Finite Group Databasebeta

← #7655928

Subgroups — #7655928

Order 512.

4994 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41646C218yesmaximal, complemented
2#41395C214yesmaximal, complemented
3#40956C218yesmaximal, complemented
4#40545C214yesmaximal, complemented
5#39678C214yesmaximal, complemented
6#37957C214yesmaximal, complemented
7#37881C214yesmaximal, complemented
8#37460C214yesmaximal, complemented
9#37451C212yesmaximal
10#36156C214yesmaximal, complemented
11#36024C214yesmaximal, complemented
12#35742C214yesmaximal, complemented
13#35052C211yesmaximal, characteristic, complemented
14#35012C212yesmaximal, complemented
15#34578C212yesmaximal, complemented
16C2×#2659C211yesmaximal, characteristic, complemented
17#34245C212yesmaximal, complemented
18C2×#2364C211yesmaximal, characteristic
19C2×#552C2214yescomplemented
20C22×C22⋊Q8C2212yes—
21C22×#121C2211yescharacteristic
22C22×C4×D4C2212yes—
23#2851C2214yes—
24#2848C2214yes—
25#2848C2214yes—
26#2836C2218yescomplemented
27#2831C2218yescomplemented
28#2816C2214yes—
29#2816C2214yes—
30#2799C2218yescomplemented
31#2791C2218yescomplemented
32#2791C2218yescomplemented
33#2786C2218yescomplemented
34#2781C2218yescomplemented
35#2779C2218yescomplemented
36#2755C2218yescomplemented
37#2741C2218yescomplemented
38#2740C2218yescomplemented
39#2715C2218yescomplemented
40#2702C2218yescomplemented
41#2700C2218yescomplemented
42#2667C2218yescomplemented
43#2665C2218yescomplemented
44#2664C2218yescomplemented
45#2659C2211yescharacteristic
46#2659C2214yes—
47#2659C2212yes—
48#2659C2211yescharacteristic
49#2659C2212yes—
50#2659C2214yescomplemented
51#2659C2214yescomplemented
52#2654C2218yescomplemented
53#2650C2218yescomplemented
54#2646C2214yes—
55#2646C2212yes—
56#2637C2218yescomplemented
57#2626C2214yes—
58#2626C2214yes—
59#2626C2214yes—
60#2620C2218yes—
61#2618C2214yes—
62#2618C2214yes—
63#2601C2218yescomplemented
64#2588C2218yescomplemented
65#2574C2218yescomplemented
66#2569C2214yescomplemented
67#2565C2218yescomplemented
68#2562C2214yescomplemented
69#2560C2218yescomplemented
70#2556C2218yescomplemented
71#2549C2214yescomplemented
72#2536C2214yescomplemented
73#2522C2218yescomplemented
74#2521C2218yescomplemented
75#2520C2218yescomplemented
76#2519C2218yescomplemented
77#2506C2218yescomplemented
78#2505C2218yes—
79#2502C2214yes—
80#2501C2214yes—
81#2498C2218yescomplemented
82#2488C2218yescomplemented
83#2486C2214yescomplemented
84#2485C2214yescomplemented
85#2481C2218yescomplemented
86#2480C2218yes—
87#2480C2218yes—
88#2474C2218yescomplemented
89#2473C2218yes—
90#2469C2218yescomplemented
91#2468C2218yescomplemented
92#2465C2218yescomplemented
93#2460C2218yescomplemented
94#2438C2218yescomplemented
95#2436C2214yes—
96#2435C2214yes—
97#2419C2218yescomplemented
98#2417C2214yescomplemented
99#2415C2214yescomplemented
100#2413C2218yescomplemented
101#2405C2218yes—
102#2396C2218yescomplemented
103#2396C2218yescomplemented
104C2×#398C2214yescomplemented
105C2×#395C2214yescomplemented
106#2368C2218yes—
107#2364C2214yes—
108#2364C2214yes—
109#2364C2218yes—
110#2362C2214yescomplemented
111#2362C2214yescomplemented
112#2359C2218yescomplemented
113#2352C2214yescomplemented
114#2344C2212yescomplemented
115#2344C2212yescomplemented
116#2342C2214yes—
117#2342C2214yes—
118Q8×C22⋊C4C2212yescomplemented
119Q8×C22⋊C4C2212yescomplemented
120#2332C2218yescomplemented
