Finite Group Databasebeta

← #7657999

Subgroups — #7657999

Order 512.

5010 conjugacy classes of subgroups.

The subgroup lattice has 971 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42587C214yesmaximal, complemented
2#42582C214yesmaximal, complemented
3#40788C218yesmaximal, complemented
4#40784C218yesmaximal, complemented
5#39734C212yesmaximal, complemented
6#39506C211yesmaximal, characteristic, complemented
7#39385C211yesmaximal, characteristic, complemented
8#37894C212yesmaximal, complemented
9#37695C212yesmaximal, complemented
10#37663C214yesmaximal, complemented
11#37628C212yesmaximal, complemented
12#37495C214yesmaximal, complemented
13#36165C211yesmaximal, characteristic, complemented
14D4×C4⋊Q8C211yesmaximal, characteristic, complemented
15D4×C22⋊Q8C212yesmaximal
16#35873C214yesmaximal
17#35858C214yesmaximal, complemented
18#35319C211yesmaximal, characteristic, complemented
19#35310C212yesmaximal, complemented
20#34629C211yesmaximal, characteristic, complemented
21C2×#2621C212yesmaximal, complemented
22#34334C212yesmaximal, complemented
23D4×#117C211yesmaximal, characteristic
24C2×D4×Q8C2212yes—
25C2×#541C2212yes—
26C2×#541C2212yescomplemented
27C22×C4⋊Q8C2212yescomplemented
28C22×C22⋊Q8C2214yes—
29C22×C4×D4C2211yescharacteristic
30C22×#117C2212yes—
31#2868C2211yescharacteristic, complemented
32#2859C2211yescharacteristic, complemented
33#2857C2212yes—
34#2857C2212yescomplemented
35#2851C2212yescomplemented
36#2848C2214yes—
37#2836C2218yescomplemented
38#2833C2218yescomplemented
39#2831C2218yescomplemented
40#2783C2218yescomplemented
41#2772C2218yescomplemented
42#2766C2218yescomplemented
43#2766C2218yescomplemented
44#2747C2218yes—
45#2721C2218yescomplemented
46#2716C2218yescomplemented
47#2713C2218yescomplemented
48#2704C2218yescomplemented
49#2698C2218yes—
50#2690C2218yescomplemented
51#2689C2218yes—
52#2666C2218yescomplemented
53#2655C2214yescomplemented
54#2654C2218yescomplemented
55#2652C2214yes—
56#2650C2218yescomplemented
57#2647C2211yescharacteristic, complemented
58#2647C2214yescomplemented
59#2646C2218yescomplemented
60#2645C2212yescomplemented
61#2644C2214yes—
62#2643C2218yes—
63#2642C2211yescharacteristic, complemented
64#2642C2212yescomplemented
65#2629C2211yescharacteristic
66#2625C2212yes—
67#2625C2214yescomplemented
68#2621C2214yes—
69#2621C2211yescharacteristic
70#2621C2218yes—
71#2621C2212yes—
72#2621C2212yescomplemented
73#2621C2212yescomplemented
74#2621C2218yescomplemented
75#2621C2214yescomplemented
76#2571C2212yescomplemented
77#2570C2214yescomplemented
78#2569C2218yescomplemented
79#2552C2214yescomplemented
80#2551C2214yescomplemented
81#2546C2212yescomplemented
82#2542C2212yes—
83#2538C2212yes—
84#2514C2214yescomplemented
85#2513C2214yes—
86#2513C2214yes—
87#2512C2214yes—
88#2510C2218yes—
89#2510C2218yes—
90#2508C2214yescomplemented
91#2508C2214yescomplemented
92#2507C2214yescomplemented
93#2507C2214yescomplemented
94#2506C2214yescomplemented
95#2506C2214yescomplemented
96#2505C2218yescomplemented
97#2505C2218yescomplemented
98#2496C2214yes—
99#2496C2214yes—
100#2495C2214yes—
101#2494C2214yes—
102#2489C2214yescomplemented
103#2481C2218yes—
104#2480C2218yes—
105#2480C2218yes—
106#2480C2218yes—
107#2478C2218yescomplemented
108#2475C2218yes—
109#2473C2218yescomplemented
110#2473C2218yescomplemented
111#2473C2218yescomplemented
112#2452C2214yes—
113#2449C2218yes—
114#2446C2214yescomplemented
115#2442C2218yescomplemented
116#2442C2214yescomplemented
117#2440C2214yes—
118#2440C2218yescomplemented
119#2437C2218yes—
120#2434C2214yescomplemented
121#2429C2214yescomplemented
122#2429C2214yescomplemented
123#2421C2214yescomplemented
124#2417C2214yes—
125#2409C2214yes—
126#2402C2214yescomplemented
