Finite Group Databasebeta

← #7715097

Subgroups — #7715097

Order 512.

5118 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51966C214yesmaximal, complemented
2#51958C214yesmaximal, complemented
3#51873C214yesmaximal, complemented
4#51860C214yesmaximal, complemented
5#46787C218yesmaximal, complemented
6#46540C218yesmaximal, complemented
7#39052C214yesmaximal, complemented
8#39046C214yesmaximal, complemented
9#37898C212yesmaximal, complemented
10#37889C212yesmaximal, complemented
11#37706C212yesmaximal, complemented
12#37694C212yesmaximal, complemented
13#37515C212yesmaximal, complemented
14#37286C212yesmaximal, complemented
15#37273C212yesmaximal, complemented
16#35333C211yesmaximal, characteristic, complemented
17#35272C211yesmaximal, characteristic, complemented
18#35271C212yesmaximal, complemented
19#35259C212yesmaximal, complemented
20#34415C212yesmaximal, complemented
21#34070C211yesmaximal, characteristic, complemented
22C2×#540C2212yes—
23C2×#535C2212yes—
24C2×#532C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C22×#125C2211yescharacteristic, complemented
27C2×C4×#41C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic, complemented
29#2856C2212yes—
30#2856C2212yes—
31#2854C2214yescomplemented
32#2854C2214yescomplemented
33#2851C2212yes—
34#2851C2212yescomplemented
35#2825C2218yescomplemented
36#2795C2218yescomplemented
37#2787C2218yes—
38#2781C2218yescomplemented
39#2779C2218yes—
40#2778C2218yescomplemented
41#2761C2218yescomplemented
42#2753C2218yescomplemented
43#2735C2218yes—
44#2733C2214yescomplemented
45#2731C2214yescomplemented
46#2718C2218yescomplemented
47#2711C2218yescomplemented
48#2709C2218yes—
49#2707C2218yescomplemented
50#2706C2218yescomplemented
51#2705C2218yescomplemented
52#2703C2218yescomplemented
53#2697C2218yes—
54#2693C2218yescomplemented
55#2691C2218yescomplemented
56#2688C2218yescomplemented
57#2684C2214yes—
58#2678C2218yes—
59#2673C2218yes—
60#2673C2218yescomplemented
61#2669C2214yes—
62#2661C2218yescomplemented
63#2653C2218yescomplemented
64#2647C2212yescomplemented
65#2644C2214yescomplemented
66#2641C2212yes—
67#2629C2212yes—
68#2629C2212yescomplemented
69#2629C2212yescomplemented
70#2619C2212yes—
71#2619C2212yes—
72#2619C2212yes—
73#2615C2214yescomplemented
74#2603C2218yescomplemented
75#2602C2218yescomplemented
76#2597C2218yescomplemented
77#2579C2214yes—
78#2579C2214yescomplemented
79#2576C2218yescomplemented
80#2566C2214yes—
81#2565C2214yescomplemented
82#2554C2218yescomplemented
83#2548C2214yes—
84#2541C2214yes—
85#2534C2218yes—
86#2531C2218yescomplemented
87#2531C2218yescomplemented
88#2529C2218yescomplemented
89#2528C2218yescomplemented
90#2526C2218yescomplemented
91#2512C2214yescomplemented
92#2509C2214yescomplemented
93#2494C2214yescomplemented
94#2490C2214yescomplemented
95#2485C2214yes—
96#2480C2218yes—
97#2464C2218yescomplemented
98#2458C2218yescomplemented
99#2456C2218yescomplemented
100#2456C2218yescomplemented
101#2456C2218yescomplemented
102#2456C2218yescomplemented
103#2454C2214yescomplemented
104#2445C2214yes—
105#2444C2218yescomplemented
106#2443C2218yescomplemented
107#2428C2214yes—
108#2425C2218yescomplemented
109#2422C2214yescomplemented
110#2422C2218yescomplemented
111#2416C2214yescomplemented
112#2416C2218yescomplemented
113#2414C2214yescomplemented
114#2410C2218yes—
115#2408C2214yes—
116#2408C2214yes—
117#2408C2214yes—
118#2405C2218yes—
119#2379C2214yescomplemented
120#2375C2214yes—
121#2372C2214yescomplemented
122#2363C2214yescomplemented
123#2361C2214yescomplemented
124#2358C2214yes—
125#2346C2214yes—
126D4×C22⋊C4C2214yes—
127#2330C2212yescomplemented
