Finite Group Databasebeta

← #7635360

Subgroups — #7635360

Order 512.

4892 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52233C218yesmaximal, complemented
2#37963C214yesmaximal, complemented
3#37962C214yesmaximal, complemented
4#37961C214yesmaximal, complemented
5#37960C214yesmaximal, complemented
6#37959C214yesmaximal, complemented
7#37958C214yesmaximal, complemented
8#37957C214yesmaximal
9#37956C214yesmaximal, complemented
10#36625C211yesmaximal, characteristic, complemented
11#34946C212yesmaximal
12#34867C218yesmaximal, complemented
13#34814C212yesmaximal, complemented
14#34814C212yesmaximal, complemented
15#34642C211yesmaximal, characteristic, complemented
16#34634C211yesmaximal, characteristic, complemented
17#34145C212yesmaximal, complemented
18#34074C211yesmaximal, characteristic, complemented
19#34048C211yesmaximal, characteristic, complemented
20C2×#2290C211yesmaximal, characteristic
21#34012C211yesmaximal, characteristic, complemented
22C2×#533C2211yescharacteristic
23C2×#533C2212yes—
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2857C2212yescomplemented
28#2857C2212yescomplemented
29#2855C2214yes—
30#2851C2214yescomplemented
31#2848C2214yes—
32#2789C2218yescomplemented
33#2788C2218yescomplemented
34#2787C2218yescomplemented
35#2786C2218yes—
36#2783C2218yescomplemented
37#2777C2218yescomplemented
38#2775C2218yescomplemented
39#2767C2218yescomplemented
40#2762C2218yescomplemented
41#2759C2218yescomplemented
42#2758C2218yescomplemented
43#2745C2218yescomplemented
44#2740C2218yes—
45#2715C2218yes—
46#2700C2218yes—
47#2689C2218yescomplemented
48#2660C2212yescomplemented
49#2660C2212yescomplemented
50#2660C2212yescomplemented
51#2660C2212yescomplemented
52#2659C2214yes—
53#2659C2214yes—
54#2629C2212yescomplemented
55#2629C2212yescomplemented
56#2628C2214yescomplemented
57#2627C2214yes—
58#2626C2214yes—
59#2605C2218yescomplemented
60#2604C2218yescomplemented
61#2601C2218yes—
62#2599C2218yescomplemented
63#2594C2218yescomplemented
64#2588C2218yescomplemented
65#2577C2218yescomplemented
66#2563C2214yes—
67#2562C2214yes—
68#2562C2214yes—
69#2561C2214yes—
70#2561C2214yes—
71#2560C2218yes—
72#2547C2214yes—
73#2532C2218yescomplemented
74#2528C2218yescomplemented
75#2524C2218yescomplemented
76#2521C2218yes—
77#2503C2214yes—
78#2497C2214yescomplemented
79#2497C2214yescomplemented
80#2496C2214yescomplemented
81#2496C2214yescomplemented
82#2495C2214yescomplemented
83#2495C2214yescomplemented
84#2494C2214yescomplemented
85#2494C2214yescomplemented
86#2493C2218yes—
87#2493C2218yes—
88#2480C2218yes—
89#2480C2218yes—
90#2478C2218yescomplemented
91#2474C2218yes—
92#2469C2218yescomplemented
93#2465C2218yescomplemented
94#2435C2214yes—
95#2401C2218yescomplemented
96#2401C2218yescomplemented
97#2399C2218yescomplemented
98#2398C2218yes—
99#2396C2218yescomplemented
100#2370C2214yescomplemented
101#2370C2214yescomplemented
102#2369C2214yescomplemented
103#2368C2218yes—
104#2365C2214yescomplemented
105#2360C2218yes—
106#2331C2214yescomplemented
107#2330C2214yescomplemented
108#2329C2214yes—
109#2329C2214yes—
110#2314C2214yescomplemented
111#2314C2212yescomplemented
112#2314C2212yescomplemented
113#2313C2214yes—
114#2312C2214yes—
115C4×#126C2218yescomplemented
116C4×#126C2218yescomplemented
117C4×#124C2218yes—
118C4×C22⋊Q8C2214yescomplemented
119C4×C22⋊Q8C2214yescomplemented
120#2298C2218yescomplemented
121#2296C2212yes—
