Finite Group Databasebeta

← #8756105

Subgroups — #8756105

Order 512.

5332 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58924C214yesmaximal, complemented
2#57971C214yesmaximal, complemented
3#57737C218yesmaximal, complemented
4#53969C218yesmaximal, complemented
5#52004C212yesmaximal, complemented
6#51749C212yesmaximal, complemented
7#50274C214yesmaximal, complemented
8#47929C214yesmaximal, complemented
9#47563C212yesmaximal, complemented
10#47036C212yesmaximal, complemented
11#46619C218yesmaximal, complemented
12#46232C212yesmaximal, complemented
13#45986C214yesmaximal, complemented
14#45977C214yesmaximal, complemented
15#45977C212yesmaximal, complemented
16#35327C211yesmaximal, characteristic, complemented
17#35129C212yesmaximal, complemented
18C2×H(3,𝔽4)C2212yescomplemented
19C2×H(3,𝔽4)C2212yescomplemented
20C2×D42C2212yescomplemented
21C2×#536C2211yescharacteristic, complemented
22C2×#535C2211yescharacteristic
23C22×#124C2212yescomplemented
24C22×#124C2211yescharacteristic, complemented
25C2×C4×#41C2211yescharacteristic, complemented
26#2850C2214yescomplemented
27#2850C2214yescomplemented
28#2850C2214yescomplemented
29#2844C2212yescomplemented
30#2840C2212yescomplemented
31#2830C2218yescomplemented
32#2829C2218yescomplemented
33#2825C2218yescomplemented
34#2819C2212yescomplemented
35#2819C2214yescomplemented
36#2815C2212yes—
37#2797C2218yescomplemented
38#2795C2214yescomplemented
39#2778C2218yescomplemented
40#2760C2214yescomplemented
41#2759C2218yescomplemented
42#2759C2218yescomplemented
43#2752C2214yescomplemented
44#2749C2218yescomplemented
45#2735C2218yescomplemented
46#2733C2218yescomplemented
47#2733C2214yescomplemented
48#2731C2214yescomplemented
49#2730C2218yescomplemented
50#2712C2218yescomplemented
51#2712C2218yescomplemented
52#2712C2218yescomplemented
53#2703C2218yescomplemented
54#2700C2218yescomplemented
55#2700C2218yescomplemented
56#2697C2218yescomplemented
57#2692C2218yescomplemented
58#2688C2218yescomplemented
59#2686C2218yescomplemented
60#2684C2218yescomplemented
61#2684C2214yescomplemented
62#2684C2214yescomplemented
63#2684C2218yescomplemented
64#2684C2214yescomplemented
65#2680C2214yescomplemented
66#2678C2218yescomplemented
67#2678C2218yescomplemented
68#2676C2218yescomplemented
69#2670C2214yescomplemented
70#2670C2214yescomplemented
71#2670C2218yescomplemented
72#2670C2218yescomplemented
73#2670C2218yescomplemented
74#2670C2218yescomplemented
75#2669C2214yes—
76#2668C2218yescomplemented
77#2653C2218yescomplemented
78#2640C2214yescomplemented
79#2632C2214yescomplemented
80#2631C2214yescomplemented
81#2631C2214yescomplemented
82#2620C2214yescomplemented
83#2613C2218yescomplemented
84#2610C2214yescomplemented
85#2610C2214yescomplemented
86#2610C2214yescomplemented
87#2610C2218yescomplemented
88#2610C2218yescomplemented
89#2607C2212yescomplemented
90#2598C2214yescomplemented
91#2595C2218yescomplemented
92#2592C2214yescomplemented
93#2557C2218yescomplemented
94#2555C2218yescomplemented
95#2545C2214yescomplemented
96#2544C2214yescomplemented
97#2540C2214yescomplemented
98#2534C2214yescomplemented
99#2534C2214yescomplemented
100#2532C2218yescomplemented
101#2527C2218yescomplemented
102#2482C2214yescomplemented
103#2477C2218yescomplemented
104#2476C2218yescomplemented
