Finite Group Databasebeta

← #7672806

Subgroups — #7672806

Order 512.

4764 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#43516C214yesmaximal, complemented
2#43085C214yesmaximal, complemented
3#43058C218yesmaximal, complemented
4#39512C214yesmaximal, complemented
5#39508C214yesmaximal, complemented
6#39291C218yesmaximal, complemented
7#39288C218yesmaximal, complemented
8#37959C214yesmaximal, complemented
9#37956C214yesmaximal, complemented
10#35456C212yesmaximal, complemented
11#35455C212yesmaximal
12#35010C211yesmaximal, characteristic
13#35002C211yesmaximal, characteristic, complemented
14#34995C212yesmaximal
15C2×#2627C211yesmaximal, characteristic, complemented
16#34270C212yesmaximal, complemented
17#34212C211yesmaximal, characteristic, complemented
18#34185C211yesmaximal, characteristic
19C2×#2322C211yesmaximal, characteristic
20C2×#2313C211yesmaximal, characteristic, complemented
21C2×#543C2212yes—
22C22×#123C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26#2857C2214yes—
27#2855C2212yes—
28#2852C2218yes—
29#2848C2212yes—
30#2810C2218yescomplemented
31#2805C2218yescomplemented
32#2798C2218yescomplemented
33#2793C2218yescomplemented
34#2789C2218yescomplemented
35#2788C2218yescomplemented
36#2787C2218yescomplemented
37#2776C2218yescomplemented
38#2776C2218yescomplemented
39#2767C2218yescomplemented
40#2762C2218yescomplemented
41#2759C2218yescomplemented
42#2758C2218yescomplemented
43#2745C2218yescomplemented
44#2716C2218yescomplemented
45#2689C2218yescomplemented
46#2659C2214yes—
47#2643C2218yes—
48#2627C2214yes—
49#2627C2214yes—
50#2627C2212yes—
51#2627C2214yescomplemented
52#2627C2214yescomplemented
53#2626C2212yes—
54#2605C2218yescomplemented
55#2599C2218yescomplemented
56#2596C2218yescomplemented
57#2594C2218yescomplemented
58#2588C2218yescomplemented
59#2581C2218yescomplemented
60#2579C2214yes—
61#2577C2218yescomplemented
62#2570C2218yescomplemented
63#2564C2214yes—
64#2561C2218yes—
65#2549C2214yescomplemented
66#2549C2214yescomplemented
67#2528C2218yescomplemented
68#2525C2218yescomplemented
69#2524C2218yescomplemented
70#2514C2218yescomplemented
71#2510C2218yes—
72#2503C2218yes—
73#2493C2218yes—
74#2493C2218yes—
75#2493C2218yes—
76#2493C2218yescomplemented
77#2493C2218yescomplemented
78#2493C2218yescomplemented
79#2493C2218yescomplemented
80#2488C2218yes—
81#2488C2218yes—
82#2488C2218yes—
83#2488C2218yes—
84#2487C2212yes—
85#2481C2218yes—
86#2480C2218yes—
87#2478C2218yescomplemented
88#2469C2218yescomplemented
89#2465C2218yescomplemented
90#2446C2218yescomplemented
91#2440C2214yescomplemented
92#2440C2214yescomplemented
93#2417C2214yes—
94#2409C2212yes—
95C2×#400C2212yescomplemented
96C2×#398C2214yescomplemented
97C2×#395C2212yescomplemented
98#2368C2218yes—
99#2368C2218yescomplemented
100#2368C2214yescomplemented
101#2360C2218yes—
102#2360C2218yescomplemented
103#2360C2214yescomplemented
104#2353C2214yes—
105#2353C2214yes—
106#2352C2214yes—
107#2352C2214yes—
108#2345C2214yescomplemented
109#2345C2212yescomplemented
110Q8×C22⋊C4C2212yescomplemented
111#2329C2214yes—
112#2329C2218yescomplemented
113#2322C2214yes—
114#2322C2214yes—
115#2322C2214yes—
116#2322C2214yes—
117#2315C2212yes—
118#2315C2212yes—
119#2315C2212yes—
120#2313C2214yes—
121#2313C2214yes—
122#2313C2212yes—
123#2313C2214yescomplemented
124#2313C2214yescomplemented
