Finite Group Databasebeta

← #8093392

Subgroups — #8093392

Order 512.

5728 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52799C214yesmaximal, complemented
2#52723C218yesmaximal, complemented
3#52586C214yesmaximal, complemented
4#52549C214yesmaximal, complemented
5#52548C214yesmaximal, complemented
6#52375C218yesmaximal, complemented
7#52347C218yesmaximal, complemented
8#52320C218yesmaximal, complemented
9#35463C211yesmaximal, characteristic, complemented
10#35447C212yesmaximal, complemented
11#35446C211yesmaximal, characteristic, complemented
12#35370C212yesmaximal, complemented
13#35360C212yesmaximal, complemented
14#35358C212yesmaximal, complemented
15#35347C212yesmaximal, complemented
16C2×#2623C211yesmaximal, characteristic, complemented
17C2×#2618C212yesmaximal, complemented
18C22×H(5,𝔽2)C2211yescharacteristic
19C2×#534C2212yes—
20C2×#534C2212yes—
21C2×#534C2211yescharacteristic, complemented
22C22×#123C2211yescharacteristic
23C22×#123C2212yes—
24C22×#123C2212yescomplemented
25C22×#121C2212yes—
26C2×#518C2212yescomplemented
27C23×C4⋊C4C2211yescharacteristic, complemented
28#2843C2214yescomplemented
29#2842C2214yescomplemented
30#2841C2218yescomplemented
31#2838C2218yescomplemented
32#2837C2218yescomplemented
33#2837C2218yescomplemented
34#2834C2214yescomplemented
35#2830C2214yescomplemented
36#2829C2218yescomplemented
37#2829C2218yescomplemented
38#2829C2218yescomplemented
39#2828C2214yescomplemented
40#2827C2218yescomplemented
41#2827C2218yescomplemented
42#2826C2218yescomplemented
43#2826C2214yescomplemented
44#2825C2218yescomplemented
45#2823C2214yescomplemented
46#2813C2218yescomplemented
47#2812C2214yescomplemented
48#2807C2214yescomplemented
49#2795C2214yescomplemented
50#2792C2214yescomplemented
51#2790C2218yescomplemented
52#2790C2218yescomplemented
53#2784C2214yescomplemented
54#2780C2218yescomplemented
55#2757C2218yescomplemented
56#2756C2218yescomplemented
57#2749C2218yescomplemented
58#2748C2218yescomplemented
59#2746C2218yescomplemented
60#2735C2214yescomplemented
61#2705C2218yescomplemented
62#2699C2214yescomplemented
63#2697C2218yescomplemented
64#2693C2214yescomplemented
65#2691C2218yescomplemented
66#2685C2218yescomplemented
67#2668C2214yescomplemented
68#2623C2218yescomplemented
69#2623C2218yescomplemented
70#2618C2218yescomplemented
71#2618C2218yescomplemented
72#2618C2218yescomplemented
73#2618C2218yescomplemented
74#2543C2218yescomplemented
75#2539C2212yescomplemented
76#2539C2218yescomplemented
77#2539C2212yescomplemented
78#2534C2218yescomplemented
79#2510C2218yescomplemented
80#2510C2218yescomplemented
81#2501C2212yescomplemented
82#2501C2212yescomplemented
83#2501C2218yescomplemented
84#2498C2218yescomplemented
85#2493C2218yescomplemented
86#2486C2218yescomplemented
87#2481C2218yescomplemented
88#2481C2218yescomplemented
89#2480C2218yescomplemented
90#2444C2218yescomplemented
91#2443C2218yescomplemented
92#2430C2218yes—
93#2430C2218yescomplemented
94#2425C2218yescomplemented
95#2425C2218yescomplemented
96#2425C2218yescomplemented
97#2424C2218yescomplemented
98#2419C2218yescomplemented
