. #2462C22semidirect
98. #2462C22semidirect
99. #2453C22semidirect
100. #2451C22semidirect
101. #2451C22semidirect
102. #2451C22semidirect
103. #2451C22semidirect
104. #2446C22semidirect
121. #2365C22semidirect
122. #2365C22semidirect
128. Q8×C4⋊C4C22semidirect
129. Q8×C4⋊C4C22semidirect
130. Q8×C4⋊C4C22semidirect
176. C2×C22⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#488462
#479722
#450252
#449972
#449232
#448942
#397522
#394962
#394922
#376882
#367522
Q8×C22⋊Q82
#361332
#352532
#351732
#350132
#350022
#345782
#343802
C2×#23622