105#2474C2218yescomplemented
106#2472C2218yescomplemented
107#2472C2218yescomplemented
108#2472C2218yescomplemented
109#2471C2218yescomplemented
110#2461C2218yescomplemented
111#2459C2218yescomplemented
112#2436C2214yescomplemented
113#2436C2218yescomplemented
114#2435C2218yescomplemented
115#2410C2218yescomplemented
116#2410C2218yescomplemented
117#2410C2218yescomplemented
118#2409C2212yescomplemented
119#2409C2212yescomplemented
120#2408C2212yescomplemented
121#2408C2212yescomplemented
122#2404C2214yescomplemented
123#2403C2218yescomplemented
124#2403C2214yescomplemented
125#2403C2218yescomplemented
126#2403C2212yescomplemented
127#2380C2212yescomplemented
128#2379C2214yescomplemented
129#2379C2212yescomplemented
130#2372C2212yescomplemented
131#2333C2214yescomplemented
132#2321C2214yescomplemented
133#2321C2214yescomplemented
134#2310C2211yescharacteristic, complemented
135#2309C2214yescomplemented
136#2309C2211yescharacteristic, complemented
137#2285C2211yescharacteristic, complemented
138#2283C2212yescomplemented
139C22×#41C2311yescharacteristic
140C23×Q8C2311yescharacteristic
141C23×Q8C2312yes—
142C23×D4C2311yescharacteristic
143C23×D4C2314yes—
144C23×D4C2318yes—
145C23×D4C2312yes—
146H(3,𝔽4)—48no—
147H(3,𝔽4)—48no—
148D42—48no—
149#536—44no—
150#535—44no—
151C2×C4⋊Q8C2312yes—
152C2×#127C2312yes—
153C2×#124—48no—
154C2×#124—44no—
155C2×#124C2314yes—
156C2×#124C2312yes—
157C2×#124C2312yes—
158C2×#124C2314yes—
159C2×#124C2314yes—
160C2×#124C2314yes—
161C2×#124C2312yes—
162C2×#124C2312yes—
163C2×#124C2314yes—
164C2×#124C2314yes—
165C2×#124C2314yes—
166C2×#124C2318yes—
167C2×#124C2314yes—
168C2×#124C2318yes—
169C2×#124C2318yes—
170C2×#124C2318yes—
171C2×#123C2314yes—
172C2×#123C2318yes—
173C2×C22⋊Q8C2314yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2318yes—
177C2×#121C2314yes—
178C2×#121C2314yes—
179C2×#121C2318yes—
180C2×#121C2314yes—
181C2×#121C2314yes—
182C2×#121C2318yes—
183C2×#120C2314yes—
184C2×#120C2314yes—
185C2×#120C2318yes—
186C2×#120C2314yes—
187C2×#120C2314yes—
188C2×#120C2318yes—
189C2×#120C2314yes—
190C2×#120C2318yes—
191C2×#120C2318yes—
192C2×#120C2318yes—
193C4×#41—44no—
194C2×C4×Q8C2312yes—
195C2×C4×D4C2312yes—
196C2×C4×D4C2312yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2312yes—
199C2×#117C2311yescharacteristic
200C2×#117C2311yescharacteristic
201C2×#117C2311yescharacteristic
202C2×#117C2312yes—
203C2×#117C2318yes—
204C22×C22⋊C4C2314yes—
205C22×C22⋊C4C2314yes—
206C22×C22⋊C4C2314yes—
207C22×C42C2312yes—
208C22×C42C2311yescharacteristic
209#401C2318yes—
210#400C2318yes—
211#400C2314yes—
212#399C2318yes—
213#399C2314yes—
214#398C2318yes—
215#397C2318yes—
216#397C2318yes—
217#397C2318yes—
218#397C2318yes—
219#397C2318yes—
220#397C2318yes—
221#397C2318yes—
222#397C2318yes—
223#397C2318yes—
224#397C2318yes—
225#396C2318yes—
226#396C2318yes—
227#396C2318yes—
228#396C2318yes—
229#395C2314yes—
230#395C2314yes—
231#395C2318yes—
232#395C2314yes—
233#394C2318yes—
234#394C2314yes—
235#394C2314yes—
236#394C2318yes—
237#394C2314yes—
238#394C2318yes—
239#394C2318yes—
240#394C2318yes—
241#394C2318yes—
242#394C2318yes—
243#394C2318yes—
244#394C2318yes—
245#394C2318yes—
246#394C2314yes—
247#394C2318yes—
248#394C2318yes—
249#394C2318yes—
250#394C2318yes—
251#393C2318yes—
252#393C2318yes—
253#393C2318yes—
