Finite Group Databasebeta

← #7642211

Subgroups — #7642211

Order 512.

4370 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37432C212yesmaximal, complemented
2#37396C212yesmaximal, complemented
3#37322C212yesmaximal, complemented
4#37320C212yesmaximal, complemented
5#37287C214yesmaximal, complemented
6#37282C214yesmaximal, complemented
7#37013C214yesmaximal, complemented
8#37010C214yesmaximal, complemented
9#37007C218yesmaximal, complemented
10#36816C214yesmaximal, complemented
11#36813C214yesmaximal, complemented
12#36806C218yesmaximal, complemented
13#35344C211yesmaximal, characteristic, complemented
14#35325C211yesmaximal, characteristic, complemented
15#35301C211yesmaximal, characteristic
16#35298C211yesmaximal, characteristic, complemented
17#35214C214yesmaximal, complemented
18#35194C214yesmaximal, complemented
19#34086C211yesmaximal, characteristic, complemented
20#34085C211yesmaximal, characteristic, complemented
21#34048C211yesmaximal, characteristic, complemented
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24C22×#117C2211yescharacteristic
25#2868C2211yescharacteristic, complemented
26#2865C2218yescomplemented
27#2864C2212yescomplemented
28#2862C2212yescomplemented
29#2862C2211yescharacteristic, complemented
30#2861C2218yes—
31#2858C2211yescharacteristic, complemented
32#2858C2211yescharacteristic, complemented
33#2855C2212yes—
34#2855C2218yescomplemented
35#2854C2212yes—
36#2852C2218yes—
37#2848C2212yes—
38#2847C2212yes—
39#2799C2218yescomplemented
40#2797C2218yes—
41#2794C2218yescomplemented
42#2793C2218yescomplemented
43#2786C2218yescomplemented
44#2784C2218yes—
45#2779C2218yes—
46#2775C2218yescomplemented
47#2765C2218yescomplemented
48#2762C2218yescomplemented
49#2759C2218yes—
50#2754C2218yes—
51#2752C2218yes—
52#2751C2218yes—
53#2751C2218yescomplemented
54#2750C2218yes—
55#2746C2218yes—
56#2743C2218yes—
57#2740C2218yescomplemented
58#2737C2218yes—
59#2730C2218yes—
60#2721C2218yes—
61#2720C2218yescomplemented
62#2716C2218yes—
63#2715C2218yes—
64#2713C2218yescomplemented
65#2712C2218yes—
66#2700C2218yescomplemented
67#2694C2218yes—
68#2687C2218yes—
69#2685C2218yes—
70#2684C2218yes—
71#2653C2218yes—
72#2652C2218yescomplemented
73#2651C2218yes—
74#2650C2218yescomplemented
75#2628C2214yes—
76#2628C2212yes—
77#2628C2212yes—
78#2621C2212yes—
79#2620C2214yes—
80#2619C2212yes—
81#2611C2214yes—
82#2610C2214yes—
83#2607C2214yes—
84#2607C2214yes—
85#2605C2214yescomplemented
86#2605C2214yescomplemented
87#2599C2214yes—
88#2598C2214yes—
89#2597C2218yes—
90#2591C2212yes—
91#2589C2218yescomplemented
92#2583C2212yes—
93#2577C2218yescomplemented
94#2566C2214yescomplemented
95#2561C2212yes—
96#2560C2218yes—
97#2545C2214yescomplemented
98#2539C2212yes—
99#2527C2218yescomplemented
100#2526C2218yes—
101#2514C2214yescomplemented
102#2513C2214yescomplemented
103#2507C2214yescomplemented
104#2506C2214yescomplemented
105#2500C2214yes—
106#2497C2214yes—
107#2496C2214yes—
108#2492C2214yes—
109#2491C2214yes—
110#2484C2212yes—
111#2482C2212yes—
112#2475C2218yescomplemented
113#2474C2218yes—
114#2452C2214yescomplemented
115#2451C2214yescomplemented
116#2448C2214yescomplemented
117#2447C2214yescomplemented
