Finite Group Databasebeta

← #7642329

Subgroups — #7642329

Order 512.

4928 conjugacy classes of subgroups.

The subgroup lattice has 959 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38482C218yesmaximal, complemented
2#38461C218yesmaximal, complemented
3#38122C214yesmaximal, complemented
4#38113C214yesmaximal, complemented
5#37894C212yesmaximal, complemented
6#37882C212yesmaximal, complemented
7#37705C212yesmaximal, complemented
8#37695C212yesmaximal, complemented
9#36762C214yesmaximal, complemented
10#36760C214yesmaximal, complemented
11C2×#2857C211yesmaximal, characteristic, complemented
12C2×#2851C211yesmaximal, characteristic, complemented
13#35370C214yesmaximal
14#35368C214yesmaximal, complemented
15#35315C212yesmaximal, complemented
16#35310C212yesmaximal, complemented
17#35087C212yesmaximal, complemented
18#35086C212yesmaximal, complemented
19#35010C212yesmaximal
20#34212C212yesmaximal, complemented
21C2×#2290C211yesmaximal, characteristic
22C2×#541C2212yescomplemented
23C22×C4⋊Q8C2211yescharacteristic, complemented
24C22×#125C2211yescharacteristic, complemented
25C22×C22⋊Q8C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2857C2212yes—
30#2857C2214yes—
31#2857C2212yes—
32#2857C2212yescomplemented
33#2857C2214yescomplemented
34#2857C2212yescomplemented
35#2855C2214yes—
36#2851C2212yes—
37#2851C2214yes—
38#2851C2212yes—
39#2851C2214yescomplemented
40#2851C2212yescomplemented
41#2851C2212yescomplemented
42#2848C2214yes—
43#2802C2218yescomplemented
44#2798C2218yescomplemented
45#2794C2218yescomplemented
46#2789C2218yescomplemented
47#2783C2218yescomplemented
48#2776C2218yescomplemented
49#2772C2218yescomplemented
50#2766C2218yescomplemented
51#2758C2218yescomplemented
52#2754C2218yescomplemented
53#2725C2218yescomplemented
54#2725C2218yescomplemented
55#2721C2218yescomplemented
56#2719C2218yescomplemented
57#2716C2218yescomplemented
58#2713C2218yescomplemented
59#2655C2218yescomplemented
60#2652C2218yescomplemented
61#2647C2212yescomplemented
62#2645C2214yescomplemented
63#2642C2212yescomplemented
64#2629C2212yescomplemented
65#2627C2214yes—
66#2626C2214yes—
67#2625C2214yescomplemented
68#2621C2212yescomplemented
69#2579C2218yes—
70#2569C2218yescomplemented
71#2569C2218yescomplemented
72#2564C2218yes—
73#2533C2218yescomplemented
74#2528C2218yescomplemented
75#2514C2214yescomplemented
76#2510C2218yes—
77#2510C2218yes—
78#2510C2218yes—
79#2510C2218yes—
80#2506C2214yescomplemented
81#2505C2218yes—
82#2505C2218yes—
83#2505C2218yescomplemented
84#2505C2218yescomplemented
85#2496C2214yescomplemented
86#2493C2218yes—
87#2493C2218yes—
88#2489C2214yescomplemented
89#2487C2214yes—
90#2481C2218yes—
91#2481C2218yes—
92#2481C2218yes—
93#2481C2218yes—
94#2480C2218yes—
95#2480C2218yes—
96#2478C2218yescomplemented
97#2475C2218yescomplemented
98#2473C2218yes—
99#2473C2218yes—
100#2473C2218yescomplemented
101#2473C2218yescomplemented
102#2453C2214yescomplemented
103#2446C2214yescomplemented
104#2442C2218yescomplemented
105#2442C2218yescomplemented
106#2429C2214yescomplemented
107#2421C2214yescomplemented
108#2417C2214yes—
109#2417C2214yes—
110#2409C2214yes—
111#2368C2218yescomplemented
112#2360C2214yescomplemented
113#2360C2214yescomplemented
114#2345C2218yescomplemented
115#2345C2214yescomplemented
116Q8×C22⋊C4C2214yescomplemented
117#2336C2218yescomplemented
118#2334C2218yescomplemented
119#2330C2212yescomplemented
120#2329C2214yes—
121#2329C2214yes—