128#2328C2212yes—
129#2328C2212yes—
130#2328C2218yescomplemented
131#2327C2212yescomplemented
132#2326C2212yes—
133#2326C2212yescomplemented
134#2325C2214yes—
135#2325C2214yescomplemented
136#2324C2214yescomplemented
137#2321C2218yes—
138#2319C2214yescomplemented
139#2317C2212yescomplemented
140#2314C2212yescomplemented
141#2311C2212yes—
142#2309C2212yes—
143C4×#121C2214yescomplemented
144C4×#121C2214yescomplemented
145#2297C2211yescharacteristic
146#2297C2211yescharacteristic, complemented
147#2290C2212yes—
148#2290C2212yes—
149#2290C2212yescomplemented
150#2290C2212yescomplemented
151#2285C2211yescharacteristic
152#2285C2211yescharacteristic, complemented
153#2285C2211yescharacteristic, complemented
154C2×#376C2211yescharacteristic, complemented
155C22×#41C2311yescharacteristic
156C22×#41C2311yescharacteristic
157C23×D4C2312yes—
158C23×D4C2314yes—
159#540—48no—
160#535—216no—
161#532—28no—
162C2×C4⋊Q8C2311yescharacteristic
163C2×#127—44no—
164C2×#127C2311yescharacteristic
165C2×#127C2312yes—
166C2×#127C2314yes—
167C2×#127C2312yes—
168C2×#127C2314yes—
169C2×#126C2318yes—
170C2×#125—44no—
171C2×#125C2312yes—
172C2×#125C2314yes—
173C2×#125C2312yes—
174C2×#124C2311yescharacteristic
175C2×#124C2311yescharacteristic
176C2×#124C2314yes—
177C2×#123C2318yes—
178C2×#123C2318yes—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×#123C2318yes—
182C2×#121C2314yes—
183C2×#121C2312yes—
184C2×#121C2312yes—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#121C2314yes—
188C2×#121C2318yes—
189C2×#121C2318yes—
190C2×#121C2318yes—
191C2×#121C2318yes—
192C2×#121C2318yes—
193C2×#120C2314yes—
194C2×#120C2314yes—
195C2×#120C2318yes—
196C4×#41—44no—
197C4×#41—44no—
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2312yes—
200C2×C4×D4C2312yes—
201C2×C4×D4C2312yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2318yes—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C2×#117C2311yescharacteristic
215C2×#117C2312yes—
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2314yes—
221C22×C22⋊C4C2318yes—
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2312yes—
227C22×C42C2311yescharacteristic
228#401C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#399C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#394C2318yes—
264#394C2318yes—
265#394C2318yes—
266#393C2318yes—
267#392C2318yes—
268#392C2318yes—
269#392C2318yes—
270#392C2318yes—
271#392C2318yes—
272#392C2318yes—
273#392C2318yes—
274#392C2318yes—
275#392C2318yes—
276#391C2314yes—
277#391C2312yes—
278#391C2312yes—
279#390C2314yes—
280#390C2314yes—
281#390C2314yes—
282#390C2314yes—
283#390C2314yes—
284#390C2314yes—
285#390C2318yes—
286#390C2314yes—
287#390C2312yes—
288#390C2312yes—
289#390C2314yes—
290#390C2318yes—
291#390C2314yes—
292#390C2318yes—
293#390C2318yes—
294#390C2318yes—
295#390C2318yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2318yes—
302#389C2314yes—
303#389C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2314yes—
315#388C2314yes—
316#388C2314yes—
317#388C2314yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2314yes—
331#387C2318yes—
332#387C2314yes—
333#387C2314yes—
334#387C2314yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#386C2314yes—
339#386C2314yes—
340#386C2318yes—
341#386C2314yes—
342#386C2318yes—
343#386C2318yes—
344#386C2312yes—
345#386C2318yes—
346#386C2314yes—
347#386C2314yes—
348#386C2312yes—
349#386C2314yes—
350#386C2314yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2314yes—
364#385C2314yes—
365#385C2318yes—
366#385C2318yes—
367#385C2314yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#385C2318yes—
