Finite Group Databasebeta

← #7683727

Subgroups — #7683727

Order 512.

5454 conjugacy classes of subgroups.

The subgroup lattice has 1103 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59486C214yesmaximal, complemented
2#59482C214yesmaximal, complemented
3#59479C214yesmaximal, complemented
4#59475C214yesmaximal, complemented
5#59196C218yesmaximal, complemented
6#45230C214yesmaximal, complemented
7#45192C214yesmaximal, complemented
8#45182C214yesmaximal, complemented
9#45082C214yesmaximal, complemented
10#43933C218yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35672C211yesmaximal, characteristic, complemented
13#35668C211yesmaximal, characteristic, complemented
14#35644C211yesmaximal, characteristic, complemented
15#35626C211yesmaximal, characteristic, complemented
16#35529C211yesmaximal, characteristic, complemented
17#34814C211yesmaximal, characteristic, complemented
18#34814C211yesmaximal, characteristic, complemented
19C2×#2432C211yesmaximal, characteristic
20#34255C211yesmaximal, characteristic, complemented
21#34254C211yesmaximal, characteristic, complemented
22#34211C211yesmaximal, characteristic, complemented
23#34209C211yesmaximal, characteristic, complemented
24#34174C211yesmaximal, characteristic
25#34172C211yesmaximal, characteristic
26C23×#41C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#518C2211yescharacteristic
36#2796C2218yescomplemented
37#2786C2218yescomplemented
38#2761C2218yescomplemented
39#2757C2218yescomplemented
40#2751C2218yescomplemented
41#2745C2218yescomplemented
42#2744C2218yescomplemented
43#2740C2218yescomplemented
44#2739C2218yescomplemented
45#2738C2218yescomplemented
46#2737C2218yescomplemented
47#2723C2218yescomplemented
48#2601C2218yescomplemented
49#2597C2218yescomplemented
50#2595C2218yescomplemented
51#2575C2218yescomplemented
52#2573C2218yescomplemented
53#2569C2218yescomplemented
54#2568C2212yescomplemented
55#2567C2212yescomplemented
56#2566C2212yescomplemented
57#2566C2212yescomplemented
58#2565C2212yescomplemented
59#2565C2212yescomplemented
60#2563C2212yescomplemented
61#2561C2214yes—
62#2560C2218yescomplemented
63#2542C2212yescomplemented
64#2531C2218yescomplemented
65#2527C2218yescomplemented
66#2526C2218yescomplemented
67#2516C2218yescomplemented
68#2515C2218yescomplemented
69#2505C2218yescomplemented
70#2505C2218yescomplemented
71#2503C2214yes—
72#2497C2212yescomplemented
73#2497C2212yescomplemented
74#2496C2212yescomplemented
75#2496C2212yescomplemented
76#2495C2212yescomplemented
77#2495C2212yescomplemented
78#2494C2212yescomplemented
79#2494C2212yescomplemented
80#2493C2214yes—
81#2493C2214yes—
82#2493C2218yescomplemented
83#2493C2218yescomplemented
84#2492C2214yescomplemented
85#2492C2214yescomplemented
86#2489C2214yescomplemented
87#2489C2214yescomplemented
88#2484C2214yes—
89#2484C2218yes—
90#2483C2218yes—
91#2482C2214yes—
92#2480C2214yes—
93#2480C2214yes—
94#2479C2218yescomplemented
95#2454C2214yescomplemented
96#2453C2214yescomplemented
97#2452C2214yescomplemented
98#2451C2214yescomplemented
99#2447C2214yescomplemented
100#2447C2214yescomplemented
101#2447C2214yescomplemented
102#2447C2214yescomplemented
103#2446C2214yescomplemented
104#2446C2214yescomplemented
105#2446C2214yescomplemented
106#2446C2214yescomplemented
107#2438C2218yes—
108#2438C2218yescomplemented
109#2437C2218yes—
110#2432C2214yes—
111#2432C2214yes—
112#2432C2214yes—
113#2432C2214yes—
114#2423C2214yescomplemented
115#2423C2214yescomplemented
116#2421C2214yescomplemented
117#2421C2214yescomplemented
118#2401C2214yescomplemented
119#2401C2214yescomplemented
