Finite Group Databasebeta

← #7644120

Subgroups — #7644120

Order 512.

4696 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42500C214yesmaximal, complemented
2#42499C214yesmaximal, complemented
3#42498C214yesmaximal, complemented
4#42497C214yesmaximal, complemented
5#42496C214yesmaximal, complemented
6#42495C214yesmaximal, complemented
7#42494C214yesmaximal, complemented
8#42493C214yesmaximal, complemented
9#37478C214yesmaximal, complemented
10#37477C214yesmaximal, complemented
11#36750C214yesmaximal, complemented
12#36749C214yesmaximal, complemented
13#35585C212yesmaximal, complemented
14#35566C212yesmaximal, complemented
15#35529C212yesmaximal
16#35515C212yesmaximal
17#35181C211yesmaximal, characteristic, complemented
18#35167C211yesmaximal, characteristic, complemented
19#34642C211yesmaximal, characteristic, complemented
20#34638C211yesmaximal, characteristic, complemented
21#34186C211yesmaximal, characteristic
22#34181C211yesmaximal, characteristic
23C2×#2319C211yesmaximal, characteristic
24C2×#544C2212yes—
25C2×#533C2212yes—
26C2×#518C2212yes—
27C22×C4×D4C2211yescharacteristic
28#2857C2214yes—
29#2851C2214yes—
30#2841C2218yescomplemented
31#2841C2218yescomplemented
32#2841C2218yescomplemented
33#2841C2218yescomplemented
34#2807C2218yescomplemented
35#2790C2218yescomplemented
36#2790C2218yescomplemented
37#2788C2218yescomplemented
38#2788C2218yescomplemented
39#2768C2218yescomplemented
40#2768C2218yescomplemented
41#2763C2218yescomplemented
42#2742C2218yescomplemented
43#2729C2218yescomplemented
44#2729C2218yescomplemented
45#2720C2218yescomplemented
46#2720C2218yescomplemented
47#2704C2218yescomplemented
48#2704C2218yescomplemented
49#2677C2218yescomplemented
50#2667C2218yescomplemented
51#2665C2218yescomplemented
52#2660C2212yescomplemented
53#2660C2212yescomplemented
54#2660C2212yescomplemented
55#2660C2212yescomplemented
56#2659C2212yes—
57#2659C2212yes—
58#2659C2212yes—
59#2659C2212yes—
60#2659C2214yes—
61#2659C2218yescomplemented
62#2647C2212yescomplemented
63#2647C2212yescomplemented
64#2647C2212yescomplemented
65#2647C2212yescomplemented
66#2646C2212yes—
67#2646C2212yes—
68#2646C2212yes—
69#2646C2212yes—
70#2646C2214yes—
71#2646C2218yescomplemented
72#2629C2218yescomplemented
73#2628C2218yescomplemented
74#2627C2218yescomplemented
75#2627C2218yescomplemented
76#2584C2214yescomplemented
77#2584C2214yescomplemented
78#2580C2214yes—
79#2580C2214yes—
80#2571C2212yescomplemented
81#2571C2212yescomplemented
82#2570C2214yescomplemented
83#2570C2214yescomplemented
84#2569C2218yes—
85#2567C2214yescomplemented
86#2566C2214yes—
87#2566C2214yes—
88#2563C2214yes—
89#2552C2212yescomplemented
90#2552C2214yescomplemented
91#2552C2212yescomplemented
92#2552C2212yescomplemented
93#2552C2212yescomplemented
94#2551C2212yescomplemented
95#2551C2212yescomplemented
96#2551C2214yescomplemented
97#2550C2214yescomplemented
98#2550C2214yescomplemented
99#2550C2214yescomplemented
100#2550C2214yescomplemented
101#2549C2218yes—
102#2546C2214yescomplemented
103#2542C2214yes—
104#2538C2214yes—
105#2538C2214yes—
106#2509C2214yescomplemented
107#2509C2214yescomplemented
108#2508C2214yescomplemented
109#2508C2214yescomplemented
110#2507C2214yescomplemented
111#2507C2214yescomplemented
112#2506C2214yescomplemented