122#2296C2212yes—
123#2296C2212yes—
124#2295C2214yescomplemented
125#2295C2214yescomplemented
126#2295C2218yescomplemented
127#2295C2214yescomplemented
128#2290C2214yes—
129#2290C2214yes—
130#2290C2214yes—
131#2290C2214yes—
132C2×#388C2212yes—
133C2×#387C2212yes—
134C2×#386C2212yes—
135C2×#385C2212yes—
136#2285C2211yescharacteristic
137#2285C2211yescharacteristic
138#2285C2211yescharacteristic
139#2285C2212yes—
140#2285C2212yescomplemented
141#2285C2212yescomplemented
142#2283C2214yes—
143#2283C2214yescomplemented
144#2283C2214yescomplemented
145#2280C2212yes—
146#2280C2212yes—
147#2280C2214yes—
148#2280C2212yes—
149#2280C2212yes—
150C42×Q8C2214yescomplemented
151C4×#117C2212yes—
152C4×#117C2212yes—
153C4×#117C2212yes—
154C4×#117C2214yescomplemented
155C2×C4×C4⋊C4C2211yescharacteristic
156C2×C4×C22⋊C4C2211yescharacteristic
157C2×C4×C22⋊C4C2211yescharacteristic
158C2×#376C2211yescharacteristic
159C23×D4C2311yescharacteristic
160C24×C4C2311yescharacteristic
161C24×C4C2311yescharacteristic
162C24×C4C2312yes—
163#533—28no—
164#533—216no—
165C2×C4⋊Q8C2312yes—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2312yes—
168C2×#126C2318yes—
169C2×#126C2318yes—
170C2×#125C2312yes—
171C2×#125C2312yes—
172C2×#125C2312yes—
173C2×#124C2318yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C4×Q8C2314yes—
180C2×C4×Q8C2314yes—
181C2×C4×Q8C2314yes—
182C2×C4×Q8C2318yes—
183C2×C4×D4—28no—
184C2×C4×D4C2314yes—
185C2×C4×D4C2314yes—
186C2×#117—28no—
187C2×#117C2312yes—
188C2×#117C2312yes—
189C2×#117C2314yes—
190C2×#117C2312yes—
191C2×#117C2312yes—
192C2×#117C2312yes—
193C2×#117C2312yes—
194C2×#117C2314yes—
195C2×#117C2314yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C42—28no—
205C22×C42C2312yes—
206C22×C42C2312yes—
207C22×C42C2312yes—
208C22×C42C2311yescharacteristic
209C22×C42C2312yes—
210C22×C42C2312yes—
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215#401C2318yes—
216#401C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#399C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#397C2318yes—
234#397C2318yes—
235#397C2318yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#396C2318yes—
242#396C2318yes—
243#396C2318yes—
244#396C2318yes—
245#395C2318yes—
246#395C2318yes—
247#395C2318yes—
248#395C2318yes—
249#395C2318yes—
250#394C2318yes—
251#394C2318yes—
252#393C2318yes—
253#393C2318yes—
254#393C2318yes—
255#391C2318yes—
256#391C2318yes—
257#391C2318yes—
258#391C2318yes—
259#391C2314yes—
260#391C2314yes—
261#391C2318yes—
262#391C2318yes—
263#390C2318yes—
264#389C2318yes—
265#389C2318yes—
266#389C2314yes—
267#389C2314yes—
268#389C2318yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#389C2318yes—
274#389C2318yes—
275#389C2314yes—
276#389C2314yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#388C2318yes—
282#388C2318yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#388C2318yes—
289#388C2318yes—
290#388C2318yes—
291#388C2314yes—
292#388C2314yes—
293#388C2314yes—
294#388C2314yes—
295#387C2318yes—
296#387C2318yes—
297#387C2318yes—
298#387C2318yes—
299#387C2318yes—
300#387C2318yes—
301#387C2318yes—
302#387C2318yes—
303#387C2318yes—
304#387C2318yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2314yes—
312#387C2318yes—
313#387C2318yes—
314#387C2314yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2314yes—
320#387C2314yes—
321#386C2314yes—
322#386C2314yes—
323#386C2314yes—
324#386C2314yes—
325#385C2314yes—
326#385C2318yes—
