Finite Group Databasebeta

← #7645618

Subgroups — #7645618

Order 512.

5890 conjugacy classes of subgroups.

The subgroup lattice has 1065 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40645C218yesmaximal, complemented
2#40545C214yesmaximal, complemented
3#40543C214yesmaximal, complemented
4#38111C214yesmaximal, complemented
5#38055C214yesmaximal, complemented
6#37696C214yesmaximal, complemented
7#37665C214yesmaximal, complemented
8#37494C214yesmaximal, complemented
9#36809C218yesmaximal, complemented
10#35360C212yesmaximal, complemented
11#35359C212yesmaximal, complemented
12#35243C214yesmaximal, complemented
13#35002C211yesmaximal, characteristic, complemented
14#35000C211yesmaximal, characteristic
15#34995C212yesmaximal, complemented
16#34993C212yesmaximal, complemented
17C2×#2436C211yesmaximal, characteristic, complemented
18C2×#2409C211yesmaximal, characteristic, complemented
19#34205C211yesmaximal, characteristic, complemented
20C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
21#34057C211yesmaximal, characteristic, complemented
22C24×Q8C2211yescharacteristic
23C2×#543C2212yes—
24C2×#542C2214yescomplemented
25C2×#534C2212yes—
26C22×#124C2212yescomplemented
27C22×C22⋊Q8C2212yescomplemented
28C22×#121C2211yescharacteristic
29C2×#518C2212yes—
30C22×C4×Q8C2212yescomplemented
31C22×C4×D4C2211yescharacteristic
32#2857C2214yescomplemented
33#2854C2212yes—
34#2852C2218yescomplemented
35#2850C2218yescomplemented
36#2847C2212yes—
37#2832C2218yescomplemented
38#2831C2218yescomplemented
39#2799C2218yescomplemented
40#2798C2218yescomplemented
41#2764C2218yescomplemented
42#2763C2218yescomplemented
43#2759C2218yescomplemented
44#2759C2218yescomplemented
45#2755C2218yescomplemented
46#2754C2218yescomplemented
47#2715C2218yescomplemented
48#2712C2218yescomplemented
49#2710C2218yescomplemented
50#2702C2218yescomplemented
51#2700C2218yescomplemented
52#2700C2218yescomplemented
53#2692C2218yescomplemented
54#2687C2218yescomplemented
55#2665C2218yescomplemented
56#2659C2214yescomplemented
57#2653C2218yescomplemented
58#2645C2214yescomplemented
59#2643C2218yescomplemented
60#2640C2214yescomplemented
61#2639C2218yescomplemented
62#2637C2218yescomplemented
63#2632C2218yescomplemented
64#2625C2214yescomplemented
65#2620C2214yescomplemented
66#2618C2212yes—
67#2617C2212yes—
68#2564C2218yescomplemented
69#2549C2214yescomplemented
70#2549C2214yescomplemented
71#2543C2214yes—
72#2534C2214yes—
73#2511C2214yescomplemented
74#2510C2218yescomplemented
75#2498C2218yes—
76#2493C2218yescomplemented
77#2492C2214yescomplemented
78#2488C2218yes—
79#2488C2218yescomplemented
80#2486C2212yes—
81#2481C2218yescomplemented
82#2480C2218yescomplemented
83#2472C2218yes—
84#2472C2218yescomplemented
85#2465C2218yescomplemented
86#2458C2218yescomplemented
87#2451C2214yescomplemented
88#2450C2218yescomplemented
89#2449C2218yescomplemented
90#2448C2214yescomplemented
91#2447C2214yescomplemented
92#2444C2218yescomplemented
93#2443C2218yescomplemented
94#2440C2214yescomplemented
95#2440C2214yescomplemented
96#2438C2218yescomplemented
97#2437C2218yescomplemented
98#2436C2214yes—
99#2436C2214yes—
100#2436C2212yescomplemented
101#2436C2212yescomplemented
102#2436C2214yescomplemented
103#2427C2214yescomplemented
104#2426C2214yescomplemented