118#2432C2214yes—
119#2427C2214yes—
120#2426C2214yes—
121#2421C2214yes—
122#2420C2214yes—
123#2406C2212yes—
124#2404C2212yes—
125#2337C2214yescomplemented
126#2336C2214yescomplemented
127#2333C2214yes—
128#2332C2214yes—
129#2331C2214yescomplemented
130#2331C2212yescomplemented
131#2331C2212yescomplemented
132#2328C2212yescomplemented
133#2327C2212yescomplemented
134#2326C2214yescomplemented
135#2324C2214yes—
136#2324C2214yes—
137#2323C2214yes—
138#2323C2214yes—
139#2314C2214yes—
140#2314C2214yes—
141#2313C2212yes—
142#2313C2212yes—
143#2312C2212yes—
144#2312C2212yes—
145#2298C2212yes—
146#2298C2212yes—
147#2298C2212yes—
148#2298C2212yes—
149#2298C2214yes—
150#2297C2214yes—
151#2295C2212yescomplemented
152#2295C2214yescomplemented
153#2293C2212yescomplemented
154#2290C2214yescomplemented
155#2285C2212yes—
156#2283C2211yescharacteristic
157#2283C2211yescharacteristic
158#2280C2212yes—
159C42×Q8C2212yescomplemented
160C42×D4C2212yescomplemented
161C4×#117C2211yescharacteristic
162C4×#117C2211yescharacteristic
163C22×#41C2312yes—
164C24×C4C2311yescharacteristic
165#533—28no—
166#532—28no—
167C2×C4⋊Q8C2311yescharacteristic
168C2×C4⋊Q8C2311yescharacteristic
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2314yes—
171C2×C4⋊Q8C2314yes—
172C2×#127C2311yescharacteristic
173C2×#126C2318yes—
174C2×#125C2312yes—
175C2×#125C2318yes—
176C2×#124C2312yes—
177C2×#124C2314yes—
178C2×#124C2314yes—
179C2×#124C2318yes—
180C2×#123C2314yes—
181C2×C22⋊Q8C2312yes—
182C2×C22⋊Q8C2312yes—
183C2×C22⋊Q8C2314yes—
184C2×C22⋊Q8C2318yes—
185C2×#121C2312yes—
186C2×#121C2312yes—
187C2×#121C2314yes—
188C2×#120C2314yes—
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2314yes—
192C2×C4×D4C2312yes—
193C2×C4×D4C2312yes—
194C2×C4×D4C2314yes—
195C2×#117—28no—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2312yes—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C2×#117C2314yes—
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2314yes—
210C22×C42C2311yescharacteristic
211#401C2318yes—
212#400C2318yes—
213#400C2318yes—
214#400C2314yes—
215#400C2318yes—
216#400C2318yes—
217#400C2314yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#399C2318yes—
222#399C2314yes—
223#399C2318yes—
224#399C2314yes—
225#398C2318yes—
226#398C2318yes—
227#398C2314yes—
228#398C2318yes—
229#398C2314yes—
230#398C2318yes—
231#397C2318yes—
232#397C2314yes—
233#397C2318yes—
234#397C2318yes—
235#397C2318yes—
236#397C2318yes—
237#397C2314yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#396C2318yes—
243#396C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#395C2314yes—
248#395C2318yes—
249#395C2314yes—
250#395C2318yes—
251#394C2318yes—
252#394C2314yes—
253#394C2318yes—
254#394C2314yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#393C2318yes—
260#393C2314yes—
261#393C2318yes—
262#393C2318yes—
263#393C2314yes—
264#393C2318yes—
265#392C2314yes—
266#392C2314yes—
267#391C2318yes—
268#391C2314yes—
269#391C2314yes—
270#391C2314yes—
271#391C2318yes—
272#391C2318yes—
273#391C2318yes—
274#391C2318yes—
275#391C2318yes—
276#391C2318yes—
277#391C2318yes—
278#391C2314yes—
279#390C2318yes—
280#390C2314yes—
281#390C2314yes—