254#393C2318yes—
255#393C2318yes—
256#393C2314yes—
257#393C2318yes—
258#393C2314yes—
259#393C2318yes—
260#393C2314yes—
261#393C2318yes—
262#392C2318yes—
263#392C2318yes—
264#392C2318yes—
265#392C2318yes—
266#392C2318yes—
267#392C2318yes—
268#392C2318yes—
269#392C2314yes—
270#392C2314yes—
271#392C2314yes—
272#392C2318yes—
273#392C2314yes—
274#392C2318yes—
275#392C2318yes—
276#392C2318yes—
277#391C2314yes—
278#391C2314yes—
279#391C2314yes—
280#391C2314yes—
281#391C2318yes—
282#391C2314yes—
283#391C2318yes—
284#391C2314yes—
285#391C2318yes—
286#390C2318yes—
287#390C2318yes—
288#390C2314yes—
289#390C2314yes—
290#390C2318yes—
291#390C2318yes—
292#390C2318yes—
293#390C2318yes—
294#390C2314yes—
295#390C2314yes—
296#390C2318yes—
297#388C2318yes—
298#388C2318yes—
299#388C2318yes—
300#388C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#386C2318yes—
324#386C2318yes—
325#386C2318yes—
326#386C2318yes—
327#386C2318yes—
328#386C2314yes—
329#386C2314yes—
330#386C2318yes—
331#386C2318yes—
332#386C2318yes—
333#386C2318yes—
334#386C2318yes—
335#386C2318yes—
336#386C2318yes—
337#386C2314yes—
338#386C2314yes—
339#386C2318yes—
340#386C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2318yes—
345#386C2318yes—
346#385C2314yes—
347#385C2314yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#384C2312yes—
352#383C2314yes—
353#383C2314yes—
354#382C2314yes—
355#382C2312yes—
356#381C2312yes—
357#381C2312yes—
358#381C2318yes—
359#381C2314yes—
360#380C2312yes—
361#380C2312yes—
362#380C2314yes—
363#379C2312yes—
364#379C2314yes—
365#379C2312yes—
366#379C2318yes—
367#379C2314yes—
368#379C2314yes—
369#379C2318yes—
370#379C2318yes—
371#379C2318yes—
372C4×C4⋊C4C2314yes—
373C4×C4⋊C4C2314yes—
374C4×C22⋊C4C2314yes—
375C4×C22⋊C4C2318yes—
376C4×C22⋊C4C2314yes—
377C4×C22⋊C4C2318yes—
378#376C2314yes—
379#376C2314yes—
380C25C2414yes—
381C25C2412yes—
382C25C2414yes—
383C2×#41—24no—
384C2×#41—42no—
385C2×#41—42no—
386C22×Q8—42no—
387C22×Q8—42no—
388C22×Q8—44no—
389C22×Q8—42no—
390C22×Q8—84no—
391C22×Q8C2411yescharacteristic
392C22×Q8C2412yes—
393C22×Q8C2414yes—
394C22×Q8C2412yes—
395C22×Q8C2414yes—
396C22×Q8C2414yes—
397C22×D4—42no—
398C22×D4—44no—
399C22×D4—42no—
400C22×D4—42no—
401C22×D4—416no—
402C22×D4—48no—
403C22×D4—88no—
404C22×D4—84no—
405C22×D4—88no—
406C22×D4—88no—
407C22×D4C2412yes—
408C22×D4C2418yes—
409C22×D4C2418yes—
410C22×D4C2412yes—
411C22×D4C2414yes—
412C22×D4C2418yes—
413C22×D4C2412yes—
414C22×D4C2414yes—
415C22×D4C2414yes—
416C22×D4C2418yes—
417C22×D4C2414yes—
418C22×D4C2418yes—
419C22×D4C2414yes—
420C22×D4C2418yes—
421C22×D4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2414yes—
429C23×C4C2414yes—
430C23×C4C2418yes—
431C4⋊Q8—44no—
432#127—28no—
433#124—28no—
434#124—216no—
435#124—28no—
436#124—48no—
437#124—48no—
438#124—48no—
439#124—48no—
440#124—44no—
441#124—48no—
442#124—44no—
443#124—416no—
444#124—48no—
445#124—416no—
446#124—48no—
447#124—88no—
448#124—88no—
449#123—48no—
450#123—88no—
451C22⋊Q8—48no—
452C22⋊Q8—84no—
453C22⋊Q8—84no—
454C22⋊Q8—88no—
455#121—416no—
456#121—48no—
457#121—48no—
458#121—88no—
459#121—84no—
460#121—84no—
461#120—216no—
462#120—48no—
463#120—48no—
464#120—416no—
465#120—416no—
466#120—48no—
467#120—48no—
468#120—88no—
469#120—88no—
470#120—88no—
471C4×Q8—44no—
472C4×D4—48no—
