Finite Group Databasebeta

← #7632741

Subgroups — #7632741

Order 512.

4980 conjugacy classes of subgroups.

The subgroup lattice has 1049 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36485C214yesmaximal, complemented
2#36421C214yesmaximal, complemented
3#36344C218yesmaximal, complemented
4#35974C214yesmaximal, complemented
5#35869C214yesmaximal, complemented
6#35824C218yesmaximal, complemented
7#35679C211yesmaximal, characteristic
8#35674C211yesmaximal, characteristic, complemented
9#35658C214yesmaximal, complemented
10#35630C211yesmaximal, characteristic, complemented
11#35610C214yesmaximal, complemented
12#35558C211yesmaximal, characteristic
13#35338C211yesmaximal, characteristic
14#35188C214yesmaximal, complemented
15#35179C211yesmaximal, characteristic, complemented
16#34948C211yesmaximal, characteristic, complemented
17#34902C214yesmaximal, complemented
18C2×#2545C211yesmaximal, characteristic
19#34255C211yesmaximal, characteristic
20#34254C211yesmaximal, characteristic, complemented
21#34211C211yesmaximal, characteristic
22#34211C211yesmaximal, characteristic
23#34209C211yesmaximal, characteristic, complemented
24#34145C211yesmaximal, characteristic, complemented
25C4×#519C211yesmaximal, characteristic, complemented
26C2×#533C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C2×#519C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2866C2218yescomplemented
36#2865C2218yescomplemented
37#2861C2212yes—
38#2861C2212yes—
39#2855C2214yes—
40#2654C2218yescomplemented
41#2650C2218yescomplemented
42#2640C2212yes—
43#2640C2212yes—
44#2627C2214yes—
45#2596C2218yescomplemented
46#2596C2218yescomplemented
47#2594C2218yescomplemented
48#2594C2218yescomplemented
49#2592C2214yes—
50#2592C2214yes—
51#2589C2218yescomplemented
52#2587C2218yescomplemented
53#2582C2214yescomplemented
54#2581C2214yescomplemented
55#2577C2218yescomplemented
56#2575C2218yescomplemented
57#2574C2218yescomplemented
58#2573C2218yescomplemented
59#2571C2212yescomplemented
60#2570C2212yescomplemented
61#2570C2212yescomplemented
62#2569C2214yes—
63#2568C2212yescomplemented
64#2567C2212yescomplemented
65#2565C2212yescomplemented
66#2565C2212yescomplemented
67#2561C2214yes—
68#2561C2214yes—
69#2552C2212yescomplemented
70#2545C2212yes—
71#2545C2214yes—
72#2545C2214yes—
73#2545C2212yes—
74#2545C2212yes—
75#2545C2212yes—
76#2532C2218yescomplemented
77#2532C2218yescomplemented
78#2530C2218yescomplemented
79#2529C2218yescomplemented
80#2529C2218yescomplemented
81#2527C2218yescomplemented
82#2525C2218yescomplemented
83#2525C2218yescomplemented
84#2522C2218yescomplemented
85#2519C2218yescomplemented
86#2515C2218yescomplemented
87#2514C2214yescomplemented
88#2514C2214yescomplemented
89#2513C2214yes—
90#2513C2214yes—
91#2512C2214yes—
92#2512C2214yes—
93#2511C2214yescomplemented
94#2511C2214yescomplemented
95#2493C2218yes—
96#2484C2218yes—
97#2482C2218yes—
98#2480C2218yes—
99#2478C2218yescomplemented
100#2475C2218yescomplemented
101#2469C2218yescomplemented
102#2448C2214yes—
103#2448C2214yes—
104#2448C2214yes—
105#2448C2214yes—
106#2446C2214yescomplemented
107#2446C2214yescomplemented
108#2446C2214yescomplemented
109#2446C2214yescomplemented
110#2442C2214yes—
111#2402C2214yescomplemented
112#2401C2218yescomplemented
113#2396C2218yescomplemented
114C2×#396C2214yes—
115#2370C2212yescomplemented
116#2370C2212yescomplemented
117#2369C2212yescomplemented
118#2368C2214yes—
119#2367C2214yes—
120#2367C2214yes—
121#2367C2214yes—
122#2367C2214yes—
123#2365C2212yescomplemented
124#2365C2214yescomplemented
125#2365C2214yescomplemented
126#2360C2214yes—
127#2357C2214yes—
128#2356C2214yescomplemented
129#2355C2214yescomplemented
130#2354C2214yes—
131#2344C2218yes—
132#2343C2218yes—
133#2342C2214yes—
134#2342C2218yes—
135#2342C2214yes—
136#2342C2218yes—
137#2327C2214yescomplemented
138#2326C2214yes—
139#2326C2214yes—
140#2320C2214yescomplemented
141#2319C2214yes—
142#2317C2211yescharacteristic
143#2317C2211yescharacteristic
144#2310C2211yescharacteristic
145#2310C2211yescharacteristic
146#2310C2211yescharacteristic
147#2310C2211yescharacteristic
148#2310C2211yescharacteristic