121#2329C2214yes—
122#2329C2214yes—
123#2313C2214yescomplemented
124#2312C2214yes—
125C4×C22⋊Q8C2214yes—
126C4×C22⋊Q8C2214yes—
127C4×C22⋊Q8C2214yes—
128C2×#388C2212yes—
129C2×#387C2212yes—
130C2×#386C2212yes—
131C2×#386C2212yes—
132#2280C2214yes—
133#2280C2212yes—
134C2×#380C2214yes—
135#2274C2214yescomplemented
136C2×C4×C22⋊C4C2212yes—
137C2×C4×C22⋊C4C2211yescharacteristic
138C22×#95C2211yescharacteristic
139C23×Q8C2312yes—
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2312yes—
144C24×C4C2311yescharacteristic
145#552—416no—
146C2×#126C2318yes—
147C2×#126C2318yes—
148C2×#125C2314yes—
149C2×#125C2318yes—
150C2×#124C2318yes—
151C2×#123C2318yes—
152C2×#123C2318yes—
153C2×C22⋊Q8—216no—
154C2×C22⋊Q8C2312yes—
155C2×C22⋊Q8C2312yes—
156C2×C22⋊Q8C2314yes—
157C2×C22⋊Q8C2314yes—
158C2×C22⋊Q8C2314yes—
159C2×C22⋊Q8C2312yes—
160C2×C22⋊Q8C2312yes—
161C2×C22⋊Q8C2314yes—
162C2×C22⋊Q8C2314yes—
163C2×C22⋊Q8C2314yes—
164C2×C22⋊Q8C2314yes—
165C2×#121—28no—
166C2×#121C2314yes—
167C2×#121C2314yes—
168C2×C4×Q8C2314yes—
169C2×C4×Q8C2314yes—
170C2×C4×Q8C2314yes—
171C2×C4×D4—48no—
172C2×C4×D4C2314yes—
173C2×C4×D4C2314yes—
174C2×C4×D4C2314yes—
175C2×C4×D4C2314yes—
176C2×#117C2314yes—
177C2×#117C2314yes—
178C2×#117C2314yes—
179C2×#117C2314yes—
180C2×#117C2314yes—
181C22×C4⋊C4C2314yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2314yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2314yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2314yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C42C2312yes—
195C22×C42C2312yes—
196#400C2318yes—
197#400C2318yes—
198#400C2318yes—
199#400C2318yes—
200#400C2318yes—
201#400C2318yes—
202#400C2318yes—
203#399C2318yes—
204#399C2318yes—
205#399C2318yes—
206#398C2318yes—
207#398C2314yes—
208#398C2314yes—
209#398C2314yes—
210#398C2314yes—
211#398C2318yes—
212#398C2318yes—
213#398C2318yes—
214#398C2318yes—
215#398C2318yes—
216#398C2318yes—
217#398C2314yes—
218#398C2318yes—
219#398C2318yes—
220#398C2318yes—
221#398C2314yes—
222#398C2314yes—
223#398C2314yes—
224#397C2318yes—
225#397C2318yes—
226#397C2318yes—
227#397C2318yes—
228#397C2318yes—
229#397C2318yes—
230#396C2318yes—
231#396C2318yes—
232#396C2318yes—
233#396C2318yes—
234#396C2318yes—
235#396C2318yes—
236#396C2318yes—
237#396C2318yes—
238#395C2314yes—
239#395C2314yes—
240#395C2318yes—
241#395C2314yes—
242#395C2314yes—
243#395C2318yes—
244#395C2318yes—
245#394C2314yes—
246#394C2318yes—
247#394C2314yes—
248#394C2314yes—
249#394C2314yes—
250#394C2318yes—
251#394C2318yes—
252#394C2318yes—
253#393C2318yes—
254#393C2318yes—
255#393C2318yes—
256#391C2318yes—
257#391C2318yes—
258#391C2314yes—
259#391C2314yes—
260#391C2318yes—
261#391C2318yes—
262#391C2318yes—
263#391C2314yes—
264#390C2318yes—
265#389C2314yes—
266#389C2318yes—
267#389C2318yes—
268#389C2318yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2318yes—
273#389C2314yes—
274#388C2318yes—
275#388C2318yes—
276#388C2318yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#388C2318yes—
282#388C2318yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#388C2318yes—
289#388C2318yes—
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#386C2318yes—
310#386C2318yes—
311#386C2318yes—
312#386C2318yes—
313#386C2318yes—
314#386C2318yes—
315#385C2318yes—
316#385C2318yes—
317#385C2318yes—
318#385C2318yes—
319#385C2318yes—
320#385C2318yes—
321#385C2318yes—
322#385C2318yes—