99#2418C2218yescomplemented
100#2416C2218yescomplemented
101#2413C2214yescomplemented
102#2413C2218yescomplemented
103#2412C2214yescomplemented
104#2412C2218yescomplemented
105#2412C2218yescomplemented
106#2411C2214yescomplemented
107#2410C2218yes—
108#2410C2218yescomplemented
109#2410C2214yescomplemented
110#2406C2214yescomplemented
111#2406C2212yescomplemented
112#2406C2212yescomplemented
113#2406C2218yescomplemented
114#2405C2214yescomplemented
115#2405C2212yescomplemented
116#2405C2218yescomplemented
117#2405C2212yescomplemented
118#2404C2214yescomplemented
119#2403C2214yescomplemented
120C2×#400C2212yescomplemented
121C2×#399C2212yescomplemented
122C2×#398C2212yescomplemented
123C2×#398C2214yescomplemented
124C2×#397C2212yescomplemented
125C2×#396C2214yescomplemented
126C2×#396C2214yescomplemented
127C2×#394C2214yescomplemented
128#2315C2212yescomplemented
129#2308C2212yes—
130#2308C2212yes—
131#2308C2211yescharacteristic
132C2×#386C2212yes—
133C2×#386C2212yes—
134C2×#386C2212yescomplemented
135C2×#385C2212yescomplemented
136C2×#381C2211yescharacteristic, complemented
137C2×#380C2212yescomplemented
138#2273C2211yescharacteristic, complemented
139C2×H(5,𝔽2)—44no—
140C2×H(5,𝔽2)—48no—
141C22×#41C2314yes—
142C22×#41C2312yes—
143C23×D4C2312yes—
144C23×D4C2311yescharacteristic
145C23×D4C2312yes—
146C23×D4C2314yes—
147C23×D4C2312yes—
148C23×D4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2312yes—
151#534—48no—
152#534—48no—
153#534—44no—
154C2×#126C2318yes—
155C2×#123—48no—
156C2×#123—44no—
157C2×#123—48no—
158C2×#123C2318yes—
159C2×#123C2314yes—
160C2×#123C2314yes—
161C2×#123C2314yes—
162C2×#123C2314yes—
163C2×#123C2318yes—
164C2×#123C2318yes—
165C2×#123C2314yes—
166C2×#123C2314yes—
167C2×#123C2314yes—
168C2×#123C2314yes—
169C2×#123C2314yes—
170C2×#123C2318yes—
171C2×#121—48no—
172C2×#121C2318yes—
173C2×#121C2318yes—
174C2×#121C2318yes—
175C2×#121C2318yes—
176C2×#121C2312yes—
177C2×#121C2312yes—
178C2×#121C2318yes—
179C2×#120C2314yes—
180C2×#120C2314yes—
181C2×#120C2314yes—
182C2×#120C2314yes—
183C2×#120C2314yes—
184C2×#120C2318yes—
185#518—48no—
186C2×C4×D4C2318yes—
187C2×C4×D4C2318yes—
188C2×#117C2314yes—
189C22×C4⋊C4—44no—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2314yes—
193C22×C4⋊C4C2314yes—
194C22×C4⋊C4C2314yes—
195C22×C4⋊C4C2314yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2314yes—
200C22×C4⋊C4C2314yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2314yes—
206C22×C22⋊C4C2314yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2314yes—
212C22×C22⋊C4C2314yes—
213C22×C22⋊C4C2314yes—
214C22×C22⋊C4C2314yes—
215#401C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2314yes—
220#400C2318yes—
221#400C2318yes—
222#400C2314yes—
223#399C2318yes—
224#399C2314yes—
225#399C2318yes—
226#399C2314yes—
227#399C2318yes—
228#399C2314yes—
229#399C2314yes—
230#399C2318yes—
231#398C2318yes—
232#398C2314yes—
233#398C2314yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2314yes—
252#397C2318yes—
253#397C2314yes—
254#396C2318yes—
255#396C2318yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#395C2314yes—
