Finite Group Databasebeta

← #8932958

Subgroups — #8932958

Order 512.

6090 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59621C214yesmaximal, complemented
2#59191C214yesmaximal, complemented
3#59006C214yesmaximal, complemented
4#51530C214yesmaximal, complemented
5#48949C214yesmaximal, complemented
6#48679C218yesmaximal, complemented
7#48333C218yesmaximal, complemented
8#48113C214yesmaximal, complemented
9#47903C218yesmaximal, complemented
10#46997C212yesmaximal, complemented
11#46388C212yesmaximal, complemented
12#46386C212yesmaximal, complemented
13#35616C211yesmaximal, characteristic, complemented
14#35451C212yesmaximal, complemented
15#35446C211yesmaximal, characteristic, complemented
16#35354C212yesmaximal, complemented
17#35350C212yesmaximal, complemented
18#35346C211yesmaximal, characteristic
19C22×H(5,𝔽2)C2211yescharacteristic
20C2×#551C2214yescomplemented
21C2×#536C2212yescomplemented
22C22×#124C2211yescharacteristic, complemented
23C22×#123C2211yescharacteristic, complemented
24C22×#123C2212yescomplemented
25C22×#120C2211yescharacteristic
26C22×#120C2212yes—
27C2×#518C2212yescomplemented
28#2842C2212yescomplemented
29#2782C2218yescomplemented
30#2780C2218yescomplemented
31#2779C2218yescomplemented
32#2778C2218yescomplemented
33#2765C2218yescomplemented
34#2761C2218yescomplemented
35#2750C2218yescomplemented
36#2748C2214yescomplemented
37#2746C2218yescomplemented
38#2746C2218yescomplemented
39#2745C2218yescomplemented
40#2743C2218yescomplemented
41#2735C2218yescomplemented
42#2729C2218yescomplemented
43#2717C2214yescomplemented
44#2706C2218yescomplemented
45#2706C2218yescomplemented
46#2697C2214yescomplemented
47#2697C2218yescomplemented
48#2695C2218yescomplemented
49#2693C2218yescomplemented
50#2689C2218yescomplemented
51#2687C2218yescomplemented
52#2685C2218yescomplemented
53#2684C2214yescomplemented
54#2649C2218yescomplemented
55#2630C2218yescomplemented
56#2628C2218yescomplemented
57#2609C2218yescomplemented
58#2602C2218yescomplemented
59#2576C2218yescomplemented
60#2576C2218yescomplemented
61#2575C2218yescomplemented
62#2574C2218yescomplemented
63#2553C2218yescomplemented
64#2534C2218yescomplemented
65#2534C2214yescomplemented
66#2534C2214yescomplemented
67#2487C2214yescomplemented
68#2483C2212yescomplemented
69#2482C2214yescomplemented
70#2482C2214yescomplemented
71#2480C2218yescomplemented
72#2480C2218yescomplemented
73#2474C2218yescomplemented
74#2472C2218yescomplemented
75#2471C2218yescomplemented
76#2470C2218yescomplemented
77#2461C2218yescomplemented
78#2459C2218yescomplemented
79#2457C2218yescomplemented
80#2457C2218yescomplemented
81#2455C2218yescomplemented
82#2449C2218yescomplemented
83#2437C2218yescomplemented
84#2435C2214yes—
85#2435C2214yescomplemented
86#2432C2214yescomplemented
87#2432C2214yescomplemented
88#2418C2218yescomplemented
89#2418C2218yescomplemented
90#2418C2218yescomplemented
91#2418C2218yescomplemented
92#2418C2218yescomplemented
93#2418C2218yescomplemented
94#2412C2218yescomplemented
95#2411C2218yescomplemented
96#2409C2214yescomplemented
97#2406C2214yescomplemented
98#2406C2214yescomplemented
99#2406C2214yescomplemented
100#2405C2212yes—
101#2405C2212yes—
102#2405C2214yes—