149#2309C2211yescharacteristic
150#2309C2211yescharacteristic
151#2309C2211yescharacteristic
152C4×C4⋊Q8C2214yescomplemented
153C4×#125C2214yescomplemented
154C4×#126C2218yescomplemented
155C4×#124C2214yes—
156C4×#124C2214yes—
157#2298C2218yescomplemented
158#2296C2211yescharacteristic
159#2296C2211yescharacteristic
160#2296C2211yescharacteristic
161#2296C2211yescharacteristic
162#2295C2212yescomplemented
163#2295C2212yescomplemented
164#2295C2214yescomplemented
165#2295C2212yescomplemented
166C2×#391C2211yescharacteristic
167#2293C2214yes—
168C2×#390C2211yescharacteristic
169C2×#388C2214yes—
170#2285C2211yescharacteristic
171#2285C2211yescharacteristic
172#2285C2211yescharacteristic
173#2276C2214yescomplemented
174#2276C2214yescomplemented
175#2274C2211yescharacteristic
176#2274C2211yescharacteristic
177#2274C2214yes—
178C42×Q8C2214yescomplemented
179C42×Q8C2212yescomplemented
180C42×Q8C2214yescomplemented
181C4×#117C2211yescharacteristic
182C4×#117C2211yescharacteristic
183C4×#117C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2214yes—
186C2×C4×C4⋊C4C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×D4C2311yescharacteristic
190#533—28no—
191C2×C4⋊Q8—28no—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2311yescharacteristic
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2314yes—
197C2×#126C2318yes—
198C2×#125C2311yescharacteristic
199C2×#125C2311yescharacteristic
200C2×#125C2314yes—
201C2×#124—28no—
202C2×#124—28no—
203C2×#124C2312yes—
204C2×#124C2312yes—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2314yes—
209C2×#124C2312yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2312yes—
212#519—28no—
213#519—28no—
214#519—28no—
215#518—28no—
216C2×C4×Q8—28no—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2314yes—
240C2×#117C2314yes—
241C2×#117C2314yes—
242C2×#117C2318yes—
243C2×#117C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2312yes—
250C22×C22⋊C4C2314yes—
251C22×C22⋊C4C2314yes—
252C22×C22⋊C4C2314yes—
253C22×C42C2312yes—
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257#401C2318yes—
258#400C2318yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#399C2318yes—
269#399C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#398C2318yes—
277#398C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#395C2318yes—
291#393C2318yes—
292#393C2318yes—
293#391C2314yes—
294#391C2314yes—
295#391C2312yes—
296#391C2312yes—
297#391C2312yes—
298#391C2312yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2314yes—
307#391C2318yes—
308#391C2314yes—
309#391C2312yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2312yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2312yes—
318#390C2312yes—
319#390C2312yes—
320#390C2312yes—
321#390C2314yes—
322#390C2312yes—
323#390C2314yes—
324#390C2312yes—
325#389C2314yes—
326#389C2314yes—
327#389C2318yes—
328#389C2318yes—
329#389C2318yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#387C2314yes—
371#387C2318yes—
372#387C2318yes—
373#387C2314yes—
374#387C2314yes—
375#387C2314yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2314yes—
384#387C2318yes—
385#387C2318yes—
386#387C2314yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2318yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2314yes—
396#387C2318yes—
397#385C2314yes—
398#385C2314yes—
399#385C2314yes—
400#385C2314yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2314yes—
406#385C2314yes—
407#384C2312yes—
408#384C2312yes—
409#384C2312yes—
410#384C2312yes—
411#384C2312yes—
412#383C2318yes—
413#383C2318yes—
414#382C2314yes—
415#382C2312yes—
416#382C2312yes—
417#382C2312yes—
418#382C2312yes—
419#382C2312yes—
420#382C2318yes—
421#381C2314yes—
422#381C2314yes—
423#381C2314yes—
424#381C2314yes—
425#381C2314yes—
426#381C2318yes—
427#380C2312yes—
428#380C2314yes—
429#380C2314yes—
430#380C2318yes—
431#380C2312yes—
432#379C2314yes—
433#379C2314yes—
434#379C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2318yes—
437C4×C4⋊C4C2318yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2318yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2318yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2318yes—