120C2×#394C2214yes—
121#2368C2218yescomplemented
122#2367C2214yescomplemented
123#2367C2214yescomplemented
124#2365C2214yescomplemented
125#2365C2214yescomplemented
126#2357C2214yescomplemented
127#2356C2214yescomplemented
128#2355C2214yescomplemented
129#2354C2214yescomplemented
130#2344C2218yes—
131#2343C2218yes—
132#2343C2218yescomplemented
133#2342C2218yes—
134#2342C2218yes—
135#2341C2214yes—
136#2341C2214yes—
137#2341C2214yes—
138#2341C2214yes—
139#2339C2214yes—
140#2339C2214yes—
141#2339C2214yes—
142#2339C2214yes—
143#2327C2212yescomplemented
144#2327C2212yescomplemented
145#2326C2212yescomplemented
146#2326C2212yescomplemented
147#2320C2214yescomplemented
148#2319C2214yescomplemented
149#2317C2211yescharacteristic
150#2317C2211yescharacteristic
151#2310C2211yescharacteristic
152#2310C2211yescharacteristic
153#2310C2211yescharacteristic
154#2310C2211yescharacteristic
155#2310C2211yescharacteristic
156#2309C2211yescharacteristic
157#2309C2214yes—
158#2309C2211yescharacteristic
159#2308C2214yes—
160C4×C4⋊Q8C2212yescomplemented
161C4×C4⋊Q8C2212yescomplemented
162C4×#126C2214yescomplemented
163C4×#126C2214yescomplemented
164C4×#124C2212yescomplemented
165C4×#124C2212yescomplemented
166#2296C2211yescharacteristic
167#2296C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2295C2214yescomplemented
171C2×#391C2211yescharacteristic
172#2293C2214yescomplemented
173C2×#390C2211yescharacteristic
174C2×#385C2214yes—
175#2285C2211yescharacteristic
176#2285C2211yescharacteristic
177#2280C2211yescharacteristic
178#2280C2211yescharacteristic
179#2280C2214yes—
180#2280C2211yescharacteristic
181#2280C2211yescharacteristic
182C2×#381C2214yes—
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41—28no—
188C22×#41—28no—
189C22×#41—44no—
190C22×#41C2314yes—
191C22×#41C2314yes—
192C23×Q8C2311yescharacteristic
193C23×Q8C2311yescharacteristic
194C23×D4C2312yes—
195C23×D4C2311yescharacteristic
196C24×C4C2311yescharacteristic
197C24×C4C2312yes—
198#544—44no—
199C2×C4⋊Q8—28no—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×#126C2314yes—
206C2×#126C2314yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#124—28no—
210C2×#124C2312yes—
211C2×#124C2314yes—
212C2×#124C2312yes—
213C2×C22⋊Q8—44no—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218#519—28no—
219#519—44no—
220#519—44no—
221#518—28no—
222#518—44no—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2314yes—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2314yes—
249C2×#117C2314yes—
250C2×#117C2318yes—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2312yes—
254C22×C22⋊C4C2314yes—
255C22×C22⋊C4C2314yes—
256C22×C22⋊C4C2312yes—
257C22×C22⋊C4C2314yes—
258C22×C22⋊C4C2314yes—
259C22×C22⋊C4C2312yes—
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262#401C2314yes—
263#401C2314yes—
264#400C2318yes—
265#400C2314yes—
266#400C2318yes—
267#400C2314yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#399C2318yes—
277#399C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2314yes—
289#397C2314yes—
290#397C2314yes—
291#397C2314yes—
292#397C2314yes—
293#397C2314yes—
294#397C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2314yes—
298#396C2314yes—
299#395C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#393C2318yes—
305#393C2318yes—
306#391C2318yes—
307#391C2312yes—
308#391C2312yes—
309#391C2312yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2314yes—
316#391C2312yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2318yes—
325#390C2318yes—
326#390C2312yes—
327#390C2312yes—
328#390C2312yes—
329#390C2314yes—
330#390C2312yes—
331#390C2312yes—