103#2405C2212yescomplemented
104#2405C2212yescomplemented
105#2405C2218yescomplemented
106#2405C2212yescomplemented
107#2405C2214yescomplemented
108#2405C2212yescomplemented
109#2405C2214yescomplemented
110#2404C2214yes—
111#2404C2214yes—
112#2404C2214yes—
113#2403C2212yes—
114#2403C2214yes—
115#2403C2214yes—
116#2403C2212yes—
117#2379C2214yescomplemented
118#2376C2218yescomplemented
119#2374C2214yescomplemented
120#2358C2214yescomplemented
121#2352C2218yescomplemented
122#2342C2218yescomplemented
123D4×C22⋊C4C2218yescomplemented
124#2322C2214yescomplemented
125#2321C2214yescomplemented
126#2315C2214yescomplemented
127#2312C2212yescomplemented
128#2312C2212yescomplemented
129#2309C2211yescharacteristic, complemented
130#2308C2211yescharacteristic
131#2308C2212yes—
132#2308C2212yescomplemented
133#2308C2211yescharacteristic, complemented
134#2308C2212yescomplemented
135C4×#123C2214yescomplemented
136C4×#120C2214yescomplemented
137#2297C2212yescomplemented
138C2×#379C2214yescomplemented
139C26C2311yescharacteristic
140C2×H(5,𝔽2)—44no—
141C2×H(5,𝔽2)—48no—
142C22×#41C2312yes—
143C22×#41C2312yes—
144C22×#41C2312yes—
145C23×Q8C2311yescharacteristic, complemented
146C23×D4C2311yescharacteristic
147C23×D4C2312yes—
148C23×D4C2311yescharacteristic
149C23×D4C2312yes—
150C23×D4C2312yes—
151C23×D4C2311yescharacteristic
152C23×D4C2312yes—
153C23×D4C2314yes—
154C24×C4C2311yescharacteristic, complemented
155#551—416no—
156#536—48no—
157C2×C4⋊Q8C2314yescomplemented
158C2×#126C2318yes—
159C2×#124—44no—
160C2×#124C2314yes—
161C2×#124C2314yes—
162C2×#124C2314yescomplemented
163C2×#123—44no—
164C2×#123—48no—
165C2×#123C2314yes—
166C2×#123C2314yes—
167C2×#123C2318yes—
168C2×#123C2314yes—
169C2×#123C2314yes—
170C2×#123C2314yes—
171C2×#123C2314yes—
172C2×#123C2318yes—
173C2×#123C2314yescomplemented
174C2×#123C2314yescomplemented
175C2×#123C2314yescomplemented
176C2×#123C2314yescomplemented
177C2×C22⋊Q8C2318yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yescomplemented
180C2×#120—48no—
181C2×#120—44no—
182C2×#120C2314yes—
183C2×#120C2314yes—
184C2×#120C2314yes—
185C2×#120C2314yes—
186C2×#120C2314yes—
187C2×#120C2314yes—
188C2×#120C2314yes—
189C2×#120C2314yes—
190#518—48no—
191C2×C4×D4C2314yes—
192C2×C4×D4C2314yes—
193C2×C4×D4C2318yes—
194C2×C4×D4C2318yes—
195C2×C4×D4C2314yes—
196C2×C4×D4C2314yes—
197C2×#117C2318yes—
198C2×#117C2314yes—
199C2×#117C2312yescomplemented
200C22×C4⋊C4C2312yescomplemented
201C22×C4⋊C4C2314yescomplemented
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2314yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2314yes—
209C22×C22⋊C4C2314yes—
210C22×C22⋊C4C2318yes—
211C22×C22⋊C4C2314yes—
212C22×C22⋊C4C2318yes—
213C22×C22⋊C4C2312yescomplemented
214C22×C22⋊C4C2311yescharacteristic, complemented
215C22×C22⋊C4C2312yescomplemented
216C22×C42C2311yescharacteristic, complemented
217#401C2318yescomplemented
218#400C2318yescomplemented
219#400C2318yescomplemented
220#400C2318yescomplemented
221#400C2318yescomplemented
222#400C2318yescomplemented
223#399C2318yes—
224#399C2318yes—
225#399C2318yes—
226#399C2318yescomplemented
227#398C2318yescomplemented
228#398C2318yescomplemented
229#398C2318yescomplemented
230#397C2318yes—
231#397C2318yes—