323#385C2318yes—
324#384C2318yes—
325#382C2318yes—
326#382C2314yes—
327#381C2314yes—
328#381C2314yes—
329#381C2314yes—
330#381C2318yes—
331#380C2314yes—
332#380C2314yes—
333#380C2314yes—
334#380C2314yes—
335#380C2314yes—
336#380C2314yes—
337#380C2314yes—
338#380C2314yes—
339#380C2314yes—
340#380C2312yes—
341#380C2314yes—
342#380C2312yes—
343#380C2314yes—
344#380C2314yes—
345#380C2318yes—
346#380C2318yes—
347#380C2314yes—
348#380C2314yes—
349#379C2318yes—
350#379C2314yes—
351#379C2318yes—
352C4×C4⋊C4C2318yes—
353C4×C4⋊C4C2314yes—
354C4×C4⋊C4C2318yes—
355C4×C4⋊C4C2318yes—
356C4×C4⋊C4C2318yes—
357C4×C4⋊C4C2314yes—
358C4×C4⋊C4C2314yes—
359C4×C4⋊C4C2318yes—
360C4×C22⋊C4C2318yes—
361C4×C22⋊C4C2318yes—
362C4×C22⋊C4C2312yes—
363C4×C22⋊C4C2314yes—
364C4×C22⋊C4C2318yes—
365C4×C22⋊C4C2314yes—
366C4×C22⋊C4C2314yes—
367C4×C22⋊C4C2314yes—
368C4×C22⋊C4C2314yes—
369C4×C22⋊C4C2312yes—
370C4×C22⋊C4C2318yes—
371C4×C22⋊C4C2318yes—
372C2×#95C2314yes—
373C2×#95C2312yes—
374C2×#95C2312yes—
375C2×#95C2318yes—
376C2×#95C2314yes—
377C2×#95C2312yes—
378C2×#95C2311yescharacteristic
379C2×#95C2311yescharacteristic
380C2×#95C2312yes—
381C25C2411yescharacteristic
382C25C2412yes—
383C22×Q8—28no—
384C22×Q8—84no—
385C22×Q8C2412yes—
386C22×Q8C2412yes—
387C22×Q8C2414yes—
388C22×Q8C2414yes—
389C22×D4—28no—
390C22×D4—24no—
391C22×D4—44no—
392C22×D4—44no—
393C22×D4—82no—
394C22×D4C2414yes—
395C22×D4C2414yes—
396C22×D4C2414yes—
397C23×C4—28no—
398C23×C4—28no—
399C23×C4—44no—
400C23×C4—44no—
401C23×C4—82no—
402C23×C4—82no—
403C23×C4—82no—
404C23×C4#4118yes—
405C23×C4C2414yes—
406C23×C4C2412yes—
407C23×C4C2414yes—
408C23×C4C2414yes—
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2414yes—
412C23×C4C2412yes—
413C23×C4C2414yes—
414C23×C4C2414yes—
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2412yes—
419C23×C4C2412yes—
420#126—416no—
421#126—88no—
422#125—48no—
423#125—416no—
424#124—88no—
425#123—416no—
426#123—416no—
427C22⋊Q8—28no—
428C22⋊Q8—28no—
429C22⋊Q8—216no—
430C22⋊Q8—28no—
431C22⋊Q8—28no—
432C22⋊Q8—216no—
433C22⋊Q8—216no—
434C22⋊Q8—48no—
435C22⋊Q8—48no—
436C22⋊Q8—84no—
437C22⋊Q8—84no—
438#121—216no—
439#121—216no—
440C4×Q8—48no—
441C4×Q8—84no—
442C4×Q8—84no—
443C4×D4—216no—
444C4×D4—48no—
445C4×D4—48no—
446C4×D4—48no—
447#117—216no—
448#117—48no—
449#117—48no—
450#117—84no—
451#117—84no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—28no—
454C2×C4⋊C4—216no—
455C2×C4⋊C4—44no—
456C2×C4⋊C4—48no—
457C2×C4⋊C4—84no—
458C2×C4⋊C4C2414yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2412yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2414yes—
474C2×C4⋊C4C2414yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2414yes—
478C2×C4⋊C4C2414yes—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2418yes—
484C2×C4⋊C4C2418yes—
485C2×C4⋊C4C2418yes—
486C2×C4⋊C4C2418yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2418yes—
490C2×C22⋊C4—216no—
491C2×C22⋊C4—28no—
492C2×C22⋊C4—28no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—44no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—82no—
497C2×C22⋊C4C2412yes—
498C2×C22⋊C4C2411yescharacteristic
499C2×C22⋊C4C2412yes—
500C2×C22⋊C4C2414yes—
501C2×C22⋊C4C2418yes—
502C2×C22⋊C4C2414yes—
503C2×C22⋊C4C2414yes—
504C2×C22⋊C4C2414yes—
505C2×C22⋊C4C2414yes—
506C2×C22⋊C4C2418yes—
507C2×C22⋊C4C2414yes—