122#2327C2212yescomplemented
123#2323C2214yescomplemented
124#2320C2214yescomplemented
125#2315C2214yes—
126#2315C2214yes—
127#2314C2212yescomplemented
128#2308C2214yes—
129C4×C22⋊Q8C2214yes—
130C4×C22⋊Q8C2214yes—
131C2×#391C2212yescomplemented
132C2×#389C2212yescomplemented
133C2×#389C2214yescomplemented
134#2290C2212yes—
135#2290C2214yes—
136#2290C2212yes—
137#2290C2214yes—
138#2290C2212yes—
139#2290C2212yes—
140C2×#388C2212yes—
141C2×#387C2212yes—
142C2×#387C2214yescomplemented
143C2×#386C2212yes—
144C2×#385C2214yes—
145C2×#385C2212yes—
146C2×#384C2211yescharacteristic, complemented
147C2×#382C2211yescharacteristic, complemented
148C2×#380C2212yes—
149C2×#380C2214yes—
150#2273C2214yes—
151C2×C4×C4⋊C4C2211yescharacteristic
152C2×C4×C22⋊C4C2211yescharacteristic
153C2×C4×C22⋊C4C2211yescharacteristic
154C2×#376C2211yescharacteristic
155C23×Q8C2312yes—
156C23×D4C2311yescharacteristic
157C24×C4C2311yescharacteristic
158C24×C4C2312yes—
159C24×C4C2311yescharacteristic
160#541—48no—
161C2×C4⋊Q8—44no—
162C2×C4⋊Q8C2312yes—
163C2×C4⋊Q8C2312yes—
164C2×C4⋊Q8C2314yes—
165C2×#126C2318yes—
166C2×#126C2318yes—
167C2×#125—44no—
168C2×#125C2312yes—
169C2×#125C2318yes—
170C2×#125C2312yes—
171C2×#125C2314yes—
172C2×#125C2318yes—
173C2×C22⋊Q8—216no—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C4×Q8C2314yes—
181C2×C4×Q8C2314yes—
182C2×C4×D4—28no—
183C2×C4×D4C2312yes—
184C2×C4×D4C2312yes—
185C2×C4×D4C2312yes—
186C2×C4×D4C2312yes—
187C2×#117—44no—
188C2×#117C2312yes—
189C2×#117C2312yes—
190C2×#117C2314yes—
191C22×C4⋊C4C2314yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2314yes—
198C22×C4⋊C4C2314yes—
199C22×C4⋊C4C2314yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2314yes—
202C22×C22⋊C4C2314yes—
203C22×C22⋊C4C2314yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C42—44no—
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2312yes—
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222#401C2318yes—
223#401C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#399C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#395C2318yes—
261#393C2318yes—
262#391C2314yes—
263#391C2314yes—
264#391C2314yes—
265#391C2318yes—
266#391C2318yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#391C2314yes—
271#391C2314yes—
272#389C2314yes—
273#389C2314yes—
274#389C2318yes—
275#389C2318yes—
276#389C2318yes—
277#389C2314yes—
278#389C2318yes—
279#389C2318yes—
280#389C2318yes—
281#389C2318yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2318yes—
288#389C2318yes—
289#389C2318yes—
290#388C2318yes—
291#388C2318yes—
292#388C2318yes—
293#388C2318yes—
294#388C2318yes—
295#388C2318yes—
296#388C2314yes—
297#388C2314yes—
298#388C2314yes—
299#388C2314yes—
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#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2314yes—
327#387C2314yes—
328#387C2314yes—
329#387C2314yes—
330#386C2318yes—
331#386C2318yes—
332#386C2318yes—
333#386C2318yes—
334#386C2314yes—
335#386C2314yes—
336#386C2314yes—
337#386C2314yes—
338#385C2318yes—
339#385C2318yes—
340#385C2318yes—
341#385C2314yes—
342#385C2314yes—
343#385C2318yes—
344#385C2318yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2314yes—
355#385C2314yes—
356#384C2312yes—
357#384C2314yes—
358#384C2312yes—
359#383C2318yes—
360#383C2318yes—
361#382C2312yes—
362#382C2318yes—
363#382C2318yes—
364#382C2312yes—
365#382C2314yes—
366#381C2318yes—
367#380C2318yes—
368#380C2318yes—
369#380C2318yes—