372#385C2318yes—
373#384C2314yes—
374#384C2312yes—
375#384C2312yes—
376#384C2312yes—
377#382C2314yes—
378#382C2312yes—
379#382C2312yes—
380#382C2318yes—
381#382C2312yes—
382#381C2318yes—
383#380C2314yes—
384#380C2314yes—
385#380C2314yes—
386#380C2318yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2318yes—
392#379C2314yes—
393#379C2314yes—
394#379C2318yes—
395#379C2318yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2312yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2314yes—
402C4×C22⋊C4C2318yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2312yes—
405C4×C22⋊C4C2318yes—
406C4×C22⋊C4C2312yes—
407C4×C22⋊C4C2312yes—
408C4×C22⋊C4C2312yes—
409#376C2312yes—
410#376C2312yes—
411#376C2312yes—
412#376C2312yes—
413#376C2318yes—
414C2×#95C2314yes—
415C25C2414yes—
416C2×#41—24no—
417C2×#41—42no—
418C2×#41—42no—
419C2×#41—42no—
420C2×#41—42no—
421C2×#41#4118yes—
422C22×Q8C2411yescharacteristic
423C22×Q8C2411yescharacteristic
424C22×D4—28no—
425C22×D4—44no—
426C22×D4—48no—
427C22×D4—44no—
428C22×D4—88no—
429C22×D4C2414yes—
430C22×D4C2412yes—
431C22×D4C2411yescharacteristic
432C22×D4C2412yes—
433C22×D4C2418yes—
434C22×D4C2418yes—
435C22×D4C2412yes—
436C22×D4C2418yes—
437C22×D4C2414yes—
438C22×D4C2418yes—
439C22×D4C2418yes—
440C22×D4C2418yes—
441C22×D4C2411yescharacteristic
442C22×D4C2411yescharacteristic
443C22×D4C2411yescharacteristic
444C23×C4C2412yes—
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2412yes—
451C23×C4C2412yes—
452C23×C4C2418yes—
453C23×C4C2418yes—
454C23×C4C2414yes—
455C23×C4C2414yes—
456C23×C4C2412yes—
457C4⋊Q8—24no—
458#127—24no—
459#127—216no—
460#127—28no—
461#127—44no—
462#127—48no—
463#126—88no—
464#125—28no—
465#125—44no—
466#125—48no—
467#124—24no—
468#124—216no—
469#124—24no—
470#123—416no—
471#123—88no—
472#123—88no—
473#123—88no—
474#123—88no—
475#121—28no—
476#121—28no—
477#121—216no—
478#121—216no—
479#121—416no—
480#121—48no—
481#121—48no—
482#121—88no—
483#121—88no—
484#121—88no—
485#121—88no—
486#120—216no—
487#120—216no—
488#120—88no—
489C4×Q8—44no—
490C4×Q8—44no—
491C4×D4—28no—
492C4×D4—28no—
493C4×D4—44no—
494C4×D4—48no—
495C4×D4—48no—
496C4×D4—44no—
497C4×D4—44no—
498C4×D4—44no—
499C4×D4—48no—
500C4×D4—88no—
501C4×D4—88no—
502C4×D4—88no—
503#117—28no—
504#117—28no—
505#117—42no—
506#117—42no—
507#117—42no—
508#117—42no—
509#117—44no—
510C2×C4⋊C4—44no—
511C2×C4⋊C4—48no—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2414yes—
535C2×C22⋊C4—88no—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2412yes—
539C2×C22⋊C4C2412yes—
540C2×C22⋊C4C2412yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2412yes—
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—24no—
576C2×C42—24no—
577C2×C42—44no—
578C2×C42—42no—
579C2×C42C2412yes—
580C2×C42C2411yescharacteristic
581C2×C42C2411yescharacteristic
582C2×C42C2411yescharacteristic
583C2×C42C2414yes—
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2412yes—
589C2×C42C2411yescharacteristic
590C2×C42C2411yescharacteristic
591C2×C42C2414yes—
592C2×C42C2418yes—
593C2×C42C2414yes—
594C2×C42C2418yes—
595C2×C42C2412yes—
596C2×C42C2411yescharacteristic
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2418yes—
613#95C2418yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621C24—28no—
622C24—44no—
623C24—48no—
624C24—48no—
625C24—44no—
626C24C2518yes—
627C24C2512yes—
628C24C2511yescharacteristic
629C24C2511yescharacteristic
630C24C2511yescharacteristic
631#41—416no—
632#41—416no—
633C2×Q8—22no—
634C2×Q8—41no—
635C2×Q8—41no—
636C2×Q8—41no—
637C2×Q8—41no—
638C2×Q8C2×#4114yes—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—216no—
