Finite Group Databasebeta

← #7657404

Subgroups — #7657404

Order 512.

5130 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42586C214yesmaximal, complemented
2#42577C214yesmaximal, complemented
3#40802C218yesmaximal, complemented
4#40792C218yesmaximal, complemented
5#39737C212yesmaximal, complemented
6#39507C211yesmaximal, characteristic, complemented
7#39385C211yesmaximal, characteristic, complemented
8#37897C212yesmaximal, complemented
9#37701C212yesmaximal, complemented
10#37671C214yesmaximal, complemented
11#37627C212yesmaximal, complemented
12#37500C214yesmaximal, complemented
13#36192C211yesmaximal, characteristic, complemented
14#36127C211yesmaximal, characteristic, complemented
15#36100C212yesmaximal, complemented
16#35725C214yesmaximal, complemented
17#35699C214yesmaximal, complemented
18#35319C211yesmaximal, characteristic, complemented
19#35310C212yesmaximal, complemented
20#34633C212yesmaximal, complemented
21#34621C211yesmaximal, characteristic, complemented
22#34316C212yesmaximal, complemented
23D4×#117C211yesmaximal, characteristic, complemented
24C2×#547C2212yes—
25C2×#541C2212yes—
26C2×#541C2212yescomplemented
27C2×#532C2212yescomplemented
28C2×#525C2214yes—
29C22×C4×D4C2211yescharacteristic
30C22×#117C2212yes—
31#2868C2211yescharacteristic, complemented
32#2859C2211yescharacteristic, complemented
33#2857C2212yes—
34#2857C2212yescomplemented
35#2851C2212yescomplemented
36#2848C2214yes—
37#2837C2218yescomplemented
38#2827C2218yescomplemented
39#2826C2218yes—
40#2803C2218yescomplemented
41#2772C2218yescomplemented
42#2747C2218yescomplemented
43#2741C2218yes—
44#2741C2218yes—
45#2721C2218yescomplemented
46#2714C2218yes—
47#2711C2218yescomplemented
48#2707C2218yescomplemented
49#2694C2218yescomplemented
50#2685C2218yes—
51#2685C2218yes—
52#2652C2218yescomplemented
53#2651C2214yescomplemented
54#2651C2218yescomplemented
55#2649C2218yescomplemented
56#2649C2218yescomplemented
57#2648C2214yes—
58#2648C2218yes—
59#2647C2211yescharacteristic, complemented
60#2644C2212yescomplemented
61#2642C2212yescomplemented
62#2641C2211yescharacteristic, complemented
63#2629C2211yescharacteristic
64#2629C2214yescomplemented
65#2625C2214yescomplemented
66#2624C2212yes—
67#2624C2214yes—
68#2621C2212yes—
69#2621C2212yescomplemented
70#2620C2214yes—
71#2620C2214yescomplemented
72#2619C2211yescharacteristic
73#2619C2212yescomplemented
74#2618C2218yescomplemented
75#2617C2218yes—
76#2597C2218yescomplemented
77#2596C2218yescomplemented
78#2587C2218yescomplemented
79#2585C2218yescomplemented
80#2562C2214yes—
81#2552C2212yescomplemented
82#2552C2214yescomplemented
83#2547C2212yescomplemented
84#2542C2212yes—
85#2537C2212yes—
86#2537C2214yes—
87#2522C2218yescomplemented
88#2512C2214yes—
89#2511C2214yescomplemented
90#2506C2214yescomplemented
91#2506C2214yescomplemented
92#2497C2214yescomplemented
93#2497C2214yescomplemented
94#2496C2214yes—
95#2496C2214yes—
96#2490C2214yes—
97#2490C2214yescomplemented
98#2485C2214yes—
99#2485C2214yescomplemented
100#2480C2218yes—
101#2478C2218yescomplemented
102#2475C2218yes—
103#2473C2218yescomplemented
104#2468C2218yes—
105#2467C2218yescomplemented
106#2466C2218yes—
107#2460C2218yescomplemented
108#2460C2218yescomplemented
109#2455C2218yes—
110#2454C2214yes—
111#2454C2218yescomplemented
112#2448C2214yescomplemented
113#2441C2214yescomplemented
114#2441C2214yescomplemented
115#2432C2214yescomplemented
116#2429C2214yescomplemented
117#2426C2214yescomplemented
118#2423C2214yescomplemented
119#2422C2214yes—
120#2422C2218yescomplemented
121#2418C2218yes—
122#2415C2214yes—
123#2414C2214yes—
124#2408C2214yes—
125#2407C2214yes—
126#2395C2214yescomplemented
127#2392C2214yes—
128#2392C2218yes—
129#2392C2218yescomplemented
130#2374C2218yescomplemented
