Finite Group Databasebeta

← #7646847

Subgroups — #7646847

Order 512.

4280 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42780C214yesmaximal, complemented
2#42773C214yesmaximal, complemented
3#42748C214yesmaximal, complemented
4#42738C214yesmaximal, complemented
5#40155C214yesmaximal, complemented
6#40075C214yesmaximal, complemented
7#39534C214yesmaximal, complemented
8#39011C214yesmaximal, complemented
9#37460C214yesmaximal
10#36977C214yesmaximal, complemented
11#36760C214yesmaximal
12#35544C212yesmaximal
13#35543C212yesmaximal, complemented
14#35315C214yesmaximal, complemented
15#35265C212yesmaximal, complemented
16#35167C211yesmaximal, characteristic, complemented
17#35159C211yesmaximal, characteristic, complemented
18#35151C211yesmaximal, characteristic
19#35151C211yesmaximal, characteristic
20#34814C212yesmaximal
21#34271C211yesmaximal, characteristic, complemented
22C2×#2346C211yesmaximal, characteristic
23C4×#544C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2864C2214yescomplemented
28#2859C2214yescomplemented
29#2857C2214yes—
30#2855C2214yes—
31#2855C2214yes—
32#2851C2214yes—
33#2836C2218yes—
34#2831C2218yes—
35#2798C2218yes—
36#2783C2218yes—
37#2772C2218yes—
38#2766C2218yescomplemented
39#2766C2218yescomplemented
40#2762C2218yescomplemented
41#2762C2218yescomplemented
42#2755C2218yescomplemented
43#2755C2218yescomplemented
44#2754C2218yes—
45#2725C2218yes—
46#2725C2218yes—
47#2721C2218yes—
48#2719C2218yescomplemented
49#2719C2218yescomplemented
50#2716C2218yes—
51#2664C2218yes—
52#2659C2214yes—
53#2654C2218yes—
54#2650C2218yes—
55#2647C2214yescomplemented
56#2647C2214yescomplemented
57#2647C2214yescomplemented
58#2646C2214yes—
59#2645C2214yescomplemented
60#2645C2214yescomplemented
61#2642C2214yescomplemented
62#2637C2218yes—
63#2626C2214yes—
64#2626C2214yes—
65#2571C2214yescomplemented
66#2570C2214yescomplemented
67#2570C2214yescomplemented
68#2552C2214yescomplemented
69#2552C2214yescomplemented
70#2551C2214yescomplemented
71#2550C2214yescomplemented
72#2550C2214yescomplemented
73#2533C2218yescomplemented
74#2533C2218yescomplemented
75#2528C2218yescomplemented
76#2528C2218yescomplemented
77#2519C2218yes—
78#2509C2214yescomplemented
79#2509C2214yescomplemented
80#2509C2214yescomplemented
81#2508C2214yescomplemented
82#2508C2214yescomplemented
83#2508C2214yescomplemented
84#2507C2214yescomplemented
85#2507C2214yescomplemented
86#2507C2214yescomplemented
87#2506C2214yescomplemented
88#2506C2214yescomplemented
89#2506C2214yescomplemented
90#2505C2218yes—
91#2505C2218yes—
92#2497C2212yes—
93#2497C2214yes—
94#2497C2214yes—
95#2497C2212yes—
96#2496C2214yes—
97#2496C2214yes—
98#2496C2212yes—
99#2496C2212yes—
100#2495C2214yes—
101#2495C2214yes—
102#2495C2212yes—
103#2495C2212yes—
104#2494C2212yes—
105#2494C2212yes—
106#2494C2214yes—
107#2494C2214yes—
108#2493C2214yes—
109#2493C2218yes—
110#2493C2214yes—
111#2480C2214yes—
112#2480C2218yes—
113#2480C2214yes—
114#2473C2218yes—
115#2473C2218yes—
116#2469C2218yes—
117#2441C2214yes—
118#2441C2214yes—
119#2441C2214yes—
120#2441C2214yes—
121#2439C2214yes—
122#2439C2214yes—
123#2439C2214yes—
124#2439C2214yes—
125#2401C2214yes—
126#2401C2214yes—
127#2370C2214yescomplemented
128#2370C2214yescomplemented
129#2369C2214yescomplemented
130#2365C2214yescomplemented
131#2346C2214yes—
132#2346C2214yes—
133#2346C2214yes—
134#2346C2214yes—
135#2331C2214yescomplemented
136#2330C2214yescomplemented
137#2330C2214yescomplemented
138#2329C2214yes—
139#2329C2214yes—
140#2327C2214yescomplemented
141#2320C2214yescomplemented
142#2320C2214yescomplemented
143#2317C2212yes—
144#2317C2212yes—
145#2317C2212yes—
146#2317C2212yes—
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2316C2212yes—
