Finite Group Databasebeta

← #7645619

Subgroups — #7645619

Order 512.

5398 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40643C218yesmaximal, complemented
2#40547C214yesmaximal, complemented
3#40541C214yesmaximal, complemented
4#38113C214yesmaximal, complemented
5#38057C214yesmaximal, complemented
6#37695C214yesmaximal, complemented
7#37663C214yesmaximal, complemented
8#37495C214yesmaximal, complemented
9#36810C218yesmaximal, complemented
10#35370C212yesmaximal
11#35368C212yesmaximal, complemented
12#35244C214yesmaximal, complemented
13#35020C211yesmaximal, characteristic, complemented
14#35010C211yesmaximal, characteristic
15#34995C212yesmaximal
16#34994C212yesmaximal, complemented
17C2×#2434C211yesmaximal, characteristic, complemented
18C2×#2409C211yesmaximal, characteristic
19#34212C211yesmaximal, characteristic, complemented
20C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
21#34057C211yesmaximal, characteristic
22C24×Q8C2211yescharacteristic
23C2×#541C2214yescomplemented
24C22×C4⋊Q8C2212yescomplemented
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2212yes—
27C22×C4×Q8C2212yescomplemented
28C22×C4×D4C2211yescharacteristic
29#2855C2212yes—
30#2852C2218yes—
31#2851C2214yescomplemented
32#2851C2218yescomplemented
33#2848C2212yes—
34#2833C2218yescomplemented
35#2831C2218yescomplemented
36#2798C2218yescomplemented
37#2789C2218yescomplemented
38#2762C2218yescomplemented
39#2762C2218yescomplemented
40#2758C2218yescomplemented
41#2758C2218yescomplemented
42#2755C2218yescomplemented
43#2754C2218yescomplemented
44#2716C2218yescomplemented
45#2716C2218yescomplemented
46#2713C2218yescomplemented
47#2713C2218yescomplemented
48#2704C2218yescomplemented
49#2698C2218yescomplemented
50#2690C2218yescomplemented
51#2689C2218yescomplemented
52#2666C2218yescomplemented
53#2650C2218yescomplemented
54#2646C2218yescomplemented
55#2646C2214yescomplemented
56#2645C2214yescomplemented
57#2643C2218yes—
58#2642C2214yescomplemented
59#2637C2218yescomplemented
60#2634C2218yescomplemented
61#2627C2212yes—
62#2626C2212yes—
63#2625C2214yescomplemented
64#2621C2214yescomplemented
65#2579C2214yes—
66#2569C2218yes—
67#2569C2214yes—
68#2569C2214yescomplemented
69#2564C2214yes—
70#2514C2214yescomplemented
71#2510C2218yes—
72#2510C2218yes—
73#2510C2218yes—
74#2505C2218yes—
75#2505C2218yescomplemented
76#2505C2218yescomplemented
77#2505C2218yescomplemented
78#2493C2218yes—
79#2493C2218yes—
80#2489C2214yescomplemented
81#2487C2212yes—
82#2481C2218yes—
83#2481C2218yes—
84#2481C2218yes—
85#2480C2218yes—
86#2480C2218yes—
87#2473C2218yes—
88#2473C2218yescomplemented
89#2473C2218yescomplemented
90#2473C2218yescomplemented
91#2469C2218yescomplemented
92#2462C2218yescomplemented
93#2453C2214yescomplemented
94#2446C2214yescomplemented
95#2446C2214yescomplemented
96#2442C2218yes—
97#2442C2214yes—
98#2442C2214yescomplemented
99#2434C2214yes—
100#2434C2214yes—
101#2434C2212yescomplemented
102#2434C2212yescomplemented
103#2434C2214yescomplemented
104#2429C2214yescomplemented
105#2429C2214yescomplemented
106#2421C2214yescomplemented
107#2417C2214yes—
108#2409C2212yes—
109#2409C2214yes—
110#2409C2212yes—
111#2409C2212yes—
112#2409C2214yes—
113#2409C2214yes—
114C2×#395C2212yes—
115C2×#395C2214yescomplemented
116C2×#393C2212yes—
117#2368C2214yes—
118#2360C2214yes—
119#2345C2214yescomplemented
120#2345C2212yescomplemented
121Q8×C22⋊C4C2214yes—
122Q8×C22⋊C4C2214yes—
123Q8×C22⋊C4C2214yescomplemented
124Q8×C22⋊C4C2214yescomplemented