113#2506C2214yescomplemented
114#2454C2214yes—
115#2454C2214yes—
116#2454C2214yes—
117#2454C2214yes—
118#2452C2214yes—
119#2452C2214yes—
120#2452C2214yes—
121#2452C2214yes—
122#2442C2218yes—
123#2442C2218yescomplemented
124#2440C2218yes—
125#2440C2218yescomplemented
126#2438C2218yescomplemented
127#2438C2218yescomplemented
128#2437C2218yes—
129#2437C2218yes—
130#2437C2218yes—
131#2437C2218yes—
132#2402C2214yescomplemented
133#2402C2214yescomplemented
134#2399C2214yescomplemented
135#2399C2214yescomplemented
136#2357C2214yes—
137#2357C2214yes—
138#2354C2212yes—
139#2354C2212yes—
140#2354C2212yes—
141#2354C2212yes—
142#2349C2214yes—
143#2349C2214yes—
144D4×C4⋊C4C2212yes—
145D4×C4⋊C4C2212yes—
146D4×C4⋊C4C2212yes—
147D4×C4⋊C4C2212yes—
148#2319C2214yes—
149#2319C2214yes—
150#2319C2214yes—
151#2319C2214yes—
152#2317C2212yes—
153#2317C2212yes—
154#2316C2212yes—
155#2316C2212yes—
156#2315C2214yes—
157#2312C2214yes—
158#2309C2212yes—
159#2296C2212yes—
160#2296C2212yes—
161C2×#390C2211yescharacteristic
162C2×#390C2211yescharacteristic
163C2×#389C2211yescharacteristic
164C2×#389C2211yescharacteristic
165C2×#388C2212yes—
166C2×#388C2212yes—
167#2285C2212yes—
168#2285C2211yescharacteristic
169#2285C2211yescharacteristic
170#2285C2211yescharacteristic
171#2285C2211yescharacteristic
172#2280C2214yes—
173C2×#381C2212yes—
174C2×#380C2212yes—
175C2×#380C2214yes—
176#2274C2212yes—
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×#376C2211yescharacteristic
179C23×D4C2311yescharacteristic
180C24×C4C2312yes—
181#544—48no—
182#533—48no—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2314yes—
188C2×C4⋊Q8C2318yes—
189C2×#125C2314yes—
190C2×#125C2314yes—
191C2×#125C2312yes—
192C2×#125C2312yes—
193C2×#125C2314yes—
194C2×#125C2318yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2318yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2318yes—
201C2×C22⋊Q8C2318yes—
202#518—48no—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×D4Q8116yescomplemented
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2312yes—
213C2×C4×D4C2312yes—
214C2×#117C2312yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2314yes—
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C22⋊C4C2318yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2314yes—
242#400C2314yes—
243#400C2318yes—
244#400C2318yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#399C2318yes—
252#399C2318yes—
253#399C2318yes—
254#399C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2314yes—
262#398C2314yes—
263#398C2314yes—
264#398C2314yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#396C2318yes—
291#395C2318yes—
292#395C2318yes—
293#395C2318yes—
294#395C2318yes—
295#395C2314yes—
296#395C2314yes—
297#395C2318yes—
298#395C2318yes—
299#395C2314yes—
300#395C2314yes—
301#395C2314yes—
302#395C2314yes—
303#395C2314yes—
304#395C2314yes—
305#393C2318yes—
306#393C2318yes—
307#393C2318yes—
308#393C2318yes—
309#391C2318yes—
310#391C2318yes—
311#391C2318yes—
312#390C2314yes—
313#390C2314yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#389C2312yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2318yes—
343#389C2318yes—
344#389C2318yes—
345#389C2318yes—
346#389C2318yes—
347#389C2314yes—
348#389C2314yes—
349#389C2318yes—