508C2×C22⋊C4C2414yes—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2412yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2411yescharacteristic
523C2×C42—44no—
524C2×C42—82no—
525C2×C42C2418yes—
526C2×C42C2414yes—
527C2×C42C2418yes—
528C2×C42C2418yes—
529C2×C42C2418yes—
530C2×C42C2414yes—
531C2×C42C2418yes—
532C2×C42C2414yes—
533C2×C42C2414yes—
534#95C2414yes—
535#95C2418yes—
536#95C2414yes—
537#95C2414yes—
538#95C2414yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545#95C2418yes—
546#95C2418yes—
547#95C2418yes—
548#95C2418yes—
549#95C2418yes—
550#95C2418yes—
551#95C2414yes—
552#95C2414yes—
553#95C2418yes—
554#95C2418yes—
555#95C2418yes—
556#95C2418yes—
557#95C2418yes—
558#95C2418yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563C24—22no—
564C24—24no—
565C24—22no—
566C24—24no—
567C24—24no—
568C24—24no—
569C24—42no—
570C24—42no—
571C24—42no—
572C24—42no—
573C24—42no—
574C24C2×#4114yes—
575C24C2514yes—
576C24C2511yescharacteristic
577C24C2511yescharacteristic
578C24C2511yescharacteristic
579C2×Q8—24no—
580C2×Q8—24no—
581C2×Q8—28no—
582C2×Q8—28no—
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—48no—
588C2×Q8—816no—
589C2×D4—28no—
590C2×D4—28no—
591C2×D4—28no—
592C2×D4—28no—
593C2×D4—28no—
594C2×D4—44no—
595C2×D4—44no—
596C2×D4—48no—
597C2×D4—432no—
598C2×D4—88no—
599C22×C4—28no—
600C22×C4—24no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—24no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—44no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—48no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—88no—
635C22×C4—816no—
636C22×C4—816no—
637C22×C4C2×#4114yes—
638C22×C4C2×#4118yes—
639C22×C4C2×#4114yes—
640C22×C4C2×#4118yes—
641C22×C42−1+418yes—
642C22×C4C2514yes—
643C22×C4C2512yes—
644C22×C4C2514yes—
645C22×C4C2518yes—
646C22×C4C2514yes—
647C22×C4C2514yes—
648C22×C4C2514yes—
649C22×C4C2518yes—
650C22×C4C2514yes—
651C22×C4C2514yes—
652C22×C4C2512yes—
653C22×C4C2512yes—
654C22×C4C2512yes—
655C22×C4C2514yes—
656C4⋊C4—28no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—216no—
666C4⋊C4—28no—
667C4⋊C4—216no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—48no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—48no—
681C4⋊C4—48no—
682C4⋊C4—48no—
683C4⋊C4—48no—
684C4⋊C4—48no—
685C4⋊C4—48no—
686C4⋊C4—48no—
687C4⋊C4—48no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—22no—
693C22⋊C4—28no—
694C22⋊C4—216no—
695C22⋊C4—24no—
696C22⋊C4—28no—
697C22⋊C4—216no—
698C22⋊C4—24no—
699C22⋊C4—28no—
700C22⋊C4—216no—
701C22⋊C4—42no—
702C22⋊C4—44no—
703C22⋊C4—48no—
704C22⋊C4—48no—
705C22⋊C4—48no—
706C22⋊C4—48no—
707C22⋊C4—48no—
708C22⋊C4—48no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4H(5,𝔽2)14yes—
714C42—28no—
715C42—216no—
716C42—44no—
717C42—44no—
718C42—44no—
719C42—48no—
720C42—48no—
721C42—48no—
722C42—48no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—22no—
732C23—28no—
733C23—28no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—44no—
742C23—48no—
743C23—48no—
744C23—48no—
745C23—48no—
746C23—48no—
747C23—84no—
748C23—84no—
749C23—84no—
750C23—84no—
751C23C22×#4112yes—
752C23C22×#4112yes—
753C23C22×#4112yes—
754C23C2×H(5,𝔽2)12yes—
755C23C2×2−1+414yes—
756C23#58512yes—
757C23C2611yescharacteristic
758Q8—48no—
759Q8—48no—
760Q8—88no—
761Q8—88no—
762D4—416no—
763D4—416no—
764D4—88no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—28no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—28no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—24no—