131#2370C2214yescomplemented
132#2365C2212yescomplemented
133#2363C2214yes—
134#2362C2214yescomplemented
135#2361C2214yes—
136#2354C2212yes—
137#2354C2212yes—
138#2354C2212yescomplemented
139#2352C2214yes—
140D4×C4⋊C4C2214yes—
141D4×C4⋊C4C2212yes—
142D4×C4⋊C4C2214yescomplemented
143#2345C2214yescomplemented
144#2344C2212yes—
145#2342C2214yes—
146#2341C2214yescomplemented
147D4×C22⋊C4C2212yes—
148#2335C2218yescomplemented
149#2327C2212yescomplemented
150#2324C2214yes—
151#2323C2214yes—
152#2314C2212yescomplemented
153C4×C4⋊Q8C2212yescomplemented
154C4×#127C2211yescharacteristic, complemented
155C4×#125C2211yescharacteristic, complemented
156C4×C22⋊Q8C2214yescomplemented
157C4×#121C2212yes—
158#2297C2214yescomplemented
159#2293C2211yescharacteristic
160#2293C2211yescharacteristic
161#2293C2212yescomplemented
162#2290C2212yes—
163#2290C2212yes—
164#2285C2211yescharacteristic
165#2285C2212yescomplemented
166#2280C2212yes—
167#2274C2214yescomplemented
168C42×D4C2211yescharacteristic
169C42×D4C2211yescharacteristic
170C4×#117C2211yescharacteristic
171C22×#41C2314yes—
172C23×D4C2311yescharacteristic
173C24×C4C2312yes—
174#547—216no—
175#541—48no—
176#541—48no—
177#532—48no—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2312yes—
180C2×C4⋊Q8C2312yes—
181C2×#127C2311yescharacteristic
182C2×#126C2318yes—
183C2×#126C2318yes—
184C2×#125C2311yescharacteristic
185C2×#125C2314yes—
186C2×#125C2312yes—
187C2×#125C2318yes—
188C2×#125C2318yes—
189C2×#124C2314yes—
190#525—416no—
191C2×#123C2318yes—
192C2×#123C2318yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×#121C2314yes—
198C2×#121C2312yes—
199C2×#121C2314yes—
200C2×#121C2318yes—
201C2×#121C2314yes—
202C2×#120C2318yes—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×D4—28no—
206C2×C4×D4C2312yes—
207C2×C4×D4C2311yescharacteristic
208C2×C4×D4C2312yes—
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2312yes—
211C2×C4×D4C2311yescharacteristic
212C2×C4×D4C2314yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2318yes—
217C2×C4×D4C2318yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2311yescharacteristic
220C2×#117—48no—
221C2×#117C2312yes—
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2312yes—
225C2×#117C2314yes—
226C2×#117C2314yes—
227C2×#117C2314yes—
228C2×#117C2314yes—
229C2×#117C2314yes—
230C2×#117C2312yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2314yes—
233C22×C4⋊C4C2314yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2314yes—
236C22×C42C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2312yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2314yes—
245#399C2318yes—
246#399C2318yes—
247#399C2318yes—
248#399C2318yes—
249#399C2314yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2314yes—
255#398C2318yes—
256#398C2318yes—
257#398C2314yes—
258#397C2318yes—
259#397C2318yes—
260#397C2314yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2314yes—
268#397C2314yes—
269#397C2314yes—
270#396C2314yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2314yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2314yes—
291#394C2318yes—
292#394C2314yes—
293#394C2314yes—
294#394C2314yes—
295#394C2314yes—
296#392C2318yes—
297#392C2314yes—
298#392C2318yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#390C2312yes—
304#390C2314yes—
305#390C2318yes—
306#390C2314yes—
307#390C2318yes—
308#390C2312yes—
309#390C2312yes—
310#390C2312yes—
311#390C2314yes—
312#390C2318yes—
313#390C2314yes—
314#390C2312yes—
315#390C2312yes—
316#390C2318yes—
317#389C2312yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2318yes—
322#389C2314yes—
323#389C2318yes—
324#389C2318yes—
325#389C2318yes—
326#389C2318yes—
327#389C2312yes—
328#389C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2312yes—
334#389C2314yes—