350#389C2318yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2314yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#385C2314yes—
386#385C2314yes—
387#384C2312yes—
388#384C2314yes—
389#384C2318yes—
390#384C2314yes—
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#384C2314yes—
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2312yes—
401#382C2312yes—
402#382C2314yes—
403#382C2312yes—
404#382C2312yes—
405#382C2312yes—
406#382C2314yes—
407#382C2314yes—
408#382C2312yes—
409#382C2312yes—
410#382C2318yes—
411#381C2318yes—
412#381C2318yes—
413#381C2318yes—
414#380C2318yes—
415#380C2318yes—
416#380C2312yes—
417#380C2312yes—
418#380C2314yes—
419#380C2318yes—
420#380C2318yes—
421#380C2312yes—
422#380C2312yes—
423#380C2318yes—
424#380C2318yes—
425#380C2314yes—
426#380C2314yes—
427#380C2318yes—
428#380C2314yes—
429#380C2314yes—
430#380C2318yes—
431#380C2312yes—
432#380C2312yes—
433#380C2312yes—
434#380C2312yes—
435#380C2314yes—
436#380C2318yes—
437#379C2318yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2318yes—
462#376C2312yes—
463#376C2312yes—
464#376C2312yes—
465#376C2312yes—
466C2×#95C2312yes—
467C2×#95C2318yes—
468C2×#95C2311yescharacteristic
469C2×#95C2311yescharacteristic
470C2×#95C2311yescharacteristic
471C2×#95C2311yescharacteristic
472C2×#95C2312yes—
473C2×#95C2312yes—
474C25C2412yes—
475C22×Q8C2414yes—
476C22×Q8C2414yes—
477C22×Q8C2418yes—
478C22×D4—24no—
479C22×D4—24no—
480C22×D4C2×Q818yes—
481C22×D4C2412yes—
482C22×D4C2412yes—
483C23×C4—82no—
484C23×C4—82no—
485C23×C4C2×Q8116yes—
486C23×C4C2411yescharacteristic
487C23×C4C2412yes—
488C23×C4C2411yescharacteristic
489C23×C4C2412yes—
490C23×C4C2411yescharacteristic
491C23×C4C2411yescharacteristic
492C23×C4C2418yes—
493C23×C4C2418yes—
494C23×C4C2411yescharacteristic
495C23×C4C2412yes—
496C23×C4C2414yes—
497C23×C4C2414yes—
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C4⋊Q8—44no—
501C4⋊Q8—44no—
502C4⋊Q8—48no—
503C4⋊Q8—48no—
504C4⋊Q8—84no—
505C4⋊Q8—88no—
506#125—44no—
507#125—44no—
508#125—48no—
509#125—48no—
510#125—84no—
511#125—88no—
512C22⋊Q8—48no—
513C22⋊Q8—48no—
514C22⋊Q8—416no—
515C22⋊Q8—88no—
516C22⋊Q8—88no—
517C22⋊Q8—88no—
518C22⋊Q8—88no—
519C4×Q8—48no—
520C4×Q8—48no—
521C4×D4—48no—
522C4×D4—48no—
523C4×D4—48no—
524C4×D4—48no—
525C4×D4C2×Q8116yes—
526C4×D4C2×Q8116yes—
527C4×D4C2×Q8116yes—
528C4×D4C2×Q8116yes—
529#117—28no—
530#117—28no—
531#117—28no—
532#117—28no—
533#117—84no—
534#117—84no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—24no—
537C2×C4⋊C4—84no—
538C2×C4⋊C4—84no—
539C2×C4⋊C4—82no—
540C2×C4⋊C4—82no—
541C2×C4⋊C4C2×Q818yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C22⋊C4—416no—
604C2×C22⋊C4—82no—
605C2×C22⋊C4—82no—
606C2×C22⋊C4—82no—
607C2×C22⋊C4—82no—
608C2×C22⋊C4C2×Q8116yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C42—24no—
626C2×C42—24no—
627C2×C42—82no—
628C2×C42C2×Q818yes—
629C2×C42C2414yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635C2×C42C2412yes—
636C2×C42C2412yes—
637C2×C42C2418yes—
638C2×C42C2418yes—
639C2×C42C2414yes—
640C2×C42C2414yes—
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#95C2414yes—
646#95C2414yes—
647#95C2412yes—
648#95C2412yes—
649#95C2412yes—
650#95C2412yes—
651#95C2412yes—
652#95C2412yes—
653#95C2412yes—
654#95C2412yes—
655#95C2414yes—
656#95C2414yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2414yes—