125#2312C2212yes—
126#2308C2212yes—
127#2308C2212yes—
128C4×C22⋊Q8C2214yes—
129C4×C22⋊Q8C2218yescomplemented
130C2×#389C2212yes—
131C2×#388C2212yes—
132C2×#387C2212yes—
133C2×#387C2214yescomplemented
134C2×#387C2214yescomplemented
135C2×#386C2211yescharacteristic
136C2×#385C2212yes—
137C2×#385C2211yescharacteristic
138C2×#385C2212yes—
139#2283C2212yes—
140#2280C2212yes—
141C2×#381C2211yescharacteristic
142C2×#381C2212yes—
143C2×#381C2212yes—
144C2×#380C2211yescharacteristic
145C2×#380C2211yescharacteristic
146C2×#380C2211yescharacteristic
147#2273C2212yes—
148#2273C2212yes—
149C2×C4×C22⋊C4C2211yescharacteristic
150C2×C4×C22⋊C4C2212yes—
151C23×Q8C2311yescharacteristic
152C23×D4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C24×C4C2311yescharacteristic
157#543—216no—
158C2×C4⋊Q8C2314yes—
159C2×#126C2318yes—
160C2×#123—28no—
161C2×#123C2314yes—
162C2×#123C2314yes—
163C2×C22⋊Q8—28no—
164C2×C22⋊Q8C2318yes—
165C2×C22⋊Q8C2312yes—
166C2×C22⋊Q8C2312yes—
167C2×C22⋊Q8C2318yes—
168C2×C22⋊Q8C2318yes—
169C2×C22⋊Q8C2312yes—
170C2×C22⋊Q8C2312yes—
171C2×C22⋊Q8C2314yes—
172C2×C4×Q8C2314yes—
173C2×C4×Q8C2318yes—
174C2×C4×D4—28no—
175C2×C4×D4C2312yes—
176C2×C4×D4C2312yes—
177C2×C4×D4C2312yes—
178C2×C4×D4C2312yes—
179C2×#117C2314yes—
180C22×C4⋊C4—28no—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2314yes—
195C22×C4⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2314yes—
208C22×C42C2312yes—
209#401C2318yes—
210#401C2318yes—
211#401C2318yes—
212#400C2314yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#399C2314yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#396C2318yes—
242#396C2318yes—
243#395C2314yes—
244#395C2318yes—
245#395C2318yes—
246#395C2318yes—
247#395C2318yes—
248#393C2318yes—
249#393C2318yes—
250#393C2314yes—
251#391C2318yes—
252#391C2318yes—
253#391C2318yes—
254#391C2318yes—
255#391C2318yes—
256#391C2318yes—
257#391C2314yes—
258#391C2314yes—
259#391C2318yes—
260#389C2318yes—
261#389C2318yes—
262#389C2318yes—
263#389C2318yes—
264#389C2318yes—
265#389C2314yes—
266#389C2318yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2318yes—
271#388C2318yes—
272#388C2318yes—
273#388C2318yes—
274#388C2318yes—
275#388C2318yes—
276#388C2318yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#388C2318yes—
282#387C2318yes—
283#387C2318yes—
284#387C2318yes—
285#387C2318yes—
286#387C2318yes—
287#387C2318yes—
288#387C2318yes—
289#387C2318yes—
290#387C2318yes—
291#387C2318yes—
292#387C2318yes—
293#387C2318yes—
294#387C2318yes—
295#387C2318yes—
296#387C2318yes—
297#387C2318yes—
298#387C2318yes—
299#387C2318yes—
300#387C2318yes—
301#387C2318yes—
302#387C2318yes—
303#387C2318yes—
304#387C2318yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2318yes—
312#387C2318yes—
313#386C2318yes—
314#386C2314yes—
315#386C2314yes—
316#386C2318yes—
317#386C2318yes—
318#386C2314yes—
319#386C2314yes—
320#385C2318yes—
321#385C2314yes—
322#385C2314yes—
323#385C2318yes—
324#385C2314yes—
325#385C2318yes—
326#385C2318yes—
327#385C2314yes—
328#385C2318yes—
329#385C2318yes—
330#385C2314yes—
331#385C2318yes—
332#385C2314yes—
333#385C2314yes—
334#385C2318yes—
335#385C2314yes—
336#384C2314yes—
337#383C2318yes—
338#383C2318yes—
339#383C2318yes—
340#383C2314yes—
341#382C2318yes—
342#382C2318yes—
343#382C2314yes—
344#381C2318yes—
345#381C2318yes—