125Q8×C22⋊C4C2212yescomplemented
126#2329C2214yescomplemented
127#2327C2214yescomplemented
128#2323C2214yescomplemented
129#2320C2214yescomplemented
130#2318C2214yes—
131#2318C2214yes—
132#2315C2211yescharacteristic
133#2315C2211yescharacteristic
134#2315C2212yes—
135#2315C2212yes—
136#2315C2212yes—
137#2315C2212yes—
138#2313C2212yes—
139#2312C2212yes—
140#2308C2211yescharacteristic
141#2308C2211yescharacteristic
142#2308C2212yes—
143C4×C22⋊Q8C2214yescomplemented
144C2×#391C2212yes—
145C2×#391C2212yescomplemented
146C2×#391C2214yescomplemented
147C2×#391C2212yescomplemented
148#2290C2214yes—
149#2290C2214yes—
150C2×#386C2212yes—
151C2×#385C2212yes—
152C2×#385C2212yes—
153C2×#385C2212yes—
154#2283C2212yes—
155#2280C2212yes—
156C2×#380C2212yes—
157C2×#380C2211yescharacteristic
158C2×#380C2211yescharacteristic
159#2273C2212yes—
160C2×C4×C22⋊C4C2211yescharacteristic
161C2×C4×C22⋊C4C2211yescharacteristic
162C2×C4×C22⋊C4C2212yes—
163C23×Q8—28no—
164C23×Q8—48no—
165C23×Q8C2311yescharacteristic
166C23×Q8C2312yes—
167C23×Q8C2312yes—
168C23×Q8C2312yes—
169C23×Q8C2312yes—
170C23×Q8C2312yes—
171C23×Q8C2311yescharacteristic
172C23×Q8C2311yescharacteristic
173C23×D4C2311yescharacteristic
174C24×C4C2312yes—
175C24×C4C2311yescharacteristic
176C24×C4C2311yescharacteristic
177#541—416no—
178C2×C4⋊Q8—48no—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2318yes—
182C2×#126C2318yes—
183C2×#126C2318yes—
184C2×#125C2318yes—
185C2×#125C2314yes—
186C2×#125C2318yes—
187C2×C22⋊Q8—28no—
188C2×C22⋊Q8—48no—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2318yes—
197C2×C4×Q8—48no—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2314yes—
201C2×C4×Q8C2318yes—
202C2×C4×D4—28no—
203C2×C4×D4C2312yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2312yes—
207C2×#117C2314yes—
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2314yes—
213C22×C4⋊C4C2314yes—
214C22×C4⋊C4C2314yes—
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2314yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2314yes—
227C22×C42C2311yescharacteristic
228C22×C42C2314yes—
229C22×C42C2312yes—
230C22×C42C2312yes—
231#401C2318yes—
232#401C2318yes—
233#400C2314yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#399C2314yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#395C2314yes—
272#395C2318yes—
273#395C2314yes—
274#395C2314yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#395C2318yes—
279#393C2314yes—
280#393C2314yes—
281#393C2314yes—
282#393C2318yes—
283#391C2318yes—
284#391C2314yes—
285#391C2314yes—
286#391C2314yes—
287#391C2318yes—
288#391C2314yes—
289#391C2314yes—
290#391C2318yes—
291#391C2318yes—
292#391C2318yes—
293#391C2318yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2318yes—
298#391C2318yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2318yes—
306#389C2314yes—
307#389C2318yes—
308#388C2314yes—
309#388C2314yes—
310#388C2314yes—
311#388C2314yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#387C2318yes—
319#387C2314yes—
320#387C2314yes—
321#387C2314yes—
322#387C2314yes—
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#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#386C2318yes—
343#386C2314yes—
344#386C2314yes—
345#386C2314yes—
346#386C2314yes—
347#386C2314yes—
348#386C2314yes—
349#386C2314yes—
350#386C2314yes—
351#386C2318yes—
352#385C2318yes—
353#385C2314yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2314yes—
358#385C2314yes—
359#385C2314yes—
360#385C2314yes—
361#385C2314yes—
362#385C2314yes—
363#385C2318yes—