327#385C2318yes—
328#385C2318yes—
329#385C2318yes—
330#385C2314yes—
331#385C2318yes—
332#385C2314yes—
333#385C2314yes—
334#384C2312yes—
335#384C2311yescharacteristic
336#384C2311yescharacteristic
337#384C2311yescharacteristic
338#384C2311yescharacteristic
339#384C2312yes—
340#384C2312yes—
341#383C2318yes—
342#383C2318yes—
343#383C2318yes—
344#382C2318yes—
345#382C2312yes—
346#382C2312yes—
347#382C2312yes—
348#382C2312yes—
349#382C2312yes—
350#382C2314yes—
351#382C2314yes—
352#381C2314yes—
353#381C2314yes—
354#381C2314yes—
355#381C2314yes—
356#381C2318yes—
357#380C2314yes—
358#380C2314yes—
359#380C2314yes—
360#380C2314yes—
361#380C2314yes—
362#380C2314yes—
363#380C2314yes—
364#380C2314yes—
365#380C2314yes—
366#380C2314yes—
367#380C2314yes—
368#380C2314yes—
369#380C2314yes—
370#380C2318yes—
371#380C2314yes—
372#380C2314yes—
373#379C2314yes—
374#379C2314yes—
375#379C2314yes—
376#379C2314yes—
377C4×C4⋊C4C2314yes—
378C4×C4⋊C4C2318yes—
379C4×C4⋊C4C2318yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2314yes—
385C4×C4⋊C4C2314yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2318yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2312yes—
399C4×C4⋊C4C2314yes—
400C4×C22⋊C4C2312yes—
401C4×C22⋊C4C2314yes—
402C4×C22⋊C4C2318yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2318yes—
405C4×C22⋊C4C2318yes—
406C4×C22⋊C4C2318yes—
407C4×C22⋊C4C2314yes—
408C4×C22⋊C4C2318yes—
409C4×C22⋊C4C2314yes—
410C4×C22⋊C4C2318yes—
411C4×C22⋊C4C2312yes—
412C4×C22⋊C4C2314yes—
413C4×C22⋊C4C2314yes—
414#376C2312yes—
415#376C2312yes—
416#376C2318yes—
417#376C2314yes—
418#376C2314yes—
419#376C2314yes—
420#376C2314yes—
421C2×#95C2312yes—
422C2×#95C2312yes—
423C2×#95C2312yes—
424C2×#95C2312yes—
425C2×#95C2312yes—
426C43C2314yes—
427C43C2314yes—
428C43C2314yes—
429C25C2411yescharacteristic
430C25C2411yescharacteristic
431C22×Q8C2414yes—
432C22×Q8C2414yes—
433C22×Q8C2414yes—
434C22×D4—24no—
435C22×D4—44no—
436C22×D4C2414yes—
437C23×C4—24no—
438C23×C4—24no—
439C23×C4—24no—
440C23×C4—28no—
441C23×C4—24no—
442C23×C4—24no—
443C23×C4—24no—
444C23×C4—44no—
445C23×C4—44no—
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2412yes—
451C23×C4C2412yes—
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2411yescharacteristic
460C23×C4C2412yes—
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C4⋊Q8—28no—
464C4⋊Q8—28no—
465C4⋊Q8—28no—
466#126—416no—
467#126—416no—
468#125—28no—
469#125—28no—
470#125—28no—
471#124—416no—
472C22⋊Q8—216no—
473C22⋊Q8—216no—
474C22⋊Q8—216no—
475C22⋊Q8—48no—
476C22⋊Q8—48no—
477C4×Q8—216no—
478C4×Q8—216no—
479C4×Q8—216no—
480C4×Q8—416no—
481C4×D4—216no—
482C4×D4—216no—
483#117—28no—
484#117—28no—
485#117—28no—
486#117—28no—
487#117—216no—
488#117—28no—
489#117—28no—
490#117—48no—
491#117—48no—
492C2×C4⋊C4—28no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—44no—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C22⋊C4—28no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—44no—
532C2×C22⋊C4—44no—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2414yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C42—24no—
554C2×C42—28no—
555C2×C42—24no—
556C2×C42—24no—
557C2×C42—28no—
558C2×C42—28no—
559C2×C42—28no—
560C2×C42—28no—
561C2×C42#4118yes—
562C2×C42#4118yes—
563C2×C42C2412yes—
564C2×C42C2418yes—
565C2×C42C2412yes—
566C2×C42C2412yes—
567C2×C42C2412yes—
568C2×C42C2412yes—
569C2×C42C2412yes—
570C2×C42C2412yes—