150C4×C4⋊Q8C2214yescomplemented
151C4×#125C2214yescomplemented
152C4×#126C2214yes—
153C4×#126C2214yes—
154C4×C22⋊Q8C2214yes—
155C4×C22⋊Q8C2214yes—
156#2296C2212yes—
157#2296C2212yes—
158C2×#389C2211yescharacteristic
159C2×#389C2211yescharacteristic
160C2×#388C2212yes—
161C2×#388C2212yes—
162#2285C2212yes—
163C2×#382C2212yes—
164#2280C2212yes—
165#2280C2212yes—
166C2×#380C2211yescharacteristic
167#2274C2212yes—
168C4×#117C2212yes—
169C2×C4×C4⋊C4C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C22⋊C4C2211yescharacteristic
172C2×#376C2212yes—
173C24×C4C2311yescharacteristic
174#544—28no—
175#544—28no—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2314yes—
179C2×#126C2314yes—
180C2×#126C2314yes—
181C2×#126C2318yes—
182C2×#125C2314yes—
183C2×#125C2314yes—
184C2×#125C2314yes—
185C2×#125C2318yes—
186C2×#125C2318yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C4×Q8C2314yes—
190C2×C4×Q8C2314yes—
191C2×#117—28no—
192C2×#117C2312yes—
193C2×#117C2312yes—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C2×#117C2314yes—
197C2×#117C2314yes—
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C42C2312yes—
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2312yes—
212C22×C42C2312yes—
213#401C2314yes—
214#401C2318yes—
215#401C2314yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2314yes—
225#400C2318yes—
226#400C2314yes—
227#400C2318yes—
228#400C2318yes—
229#400C2314yes—
230#400C2318yes—
231#400C2318yes—
232#400C2314yes—
233#400C2314yes—
234#400C2314yes—
235#399C2318yes—
236#399C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#397C2314yes—
250#397C2314yes—
251#397C2318yes—
252#397C2314yes—
253#397C2318yes—
254#397C2318yes—
255#397C2314yes—
256#397C2314yes—
257#397C2314yes—
258#396C2318yes—
259#396C2318yes—
260#396C2314yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2314yes—
265#395C2318yes—
266#395C2318yes—
267#393C2318yes—
268#393C2318yes—
269#391C2318yes—
270#391C2314yes—
271#391C2314yes—
272#391C2314yes—
273#391C2314yes—
274#391C2314yes—
275#391C2314yes—
276#391C2314yes—
277#391C2318yes—
278#391C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2318yes—
284#389C2314yes—
285#389C2314yes—
286#389C2318yes—
287#389C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2318yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2318yes—
309#389C2318yes—
310#389C2318yes—
311#389C2318yes—
312#389C2314yes—
313#389C2314yes—
314#389C2312yes—
315#389C2318yes—
316#389C2312yes—
317#389C2312yes—
318#389C2312yes—
319#389C2312yes—
320#389C2312yes—
321#389C2312yes—
322#389C2312yes—
323#388C2314yes—
324#388C2314yes—
325#388C2314yes—
326#388C2314yes—
327#388C2314yes—
328#388C2314yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#387C2314yes—
337#387C2314yes—
338#387C2314yes—
339#387C2314yes—
340#387C2314yes—
341#387C2314yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2314yes—
370#385C2314yes—
371#385C2314yes—
372#385C2314yes—
373#384C2314yes—
374#384C2312yes—
375#384C2314yes—
376#384C2314yes—
377#384C2314yes—
378#384C2314yes—
379#384C2312yes—
380#383C2314yes—
381#383C2314yes—
382#383C2318yes—
383#382C2314yes—
384#382C2314yes—
385#382C2312yes—
386#382C2314yes—
387#382C2312yes—
388#382C2318yes—
389#382C2314yes—
390#382C2318yes—
391#382C2314yes—
392#382C2318yes—
393#382C2318yes—
394#381C2314yes—
395#381C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2318yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2312yes—
404#380C2312yes—
405#380C2312yes—
406#380C2312yes—
407#380C2312yes—
408#380C2312yes—
409#380C2312yes—
410#380C2312yes—
411#379C2314yes—
412#379C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2318yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2318yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2318yes—