268#395C2314yes—
269#395C2318yes—
270#394C2318yes—
271#394C2314yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2314yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#393C2318yes—
289#392C2314yes—
290#392C2318yes—
291#392C2318yes—
292#392C2318yes—
293#392C2318yes—
294#392C2314yes—
295#390C2314yes—
296#390C2318yes—
297#390C2318yes—
298#390C2318yes—
299#390C2314yes—
300#389C2318yes—
301#389C2318yes—
302#389C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#386C2318yes—
318#386C2314yes—
319#386C2318yes—
320#386C2314yes—
321#386C2318yes—
322#386C2318yes—
323#386C2318yes—
324#386C2318yes—
325#386C2318yes—
326#386C2318yes—
327#386C2318yes—
328#386C2318yes—
329#386C2318yes—
330#386C2318yes—
331#386C2314yes—
332#386C2314yes—
333#386C2314yes—
334#386C2318yes—
335#386C2314yes—
336#386C2318yes—
337#386C2314yes—
338#386C2314yes—
339#386C2318yes—
340#385C2314yes—
341#385C2318yes—
342#385C2318yes—
343#385C2318yes—
344#385C2318yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2314yes—
349#385C2318yes—
350#385C2314yes—
351#385C2314yes—
352#385C2318yes—
353#384C2314yes—
354#384C2314yes—
355#383C2318yes—
356#381C2314yes—
357#381C2314yes—
358#381C2312yes—
359#381C2318yes—
360#381C2318yes—
361#380C2318yes—
362#380C2318yes—
363#380C2318yes—
364#380C2318yes—
365#380C2318yes—
366#380C2318yes—
367#379C2314yes—
368#379C2314yes—
369#379C2312yes—
370#379C2314yes—
371#379C2318yes—
372#379C2314yes—
373C4×C22⋊C4C2318yes—
374C4×C22⋊C4C2312yes—
375C4×C22⋊C4C2312yes—
376C2×#95C2314yes—
377C2×#95C2314yes—
378C2×#95C2314yes—
379C2×#95C2312yes—
380C2×#95C2314yes—
381C2×#95C2314yes—
382C2×#95C2312yes—
383C25C2412yes—
384C25C2411yescharacteristic
385C25C2412yes—
386C25C2412yes—
387C25C2411yescharacteristic
388H(5,𝔽2)—464no—
389C2×#41—48no—
390C2×#41—48no—
391C2×#41—44no—
392C2×#41—48no—
393C2×#41—48no—
394C22×Q8C2412yes—
395C22×D4—28no—
396C22×D4—28no—
397C22×D4—28no—
398C22×D4—28no—
399C22×D4—28no—
400C22×D4—24no—
401C22×D4—28no—
402C22×D4—28no—
403C22×D4—44no—
404C22×D4—48no—
405C22×D4—48no—
406C22×D4—44no—
407C22×D4—48no—
408C22×D4—48no—
409C22×D4—84no—
410C22×D4C2414yes—
411C22×D4C2414yes—
412C22×D4C2414yes—
413C22×D4C2414yes—
414C22×D4C2414yes—
415C22×D4C2418yes—
416C22×D4C2418yes—
417C22×D4C2412yes—
418C22×D4C2412yes—
419C22×D4C2418yes—
420C22×D4C2412yes—
421C22×D4C2414yes—
422C23×C4—24no—
423C23×C4—28no—
424C23×C4—28no—
425C23×C4—84no—
426C23×C4C2414yes—
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2414yes—
433C23×C4C2414yes—
434C23×C4C2411yescharacteristic
435C23×C4C2412yes—
436C23×C4C2414yes—
437C23×C4C2414yes—
438C23×C4C2411yescharacteristic
439C23×C4C2414yes—
440C23×C4C2412yes—
441C23×C4C2418yes—
442C23×C4C2414yes—
443C23×C4C2412yes—
444#126—88no—
445#123—416no—
446#123—48no—
447#123—48no—
448#123—416no—
449#123—416no—
450#123—48no—
451#123—48no—
452#123—48no—
453#123—48no—
454#123—48no—
455#123—48no—
456#123—48no—
457#123—88no—
458#121—416no—
459#121—416no—
460#121—416no—
461#121—44no—
462#121—44no—
463#121—416no—
464#121—88no—
465#120—48no—
466#120—48no—
467#120—48no—
468#120—48no—
469#120—48no—