335#389C2312yes—
336#389C2312yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2314yes—
343#388C2314yes—
344#388C2318yes—
345#388C2314yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2314yes—
351#388C2318yes—
352#388C2314yes—
353#388C2318yes—
354#388C2318yes—
355#388C2314yes—
356#388C2314yes—
357#388C2318yes—
358#387C2314yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2314yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2314yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#386C2314yes—
374#386C2318yes—
375#386C2318yes—
376#386C2314yes—
377#386C2318yes—
378#386C2314yes—
379#385C2318yes—
380#385C2314yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2314yes—
389#384C2311yescharacteristic
390#384C2312yes—
391#384C2312yes—
392#384C2314yes—
393#384C2314yes—
394#384C2314yes—
395#384C2314yes—
396#382C2311yescharacteristic
397#382C2312yes—
398#382C2312yes—
399#381C2314yes—
400#380C2312yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2312yes—
406#380C2318yes—
407#380C2314yes—
408#380C2312yes—
409#380C2314yes—
410#380C2318yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2318yes—
416#379C2318yes—
417#379C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2318yes—
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2311yescharacteristic
435C4×C22⋊C4C2318yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2318yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2312yes—
440C4×C22⋊C4C2318yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2318yes—
446C4×C22⋊C4C2312yes—
447C4×C22⋊C4C2312yes—
448C4×C22⋊C4C2312yes—
449#376C2311yescharacteristic
450#376C2311yescharacteristic
451C43C2311yescharacteristic
452C43C2311yescharacteristic
453C25C2412yes—
454C2×#41—216no—
455C2×#41—48no—
456C2×#41—48no—
457C22×Q8C2414yes—
458C22×D4—24no—
459C22×D4—44no—
460C22×D4C2411yescharacteristic
461C22×D4C2412yes—
462C22×D4C2411yescharacteristic
463C22×D4C2414yes—
464C22×D4C2414yes—
465C22×D4C2412yes—
466C22×D4C2418yes—
467C22×D4C2418yes—
468C23×C4—28no—
469C23×C4—28no—
470C23×C4—44no—
471C23×C4C2414yes—
472C23×C4C2411yescharacteristic
473C23×C4C2412yes—
474C23×C4C2412yes—
475C23×C4C2412yes—
476C23×C4C2412yes—
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2414yes—
481C23×C4C2418yes—
482C23×C4C2414yes—
483C4⋊Q8—28no—
484C4⋊Q8—28no—
485C4⋊Q8—44no—
486#127—24no—
487#126—416no—
488#126—416no—
489#125—24no—
490#125—48no—
491#125—44no—
492#125—416no—
493#125—416no—
494#124—48no—
495#123—232no—
496#123—416no—
497C22⋊Q8—216no—
498C22⋊Q8—216no—
499C22⋊Q8—48no—
500C22⋊Q8—48no—
501#121—216no—
502#121—28no—
503#121—48no—
504#121—48no—
505#121—416no—
506#120—416no—
507C4×Q8—48no—
508C4×Q8—48no—
509C4×D4—24no—
510C4×D4—28no—
511C4×D4—24no—
512C4×D4—28no—
513C4×D4—24no—
514C4×D4—28no—
515C4×D4—44no—
516C4×D4—44no—
517C4×D4—416no—
518C4×D4—48no—
519C4×D4—48no—
520C4×D4—416no—
521C4×D4—416no—
522C4×D4#4118yes—
523#117—24no—
524#117—24no—
525#117—28no—
526#117—44no—
527#117—44no—
528#117—48no—
529#117—48no—
530#117—48no—
531#117—48no—
532#117—48no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—216no—
535C2×C4⋊C4—48no—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2411yescharacteristic
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2411yescharacteristic
573C2×C22⋊C4—28no—
574C2×C22⋊C4—48no—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2412yes—
611C2×C42—24no—
612C2×C42—28no—
613C2×C42—44no—
614C2×C42C2411yescharacteristic
615C2×C42C2414yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2414yes—
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2412yes—
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2414yes—
627C2×C42C2418yes—
628C2×C42C2418yes—
629C2×C42C2418yes—
630C2×C42C2418yes—
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635#95C2412yes—