370#380C2318yes—
371#380C2314yes—
372#380C2318yes—
373#380C2318yes—
374#380C2314yes—
375#380C2314yes—
376#380C2314yes—
377#380C2314yes—
378#380C2314yes—
379#380C2318yes—
380#380C2318yes—
381#379C2318yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2318yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2312yes—
388C4×C4⋊C4C2312yes—
389C4×C22⋊C4C2318yes—
390C4×C22⋊C4C2318yes—
391C4×C22⋊C4C2318yes—
392C4×C22⋊C4C2318yes—
393C4×C22⋊C4C2314yes—
394C4×C22⋊C4C2312yes—
395C4×C22⋊C4C2318yes—
396C4×C22⋊C4C2312yes—
397C4×C22⋊C4C2318yes—
398C4×C22⋊C4C2312yes—
399C4×C22⋊C4C2312yes—
400C4×C22⋊C4C2312yes—
401C4×C22⋊C4C2312yes—
402#376C2312yes—
403#376C2312yes—
404#376C2314yes—
405C2×#95C2314yes—
406C2×#95C2314yes—
407C2×#95C2314yes—
408C2×#95C2312yes—
409C2×#95C2312yes—
410C2×#95C2312yes—
411C2×#95C2312yes—
412C2×#95C2312yes—
413C2×#95C2314yes—
414C2×#95C2314yes—
415C25C2411yescharacteristic
416C25C2411yescharacteristic
417C22×Q8—28no—
418C22×Q8—44no—
419C22×Q8—44no—
420C22×Q8C2414yes—
421C22×Q8C2414yes—
422C22×D4—24no—
423C22×D4—28no—
424C22×D4C2412yes—
425C22×D4C2412yes—
426C23×C4—28no—
427C23×C4—24no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—44no—
432C23×C4—42no—
433C23×C4—44no—
434C23×C4#4118yes—
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2412yes—
446C23×C4C2411yescharacteristic
447C23×C4C2412yes—
448C23×C4C2414yes—
449C23×C4C2414yes—
450C23×C4C2411yescharacteristic
451C23×C4C2414yes—
452C23×C4C2414yes—
453C23×C4C2412yes—
454C23×C4C2412yes—
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C4⋊Q8—28no—
459C4⋊Q8—48no—
460C4⋊Q8—44no—
461#126—416no—
462#126—416no—
463#125—28no—
464#125—44no—
465#125—48no—
466#125—416no—
467#125—416no—
468C22⋊Q8—216no—
469C22⋊Q8—216no—
470C22⋊Q8—216no—
471C22⋊Q8—216no—
472C22⋊Q8—48no—
473C22⋊Q8—48no—
474C4×Q8—48no—
475C4×Q8—48no—
476C4×D4—28no—
477C4×D4—28no—
478C4×D4—28no—
479C4×D4—28no—
480#117—28no—
481#117—44no—
482#117—48no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—28no—
485C2×C4⋊C4—216no—
486C2×C4⋊C4—44no—
487C2×C4⋊C4—44no—
488C2×C4⋊C4—48no—
489C2×C4⋊C4—48no—
490C2×C4⋊C4—44no—
491C2×C4⋊C4—44no—
492C2×C4⋊C4—48no—
493C2×C4⋊C4—48no—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—216no—
526C2×C22⋊C4—216no—
527C2×C22⋊C4—28no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—44no—
530C2×C22⋊C4—44no—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2412yes—
533C2×C22⋊C4C2412yes—
534C2×C22⋊C4C2412yes—
535C2×C22⋊C4C2412yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C42—24no—
550C2×C42—24no—
551C2×C42—24no—
552C2×C42—24no—
553C2×C42—42no—
554C2×C42—44no—
555C2×C42—42no—
556C2×C42—42no—
557C2×C42—44no—
558C2×C42—42no—
559C2×C42—44no—
560C2×C42—42no—
561C2×C42C2412yes—
562C2×C42C2412yes—
563C2×C42C2411yescharacteristic
564C2×C42C2412yes—
565C2×C42C2412yes—
566C2×C42C2412yes—
567C2×C42C2411yescharacteristic
568C2×C42C2412yes—
569C2×C42C2411yescharacteristic
570C2×C42C2412yes—
571C2×C42C2412yes—
572C2×C42C2418yes—
573C2×C42C2418yes—
574C2×C42C2418yes—
575C2×C42C2418yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2411yescharacteristic
581#95C2414yes—
582#95C2414yes—
583#95C2414yes—
584#95C2414yes—
585#95C2414yes—
586#95C2414yes—
587#95C2414yes—
588#95C2414yes—
589#95C2418yes—
590#95C2414yes—
591#95C2414yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2418yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617C24—22no—
618C24—24no—
619C24—41no—
620C24—41no—
621C24—42no—