127#2401C2214yes—
128C2×#398C2218yescomplemented
129C2×#397C2218yes—
130#2369C2214yescomplemented
131#2368C2218yescomplemented
132#2365C2212yescomplemented
133#2360C2214yescomplemented
134#2355C2212yescomplemented
135#2354C2212yes—
136#2352C2214yes—
137#2349C2214yes—
138#2349C2214yes—
139D4×C4⋊C4C2212yes—
140D4×C4⋊C4C2214yes—
141D4×C4⋊C4C2214yes—
142D4×C4⋊C4C2212yes—
143#2344C2212yes—
144#2342C2214yes—
145Q8×C22⋊C4C2214yescomplemented
146D4×C22⋊C4C2212yes—
147D4×C22⋊C4C2214yes—
148#2331C2214yescomplemented
149#2329C2218yescomplemented
150#2327C2212yescomplemented
151#2323C2214yes—
152#2314C2212yescomplemented
153C4×C4⋊Q8C2211yescharacteristic, complemented
154C4×C4⋊Q8C2212yescomplemented
155C4×#125C2211yescharacteristic, complemented
156C4×C22⋊Q8C2212yes—
157C4×C22⋊Q8C2214yescomplemented
158#2295C2212yescomplemented
159C2×#391C2214yescomplemented
160#2293C2211yescharacteristic
161#2293C2211yescharacteristic
162#2290C2212yes—
163#2290C2212yes—
164#2285C2211yescharacteristic
165C2×#382C2212yescomplemented
166#2280C2212yes—
167#2275C2214yes—
168C42×D4C2211yescharacteristic
169C42×D4C2211yescharacteristic
170C4×#117C2211yescharacteristic
171C23×Q8C2314yes—
172C23×D4C2311yescharacteristic
173C24×C4C2312yes—
174D4×Q8—216no—
175#541—48no—
176#541—48no—
177C2×C4⋊Q8—48no—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2311yescharacteristic
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2312yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2318yes—
185C2×#126C2318yes—
186C2×#126C2318yes—
187C2×#125C2311yescharacteristic
188C2×#125C2312yes—
189C2×#125C2318yes—
190C2×#125C2318yes—
191C2×C22⋊Q8—416no—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2318yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2312yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2318yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2318yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×C4×D4—28no—
205C2×C4×D4C2312yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2312yes—
211C2×C4×D4C2311yescharacteristic
212C2×C4×D4C2312yes—
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2311yescharacteristic
215C2×#117—48no—
216C2×#117C2312yes—
217C2×#117C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2312yes—
220C2×#117C2314yes—
221C2×#117C2314yes—
222C2×#117C2312yes—
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2314yes—
225C22×C4⋊C4C2314yes—
226C22×C4⋊C4C2318yes—
227C22×C4⋊C4C2318yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2314yes—
230C22×C22⋊C4C2318yes—
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2312yes—
234#401C2314yes—
235#401C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2314yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
252#399C2318yes—
253#398C2314yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2314yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2314yes—
270#398C2314yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2314yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2314yes—
284#397C2314yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2314yes—
290#395C2318yes—
291#395C2318yes—
292#395C2318yes—
293#393C2318yes—
294#391C2314yes—
295#391C2312yes—
296#391C2318yes—
297#391C2314yes—
298#391C2314yes—
299#391C2318yes—
300#391C2318yes—
301#391C2318yes—
302#391C2312yes—
303#391C2314yes—
304#391C2314yes—
305#391C2312yes—
306#391C2312yes—
307#390C2312yes—
308#390C2312yes—
309#390C2314yes—
310#390C2314yes—
311#389C2312yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2318yes—
320#389C2318yes—
321#389C2314yes—
322#389C2314yes—
323#389C2312yes—
324#389C2312yes—
325#389C2314yes—
326#389C2318yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2318yes—
