Finite Group Databasebeta

← #7657473

Subgroups — #7657473

Order 512.

4806 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42638C214yesmaximal, complemented
2#42636C214yesmaximal, complemented
3#40735C218yesmaximal, complemented
4#40695C218yesmaximal, complemented
5#39607C212yesmaximal, complemented
6#39514C211yesmaximal, characteristic, complemented
7#39379C211yesmaximal, characteristic, complemented
8#37882C212yesmaximal, complemented
9#37850C214yesmaximal, complemented
10#37705C212yesmaximal, complemented
11#37637C212yesmaximal, complemented
12#37504C214yesmaximal, complemented
13#36180C211yesmaximal, characteristic, complemented
14#36154C212yesmaximal
15D4×#125C211yesmaximal, characteristic, complemented
16#35914C214yesmaximal
17#35858C214yesmaximal, complemented
18#35310C212yesmaximal, complemented
19#35284C211yesmaximal, characteristic, complemented
20#34629C211yesmaximal, characteristic, complemented
21C2×#2629C212yesmaximal, complemented
22#34332C212yesmaximal, complemented
23D4×#117C211yesmaximal, characteristic
24C2×#554C2212yes—
25C2×#541C2212yescomplemented
26C22×#125C2212yescomplemented
27C22×C4×D4C2211yescharacteristic
28C22×#117C2212yes—
29#2868C2211yescharacteristic, complemented
30#2859C2211yescharacteristic, complemented
31#2857C2212yes—
32#2857C2212yescomplemented
33#2851C2212yescomplemented
34#2848C2214yes—
35#2839C2218yescomplemented
36#2836C2218yescomplemented
37#2831C2218yescomplemented
38#2794C2218yescomplemented
39#2755C2218yescomplemented
40#2747C2218yescomplemented
41#2744C2218yes—
42#2739C2218yes—
43#2725C2218yescomplemented
44#2725C2218yescomplemented
45#2722C2218yescomplemented
46#2721C2218yescomplemented
47#2719C2218yescomplemented
48#2716C2218yescomplemented
49#2704C2218yes—
50#2664C2218yescomplemented
51#2655C2214yescomplemented
52#2655C2218yescomplemented
53#2652C2214yes—
54#2647C2214yescomplemented
55#2647C2211yescharacteristic, complemented
56#2647C2212yescomplemented
57#2646C2218yescomplemented
58#2645C2212yescomplemented
59#2644C2214yes—
60#2643C2218yes—
61#2642C2211yescharacteristic, complemented
62#2637C2218yescomplemented
63#2629C2218yes—
64#2629C2211yescharacteristic
65#2629C2214yes—
66#2629C2212yes—
67#2629C2214yescomplemented
68#2629C2212yescomplemented
69#2629C2218yescomplemented
70#2629C2212yescomplemented
71#2625C2212yes—
72#2625C2214yescomplemented
73#2621C2211yescharacteristic
74#2570C2214yescomplemented
75#2569C2218yescomplemented
76#2567C2212yescomplemented
77#2563C2212yes—
78#2552C2212yescomplemented
79#2552C2214yescomplemented
80#2552C2214yescomplemented
81#2538C2212yes—
82#2512C2214yes—
83#2512C2214yes—
84#2512C2214yes—
85#2508C2214yescomplemented
86#2507C2214yescomplemented
87#2507C2214yescomplemented
88#2506C2214yescomplemented
89#2506C2214yescomplemented
90#2506C2214yescomplemented
91#2505C2218yescomplemented
92#2502C2214yescomplemented
93#2497C2214yes—
94#2497C2214yes—
95#2497C2214yes—
96#2496C2214yescomplemented
97#2496C2214yescomplemented
98#2489C2214yescomplemented
99#2487C2214yes—
100#2481C2218yes—
101#2481C2218yes—
102#2481C2218yes—
103#2480C2218yes—
104#2480C2218yes—
105#2480C2218yes—
106#2478C2218yescomplemented
107#2475C2218yes—
108#2473C2218yescomplemented
109#2473C2218yescomplemented
110#2473C2218yescomplemented
111#2473C2218yescomplemented
112#2454C2214yes—
113#2453C2214yescomplemented
114#2450C2218yes—
115#2446C2214yescomplemented
116#2442C2214yes—
117#2442C2214yescomplemented
118#2442C2218yescomplemented
119#2440C2218yescomplemented
120#2437C2218yes—
121#2429C2214yes—
122#2421C2214yescomplemented
123#2417C2214yes—
124#2402C2214yescomplemented
125#2401C2214yes—
126C2×#398C2218yescomplemented