473C4×D4—44no—
474C4×D4—44no—
475C4×D4—44no—
476#117—42no—
477#117—44no—
478#117—42no—
479#117—42no—
480#117—88no—
481C2×C4⋊C4C2412yes—
482C2×C4⋊C4C2412yes—
483C2×C4⋊C4C2412yes—
484C2×C4⋊C4C2412yes—
485C2×C4⋊C4C2412yes—
486C2×C4⋊C4C2418yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2418yes—
496C2×C22⋊C4—48no—
497C2×C22⋊C4—48no—
498C2×C22⋊C4—48no—
499C2×C22⋊C4C2418yes—
500C2×C22⋊C4C2418yes—
501C2×C22⋊C4C2418yes—
502C2×C22⋊C4C2418yes—
503C2×C22⋊C4C2414yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C2418yes—
506C2×C22⋊C4C2418yes—
507C2×C22⋊C4C2418yes—
508C2×C22⋊C4C2411yescharacteristic
509C2×C22⋊C4C2411yescharacteristic
510C2×C22⋊C4C2412yes—
511C2×C22⋊C4C2412yes—
512C2×C22⋊C4C2412yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C2412yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2414yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2414yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C2418yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2418yes—
538C2×C42—24no—
539C2×C42—28no—
540C2×C42C2412yes—
541C2×C42C2411yescharacteristic
542C2×C42C2412yes—
543C2×C42C2412yes—
544C2×C42C2412yes—
545C2×C42C2412yes—
546C2×C42C2412yes—
547C2×C42C2418yes—
548C2×C42C2418yes—
549C2×C42C2414yes—
550C2×C42C2414yes—
551C2×C42C2411yescharacteristic
552#95C2414yes—
553#95C2414yes—
554#95C2414yes—
555#95C2418yes—
556#95C2418yes—
557#95C2414yes—
558#95C2418yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C2418yes—
566#95C2418yes—
567#95C2418yes—
568#95C2414yes—
569#95C2414yes—
570#95C2418yes—
571#95C2418yes—
572#95C2418yes—
573#95C2418yes—
574C24—28no—
575C24—24no—
576C24—42no—
577C24—44no—
578C24—44no—
579C24—48no—
580C24—48no—
581C24—48no—
582C24—48no—
583C24—42no—
584C24—44no—
585C24—48no—
586C24—44no—
587C24—44no—
588C24C2518yes—
589C24C2514yes—
590C24C2512yes—
591C24C2511yescharacteristic
592#41—416no—
593C2×Q8—22no—
594C2×Q8—24no—
595C2×Q8—28no—
596C2×Q8—24no—
597C2×Q8—41no—
598C2×Q8—41no—
599C2×Q8—42no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×Q8—42no—
603C2×Q8—44no—
604C2×Q8—48no—
605C2×Q8—42no—
606C2×Q8—42no—
607C2×Q8—48no—
608C2×Q8—44no—
609C2×Q8—88no—
610C2×Q8—816no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—216no—
614C2×D4—216no—
615C2×D4—216no—
616C2×D4—24no—
617C2×D4—28no—
618C2×D4—24no—
619C2×D4—41no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—48no—
623C2×D4—41no—
624C2×D4—48no—
625C2×D4—48no—
626C2×D4—48no—
627C2×D4—48no—
628C2×D4—48no—
629C2×D4—48no—
630C2×D4—48no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—48no—
635C2×D4—48no—
636C2×D4—48no—
637C2×D4—48no—
638C2×D4—42no—
639C2×D4—44no—
640C2×D4—48no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—48no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—48no—
647C2×D4—44no—
648C2×D4—48no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—44no—
652C2×D4—88no—
653C2×D4—816no—
654C2×D4—832no—
655C2×D4—864no—
656C2×D4H(5,𝔽2)14yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—48no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—44no—
672C22×C4—48no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—48no—
676C22×C4—48no—
677C22×C4—42no—
678C22×C4—48no—
679C22×C4C2518yes—
680C22×C4C2512yes—
681C22×C4C2514yes—
682C22×C4C2514yes—
683C22×C4C2518yes—
684C22×C4C2518yes—
685C22×C4C2512yes—