799C2×C4—48no—
800C2×C4—48no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—48no—
804C2×C4—416no—
805C2×C4—416no—
806C2×C4—48no—
807C2×C4—48no—
808C2×C4—416no—
809C2×C4—88no—
810C2×C4—88no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—88no—
814C2×C4C22×#4114yes—
815C2×C4C22×#4114yes—
816C2×C4C2×H(5,𝔽2)14yes—
817C2×C4C2×2−1+418yes—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—24no—
822C22—24no—
823C22—22no—
824C22—24no—
825C22—24no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—416no—
830C22—42no—
831C22—42no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—816no—
840C22#346014yes—
841C22#350914yes—
842C22C23×#4111yescharacteristic
843C22C22×H(5,𝔽2)11yescharacteristic
844C22C22×2−1+412yes—
845C22C2×#58511yescharacteristic
846C22H(7,𝔽2)12yes—
847C4—24no—
848C4—24no—
849C4—28no—
850C4—24no—
851C4—44no—
852C4—44no—
853C4—42no—
854C4—44no—
855C4—48no—
856C4—44no—
857C4—44no—
858C4—44no—
859C4—48no—
860C4—44no—
861C2—24no—
862C2—24no—
863C2—42no—
864C2—84no—
865C2C2×#346011yescharacteristic
866C2C2×#350911yescharacteristic
867C2#6284411yescharacteristic
868C2#6289412yes—
869C2#6295812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41646C2semidirect
2. #41395C2semidirect
3. #40956C2semidirect
4. #40545C2semidirect
5. #39678C2semidirect
6. #37957C2semidirect
7. #37881C2semidirect
8. #37460C2semidirect
10. #36156C2semidirect
11. #36024C2semidirect
12. #35742C2semidirect
13. #35052C2semidirect
14. #35012C2semidirect
15. #34578C2semidirect
16. C2×#2659C2semidirect
17. #34245C2semidirect
19. C2×#552C22semidirect
26. #2836C22semidirect
27. #2831C22semidirect
30. #2799C22semidirect
31. #2791C22semidirect
32. #2791C22semidirect
33. #2786C22semidirect
34. #2781C22semidirect
35. #2779C22semidirect
36. #2755C22semidirect
37. #2741C22semidirect
38. #2740C22semidirect
39. #2715C22semidirect
40. #2702C22semidirect
41. #2700C22semidirect
42. #2667C22semidirect
43. #2665C22semidirect
44. #2664C22semidirect
50. #2659C22semidirect
51. #2659C22semidirect
52. #2654C22semidirect
53. #2650C22semidirect
56. #2637C22semidirect
63. #2601C22semidirect
64. #2588C22semidirect
65. #2574C22semidirect
66. #2569C22semidirect
67. #2565C22semidirect
68. #2562C22semidirect
69. #2560C22semidirect
70. #2556C22semidirect
71. #2549C22semidirect
72. #2536C22semidirect
73. #2522C22semidirect
74. #2521C22semidirect
75. #2520C22semidirect
76. #2519C22semidirect
77. #2506C22semidirect
81. #2498C22semidirect
82. #2488C22semidirect
83. #2486C22semidirect
84. #2485C22semidirect
85. #2481C22semidirect
88. #2474C22semidirect
90. #2469C22semidirect
91. #2468C22semidirect
92. #2465C22semidirect
93. #2460C22semidirect
94. #2438C22semidirect
97. #2419C22semidirect
98. #2417C22semidirect
99. #2415C22semidirect
100. #2413C22semidirect
102. #2396C22semidirect
103. #2396C22semidirect
104. C2×#398C22semidirect
105. C2×#395C22semidirect
110. #2362C22semidirect
111. #2362C22semidirect
112. #2359C22semidirect
113. #2352C22semidirect
114. #2344C22semidirect
115. #2344C22semidirect
118. Q8×C22⋊C4C22semidirect
119. Q8×C22⋊C4C22semidirect
120. #2332C22semidirect
123. #2313C22semidirect
135. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#416462
#413952
#409562
#405452
#396782
#379572
#378812
#374602
#374512
#361562
#360242
#357422
#350522
#350122
#345782
C2×#26592
#342452
C2×#23642