232#397C2318yes—
233#397C2318yes—
234#397C2318yes—
235#397C2318yescomplemented
236#397C2318yescomplemented
237#397C2318yescomplemented
238#396C2318yes—
239#396C2318yes—
240#396C2318yes—
241#396C2318yescomplemented
242#396C2318yescomplemented
243#396C2318yescomplemented
244#396C2318yescomplemented
245#395C2318yescomplemented
246#395C2318yescomplemented
247#394C2318yes—
248#394C2318yes—
249#394C2318yes—
250#394C2318yes—
251#394C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yescomplemented
260#393C2318yes—
261#393C2318yes—
262#392C2318yes—
263#392C2318yes—
264#392C2318yes—
265#391C2314yescomplemented
266#391C2318yescomplemented
267#390C2314yes—
268#390C2318yes—
269#390C2318yes—
270#390C2314yes—
271#390C2314yescomplemented
272#389C2318yescomplemented
273#389C2318yescomplemented
274#389C2318yescomplemented
275#388C2318yes—
276#388C2318yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#388C2318yes—
282#388C2318yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yescomplemented
287#388C2318yescomplemented
288#388C2318yescomplemented
289#388C2318yescomplemented
290#388C2318yescomplemented
291#388C2318yescomplemented
292#388C2318yescomplemented
293#388C2318yescomplemented
294#387C2318yescomplemented
295#387C2318yescomplemented
296#387C2318yescomplemented
297#387C2318yescomplemented
298#387C2318yescomplemented
299#387C2318yescomplemented
300#387C2318yescomplemented
301#386C2314yes—
302#386C2314yes—
303#386C2314yes—
304#386C2314yes—
305#386C2314yes—
306#386C2314yes—
307#386C2318yes—
308#386C2314yes—
309#386C2314yes—
310#386C2314yes—
311#386C2318yes—
312#386C2314yes—
313#386C2318yes—
314#386C2318yes—
315#386C2314yes—
316#386C2318yes—
317#386C2314yes—
318#386C2318yes—
319#386C2318yes—
320#386C2318yes—
321#386C2318yes—
322#386C2314yes—
323#386C2318yes—
324#386C2314yes—
325#386C2314yescomplemented
326#386C2314yescomplemented
327#386C2314yescomplemented
328#386C2314yescomplemented
329#385C2318yes—
330#385C2318yes—
331#385C2314yes—
332#385C2314yes—
333#385C2314yes—
334#385C2314yes—
335#385C2318yes—
336#385C2318yes—
337#385C2318yes—
338#385C2318yes—
339#385C2318yes—
340#385C2314yescomplemented
341#385C2314yescomplemented
342#385C2314yescomplemented
343#385C2318yescomplemented
344#385C2318yescomplemented
345#385C2318yescomplemented
346#385C2318yescomplemented
347#385C2314yescomplemented
348#382C2318yescomplemented
349#382C2318yescomplemented
350#381C2314yes—
351#381C2312yes—
352#381C2314yes—
353#381C2318yes—
354#381C2314yescomplemented
355#381C2312yescomplemented
356#381C2314yescomplemented
357#381C2314yescomplemented
358#380C2318yes—
359#380C2318yes—
360#380C2318yes—
361#380C2318yes—
362#380C2318yes—
363#380C2314yescomplemented
364#380C2314yescomplemented
365#380C2318yescomplemented
366#379C2312yes—
367#379C2314yes—
368#379C2312yes—
369#379C2312yes—
370#379C2314yes—
371#379C2318yes—
372#379C2318yes—
373#379C2314yes—
374#379C2314yes—
375#379C2314yes—
376#379C2318yes—
377#379C2314yes—
378#379C2312yescomplemented
379#379C2314yescomplemented
380#379C2314yescomplemented
381C4×C4⋊C4C2318yescomplemented
382C4×C22⋊C4C2318yes—
383C4×C22⋊C4C2314yes—
384C4×C22⋊C4C2318yes—
385C4×C22⋊C4C2314yescomplemented
386C4×C22⋊C4C2314yescomplemented