105#2423C2214yescomplemented
106#2419C2218yescomplemented
107#2418C2218yescomplemented
108#2417C2218yescomplemented
109#2416C2214yes—
110#2412C2218yes—
111#2409C2214yes—
112#2409C2214yes—
113#2409C2212yescomplemented
114#2409C2212yescomplemented
115#2409C2214yescomplemented
116#2408C2212yes—
117C2×#395C2212yescomplemented
118C2×#393C2212yescomplemented
119C2×#393C2214yescomplemented
120#2364C2214yes—
121#2361C2214yes—
122#2344C2212yescomplemented
123#2342C2214yescomplemented
124Q8×C22⋊C4C2214yescomplemented
125Q8×C22⋊C4C2214yescomplemented
126Q8×C22⋊C4C2214yescomplemented
127Q8×C22⋊C4C2214yescomplemented
128D4×C22⋊C4C2212yescomplemented
129#2326C2214yescomplemented
130#2325C2214yescomplemented
131#2323C2214yescomplemented
132#2320C2214yescomplemented
133#2318C2214yes—
134#2318C2214yescomplemented
135#2315C2211yescharacteristic
136#2315C2211yescharacteristic
137#2315C2212yes—
138#2313C2212yescomplemented
139#2312C2212yescomplemented
140#2308C2211yescharacteristic
141#2308C2211yescharacteristic
142#2308C2212yes—
143#2308C2212yes—
144C4×#121C2214yescomplemented
145C2×#391C2212yescomplemented
146C2×#391C2214yescomplemented
147C2×#391C2212yescomplemented
148C2×#391C2212yescomplemented
149#2290C2214yes—
150#2290C2214yescomplemented
151C2×#386C2212yes—
152C2×#386C2212yes—
153C2×#386C2212yes—
154C2×#385C2212yes—
155#2283C2212yescomplemented
156#2280C2212yescomplemented
157C2×#380C2212yes—
158C2×#380C2211yescharacteristic
159C2×#380C2211yescharacteristic
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×D4C2311yescharacteristic
173C23×D4C2312yes—
174C23×D4C2311yescharacteristic
175C24×C4C2312yes—
176C24×C4C2311yescharacteristic
177C24×C4C2311yescharacteristic
178#543—48no—
179#542—416no—
180#534—48no—
181C2×C4⋊Q8C2314yes—
182C2×#126C2318yes—
183C2×#124—48no—
184C2×#124C2314yes—
185C2×#124C2318yes—
186C2×#124C2314yes—
187C2×#124C2318yes—
188C2×#123C2314yes—
189C2×#123C2318yes—
190C2×#123C2314yes—
191C2×C22⋊Q8—48no—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2318yes—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2318yes—
198C2×C22⋊Q8C2318yes—
199C2×#121—28no—
200C2×#121C2312yes—
201C2×#121C2312yes—
202C2×#121C2312yes—
203C2×#121C2312yes—
204C2×#121C2314yes—
205C2×#121C2318yes—
206C2×#120C2314yes—
207C2×#120C2314yes—
208#518—48no—
209C2×C4×Q8—48no—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2314yes—
212C2×C4×Q8C2318yes—
213C2×C4×D4—28no—
214C2×C4×D4C2312yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2318yes—
220C2×C4×D4C2314yes—
221C2×#117C2314yes—
222C2×#117C2314yes—
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2314yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2314yes—
239C22×C22⋊C4C2314yes—
240C22×C22⋊C4C2314yes—
241C22×C22⋊C4C2314yes—
242C22×C42C2311yescharacteristic
243C22×C42C2314yes—
244C22×C42C2312yes—
245C22×C42C2312yes—
246#401C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#399C2318yes—
255#399C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2314yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2314yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#395C2318yes—
276#395C2314yes—
277#395C2318yes—
278#395C2314yes—
279#395C2318yes—
280#395C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2314yes—
285#394C2318yes—
286#394C2318yes—