364#385C2314yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#385C2314yes—
372#385C2314yes—
373#385C2314yes—
374#385C2318yes—
375#385C2318yes—
376#383C2314yes—
377#383C2318yes—
378#383C2318yes—
379#382C2314yes—
380#382C2318yes—
381#382C2314yes—
382#382C2318yes—
383#381C2312yes—
384#381C2312yes—
385#381C2314yes—
386#381C2314yes—
387#380C2318yes—
388#380C2312yes—
389#380C2312yes—
390#380C2312yes—
391#380C2312yes—
392#380C2318yes—
393#380C2312yes—
394#380C2318yes—
395#380C2312yes—
396#380C2318yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2312yes—
402#380C2312yes—
403#380C2312yes—
404#380C2312yes—
405#380C2318yes—
406#380C2312yes—
407#380C2312yes—
408#379C2312yes—
409#379C2312yes—
410#379C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C22⋊C4C2312yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2312yes—
429#376C2314yes—
430C2×#95C2312yes—
431C2×#95C2312yes—
432C2×#95C2314yes—
433C2×#95C2312yes—
434C2×#95C2312yes—
435C2×#95C2314yes—
436C2×#95C2314yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C2×#95C2314yes—
440C25C2411yescharacteristic
441C25C2411yescharacteristic
442C22×Q8—28no—
443C22×Q8—28no—
444C22×Q8—28no—
445C22×Q8—24no—
446C22×Q8—28no—
447C22×Q8—28no—
448C22×Q8—28no—
449C22×Q8—24no—
450C22×Q8—28no—
451C22×Q8—28no—
452C22×Q8—24no—
453C22×Q8—48no—
454C22×Q8—44no—
455C22×Q8—44no—
456C22×Q8—44no—
457C22×Q8—48no—
458C22×Q8—48no—
459C22×Q8—44no—
460C22×Q8—464no—
461C22×Q8C2412yes—
462C22×Q8C2412yes—
463C22×Q8C2412yes—
464C22×Q8C2414yes—
465C22×Q8C2414yes—
466C22×Q8C2412yes—
467C22×Q8C2412yes—
468C22×Q8C2412yes—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4C2412yes—
473C22×D4C2412yes—
474C23×C4—28no—
475C23×C4—24no—
476C23×C4—44no—
477C23×C4—48no—
478C23×C4—44no—
479C23×C4#4118yes—
480C23×C4C2412yes—
481C23×C4C2411yescharacteristic
482C23×C4C2412yes—
483C23×C4C2414yes—
484C23×C4C2414yes—
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2414yes—
489C23×C4C2411yescharacteristic
490C23×C4C2411yescharacteristic
491C23×C4C2412yes—
492C23×C4C2412yes—
493C23×C4C2412yes—
494C23×C4C2414yes—
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2412yes—
500C23×C4C2411yescharacteristic
501C23×C4C2411yescharacteristic
502C23×C4C2411yescharacteristic
503C4⋊Q8—216no—
504C4⋊Q8—48no—
505C4⋊Q8—416no—
506#126—416no—
507#126—416no—
508#125—48no—
509#125—416no—
510#125—416no—
511C22⋊Q8—216no—
512C22⋊Q8—28no—
513C22⋊Q8—28no—
514C22⋊Q8—28no—
515C22⋊Q8—28no—
516C22⋊Q8—416no—
517C22⋊Q8—48no—
518C22⋊Q8—48no—
519C4×Q8—216no—
520C4×Q8—48no—
521C4×Q8—416no—
522C4×Q8—48no—
523C4×D4—28no—
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—28no—
527#117—48no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—28no—
531C2×C4⋊C4—44no—
532C2×C4⋊C4—48no—
533C2×C4⋊C4—44no—
534C2×C4⋊C4—48no—
535C2×C4⋊C4—48no—
536C2×C4⋊C4—48no—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—28no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—28no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—48no—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2418yes—
603C2×C42—24no—
604C2×C42—44no—
605C2×C42—48no—
606C2×C42—44no—
607C2×C42C2414yes—
608C2×C42C2414yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2418yes—
612C2×C42C2414yes—
613C2×C42C2418yes—
614C2×C42C2418yes—
615C2×C42C2414yes—
616C2×C42C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2418yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2418yes—
642#95C2418yes—
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2418yes—
