Finite Group Databasebeta

← #7710068

Subgroups — #7710068

Order 512.

4782 conjugacy classes of subgroups.

The subgroup lattice has 1093 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59682C214yesmaximal, complemented
2#59653C212yesmaximal, complemented
3#59427C212yesmaximal, complemented
4#46159C214yesmaximal, complemented
5#46158C212yesmaximal, complemented
6#46023C212yesmaximal, complemented
7#39811C214yesmaximal, complemented
8#39761C212yesmaximal, complemented
9#39744C212yesmaximal, complemented
10#39640C212yesmaximal, complemented
11#39574C214yesmaximal, complemented
12#39527C214yesmaximal, complemented
13#39511C212yesmaximal
14#37885C214yesmaximal, complemented
15#37537C212yesmaximal
16#36760C214yesmaximal, complemented
17#36645C211yesmaximal, characteristic, complemented
18#36635C211yesmaximal, characteristic, complemented
19#36545C212yesmaximal, complemented
20#36207C214yesmaximal, complemented
21#36161C212yesmaximal
22#35033C212yesmaximal, complemented
23#35014C212yesmaximal, complemented
24#34399C212yesmaximal, complemented
25C2×C4×#124C211yesmaximal, characteristic
26C2×#557C2212yescomplemented
27C2×#556C2212yes—
28C2×#533C2212yes—
29C22×#124C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32#2868C2211yescharacteristic, complemented
33#2868C2211yescharacteristic, complemented
34#2864C2212yescomplemented
35#2863C2212yescomplemented
36#2863C2212yescomplemented
37#2862C2211yescharacteristic, complemented
38#2862C2212yescomplemented
39#2859C2211yescharacteristic, complemented
40#2859C2212yescomplemented
41#2859C2212yescomplemented
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2212yes—
45#2857C2212yes—
46#2857C2212yes—
47#2857C2212yes—
48#2855C2212yes—
49#2855C2212yes—
50#2851C2212yes—
51#2851C2214yes—
52#2848C2214yes—
53#2820C2214yes—
54#2820C2214yes—
55#2808C2214yes—
56#2806C2214yescomplemented
57#2805C2214yescomplemented
58#2800C2218yes—
59#2798C2218yescomplemented
60#2793C2218yescomplemented
61#2783C2218yescomplemented
62#2774C2218yescomplemented
63#2773C2218yescomplemented
64#2772C2218yescomplemented
65#2754C2218yescomplemented
66#2754C2218yescomplemented
67#2727C2214yes—
68#2725C2218yescomplemented
69#2725C2218yescomplemented
70#2721C2218yescomplemented
71#2721C2218yescomplemented
72#2716C2218yescomplemented
73#2658C2214yes—
74#2646C2214yes—
75#2640C2214yes—
76#2632C2218yes—
77#2626C2214yes—
78#2626C2214yes—
79#2626C2214yes—
80#2608C2218yescomplemented
81#2607C2218yescomplemented
82#2592C2214yes—
83#2589C2218yescomplemented
84#2587C2218yescomplemented
85#2584C2214yescomplemented
86#2582C2212yescomplemented
87#2581C2214yescomplemented
88#2575C2218yescomplemented
89#2568C2214yescomplemented
90#2547C2212yes—
91#2546C2214yescomplemented
92#2546C2212yescomplemented
93#2545C2214yes—
94#2545C2214yes—
95#2545C2214yes—
96#2538C2212yes—
97#2532C2218yescomplemented
98#2529C2218yescomplemented
99#2525C2218yescomplemented
100#2519C2218yescomplemented
101#2517C2218yescomplemented
102#2515C2218yescomplemented
103#2512C2214yes—
104#2511C2214yescomplemented
105#2505C2218yes—
106#2499C2214yescomplemented
107#2497C2214yescomplemented
108#2496C2214yescomplemented
109#2495C2214yescomplemented
110#2492C2214yescomplemented
111#2489C2214yescomplemented
112#2485C2214yes—
113#2482C2218yes—
114#2480C2218yes—
115#2480C2218yes—
116#2473C2218yes—
117#2466C2218yes—
118#2462C2218yescomplemented
119#2448C2214yes—
120#2447C2214yes—
121#2446C2214yescomplemented
