Finite Group Databasebeta

← #7664675

Subgroups — #7664675

Order 512.

5052 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39508C214yesmaximal, complemented
2#38979C218yesmaximal, complemented
3#38235C218yesmaximal, complemented
4#38233C218yesmaximal, complemented
5#37959C214yesmaximal, complemented
6#37957C214yesmaximal, complemented
7#36337C218yesmaximal, complemented
8#36204C214yesmaximal, complemented
9#35019C212yesmaximal
10#35011C211yesmaximal, characteristic, complemented
11#34995C214yesmaximal, complemented
12#34985C212yesmaximal, complemented
13C2×#2368C212yesmaximal, complemented
14C2×#2364C211yesmaximal, characteristic
15C4×#543C211yesmaximal, characteristic, complemented
16#34057C212yesmaximal, complemented
17C2×#543C2211yescharacteristic
18C22×C22⋊Q8C2212yes—
19C22×#121C2211yescharacteristic
20C22×C4×D4C2212yes—
21#2857C2214yes—
22#2855C2214yes—
23#2852C2218yescomplemented
24#2852C2218yescomplemented
25#2850C2218yes—
26#2848C2214yes—
27#2798C2218yescomplemented
28#2793C2218yescomplemented
29#2789C2218yescomplemented
30#2786C2218yescomplemented
31#2767C2218yescomplemented
32#2762C2218yescomplemented
33#2759C2218yescomplemented
34#2758C2218yescomplemented
35#2740C2218yescomplemented
36#2716C2218yescomplemented
37#2715C2218yescomplemented
38#2700C2218yescomplemented
39#2659C2214yes—
40#2643C2218yescomplemented
41#2643C2218yescomplemented
42#2639C2218yes—
43#2627C2214yes—
44#2626C2214yes—
45#2605C2218yescomplemented
46#2601C2218yescomplemented
47#2596C2218yescomplemented
48#2594C2218yescomplemented
49#2591C2218yes—
50#2588C2218yescomplemented
51#2583C2218yescomplemented
52#2573C2218yescomplemented
53#2561C2218yes—
54#2560C2218yescomplemented
55#2528C2218yescomplemented
56#2527C2218yescomplemented
57#2525C2218yescomplemented
58#2524C2218yescomplemented
59#2523C2218yescomplemented
60#2521C2218yescomplemented
61#2510C2218yescomplemented
62#2510C2218yescomplemented
63#2504C2214yes—
64#2503C2214yes—
65#2502C2214yescomplemented
66#2499C2214yescomplemented
67#2496C2214yescomplemented
68#2494C2214yescomplemented
69#2493C2218yes—
70#2493C2218yes—
71#2492C2214yescomplemented
72#2481C2218yescomplemented
73#2481C2218yescomplemented
74#2480C2218yes—
75#2480C2218yes—
76#2474C2218yescomplemented
77#2469C2218yescomplemented
78#2450C2218yescomplemented
79#2450C2218yescomplemented
80#2449C2218yescomplemented
81#2449C2218yescomplemented
82#2439C2214yescomplemented
83#2436C2214yes—
84#2435C2214yes—
85#2434C2214yescomplemented
86#2421C2214yescomplemented
87#2373C2218yescomplemented
88#2368C2218yes—
89#2368C2214yes—
90#2368C2214yes—
91#2368C2214yescomplemented
92#2368C2218yescomplemented
93#2368C2214yescomplemented
94#2364C2214yes—
95#2364C2218yes—
96#2364C2214yes—
97#2362C2214yescomplemented
98#2347C2214yescomplemented
99#2329C2214yes—
100#2329C2218yescomplemented
101#2318C2218yescomplemented
102#2318C2218yescomplemented
103#2315C2211yescharacteristic
104#2315C2212yes—
105#2315C2212yes—
106#2315C2212yes—
107#2313C2214yes—
108#2312C2214yes—
109#2308C2214yes—
110#2308C2214yes—
111C4×C22⋊Q8C2214yes—
112C4×C22⋊Q8C2218yescomplemented
113C2×#391C2214yescomplemented
114#2290C2218yescomplemented
115#2290C2218yescomplemented
116C2×#388C2212yes—
117C2×#387C2212yes—
118C2×#387C2214yescomplemented
