Finite Group Databasebeta

← #7718198

Subgroups — #7718198

Order 512.

4942 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51626C218yesmaximal, complemented
2#51623C218yesmaximal, complemented
3#44461C214yesmaximal, complemented
4#43961C214yesmaximal, complemented
5#43515C214yesmaximal, complemented
6#43082C214yesmaximal, complemented
7#39677C214yesmaximal, complemented
8#37956C214yesmaximal, complemented
9#37880C214yesmaximal, complemented
10#36977C212yesmaximal, complemented
11#36728C212yesmaximal, complemented
12#36156C214yesmaximal
13#35084C212yesmaximal
14#35052C211yesmaximal, characteristic, complemented
15#35052C212yesmaximal, complemented
16#35013C212yesmaximal, complemented
17C2×#2659C211yesmaximal, characteristic, complemented
18#34380C212yesmaximal, complemented
19C2×#2349C211yesmaximal, characteristic
20C2×#552C2214yes—
21C22×C22⋊Q8C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24#2855C2214yes—
25#2851C2214yes—
26#2848C2214yes—
27#2848C2214yes—
28#2848C2214yes—
29#2806C2218yescomplemented
30#2802C2218yescomplemented
31#2788C2218yescomplemented
32#2787C2218yescomplemented
33#2787C2218yescomplemented
34#2774C2218yescomplemented
35#2770C2218yescomplemented
36#2766C2218yescomplemented
37#2762C2218yescomplemented
38#2755C2218yescomplemented
39#2747C2218yescomplemented
40#2747C2218yescomplemented
41#2745C2218yescomplemented
42#2726C2218yescomplemented
43#2722C2218yescomplemented
44#2719C2218yescomplemented
45#2704C2218yescomplemented
46#2690C2218yescomplemented
47#2690C2218yescomplemented
48#2689C2218yescomplemented
49#2659C2214yes—
50#2659C2212yes—
51#2659C2212yes—
52#2659C2212yes—
53#2659C2218yescomplemented
54#2646C2212yes—
55#2646C2214yes—
56#2638C2214yes—
57#2638C2214yes—
58#2627C2214yes—
59#2599C2218yescomplemented
60#2590C2218yescomplemented
61#2586C2218yescomplemented
62#2585C2218yescomplemented
63#2584C2218yescomplemented
64#2583C2214yes—
65#2577C2218yescomplemented
66#2569C2214yescomplemented
67#2569C2218yescomplemented
68#2562C2214yes—
69#2561C2214yes—
70#2549C2218yescomplemented
71#2549C2214yescomplemented
72#2536C2214yes—
73#2520C2218yescomplemented
74#2493C2218yes—
75#2493C2218yescomplemented
76#2486C2212yes—
77#2486C2212yes—
78#2486C2214yes—
79#2485C2214yes—
80#2484C2218yescomplemented
81#2483C2214yes—
82#2480C2218yes—
83#2478C2218yescomplemented
84#2473C2218yes—
85#2473C2218yes—
86#2473C2218yescomplemented
87#2468C2218yes—
88#2465C2218yescomplemented
89#2462C2218yescomplemented
90#2462C2218yescomplemented
91#2460C2218yes—
92#2453C2218yescomplemented
93#2438C2218yescomplemented
94#2438C2218yescomplemented
95#2438C2218yescomplemented
96#2438C2218yescomplemented
97#2419C2218yes—
98#2417C2214yes—
99#2415C2214yes—
100#2415C2214yes—
101#2415C2214yes—
102#2409C2212yes—
103#2409C2212yes—
104#2405C2214yes—
105C2×#398C2214yescomplemented
106C2×#395C2214yescomplemented
107#2378C2218yescomplemented
108#2360C2218yes—
109#2359C2218yes—
110#2352C2214yes—
111#2349C2214yes—
112#2349C2214yes—
113#2349C2214yes—
114#2349C2214yes—
115#2344C2214yescomplemented
116#2342C2218yes—
117Q8×C22⋊C4C2214yescomplemented
118#2329C2214yes—
119#2329C2214yes—
120#2329C2214yes—
121#2329C2214yes—
122#2323C2218yescomplemented
123#2322C2214yes—
124#2322C2214yes—
125#2316C2214yescomplemented
126#2313C2214yes—
127#2313C2214yescomplemented
128C4×C22⋊Q8C2214yes—
129C2×#389C2212yes—