470#120—88no—
471C4×D4—416no—
472C4×D4—416no—
473#117—48no—
474C2×C4⋊C4—48no—
475C2×C4⋊C4—44no—
476C2×C4⋊C4—44no—
477C2×C4⋊C4—48no—
478C2×C4⋊C4—44no—
479C2×C4⋊C4—48no—
480C2×C4⋊C4—48no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—84no—
484C2×C4⋊C4—84no—
485C2×C4⋊C4C2412yes—
486C2×C4⋊C4C2412yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C2418yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2418yes—
509C2×C22⋊C4—28no—
510C2×C22⋊C4—28no—
511C2×C22⋊C4—28no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—48no—
514C2×C22⋊C4—44no—
515C2×C22⋊C4—44no—
516C2×C22⋊C4—48no—
517C2×C22⋊C4—48no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—84no—
521C2×C22⋊C4—84no—
522C2×C22⋊C4—84no—
523C2×C22⋊C4C2414yes—
524C2×C22⋊C4C2414yes—
525C2×C22⋊C4C2414yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2414yes—
528C2×C22⋊C4C2414yes—
529C2×C22⋊C4C2414yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C42C2418yes—
558C2×C42C2414yes—
559C2×C42C2414yes—
560#95C2414yes—
561#95C2414yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C2414yes—
566#95C2414yes—
567#95C2418yes—
568#95C2418yes—
569#95C2418yes—
570#95C2418yes—
571#95C2418yes—
572#95C2418yes—
573#95C2418yes—
574#95C2414yes—
575#95C2414yes—
576#95C2418yes—
577#95C2418yes—
578#95C2418yes—
579#95C2418yes—
580#95C2418yes—
581#95C2414yes—
582#95C2418yes—
583#95C2414yes—
584C24—24no—
585C24—24no—
586C24—24no—
587C24—22no—
588C24—24no—
589C24—24no—
590C24—24no—
591C24—24no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24—44no—
596C24—42no—
597C24—44no—
598C24—44no—
599C24—42no—
600C24—44no—
601C24—44no—
602C24—44no—
603C24—44no—
604C24H(5,𝔽2)18yes—
605C24H(5,𝔽2)14yes—
606C24C2512yes—
607C24C2514yes—
608C24C2514yes—
609C24C2512yes—
610C24C2511yescharacteristic
611#41—464no—
612#41—432no—
613C2×Q8—42no—
614C2×Q8—44no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—28no—
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—28no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—28no—
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—42no—
634C2×D4—44no—
635C2×D4—48no—
636C2×D4—48no—
637C2×D4—48no—
638C2×D4—48no—
639C2×D4—48no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—48no—
647C2×D4—48no—
648C2×D4—464no—
649C2×D4—432no—
650C2×D4—432no—
651C2×D4—432no—
652C2×D4—416no—
653C2×D4—816no—
654C22×C4—24no—
655C22×C4—28no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—28no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—22no—
665C22×C4—24no—
666C22×C4—28no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—28no—
672C22×C4—28no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—42no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—42no—
692C22×C4—44no—
693C22×C4—42no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—48no—
698C22×C4—48no—
699C22×C4—48no—
700C22×C4—416no—
701C22×C4—816no—
702C22×C4C2512yes—
703C22×C4C2518yes—
704C22×C4C2514yes—
705C22×C4C2512yes—
706C22×C4C2514yes—
707C22×C4C2518yes—
708C22×C4C2518yes—
709C22×C4C2514yes—
710C22×C4C2512yes—
711C22×C4C2514yes—
712C22×C4C2512yes—