622C24—41no—
623C24—42no—
624C24—41no—
625C24C2×#4114yes—
626C242−1+418yes—
627C24C2512yes—
628C24C2511yescharacteristic
629C24C2511yescharacteristic
630C24C2511yescharacteristic
631C2×Q8—28no—
632C2×Q8—28no—
633C2×Q8—28no—
634C2×Q8—28no—
635C2×Q8—44no—
636C2×Q8—44no—
637C2×Q8—816no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—28no—
641C2×D4—28no—
642C2×D4—416no—
643C22×C4—24no—
644C22×C4—22no—
645C22×C4—24no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—24no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—28no—
666C22×C4—28no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—416no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—41no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—42no—
688C22×C4—41no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—41no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—42no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—432no—
706C22×C4—416no—
707C22×C4C2×#4114yes—
708C22×C4C2×#4114yes—
709C22×C4C2×#4114yes—
710C22×C4C2×#4114yes—
711C22×C4C2×#4114yes—
712C22×C4C2×#4114yes—
713C22×C4C2512yes—
714C22×C4C2514yes—
715C22×C4C2512yes—
716C22×C4C2512yes—
717C22×C4C2518yes—
718C22×C4C2514yes—
719C22×C4C2512yes—
720C22×C4C2518yes—
721C22×C4C2518yes—
722C22×C4C2518yes—
723C22×C4C2512yes—
724C22×C4C2511yescharacteristic
725C22×C4C2511yescharacteristic
726C22×C4C2511yescharacteristic
727C22×C4C2512yes—
728C22×C4C2512yes—
729C22×C4C2511yescharacteristic
730C4⋊C4—24no—
731C4⋊C4—24no—
732C4⋊C4—28no—
733C4⋊C4—28no—
734C4⋊C4—216no—
735C4⋊C4—216no—
736C4⋊C4—28no—
737C4⋊C4—28no—
738C4⋊C4—216no—
739C4⋊C4—216no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—216no—
743C4⋊C4—216no—
744C4⋊C4—44no—
745C4⋊C4—48no—
746C4⋊C4—44no—
747C4⋊C4—48no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C22⋊C4—24no—
761C22⋊C4—24no—
762C22⋊C4—216no—
763C22⋊C4—216no—
764C22⋊C4—28no—
765C22⋊C4—216no—
766C22⋊C4—216no—
767C22⋊C4—28no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—48no—
775C22⋊C4—48no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C42—24no—
779C42—24no—
780C42—24no—
781C42—22no—
782C42—24no—
783C42—22no—
784C42—22no—
785C42—24no—
786C42—24no—
787C42—24no—
788C42—42no—
789C42—42no—
790C42—42no—
791C42—42no—
792C42—42no—
793C42—48no—
794C42—48no—
795C42—48no—
796C42—48no—
797C42H(5,𝔽2)14yes—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—22no—
805C23—21no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—24no—
810C23—24no—
811C23—22no—
812C23—44no—
813C23—48no—
814C23—44no—
815C23—48no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—84no—
820C23—84no—
821C23#541116yescomplemented
822C23C22×#4112yes—
823C23C22×#4112yes—
824C23C22×#4112yes—
825C23C2×2−1+414yes—
826C23C2×2−1+414yes—
827C23C2×2−1+414yes—
828C23C2611yescharacteristic
829Q8—416no—
830Q8—88no—
831D4—48no—
832D4—48no—
833C2×C4—216no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—28no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—28no—
850C2×C4—22no—
851C2×C4—28no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—28no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—28no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—28no—
872C2×C4—28no—
873C2×C4—28no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—48no—
882C2×C4—48no—
883C2×C4—48no—
884C2×C4—48no—
885C2×C4—48no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—48no—
889C2×C4—44no—
890C2×C4—48no—
891C2×C4—88no—
892C2×C4—88no—