636#95C2412yes—
637#95C2412yes—
638#95C2412yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2412yes—
643#95C2412yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2418yes—
656#95C2414yes—
657#95C2418yes—
658#95C2414yes—
659#95C2414yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666C24—24no—
667C24—24no—
668C24—42no—
669C24—44no—
670C24—44no—
671C24C2512yes—
672C24C2514yes—
673C24C2512yes—
674C24C2511yescharacteristic
675#41—832no—
676C2×Q8—28no—
677C2×Q8—28no—
678C2×Q8—28no—
679C2×D4—24no—
680C2×D4—28no—
681C2×D4—216no—
682C2×D4—22no—
683C2×D4—24no—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—416no—
700C2×D4C2×#4114yes—
701C22×C4—22no—
702C22×C4—24no—
703C22×C4—22no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—28no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—24no—
719C22×C4—22no—
720C22×C4—216no—
721C22×C4—28no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—432no—
726C22×C4—44no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—42no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×#4118yes—
735C22×C4H(5,𝔽2)14yes—
736C22×C4C2511yescharacteristic
737C22×C4C2511yescharacteristic
738C22×C4C2512yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2518yes—
743C22×C4C2514yes—
744C22×C4C2512yes—
745C22×C4C2512yes—
746C22×C4C2514yes—
747C22×C4C2518yes—
748C22×C4C2512yes—
749C22×C4C2512yes—
750C22×C4C2511yescharacteristic
751C22×C4C2512yes—
752C22×C4C2511yescharacteristic
753C22×C4C2511yescharacteristic
754C22×C4C2511yescharacteristic
755C4⋊C4—24no—
756C4⋊C4—22no—
757C4⋊C4—28no—
758C4⋊C4—216no—
759C4⋊C4—24no—
760C4⋊C4—28no—
761C4⋊C4—24no—
762C4⋊C4—28no—
763C4⋊C4—24no—
764C4⋊C4—24no—
765C4⋊C4—28no—
766C4⋊C4—216no—
767C4⋊C4—216no—
768C4⋊C4—24no—
769C4⋊C4—28no—
770C4⋊C4—24no—
771C4⋊C4—28no—
772C4⋊C4—24no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—48no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—48no—
784C4⋊C4—48no—
785C4⋊C4—48no—
786C4⋊C4—48no—
787C4⋊C4—48no—
788C4⋊C4—48no—
789C4⋊C4—48no—
790C4⋊C4—48no—
791C4⋊C4C2×#4114yes—
792C22⋊C4—24no—
793C22⋊C4—216no—
794C22⋊C4—24no—
795C22⋊C4—216no—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—28no—
799C22⋊C4—24no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—44no—
812C22⋊C4—44no—
813C22⋊C4—48no—
814C22⋊C4—48no—
815C22⋊C4—44no—
816C22⋊C4—44no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C22⋊C4—44no—
821C22⋊C4—48no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4C2×#4118yes—
828C42—22no—
829C42—22no—
830C42—22no—
831C42—28no—
832C42—24no—
833C42—22no—
834C42—24no—
835C42—22no—
836C42—22no—
837C42—24no—
838C42—28no—
839C42—24no—
840C42—44no—
841C42—42no—
842C42—42no—
843C42—48no—
844C42—48no—
845C42—48no—
846C42—48no—
847C42C2×#4114yes—
848C42H(5,𝔽2)14yes—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—22no—
857C23—22no—
858C23—24no—
859C23—22no—
860C23—24no—
861C23—22no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—48no—
870C23—48no—
871C23—84no—
872C23—88no—
873C23—88no—
874C23C22×#4114yes—
875C23C2×H(5,𝔽2)12yes—
876C23C2611yescharacteristic
877Q8—416no—
878D4—28no—
879D4—416no—
880D4—416no—
881D4—48no—
882D4—44no—
883D4—48no—
884D4—816no—
885D4—816no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—21no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—28no—
894C2×C4—216no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—28no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—24no—
906C2×C4—28no—
907C2×C4—24no—
908C2×C4—28no—
909C2×C4—28no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—28no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—28no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—48no—
933C2×C4—48no—
934C2×C4—48no—
935C2×C4—416no—
936C2×C4—44no—
937C2×C4—48no—
938C2×C4—82no—