346#381C2314yes—
347#381C2314yes—
348#381C2318yes—
349#381C2314yes—
350#381C2314yes—
351#381C2314yes—
352#381C2314yes—
353#381C2314yes—
354#380C2318yes—
355#380C2312yes—
356#380C2312yes—
357#380C2312yes—
358#380C2312yes—
359#380C2312yes—
360#380C2312yes—
361#380C2312yes—
362#380C2312yes—
363#380C2312yes—
364#380C2314yes—
365#380C2314yes—
366#380C2318yes—
367#380C2314yes—
368#380C2312yes—
369#380C2314yes—
370#380C2312yes—
371#380C2312yes—
372#379C2314yes—
373#379C2314yes—
374C4×C4⋊C4C2318yes—
375C4×C4⋊C4C2318yes—
376C4×C4⋊C4C2314yes—
377C4×C4⋊C4C2318yes—
378C4×C4⋊C4C2318yes—
379C4×C4⋊C4C2314yes—
380C4×C22⋊C4C2318yes—
381C4×C22⋊C4C2314yes—
382C4×C22⋊C4C2318yes—
383C4×C22⋊C4C2314yes—
384C4×C22⋊C4C2318yes—
385C4×C22⋊C4C2314yes—
386C4×C22⋊C4C2312yes—
387C4×C22⋊C4C2312yes—
388C4×C22⋊C4C2312yes—
389C4×C22⋊C4C2312yes—
390C4×C22⋊C4C2318yes—
391C4×C22⋊C4C2318yes—
392C4×C22⋊C4C2314yes—
393C4×C22⋊C4C2314yes—
394C4×C22⋊C4C2318yes—
395#376C2314yes—
396C2×#95C2312yes—
397C2×#95C2312yes—
398C2×#95C2314yes—
399C2×#95C2312yes—
400C2×#95C2312yes—
401C2×#95C2312yes—
402C2×#95C2314yes—
403C2×#95C2314yes—
404C2×#95C2314yes—
405C2×#95C2314yes—
406C2×#95C2314yes—
407C2×#95C2312yes—
408C2×#95C2312yes—
409C2×#95C2312yes—
410C25C2411yescharacteristic
411C25C2411yescharacteristic
412C22×Q8—24no—
413C22×Q8—82no—
414C22×Q8C2412yes—
415C22×Q8C2418yes—
416C22×Q8C2412yes—
417C22×D4—24no—
418C22×D4—24no—
419C22×D4—24no—
420C22×D4C2412yes—
421C22×D4C2412yes—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—24no—
426C23×C4—24no—
427C23×C4—82no—
428C23×C4—82no—
429C23×C4—82no—
430C23×C4#4118yes—
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2414yes—
441C23×C4C2412yes—
442C23×C4C2414yes—
443C23×C4C2414yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C4⋊Q8—84no—
456#126—88no—
457#123—216no—
458#123—216no—
459C22⋊Q8—28no—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8—232no—
464C22⋊Q8—232no—
465C22⋊Q8—232no—
466C22⋊Q8—84no—
467C4×Q8—88no—
468C4×Q8—84no—
469C4×D4—28no—
470C4×D4—28no—
471C4×D4—28no—
472C4×D4—28no—
473#117—84no—
474C2×C4⋊C4—28no—
475C2×C4⋊C4—28no—
476C2×C4⋊C4—28no—
477C2×C4⋊C4—28no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4—28no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—28no—
483C2×C4⋊C4—28no—
484C2×C4⋊C4—82no—
485C2×C4⋊C4—82no—
486C2×C4⋊C4—82no—
487C2×C4⋊C4—84no—
488C2×C4⋊C4—82no—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2412yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—28no—
520C2×C22⋊C4—28no—
521C2×C22⋊C4—28no—
522C2×C22⋊C4—28no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—28no—
526C2×C22⋊C4—82no—
527C2×C22⋊C4#4118yes—
528C2×C22⋊C4C2412yes—
529C2×C22⋊C4C2412yes—
530C2×C22⋊C4C2412yes—
531C2×C22⋊C4C2412yes—
532C2×C22⋊C4C2414yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2414yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2418yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2412yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2412yes—
550C2×C42—24no—
551C2×C42—84no—
552C2×C42—82no—
553C2×C42C2412yes—
554C2×C42C2412yes—
555C2×C42C2418yes—
556C2×C42C2418yes—
557C2×C42C2418yes—
558C2×C42C2414yes—
559C2×C42C2418yes—
560C2×C42C2414yes—
561C2×C42C2418yes—
562C2×C42C2418yes—
563#95C2414yes—
564#95C2414yes—
565#95C2414yes—
566#95C2414yes—
567#95C2418yes—
568#95C2418yes—
569#95C2414yes—