287#393C2318yes—
288#393C2318yes—
289#393C2314yes—
290#393C2318yes—
291#393C2314yes—
292#393C2318yes—
293#393C2318yes—
294#393C2318yes—
295#393C2318yes—
296#393C2318yes—
297#392C2314yes—
298#391C2318yes—
299#391C2314yes—
300#391C2314yes—
301#391C2318yes—
302#391C2314yes—
303#391C2314yes—
304#391C2318yes—
305#391C2318yes—
306#391C2318yes—
307#391C2318yes—
308#391C2318yes—
309#391C2314yes—
310#391C2314yes—
311#391C2318yes—
312#391C2318yes—
313#391C2318yes—
314#390C2314yes—
315#390C2314yes—
316#390C2318yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2318yes—
321#389C2314yes—
322#389C2318yes—
323#388C2314yes—
324#388C2314yes—
325#388C2314yes—
326#388C2314yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2314yes—
342#387C2314yes—
343#387C2314yes—
344#387C2314yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#386C2314yes—
352#386C2314yes—
353#386C2314yes—
354#386C2314yes—
355#386C2314yes—
356#386C2318yes—
357#386C2314yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2314yes—
364#386C2314yes—
365#386C2314yes—
366#386C2314yes—
367#386C2314yes—
368#386C2314yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2314yes—
375#385C2314yes—
376#385C2314yes—
377#385C2314yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2314yes—
383#385C2314yes—
384#385C2318yes—
385#384C2314yes—
386#383C2314yes—
387#383C2318yes—
388#382C2314yes—
389#382C2318yes—
390#381C2312yes—
391#381C2312yes—
392#381C2314yes—
393#381C2314yes—
394#381C2314yes—
395#381C2318yes—
396#380C2312yes—
397#380C2318yes—
398#380C2312yes—
399#380C2312yes—
400#380C2312yes—
401#380C2318yes—
402#380C2314yes—
403#380C2314yes—
404#380C2312yes—
405#380C2312yes—
406#380C2312yes—
407#380C2312yes—
408#380C2312yes—
409#380C2312yes—
410#380C2318yes—
411#380C2312yes—
412#380C2312yes—
413#380C2318yes—
414#379C2312yes—
415#379C2312yes—
416#379C2314yes—
417#379C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2312yes—
425C4×C22⋊C4C2312yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2312yes—
431C4×C22⋊C4C2312yes—
432#376C2314yes—
433C2×#95C2314yes—
434C2×#95C2312yes—
435C2×#95C2312yes—
436C2×#95C2312yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C2×#95C2314yes—
442C2×#95C2312yes—
443C25C2412yes—
444C25C2411yescharacteristic
445C25C2411yescharacteristic
446C22×Q8—28no—
447C22×Q8—28no—
448C22×Q8—28no—
449C22×Q8—24no—
450C22×Q8—28no—
451C22×Q8—28no—
452C22×Q8—28no—
453C22×Q8—24no—
454C22×Q8—28no—
455C22×Q8—28no—
456C22×Q8—48no—
457C22×Q8—44no—
458C22×Q8—44no—
459C22×Q8—44no—
460C22×Q8—48no—
461C22×Q8—48no—
462C22×Q8—464no—
463C22×Q8C2412yes—
464C22×Q8C2412yes—
465C22×Q8C2414yes—
466C22×Q8C2414yes—
467C22×Q8C2412yes—
468C22×Q8C2412yes—
469C22×Q8C2418yes—
470C22×D4—24no—
471C22×D4—28no—
472C22×D4—28no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4—28no—
476C22×D4—24no—
477C22×D4—44no—
478C22×D4C2412yes—
479C22×D4C2414yes—
480C22×D4C2412yes—
481C22×D4C2412yes—
482C22×D4C2414yes—
483C22×D4C2412yes—
484C22×D4C2418yes—
485C23×C4—28no—
486C23×C4—24no—
487C23×C4—44no—
488C23×C4—48no—
489C23×C4—44no—
490C23×C4#4118yes—
491C23×C4C2412yes—
492C23×C4C2412yes—
493C23×C4C2411yescharacteristic
494C23×C4C2412yes—
495C23×C4C2414yes—
496C23×C4C2414yes—
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2412yes—
501C23×C4C2412yes—
502C23×C4C2414yes—