122#2446C2214yescomplemented
123#2441C2214yescomplemented
124#2441C2214yescomplemented
125#2441C2214yescomplemented
126#2439C2214yescomplemented
127#2439C2214yescomplemented
128#2435C2214yes—
129#2434C2214yes—
130#2429C2214yescomplemented
131#2423C2214yescomplemented
132#2423C2214yescomplemented
133#2415C2214yes—
134#2382C2214yescomplemented
135#2382C2214yescomplemented
136#2373C2218yescomplemented
137#2367C2214yes—
138#2365C2214yescomplemented
139#2362C2214yescomplemented
140#2360C2214yes—
141#2360C2214yes—
142#2356C2214yescomplemented
143#2355C2212yescomplemented
144#2354C2212yes—
145#2351C2214yescomplemented
146#2346C2214yescomplemented
147#2343C2218yes—
148#2331C2214yescomplemented
149#2329C2214yes—
150#2329C2214yes—
151#2329C2214yes—
152#2327C2214yescomplemented
153#2320C2218yescomplemented
154#2312C2214yes—
155C4×C4⋊Q8C2211yescharacteristic, complemented
156C4×C4⋊Q8C2212yescomplemented
157C4×C4⋊Q8C2211yescharacteristic, complemented
158C4×C4⋊Q8C2212yescomplemented
159C4×C4⋊Q8C2212yescomplemented
160C4×C4⋊Q8C2212yescomplemented
161C4×#125C2212yescomplemented
162C4×#124C2212yes—
163C4×#124C2212yes—
164C4×#124C2212yes—
165C4×#124C2212yes—
166C4×#124C2212yes—
167C4×#124C2212yes—
168C4×#124C2212yes—
169C4×#124C2212yes—
170C4×C22⋊Q8C2212yes—
171C4×C22⋊Q8C2212yes—
172C4×C22⋊Q8C2214yes—
173#2295C2212yescomplemented
174#2295C2212yescomplemented
175C2×#391C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#388C2212yes—
178C2×#388C2212yes—
179#2285C2212yes—
180#2285C2212yes—
181#2283C2212yes—
182C2×#382C2211yescharacteristic
183#2280C2214yes—
184C2×C4×C22⋊C4C2212yes—
185C2×C4×C22⋊C4C2212yes—
186C2×C43C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188C23×D4C2311yescharacteristic
189C24×C4C2312yes—
190#557—48no—
191#556—48no—
192#533—216no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×#126C2318yes—
204C2×#126C2318yes—
205C2×#125C2314yes—
206C2×#125C2312yes—
207C2×#125C2314yes—
208C2×#125C2318yes—
209C2×#124—28no—
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#124C2314yes—
215C2×#124C2314yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C4×Q8—44no—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×D4—44no—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×#117C2314yes—
240C2×#117C2314yes—
241C2×#117C2314yes—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2312yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2312yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2312yes—
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#399C2318yes—
265#399C2318yes—
266#399C2318yes—
267#399C2318yes—
268#399C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#396C2318yes—
291#395C2318yes—
292#395C2318yes—
293#394C2318yes—
294#394C2318yes—
295#393C2318yes—
296#393C2318yes—
297#393C2318yes—
298#391C2314yes—
299#391C2314yes—
300#391C2312yes—
301#391C2312yes—
302#391C2314yes—
303#391C2314yes—
304#391C2312yes—
305#391C2314yes—
306#391C2318yes—
307#391C2314yes—
308#391C2318yes—
309#391C2318yes—
310#391C2312yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#390C2312yes—
323#390C2314yes—
324#390C2314yes—
325#390C2312yes—
326#390C2312yes—
327#390C2312yes—
328#389C2312yes—
329#389C2312yes—
330#389C2314yes—
331#389C2314yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2318yes—
343#389C2318yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2312yes—
348#389C2318yes—
349#389C2314yes—
350#389C2318yes—
351#389C2318yes—