127C2×#396C2218yes—
128#2370C2214yescomplemented
129#2369C2212yescomplemented
130#2360C2218yescomplemented
131#2360C2214yescomplemented
132#2354C2212yes—
133#2352C2214yes—
134Q8×C4⋊C4C2212yescomplemented
135#2349C2214yes—
136D4×C4⋊C4C2214yes—
137D4×C4⋊C4C2212yes—
138D4×C4⋊C4C2212yes—
139D4×C4⋊C4C2214yes—
140D4×C4⋊C4C2214yes—
141#2345C2214yescomplemented
142#2344C2212yes—
143#2342C2214yes—
144D4×C22⋊C4C2214yes—
145D4×C22⋊C4C2212yes—
146#2330C2214yescomplemented
147#2330C2212yescomplemented
148#2329C2218yescomplemented
149#2323C2214yes—
150#2314C2212yes—
151#2314C2212yescomplemented
152C4×C4⋊Q8C2212yescomplemented
153C4×C4⋊Q8C2211yescharacteristic, complemented
154C4×#125C2211yescharacteristic, complemented
155C4×C22⋊Q8C2212yes—
156C4×C22⋊Q8C2214yescomplemented
157#2295C2212yescomplemented
158#2293C2211yescharacteristic
159#2293C2211yescharacteristic
160C2×#389C2214yescomplemented
161#2290C2212yes—
162#2290C2212yes—
163#2285C2211yescharacteristic
164C2×#384C2212yescomplemented
165#2280C2212yes—
166C2×#380C2214yes—
167#2275C2214yes—
168C42×D4C2211yescharacteristic
169C42×D4C2211yescharacteristic
170C4×#117C2211yescharacteristic
171C23×D4C2311yescharacteristic
172C24×C4C2312yes—
173#554—216no—
174#541—48no—
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2311yescharacteristic
177C2×C4⋊Q8C2314yes—
178C2×#126C2318yes—
179C2×#126C2318yes—
180C2×#126C2318yes—
181C2×#125—48no—
182C2×#125C2311yescharacteristic
183C2×#125C2312yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×#125C2318yes—
187C2×#125C2318yes—
188C2×#125C2318yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2318yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×D4—28no—
198C2×C4×D4C2311yescharacteristic
199C2×C4×D4C2312yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2311yescharacteristic
204C2×C4×D4C2312yes—
205C2×C4×D4C2311yescharacteristic
206C2×C4×D4C2312yes—
207C2×C4×D4C2311yescharacteristic
208C2×#117—48no—
209C2×#117C2311yescharacteristic
210C2×#117C2312yes—
211C2×#117C2311yescharacteristic
212C2×#117C2312yes—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C2312yes—
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2314yes—
218C22×C4⋊C4C2314yes—
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2318yes—
221C22×C4⋊C4C2318yes—
222C22×C4⋊C4C2318yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2314yes—
225C22×C22⋊C4C2318yes—
226C22×C42C2312yes—
227C22×C42C2311yescharacteristic
228C22×C42C2312yes—
229#401C2314yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2314yes—
235#400C2318yes—
236#400C2314yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2314yes—
243#400C2314yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#399C2318yes—
248#398C2314yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2314yes—
262#398C2314yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2314yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2314yes—
275#397C2314yes—
276#397C2314yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#396C2314yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#395C2318yes—
288#393C2318yes—
289#391C2314yes—
290#391C2312yes—
291#391C2314yes—
292#391C2318yes—
293#391C2314yes—
294#391C2312yes—
295#391C2312yes—
296#391C2312yes—
297#390C2314yes—
298#390C2312yes—
299#390C2312yes—
300#390C2314yes—
301#389C2312yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2312yes—
308#389C2314yes—
309#389C2314yes—
310#389C2318yes—
311#389C2318yes—
312#389C2318yes—
313#389C2318yes—
314#389C2314yes—
315#389C2314yes—
316#389C2318yes—
317#389C2318yes—
318#389C2312yes—
319#389C2312yes—
320#389C2314yes—
321#389C2314yes—
322#389C2318yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2312yes—