939C2×C4—88no—
940C2×C4—816no—
941C2×C4—88no—
942C2×C4C22×#4112yes—
943C2×C4C22×#4114yes—
944C2×C4C22×#4112yes—
945C2×C4C22×#4112yes—
946C2×C4C2×H(5,𝔽2)14yes—
947C2×C4C2×H(5,𝔽2)12yes—
948C2×C4C2×H(5,𝔽2)12yes—
949C2×C4C2×H(5,𝔽2)12yes—
950C2×C4#58514yes—
951C22—22no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—41no—
957C22—44no—
958C22—44no—
959C22—42no—
960C22—41no—
961C22—42no—
962C22—44no—
963C22—44no—
964C22—42no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—42no—
973C22—816no—
974C22C23×#4111yescharacteristic
975C22C22×H(5,𝔽2)11yescharacteristic
976C22C22×H(5,𝔽2)11yescharacteristic
977C22C2×#58512yes—
978C222−1+612yes—
979C4—22no—
980C4—24no—
981C4—22no—
982C4—24no—
983C4—42no—
984C4—48no—
985C4—41no—
986C4—44no—
987C4—42no—
988C4—42no—
989C4—44no—
990C4—44no—
991C4—42no—
992C4—44no—
993C4—48no—
994C4—44no—
995C4—41no—
996C4#345514yes—
997C4#351914yes—
998C2—44no—
999C2—42no—
1000C2—84no—
1001C2—82no—
1002C2C2×#345511yescharacteristic
1003C2C2×#351911yescharacteristic
1004C2#6286111yescharacteristic
1005C2#6292512yes—
1006C2#6292512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42586C2semidirect
2. #42577C2semidirect
3. #40802C2semidirect
4. #40792C2semidirect
5. #39737C2semidirect
6. #39507C2semidirect
7. #39385C2semidirect
8. #37897C2semidirect
9. #37701C2semidirect
10. #37671C2semidirect
11. #37627C2semidirect
12. #37500C2semidirect
13. #36192C2semidirect
14. #36127C2semidirect
15. #36100C2semidirect
16. #35725C2semidirect
17. #35699C2semidirect
18. #35319C2semidirect
19. #35310C2semidirect
20. #34633C2semidirect
21. #34621C2semidirect
22. #34316C2semidirect
23. D4×#117C2semidirect
26. C2×#541C22semidirect
27. C2×#532C22semidirect
31. #2868C22semidirect
32. #2859C22semidirect
34. #2857C22semidirect
35. #2851C22semidirect
37. #2837C22semidirect
38. #2827C22semidirect
40. #2803C22semidirect
41. #2772C22semidirect
42. #2747C22semidirect
45. #2721C22semidirect
47. #2711C22semidirect
48. #2707C22semidirect
49. #2694C22semidirect
52. #2652C22semidirect
53. #2651C22semidirect
54. #2651C22semidirect
55. #2649C22semidirect
56. #2649C22semidirect
59. #2647C22semidirect
60. #2644C22semidirect
61. #2642C22semidirect
62. #2641C22semidirect
64. #2629C22semidirect
65. #2625C22semidirect
69. #2621C22semidirect
71. #2620C22semidirect
73. #2619C22semidirect
74. #2618C22semidirect
76. #2597C22semidirect
77. #2596C22semidirect
78. #2587C22semidirect
79. #2585C22semidirect
81. #2552C22semidirect
82. #2552C22semidirect
83. #2547C22semidirect
87. #2522C22semidirect
89. #2511C22semidirect
90. #2506C22semidirect
91. #2506C22semidirect
92. #2497C22semidirect
93. #2497C22semidirect
97. #2490C22semidirect
99. #2485C22semidirect
101. #2478C22semidirect
103. #2473C22semidirect
105. #2467C22semidirect
107. #2460C22semidirect
108. #2460C22semidirect
111. #2454C22semidirect
112. #2448C22semidirect
113. #2441C22semidirect
114. #2441C22semidirect
115. #2432C22semidirect
116. #2429C22semidirect
117. #2426C22semidirect
118. #2423C22semidirect
120. #2422C22semidirect
126. #2395C22semidirect
129. #2392C22semidirect
130. #2374C22semidirect
131. #2370C22semidirect
132. #2365C22semidirect
134. #2362C22semidirect
138. #2354C22semidirect
142. D4×C4⋊C4C22semidirect
143. #2345C22semidirect
146. #2341C22semidirect
148. #2335C22semidirect
149. #2327C22semidirect
152. #2314C22semidirect
153. C4×C4⋊Q8C22semidirect
154. C4×#127C22semidirect
155. C4×#125C22semidirect
156. C4×C22⋊Q8C22semidirect
158. #2297C22semidirect
161. #2293C22semidirect
165. #2285C22semidirect
167. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#425862
#425772
#408022
#407922
#397372
#395072
#393852
#378972
#377012
#376712
#376272
#375002
#361922
#361272
#361002
#357252
#356992
#353192
#353102
#346332
#346212
#343162
D4×#1172