352#389C2318yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2314yes—
415#385C2314yes—
416#385C2318yes—
417#384C2312yes—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2312yes—
421#384C2312yes—
422#384C2312yes—
423#384C2312yes—
424#384C2312yes—
425#384C2312yes—
426#384C2312yes—
427#383C2314yes—
428#383C2318yes—
429#382C2312yes—
430#382C2312yes—
431#382C2312yes—
432#382C2318yes—
433#382C2314yes—
434#382C2312yes—
435#382C2318yes—
436#382C2314yes—
437#382C2312yes—
438#382C2314yes—
439#382C2312yes—
440#382C2312yes—
441#381C2318yes—
442#381C2314yes—
443#380C2312yes—
444#380C2314yes—
445#380C2312yes—
446#380C2312yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2312yes—
451#380C2314yes—
452#380C2314yes—
453#380C2314yes—
454#380C2314yes—
455#379C2318yes—
456#379C2318yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C22⋊C4C2318yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2318yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484#376C2318yes—
485#376C2314yes—
486C2×#95C2312yes—
487C2×#95C2312yes—
488C2×#95C2312yes—
489C2×#95C2312yes—
490C43C2311yescharacteristic
491C43C2311yescharacteristic
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494C43C2311yescharacteristic
495C43C2311yescharacteristic
496C43C2311yescharacteristic
497C43C2311yescharacteristic
498C25C2412yes—
499C22×Q8—24no—
500C22×Q8—42no—
501C22×Q8—42no—
502C22×Q8C2412yes—
503C22×Q8C2414yes—
504C22×Q8C2412yes—
505C22×Q8C2412yes—
506C22×Q8C2414yes—
507C22×Q8C2412yes—
508C22×D4—24no—
509C22×D4—42no—
510C22×D4—42no—
511C22×D4C2412yes—
512C22×D4C2412yes—
513C23×C4—28no—
514C23×C4—44no—
515C23×C4—44no—
516C23×C4C2414yes—
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2414yes—
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C4⋊Q8—28no—
529C4⋊Q8—28no—
530C4⋊Q8—28no—
531C4⋊Q8—42no—
532C4⋊Q8—44no—
533C4⋊Q8—44no—
534C4⋊Q8—42no—
535C4⋊Q8—44no—
536C4⋊Q8—48no—
537C4⋊Q8—48no—
538#126—416no—
539#126—416no—
540#125—216no—
541#125—44no—
542#125—48no—
543#125—416no—
544#124—28no—
545#124—28no—
546#124—28no—
547#124—28no—
548#124—48no—
549#124—48no—
550C22⋊Q8—216no—
551C22⋊Q8—216no—
552C22⋊Q8—28no—
553C22⋊Q8—28no—
554C22⋊Q8—48no—
555C22⋊Q8—48no—
556C4×Q8—216no—
557C4×Q8—216no—
558C4×Q8—28no—
559C4×Q8—28no—
560C4×Q8—44no—
561C4×Q8—44no—
562C4×Q8—44no—
563C4×Q8—44no—
564C4×Q8—48no—
565C4×Q8—48no—
566C4×Q8—48no—
567C4×D4—28no—
568C4×D4—44no—
569C4×D4—44no—
570C4×D4—44no—
571#117—216no—
572#117—48no—
573#117—48no—
574C2×C4⋊C4—42no—
575C2×C4⋊C4—42no—
576C2×C4⋊C4—44no—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C22⋊C4—28no—
622C2×C22⋊C4—28no—
623C2×C22⋊C4—28no—
624C2×C22⋊C4—44no—
625C2×C22⋊C4—44no—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C42—24no—
648C2×C42—24no—
649C2×C42—24no—
650C2×C42—44no—
651C2×C42—42no—
652C2×C42—42no—
653C2×C42—42no—
654C2×C42#4118yes—
655C2×C42C2418yes—
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2414yes—
660C2×C42C2414yes—
661C2×C42C2411yescharacteristic
662C2×C42C2414yes—
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2418yes—
677C2×C42C2418yes—
678C2×C42C2418yes—
679C2×C42C2414yes—
680C2×C42C2418yes—
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2418yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2418yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2414yes—
721#95C2418yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730C24—24no—
731C24—24no—
732C24—24no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24C2514yes—
738C24C2511yescharacteristic