329#389C2312yes—
330#389C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2314yes—
334#388C2318yes—
335#388C2318yes—
336#388C2314yes—
337#388C2314yes—
338#388C2314yes—
339#388C2318yes—
340#388C2318yes—
341#387C2314yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2314yes—
349#387C2318yes—
350#387C2314yes—
351#387C2314yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2314yes—
358#387C2314yes—
359#387C2318yes—
360#387C2318yes—
361#386C2314yes—
362#386C2314yes—
363#386C2318yes—
364#386C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2314yes—
373#385C2314yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2314yes—
379#384C2312yes—
380#384C2311yescharacteristic
381#384C2314yes—
382#384C2312yes—
383#384C2312yes—
384#384C2314yes—
385#384C2314yes—
386#384C2312yes—
387#384C2314yes—
388#384C2318yes—
389#382C2311yescharacteristic
390#382C2314yes—
391#382C2312yes—
392#382C2312yes—
393#382C2318yes—
394#381C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2318yes—
399#380C2318yes—
400#380C2314yes—
401#380C2314yes—
402#380C2312yes—
403#380C2314yes—
404#380C2312yes—
405#380C2318yes—
406#380C2318yes—
407#380C2314yes—
408#380C2312yes—
409#380C2318yes—
410#380C2314yes—
411#380C2318yes—
412#379C2318yes—
413#379C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2318yes—
431C4×C4⋊C4C2312yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2312yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2312yes—
440C4×C22⋊C4C2318yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2312yes—
443C4×C22⋊C4C2312yes—
444#376C2311yescharacteristic
445#376C2314yes—
446#376C2311yescharacteristic
447C2×#95C2318yes—
448C2×#95C2318yes—
449C43C2311yescharacteristic
450C43C2311yescharacteristic
451C25C2412yes—
452C22×Q8C2412yes—
453C22×Q8C2414yes—
454C22×D4—24no—
455C22×D4—28no—
456C22×D4C2412yes—
457C22×D4C2411yescharacteristic
458C22×D4C2411yescharacteristic
459C23×C4—28no—
460C23×C4—28no—
461C23×C4—44no—
462C23×C4C2411yescharacteristic
463C23×C4C2412yes—
464C23×C4C2414yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2411yescharacteristic
470C23×C4C2411yescharacteristic
471C23×C4C2418yes—
472C23×C4C2418yes—
473C23×C4C2414yes—
474C4⋊Q8—28no—
475C4⋊Q8—24no—
476C4⋊Q8—84no—
477#126—416no—
478#126—88no—
479#126—88no—
480#125—216no—
481#125—24no—
482#125—28no—
483#125—48no—
484#125—416no—
485#125—416no—
486#125—88no—
487C22⋊Q8—216no—
488C22⋊Q8—28no—
489C22⋊Q8—232no—
490C22⋊Q8—48no—
491C22⋊Q8—84no—
492C4×Q8—28no—
493C4×Q8—48no—
494C4×Q8—84no—
495C4×D4—24no—
496C4×D4—216no—
497C4×D4—28no—
498C4×D4—216no—
499C4×D4—28no—
500C4×D4—28no—
501C4×D4—24no—
502C4×D4—28no—
503C4×D4—24no—
504C4×D4#4118yes—
505#117—24no—
506#117—24no—
507#117—28no—
508#117—44no—
509#117—44no—
510#117—48no—
511#117—48no—
512C2×C4⋊C4—216no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—48no—
515C2×C4⋊C4—48no—
516C2×C4⋊C4—416no—
517C2×C4⋊C4—88no—
518C2×C4⋊C4—88no—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2411yescharacteristic
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2411yescharacteristic
564C2×C22⋊C4—28no—
565C2×C22⋊C4—48no—
566C2×C22⋊C4—88no—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2412yes—
589C2×C42—24no—
590C2×C42—28no—
591C2×C42—44no—
592C2×C42C2411yescharacteristic
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2414yes—
596C2×C42C2411yescharacteristic
597C2×C42C2411yescharacteristic
598C2×C42C2411yescharacteristic
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601C2×C42C2414yes—
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2414yes—
605C2×C42C2414yes—
606C2×C42C2412yes—
607C2×C42C2418yes—
608C2×C42C2418yes—
609C2×C42C2418yes—
610C2×C42C2412yes—