332#390C2318yes—
333#390C2318yes—
334#390C2314yes—
335#390C2318yes—
336#390C2312yes—
337#390C2314yes—
338#389C2318yes—
339#389C2318yes—
340#389C2318yes—
341#389C2314yes—
342#389C2314yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#388C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2314yes—
355#388C2314yes—
356#388C2314yes—
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#387C2314yes—
370#387C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2314yes—
374#387C2314yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2314yes—
400#385C2314yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2314yes—
405#385C2314yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2314yes—
410#385C2314yes—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2312yes—
415#384C2312yes—
416#384C2311yescharacteristic
417#383C2314yes—
418#383C2314yes—
419#383C2318yes—
420#382C2311yescharacteristic
421#382C2312yes—
422#382C2311yescharacteristic
423#382C2312yes—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2318yes—
427#382C2318yes—
428#381C2314yes—
429#381C2314yes—
430#381C2314yes—
431#381C2314yes—
432#381C2314yes—
433#381C2318yes—
434#381C2318yes—
435#381C2318yes—
436#381C2318yes—
437#381C2318yes—
438#381C2312yes—
439#381C2312yes—
440#381C2312yes—
441#381C2312yes—
442#380C2318yes—
443#380C2318yes—
444#380C2318yes—
445#380C2312yes—
446#380C2312yes—
447#380C2312yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451#380C2318yes—
452#380C2312yes—
453#380C2312yes—
454#380C2314yes—
455#380C2314yes—
456#379C2312yes—
457#379C2312yes—
458#379C2312yes—
459#379C2314yes—
460#379C2314yes—
461#379C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2312yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495#376C2312yes—
496#376C2312yes—
497#376C2318yes—
498C2×#95C2318yes—
499C2×#95C2318yes—
500C2×#95C2314yes—
501C2×#95C2312yes—
502C43C2312yes—
503C43C2312yes—
504C25C2411yescharacteristic
505C25C2412yes—
506C2×#41—216no—
507C2×#41—216no—
508C2×#41—216no—
509C2×#41—216no—
510C2×#41—48no—
511C2×#41—48no—
512C2×#41—464no—
513C22×Q8—24no—
514C22×Q8—24no—
515C22×Q8—24no—
516C22×Q8—24no—
517C22×Q8—24no—
518C22×Q8#4118yes—
519C22×Q8C2412yes—
520C22×Q8C2412yes—
521C22×Q8C2412yes—
522C22×Q8C2412yes—
523C22×Q8C2414yes—
524C22×D4—28no—
525C22×D4—24no—
526C22×D4—28no—
527C22×D4—24no—
528C22×D4—44no—
529C22×D4#4118yes—
530C22×D4C2418yes—
531C22×D4C2412yes—
532C22×D4C2412yes—
533C23×C4—28no—
534C23×C4—28no—
535C23×C4—24no—
536C23×C4—24no—
537C23×C4—24no—
538C23×C4—44no—
539C23×C4C2412yes—
540C23×C4C2411yescharacteristic
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2418yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2418yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C23×C4C2411yescharacteristic
552C4⋊Q8—28no—
553C4⋊Q8—28no—
554C4⋊Q8—216no—
555C4⋊Q8—44no—
556C4⋊Q8—44no—
557#126—48no—
558#126—48no—
559#125—44no—
560#125—44no—
561#124—28no—
562#124—216no—
563#124—28no—
564C22⋊Q8—48no—
565C22⋊Q8—416no—
566C22⋊Q8—48no—
567C22⋊Q8—48no—
568C4×Q8—216no—
569C4×Q8—216no—
570C4×Q8—44no—
571C4×Q8—44no—
572C4×Q8—44no—
573C4×Q8—44no—
574C4×Q8—44no—
575C4×Q8—44no—
576C4×Q8—44no—
577C4×Q8—44no—
578C4×D4—216no—
579C4×D4—216no—
580C4×D4—44no—
581C4×D4—44no—
582C4×D4—44no—
583C4×D4—44no—
584#117—24no—
585#117—24no—
586#117—216no—
587#117—24no—
588#117—24no—
589#117—24no—
590#117—24no—
591#117—24no—
592#117—24no—
593#117—416no—
594#117—48no—
595#117—48no—
596C2×C4⋊C4—216no—
597C2×C4⋊C4—24no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C22⋊C4—216no—
639C2×C22⋊C4—216no—
640C2×C22⋊C4—48no—
641C2×C22⋊C4—44no—