443C4×C22⋊C4C2312yes—
444C4×C22⋊C4C2312yes—
445C4×C22⋊C4C2314yes—
446#376C2314yes—
447#376C2314yes—
448#376C2314yes—
449#376C2314yes—
450#376C2314yes—
451C2×#95C2312yes—
452C2×#95C2312yes—
453C2×#95C2311yescharacteristic
454C2×#95C2312yes—
455C2×#95C2311yescharacteristic
456C2×#95C2312yes—
457C2×#95C2312yes—
458C43C2314yes—
459C25C2411yescharacteristic
460C22×Q8C2414yes—
461C22×Q8C2414yes—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—24no—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C23×C4C2412yes—
471C23×C4C2411yescharacteristic
472C23×C4C2412yes—
473C23×C4C2411yescharacteristic
474C23×C4C2412yes—
475C23×C4C2412yes—
476C23×C4C2411yescharacteristic
477C4⋊Q8—216no—
478C4⋊Q8—216no—
479C4⋊Q8—48no—
480#126—48no—
481#126—48no—
482#126—88no—
483#125—216no—
484#125—216no—
485#125—48no—
486#125—88no—
487#125—88no—
488C22⋊Q8—216no—
489C22⋊Q8—216no—
490C4×Q8—48no—
491C4×Q8—48no—
492#117—28no—
493#117—28no—
494#117—28no—
495#117—28no—
496#117—216no—
497#117—216no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—82no—
502C2×C4⋊C4—82no—
503C2×C4⋊C4#4118yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C22⋊C4—28no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—82no—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2412yes—
561C2×C22⋊C4C2412yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C42—28no—
571C2×C42—24no—
572C2×C42—24no—
573C2×C42—44no—
574C2×C42—44no—
575C2×C42C2414yes—
576C2×C42C2414yes—
577C2×C42C2414yes—
578C2×C42C2414yes—
579C2×C42C2414yes—
580C2×C42C2414yes—
581C2×C42C2414yes—
582C2×C42C2414yes—
583C2×C42C2414yes—
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2418yes—
589C2×C42C2414yes—
590C2×C42C2418yes—
591C2×C42C2414yes—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2414yes—
595#95C2411yescharacteristic
596#95C2411yescharacteristic
597#95C2411yescharacteristic
598#95C2411yescharacteristic
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2412yes—
606#95C2412yes—
607#95C2418yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2418yes—
614#95C2418yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2414yes—
633#95C2418yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—41no—
651C24—41no—
652C24—41no—
653C24—41no—
654C24C2512yes—
655C24C2511yescharacteristic
656C2×Q8—28no—
657C2×Q8—28no—
658C2×Q8—44no—
659C2×Q8—44no—
660C2×Q8—44no—
661C2×Q8—44no—
662C22×C4—22no—
663C22×C4—24no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
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—22no—
679C22×C4—22no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—41no—
693C22×C4—41no—
694C22×C4—416no—
695C22×C4C2×#4118yes—
696C22×C4C2×#4114yes—
697C22×C42−1+414yes—
698C22×C42−1+414yes—
699C22×C4C2511yescharacteristic
700C22×C4C2511yescharacteristic
701C22×C4C2511yescharacteristic
702C22×C4C2511yescharacteristic
703C22×C4C2514yes—
704C22×C4C2514yes—
705C22×C4C2512yes—
706C22×C4C2514yes—
707C22×C4C2514yes—
708C22×C4C2514yes—
709C22×C4C2512yes—
710C22×C4C2514yes—
711C22×C4C2514yes—
712C22×C4C2514yes—
713C22×C4C2514yes—
714C22×C4C2514yes—
715C22×C4C2514yes—
716C22×C4C2514yes—
717C22×C4C2511yescharacteristic
718C22×C4C2511yescharacteristic
719C22×C4C2512yes—
720C4⋊C4—28no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—216no—
728C4⋊C4—216no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—24no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—28no—
736C4⋊C4—28no—
737C4⋊C4—28no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—48no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—48no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—48no—
763C4⋊C4C2×#41116yes—