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613#95C2414yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2412yes—
625#95C2412yes—
626#95C2412yes—
627#95C2412yes—
628#95C2414yes—
629#95C2414yes—
630#95C2412yes—
631#95C2412yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654C24—24no—
655C24—24no—
656C24—28no—
657C24—42no—
658C24—44no—
659C24C2512yes—
660C24C2511yescharacteristic
661C24C2512yes—
662C2×Q8—24no—
663C2×Q8—28no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×D4—24no—
669C2×D4—28no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—416no—
673C2×D4C2×#4114yes—
674C2×D42−1+418yes—
675C22×C4—22no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—28no—
681C22×C4—24no—
682C22×C4—216no—
683C22×C4—216no—
684C22×C4—28no—
685C22×C4—22no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—28no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—22no—
696C22×C4—42no—
697C22×C4—44no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—432no—
701C22×C4—44no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—44no—
706C22×C4—48no—
707C22×C4—42no—
708C22×C4C2×#4118yes—
709C22×C42−1+414yes—
710C22×C4C2511yescharacteristic
711C22×C4C2512yes—
712C22×C4C2512yes—
713C22×C4C2514yes—
714C22×C4C2512yes—
715C22×C4C2512yes—
716C22×C4C2514yes—
717C22×C4C2514yes—
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2518yes—
721C22×C4C2518yes—
722C22×C4C2514yes—
723C22×C4C2511yescharacteristic
724C22×C4C2511yescharacteristic
725C22×C4C2512yes—
726C22×C4C2512yes—
727C22×C4C2511yescharacteristic
728C22×C4C2511yescharacteristic
729C22×C4C2511yescharacteristic
730C4⋊C4—24no—
731C4⋊C4—24no—
732C4⋊C4—22no—
733C4⋊C4—216no—
734C4⋊C4—28no—
735C4⋊C4—28no—
736C4⋊C4—28no—
737C4⋊C4—216no—
738C4⋊C4—24no—
739C4⋊C4—28no—
740C4⋊C4—24no—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—216no—
744C4⋊C4—28no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—24no—
748C4⋊C4—28no—
749C4⋊C4—24no—
750C4⋊C4—28no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—48no—
763C4⋊C4—48no—
764C4⋊C4—48no—
765C4⋊C4—44no—
766C4⋊C4—48no—
767C4⋊C4—48no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—48no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—48no—
774C4⋊C4C2×#4114yes—
775C22⋊C4—24no—
776C22⋊C4—216no—
777C22⋊C4—24no—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—216no—
781C22⋊C4—28no—
782C22⋊C4—24no—
783C22⋊C4—24no—
784C22⋊C4—24no—
785C22⋊C4—28no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—48no—
795C22⋊C4—44no—
796C22⋊C4C2×#4118yes—
797C42—22no—
798C42—22no—
799C42—22no—
800C42—28no—
801C42—28no—
802C42—24no—
803C42—22no—
804C42—24no—
805C42—22no—
806C42—22no—
807C42—24no—
808C42—24no—
809C42—28no—
810C42—44no—
811C42—48no—
812C42—42no—
813C42—48no—
814C42—48no—
815C42—42no—
816C42C2×#4114yes—
817C42H(5,𝔽2)14yes—
818C23—22no—
819C23—22no—
820C23—24no—
821C23—21no—
822C23—21no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—48no—
831C23—416no—
832C23—48no—
833C23—84no—
834C23—88no—
835C23C22×#4114yes—
836C23C2×2−1+412yes—
837C23C2×2−1+418yes—
838C23C2611yescharacteristic
839Q8—48no—
840Q8—88no—
841D4—48no—
842D4—44no—
843D4#541116yescomplemented
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—28no—
852C2×C4—216no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—28no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—28no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—22no—
884C2×C4—28no—
885C2×C4—28no—
886C2×C4—28no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—48no—
894C2×C4—416no—
895C2×C4—48no—
896C2×C4—48no—
897C2×C4—44no—
898C2×C4—48no—
899C2×C4—82no—
900C2×C4—816no—
901C2×C4—88no—
902C2×C4—816no—
903C2×C4C22×#4112yes—
904C2×C4C22×#4114yes—