739C2×Q8—28no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—28no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—28no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—28no—
750C2×Q8—24no—
751C2×Q8—42no—
752C2×Q8—42no—
753C2×Q8—42no—
754C2×Q8—42no—
755C2×Q8—44no—
756C2×Q8—44no—
757C2×Q8—416no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—42no—
763C2×D4—42no—
764C2×D4—416no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—24no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—22no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—22no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—42no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—42no—
796C22×C4—816no—
797C22×C4C2×#4114yes—
798C22×C4C2×#4114yes—
799C22×C4C2×#4114yes—
800C22×C42−1+414yes—
801C22×C42−1+414yes—
802C22×C4C2511yescharacteristic
803C22×C4C2514yes—
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2511yescharacteristic
807C22×C4C2514yes—
808C22×C4C2518yes—
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2518yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—216no—
828C4⋊C4—216no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—44no—
849C4⋊C4—42no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—42no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—42no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—42no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C22⋊C4—216no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C42—216no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—28no—
895C42—28no—
896C42—22no—
897C42—22no—
898C42—22no—
899C42—22no—
900C42—22no—
901C42—22no—
902C42—22no—
903C42—22no—
904C42—22no—
905C42—22no—
906C42—22no—
907C42—22no—
908C42—22no—
909C42—22no—
910C42—28no—
911C42—41no—
912C42—41no—
913C42—41no—
914C42—41no—
915C42—41no—
916C42—41no—
917C42—44no—
918C42—48no—
919C42—48no—
920C42—48no—
921C42—48no—
922C42C2×#4114yes—
923C42C2×#4114yes—
924C42C2×#4114yes—
925C42C2×#4114yes—
926C42H(5,𝔽2)14yes—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—48no—
939C23—48no—
940C23—48no—
941C23—84no—
942C23—84no—
943C23—84no—
944C23—84no—
945C23C22×#4112yes—
946C23C2×2−1+412yes—
947C23C2×2−1+412yes—
948C23C2611yescharacteristic
949Q8—48no—
950Q8—416no—
951Q8—48no—
952Q8—48no—
953Q8—88no—
954Q8—84no—
955D4—48no—
956D4—48no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—28no—
978C2×C4—28no—
979C2×C4—28no—
980C2×C4—28no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—21no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—28no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—21no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—28no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—28no—
1012C2×C4—24no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—48no—
1018C2×C4—416no—
1019C2×C4—88no—
1020C2×C4—84no—
1021C2×C4—84no—
1022C2×C4C22×#4112yes—
1023C2×C4C22×#4112yes—
1024C2×C4C22×#4112yes—
1025C2×C4C22×#4112yes—
1026C2×C4C22×#4112yes—
1027C2×C4C22×#4112yes—
1028C2×C4C2×H(5,𝔽2)12yes—
1029C2×C4C2×H(5,𝔽2)12yes—
1030C2×C4C2×H(5,𝔽2)12yes—
1031C2×C4C2×2−1+412yes—
1032C2×C4C2×2−1+412yes—
1033C2×C4C2×2−1+412yes—
1034C2×C4C2×2−1+412yes—
1035C2×C4#58512yes—
1036C2×C4#58512yes—
1037C2×C4#58512yes—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—44no—
1050C22—44no—
1051C22—816no—
1052C22#350914yes—
1053C22C23×#4111yescharacteristic
1054C22C22×H(5,𝔽2)11yescharacteristic
1055C22C22×2−1+411yescharacteristic