643C2×D4—216no—
644C2×D4—28no—
645C2×D4—22no—
646C2×D4—28no—
647C2×D4—28no—
648C2×D4—216no—
649C2×D4—28no—
650C2×D4—41no—
651C2×D4—41no—
652C2×D4—41no—
653C2×D4—41no—
654C2×D4—42no—
655C2×D4—41no—
656C2×D4—41no—
657C2×D4—41no—
658C2×D4—41no—
659C2×D4—42no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—44no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—44no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—48no—
671C2×D4—48no—
672C2×D4—48no—
673C2×D4—44no—
674C2×D4—48no—
675C2×D4—44no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—816no—
680C2×D4—832no—
681C2×D4C2×#4114yes—
682C2×D4C2×#4114yes—
683C2×D4C2×#4114yes—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—42no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—48no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—48no—
709C22×C4—48no—
710C22×C4—48no—
711C22×C4—48no—
712C22×C4—48no—
713C22×C4—48no—
714C22×C4C2×#4114yes—
715C22×C4C2×#4114yes—
716C22×C4C2×#4114yes—
717C22×C4C2514yes—
718C22×C4C2512yes—
719C22×C4C2512yes—
720C22×C4C2512yes—
721C22×C4C2518yes—
722C22×C4C2518yes—
723C22×C4C2512yes—
724C22×C4C2514yes—
725C22×C4C2512yes—
726C22×C4C2518yes—
727C22×C4C2512yes—
728C22×C4C2511yescharacteristic
729C22×C4C2511yescharacteristic
730C22×C4C2511yescharacteristic
731C22×C4C2512yes—
732C22×C4C2511yescharacteristic
733C4⋊C4—28no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—28no—
737C4⋊C4—216no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—44no—
741C4⋊C4—48no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—48no—
747C4⋊C4—48no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—44no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—44no—
756C22⋊C4—28no—
757C22⋊C4—24no—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—24no—
761C22⋊C4—216no—
762C22⋊C4—216no—
763C22⋊C4—28no—
764C22⋊C4—44no—
765C22⋊C4—48no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C22⋊C4—44no—
769C22⋊C4—42no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—48no—
774C22⋊C4—48no—
775C22⋊C4—44no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—48no—
784C22⋊C4—44no—
785C22⋊C4—48no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C42—24no—
794C42—22no—
795C42—22no—
796C42—28no—
797C42—22no—
798C42—22no—
799C42—22no—
800C42—24no—
801C42—24no—
802C42—24no—
803C42—24no—
804C42—24no—
805C42—42no—
806C42—44no—
807C42—44no—
808C42—48no—
809C42—48no—
810C42H(5,𝔽2)14yes—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—22no—
821C23—28no—
822C23—22no—
823C23—28no—
824C23—28no—
825C23—22no—
826C23—28no—
827C23—28no—
828C23—24no—
829C23—24no—
830C23—28no—
831C23—28no—
832C23—88no—
833C23—816no—
834C23—88no—
835C23—88no—
836C23—168no—
837C23C22×#4112yes—
838C23C22×#4112yes—
839C23C22×#4112yes—
840C23C2611yescharacteristic
841Q8—44no—
842Q8—44no—
843D4—44no—
844D4—44no—
845D4—44no—
846D4—44no—
847D4—48no—
848D4—416no—
849D4—88no—
850D4—816no—
851D4—84no—
852D4—84no—
853D4—816no—
854D4—816no—
855D4—816no—
856D4—816no—
857D4—168no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—24no—
865C2×C4—28no—
866C2×C4—28no—
867C2×C4—28no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—28no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—28no—
878C2×C4—24no—
879C2×C4—28no—
880C2×C4—22no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—28no—
886C2×C4—28no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—28no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—28no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—48no—
897C2×C4—48no—
898C2×C4—84no—
899C2×C4—84no—
900C2×C4—84no—
901C2×C4—88no—
902C2×C4—88no—