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2412yes—
506C23×C4C2414yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2418yes—
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C4⋊Q8—48no—
515#126—416no—
516#124—216no—
517#124—416no—
518#124—48no—
519#124—416no—
520#123—416no—
521#123—48no—
522#123—48no—
523C22⋊Q8—216no—
524C22⋊Q8—416no—
525C22⋊Q8—416no—
526C22⋊Q8—416no—
527C22⋊Q8—416no—
528C22⋊Q8—416no—
529C22⋊Q8—48no—
530#121—28no—
531#121—28no—
532#121—28no—
533#121—28no—
534#121—48no—
535#121—416no—
536#120—48no—
537#120—48no—
538C4×Q8—216no—
539C4×Q8—48no—
540C4×Q8—416no—
541C4×D4—28no—
542C4×D4—28no—
543C4×D4—28no—
544C4×D4—28no—
545C4×D4—48no—
546C4×D4—416no—
547C4×D4—416no—
548#117—48no—
549#117—48no—
550C2×C4⋊C4—24no—
551C2×C4⋊C4—24no—
552C2×C4⋊C4—44no—
553C2×C4⋊C4—48no—
554C2×C4⋊C4—44no—
555C2×C4⋊C4—48no—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2418yes—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—28no—
582C2×C22⋊C4—28no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—28no—
588C2×C22⋊C4—48no—
589C2×C22⋊C4—48no—
590C2×C22⋊C4—48no—
591C2×C22⋊C4—48no—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2412yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2412yes—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C42—24no—
628C2×C42—44no—
629C2×C42—48no—
630C2×C42—44no—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635C2×C42C2418yes—
636C2×C42C2418yes—
637C2×C42C2414yes—
638C2×C42C2418yes—
639C2×C42C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2418yes—
667#95C2414yes—
668#95C2418yes—
669#95C2414yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674C24—22no—
675C24—22no—
676C24—24no—
677C24—24no—
678C24—22no—
679C24—24no—
680C24—42no—
681C24—42no—
682C24—42no—
683C24—42no—
684C24—44no—
685C24—44no—
686C24C2×#4114yes—
687C24H(5,𝔽2)14yes—
688C242−1+414yes—
689C24C2512yes—
690C24C2514yes—
691C24C2511yescharacteristic
692C24C2511yescharacteristic
693C24C2511yescharacteristic
694C2×Q8—232no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—28no—
698C2×Q8—28no—
699C2×Q8—24no—
700C2×Q8—24no—
701C2×Q8—28no—
702C2×Q8—24no—
703C2×Q8—28no—
704C2×Q8—24no—
705C2×Q8—28no—
706C2×Q8—24no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×Q8—44no—
710C2×Q8—48no—
711C2×Q8—48no—
712C2×Q8—48no—
713C2×Q8—432no—
714C2×Q8—432no—
715C2×Q8—432no—
716C2×Q8—416no—
717C2×Q8—432no—
718C2×Q8—432no—
719C2×Q8H(5,𝔽2)18yes—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—28no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—28no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—28no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—416no—
740C2×D4—432no—
741C2×D4—88no—
742C22×C4—24no—
743C22×C4—28no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—22no—
748C22×C4—24no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—22no—
754C22×C4—24no—
755C22×C4—22no—
756C22×C4—24no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—24no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—24no—
769C22×C4—416no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—42no—
784C22×C4—44no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—42no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—432no—
795C22×C4—88no—
796C22×C4C2×#4114yes—
797C22×C4C2×#4114yes—