130C2×#385C2212yes—
131C2×#385C2212yes—
132C2×#382C2211yescharacteristic
133#2280C2212yes—
134#2280C2214yes—
135C2×#380C2214yes—
136C2×#380C2211yescharacteristic
137C2×#380C2211yescharacteristic
138C2×C4×C4⋊C4C2211yescharacteristic
139C22×#95C2211yescharacteristic
140C22×#95C2211yescharacteristic
141C23×Q8C2312yes—
142C23×D4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147#552—416no—
148C2×#126C2318yes—
149C2×#125C2314yes—
150C2×#125C2318yes—
151C2×#125C2318yes—
152C2×#123C2314yes—
153C2×#123C2314yes—
154C2×C22⋊Q8—216no—
155C2×C22⋊Q8C2314yes—
156C2×C22⋊Q8C2314yes—
157C2×C22⋊Q8C2314yes—
158C2×C22⋊Q8C2314yes—
159C2×C22⋊Q8C2314yes—
160C2×C22⋊Q8C2314yes—
161C2×C22⋊Q8C2314yes—
162C2×C22⋊Q8C2314yes—
163C2×C22⋊Q8C2314yes—
164C2×C22⋊Q8C2314yes—
165C2×C22⋊Q8C2314yes—
166C2×C4×Q8C2314yes—
167C2×C4×Q8C2318yes—
168C2×C4×D4—28no—
169C2×C4×D4—48no—
170C2×C4×D4C2312yes—
171C2×C4×D4C2312yes—
172C2×C4×D4C2314yes—
173C2×C4×D4C2312yes—
174C2×C4×D4C2312yes—
175C2×C4×D4C2314yes—
176C2×C4×D4C2314yes—
177C2×C4×D4C2314yes—
178C2×#117C2318yes—
179C2×#117C2314yes—
180C2×#117C2314yes—
181C2×#117C2314yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2314yes—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2314yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2314yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2314yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C42C2311yescharacteristic
197C22×C42C2312yes—
198#401C2318yes—
199#400C2318yes—
200#400C2318yes—
201#400C2318yes—
202#400C2318yes—
203#400C2318yes—
204#400C2318yes—
205#400C2318yes—
206#400C2318yes—
207#400C2318yes—
208#398C2318yes—
209#398C2318yes—
210#398C2318yes—
211#398C2314yes—
212#398C2314yes—
213#398C2318yes—
214#398C2318yes—
215#398C2318yes—
216#398C2318yes—
217#398C2318yes—
218#398C2318yes—
219#398C2318yes—
220#398C2318yes—
221#398C2318yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#397C2314yes—
227#397C2314yes—
228#397C2318yes—
229#397C2318yes—
230#397C2318yes—
231#397C2318yes—
232#397C2318yes—
233#396C2318yes—
234#395C2314yes—
235#395C2314yes—
236#395C2318yes—
237#395C2318yes—
238#395C2318yes—
239#395C2318yes—
240#395C2318yes—
241#395C2318yes—
242#394C2318yes—
243#394C2318yes—
244#393C2314yes—
245#393C2314yes—
246#391C2318yes—
247#391C2318yes—
248#391C2318yes—
249#391C2318yes—
250#391C2318yes—
251#391C2314yes—
252#391C2314yes—
253#391C2314yes—
254#389C2318yes—
255#389C2318yes—
256#389C2318yes—
257#389C2318yes—
258#389C2318yes—
259#389C2318yes—
260#389C2318yes—
261#389C2314yes—
262#389C2318yes—
263#389C2318yes—
264#389C2318yes—
265#389C2318yes—
266#389C2318yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2314yes—
271#389C2318yes—
272#388C2318yes—
273#388C2318yes—
274#388C2318yes—
275#388C2318yes—
276#388C2318yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#387C2318yes—
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#386C2314yes—
308#386C2314yes—
309#385C2318yes—
310#385C2318yes—
311#385C2318yes—
312#385C2318yes—
313#385C2318yes—
314#385C2314yes—
315#385C2314yes—
316#385C2318yes—
317#385C2318yes—
318#385C2318yes—
319#385C2318yes—
320#385C2318yes—
321#385C2318yes—
322#385C2318yes—
323#385C2318yes—
324#385C2318yes—
325#385C2318yes—
326#383C2318yes—
327#382C2314yes—
328#382C2314yes—
329#382C2314yes—
330#381C2318yes—
331#381C2318yes—
332#381C2314yes—
333#381C2314yes—
334#381C2314yes—
335#381C2318yes—