905C2×C4C22×#4112yes—
906C2×C4C22×#4112yes—
907C2×C4C2×H(5,𝔽2)14yes—
908C2×C4C2×H(5,𝔽2)12yes—
909C2×C4C2×2−1+412yes—
910C2×C4C2×2−1+414yes—
911C2×C4C2×2−1+412yes—
912C22—24no—
913C22—24no—
914C22—28no—
915C22—28no—
916C22—22no—
917C22—24no—
918C22—41no—
919C22—41no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—44no—
925C22—44no—
926C22—816no—
927C22C2×#54118yes—
928C22C23×#4111yescharacteristic
929C22C22×H(5,𝔽2)11yescharacteristic
930C22C22×2−1+411yescharacteristic
931C22C22×2−1+412yes—
932C22H(7,𝔽2)12yes—
933C4—22no—
934C4—24no—
935C4—22no—
936C4—24no—
937C4—42no—
938C4—44no—
939C4—41no—
940C4—44no—
941C4—48no—
942C4—41no—
943C4—44no—
944C4—44no—
945C4—48no—
946C4—42no—
947C4—44no—
948C4—42no—
949C4—42no—
950C4—44no—
951C4C2×#54114yes—
952C4#352014yes—
953C2—28no—
954C2—42no—
955C2—82no—
956C2C22×#54111yescharacteristic
957C2C2×#352011yescharacteristic
958C2#6285811yescharacteristic
959C2#6294412yes—
960C2#6294512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42638C2semidirect
2. #42636C2semidirect
3. #40735C2semidirect
4. #40695C2semidirect
5. #39607C2semidirect
6. #39514C2semidirect
7. #39379C2semidirect
8. #37882C2semidirect
9. #37850C2semidirect
10. #37705C2semidirect
11. #37637C2semidirect
12. #37504C2semidirect
13. #36180C2semidirect
15. D4×#125C2semidirect
17. #35858C2semidirect
18. #35310C2semidirect
19. #35284C2semidirect
20. #34629C2semidirect
21. C2×#2629C2semidirect
22. #34332C2semidirect
25. C2×#541C22semidirect
26. C22×#125C22semidirect
29. #2868C22semidirect
30. #2859C22semidirect
32. #2857C22semidirect
33. #2851C22semidirect
35. #2839C22semidirect
36. #2836C22semidirect
37. #2831C22semidirect
38. #2794C22semidirect
39. #2755C22semidirect
40. #2747C22semidirect
43. #2725C22semidirect
44. #2725C22semidirect
45. #2722C22semidirect
46. #2721C22semidirect
47. #2719C22semidirect
48. #2716C22semidirect
50. #2664C22semidirect
51. #2655C22semidirect
52. #2655C22semidirect
54. #2647C22semidirect
55. #2647C22semidirect
56. #2647C22semidirect
57. #2646C22semidirect
58. #2645C22semidirect
61. #2642C22semidirect
62. #2637C22semidirect
67. #2629C22semidirect
68. #2629C22semidirect
69. #2629C22semidirect
70. #2629C22semidirect
72. #2625C22semidirect
74. #2570C22semidirect
75. #2569C22semidirect
76. #2567C22semidirect
78. #2552C22semidirect
79. #2552C22semidirect
80. #2552C22semidirect
85. #2508C22semidirect
86. #2507C22semidirect
87. #2507C22semidirect
88. #2506C22semidirect
89. #2506C22semidirect
90. #2506C22semidirect
91. #2505C22semidirect
92. #2502C22semidirect
96. #2496C22semidirect
97. #2496C22semidirect
98. #2489C22semidirect
106. #2478C22semidirect
108. #2473C22semidirect
109. #2473C22semidirect
110. #2473C22semidirect
111. #2473C22semidirect
113. #2453C22semidirect
115. #2446C22semidirect
117. #2442C22semidirect
118. #2442C22semidirect
119. #2440C22semidirect
122. #2421C22semidirect
124. #2402C22semidirect
126. C2×#398C22semidirect
128. #2370C22semidirect
129. #2369C22semidirect
130. #2360C22semidirect
131. #2360C22semidirect
134. Q8×C4⋊C4C22semidirect
141. #2345C22semidirect
146. #2330C22semidirect
147. #2330C22semidirect
148. #2329C22semidirect
151. #2314C22semidirect
152. C4×C4⋊Q8C22semidirect
153. C4×C4⋊Q8C22semidirect
154. C4×#125C22semidirect
156. C4×C22⋊Q8C22semidirect
157. #2295C22semidirect
160. C2×#389C22semidirect
164. C2×#384C22semidirect
843. D4#541semidirect

Maximal subgroups

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

subgroupindex
#426382
#426362
#407352
#406952
#396072
#395142
#393792
#378822
#378502
#377052
#376372
#375042
#361802
#361542
D4×#1252
#359142
#358582
#353102
#352842
#346292
C2×#26292
#343322
D4×#1172