571C2×C42C2412yes—
572C2×C42C2414yes—
573C2×C42C2414yes—
574C2×C42C2414yes—
575C2×C42C2414yes—
576C2×C42C2411yescharacteristic
577C2×C42C2411yescharacteristic
578C2×C42C2412yes—
579C2×C42C2418yes—
580C2×C42C2418yes—
581C2×C42C2418yes—
582C2×C42C2418yes—
583C2×C42C2418yes—
584C2×C42C2411yescharacteristic
585C2×C42C2411yescharacteristic
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2412yes—
589#95C2414yes—
590#95C2414yes—
591#95C2414yes—
592#95C2414yes—
593#95C2414yes—
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624C24—22no—
625C24—24no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24C2512yes—
635C24C2512yes—
636C24C2511yescharacteristic
637C2×Q8—28no—
638C2×Q8—28no—
639C2×Q8—28no—
640C2×Q8—48no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—48no—
644C2×D4—28no—
645C2×D4—28no—
646C2×D4—44no—
647C2×D4—416no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—432no—
692C22×C4—416no—
693C22×C4—416no—
694C22×C4C2×#4118yes—
695C22×C4C2×#4114yes—
696C22×C4C2×#4114yes—
697C22×C4C2×#4114yes—
698C22×C4C2×#4114yes—
699C22×C42−1+414yes—
700C22×C4C2512yes—
701C22×C4C2512yes—
702C22×C4C2512yes—
703C22×C4C2514yes—
704C22×C4C2518yes—
705C22×C4C2514yes—
706C22×C4C2514yes—
707C22×C4C2514yes—
708C22×C4C2514yes—
709C22×C4C2518yes—
710C22×C4C2514yes—
711C22×C4C2512yes—
712C22×C4C2512yes—
713C22×C4C2512yes—
714C22×C4C2512yes—
715C22×C4C2512yes—
716C22×C4C2511yescharacteristic
717C22×C4C2511yescharacteristic
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—216no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—28no—
734C4⋊C4—28no—
735C4⋊C4—28no—
736C4⋊C4—216no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—48no—
743C4⋊C4—44no—
744C4⋊C4—44no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4—48no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C22⋊C4—28no—
752C22⋊C4—28no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—216no—
757C22⋊C4—216no—
758C22⋊C4—28no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—28no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—48no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C22⋊C4—48no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C42—22no—
772C42—24no—
773C42—24no—
774C42—24no—
775C42—24no—
776C42—24no—
777C42—22no—
778C42—24no—
779C42—24no—
780C42—28no—
781C42—28no—
782C42—28no—
783C42—24no—
784C42—24no—
785C42—28no—
786C42—216no—
787C42—48no—
788C42—48no—
789C42—48no—
790C42—48no—
791C42—48no—
792C42C2×#4118yes—
793C42C2×#4114yes—
794C42C2×#4114yes—
795C42C2×#4118yes—
796C42C2×#4118yes—
797C23—22no—
798C23—22no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—24no—
810C23—24no—
811C23—48no—
812C23—48no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—84no—
819C23—84no—
820C23C22×#4112yes—
821C23C22×#4112yes—
822C23C2×2−1+412yes—
823C23#58514yes—
824C23C2611yescharacteristic
825Q8—416no—
826Q8—88no—
827Q8—88no—
828D4—416no—
829C2×C4—216no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—28no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—28no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—28no—
854C2×C4—28no—
855C2×C4—28no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—28no—
859C2×C4—28no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—48no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—48no—
871C2×C4—48no—
872C2×C4—48no—
873C2×C4—48no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—48no—
877C2×C4—48no—