686C22×C4C2514yes—
687C22×C4C2512yes—
688C22×C4C2512yes—
689C22×C4C2511yescharacteristic
690C22×C4C2511yescharacteristic
691C22×C4C2512yes—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—48no—
698C4⋊C4—48no—
699C4⋊C4—44no—
700C4⋊C4—44no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—48no—
704C4⋊C4—48no—
705C4⋊C4—48no—
706C4⋊C4—48no—
707C22⋊C4—28no—
708C22⋊C4—216no—
709C22⋊C4—216no—
710C22⋊C4—216no—
711C22⋊C4—216no—
712C22⋊C4—216no—
713C22⋊C4—48no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—41no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—41no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—48no—
723C22⋊C4—48no—
724C22⋊C4—48no—
725C22⋊C4—44no—
726C22⋊C4—44no—
727C22⋊C4—48no—
728C22⋊C4—48no—
729C22⋊C4—48no—
730C22⋊C4—44no—
731C22⋊C4—48no—
732C22⋊C4—48no—
733C22⋊C4—48no—
734C22⋊C4—48no—
735C22⋊C4—48no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—48no—
739C22⋊C4—48no—
740C22⋊C4—48no—
741C22⋊C4—48no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C42—22no—
747C42—24no—
748C42—24no—
749C42—24no—
750C42—24no—
751C42—24no—
752C42—24no—
753C42—48no—
754C42—48no—
755C42—44no—
756C42—44no—
757C42H(5,𝔽2)14yes—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—22no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—28no—
767C23—28no—
768C23—24no—
769C23—28no—
770C23—24no—
771C23—28no—
772C23—28no—
773C23—28no—
774C23—28no—
775C23—28no—
776C23—28no—
777C23—816no—
778C23—88no—
779C23—84no—
780C23—88no—
781C23—88no—
782C23—816no—
783C23—88no—
784C23—88no—
785C23—88no—
786C23—164no—
787C23—168no—
788C23—164no—
789C23—164no—
790C23—168no—
791C23C2×H(5,𝔽2)14yes—
792C23#58512yes—
793C23C2611yescharacteristic
794Q8—44no—
795Q8—84no—
796Q8—84no—
797Q8—88no—
798Q8—88no—
799Q8—164no—
800D4—44no—
801D4—48no—
802D4—416no—
803D4—84no—
804D4—84no—
805D4—88no—
806D4—816no—
807D4—816no—
808D4—816no—
809D4—816no—
810D4—816no—
811D4—88no—
812D4—164no—
813D4—164no—
814D4—168no—
815C2×C4—28no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—28no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—28no—
837C2×C4—28no—
838C2×C4—28no—
839C2×C4—28no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—28no—
843C2×C4—28no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—48no—
847C2×C4—48no—
848C2×C4—416no—
849C2×C4—84no—
850C2×C4—84no—
851C2×C4—84no—
852C2×C4—816no—
853C2×C4—88no—
854C2×C4C2×H(5,𝔽2)12yes—
855C2×C4C2×H(5,𝔽2)12yes—
856C2×C4C2×H(5,𝔽2)14yes—
857C22—28no—
858C22—24no—
859C22—22no—
860C22—24no—
861C22—42no—
862C22—44no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—48no—
867C22—48no—
868C22—48no—
869C22—44no—
870C22—48no—
871C22—44no—
872C22—48no—
873C22—44no—
874C22—48no—
875C22—48no—
876C22—48no—
877C22—48no—
878C22—168no—
879C22—1616no—
880C22—1616no—
881C22C22×H(5,𝔽2)11yescharacteristic
882C22C22×H(5,𝔽2)11yescharacteristic
883C22C2×#58511yescharacteristic
884C22H(7,𝔽2)14yes—
885C4—22no—
886C4—22no—
887C4—24no—
888C4—44no—
889C4—48no—
890C4—44no—
891C4—48no—
892C4—42no—
893C4—44no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—48no—
898C2—44no—
899C2—42no—
900C2—88no—
901C2—84no—
902C2#6281811yescharacteristic
903C2#6287412yes—
904C2#6304512yes—
905C2#6304612yes—
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. #58924C2semidirect
2. #57971C2semidirect