387C4×C22⋊C4C2314yescomplemented
388C4×C22⋊C4C2318yescomplemented
389C25—42no—
390C25—44no—
391C25—48no—
392C25C2412yes—
393C25C2414yes—
394C25C2411yescharacteristic
395C25C2411yescharacteristic
396C25C2412yes—
397C25C2411yescharacteristic
398C25C2411yescharacteristic
399H(5,𝔽2)—464no—
400C2×#41—28no—
401C2×#41—44no—
402C2×#41—44no—
403C2×#41—44no—
404C2×#41—44no—
405C2×#41—44no—
406C2×#41—44no—
407C2×#41—44no—
408C2×#41—44no—
409C22×Q8—42no—
410C22×Q8—44no—
411C22×Q8C2414yes—
412C22×Q8C2412yes—
413C22×D4—28no—
414C22×D4—24no—
415C22×D4—24no—
416C22×D4—24no—
417C22×D4—28no—
418C22×D4—28no—
419C22×D4—44no—
420C22×D4—44no—
421C22×D4—44no—
422C22×D4—48no—
423C22×D4—44no—
424C22×D4—44no—
425C22×D4—44no—
426C22×D4—44no—
427C22×D4—44no—
428C22×D4—44no—
429C22×D4—44no—
430C22×D4—48no—
431C22×D4—416no—
432C22×D4C2414yes—
433C22×D4C2414yes—
434C22×D4C2418yes—
435C22×D4C2412yes—
436C22×D4C2412yes—
437C22×D4C2412yes—
438C22×D4C2412yes—
439C22×D4C2412yes—
440C22×D4C2412yes—
441C22×D4C2418yes—
442C22×D4C2412yes—
443C22×D4C2412yes—
444C22×D4C2412yes—
445C23×C4—42no—
446C23×C4—44no—
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2418yes—
451C23×C4C2412yes—
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2414yes—
458C23×C4C2411yescharacteristic
459C23×C4C2414yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2414yes—
463C23×C4C2412yes—
464C4⋊Q8—48no—
465#126—416no—
466#124—216no—
467#124—48no—
468#124—48no—
469#123—216no—
470#123—48no—
471#123—48no—
472#123—48no—
473#123—48no—
474#123—48no—
475#123—48no—
476#123—416no—
477#123—48no—
478#123—48no—
479#123—416no—
480#123—48no—
481C22⋊Q8—48no—
482C22⋊Q8—48no—
483C22⋊Q8—416no—
484#120—216no—
485#120—48no—
486#120—48no—
487#120—48no—
488#120—48no—
489#120—48no—
490#120—48no—
491#120—48no—
492C4×D4—416no—
493C4×D4—48no—
494C4×D4—48no—
495C4×D4—48no—
496C4×D4—48no—
497C4×D4—416no—
498#117—44no—
499#117—416no—
500#117—48no—
501C2×C4⋊C4—48no—
502C2×C4⋊C4—44no—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2418yes—
519C2×C22⋊C4—28no—
520C2×C22⋊C4—28no—
521C2×C22⋊C4—48no—
522C2×C22⋊C4—416no—
523C2×C22⋊C4—48no—
524C2×C22⋊C4—44no—
525C2×C22⋊C4—48no—
526C2×C22⋊C4—416no—
527C2×C22⋊C4—44no—
528C2×C22⋊C4—48no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—44no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—44no—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2414yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2418yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C42—42no—
573C2×C42C2414yes—
574C2×C42C2414yes—
575C2×C42C2414yes—
576C2×C42C2418yes—
577C2×C42C2418yes—
578C2×C42C2414yes—
579#95C2418yes—
580#95C2418yes—
581#95C2418yes—
582#95C2418yes—
583#95C2418yes—
584#95C2418yes—
585#95C2418yes—
586#95C2418yes—
587#95C2418yes—
588#95C2418yes—
589#95C2418yes—
590#95C2418yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2418yes—
599C24—24no—
600C24—22no—
601C24—24no—
602C24—22no—
603C24—24no—
604C24—28no—
605C24—28no—
606C24—216no—
607C24—24no—
608C24—22no—
609C24—24no—
610C24—44no—
611C24—48no—
612C24—42no—
613C24—42no—
614C24—42no—
615C24—44no—
616C24—44no—
617C24—44no—
618C24—44no—
619C24—44no—
620C24—44no—
621C24—48no—
622C24—44no—
623C24—88no—
624C24—816no—