455C4×C4⋊C4C2318yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C22⋊C4C2318yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2318yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2314yes—
488#376C2312yes—
489#376C2312yes—
490#376C2312yes—
491#376C2318yes—
492#376C2312yes—
493#376C2318yes—
494C2×#95C2312yes—
495C2×#95C2314yes—
496C43C2318yes—
497C43C2312yes—
498C43C2312yes—
499C43C2312yes—
500C43C2312yes—
501C25C2412yes—
502C22×Q8—24no—
503C22×Q8—24no—
504C22×Q8—24no—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8#4118yes—
508C22×Q8C2412yes—
509C22×Q8C2412yes—
510C22×Q8C2412yes—
511C22×Q8C2412yes—
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×D4—24no—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4C2412yes—
518C22×D4C2412yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2418yes—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C4⋊Q8—28no—
529C4⋊Q8—28no—
530C4⋊Q8—216no—
531C4⋊Q8—24no—
532C4⋊Q8—24no—
533#126—416no—
534#125—24no—
535#125—24no—
536#125—48no—
537#124—28no—
538#124—216no—
539#124—28no—
540#124—28no—
541#124—28no—
542#124—28no—
543#124—28no—
544C22⋊Q8—28no—
545C22⋊Q8—28no—
546C4×Q8—216no—
547C4×Q8—216no—
548C4×Q8—216no—
549C4×Q8—216no—
550C4×Q8—28no—
551C4×Q8—28no—
552C4×Q8—28no—
553C4×Q8—28no—
554C4×Q8—216no—
555C4×Q8—216no—
556C4×Q8—28no—
557C4×Q8—28no—
558C4×Q8—48no—
559C4×D4—216no—
560C4×D4—216no—
561#117—24no—
562#117—216no—
563#117—24no—
564#117—24no—
565#117—24no—
566#117—24no—
567#117—24no—
568#117—24no—
569#117—216no—
570#117—216no—
571#117—416no—
572#117#4118yes—
573C2×C4⋊C4—28no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—216no—
576C2×C4⋊C4—44no—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C22⋊C4—28no—
623C2×C22⋊C4—28no—
624C2×C22⋊C4—216no—
625C2×C22⋊C4—216no—
626C2×C22⋊C4—48no—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2412yes—
650C2×C42—28no—
651C2×C42—24no—
652C2×C42—24no—
653C2×C42#4118yes—
654C2×C42C2414yes—
655C2×C42C2412yes—
656C2×C42C2418yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2418yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2418yes—
664C2×C42C2412yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2418yes—
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2418yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2414yes—
682C2×C42C2412yes—
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#95C2418yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729C24—24no—
730C24—24no—
731C24—24no—
732C24—44no—
733C24—44no—
734C24C2514yes—
735C24C2511yescharacteristic
736C2×Q8—232no—
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—24no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—44no—
750C2×Q8—44no—
751C2×Q8—416no—
752C2×Q8C2×#4118yes—
753C2×Q8C2×#4118yes—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—416no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—216no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—44no—
775C22×C4—42no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—42no—
779C22×C4C2×#4118yes—
780C22×C4C2×#4114yes—
781C22×C4C2×#4114yes—
782C22×C4C2×#4114yes—
783C22×C4C2×#4114yes—
784C22×C4C2×#4114yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2512yes—
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—216no—
813C4⋊C4—216no—
814C4⋊C4—24no—
815C4⋊C4—216no—
816C4⋊C4—216no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—216no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4C2×#4118yes—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—216no—
861C22⋊C4—216no—
862C22⋊C4—216no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—216no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4C2×#4118yes—
876C42—28no—
877C42—28no—
878C42—22no—
879C42—22no—
880C42—24no—
881C42—22no—
882C42—24no—
883C42—22no—
884C42—24no—
885C42—216no—
886C42—216no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—216no—
892C42—24no—
893C42—24no—
894C42—28no—
895C42—44no—
896C42—44no—
897C42—44no—
898C42—44no—
899C42—48no—
900C42—44no—
901C42—44no—
902C42—44no—
903C42—48no—
904C42C2×#4114yes—
905C42C2×#4114yes—
906C42C2×#4114yes—