647#95C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—42no—
661C24—42no—
662C24—42no—
663C24—42no—
664C24C2×#4114yes—
665C242−1+414yes—
666C242−1+414yes—
667C24C2512yes—
668C24C2511yescharacteristic
669C24C2511yescharacteristic
670C24C2511yescharacteristic
671C2×Q8—232no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—24no—
675C2×Q8—28no—
676C2×Q8—28no—
677C2×Q8—24no—
678C2×Q8—24no—
679C2×Q8—24no—
680C2×Q8—28no—
681C2×Q8—24no—
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—24no—
685C2×Q8—28no—
686C2×Q8—24no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—432no—
692C2×Q8—432no—
693C2×Q8—432no—
694C2×Q8—416no—
695C2×Q8—432no—
696C2×Q8—432no—
697C2×Q8—88no—
698C2×Q8H(5,𝔽2)18yes—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—416no—
706C22×C4—24no—
707C22×C4—28no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—22no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—24no—
722C22×C4—22no—
723C22×C4—24no—
724C22×C4—28no—
725C22×C4—24no—
726C22×C4—28no—
727C22×C4—24no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—24no—
732C22×C4—416no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—42no—
741C22×C4—44no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—42no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—42no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—42no—
756C22×C4—432no—
757C22×C4—88no—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2×#4114yes—
761C22×C4C2×#4114yes—
762C22×C4C2×#4114yes—
763C22×C4C2×#4114yes—
764C22×C4C2512yes—
765C22×C4C2512yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2518yes—
773C22×C4C2518yes—
774C22×C4C2514yes—
775C22×C4C2512yes—
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C22×C4C2514yes—
780C22×C4C2511yescharacteristic
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—216no—
789C4⋊C4—28no—
790C4⋊C4—216no—
791C4⋊C4—216no—
792C4⋊C4—216no—
793C4⋊C4—48no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C4⋊C4—44no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—48no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C22⋊C4—24no—
812C22⋊C4—24no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—28no—
818C22⋊C4—24no—
819C22⋊C4—24no—
820C22⋊C4—24no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—24no—
827C22⋊C4—24no—
828C22⋊C4—24no—
829C22⋊C4—216no—
830C22⋊C4—48no—
831C22⋊C4—44no—
832C22⋊C4—48no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—48no—
837C42—24no—
838C42—24no—
839C42—28no—
840C42—28no—
841C42—216no—
842C42—44no—
843C42—48no—
844C42—44no—
845C42—48no—
846C42—48no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—22no—
856C23—22no—
857C23—24no—
858C23—44no—
859C23—44no—
860C23—48no—
861C23—48no—
862C23—48no—
863C23—44no—
864C23—82no—
865C23—82no—
866C23—84no—
867C23#541116yescomplemented
868C23C22×#4112yes—
869C23C22×#4112yes—
870C23C22×#4112yes—
871C23C2×2−1+412yes—
872C23C2×2−1+412yes—
873C23C2×2−1+412yes—
874C23C2×2−1+412yes—
875C23C2×2−1+412yes—
876C23C2×2−1+412yes—
877C23C2611yescharacteristic
878Q8—216no—
879Q8—216no—
880Q8—416no—
881Q8—416no—
882Q8—48no—
883Q8—48no—
884Q8—48no—
885Q8—84no—
886D4—48no—
887D4—48no—
888C2×C4—216no—
889C2×C4—24no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—28no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—28no—
908C2×C4—28no—
909C2×C4—28no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—28no—
923C2×C4—28no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—28no—
928C2×C4—24no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—416no—
933C2×C4—416no—