282#390C2314yes—
283#390C2318yes—
284#390C2314yes—
285#390C2314yes—
286#390C2318yes—
287#390C2314yes—
288#389C2318yes—
289#389C2314yes—
290#389C2318yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2318yes—
297#388C2314yes—
298#388C2318yes—
299#388C2318yes—
300#388C2318yes—
301#388C2314yes—
302#388C2314yes—
303#388C2314yes—
304#388C2314yes—
305#388C2314yes—
306#388C2314yes—
307#388C2314yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#387C2318yes—
325#387C2314yes—
326#387C2314yes—
327#387C2314yes—
328#387C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2314yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2314yes—
357#386C2314yes—
358#386C2318yes—
359#386C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2314yes—
366#385C2314yes—
367#385C2318yes—
368#385C2318yes—
369#384C2314yes—
370#384C2314yes—
371#384C2314yes—
372#383C2318yes—
373#383C2312yes—
374#383C2312yes—
375#382C2314yes—
376#382C2314yes—
377#382C2312yes—
378#382C2312yes—
379#382C2314yes—
380#381C2314yes—
381#381C2314yes—
382#381C2312yes—
383#381C2312yes—
384#381C2318yes—
385#381C2318yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2318yes—
391#380C2312yes—
392#380C2314yes—
393#380C2312yes—
394#380C2314yes—
395#379C2314yes—
396#379C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2312yes—
399C4×C4⋊C4C2312yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C22⋊C4C2318yes—
413C4×C22⋊C4C2312yes—
414C4×C22⋊C4C2312yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2312yes—
425#376C2312yes—
426#376C2312yes—
427#376C2312yes—
428#376C2312yes—
429#376C2314yes—
430C43C2311yescharacteristic
431C43C2311yescharacteristic
432C43C2314yes—
433C43C2311yescharacteristic
434C43C2311yescharacteristic
435C25C2411yescharacteristic
436C2×#41—28no—
437C2×#41—84no—
438C22×Q8C2412yes—
439C22×Q8C2412yes—
440C22×Q8C2412yes—
441C22×Q8C2418yes—
442C22×D4C2412yes—
443C22×D4C2412yes—
444C22×D4C2414yes—
445C22×D4C2412yes—
446C22×D4C2418yes—
447C23×C4—24no—
448C23×C4—44no—
449C23×C4C2412yes—
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2412yes—
455C23×C4C2414yes—
456C23×C4C2418yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C4⋊Q8—24no—
460C4⋊Q8—24no—
461C4⋊Q8—24no—
462C4⋊Q8—48no—
463C4⋊Q8—84no—
464#127—24no—
465#126—88no—
466#125—28no—
467#125—88no—
468#124—28no—
469#124—48no—
470#124—84no—
471#124—88no—
472#123—84no—
473C22⋊Q8—28no—
474C22⋊Q8—28no—
475C22⋊Q8—48no—
476C22⋊Q8—88no—
477#121—28no—
478#121—28no—
479#121—48no—
480#120—84no—
481C4×Q8—28no—
482C4×Q8—28no—
483C4×Q8—48no—
484C4×D4—28no—
485C4×D4—28no—
486C4×D4—48no—
487#117—28no—
488#117—28no—
489#117—28no—
490#117—28no—
491#117—28no—
492#117—44no—
493#117—44no—
494#117—84no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4C2412yes—
531C2×C22⋊C4C2412yes—
532C2×C22⋊C4C2412yes—
533C2×C22⋊C4C2412yes—
534C2×C22⋊C4C2414yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C42—24no—
559C2×C42—84no—
560C2×C42#4118yes—
561C2×C42C2412yes—
562C2×C42C2412yes—
563C2×C42C2412yes—
564C2×C42C2412yes—
565C2×C42C2414yes—
566C2×C42C2412yes—
567C2×C42C2412yes—
568C2×C42C2412yes—
569C2×C42C2414yes—
570C2×C42C2418yes—
571C2×C42C2412yes—
572C2×C42C2418yes—
573C2×C42C2418yes—