570#95C2418yes—
571#95C2418yes—
572#95C2414yes—
573#95C2414yes—
574#95C2414yes—
575#95C2418yes—
576#95C2418yes—
577#95C2418yes—
578#95C2418yes—
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—
599#95C2418yes—
600#95C2418yes—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24C2×#4114yes—
609C24C2×#4114yes—
610C242−1+414yes—
611C24C2512yes—
612C24C2511yescharacteristic
613C24C2511yescharacteristic
614C24C2511yescharacteristic
615C2×Q8—24no—
616C2×Q8—216no—
617C2×Q8—24no—
618C2×Q8—44no—
619C2×Q8—48no—
620C2×Q8—44no—
621C2×Q8—48no—
622C2×Q8—88no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—24no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—416no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—22no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—24no—
645C22×C4—22no—
646C22×C4—24no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—28no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—44no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—44no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—42no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—42no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—42no—
681C22×C4—416no—
682C22×C4—88no—
683C22×C4—88no—
684C22×C4—88no—
685C22×C4C2×#4114yes—
686C22×C4C2×#4118yes—
687C22×C4C2×#4114yes—
688C22×C4C2×#4114yes—
689C22×C4C2×#4114yes—
690C22×C4C2×#4114yes—
691C22×C4C2×#4114yes—
692C22×C4C2512yes—
693C22×C4C2514yes—
694C22×C4C2512yes—
695C22×C4C2518yes—
696C22×C4C2514yes—
697C22×C4C2514yes—
698C22×C4C2518yes—
699C22×C4C2518yes—
700C22×C4C2512yes—
701C22×C4C2514yes—
702C22×C4C2514yes—
703C22×C4C2511yescharacteristic
704C22×C4C2514yes—
705C22×C4C2511yescharacteristic
706C22×C4C2511yescharacteristic
707C22×C4C2511yescharacteristic
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—28no—
717C4⋊C4—28no—
718C4⋊C4—216no—
719C4⋊C4—216no—
720C4⋊C4—216no—
721C4⋊C4—216no—
722C4⋊C4—44no—
723C4⋊C4—44no—
724C4⋊C4—48no—
725C4⋊C4—44no—
726C4⋊C4—48no—
727C4⋊C4—44no—
728C4⋊C4—48no—
729C4⋊C4—44no—
730C4⋊C4—44no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C4⋊C4—48no—
735C4⋊C4—48no—
736C4⋊C4—48no—
737C22⋊C4—24no—
738C22⋊C4—24no—
739C22⋊C4—28no—
740C22⋊C4—28no—
741C22⋊C4—28no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—28no—
745C22⋊C4—28no—
746C22⋊C4—24no—
747C22⋊C4—28no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—216no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C22⋊C4—48no—
757C22⋊C4C2×#4118yes—
758C22⋊C4C2×#4118yes—
759C42—24no—
760C42—24no—
761C42—44no—
762C42—48no—
763C42—48no—
764C42—44no—
765C42—48no—
766C42—48no—
767C42—48no—
768C42—48no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—24no—
779C23—24no—
780C23—44no—
781C23—48no—
782C23—44no—
783C23—48no—
784C23—48no—
785C23—44no—
786C23—82no—
787C23—82no—
788C23—84no—
789C23#556116yes—
790C23C22×#4112yes—
791C23C22×#4112yes—
792C23C22×#4112yes—
793C23C22×#4112yes—
794C23C22×#4112yes—
795C23C22×#4112yes—
796C23C2×2−1+412yes—
797C23C2×2−1+412yes—
798C23C2×2−1+412yes—
799C23C2611yescharacteristic
800Q8—48no—
801Q8—816no—
802Q8—84no—
803D4—48no—
804D4—48no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—28no—
815C2×C4—28no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—28no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—28no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—24no—