625C24—832no—
626C24H(5,𝔽2)14yes—
627C24C2512yes—
628C24C2511yescharacteristic
629C24C2512yes—
630C24C2511yescharacteristic
631C24C2511yescharacteristic
632C24C2512yes—
633C24C2514yes—
634#41—432no—
635#41—432no—
636#41—432no—
637C2×Q8—24no—
638C2×Q8—28no—
639C2×Q8—42no—
640C2×Q8—42no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—88no—
644C2×D4—28no—
645C2×D4—28no—
646C2×D4—216no—
647C2×D4—24no—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—216no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—216no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—416no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—432no—
684C2×D4—432no—
685C2×D4—432no—
686C2×D4—416no—
687C2×D4—416no—
688C2×D4—432no—
689C2×D4—832no—
690C2×D4H(5,𝔽2)18yes—
691C22×C4—22no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—28no—
703C22×C4—216no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—44no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—48no—
718C22×C4—48no—
719C22×C4—48no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—48no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—88no—
731C22×C4C2514yes—
732C22×C4C2518yes—
733C22×C4C2512yes—
734C22×C4C2512yes—
735C22×C4C2514yes—
736C22×C4C2514yes—
737C22×C4C2518yes—
738C22×C4C2518yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2512yes—
742C4⋊C4—216no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C22⋊C4—28no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—216no—
763C22⋊C4—28no—
764C22⋊C4—216no—
765C22⋊C4—28no—
766C22⋊C4—216no—
767C22⋊C4—216no—
768C22⋊C4—216no—
769C22⋊C4—216no—
770C22⋊C4—48no—
771C22⋊C4—44no—
772C22⋊C4—48no—
773C22⋊C4—48no—
774C22⋊C4—44no—
775C22⋊C4—48no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—48no—
780C22⋊C4—44no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—44no—
784C22⋊C4—48no—
785C22⋊C4—44no—
786C22⋊C4—48no—
787C22⋊C4—44no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—44no—
795C22⋊C4—48no—
796C22⋊C4—44no—
797C42—28no—
798C42—44no—
799C42—44no—
800C42—44no—
801C42—48no—
802C42—48no—
803C23—28no—
804C23—28no—
805C23—216no—
806C23—28no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—28no—
816C23—24no—
817C23—24no—
818C23—28no—
819C23—24no—
820C23—24no—
821C23—28no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—28no—
826C23—44no—
827C23—48no—
828C23—416no—
829C23—432no—
830C23—48no—
831C23—44no—
832C23—88no—
833C23—84no—
834C23—816no—
835C23—88no—
836C23—84no—
837C23—88no—
838C23—84no—
839C23—84no—
840C23—816no—
841C23—88no—
842C23—88no—
843C23—84no—
844C23—88no—
845C23—864no—
846C23—164no—
847C23—164no—
848C23—164no—
849C23C2×H(5,𝔽2)14yes—
850C23C2×H(5,𝔽2)12yes—
851C23C2×H(5,𝔽2)14yes—
852C23C2×H(5,𝔽2)12yes—
853C23C2×H(5,𝔽2)12yes—
854C23#58518yes—
855C23C2611yescharacteristic
856Q8—48no—
857Q8—88no—
858D4—48no—
859D4—48no—
860D4—48no—
861D4—416no—
862D4—416no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—48no—
867D4—432no—
868D4—48no—
869D4—48no—
870D4—816no—
871C2×C4—28no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—28no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—28no—
880C2×C4—24no—
881C2×C4—28no—
882C2×C4—28no—
883C2×C4—28no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—28no—