893C2×C4—84no—
894C2×C4—88no—
895C2×C4—84no—
896C2×C4—88no—
897C2×C4C22×#4112yes—
898C2×C4C22×#4112yes—
899C2×C4C22×#4112yes—
900C2×C4C22×#4112yes—
901C2×C4C2×H(5,𝔽2)14yes—
902C2×C4C2×H(5,𝔽2)12yes—
903C2×C4#58514yes—
904C2×C4#58512yes—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—416no—
918C22—42no—
919C22—42no—
920C22—44no—
921C22—44no—
922C22—42no—
923C22—88no—
924C22C2×#54114yes—
925C22C2×#54114yes—
926C22C2×#54114yes—
927C22C23×#4111yescharacteristic
928C22C22×H(5,𝔽2)11yescharacteristic
929C22C22×2−1+412yes—
930C22C2×#58511yescharacteristic
931C22C2×#58512yes—
932C4—22no—
933C4—22no—
934C4—22no—
935C4—24no—
936C4—24no—
937C4—42no—
938C4—48no—
939C4—42no—
940C4—48no—
941C4—42no—
942C4—42no—
943C4—44no—
944C4—48no—
945C4—44no—
946C4—48no—
947C4—42no—
948C4#350514yes—
949C2—24no—
950C2—24no—
951C2—24no—
952C2—82no—
953C2C22×#54111yescharacteristic
954C2C2×#350511yescharacteristic
955C2#6281511yescharacteristic
956C2#6281912yes—
957C2#6282312yes—
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. #38482C2semidirect
2. #38461C2semidirect
3. #38122C2semidirect
4. #38113C2semidirect
5. #37894C2semidirect
6. #37882C2semidirect
7. #37705C2semidirect
8. #37695C2semidirect
9. #36762C2semidirect
10. #36760C2semidirect
11. C2×#2857C2semidirect
12. C2×#2851C2semidirect
14. #35368C2semidirect
15. #35315C2semidirect
16. #35310C2semidirect
17. #35087C2semidirect
18. #35086C2semidirect
20. #34212C2semidirect
22. C2×#541C22semidirect
23. C22×C4⋊Q8C22semidirect
24. C22×#125C22semidirect
32. #2857C22semidirect
33. #2857C22semidirect
34. #2857C22semidirect
39. #2851C22semidirect
40. #2851C22semidirect
41. #2851C22semidirect
43. #2802C22semidirect
44. #2798C22semidirect
45. #2794C22semidirect
46. #2789C22semidirect
47. #2783C22semidirect
48. #2776C22semidirect
49. #2772C22semidirect
50. #2766C22semidirect
51. #2758C22semidirect
52. #2754C22semidirect
53. #2725C22semidirect
54. #2725C22semidirect
55. #2721C22semidirect
56. #2719C22semidirect
57. #2716C22semidirect
58. #2713C22semidirect
59. #2655C22semidirect
60. #2652C22semidirect
61. #2647C22semidirect
62. #2645C22semidirect
63. #2642C22semidirect
64. #2629C22semidirect
67. #2625C22semidirect
68. #2621C22semidirect
70. #2569C22semidirect
71. #2569C22semidirect
73. #2533C22semidirect
74. #2528C22semidirect
75. #2514C22semidirect
80. #2506C22semidirect
83. #2505C22semidirect
84. #2505C22semidirect
85. #2496C22semidirect
88. #2489C22semidirect
96. #2478C22semidirect
97. #2475C22semidirect
100. #2473C22semidirect
101. #2473C22semidirect
102. #2453C22semidirect
103. #2446C22semidirect
104. #2442C22semidirect
105. #2442C22semidirect
106. #2429C22semidirect
107. #2421C22semidirect
111. #2368C22semidirect
112. #2360C22semidirect
113. #2360C22semidirect
114. #2345C22semidirect
115. #2345C22semidirect
116. Q8×C22⋊C4C22semidirect
117. #2336C22semidirect
118. #2334C22semidirect
119. #2330C22semidirect
122. #2327C22semidirect
123. #2323C22semidirect
124. #2320C22semidirect
127. #2314C22semidirect
131. C2×#391C22semidirect
132. C2×#389C22semidirect
133. C2×#389C22semidirect
142. C2×#387C22semidirect
146. C2×#384C22semidirect
147. C2×#382C22semidirect
821. C23#541semidirect

Maximal subgroups

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

subgroupindex
#384822
#384612
#381222
#381132
#378942
#378822
#377052
#376952
#367622
#367602
C2×#28572
C2×#28512
#353702
#353682
#353152
#353102
#350872
#350862
#350102
#342122
C2×#22902