907C42C2×#4114yes—
908C42C2×#4118yes—
909C23—22no—
910C23—22no—
911C23—24no—
912C23—24no—
913C23—24no—
914C23—28no—
915C23—28no—
916C23—48no—
917C23—88no—
918C23—88no—
919C23—84no—
920C23—84no—
921C23C22×#4112yes—
922C23C22×#4112yes—
923C23C22×#4112yes—
924C23C2611yescharacteristic
925Q8—216no—
926Q8—216no—
927Q8—48no—
928Q8—48no—
929Q8—48no—
930Q8—84no—
931D4—48no—
932D4—48no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—216no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—28no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—44no—
982C2×C4—44no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—816no—
986C2×C4—84no—
987C2×C4—84no—
988C2×C4#529116yes—
989C2×C4C22×#4112yes—
990C2×C4C22×#4112yes—
991C2×C4C22×#4118yes—
992C2×C4C22×#4118yes—
993C2×C4C22×#4112yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4112yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4#58514yes—
1002C22—24no—
1003C22—24no—
1004C22—22no—
1005C22—22no—
1006C22—48no—
1007C22—48no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—168no—
1012C22C2×#52914yes—
1013C22C23×#4111yescharacteristic
1014C22C23×#4111yescharacteristic
1015C22C23×#4111yescharacteristic
1016C22C2×#58512yes—
1017C222−1+612yes—
1018C4—28no—
1019C4—24no—
1020C4—22no—
1021C4—22no—
1022C4—22no—
1023C4—22no—
1024C4—28no—
1025C4—44no—
1026C4—44no—
1027C4—44no—
1028C4—44no—
1029C4—44no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—44no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—42no—
1038C4—44no—
1039C4C2×#52914yes—
1040C4C2×#52914yes—
1041C2—24no—
1042C2—84no—
1043C2C22×#52911yescharacteristic
1044C2#6281511yescharacteristic
1045C2#6286011yescharacteristic
1046C2#6299512yes—
1047C2#6300512yes—
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. #36485C2semidirect
2. #36421C2semidirect
3. #36344C2semidirect
4. #35974C2semidirect
5. #35869C2semidirect
6. #35824C2semidirect
8. #35674C2semidirect
9. #35658C2semidirect
10. #35630C2semidirect
11. #35610C2semidirect
14. #35188C2semidirect
15. #35179C2semidirect
16. #34948C2semidirect
17. #34902C2semidirect
20. #34254C2semidirect
23. #34209C2semidirect
24. #34145C2semidirect
25. C4×#519C2semidirect
35. #2866C22semidirect
36. #2865C22semidirect
40. #2654C22semidirect
41. #2650C22semidirect
45. #2596C22semidirect
46. #2596C22semidirect
47. #2594C22semidirect
48. #2594C22semidirect
51. #2589C22semidirect
52. #2587C22semidirect
53. #2582C22semidirect
54. #2581C22semidirect
55. #2577C22semidirect
56. #2575C22semidirect
57. #2574C22semidirect
58. #2573C22semidirect
59. #2571C22semidirect
60. #2570C22semidirect
61. #2570C22semidirect
63. #2568C22semidirect
64. #2567C22semidirect
65. #2565C22semidirect
66. #2565C22semidirect
69. #2552C22semidirect
76. #2532C22semidirect
77. #2532C22semidirect
78. #2530C22semidirect
79. #2529C22semidirect
80. #2529C22semidirect
81. #2527C22semidirect
82. #2525C22semidirect
83. #2525C22semidirect
84. #2522C22semidirect
85. #2519C22semidirect
86. #2515C22semidirect
87. #2514C22semidirect
88. #2514C22semidirect
93. #2511C22semidirect
94. #2511C22semidirect
99. #2478C22semidirect
100. #2475C22semidirect
101. #2469C22semidirect
106. #2446C22semidirect
107. #2446C22semidirect
108. #2446C22semidirect
109. #2446C22semidirect
111. #2402C22semidirect
112. #2401C22semidirect
113. #2396C22semidirect
115. #2370C22semidirect
116. #2370C22semidirect
117. #2369C22semidirect
123. #2365C22semidirect
124. #2365C22semidirect
125. #2365C22semidirect
128. #2356C22semidirect
129. #2355C22semidirect
137. #2327C22semidirect
140. #2320C22semidirect
152. C4×C4⋊Q8C22semidirect
153. C4×#125C22semidirect
154. C4×#126C22semidirect
157. #2298C22semidirect
162. #2295C22semidirect
163. #2295C22semidirect
164. #2295C22semidirect
165. #2295C22semidirect
173. #2276C22semidirect
174. #2276C22semidirect
178. C42×Q8C22semidirect
179. C42×Q8C22semidirect
180. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#364852
#364212
#363442
#359742
#358692
#358242
#356792
#356742
#356582
#356302
#356102
#355582
#353382
#351882
#351792
#349482
#349022
C2×#25452
#342552
#342542
#342112
#342092
#341452
C4×#5192