336#380C2314yes—
337#380C2314yes—
338#380C2314yes—
339#380C2314yes—
340#380C2314yes—
341#380C2314yes—
342#380C2312yes—
343#380C2314yes—
344#380C2314yes—
345#380C2314yes—
346#380C2314yes—
347#380C2312yes—
348#380C2318yes—
349#380C2314yes—
350#380C2314yes—
351#380C2314yes—
352#380C2314yes—
353#380C2314yes—
354#380C2314yes—
355#380C2314yes—
356#380C2318yes—
357#380C2318yes—
358#380C2314yes—
359#379C2318yes—
360#379C2314yes—
361C4×C4⋊C4C2314yes—
362C4×C4⋊C4C2318yes—
363C4×C4⋊C4C2318yes—
364C4×C4⋊C4C2314yes—
365C4×C4⋊C4C2314yes—
366C4×C22⋊C4C2314yes—
367C4×C22⋊C4C2318yes—
368C4×C22⋊C4C2318yes—
369C4×C22⋊C4C2318yes—
370C4×C22⋊C4C2314yes—
371C4×C22⋊C4C2318yes—
372C2×#95C2314yes—
373C2×#95C2314yes—
374C2×#95C2311yescharacteristic
375C2×#95C2311yescharacteristic
376C2×#95C2312yes—
377C2×#95C2312yes—
378C2×#95C2314yes—
379C2×#95C2314yes—
380C2×#95C2318yes—
381C2×#95C2311yescharacteristic
382C2×#95C2311yescharacteristic
383C2×#95C2312yes—
384C25C2411yescharacteristic
385C25C2411yescharacteristic
386C22×Q8—28no—
387C22×Q8—84no—
388C22×Q8C2414yes—
389C22×Q8C2414yes—
390C22×Q8C2414yes—
391C22×D4—24no—
392C22×D4—24no—
393C22×D4—24no—
394C22×D4C2411yescharacteristic
395C22×D4C2411yescharacteristic
396C22×D4C2411yescharacteristic
397C22×D4C2411yescharacteristic
398C23×C4—24no—
399C23×C4—28no—
400C23×C4—28no—
401C23×C4—44no—
402C23×C4—44no—
403C23×C4—82no—
404C23×C4—82no—
405C23×C4—82no—
406C23×C4—82no—
407C23×C4#4118yes—
408C23×C4C2411yescharacteristic
409C23×C4C2414yes—
410C23×C4C2411yescharacteristic
411C23×C4C2414yes—
412C23×C4C2414yes—
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2414yes—
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2414yes—
421C23×C4C2414yes—
422C23×C4C2411yescharacteristic
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427#126—416no—
428#125—48no—
429#125—416no—
430#125—88no—
431#123—216no—
432#123—216no—
433C22⋊Q8—216no—
434C22⋊Q8—216no—
435C22⋊Q8—216no—
436C22⋊Q8—216no—
437C22⋊Q8—216no—
438C22⋊Q8—48no—
439C22⋊Q8—48no—
440C22⋊Q8—84no—
441C22⋊Q8—84no—
442C22⋊Q8—84no—
443C22⋊Q8—84no—
444C4×Q8—48no—
445C4×Q8—88no—
446C4×D4—216no—
447C4×D4—28no—
448C4×D4—28no—
449C4×D4—28no—
450C4×D4—28no—
451C4×D4—48no—
452C4×D4—48no—
453C4×D4—48no—
454#117—48no—
455#117—416no—
456#117—84no—
457#117—84no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—28no—
460C2×C4⋊C4—216no—
461C2×C4⋊C4—28no—
462C2×C4⋊C4—44no—
463C2×C4⋊C4—48no—
464C2×C4⋊C4—84no—
465C2×C4⋊C4—82no—
466C2×C4⋊C4—82no—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2418yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2414yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2418yes—
486C2×C4⋊C4C2418yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2418yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—216no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—44no—
504C2×C22⋊C4—44no—
505C2×C22⋊C4C2414yes—
506C2×C22⋊C4C2414yes—
507C2×C22⋊C4C2412yes—
508C2×C22⋊C4C2412yes—
509C2×C22⋊C4C2412yes—
510C2×C22⋊C4C2412yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2414yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2414yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2414yes—
519C2×C22⋊C4C2414yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C42—24no—
524C2×C42—44no—
525C2×C42C2414yes—
526C2×C42C2412yes—
527C2×C42C2412yes—
528C2×C42C2418yes—
529C2×C42C2418yes—