798C22×C4C2×#4114yes—
799C22×C4C2×#4114yes—
800C22×C4C2×#4114yes—
801C22×C4C2×#4114yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2518yes—
811C22×C4C2518yes—
812C22×C4C2512yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2514yes—
817C22×C4C2511yescharacteristic
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—216no—
825C4⋊C4—216no—
826C4⋊C4—48no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—48no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—48no—
833C4⋊C4—48no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—24no—
844C22⋊C4—28no—
845C22⋊C4—24no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—216no—
860C22⋊C4—216no—
861C22⋊C4—216no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—44no—
868C22⋊C4—48no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C42—24no—
877C42—24no—
878C42—28no—
879C42—28no—
880C42—216no—
881C42—44no—
882C42—48no—
883C42—44no—
884C42—48no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—24no—
893C23—24no—
894C23—28no—
895C23—24no—
896C23—22no—
897C23—22no—
898C23—24no—
899C23—28no—
900C23—24no—
901C23—44no—
902C23—44no—
903C23—48no—
904C23—48no—
905C23—48no—
906C23—44no—
907C23—48no—
908C23—82no—
909C23—82no—
910C23—84no—
911C23—84no—
912C23—84no—
913C23—88no—
914C23—88no—
915C23#542116yescomplemented
916C23C22×#4112yes—
917C23C22×#4112yes—
918C23C22×#4112yes—
919C23C2×H(5,𝔽2)12yes—
920C23C2×H(5,𝔽2)12yes—
921C23C2×H(5,𝔽2)12yes—
922C23C2×2−1+412yes—
923C23C2×2−1+412yes—
924C23C2×2−1+412yes—
925C23C2611yescharacteristic
926Q8—216no—
927Q8—216no—
928Q8—416no—
929Q8—416no—
930Q8—48no—
931Q8—48no—
932Q8—168no—
933D4—48no—
934D4—416no—
935D4—48no—
936D4—416no—
937D4—48no—
938D4—84no—
939D4—168no—
940C2×C4—216no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—28no—
947C2×C4—28no—
948C2×C4—28no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—28no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—28no—
962C2×C4—28no—
963C2×C4—24no—
964C2×C4—28no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—28no—
979C2×C4—24no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4—44no—
983C2×C4—416no—
984C2×C4—416no—
985C2×C4—48no—
986C2×C4—48no—
987C2×C4—48no—
988C2×C4—44no—
989C2×C4—48no—
990C2×C4—84no—
991C2×C4—82no—
992C2×C4—84no—
993C2×C4—84no—
994C2×C4—88no—
995C2×C4—88no—
996C2×C4—84no—
997C2×C4—82no—
998C2×C4—168no—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C22×#4112yes—
1002C2×C4C22×#4112yes—
1003C2×C4C2×H(5,𝔽2)18yes—
1004C2×C4C2×H(5,𝔽2)14yes—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—416no—
1018C22—42no—
1019C22—44no—
1020C22—42no—
1021C22—44no—
1022C22—44no—
1023C22—48no—
1024C22—48no—
1025C22—44no—
1026C22—42no—
1027C22—44no—
1028C22—88no—
1029C22—168no—
1030C22C2×#54214yes—
1031C22C2×#54214yes—
1032C22C2×#54214yes—
1033C22C23×#4111yescharacteristic
1034C22C22×H(5,𝔽2)12yes—
1035C22C22×H(5,𝔽2)11yescharacteristic
1036C22C22×2−1+411yescharacteristic
1037C222−1+612yes—
1038C4—22no—
1039C4—22no—
1040C4—22no—
1041C4—28no—
1042C4—44no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—44no—
1047C4—44no—
1048C4—48no—
1049C4—48no—
1050C4—44no—
1051C4—42no—
1052C4—44no—
1053C4#349014yes—
1054C2—24no—
1055C2—24no—
1056C2—24no—
1057C2—82no—
1058C2—84no—
1059C2C22×#54211yescharacteristic