713C22×C4C2512yes—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4—44no—
717C4⋊C4—44no—
718C4⋊C4—42no—
719C4⋊C4—42no—
720C4⋊C4—48no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—48no—
728C4⋊C4—48no—
729C4⋊C4—48no—
730C4⋊C4—48no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C4⋊C4—48no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—48no—
738C22⋊C4—28no—
739C22⋊C4—28no—
740C22⋊C4—28no—
741C22⋊C4—28no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—28no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C22⋊C4—48no—
750C22⋊C4—48no—
751C22⋊C4—48no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C22⋊C4—48no—
757C22⋊C4—48no—
758C22⋊C4—48no—
759C22⋊C4—48no—
760C22⋊C4—48no—
761C22⋊C4—48no—
762C22⋊C4—44no—
763C22⋊C4—48no—
764C22⋊C4—48no—
765C22⋊C4—48no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—48no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—44no—
772C42—44no—
773C42—48no—
774C42—44no—
775C23—22no—
776C23—24no—
777C23—22no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—28no—
789C23—28no—
790C23—28no—
791C23—24no—
792C23—28no—
793C23—44no—
794C23—416no—
795C23—44no—
796C23—48no—
797C23—48no—
798C23—44no—
799C23—48no—
800C23—84no—
801C23—84no—
802C23—82no—
803C23—88no—
804C23—88no—
805C23—88no—
806C23—88no—
807C23—88no—
808C23—82no—
809C23—84no—
810C23—84no—
811C23—162no—
812C23—168no—
813C23—162no—
814C23#560116yes—
815C23C2×H(5,𝔽2)14yes—
816C23C2×H(5,𝔽2)14yes—
817C23C2×H(5,𝔽2)14yes—
818C23C2×H(5,𝔽2)14yes—
819C23C2×H(5,𝔽2)12yes—
820C23C2611yescharacteristic
821Q8—48no—
822D4—416no—
823D4—48no—
824D4—416no—
825D4—416no—
826D4—416no—
827D4—416no—
828D4—416no—
829D4—816no—
830D4—162no—
831D4—168no—
832D4—168no—
833D4—162no—
834C2×C4—24no—
835C2×C4—28no—
836C2×C4—28no—
837C2×C4—22no—
838C2×C4—28no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—28no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—48no—
866C2×C4—48no—
867C2×C4—48no—
868C2×C4—416no—
869C2×C4—416no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—48no—
873C2×C4—48no—
874C2×C4—44no—
875C2×C4—82no—
876C2×C4—88no—
877C2×C4—88no—
878C2×C4—88no—
879C2×C4—82no—
880C2×C4—88no—
881C2×C4—88no—
882C2×C4—168no—
883C22—24no—
884C22—22no—
885C22—28no—
886C22—28no—
887C22—28no—
888C22—22no—
889C22—24no—
890C22—416no—
891C22—44no—
892C22—44no—
893C22—42no—
894C22—48no—
895C22—48no—
896C22—48no—
897C22—48no—
898C22—48no—
899C22—44no—
900C22—42no—
901C22—44no—
902C22—44no—
903C22—42no—
904C22—44no—
905C22—168no—
906C22—168no—
907C22—164no—
908C22—168no—
909C22C2×#56018yes—
910C22C2×#56014yes—
911C22C22×H(5,𝔽2)11yescharacteristic
912C22C22×H(5,𝔽2)12yes—
913C22H(7,𝔽2)12yes—
914C222−1+612yes—
915C4—44no—
916C4—44no—
917C4—42no—
918C4—48no—
919C4—48no—
920C4—48no—
921C4—42no—
922C4—42no—
923C4—42no—
924C4—44no—
925C4—42no—
926C4—44no—
927C2—28no—
928C2—24no—
929C2—84no—
930C2—84no—
931C2—82no—
932C2C22×#56011yescharacteristic
933C2#6286211yescharacteristic
934C2#6286614yes—
935C2#6287111yescharacteristic
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. #52799C2semidirect
2. #52723C2semidirect
3. #52586C2semidirect
4. #52549C2semidirect
