Subgroups — #25011312

Order 11008.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136848	C₂	1	4	yes	maximal
2	#19134213	C₂	1	2	yes	maximal
3	C₈×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₄₄	—	2	8	no	—
5	#14583304	—	2	4	no	—
6	#14583279	C₂²	1	4	yes	—
7	C₄×C₁₆×C₄₃	C₂²	1	2	yes	—
8	C₈²×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₇₂	—	2	8	no	—
10	#13063325	—	2	4	no	—
11	Dic₃₄₄	—	4	16	no	—
12	#13063259	—	4	8	no	—
13	C₂×C₁₆×C₄₃	D₄	1	4	yes	—
14	C₄×C₈×C₄₃	D₄	1	2	yes	—
15	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
16	C₂×Dic₈₆	—	4	4	no	—
17	C₂×C₈×C₄₃	D₈	1	4	yes	—
18	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
19	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
20	C₄⋊Dic₄₃	—	4	8	no	—
21	Dic₁₇₂	—	4	16	no	—
22	C₁₆×C₄₃	D₈	1	8	yes	—
23	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
24	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
25	C₂×Dic₄₃	—	8	4	no	—
26	Dic₈₆	—	8	8	no	—
27	C₈×C₄₃	Q₃₂	1	8	yes	complemented
28	C₈×C₄₃	C₂×D₈	1	4	yes	—
29	#12516	—	43	1	no	maximal, Sylow
30	C₂²×C₄₃	#493	1	1	yes	characteristic
31	C₄×C₄₃	#493	1	2	yes	—
32	C₄×C₄₃	C₂×Q₃₂	1	4	yes	—
33	Dic₄₃	—	16	4	no	—
34	#2247	—	43	4	no	—
35	#1713	—	43	2	no	—
36	C₈×C₁₆	D₄₃	1	1	yes	characteristic
37	C₂×C₄₃	#1712	1	1	yes	characteristic
38	C₂×C₄₃	#2247	1	2	yes	—
39	C₂×Q₃₂	—	86	8	no	—
40	#500	—	86	4	no	—
41	#494	—	43	4	no	—
42	C₄×C₁₆	C₂×D₄₃	1	2	yes	—
43	C₈²	C₂×D₄₃	1	1	yes	characteristic
44	C₄₃	#12516	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₁₆	—	86	8	no	—
46	C₄⋊Q₈	—	86	4	no	—
47	Q₃₂	—	172	16	no	—
48	C₂×C₁₆	D₁₇₂	1	4	yes	—
49	#107	—	172	8	no	—
50	C₄×C₈	D₁₇₂	1	2	yes	—
51	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
52	C₂×Q₈	—	172	4	no	—
53	Q₁₆	—	172	16	no	—
54	C₂×C₈	D₃₄₄	1	4	yes	—
55	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
56	C₄⋊C₄	—	172	8	no	—
57	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
58	C₁₆	D₃₄₄	1	8	yes	—
59	Q₈	—	344	8	no	—
60	C₂×C₄	—	344	4	no	—
61	C₂×C₄	#13063322	1	1	yes	characteristic
62	C₂×C₄	C₂×D₃₄₄	1	2	yes	—
63	C₈	Dic₃₄₄	1	8	yes	complemented
64	C₈	C₂×D₃₄₄	1	4	yes	—
65	C₂²	#14583276	1	1	yes	characteristic
66	C₄	—	688	4	no	—
67	C₄	#14583276	1	2	yes	—
68	C₄	C₂×Dic₃₄₄	1	4	yes	—
69	C₂	#19134210	1	1	yes	characteristic
70	C₂	#19136848	1	2	yes	—

	subgroup	G/H
center	C₂²	#14583276
commutator, cosocle	C₄×C₈×C₄₃	C₂³
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₈×C₁₆×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	#493
hypercenter	C₈×C₁₆	D₄₃
hypocenter	C₄₃	#12516
LCS	G ▷ C₄×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
27. C₈×C₄₃	Q₃₂	semidirect
44. C₄₃	#12516	semidirect
63. C₈	Dic₃₄₄	semidirect

Maximal subgroups

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

subgroup	index
#19136848	2
#19134213	2
C₈×C₁₆×C₄₃	2
#12516	43