897C2×C4—28no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—48no—
901C2×C4—48no—
902C2×C4—48no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—48no—
906C2×C4—816no—
907C2×C4—84no—
908C2×C4—84no—
909C2×C4—84no—
910C2×C4—88no—
911C2×C4—84no—
912C2×C4—88no—
913C2×C4—88no—
914C2×C4—164no—
915C2×C4—164no—
916C2×C4C2×H(5,𝔽2)14yes—
917C22—216no—
918C22—28no—
919C22—28no—
920C22—22no—
921C22—24no—
922C22—22no—
923C22—24no—
924C22—22no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—28no—
929C22—44no—
930C22—44no—
931C22—48no—
932C22—44no—
933C22—44no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—44no—
939C22—44no—
940C22—44no—
941C22—42no—
942C22—44no—
943C22—88no—
944C22—816no—
945C22—88no—
946C22—832no—
947C22—164no—
948C22—168no—
949C22—164no—
950C22C22×H(5,𝔽2)12yes—
951C22C22×H(5,𝔽2)11yescharacteristic
952C22C2×#58514yes—
953C4—24no—
954C4—48no—
955C4—48no—
956C4—48no—
957C4—42no—
958C4—42no—
959C4—44no—
960C4—44no—
961C4—44no—
962C4—44no—
963C4—44no—
964C2—48no—
965C2—44no—
966C2—42no—
967C2—44no—
968C2—42no—
969C2—42no—
970C2—82no—
971C2#6281711yescharacteristic
972C2#6282012yes—
973C2#6301714yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35346C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59621C2semidirect
2. #59191C2semidirect
3. #59006C2semidirect
4. #51530C2semidirect
5. #48949C2semidirect
6. #48679C2semidirect
7. #48333C2semidirect
8. #48113C2semidirect
9. #47903C2semidirect
10. #46997C2semidirect
11. #46388C2semidirect
12. #46386C2semidirect
13. #35616C2semidirect
14. #35451C2semidirect
15. #35446C2semidirect
16. #35354C2semidirect
17. #35350C2semidirect
20. C2×#551C22semidirect
21. C2×#536C22semidirect
22. C22×#124C22semidirect
23. C22×#123C22semidirect
24. C22×#123C22semidirect
27. C2×#518C22semidirect
28. #2842C22semidirect
29. #2782C22semidirect
30. #2780C22semidirect
31. #2779C22semidirect
32. #2778C22semidirect
33. #2765C22semidirect
34. #2761C22semidirect
35. #2750C22semidirect
36. #2748C22semidirect
37. #2746C22semidirect
38. #2746C22semidirect
39. #2745C22semidirect
40. #2743C22semidirect
41. #2735C22semidirect
42. #2729C22semidirect
43. #2717C22semidirect
44. #2706C22semidirect
45. #2706C22semidirect
46. #2697C22semidirect
47. #2697C22semidirect
48. #2695C22semidirect
49. #2693C22semidirect
50. #2689C22semidirect
51. #2687C22semidirect
52. #2685C22semidirect
53. #2684C22semidirect
54. #2649C22semidirect
55. #2630C22semidirect
56. #2628C22semidirect
57. #2609C22semidirect
58. #2602C22semidirect
59. #2576C22semidirect
60. #2576C22semidirect
61. #2575C22semidirect
62. #2574C22semidirect
63. #2553C22semidirect
64. #2534C22semidirect
65. #2534C22semidirect
66. #2534C22semidirect
67. #2487C22semidirect
68. #2483C22semidirect
69. #2482C22semidirect
70. #2482C22semidirect
71. #2480C22semidirect
72. #2480C22semidirect
73. #2474C22semidirect
74. #2472C22semidirect
75. #2471C22semidirect
76. #2470C22semidirect
77. #2461C22semidirect
78. #2459C22semidirect
79. #2457C22semidirect
80. #2457C22semidirect
81. #2455C22semidirect
82. #2449C22semidirect
83. #2437C22semidirect
85. #2435C22semidirect
86. #2432C22semidirect
87. #2432C22semidirect
88. #2418C22semidirect
89. #2418C22semidirect