119C2×#387C2214yescomplemented
120C2×#386C2212yes—
121C2×#386C2212yes—
122C2×#385C2214yes—
123#2283C2214yes—
124#2280C2214yes—
125C2×C4×C4⋊C4C2214yescomplemented
126C2×C4×C22⋊C4C2214yes—
127C2×C4×C22⋊C4C2211yescharacteristic
128C2×C4×C22⋊C4C2212yes—
129C2×C4×C22⋊C4C2212yes—
130C22×#95C2211yescharacteristic
131C23×Q8C2312yes—
132C23×D4C2312yes—
133C23×D4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2312yes—
136C24×C4C2311yescharacteristic
137#543—28no—
138C2×C4⋊Q8C2314yes—
139C2×#126C2318yes—
140C2×#126C2318yes—
141C2×#124C2318yes—
142C2×C22⋊Q8—216no—
143C2×C22⋊Q8C2314yes—
144C2×C22⋊Q8C2314yes—
145C2×C22⋊Q8C2314yes—
146C2×C22⋊Q8C2318yes—
147C2×C22⋊Q8C2314yes—
148C2×C22⋊Q8C2314yes—
149C2×C22⋊Q8C2314yes—
150C2×C22⋊Q8C2314yes—
151C2×#121—28no—
152C2×#121C2314yes—
153C2×#121C2314yes—
154C2×C4×Q8C2314yes—
155C2×C4×D4—216no—
156C2×C4×D4C2318yes—
157C2×C4×D4C2318yes—
158C2×#117C2314yes—
159C2×#117C2314yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2314yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2314yes—
165C22×C4⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2311yescharacteristic
175C22×C42C2312yes—
176C22×C42C2314yes—
177C22×C42C2314yes—
178C22×C42C2314yes—
179C22×C42C2312yes—
180#401C2318yes—
181#401C2318yes—
182#400C2318yes—
183#400C2318yes—
184#400C2318yes—
185#400C2318yes—
186#400C2318yes—
187#400C2318yes—
188#400C2318yes—
189#400C2318yes—
190#400C2318yes—
191#399C2318yes—
192#398C2318yes—
193#398C2318yes—
194#398C2318yes—
195#398C2318yes—
196#397C2318yes—
197#397C2318yes—
198#397C2318yes—
199#397C2318yes—
200#397C2318yes—
201#397C2318yes—
202#397C2318yes—
203#397C2318yes—
204#396C2318yes—
205#396C2318yes—
206#396C2318yes—
207#396C2318yes—
208#395C2318yes—
209#395C2318yes—
210#395C2318yes—
211#394C2318yes—
212#394C2318yes—
213#393C2318yes—
214#393C2318yes—
215#393C2318yes—
216#391C2318yes—
217#391C2314yes—
218#391C2318yes—
219#391C2318yes—
220#391C2314yes—
221#391C2314yes—
222#391C2318yes—
223#391C2318yes—
224#391C2318yes—
225#391C2318yes—
226#390C2318yes—
227#389C2318yes—
228#389C2314yes—
229#389C2314yes—
230#389C2318yes—
231#389C2314yes—
232#389C2314yes—
233#389C2314yes—
234#388C2318yes—
235#388C2318yes—
236#388C2318yes—
237#388C2318yes—
238#388C2318yes—
239#388C2318yes—
240#388C2318yes—
241#388C2318yes—
242#388C2318yes—
243#388C2318yes—
244#388C2318yes—
245#388C2318yes—
246#388C2318yes—
247#388C2318yes—
248#388C2318yes—
249#388C2318yes—
250#387C2318yes—
251#387C2318yes—
252#387C2318yes—
253#387C2318yes—
254#387C2318yes—
255#387C2318yes—
256#387C2318yes—
257#387C2318yes—
258#387C2318yes—
259#387C2318yes—
260#387C2318yes—
261#387C2318yes—
262#387C2318yes—
263#387C2318yes—
264#387C2318yes—
265#387C2318yes—
266#387C2318yes—
267#387C2318yes—
268#387C2318yes—
269#387C2318yes—
270#387C2318yes—
271#387C2318yes—
272#387C2318yes—
273#387C2318yes—
274#387C2318yes—
275#386C2318yes—
276#386C2318yes—
277#386C2318yes—
278#386C2318yes—
279#386C2318yes—
280#386C2318yes—
281#386C2318yes—
282#386C2318yes—
283#386C2318yes—
284#386C2318yes—
285#386C2318yes—
286#386C2318yes—
287#385C2318yes—
288#385C2318yes—
289#385C2318yes—
290#385C2318yes—
291#385C2318yes—
292#385C2318yes—
293#385C2318yes—
294#385C2318yes—
295#385C2318yes—
296#385C2318yes—
297#385C2318yes—
298#385C2318yes—