642C2×C22⋊C4—48no—
643C2×C22⋊C4—44no—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C42—24no—
677C2×C42—24no—
678C2×C42C2414yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2418yes—
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2412yes—
694C2×C42C2414yes—
695C2×C42C2414yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2418yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2418yes—
707#95C2418yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745C24—24no—
746C24—24no—
747C24—22no—
748C24—22no—
749C24—22no—
750C24—44no—
751C24—42no—
752C24—44no—
753C24—42no—
754C24C2×#4118yes—
755C24C2512yes—
756C24C2514yes—
757C24C2511yescharacteristic
758#41—464no—
759#41—464no—
760C2×Q8—232no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—44no—
772C2×Q8—48no—
773C2×Q8—416no—
774C2×Q8C2×#4118yes—
775C2×Q8C2×#4118yes—
776C2×D4—216no—
777C2×D4—232no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—216no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—48no—
784C2×D4—432no—
785C2×D4C2×#4118yes—
786C2×D4C2×#4118yes—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—216no—
795C22×C4—24no—
796C22×C4—22no—
797C22×C4—24no—
798C22×C4—216no—
799C22×C4—24no—
800C22×C4—216no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—48no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—44no—
812C22×C4—48no—
813C22×C4—42no—
814C22×C4—48no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—432no—
820C22×C4—416no—
821C22×C4C2×#4118yes—
822C22×C4C2×#4114yes—
823C22×C4C2×#4114yes—
824C22×C4H(5,𝔽2)14yes—
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2514yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2514yes—
844C22×C4C2512yes—
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C4⋊C4—216no—
848C4⋊C4—216no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—216no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—216no—
889C22⋊C4—216no—
890C22⋊C4—216no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—216no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—42no—
901C22⋊C4—48no—
902C22⋊C4—42no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C42—22no—
919C42—22no—
920C42—24no—
921C42—22no—
922C42—24no—
923C42—22no—
924C42—24no—
925C42—24no—
926C42—216no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—28no—
934C42—44no—
935C42—44no—
936C42—48no—
937C42—44no—
938C42—44no—
939C42—44no—
940C42—44no—
941C42—44no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—24no—
946C23—28no—
947C23—28no—
948C23—216no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—416no—
957C23—44no—
958C23—44no—
959C23—44no—
960C23—84no—
961C23—88no—
962C23—84no—
963C23—84no—
964C23—84no—
965C23C22×#4118yes—
966C23C22×#4112yes—
967C23C22×#4112yes—
968C23C2×H(5,𝔽2)12yes—
969C23C2611yescharacteristic
970Q8—216no—
971Q8—216no—
972Q8—48no—
973Q8—48no—
974Q8—164no—
975D4—216no—
976D4—216no—
977D4—432no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—216no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—28no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—48no—
1029C2×C4—432no—
1030C2×C4—44no—
1031C2×C4—48no—
1032C2×C4—48no—
1033C2×C4—48no—
1034C2×C4—84no—
1035C2×C4—816no—
1036C2×C4—84no—
1037C2×C4—164no—
1038C2×C4—164no—
1039C2×C4#551116yes—
1040C2×C4C22×#4118yes—
1041C2×C4C22×#4112yes—
1042C2×C4C22×#4112yes—
1043C2×C4C22×#4112yes—
1044C2×C4C22×#4112yes—
1045C2×C4C2×H(5,𝔽2)12yes—
1046C2×C4C2×H(5,𝔽2)12yes—
1047C2×C4#58514yes—
1048C22—24no—
1049C22—24no—
1050C22—22no—
1051C22—22no—
1052C22—216no—
1053C22—28no—
1054C22—48no—
1055C22—44no—
1056C22—44no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—816no—