90. #2418C22semidirect
91. #2418C22semidirect
92. #2418C22semidirect
93. #2418C22semidirect
94. #2412C22semidirect
95. #2411C22semidirect
96. #2409C22semidirect
97. #2406C22semidirect
98. #2406C22semidirect
99. #2406C22semidirect
103. #2405C22semidirect
104. #2405C22semidirect
105. #2405C22semidirect
106. #2405C22semidirect
107. #2405C22semidirect
108. #2405C22semidirect
109. #2405C22semidirect
117. #2379C22semidirect
118. #2376C22semidirect
119. #2374C22semidirect
120. #2358C22semidirect
121. #2352C22semidirect
122. #2342C22semidirect
123. D4×C22⋊C4C22semidirect
124. #2322C22semidirect
125. #2321C22semidirect
126. #2315C22semidirect
127. #2312C22semidirect
128. #2312C22semidirect
129. #2309C22semidirect
132. #2308C22semidirect
133. #2308C22semidirect
134. #2308C22semidirect
135. C4×#123C22semidirect
136. C4×#120C22semidirect
137. #2297C22semidirect
138. C2×#379C22semidirect
145. C23×Q8C23semidirect
154. C24×C4C23semidirect
157. C2×C4⋊Q8C23semidirect
162. C2×#124C23semidirect
173. C2×#123C23semidirect
174. C2×#123C23semidirect
175. C2×#123C23semidirect
176. C2×#123C23semidirect
179. C2×C22⋊Q8C23semidirect
199. C2×#117C23semidirect
200. C22×C4⋊C4C23semidirect
201. C22×C4⋊C4C23semidirect
213. C22×C22⋊C4C23semidirect
214. C22×C22⋊C4C23semidirect
215. C22×C22⋊C4C23semidirect
216. C22×C42C23semidirect
217. #401C23semidirect
218. #400C23semidirect
219. #400C23semidirect
220. #400C23semidirect
221. #400C23semidirect
222. #400C23semidirect
226. #399C23semidirect
227. #398C23semidirect
228. #398C23semidirect
229. #398C23semidirect
235. #397C23semidirect
236. #397C23semidirect
237. #397C23semidirect
241. #396C23semidirect
242. #396C23semidirect
243. #396C23semidirect
244. #396C23semidirect
245. #395C23semidirect
246. #395C23semidirect
259. #394C23semidirect
265. #391C23semidirect
266. #391C23semidirect
271. #390C23semidirect
272. #389C23semidirect
273. #389C23semidirect
274. #389C23semidirect
286. #388C23semidirect
287. #388C23semidirect
288. #388C23semidirect
289. #388C23semidirect
290. #388C23semidirect
291. #388C23semidirect
292. #388C23semidirect
293. #388C23semidirect
294. #387C23semidirect
295. #387C23semidirect
296. #387C23semidirect
297. #387C23semidirect
298. #387C23semidirect
299. #387C23semidirect
300. #387C23semidirect
325. #386C23semidirect
326. #386C23semidirect
327. #386C23semidirect
328. #386C23semidirect
340. #385C23semidirect
341. #385C23semidirect
342. #385C23semidirect
343. #385C23semidirect
344. #385C23semidirect
345. #385C23semidirect
346. #385C23semidirect
347. #385C23semidirect
348. #382C23semidirect
349. #382C23semidirect
354. #381C23semidirect
355. #381C23semidirect
356. #381C23semidirect
357. #381C23semidirect
363. #380C23semidirect
364. #380C23semidirect
365. #380C23semidirect
378. #379C23semidirect
379. #379C23semidirect
380. #379C23semidirect
381. C4×C4⋊C4C23semidirect
385. C4×C22⋊C4C23semidirect
386. C4×C22⋊C4C23semidirect
387. C4×C22⋊C4C23semidirect
388. C4×C22⋊C4C23semidirect

Maximal subgroups

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

subgroupindex
#596212
#591912
#590062
#515302
#489492
#486792
#483332
#481132
#479032
#469972
#463882
#463862
#356162
#354512
#354462
#353542
#353502
#353462