574C2×C42C2412yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2414yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2411yescharacteristic
582C2×C42C2411yescharacteristic
583C2×C42C2411yescharacteristic
584C2×C42C2411yescharacteristic
585#95C2414yes—
586#95C2414yes—
587#95C2414yes—
588#95C2414yes—
589#95C2414yes—
590#95C2414yes—
591#95C2414yes—
592#95C2414yes—
593#95C2418yes—
594#95C2418yes—
595#95C2414yes—
596#95C2418yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2418yes—
604#95C2414yes—
605#95C2418yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
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—
623C24—22no—
624C24—42no—
625C24—42no—
626C24—42no—
627C24C2512yes—
628C24C2514yes—
629C24C2511yescharacteristic
630#41—816no—
631C2×Q8—24no—
632C2×Q8—24no—
633C2×Q8—24no—
634C2×Q8—28no—
635C2×Q8—44no—
636C2×Q8—44no—
637C2×Q8—48no—
638C2×Q8—48no—
639C2×Q8—48no—
640C2×D4—28no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—24no—
644C2×D4—28no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—48no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—28no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—48no—
669C22×C4—48no—
670C22×C4—42no—
671C22×C4—48no—
672C22×C4—42no—
673C22×C4—416no—
674C22×C4C2×#4114yes—
675C22×C4C2×#4114yes—
676C22×C4C2×#4114yes—
677C22×C4C2512yes—
678C22×C4C2512yes—
679C22×C4C2514yes—
680C22×C4C2514yes—
681C22×C4C2518yes—
682C22×C4C2518yes—
683C22×C4C2514yes—
684C22×C4C2514yes—
685C22×C4C2514yes—
686C22×C4C2514yes—
687C22×C4C2514yes—
688C22×C4C2512yes—
689C22×C4C2511yescharacteristic
690C22×C4C2511yescharacteristic
691C22×C4C2511yescharacteristic
692C22×C4C2511yescharacteristic
693C22×C4C2511yescharacteristic
694C22×C4C2511yescharacteristic
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—24no—
706C4⋊C4—24no—
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—48no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—48no—
715C4⋊C4—48no—
716C4⋊C4—48no—
717C4⋊C4—44no—
718C4⋊C4—48no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—44no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—48no—
726C22⋊C4—28no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—44no—
734C22⋊C4—48no—
735C22⋊C4—44no—
736C22⋊C4—48no—
737C22⋊C4—44no—
738C22⋊C4—44no—
739C22⋊C4—44no—
740C22⋊C4—48no—
741C22⋊C4—48no—
742C22⋊C4—44no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C22⋊C4—48no—
750C22⋊C4—44no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—44no—
754C42—24no—
755C42—24no—
756C42—28no—
757C42—24no—
758C42—24no—
759C42—24no—
760C42—24no—
761C42—42no—
762C42—44no—
763C42—48no—
764C42—42no—
765C42—42no—
766C42—44no—
767C42—42no—
768C42—42no—
769C42—42no—
770C42—48no—
771C42—42no—
772C42—48no—
773C42—42no—
774C42C2×#4114yes—
775C42C2×#4114yes—
776C42C2×#4114yes—
777C42C2×#4114yes—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—22no—
784C23—28no—
785C23—22no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—28no—
790C23—24no—
791C23—44no—
792C23—82no—
793C23—82no—
794C23—88no—
795C23C22×#4112yes—
796C23C2611yescharacteristic
797Q8—48no—
798Q8—84no—
799Q8—84no—
800Q8—168no—
801D4—48no—
802D4—84no—
803D4—84no—
804D4—88no—