3. #57737C2semidirect
4. #53969C2semidirect
5. #52004C2semidirect
6. #51749C2semidirect
7. #50274C2semidirect
8. #47929C2semidirect
9. #47563C2semidirect
10. #47036C2semidirect
11. #46619C2semidirect
12. #46232C2semidirect
13. #45986C2semidirect
14. #45977C2semidirect
15. #45977C2semidirect
16. #35327C2semidirect
17. #35129C2semidirect
18. C2×H(3,𝔽4)C22semidirect
19. C2×H(3,𝔽4)C22semidirect
20. C2×D42C22semidirect
21. C2×#536C22semidirect
23. C22×#124C22semidirect
24. C22×#124C22semidirect
25. C2×C4×#41C22semidirect
26. #2850C22semidirect
27. #2850C22semidirect
28. #2850C22semidirect
29. #2844C22semidirect
30. #2840C22semidirect
31. #2830C22semidirect
32. #2829C22semidirect
33. #2825C22semidirect
34. #2819C22semidirect
35. #2819C22semidirect
37. #2797C22semidirect
38. #2795C22semidirect
39. #2778C22semidirect
40. #2760C22semidirect
41. #2759C22semidirect
42. #2759C22semidirect
43. #2752C22semidirect
44. #2749C22semidirect
45. #2735C22semidirect
46. #2733C22semidirect
47. #2733C22semidirect
48. #2731C22semidirect
49. #2730C22semidirect
50. #2712C22semidirect
51. #2712C22semidirect
52. #2712C22semidirect
53. #2703C22semidirect
54. #2700C22semidirect
55. #2700C22semidirect
56. #2697C22semidirect
57. #2692C22semidirect
58. #2688C22semidirect
59. #2686C22semidirect
60. #2684C22semidirect
61. #2684C22semidirect
62. #2684C22semidirect
63. #2684C22semidirect
64. #2684C22semidirect
65. #2680C22semidirect
66. #2678C22semidirect
67. #2678C22semidirect
68. #2676C22semidirect
69. #2670C22semidirect
70. #2670C22semidirect
71. #2670C22semidirect
72. #2670C22semidirect
73. #2670C22semidirect
74. #2670C22semidirect
76. #2668C22semidirect
77. #2653C22semidirect
78. #2640C22semidirect
79. #2632C22semidirect
80. #2631C22semidirect
81. #2631C22semidirect
82. #2620C22semidirect
83. #2613C22semidirect
84. #2610C22semidirect
85. #2610C22semidirect
86. #2610C22semidirect
87. #2610C22semidirect
88. #2610C22semidirect
89. #2607C22semidirect
90. #2598C22semidirect
91. #2595C22semidirect
92. #2592C22semidirect
93. #2557C22semidirect
94. #2555C22semidirect
95. #2545C22semidirect
96. #2544C22semidirect
97. #2540C22semidirect
98. #2534C22semidirect
99. #2534C22semidirect
100. #2532C22semidirect
101. #2527C22semidirect
102. #2482C22semidirect
103. #2477C22semidirect
104. #2476C22semidirect
105. #2474C22semidirect
106. #2472C22semidirect
107. #2472C22semidirect
108. #2472C22semidirect
109. #2471C22semidirect
110. #2461C22semidirect
111. #2459C22semidirect
112. #2436C22semidirect
113. #2436C22semidirect
114. #2435C22semidirect
115. #2410C22semidirect
116. #2410C22semidirect
117. #2410C22semidirect
118. #2409C22semidirect
119. #2409C22semidirect
120. #2408C22semidirect
121. #2408C22semidirect
122. #2404C22semidirect
123. #2403C22semidirect
124. #2403C22semidirect
125. #2403C22semidirect
126. #2403C22semidirect
127. #2380C22semidirect
128. #2379C22semidirect
129. #2379C22semidirect
130. #2372C22semidirect
131. #2333C22semidirect
132. #2321C22semidirect
133. #2321C22semidirect
134. #2310C22semidirect
135. #2309C22semidirect
136. #2309C22semidirect
137. #2285C22semidirect
138. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#589242
#579712
#577372
#539692
#520042
#517492
#502742
#479292
#475632
#470362
#466192
#462322
#459862
#459772
#353272
#351292