662#95C2414yes—
663#95C2418yes—
664#95C2418yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687C24—24no—
688C24—24no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24C22×Q818yes—
694C24C2514yes—
695C24C2511yescharacteristic
696C2×Q8—44no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8—48no—
703C2×Q8—48no—
704C2×Q8—48no—
705C2×D4—232no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4C22×Q818yes—
711C2×D4C22×Q818yes—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—24no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—24no—
718C22×C4—41no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—41no—
731C22×C4—41no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—41no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—48no—
741C22×C4—48no—
742C22×C4—48no—
743C22×C4—48no—
744C22×C4—48no—
745C22×C4—48no—
746C22×C4—816no—
747C22×C4C22×Q814yes—
748C22×C4C22×Q814yes—
749C22×C4C22×Q818yes—
750C22×C4C22×Q8116yes—
751C22×C4C22×Q8116yes—
752C22×C4C22×Q814yes—
753C22×C4H(5,𝔽2)14yes—
754C22×C42−1+414yes—
755C22×C4C2512yes—
756C22×C4C2514yes—
757C22×C4C2512yes—
758C22×C4C2514yes—
759C22×C4C2512yes—
760C22×C4C2514yes—
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2512yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2511yescharacteristic
770C22×C4C2511yescharacteristic
771C22×C4C2511yescharacteristic
772C22×C4C2511yescharacteristic
773C22×C4C2514yes—
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—42no—
789C4⋊C4—42no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—48no—
793C4⋊C4—48no—
794C4⋊C4—48no—
795C4⋊C4—48no—
796C4⋊C4—42no—
797C4⋊C4—42no—
798C4⋊C4—42no—
799C4⋊C4—42no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—42no—
804C4⋊C4—42no—
805C4⋊C4—42no—
806C4⋊C4—42no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—48no—
814C4⋊C4—48no—
815C4⋊C4—48no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—42no—
829C4⋊C4—42no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—44no—
835C4⋊C4C22×Q818yes—
836C4⋊C4C22×Q818yes—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4C22×Q8116yes—
852C22⋊C4C22×Q8116yes—
853C42—24no—
854C42—24no—
855C42—28no—
856C42—28no—
857C42—28no—
858C42—24no—
859C42—24no—
860C42—28no—
861C42—44no—
862C42—44no—
863C42—48no—
864C42—48no—
865C42C22×Q814yes—
866C42C22×Q814yes—
867C42C22×Q814yes—
868C42C22×Q814yes—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—24no—
874C23—24no—
875C23—24no—
876C23—24no—
877C23—24no—
878C23—24no—
879C23—216no—
880C23—48no—
881C23—48no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23—84no—
886C23C23×Q818yes—
887C23C23×Q812yes—
888C23C2×H(5,𝔽2)12yes—
889C23C2×2−1+412yes—
890C23C2611yescharacteristic
891Q8—88no—
892Q8—88no—
893Q8—168no—
894D4—216no—
895D4—216no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—44no—
949C2×C4—416no—
950C2×C4—416no—
951C2×C4—48no—
952C2×C4—44no—
953C2×C4—82no—
954C2×C4—82no—
955C2×C4—82no—
956C2×C4—84no—
957C2×C4—82no—
958C2×C4—84no—
959C2×C4—168no—
960C2×C4—168no—
961C2×C4#544116yes—
962C2×C4C23×Q812yes—
963C2×C4C23×Q812yes—
964C2×C4C23×Q812yes—
965C2×C4C23×Q812yes—
966C2×C4C23×Q818yes—
967C2×C4C23×Q812yes—
968C2×C4C23×Q812yes—
969C2×C4C2×H(5,𝔽2)12yes—
970C2×C4C2×H(5,𝔽2)12yes—
971C2×C4C2×2−1+412yes—
972C2×C4C2×2−1+412yes—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—28no—