805D4—168no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—28no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—28no—
823C2×C4—28no—
824C2×C4—22no—
825C2×C4—28no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—28no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—48no—
847C2×C4—416no—
848C2×C4—44no—
849C2×C4—48no—
850C2×C4—82no—
851C2×C4—82no—
852C2×C4—816no—
853C2×C4C22×#4112yes—
854C2×C4C22×#4112yes—
855C2×C4C22×#4112yes—
856C2×C4C22×#4112yes—
857C2×C4C22×#4112yes—
858C2×C4C22×#4112yes—
859C2×C4#58514yes—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—44no—
864C22—44no—
865C22—42no—
866C22—44no—
867C22—42no—
868C22—48no—
869C22—44no—
870C22—48no—
871C22—44no—
872C22—42no—
873C22—44no—
874C22—88no—
875C22C23×#4111yescharacteristic
876C22C2×#58512yes—
877C22H(7,𝔽2)12yes—
878C222−1+612yes—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—22no—
884C4—44no—
885C4—42no—
886C4—44no—
887C4—42no—
888C4—44no—
889C4—44no—
890C4—44no—
891C4—48no—
892C4—48no—
893C4—44no—
894C4—42no—
895C4—44no—
896C4#345514yes—
897C2—42no—
898C2—84no—
899C2—82no—
900C2C2×#345511yescharacteristic
901C2#6285511yescharacteristic
902C2#6286011yescharacteristic
903C2#6288214yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35301C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37432C2semidirect
2. #37396C2semidirect
3. #37322C2semidirect
4. #37320C2semidirect
5. #37287C2semidirect
6. #37282C2semidirect
7. #37013C2semidirect
8. #37010C2semidirect
9. #37007C2semidirect
10. #36816C2semidirect
11. #36813C2semidirect
12. #36806C2semidirect
13. #35344C2semidirect
14. #35325C2semidirect
16. #35298C2semidirect
17. #35214C2semidirect
18. #35194C2semidirect
19. #34086C2semidirect
20. #34085C2semidirect
21. #34048C2semidirect
25. #2868C22semidirect
26. #2865C22semidirect
27. #2864C22semidirect
28. #2862C22semidirect
29. #2862C22semidirect
31. #2858C22semidirect
32. #2858C22semidirect
34. #2855C22semidirect
39. #2799C22semidirect
41. #2794C22semidirect
42. #2793C22semidirect
43. #2786C22semidirect
46. #2775C22semidirect
47. #2765C22semidirect
48. #2762C22semidirect
53. #2751C22semidirect
57. #2740C22semidirect
61. #2720C22semidirect
64. #2713C22semidirect
66. #2700C22semidirect
72. #2652C22semidirect
74. #2650C22semidirect
85. #2605C22semidirect
86. #2605C22semidirect
91. #2589C22semidirect
93. #2577C22semidirect
94. #2566C22semidirect
97. #2545C22semidirect
99. #2527C22semidirect
101. #2514C22semidirect
102. #2513C22semidirect
103. #2507C22semidirect
104. #2506C22semidirect
112. #2475C22semidirect
114. #2452C22semidirect
115. #2451C22semidirect
116. #2448C22semidirect
117. #2447C22semidirect
125. #2337C22semidirect
126. #2336C22semidirect
129. #2331C22semidirect
130. #2331C22semidirect
131. #2331C22semidirect
132. #2328C22semidirect
133. #2327C22semidirect
134. #2326C22semidirect
151. #2295C22semidirect
152. #2295C22semidirect
153. #2293C22semidirect
154. #2290C22semidirect
159. C42×Q8C22semidirect
160. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#374322
#373962
#373222
#373202
#372872
#372822
#370132
#370102
#370072
#368162
#368132
#368062
#353442
#353252
#353012
#352982
#352142
#351942
#340862
#340852
#340482