764C22⋊C4—28no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—216no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—48no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C42—28no—
783C42—28no—
784C42—28no—
785C42—28no—
786C42—24no—
787C42—24no—
788C42—24no—
789C42—24no—
790C42—28no—
791C42—28no—
792C42—28no—
793C42—28no—
794C42—28no—
795C42—44no—
796C42—44no—
797C42—44no—
798C42—48no—
799C42—44no—
800C42—48no—
801C42—44no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—82no—
817C23—82no—
818C23—82no—
819C23—82no—
820C23C22×#4112yes—
821C23C2×2−1+412yes—
822C23C2×2−1+412yes—
823C23C2611yescharacteristic
824Q8—88no—
825Q8—88no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—48no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—48no—
887C2×C4—44no—
888C2×C4—48no—
889C2×C4—48no—
890C2×C4—82no—
891C2×C4—82no—
892C2×C4—84no—
893C2×C4—84no—
894C2×C4#541116yes—
895C2×C4C22×#4118yes—
896C2×C4C22×#4114yes—
897C2×C4C2×2−1+414yes—
898C2×C4C2×2−1+414yes—
899C2×C4#58512yes—
900C2×C4#58512yes—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—88no—
915C22C2×#54114yes—
916C22C23×#4111yescharacteristic
917C22C22×2−1+411yescharacteristic
918C22C22×2−1+411yescharacteristic
919C22C2×#58511yescharacteristic
920C22C2×#58511yescharacteristic
921C22H(7,𝔽2)11yescharacteristic
922C222−1+611yescharacteristic
923C4—28no—
924C4—22no—
925C4—22no—
926C4—44no—
927C4—44no—
928C4—44no—
929C4—44no—
930C4—44no—
931C4—44no—
932C4—44no—
933C4—41no—
934C4—41no—
935C4—44no—
936C4—44no—
937C4—42no—
938C4—42no—
939C4—44no—
940C4—44no—
941C4—41no—
942C4—41no—
943C4C2×#54118yes—
944C2—24no—
945C2—82no—
946C2C22×#54111yescharacteristic
947C2#6278111yescharacteristic
948C2#6285111yescharacteristic
949C2#6292811yescharacteristic
950C2#6292811yescharacteristic
951C2#6292911yescharacteristic
952C2#6292911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42780C2semidirect
2. #42773C2semidirect
3. #42748C2semidirect
4. #42738C2semidirect
5. #40155C2semidirect
6. #40075C2semidirect
7. #39534C2semidirect
8. #39011C2semidirect
10. #36977C2semidirect
13. #35543C2semidirect
14. #35315C2semidirect
15. #35265C2semidirect
16. #35167C2semidirect
17. #35159C2semidirect
21. #34271C2semidirect
23. C4×#544C2semidirect
27. #2864C22semidirect
28. #2859C22semidirect
38. #2766C22semidirect
39. #2766C22semidirect
40. #2762C22semidirect
41. #2762C22semidirect
42. #2755C22semidirect
43. #2755C22semidirect
48. #2719C22semidirect
49. #2719C22semidirect
55. #2647C22semidirect
56. #2647C22semidirect
57. #2647C22semidirect
59. #2645C22semidirect
60. #2645C22semidirect
61. #2642C22semidirect
65. #2571C22semidirect
66. #2570C22semidirect
67. #2570C22semidirect
68. #2552C22semidirect
69. #2552C22semidirect
70. #2551C22semidirect
71. #2550C22semidirect
72. #2550C22semidirect
73. #2533C22semidirect
74. #2533C22semidirect
75. #2528C22semidirect
76. #2528C22semidirect
78. #2509C22semidirect
79. #2509C22semidirect
80. #2509C22semidirect
81. #2508C22semidirect
82. #2508C22semidirect
83. #2508C22semidirect
84. #2507C22semidirect
85. #2507C22semidirect
86. #2507C22semidirect
87. #2506C22semidirect
88. #2506C22semidirect
89. #2506C22semidirect
127. #2370C22semidirect
128. #2370C22semidirect
129. #2369C22semidirect
130. #2365C22semidirect
135. #2331C22semidirect
136. #2330C22semidirect
137. #2330C22semidirect
140. #2327C22semidirect
141. #2320C22semidirect
142. #2320C22semidirect
150. C4×C4⋊Q8C22semidirect
151. C4×#125C22semidirect

Maximal subgroups

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

subgroupindex
#427802
#427732
#427482
#427382
#401552
#400752
#395342
#390112
#374602
#369772
#367602
#355442
#355432
#353152
#352652
#351672
#351592
#351512
#348142
#342712
C2×#23462
C4×#5442