299#385C2318yes—
300#384C2314yes—
301#383C2318yes—
302#383C2318yes—
303#383C2318yes—
304#382C2314yes—
305#382C2314yes—
306#382C2318yes—
307#381C2318yes—
308#381C2318yes—
309#381C2318yes—
310#380C2314yes—
311#380C2314yes—
312#380C2314yes—
313#380C2318yes—
314#380C2318yes—
315#380C2314yes—
316#380C2314yes—
317#380C2314yes—
318#380C2314yes—
319#379C2318yes—
320#379C2318yes—
321C4×C4⋊C4C2318yes—
322C4×C4⋊C4C2318yes—
323C4×C4⋊C4C2314yes—
324C4×C4⋊C4C2318yes—
325C4×C4⋊C4C2314yes—
326C4×C4⋊C4C2318yes—
327C4×C4⋊C4C2318yes—
328C4×C4⋊C4C2314yes—
329C4×C22⋊C4C2318yes—
330C4×C22⋊C4C2314yes—
331C4×C22⋊C4C2318yes—
332C4×C22⋊C4C2314yes—
333C4×C22⋊C4C2318yes—
334C4×C22⋊C4C2314yes—
335C4×C22⋊C4C2314yes—
336C4×C22⋊C4C2314yes—
337C4×C22⋊C4C2314yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341C4×C22⋊C4C2314yes—
342C4×C22⋊C4C2318yes—
343C4×C22⋊C4C2318yes—
344#376C2318yes—
345C2×#95C2314yes—
346C2×#95C2314yes—
347C2×#95C2312yes—
348C2×#95C2314yes—
349C2×#95C2312yes—
350C2×#95C2312yes—
351C2×#95C2314yes—
352C2×#95C2311yescharacteristic
353C2×#95C2312yes—
354C2×#95C2311yescharacteristic
355C2×#95C2314yes—
356C2×#95C2314yes—
357C2×#95C2312yes—
358C2×#95C2312yes—
359C25C2412yes—
360C25C2411yescharacteristic
361C22×Q8—28no—
362C22×Q8—84no—
363C22×Q8C2414yes—
364C22×Q8C2414yes—
365C22×Q8C2414yes—
366C22×D4—28no—
367C22×D4—28no—
368C22×D4—28no—
369C22×D4—24no—
370C22×D4—82no—
371C22×D4C2418yes—
372C22×D4C2414yes—
373C23×C4—28no—
374C23×C4—28no—
375C23×C4—44no—
376C23×C4—44no—
377C23×C4—82no—
378C23×C4—82no—
379C23×C4—82no—
380C23×C4#4118yes—
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2414yes—
384C23×C4C2414yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2414yes—
388C23×C4C2414yes—
389C23×C4C2414yes—
390C23×C4C2414yes—
391C23×C4C2414yes—
392C23×C4C2414yes—
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2411yescharacteristic
398C4⋊Q8—84no—
399#126—416no—
400#126—88no—
401#124—88no—
402C22⋊Q8—216no—
403C22⋊Q8—216no—
404C22⋊Q8—216no—
405C22⋊Q8—216no—
406C22⋊Q8—216no—
407C22⋊Q8—232no—
408C22⋊Q8—48no—
409C22⋊Q8—84no—
410#121—216no—
411#121—216no—
412C4×Q8—84no—
413C4×D4—232no—
414C4×D4—232no—
415#117—48no—
416#117—84no—
417C2×C4⋊C4—28no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—28no—
420C2×C4⋊C4—216no—
421C2×C4⋊C4—48no—
422C2×C4⋊C4—84no—
423C2×C4⋊C4C2418yes—
424C2×C4⋊C4C2414yes—
425C2×C4⋊C4C2418yes—
426C2×C4⋊C4C2418yes—
427C2×C4⋊C4C2414yes—
428C2×C4⋊C4C2414yes—
429C2×C4⋊C4C2418yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2418yes—
432C2×C4⋊C4C2418yes—
433C2×C4⋊C4C2418yes—
434C2×C4⋊C4C2418yes—
435C2×C4⋊C4C2414yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2418yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2414yes—
442C2×C4⋊C4C2418yes—
443C2×C4⋊C4C2418yes—
444C2×C4⋊C4C2418yes—
445C2×C22⋊C4—216no—
446C2×C22⋊C4—28no—
447C2×C22⋊C4—28no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—28no—
450C2×C22⋊C4—28no—
451C2×C22⋊C4—44no—
452C2×C22⋊C4—82no—
453C2×C22⋊C4#4118yes—
454C2×C22⋊C4C2418yes—
455C2×C22⋊C4C2414yes—
456C2×C22⋊C4C2414yes—
457C2×C22⋊C4C2418yes—
458C2×C22⋊C4C2414yes—
459C2×C22⋊C4C2418yes—
460C2×C22⋊C4C2414yes—
461C2×C22⋊C4C2414yes—
462C2×C22⋊C4C2414yes—
463C2×C22⋊C4C2414yes—
464C2×C22⋊C4C2414yes—
465C2×C22⋊C4C2418yes—
466C2×C22⋊C4C2414yes—