903C2×C4—84no—
904C2×C4—168no—
905C2×C4—168no—
906C2×C4C22×#4112yes—
907C2×C4C22×#4112yes—
908C2×C4C22×#4112yes—
909C2×C4C22×#4112yes—
910C2×C4C2×H(5,𝔽2)14yes—
911C2×C4C2×H(5,𝔽2)12yes—
912C2×C4#58512yes—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—48no—
927C22—42no—
928C22—42no—
929C22—48no—
930C22—48no—
931C22—44no—
932C22—48no—
933C22—48no—
934C22—48no—
935C22—44no—
936C22—48no—
937C22—1616no—
938C22C23×#4111yescharacteristic
939C22C22×H(5,𝔽2)11yescharacteristic
940C22C2×#58511yescharacteristic
941C22H(7,𝔽2)14yes—
942C4—22no—
943C4—22no—
944C4—22no—
945C4—24no—
946C4—42no—
947C4—42no—
948C4—42no—
949C4—48no—
950C4—42no—
951C4—42no—
952C4—42no—
953C4—44no—
954C4—48no—
955C4—44no—
956C4—48no—
957C4#350514yes—
958C2—42no—
959C2—42no—
960C2—42no—
961C2—82no—
962C2—88no—
963C2C2×#350511yescharacteristic
964C2#6285812yes—
965C2#6287412yes—
966C2#6288312yes—
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. #51966C2semidirect
2. #51958C2semidirect
3. #51873C2semidirect
4. #51860C2semidirect
5. #46787C2semidirect
6. #46540C2semidirect
7. #39052C2semidirect
8. #39046C2semidirect
9. #37898C2semidirect
10. #37889C2semidirect
11. #37706C2semidirect
12. #37694C2semidirect
13. #37515C2semidirect
14. #37286C2semidirect
15. #37273C2semidirect
16. #35333C2semidirect
17. #35272C2semidirect
18. #35271C2semidirect
19. #35259C2semidirect
20. #34415C2semidirect
21. #34070C2semidirect
26. C22×#125C22semidirect
28. C2×C4×#41C22semidirect
31. #2854C22semidirect
32. #2854C22semidirect
34. #2851C22semidirect
35. #2825C22semidirect
36. #2795C22semidirect
38. #2781C22semidirect
40. #2778C22semidirect
41. #2761C22semidirect
42. #2753C22semidirect
44. #2733C22semidirect
45. #2731C22semidirect
46. #2718C22semidirect
47. #2711C22semidirect
49. #2707C22semidirect
50. #2706C22semidirect
51. #2705C22semidirect
52. #2703C22semidirect
54. #2693C22semidirect
55. #2691C22semidirect
56. #2688C22semidirect
60. #2673C22semidirect
62. #2661C22semidirect
63. #2653C22semidirect
64. #2647C22semidirect
65. #2644C22semidirect
68. #2629C22semidirect
69. #2629C22semidirect
73. #2615C22semidirect
74. #2603C22semidirect
75. #2602C22semidirect
76. #2597C22semidirect
78. #2579C22semidirect
79. #2576C22semidirect
81. #2565C22semidirect
82. #2554C22semidirect
86. #2531C22semidirect
87. #2531C22semidirect
88. #2529C22semidirect
89. #2528C22semidirect
90. #2526C22semidirect
91. #2512C22semidirect
92. #2509C22semidirect
93. #2494C22semidirect
94. #2490C22semidirect
97. #2464C22semidirect
98. #2458C22semidirect
99. #2456C22semidirect
100. #2456C22semidirect
101. #2456C22semidirect
102. #2456C22semidirect
103. #2454C22semidirect
105. #2444C22semidirect
106. #2443C22semidirect
108. #2425C22semidirect
109. #2422C22semidirect
110. #2422C22semidirect
111. #2416C22semidirect
112. #2416C22semidirect
113. #2414C22semidirect
119. #2379C22semidirect
121. #2372C22semidirect
122. #2363C22semidirect
123. #2361C22semidirect
127. #2330C22semidirect
130. #2328C22semidirect
131. #2327C22semidirect
133. #2326C22semidirect
135. #2325C22semidirect
136. #2324C22semidirect
138. #2319C22semidirect
139. #2317C22semidirect
140. #2314C22semidirect
143. C4×#121C22semidirect
144. C4×#121C22semidirect
146. #2297C22semidirect
149. #2290C22semidirect
150. #2290C22semidirect
152. #2285C22semidirect
153. #2285C22semidirect
154. C2×#376C22semidirect

Maximal subgroups

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

subgroupindex
#519662
#519582
#518732
#518602
#467872
#465402
#390522
#390462
#378982
#378892
#377062
#376942
#375152
#372862
#372732
#353332
#352722
#352712
#352592
#344152
#340702