Subgroups — #15676678

Order 2944.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₉₂	C₂	1	6	yes	maximal, complemented
2	#13092354	C₂	1	4	yes	maximal, complemented
3	#13092327	C₂	1	4	yes	maximal, complemented
4	C₂₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₉₂	C₂²	1	6	yes	—
6	C₂²×C₄×D₂₃	C₂²	1	4	yes	—
7	C₂×C₄²×C₂₃	C₂²	1	3	yes	—
8	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	12	yes	—
9	C₂×C₄⋊Dic₂₃	C₂²	1	6	yes	—
10	C₄×D₉₂	—	2	24	no	—
11	C₂₃×#95	C₂²	1	4	yes	—
12	C₂³×D₂₃	C₂³	1	4	yes	—
13	C₂²×C₄×C₂₃	C₂³	1	6	yes	—
14	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
15	C₂²×Dic₂₃	C₂³	1	4	yes	—
16	C₂×D₉₂	—	2	24	no	—
17	C₂×D₉₂	—	2	12	no	—
18	C₂×C₄×D₂₃	—	2	24	no	—
19	C₄²×C₂₃	D₄	1	12	yes	complemented
20	(C₂×D₂₃)⋊C₄	—	2	24	no	—
21	C₄⋊Dic₂₃	—	2	12	no	—
22	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
23	C₂²×D₂₃	—	2	12	no	—
24	C₂²×D₂₃	—	2	12	no	—
25	C₂²×D₂₃	#41	1	8	yes	—
26	C₂×C₄×C₂₃	—	2	12	no	—
27	C₂×C₄×C₂₃	C₂×D₄	1	12	yes	—
28	C₂×C₄×C₂₃	C₂×D₄	1	6	yes	—
29	C₂×Dic₂₃	—	2	12	no	—
30	D₉₂	—	2	48	no	—
31	C₄×D₂₃	—	4	16	no	—
32	#2397	—	23	1	no	maximal, Sylow
33	C₂²×C₂₃	C₂²×D₄	1	3	yes	—
34	C₂²×C₂₃	C₂×#41	1	4	yes	—
35	C₂×D₂₃	—	2	24	no	—
36	C₂×D₂₃	—	4	12	no	—
37	C₂×D₂₃	—	4	4	no	—
38	C₄×C₂₃	—	2	12	no	—
39	C₄×C₂₃	#127	1	4	yes	—
40	Dic₂₃	—	4	4	no	—
41	C₂×C₄×D₄	—	23	6	no	—
42	#399	—	23	4	no	—
43	#392	—	23	4	no	—
44	#376	D₂₃	1	1	yes	characteristic, complemented
45	C₂×C₂₃	#525	1	6	yes	—
46	C₂×C₂₃	C₂×#127	1	1	yes	characteristic
47	D₂₃	—	4	8	no	—
48	C₂²×D₄	—	23	6	no	—
49	C₂³×C₄	—	23	4	no	—
50	C₄×D₄	—	46	24	no	—
51	C₂×C₄⋊C₄	—	23	6	no	—
52	C₂×C₂²⋊C₄	—	23	12	no	—
53	C₂×C₄²	C₂×D₂₃	1	3	yes	—
54	#95	C₂×D₂₃	1	4	yes	—
55	C₂₃	#2397	1	1	yes	characteristic, complemented, Sylow
56	C₂⁴	—	23	4	no	—
57	C₂×D₄	—	46	24	no	—
58	C₂×D₄	—	46	12	no	—
59	C₂²×C₄	—	23	4	no	—
60	C₂²×C₄	—	46	24	no	—
61	C₂²×C₄	C₂²×D₂₃	1	6	yes	—
62	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
63	C₄⋊C₄	—	46	12	no	—
64	C₂²⋊C₄	—	46	24	no	—
65	C₄²	D₉₂	1	12	yes	complemented
66	C₂³	—	23	8	no	—
67	C₂³	—	46	12	no	—
68	C₂³	—	46	12	no	—
69	C₂³	C₂³×D₂₃	1	1	yes	characteristic
70	D₄	—	46	48	no	—
71	C₂×C₄	—	2	12	no	—
72	C₂×C₄	—	46	12	no	—
73	C₂×C₄	—	92	16	no	—
74	C₂×C₄	C₂×D₉₂	1	12	yes	—
75	C₂×C₄	C₂×D₉₂	1	6	yes	—
76	C₂²	—	46	24	no	—
77	C₂²	—	92	12	no	—
78	C₂²	—	92	4	no	—
79	C₂²	C₂²×D₉₂	1	3	yes	—
80	C₂²	#41×D₂₃	1	4	yes	—
81	C₄	—	2	12	no	—
82	C₄	—	92	4	no	—
83	C₄	#10625045	1	4	yes	—
84	C₂	—	92	8	no	—
85	C₂	#13092929	1	6	yes	—
86	C₂	C₂×#10625045	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₂₃
commutator, socle, cosocle	C₂³×C₂₃	C₂⁴
Frattini	C₂³	C₂³×D₂₃
Fitting	C₂₃×#376	C₂
hypercenter	#376	D₂₃
hypocenter	C₂₃	#2397
LCS	G ▷ C₂³×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×D₉₂	C₂	semidirect
2. #13092354	C₂	semidirect
3. #13092327	C₂	semidirect
4. C₂₃×#376	C₂	semidirect
19. C₄²×C₂₃	D₄	semidirect
44. #376	D₂₃	semidirect
55. C₂₃	#2397	semidirect
65. C₄²	D₉₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₉₂	2
#13092354	2
#13092327	2
C₂₃×#376	2
#2397	23