467C2×C22⋊C4C2418yes—
468C2×C22⋊C4C2418yes—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C2418yes—
471C2×C22⋊C4C2418yes—
472C2×C22⋊C4C2418yes—
473C2×C22⋊C4C2418yes—
474C2×C22⋊C4C2418yes—
475C2×C22⋊C4C2414yes—
476C2×C42—28no—
477C2×C42—48no—
478C2×C42—84no—
479C2×C42—84no—
480C2×C42—82no—
481C2×C42C2418yes—
482C2×C42C2414yes—
483C2×C42C2414yes—
484C2×C42C2418yes—
485C2×C42C2414yes—
486C2×C42C2418yes—
487C2×C42C2418yes—
488C2×C42C2418yes—
489C2×C42C2414yes—
490C2×C42C2418yes—
491#95C2411yescharacteristic
492#95C2411yescharacteristic
493#95C2412yes—
494#95C2414yes—
495#95C2412yes—
496#95C2414yes—
497#95C2412yes—
498#95C2418yes—
499#95C2418yes—
500#95C2414yes—
501#95C2418yes—
502#95C2414yes—
503#95C2418yes—
504#95C2418yes—
505#95C2418yes—
506#95C2418yes—
507#95C2418yes—
508#95C2418yes—
509#95C2418yes—
510#95C2418yes—
511#95C2418yes—
512#95C2418yes—
513#95C2418yes—
514#95C2418yes—
515#95C2418yes—
516#95C2418yes—
517#95C2418yes—
518#95C2418yes—
519#95C2418yes—
520#95C2418yes—
521#95C2418yes—
522#95C2418yes—
523#95C2418yes—
524#95C2418yes—
525#95C2418yes—
526#95C2418yes—
527C24—24no—
528C24—24no—
529C24—24no—
530C24—42no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—42no—
536C24C2×#4114yes—
537C24C2×#4114yes—
538C242−1+414yes—
539C24C2514yes—
540C24C2511yescharacteristic
541C24C2512yes—
542C2×Q8—28no—
543C2×Q8—28no—
544C2×Q8—28no—
545C2×Q8—44no—
546C2×Q8—44no—
547C2×Q8—48no—
548C2×Q8—48no—
549C2×Q8—816no—
550C2×D4—216no—
551C2×D4—216no—
552C2×D4—216no—
553C2×D4—28no—
554C2×D4—48no—
555C2×D4—432no—
556C2×D4—88no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—28no—
560C22×C4—24no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—24no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—24no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—44no—
589C22×C4—42no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—44no—
599C22×C4—88no—
600C22×C4—816no—
601C22×C4—816no—
602C22×C4C2×#4118yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4118yes—
605C22×C4C2×#4118yes—
606C22×C4C2×#4114yes—
607C22×C4C2514yes—
608C22×C4C2512yes—
609C22×C4C2518yes—
610C22×C4C2514yes—
611C22×C4C2514yes—
612C22×C4C2518yes—
613C22×C4C2518yes—
614C22×C4C2518yes—
615C22×C4C2511yescharacteristic
616C22×C4C2512yes—
617C22×C4C2514yes—
618C22×C4C2511yescharacteristic
619C22×C4C2512yes—
620C4⋊C4—216no—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—216no—
625C4⋊C4—216no—
626C4⋊C4—28no—
627C4⋊C4—216no—
628C4⋊C4—216no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C22⋊C4—216no—
643C22⋊C4—216no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—216no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—44no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4C2×#41116yes—
664C42—28no—
665C42—28no—
666C42—216no—
667C42—48no—
668C42—48no—
669C42—44no—
670C42—48no—
671C42—48no—
672C42—48no—
673C42—44no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—48no—
686C23—44no—
687C23—44no—
688C23—48no—
689C23—48no—
690C23—48no—
691C23—48no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23#556116yes—
697C23C22×#4112yes—
698C23C22×#4112yes—
699C23C22×#4114yes—
700C23C22×#4114yes—
701C23C2×2−1+412yes—
702C23C2×2−1+414yes—
703C23C2611yescharacteristic
704Q8—88no—
705Q8—88no—
706Q8—88no—