5. #52548C2semidirect
6. #52375C2semidirect
7. #52347C2semidirect
8. #52320C2semidirect
9. #35463C2semidirect
10. #35447C2semidirect
11. #35446C2semidirect
12. #35370C2semidirect
13. #35360C2semidirect
14. #35358C2semidirect
15. #35347C2semidirect
16. C2×#2623C2semidirect
17. C2×#2618C2semidirect
21. C2×#534C22semidirect
24. C22×#123C22semidirect
26. C2×#518C22semidirect
27. C23×C4⋊C4C22semidirect
28. #2843C22semidirect
29. #2842C22semidirect
30. #2841C22semidirect
31. #2838C22semidirect
32. #2837C22semidirect
33. #2837C22semidirect
34. #2834C22semidirect
35. #2830C22semidirect
36. #2829C22semidirect
37. #2829C22semidirect
38. #2829C22semidirect
39. #2828C22semidirect
40. #2827C22semidirect
41. #2827C22semidirect
42. #2826C22semidirect
43. #2826C22semidirect
44. #2825C22semidirect
45. #2823C22semidirect
46. #2813C22semidirect
47. #2812C22semidirect
48. #2807C22semidirect
49. #2795C22semidirect
50. #2792C22semidirect
51. #2790C22semidirect
52. #2790C22semidirect
53. #2784C22semidirect
54. #2780C22semidirect
55. #2757C22semidirect
56. #2756C22semidirect
57. #2749C22semidirect
58. #2748C22semidirect
59. #2746C22semidirect
60. #2735C22semidirect
61. #2705C22semidirect
62. #2699C22semidirect
63. #2697C22semidirect
64. #2693C22semidirect
65. #2691C22semidirect
66. #2685C22semidirect
67. #2668C22semidirect
68. #2623C22semidirect
69. #2623C22semidirect
70. #2618C22semidirect
71. #2618C22semidirect
72. #2618C22semidirect
73. #2618C22semidirect
74. #2543C22semidirect
75. #2539C22semidirect
76. #2539C22semidirect
77. #2539C22semidirect
78. #2534C22semidirect
79. #2510C22semidirect
80. #2510C22semidirect
81. #2501C22semidirect
82. #2501C22semidirect
83. #2501C22semidirect
84. #2498C22semidirect
85. #2493C22semidirect
86. #2486C22semidirect
87. #2481C22semidirect
88. #2481C22semidirect
89. #2480C22semidirect
90. #2444C22semidirect
91. #2443C22semidirect
93. #2430C22semidirect
94. #2425C22semidirect
95. #2425C22semidirect
96. #2425C22semidirect
97. #2424C22semidirect
98. #2419C22semidirect
99. #2418C22semidirect
100. #2416C22semidirect
101. #2413C22semidirect
102. #2413C22semidirect
103. #2412C22semidirect
104. #2412C22semidirect
105. #2412C22semidirect
106. #2411C22semidirect
108. #2410C22semidirect
109. #2410C22semidirect
110. #2406C22semidirect
111. #2406C22semidirect
112. #2406C22semidirect
113. #2406C22semidirect
114. #2405C22semidirect
115. #2405C22semidirect
116. #2405C22semidirect
117. #2405C22semidirect
118. #2404C22semidirect
119. #2403C22semidirect
120. C2×#400C22semidirect
121. C2×#399C22semidirect
122. C2×#398C22semidirect
123. C2×#398C22semidirect
124. C2×#397C22semidirect
125. C2×#396C22semidirect
126. C2×#396C22semidirect
127. C2×#394C22semidirect
128. #2315C22semidirect
134. C2×#386C22semidirect
135. C2×#385C22semidirect
136. C2×#381C22semidirect
137. C2×#380C22semidirect
138. #2273C22semidirect

Maximal subgroups

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

subgroupindex
#527992
#527232
#525862
#525492
#525482
#523752
#523472
#523202
#354632
#354472
#354462
#353702
#353602
#353582
#353472
C2×#26232
C2×#26182