836C2×C4—28no—
837C2×C4—28no—
838C2×C4—28no—
839C2×C4—24no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—48no—
847C2×C4—48no—
848C2×C4—48no—
849C2×C4—48no—
850C2×C4—48no—
851C2×C4—48no—
852C2×C4—44no—
853C2×C4—84no—
854C2×C4—88no—
855C2×C4—88no—
856C2×C4—84no—
857C2×C4—82no—
858C2×C4—88no—
859C2×C4—84no—
860C2×C4—84no—
861C2×C4—82no—
862C2×C4—84no—
863C2×C4—84no—
864C2×C4C22×#4112yes—
865C2×C4C22×#4112yes—
866C2×C4C22×#4118yes—
867C2×C4C22×#4112yes—
868C2×C4C22×#4112yes—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—24no—
873C22—24no—
874C22—24no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—416no—
882C22—42no—
883C22—44no—
884C22—42no—
885C22—44no—
886C22—42no—
887C22—88no—
888C22C2×#55614yes—
889C22C2×#55614yes—
890C22C2×#55614yes—
891C22C23×#4111yescharacteristic
892C22C23×#4111yescharacteristic
893C22C22×2−1+411yescharacteristic
894C22H(7,𝔽2)12yes—
895C222−1+612yes—
896C4—22no—
897C4—22no—
898C4—22no—
899C4—22no—
900C4—28no—
901C4—42no—
902C4—44no—
903C4—44no—
904C4—48no—
905C4—48no—
906C4—42no—
907C4—44no—
908C4—48no—
909C4—44no—
910C4—44no—
911C4—42no—
912C2—24no—
913C2—24no—
914C2—24no—
915C2—82no—
916C2C22×#55611yescharacteristic
917C2#6284411yescharacteristic
918C2#6284712yes—
919C2#6286011yescharacteristic
920C2#6286512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #43516C2semidirect
2. #43085C2semidirect
3. #43058C2semidirect
4. #39512C2semidirect
5. #39508C2semidirect
6. #39291C2semidirect
7. #39288C2semidirect
8. #37959C2semidirect
9. #37956C2semidirect
10. #35456C2semidirect
13. #35002C2semidirect
15. C2×#2627C2semidirect
16. #34270C2semidirect
17. #34212C2semidirect
20. C2×#2313C2semidirect
30. #2810C22semidirect
31. #2805C22semidirect
32. #2798C22semidirect
33. #2793C22semidirect
34. #2789C22semidirect
35. #2788C22semidirect
36. #2787C22semidirect
37. #2776C22semidirect
38. #2776C22semidirect
39. #2767C22semidirect
40. #2762C22semidirect
41. #2759C22semidirect
42. #2758C22semidirect
43. #2745C22semidirect
44. #2716C22semidirect
45. #2689C22semidirect
51. #2627C22semidirect
52. #2627C22semidirect
54. #2605C22semidirect
55. #2599C22semidirect
56. #2596C22semidirect
57. #2594C22semidirect
58. #2588C22semidirect
59. #2581C22semidirect
61. #2577C22semidirect
62. #2570C22semidirect
65. #2549C22semidirect
66. #2549C22semidirect
67. #2528C22semidirect
68. #2525C22semidirect
69. #2524C22semidirect
70. #2514C22semidirect
76. #2493C22semidirect
77. #2493C22semidirect
78. #2493C22semidirect
79. #2493C22semidirect
87. #2478C22semidirect
88. #2469C22semidirect
89. #2465C22semidirect
90. #2446C22semidirect
91. #2440C22semidirect
92. #2440C22semidirect
95. C2×#400C22semidirect
96. C2×#398C22semidirect
97. C2×#395C22semidirect
99. #2368C22semidirect
100. #2368C22semidirect
102. #2360C22semidirect
103. #2360C22semidirect
108. #2345C22semidirect
109. #2345C22semidirect
110. Q8×C22⋊C4C22semidirect
112. #2329C22semidirect
123. #2313C22semidirect
124. #2313C22semidirect
129. C4×C22⋊Q8C22semidirect
133. C2×#387C22semidirect
134. C2×#387C22semidirect

Maximal subgroups

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

subgroupindex
#435162
#430852
#430582
#395122
#395082
#392912
#392882
#379592
#379562
#354562
#354552
#350102
#350022
#349952
C2×#26272
#342702
#342122
#341852
C2×#23222
C2×#23132