934C2×C4—48no—
935C2×C4—48no—
936C2×C4—48no—
937C2×C4—48no—
938C2×C4—44no—
939C2×C4—48no—
940C2×C4—84no—
941C2×C4—84no—
942C2×C4—82no—
943C2×C4—84no—
944C2×C4—88no—
945C2×C4—88no—
946C2×C4—82no—
947C2×C4—84no—
948C2×C4C22×#4112yes—
949C2×C4C22×#4112yes—
950C2×C4C22×#4112yes—
951C2×C4C22×#4112yes—
952C2×C4C2×H(5,𝔽2)18yes—
953C2×C4C2×H(5,𝔽2)14yes—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—24no—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—416no—
967C22—42no—
968C22—42no—
969C22—44no—
970C22—44no—
971C22—42no—
972C22—88no—
973C22C2×#54114yes—
974C22C2×#54114yes—
975C22C2×#54114yes—
976C22C23×#4111yescharacteristic
977C22C22×H(5,𝔽2)12yes—
978C22C22×2−1+411yescharacteristic
979C22C22×2−1+411yescharacteristic
980C222−1+612yes—
981C4—22no—
982C4—22no—
983C4—22no—
984C4—28no—
985C4—44no—
986C4—42no—
987C4—44no—
988C4—42no—
989C4—44no—
990C4—44no—
991C4—44no—
992C4—44no—
993C4—44no—
994C4—48no—
995C4—48no—
996C4—42no—
997C4#349014yes—
998C2—24no—
999C2—24no—
1000C2—24no—
1001C2—82no—
1002C2C22×#54111yescharacteristic
1003C2C2×#349011yescharacteristic
1004C2#6286011yescharacteristic
1005C2#6289312yes—
1006C2#6289312yes—
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. #40643C2semidirect
2. #40547C2semidirect
3. #40541C2semidirect
4. #38113C2semidirect
5. #38057C2semidirect
6. #37695C2semidirect
7. #37663C2semidirect
8. #37495C2semidirect
9. #36810C2semidirect
11. #35368C2semidirect
12. #35244C2semidirect
13. #35020C2semidirect
16. #34994C2semidirect
17. C2×#2434C2semidirect
19. #34212C2semidirect
20. C2×Q8×C22⋊C4C2semidirect
23. C2×#541C22semidirect
24. C22×C4⋊Q8C22semidirect
27. C22×C4×Q8C22semidirect
31. #2851C22semidirect
32. #2851C22semidirect
34. #2833C22semidirect
35. #2831C22semidirect
36. #2798C22semidirect
37. #2789C22semidirect
38. #2762C22semidirect
39. #2762C22semidirect
40. #2758C22semidirect
41. #2758C22semidirect
42. #2755C22semidirect
43. #2754C22semidirect
44. #2716C22semidirect
45. #2716C22semidirect
46. #2713C22semidirect
47. #2713C22semidirect
48. #2704C22semidirect
49. #2698C22semidirect
50. #2690C22semidirect
51. #2689C22semidirect
52. #2666C22semidirect
53. #2650C22semidirect
54. #2646C22semidirect
55. #2646C22semidirect
56. #2645C22semidirect
58. #2642C22semidirect
59. #2637C22semidirect
60. #2634C22semidirect
63. #2625C22semidirect
64. #2621C22semidirect
68. #2569C22semidirect
70. #2514C22semidirect
75. #2505C22semidirect
76. #2505C22semidirect
77. #2505C22semidirect
80. #2489C22semidirect
88. #2473C22semidirect
89. #2473C22semidirect
90. #2473C22semidirect
91. #2469C22semidirect
92. #2462C22semidirect
93. #2453C22semidirect
94. #2446C22semidirect
95. #2446C22semidirect
98. #2442C22semidirect
101. #2434C22semidirect
102. #2434C22semidirect
103. #2434C22semidirect
104. #2429C22semidirect
105. #2429C22semidirect
106. #2421C22semidirect
115. C2×#395C22semidirect
119. #2345C22semidirect
120. #2345C22semidirect
123. Q8×C22⋊C4C22semidirect
124. Q8×C22⋊C4C22semidirect
125. Q8×C22⋊C4C22semidirect
126. #2329C22semidirect
127. #2327C22semidirect
128. #2323C22semidirect
129. #2320C22semidirect
143. C4×C22⋊Q8C22semidirect
145. C2×#391C22semidirect
146. C2×#391C22semidirect
147. C2×#391C22semidirect
867. C23#541semidirect

Maximal subgroups

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

subgroupindex
#406432
#405472
#405412
#381132
#380572
#376952
#376632
#374952
#368102
#353702
#353682
#352442
#350202
#350102
#349952
#349942
C2×#24342
C2×#24092
#342122
C2×Q8×C22⋊C42
#340572