530C2×C42C2418yes—
531C2×C42C2418yes—
532C2×C42C2414yes—
533C2×C42C2418yes—
534#95C2414yes—
535#95C2414yes—
536#95C2414yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2414yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545#95C2418yes—
546#95C2418yes—
547#95C2418yes—
548#95C2418yes—
549#95C2414yes—
550#95C2414yes—
551#95C2418yes—
552#95C2418yes—
553#95C2418yes—
554#95C2418yes—
555#95C2418yes—
556#95C2418yes—
557#95C2418yes—
558#95C2418yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C2418yes—
566#95C2418yes—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—24no—
571C24—22no—
572C24—22no—
573C24—24no—
574C24—42no—
575C24—42no—
576C24C2×#4114yes—
577C24C2511yescharacteristic
578C24C2511yescharacteristic
579C24C2511yescharacteristic
580C24C2511yescharacteristic
581C24C2511yescharacteristic
582C2×Q8—28no—
583C2×Q8—28no—
584C2×Q8—28no—
585C2×Q8—48no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8—816no—
591C2×D4—232no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4H(5,𝔽2)14yes—
603C2×D42−1+414yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—22no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—24no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—28no—
624C22×C4—28no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—44no—
628C22×C4—42no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—44no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—48no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—88no—
648C22×C4—816no—
649C22×C4—816no—
650C22×C4—88no—
651C22×C4C2×#4114yes—
652C22×C4C2×#4114yes—
653C22×C4C2×#4118yes—
654C22×C4C2×#4118yes—
655C22×C42−1+418yes—
656C22×C4C2512yes—
657C22×C4C2518yes—
658C22×C4C2514yes—
659C22×C4C2514yes—
660C22×C4C2518yes—
661C22×C4C2518yes—
662C22×C4C2512yes—
663C22×C4C2514yes—
664C22×C4C2518yes—
665C22×C4C2512yes—
666C22×C4C2512yes—
667C22×C4C2511yescharacteristic
668C22×C4C2514yes—
669C22×C4C2511yescharacteristic
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—216no—
675C4⋊C4—216no—
676C4⋊C4—28no—
677C4⋊C4—216no—
678C4⋊C4—216no—
679C4⋊C4—28no—
680C4⋊C4—216no—
681C4⋊C4—216no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—48no—
686C4⋊C4—44no—
687C4⋊C4—48no—
688C4⋊C4—44no—
689C4⋊C4—48no—
690C4⋊C4—48no—
691C4⋊C4—44no—
692C4⋊C4—48no—
693C4⋊C4—48no—
694C4⋊C4—44no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—48no—
698C4⋊C4—48no—
699C4⋊C4—48no—
700C4⋊C4—48no—
701C4⋊C4—48no—
702C4⋊C4—48no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—216no—
706C22⋊C4—216no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—216no—
711C22⋊C4—216no—
712C22⋊C4—28no—
713C22⋊C4—216no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—44no—
717C22⋊C4—44no—
718C22⋊C4—48no—
719C22⋊C4—48no—
720C22⋊C4—48no—
721C42—24no—
722C42—24no—
723C42—28no—
724C42—44no—
725C42—48no—
726C42—48no—
727C42—48no—
728C42—48no—
729C42—48no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—28no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—21no—
744C23—21no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—28no—
749C23—28no—
750C23—44no—
751C23—48no—
752C23—48no—
753C23—48no—
754C23—48no—
755C23—44no—
756C23—44no—
757C23C22×#4112yes—
758C23C22×#4112yes—
759C23C22×#4112yes—
760C23C2×H(5,𝔽2)12yes—
761C23C2×H(5,𝔽2)12yes—
762C23C2×2−1+412yes—
763C23C2×2−1+412yes—
764C23C2×2−1+414yes—
765C23C2611yescharacteristic
766Q8—416no—