335#389C2318yes—
336#388C2318yes—
337#388C2314yes—
338#388C2318yes—
339#388C2318yes—
340#388C2314yes—
341#388C2314yes—
342#388C2314yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#387C2314yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2314yes—
356#387C2314yes—
357#387C2318yes—
358#387C2314yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2314yes—
364#387C2314yes—
365#387C2318yes—
366#386C2314yes—
367#386C2314yes—
368#386C2318yes—
369#386C2318yes—
370#385C2314yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2314yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2314yes—
384#384C2311yescharacteristic
385#384C2312yes—
386#384C2312yes—
387#384C2314yes—
388#384C2314yes—
389#384C2314yes—
390#383C2318yes—
391#382C2311yescharacteristic
392#382C2312yes—
393#382C2314yes—
394#382C2314yes—
395#382C2314yes—
396#382C2312yes—
397#382C2318yes—
398#382C2318yes—
399#381C2314yes—
400#380C2318yes—
401#380C2318yes—
402#380C2314yes—
403#380C2312yes—
404#380C2318yes—
405#380C2314yes—
406#380C2312yes—
407#380C2314yes—
408#380C2312yes—
409#380C2314yes—
410#380C2314yes—
411#380C2318yes—
412#380C2314yes—
413#379C2318yes—
414#379C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2318yes—
432C4×C4⋊C4C2312yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2318yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2318yes—
440C4×C22⋊C4C2312yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2312yes—
443C4×C22⋊C4C2312yes—
444C4×C22⋊C4C2312yes—
445#376C2311yescharacteristic
446#376C2314yes—
447#376C2311yescharacteristic
448C2×#95C2318yes—
449C2×#95C2318yes—
450C2×#95C2318yes—
451C43C2311yescharacteristic
452C43C2311yescharacteristic
453C25C2412yes—
454C22×Q8—216no—
455C22×Q8—48no—
456C22×Q8—48no—
457C22×Q8C2414yes—
458C22×Q8C2412yes—
459C22×Q8C2418yes—
460C22×D4—24no—
461C22×D4—28no—
462C22×D4C2412yes—
463C22×D4C2411yescharacteristic
464C22×D4C2411yescharacteristic
465C23×C4—28no—
466C23×C4—28no—
467C23×C4—44no—
468C23×C4C2411yescharacteristic
469C23×C4C2412yes—
470C23×C4C2414yes—
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2412yes—
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2418yes—
478C23×C4C2418yes—
479C23×C4C2414yes—
480C4⋊Q8—216no—
481C4⋊Q8—28no—
482C4⋊Q8—24no—
483C4⋊Q8—28no—
484C4⋊Q8—416no—
485C4⋊Q8—48no—
486C4⋊Q8—44no—
487#126—416no—
488#126—416no—
489#125—24no—
490#125—44no—
491#125—416no—
492#125—416no—
493C22⋊Q8—216no—
494C22⋊Q8—28no—
495C22⋊Q8—216no—
496C22⋊Q8—232no—
497C22⋊Q8—416no—
498C22⋊Q8—416no—
499C22⋊Q8—48no—
500C22⋊Q8—48no—
501C22⋊Q8—48no—
502C4×Q8—28no—
503C4×Q8—48no—
504C4×Q8—48no—
505C4×D4—24no—
506C4×D4—216no—
507C4×D4—28no—
508C4×D4—216no—
509C4×D4—28no—
510C4×D4—28no—
511C4×D4—24no—
512C4×D4—28no—
513C4×D4—24no—
514C4×D4#4118yes—
515#117—24no—
516#117—24no—
517#117—28no—
518#117—44no—
519#117—44no—
520#117—48no—
521#117—48no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—48no—
524C2×C4⋊C4—48no—
525C2×C4⋊C4—416no—
526C2×C4⋊C4—416no—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2411yescharacteristic
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C22⋊C4—28no—
570C2×C22⋊C4—48no—
571C2×C22⋊C4—416no—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2412yes—
594C2×C42—24no—
595C2×C42—28no—
596C2×C42—44no—
597C2×C42C2411yescharacteristic
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2414yes—
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606C2×C42C2414yes—
607C2×C42C2412yes—
608C2×C42C2412yes—
609C2×C42C2414yes—
610C2×C42C2414yes—
611C2×C42C2418yes—
612C2×C42C2418yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2418yes—
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2412yes—
634#95C2412yes—
635#95C2412yes—
636#95C2412yes—