1065C22—88no—
1066C22C2×#55114yes—
1067C22C23×#4111yescharacteristic
1068C22C23×#4111yescharacteristic
1069C22C22×H(5,𝔽2)11yescharacteristic
1070C22C2×#58512yes—
1071C222−1+612yes—
1072C4—24no—
1073C4—28no—
1074C4—42no—
1075C4—42no—
1076C4—44no—
1077C4—44no—
1078C4—44no—
1079C4—44no—
1080C4—42no—
1081C4—42no—
1082C4—44no—
1083C4—42no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—44no—
1092C4C2×#55114yes—
1093C4C2×#55114yes—
1094C2—24no—
1095C2—48no—
1096C2—82no—
1097C2C22×#55111yescharacteristic
1098C2#6283611yescharacteristic
1099C2#6288711yescharacteristic
1100C2#6299112yes—
1101C2#6300512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59486C2semidirect
2. #59482C2semidirect
3. #59479C2semidirect
4. #59475C2semidirect
5. #59196C2semidirect
6. #45230C2semidirect
7. #45192C2semidirect
8. #45182C2semidirect
9. #45082C2semidirect
10. #43933C2semidirect
11. #35674C2semidirect
12. #35672C2semidirect
13. #35668C2semidirect
14. #35644C2semidirect
15. #35626C2semidirect
16. #35529C2semidirect
17. #34814C2semidirect
18. #34814C2semidirect
20. #34255C2semidirect
21. #34254C2semidirect
22. #34211C2semidirect
23. #34209C2semidirect
36. #2796C22semidirect
37. #2786C22semidirect
38. #2761C22semidirect
39. #2757C22semidirect
40. #2751C22semidirect
41. #2745C22semidirect
42. #2744C22semidirect
43. #2740C22semidirect
44. #2739C22semidirect
45. #2738C22semidirect
46. #2737C22semidirect
47. #2723C22semidirect
48. #2601C22semidirect
49. #2597C22semidirect
50. #2595C22semidirect
51. #2575C22semidirect
52. #2573C22semidirect
53. #2569C22semidirect
54. #2568C22semidirect
55. #2567C22semidirect
56. #2566C22semidirect
57. #2566C22semidirect
58. #2565C22semidirect
59. #2565C22semidirect
60. #2563C22semidirect
62. #2560C22semidirect
63. #2542C22semidirect
64. #2531C22semidirect
65. #2527C22semidirect
66. #2526C22semidirect
67. #2516C22semidirect
68. #2515C22semidirect
69. #2505C22semidirect
70. #2505C22semidirect
72. #2497C22semidirect
73. #2497C22semidirect
74. #2496C22semidirect
75. #2496C22semidirect
76. #2495C22semidirect
77. #2495C22semidirect
78. #2494C22semidirect
79. #2494C22semidirect
82. #2493C22semidirect
83. #2493C22semidirect
84. #2492C22semidirect
85. #2492C22semidirect
86. #2489C22semidirect
87. #2489C22semidirect
94. #2479C22semidirect
95. #2454C22semidirect
96. #2453C22semidirect
97. #2452C22semidirect
98. #2451C22semidirect
99. #2447C22semidirect
100. #2447C22semidirect
101. #2447C22semidirect
102. #2447C22semidirect
103. #2446C22semidirect
104. #2446C22semidirect
105. #2446C22semidirect
106. #2446C22semidirect
108. #2438C22semidirect
114. #2423C22semidirect
115. #2423C22semidirect
116. #2421C22semidirect
117. #2421C22semidirect
118. #2401C22semidirect
119. #2401C22semidirect
121. #2368C22semidirect
122. #2367C22semidirect
123. #2367C22semidirect
124. #2365C22semidirect
125. #2365C22semidirect
126. #2357C22semidirect
127. #2356C22semidirect
128. #2355C22semidirect
129. #2354C22semidirect
132. #2343C22semidirect
143. #2327C22semidirect
144. #2327C22semidirect
145. #2326C22semidirect
146. #2326C22semidirect
147. #2320C22semidirect
148. #2319C22semidirect
160. C4×C4⋊Q8C22semidirect
161. C4×C4⋊Q8C22semidirect
162. C4×#126C22semidirect
163. C4×#126C22semidirect
164. C4×#124C22semidirect
165. C4×#124C22semidirect
170. #2295C22semidirect
172. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#594862
#594822
#594792
#594752
#591962
#452302
#451922
#451822
#450822
#439332
#356742
#356722
#356682
#356442
#356262
#355292
#348142
C2×#24322
#342552
#342542
#342112
#342092
#341742
#341722