878C2×C4—48no—
879C2×C4—48no—
880C2×C4—84no—
881C2×C4—84no—
882C2×C4#556116yes—
883C2×C4C22×#4114yes—
884C2×C4C22×#4114yes—
885C2×C4C22×#4114yes—
886C2×C4C22×#4114yes—
887C2×C4C22×#4112yes—
888C2×C4C22×#4112yes—
889C2×C4C22×#4112yes—
890C2×C4C22×#4112yes—
891C2×C4C2×2−1+412yes—
892C2×C4C2×2−1+412yes—
893C2×C4#58514yes—
894C22—24no—
895C22—24no—
896C22—22no—
897C22—22no—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—416no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—44no—
907C22—42no—
908C22—44no—
909C22—42no—
910C22—42no—
911C22—88no—
912C22C2×#55614yes—
913C22C23×#4111yescharacteristic
914C22C23×#4111yescharacteristic
915C22C22×2−1+411yescharacteristic
916C22C2×#58512yes—
917C22C2×#58512yes—
918C4—24no—
919C4—24no—
920C4—24no—
921C4—24no—
922C4—24no—
923C4—48no—
924C4—44no—
925C4—42no—
926C4—44no—
927C4—48no—
928C4—44no—
929C4—44no—
930C4—44no—
931C4—44no—
932C4—42no—
933C4—42no—
934C4C2×#55614yes—
935C4C2×#55614yes—
936C2—24no—
937C2—44no—
938C2—82no—
939C2#6268611yescharacteristic
940C2C22×#55611yescharacteristic
941C2#6275212yes—
942C2#6281412yes—
943C2#6281411yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52233C2semidirect
2. #37963C2semidirect
3. #37962C2semidirect
4. #37961C2semidirect
5. #37960C2semidirect
6. #37959C2semidirect
7. #37958C2semidirect
9. #37956C2semidirect
10. #36625C2semidirect
12. #34867C2semidirect
13. #34814C2semidirect
14. #34814C2semidirect
15. #34642C2semidirect
16. #34634C2semidirect
17. #34145C2semidirect
18. #34074C2semidirect
19. #34048C2semidirect
21. #34012C2semidirect
27. #2857C22semidirect
28. #2857C22semidirect
30. #2851C22semidirect
32. #2789C22semidirect
33. #2788C22semidirect
34. #2787C22semidirect
36. #2783C22semidirect
37. #2777C22semidirect
38. #2775C22semidirect
39. #2767C22semidirect
40. #2762C22semidirect
41. #2759C22semidirect
42. #2758C22semidirect
43. #2745C22semidirect
47. #2689C22semidirect
48. #2660C22semidirect
49. #2660C22semidirect
50. #2660C22semidirect
51. #2660C22semidirect
54. #2629C22semidirect
55. #2629C22semidirect
56. #2628C22semidirect
59. #2605C22semidirect
60. #2604C22semidirect
62. #2599C22semidirect
63. #2594C22semidirect
64. #2588C22semidirect
65. #2577C22semidirect
73. #2532C22semidirect
74. #2528C22semidirect
75. #2524C22semidirect
78. #2497C22semidirect
79. #2497C22semidirect
80. #2496C22semidirect
81. #2496C22semidirect
82. #2495C22semidirect
83. #2495C22semidirect
84. #2494C22semidirect
85. #2494C22semidirect
90. #2478C22semidirect
92. #2469C22semidirect
93. #2465C22semidirect
95. #2401C22semidirect
96. #2401C22semidirect
97. #2399C22semidirect
99. #2396C22semidirect
100. #2370C22semidirect
101. #2370C22semidirect
102. #2369C22semidirect
104. #2365C22semidirect
106. #2331C22semidirect
107. #2330C22semidirect
110. #2314C22semidirect
111. #2314C22semidirect
112. #2314C22semidirect
115. C4×#126C22semidirect
116. C4×#126C22semidirect
118. C4×C22⋊Q8C22semidirect
119. C4×C22⋊Q8C22semidirect
120. #2298C22semidirect
124. #2295C22semidirect
125. #2295C22semidirect
126. #2295C22semidirect
127. #2295C22semidirect
140. #2285C22semidirect
141. #2285C22semidirect
143. #2283C22semidirect
144. #2283C22semidirect
150. C42×Q8C22semidirect
154. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#522332
#379632
#379622
#379612
#379602
#379592
#379582
#379572
#379562
#366252
#349462
#348672
#348142
#346422
#346342
#341452
#340742
#340482
C2×#22902
#340122