707D4—432no—
708D4—88no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—22no—
733C2×C4—28no—
734C2×C4—24no—
735C2×C4—28no—
736C2×C4—24no—
737C2×C4—28no—
738C2×C4—28no—
739C2×C4—22no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—48no—
745C2×C4—416no—
746C2×C4—416no—
747C2×C4—48no—
748C2×C4—416no—
749C2×C4—416no—
750C2×C4—416no—
751C2×C4—48no—
752C2×C4—88no—
753C2×C4—88no—
754C2×C4—84no—
755C2×C4—84no—
756C2×C4—88no—
757C2×C4C22×#4118yes—
758C2×C4C22×#4112yes—
759C2×C4C22×#4112yes—
760C2×C4C22×#4114yes—
761C2×C4#58514yes—
762C22—24no—
763C22—28no—
764C22—24no—
765C22—22no—
766C22—28no—
767C22—24no—
768C22—24no—
769C22—22no—
770C22—416no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—816no—
779C22C2×#55614yes—
780C22C2×#55618yes—
781C22C23×#4111yescharacteristic
782C22C23×#4111yescharacteristic
783C22C22×2−1+411yescharacteristic
784C22C2×#58512yes—
785C22H(7,𝔽2)12yes—
786C4—24no—
787C4—28no—
788C4—22no—
789C4—24no—
790C4—22no—
791C4—44no—
792C4—42no—
793C4—48no—
794C4—48no—
795C4—48no—
796C4—44no—
797C4—48no—
798C4—44no—
799C2—24no—
800C2—28no—
801C2—84no—
802C2#6268611yescharacteristic
803C2C22×#55611yescharacteristic
804C2#6284411yescharacteristic
805C2#6290212yes—
806C2#6299012yes—
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. #39508C2semidirect
2. #38979C2semidirect
3. #38235C2semidirect
4. #38233C2semidirect
5. #37959C2semidirect
6. #37957C2semidirect
7. #36337C2semidirect
8. #36204C2semidirect
10. #35011C2semidirect
11. #34995C2semidirect
12. #34985C2semidirect
13. C2×#2368C2semidirect
15. C4×#543C2semidirect
16. #34057C2semidirect
23. #2852C22semidirect
24. #2852C22semidirect
27. #2798C22semidirect
28. #2793C22semidirect
29. #2789C22semidirect
30. #2786C22semidirect
31. #2767C22semidirect
32. #2762C22semidirect
33. #2759C22semidirect
34. #2758C22semidirect
35. #2740C22semidirect
36. #2716C22semidirect
37. #2715C22semidirect
38. #2700C22semidirect
40. #2643C22semidirect
41. #2643C22semidirect
45. #2605C22semidirect
46. #2601C22semidirect
47. #2596C22semidirect
48. #2594C22semidirect
50. #2588C22semidirect
51. #2583C22semidirect
52. #2573C22semidirect
54. #2560C22semidirect
55. #2528C22semidirect
56. #2527C22semidirect
57. #2525C22semidirect
58. #2524C22semidirect
59. #2523C22semidirect
60. #2521C22semidirect
61. #2510C22semidirect
62. #2510C22semidirect
65. #2502C22semidirect
66. #2499C22semidirect
67. #2496C22semidirect
68. #2494C22semidirect
71. #2492C22semidirect
72. #2481C22semidirect
73. #2481C22semidirect
76. #2474C22semidirect
77. #2469C22semidirect
78. #2450C22semidirect
79. #2450C22semidirect
80. #2449C22semidirect
81. #2449C22semidirect
82. #2439C22semidirect
85. #2434C22semidirect
86. #2421C22semidirect
87. #2373C22semidirect
91. #2368C22semidirect
92. #2368C22semidirect
93. #2368C22semidirect
97. #2362C22semidirect
98. #2347C22semidirect
100. #2329C22semidirect
101. #2318C22semidirect
102. #2318C22semidirect
112. C4×C22⋊Q8C22semidirect
113. C2×#391C22semidirect
114. #2290C22semidirect
115. #2290C22semidirect
118. C2×#387C22semidirect
119. C2×#387C22semidirect
125. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#395082
#389792
#382352
#382332
#379592
#379572
#363372
#362042
#350192
#350112
#349952
#349852
C2×#23682
C2×#23642
C4×#5432
#340572