637#95C2414yes—
638#95C2414yes—
639#95C2412yes—
640#95C2412yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C2414yes—
651#95C2418yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661C24—24no—
662C24—24no—
663C24—28no—
664C24—42no—
665C24—44no—
666C24C2512yes—
667C24C2511yescharacteristic
668C24C2512yes—
669C2×Q8—24no—
670C2×Q8—28no—
671C2×Q8—216no—
672C2×Q8—28no—
673C2×Q8—28no—
674C2×Q8—24no—
675C2×Q8—24no—
676C2×Q8—48no—
677C2×Q8—48no—
678C2×Q8—832no—
679C2×D4—24no—
680C2×D4—28no—
681C2×D4—22no—
682C2×D4—24no—
683C2×D4—416no—
684C2×D4C2×#4114yes—
685C2×D42−1+418yes—
686C22×C4—22no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—28no—
693C22×C4—216no—
694C22×C4—216no—
695C22×C4—28no—
696C22×C4—22no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—28no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—22no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—44no—
711C22×C4—432no—
712C22×C4—44no—
713C22×C4—48no—
714C22×C4—48no—
715C22×C4—48no—
716C22×C4—42no—
717C22×C4—44no—
718C22×C4—48no—
719C22×C4C2×#4118yes—
720C22×C4H(5,𝔽2)14yes—
721C22×C4C2511yescharacteristic
722C22×C4C2512yes—
723C22×C4C2511yescharacteristic
724C22×C4C2514yes—
725C22×C4C2514yes—
726C22×C4C2514yes—
727C22×C4C2514yes—
728C22×C4C2518yes—
729C22×C4C2512yes—
730C22×C4C2512yes—
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2518yes—
734C22×C4C2512yes—
735C22×C4C2511yescharacteristic
736C22×C4C2512yes—
737C22×C4C2512yes—
738C22×C4C2511yescharacteristic
739C22×C4C2511yescharacteristic
740C22×C4C2511yescharacteristic
741C4⋊C4—24no—
742C4⋊C4—22no—
743C4⋊C4—28no—
744C4⋊C4—24no—
745C4⋊C4—28no—
746C4⋊C4—216no—
747C4⋊C4—28no—
748C4⋊C4—24no—
749C4⋊C4—24no—
750C4⋊C4—28no—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—28no—
754C4⋊C4—216no—
755C4⋊C4—216no—
756C4⋊C4—24no—
757C4⋊C4—24no—
758C4⋊C4—28no—
759C4⋊C4—24no—
760C4⋊C4—24no—
761C4⋊C4—28no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—48no—
765C4⋊C4—48no—
766C4⋊C4—48no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—48no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4C2×#4114yes—
783C22⋊C4—24no—
784C22⋊C4—216no—
785C22⋊C4—28no—
786C22⋊C4—216no—
787C22⋊C4—24no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—216no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—28no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4C2×#4118yes—
805C42—22no—
806C42—22no—
807C42—22no—
808C42—28no—
809C42—28no—
810C42—24no—
811C42—22no—
812C42—24no—
813C42—22no—
814C42—22no—
815C42—24no—
816C42—24no—
817C42—28no—
818C42—44no—
819C42—42no—
820C42—42no—
821C42—48no—
822C42—48no—
823C42—48no—
824C42C2×#4114yes—
825C42H(5,𝔽2)14yes—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—21no—
830C23—21no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—24no—
837C23—24no—
838C23—48no—
839C23—416no—
840C23—48no—
841C23—84no—
842C23—88no—
843C23C22×#4114yes—
844C23C2×H(5,𝔽2)12yes—
845C23C2×2−1+418yes—
846C23C2611yescharacteristic
847Q8—416no—
848Q8—48no—
849Q8—816no—
850D4—48no—
851D4—44no—
852D4#541116yescomplemented
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—28no—
861C2×C4—216no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—28no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—28no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—22no—
880C2×C4—24no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—24no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—28no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—28no—
896C2×C4—22no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—48no—
903C2×C4—416no—
904C2×C4—48no—
905C2×C4—48no—
906C2×C4—44no—
907C2×C4—48no—
908C2×C4—82no—
909C2×C4—88no—
910C2×C4—816no—
911C2×C4—816no—
912C2×C4C22×#4112yes—