767Q8—88no—
768Q8—88no—
769D4—28no—
770D4—28no—
771D4—28no—
772D4—28no—
773C2×C4—28no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—28no—
784C2×C4—22no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—28no—
788C2×C4—24no—
789C2×C4—28no—
790C2×C4—24no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—28no—
804C2×C4—28no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—44no—
808C2×C4—48no—
809C2×C4—48no—
810C2×C4—44no—
811C2×C4—48no—
812C2×C4—416no—
813C2×C4—416no—
814C2×C4—44no—
815C2×C4—416no—
816C2×C4—44no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4—88no—
820C2×C4—88no—
821C2×C4—84no—
822C2×C4—84no—
823C2×C4—84no—
824C2×C4—88no—
825C2×C4C22×#4114yes—
826C2×C4C22×#4114yes—
827C2×C4C2×H(5,𝔽2)12yes—
828C2×C4C2×2−1+412yes—
829C2×C4C2×2−1+418yes—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—24no—
844C22—24no—
845C22—416no—
846C22—416no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22#349214yes—
856C22#350914yes—
857C22C23×#4111yescharacteristic
858C22C22×H(5,𝔽2)11yescharacteristic
859C22C22×2−1+411yescharacteristic
860C22C22×2−1+412yes—
861C22H(7,𝔽2)12yes—
862C4—22no—
863C4—22no—
864C4—24no—
865C4—24no—
866C4—28no—
867C4—48no—
868C4—42no—
869C4—42no—
870C4—48no—
871C4—44no—
872C4—44no—
873C4—44no—
874C4—48no—
875C4—48no—
876C2—24no—
877C2—24no—
878C2—42no—
879C2—42no—
880C2—42no—
881C2C2×#349211yescharacteristic
882C2C2×#350911yescharacteristic
883C2#6284411yescharacteristic
884C2#6289412yes—
885C2#6294512yes—
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. #51626C2semidirect
2. #51623C2semidirect
3. #44461C2semidirect
4. #43961C2semidirect
5. #43515C2semidirect
6. #43082C2semidirect
7. #39677C2semidirect
8. #37956C2semidirect
9. #37880C2semidirect
10. #36977C2semidirect
11. #36728C2semidirect
14. #35052C2semidirect
15. #35052C2semidirect
16. #35013C2semidirect
17. C2×#2659C2semidirect
18. #34380C2semidirect
29. #2806C22semidirect
30. #2802C22semidirect
31. #2788C22semidirect
32. #2787C22semidirect
33. #2787C22semidirect
34. #2774C22semidirect
35. #2770C22semidirect
36. #2766C22semidirect
37. #2762C22semidirect
38. #2755C22semidirect
39. #2747C22semidirect
40. #2747C22semidirect
41. #2745C22semidirect
42. #2726C22semidirect
43. #2722C22semidirect
44. #2719C22semidirect
45. #2704C22semidirect
46. #2690C22semidirect
47. #2690C22semidirect
48. #2689C22semidirect
53. #2659C22semidirect
59. #2599C22semidirect
60. #2590C22semidirect
61. #2586C22semidirect
62. #2585C22semidirect
63. #2584C22semidirect
65. #2577C22semidirect
66. #2569C22semidirect
67. #2569C22semidirect
70. #2549C22semidirect
71. #2549C22semidirect
73. #2520C22semidirect
75. #2493C22semidirect
80. #2484C22semidirect
83. #2478C22semidirect
86. #2473C22semidirect
88. #2465C22semidirect
89. #2462C22semidirect
90. #2462C22semidirect
92. #2453C22semidirect
93. #2438C22semidirect
94. #2438C22semidirect
95. #2438C22semidirect
96. #2438C22semidirect
105. C2×#398C22semidirect
106. C2×#395C22semidirect
107. #2378C22semidirect
115. #2344C22semidirect
117. Q8×C22⋊C4C22semidirect
122. #2323C22semidirect
125. #2316C22semidirect
127. #2313C22semidirect

Maximal subgroups

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

subgroupindex
#516262
#516232
#444612
#439612
#435152
#430822
#396772
#379562
#378802
#369772
#367282
#361562
#350842
#350522
#350132
C2×#26592
#343802
C2×#23492