1060C2C2×#349011yescharacteristic
1061C2#6286011yescharacteristic
1062C2#6289312yes—
1063C2#6289512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35000C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40645C2semidirect
2. #40545C2semidirect
3. #40543C2semidirect
4. #38111C2semidirect
5. #38055C2semidirect
6. #37696C2semidirect
7. #37665C2semidirect
8. #37494C2semidirect
9. #36809C2semidirect
10. #35360C2semidirect
11. #35359C2semidirect
12. #35243C2semidirect
13. #35002C2semidirect
15. #34995C2semidirect
16. #34993C2semidirect
17. C2×#2436C2semidirect
18. C2×#2409C2semidirect
19. #34205C2semidirect
20. C2×Q8×C22⋊C4C2semidirect
21. #34057C2semidirect
24. C2×#542C22semidirect
26. C22×#124C22semidirect
27. C22×C22⋊Q8C22semidirect
30. C22×C4×Q8C22semidirect
32. #2857C22semidirect
34. #2852C22semidirect
35. #2850C22semidirect
37. #2832C22semidirect
38. #2831C22semidirect
39. #2799C22semidirect
40. #2798C22semidirect
41. #2764C22semidirect
42. #2763C22semidirect
43. #2759C22semidirect
44. #2759C22semidirect
45. #2755C22semidirect
46. #2754C22semidirect
47. #2715C22semidirect
48. #2712C22semidirect
49. #2710C22semidirect
50. #2702C22semidirect
51. #2700C22semidirect
52. #2700C22semidirect
53. #2692C22semidirect
54. #2687C22semidirect
55. #2665C22semidirect
56. #2659C22semidirect
57. #2653C22semidirect
58. #2645C22semidirect
59. #2643C22semidirect
60. #2640C22semidirect
61. #2639C22semidirect
62. #2637C22semidirect
63. #2632C22semidirect
64. #2625C22semidirect
65. #2620C22semidirect
68. #2564C22semidirect
69. #2549C22semidirect
70. #2549C22semidirect
73. #2511C22semidirect
74. #2510C22semidirect
76. #2493C22semidirect
77. #2492C22semidirect
79. #2488C22semidirect
81. #2481C22semidirect
82. #2480C22semidirect
84. #2472C22semidirect
85. #2465C22semidirect
86. #2458C22semidirect
87. #2451C22semidirect
88. #2450C22semidirect
89. #2449C22semidirect
90. #2448C22semidirect
91. #2447C22semidirect
92. #2444C22semidirect
93. #2443C22semidirect
94. #2440C22semidirect
95. #2440C22semidirect
96. #2438C22semidirect
97. #2437C22semidirect
100. #2436C22semidirect
101. #2436C22semidirect
102. #2436C22semidirect
103. #2427C22semidirect
104. #2426C22semidirect
105. #2423C22semidirect
106. #2419C22semidirect
107. #2418C22semidirect
108. #2417C22semidirect
113. #2409C22semidirect
114. #2409C22semidirect
115. #2409C22semidirect
117. C2×#395C22semidirect
118. C2×#393C22semidirect
119. C2×#393C22semidirect
122. #2344C22semidirect
123. #2342C22semidirect
124. Q8×C22⋊C4C22semidirect
125. Q8×C22⋊C4C22semidirect
126. Q8×C22⋊C4C22semidirect
127. Q8×C22⋊C4C22semidirect
128. D4×C22⋊C4C22semidirect
129. #2326C22semidirect
130. #2325C22semidirect
131. #2323C22semidirect
132. #2320C22semidirect
134. #2318C22semidirect
138. #2313C22semidirect
139. #2312C22semidirect
144. C4×#121C22semidirect
145. C2×#391C22semidirect
146. C2×#391C22semidirect
147. C2×#391C22semidirect
148. C2×#391C22semidirect
150. #2290C22semidirect
155. #2283C22semidirect
156. #2280C22semidirect
915. C23#542semidirect

Maximal subgroups

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

subgroupindex
#406452
#405452
#405432
#381112
#380552
#376962
#376652
#374942
#368092
#353602
#353592
#352432
#350022
#350002
#349952
#349932
C2×#24362
C2×#24092
#342052
C2×Q8×C22⋊C42
#340572