1056C22C22×2−1+411yescharacteristic
1057C22C2×#58511yescharacteristic
1058C22C2×#58511yescharacteristic
1059C22C2×#58511yescharacteristic
1060C4—22no—
1061C4—22no—
1062C4—22no—
1063C4—22no—
1064C4—22no—
1065C4—22no—
1066C4—22no—
1067C4—22no—
1068C4—22no—
1069C4—22no—
1070C4—44no—
1071C4—44no—
1072C4—44no—
1073C4—41no—
1074C4—44no—
1075C4—48no—
1076C4—48no—
1077C4—44no—
1078C4—44no—
1079C4—41no—
1080C4—44no—
1081C4#350614yes—
1082C4#356114yes—
1083C2—24no—
1084C2—84no—
1085C2C2×#356111yescharacteristic
1086C2#6275211yescharacteristic
1087C2C2×#350611yescharacteristic
1088C2C2×#350911yescharacteristic
1089C2#6281511yescharacteristic
1090C2#6282311yescharacteristic
1091C2#6283511yescharacteristic
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. #59682C2semidirect
2. #59653C2semidirect
3. #59427C2semidirect
4. #46159C2semidirect
5. #46158C2semidirect
6. #46023C2semidirect
7. #39811C2semidirect
8. #39761C2semidirect
9. #39744C2semidirect
10. #39640C2semidirect
11. #39574C2semidirect
12. #39527C2semidirect
14. #37885C2semidirect
16. #36760C2semidirect
17. #36645C2semidirect
18. #36635C2semidirect
19. #36545C2semidirect
20. #36207C2semidirect
22. #35033C2semidirect
23. #35014C2semidirect
24. #34399C2semidirect
26. C2×#557C22semidirect
32. #2868C22semidirect
33. #2868C22semidirect
34. #2864C22semidirect
35. #2863C22semidirect
36. #2863C22semidirect
37. #2862C22semidirect
38. #2862C22semidirect
39. #2859C22semidirect
40. #2859C22semidirect
41. #2859C22semidirect
56. #2806C22semidirect
57. #2805C22semidirect
59. #2798C22semidirect
60. #2793C22semidirect
61. #2783C22semidirect
62. #2774C22semidirect
63. #2773C22semidirect
64. #2772C22semidirect
65. #2754C22semidirect
66. #2754C22semidirect
68. #2725C22semidirect
69. #2725C22semidirect
70. #2721C22semidirect
71. #2721C22semidirect
72. #2716C22semidirect
80. #2608C22semidirect
81. #2607C22semidirect
83. #2589C22semidirect
84. #2587C22semidirect
85. #2584C22semidirect
86. #2582C22semidirect
87. #2581C22semidirect
88. #2575C22semidirect
89. #2568C22semidirect
91. #2546C22semidirect
92. #2546C22semidirect
97. #2532C22semidirect
98. #2529C22semidirect
99. #2525C22semidirect
100. #2519C22semidirect
101. #2517C22semidirect
102. #2515C22semidirect
104. #2511C22semidirect
106. #2499C22semidirect
107. #2497C22semidirect
108. #2496C22semidirect
109. #2495C22semidirect
110. #2492C22semidirect
111. #2489C22semidirect
118. #2462C22semidirect
121. #2446C22semidirect
122. #2446C22semidirect
123. #2441C22semidirect
124. #2441C22semidirect
125. #2441C22semidirect
126. #2439C22semidirect
127. #2439C22semidirect
130. #2429C22semidirect
131. #2423C22semidirect
132. #2423C22semidirect
134. #2382C22semidirect
135. #2382C22semidirect
136. #2373C22semidirect
138. #2365C22semidirect
139. #2362C22semidirect
142. #2356C22semidirect
143. #2355C22semidirect
145. #2351C22semidirect
146. #2346C22semidirect
148. #2331C22semidirect
152. #2327C22semidirect
153. #2320C22semidirect
155. C4×C4⋊Q8C22semidirect
156. C4×C4⋊Q8C22semidirect
157. C4×C4⋊Q8C22semidirect
158. C4×C4⋊Q8C22semidirect
159. C4×C4⋊Q8C22semidirect
160. C4×C4⋊Q8C22semidirect
161. C4×#125C22semidirect
173. #2295C22semidirect
174. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#596822
#596532
#594272
#461592
#461582
#460232
#398112
#397612
#397442
#396402
#395742
#395272
#395112
#378852
#375372
#367602
#366452
#366352
#365452
#362072
#361612
#350332
#350142
#343992
C2×C4×#1242