980C22—28no—
981C22—28no—
982C22—44no—
983C22—44no—
984C22—44no—
985C22—44no—
986C22—816no—
987C22C2×#54414yes—
988C22C24×Q811yescharacteristic
989C22C22×H(5,𝔽2)11yescharacteristic
990C22C22×2−1+411yescharacteristic
991C22H(7,𝔽2)11yescharacteristic
992C22H(7,𝔽2)11yescharacteristic
993C22H(7,𝔽2)11yescharacteristic
994C222−1+611yescharacteristic
995C4—22no—
996C4—22no—
997C4—28no—
998C4—22no—
999C4—22no—
1000C4—42no—
1001C4—44no—
1002C4—44no—
1003C4—44no—
1004C4—44no—
1005C4—42no—
1006C4—42no—
1007C4—44no—
1008C4—44no—
1009C4—44no—
1010C4—44no—
1011C4—44no—
1012C4—42no—
1013C4—44no—
1014C4C2×#54414yes—
1015C4C2×#54414yes—
1016C2—24no—
1017C2—48no—
1018C2C22×#54411yescharacteristic
1019C2#6284311yescharacteristic
1020C2#6285411yescharacteristic
1021C2#6287811yescharacteristic
1022C2#6287911yescharacteristic
1023C2#6288011yescharacteristic
1024C2#6288111yescharacteristic
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. #42500C2semidirect
2. #42499C2semidirect
3. #42498C2semidirect
4. #42497C2semidirect
5. #42496C2semidirect
6. #42495C2semidirect
7. #42494C2semidirect
8. #42493C2semidirect
9. #37478C2semidirect
10. #37477C2semidirect
11. #36750C2semidirect
12. #36749C2semidirect
13. #35585C2semidirect
14. #35566C2semidirect
17. #35181C2semidirect
18. #35167C2semidirect
19. #34642C2semidirect
20. #34638C2semidirect
30. #2841C22semidirect
31. #2841C22semidirect
32. #2841C22semidirect
33. #2841C22semidirect
34. #2807C22semidirect
35. #2790C22semidirect
36. #2790C22semidirect
37. #2788C22semidirect
38. #2788C22semidirect
39. #2768C22semidirect
40. #2768C22semidirect
41. #2763C22semidirect
42. #2742C22semidirect
43. #2729C22semidirect
44. #2729C22semidirect
45. #2720C22semidirect
46. #2720C22semidirect
47. #2704C22semidirect
48. #2704C22semidirect
49. #2677C22semidirect
50. #2667C22semidirect
51. #2665C22semidirect
52. #2660C22semidirect
53. #2660C22semidirect
54. #2660C22semidirect
55. #2660C22semidirect
61. #2659C22semidirect
62. #2647C22semidirect
63. #2647C22semidirect
64. #2647C22semidirect
65. #2647C22semidirect
71. #2646C22semidirect
72. #2629C22semidirect
73. #2628C22semidirect
74. #2627C22semidirect
75. #2627C22semidirect
76. #2584C22semidirect
77. #2584C22semidirect
80. #2571C22semidirect
81. #2571C22semidirect
82. #2570C22semidirect
83. #2570C22semidirect
85. #2567C22semidirect
89. #2552C22semidirect
90. #2552C22semidirect
91. #2552C22semidirect
92. #2552C22semidirect
93. #2552C22semidirect
94. #2551C22semidirect
95. #2551C22semidirect
96. #2551C22semidirect
97. #2550C22semidirect
98. #2550C22semidirect
99. #2550C22semidirect
100. #2550C22semidirect
102. #2546C22semidirect
106. #2509C22semidirect
107. #2509C22semidirect
108. #2508C22semidirect
109. #2508C22semidirect
110. #2507C22semidirect
111. #2507C22semidirect
112. #2506C22semidirect
113. #2506C22semidirect
123. #2442C22semidirect
125. #2440C22semidirect
126. #2438C22semidirect
127. #2438C22semidirect
132. #2402C22semidirect
133. #2402C22semidirect
134. #2399C22semidirect
135. #2399C22semidirect
205. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#425002
#424992
#424982
#424972
#424962
#424952
#424942
#424932
#374782
#374772
#367502
#367492
#355852
#355662
#355292
#355152
#351812
#351672
#346422
#346382
#341862
#341812
C2×#23192