913C2×C4C22×#4114yes—
914C2×C4C22×#4112yes—
915C2×C4C22×#4112yes—
916C2×C4C2×H(5,𝔽2)14yes—
917C2×C4C2×H(5,𝔽2)12yes—
918C2×C4C2×H(5,𝔽2)12yes—
919C2×C4C2×H(5,𝔽2)12yes—
920C2×C4C2×2−1+414yes—
921C22—24no—
922C22—24no—
923C22—28no—
924C22—28no—
925C22—22no—
926C22—24no—
927C22—41no—
928C22—41no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—44no—
934C22—44no—
935C22—816no—
936C22C2×#54118yes—
937C22C23×#4111yescharacteristic
938C22C22×H(5,𝔽2)11yescharacteristic
939C22C22×H(5,𝔽2)11yescharacteristic
940C22C22×2−1+412yes—
941C222−1+612yes—
942C4—22no—
943C4—24no—
944C4—22no—
945C4—24no—
946C4—42no—
947C4—44no—
948C4—48no—
949C4—44no—
950C4—41no—
951C4—41no—
952C4—44no—
953C4—42no—
954C4—42no—
955C4—44no—
956C4—44no—
957C4—48no—
958C4—42no—
959C4—44no—
960C4C2×#54114yes—
961C4#351914yes—
962C2—28no—
963C2—42no—
964C2—82no—
965C2C22×#54111yescharacteristic
966C2C2×#351911yescharacteristic
967C2#6286111yescharacteristic
968C2#6294212yes—
969C2#6294212yes—
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. #42587C2semidirect
2. #42582C2semidirect
3. #40788C2semidirect
4. #40784C2semidirect
5. #39734C2semidirect
6. #39506C2semidirect
7. #39385C2semidirect
8. #37894C2semidirect
9. #37695C2semidirect
10. #37663C2semidirect
11. #37628C2semidirect
12. #37495C2semidirect
13. #36165C2semidirect
14. D4×C4⋊Q8C2semidirect
17. #35858C2semidirect
18. #35319C2semidirect
19. #35310C2semidirect
20. #34629C2semidirect
21. C2×#2621C2semidirect
22. #34334C2semidirect
26. C2×#541C22semidirect
27. C22×C4⋊Q8C22semidirect
31. #2868C22semidirect
32. #2859C22semidirect
34. #2857C22semidirect
35. #2851C22semidirect
37. #2836C22semidirect
38. #2833C22semidirect
39. #2831C22semidirect
40. #2783C22semidirect
41. #2772C22semidirect
42. #2766C22semidirect
43. #2766C22semidirect
45. #2721C22semidirect
46. #2716C22semidirect
47. #2713C22semidirect
48. #2704C22semidirect
50. #2690C22semidirect
52. #2666C22semidirect
53. #2655C22semidirect
54. #2654C22semidirect
56. #2650C22semidirect
57. #2647C22semidirect
58. #2647C22semidirect
59. #2646C22semidirect
60. #2645C22semidirect
63. #2642C22semidirect
64. #2642C22semidirect
67. #2625C22semidirect
72. #2621C22semidirect
73. #2621C22semidirect
74. #2621C22semidirect
75. #2621C22semidirect
76. #2571C22semidirect
77. #2570C22semidirect
78. #2569C22semidirect
79. #2552C22semidirect
80. #2551C22semidirect
81. #2546C22semidirect
84. #2514C22semidirect
90. #2508C22semidirect
91. #2508C22semidirect
92. #2507C22semidirect
93. #2507C22semidirect
94. #2506C22semidirect
95. #2506C22semidirect
96. #2505C22semidirect
97. #2505C22semidirect
102. #2489C22semidirect
107. #2478C22semidirect
109. #2473C22semidirect
110. #2473C22semidirect
111. #2473C22semidirect
114. #2446C22semidirect
115. #2442C22semidirect
116. #2442C22semidirect
118. #2440C22semidirect
120. #2434C22semidirect
121. #2429C22semidirect
122. #2429C22semidirect
123. #2421C22semidirect
126. #2402C22semidirect
128. C2×#398C22semidirect
130. #2369C22semidirect
131. #2368C22semidirect
132. #2365C22semidirect
133. #2360C22semidirect
134. #2355C22semidirect
145. Q8×C22⋊C4C22semidirect
148. #2331C22semidirect
149. #2329C22semidirect
150. #2327C22semidirect
152. #2314C22semidirect
153. C4×C4⋊Q8C22semidirect
154. C4×C4⋊Q8C22semidirect
155. C4×#125C22semidirect
157. C4×C22⋊Q8C22semidirect
158. #2295C22semidirect
159. C2×#391C22semidirect
165. C2×#382C22semidirect
852. D4#541semidirect

Maximal subgroups

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

subgroupindex
#425872
#425822
#407882
#407842
#397342
#395062
#393852
#378942
#376952
#376632
#376282
#374952
#361652
D4×C4⋊Q82
D4×C22⋊Q82
#358732
#358582
#353192
#353102
#346292
C2×#26212
#343342
D4×#1172