Subgroups — #15673517

Order 2944.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₂₃⋊C₈)	C₂	1	2	yes	maximal
2	#13092172	C₂	1	4	yes	maximal
3	C₂₃×#376	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₂₃	C₂²	1	2	yes	—
5	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×C₂₃⋊C₈	C₂²	1	4	yes	—
7	C₂₃×#95	C₄	1	4	yes	—
8	C₄⋊(C₂₃⋊C₈)	—	2	4	no	—
9	C₂²×C₄×C₂₃	C₂×C₄	1	4	yes	—
10	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
11	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
12	C₄²×C₂₃	—	2	4	no	—
13	C₄²×C₂₃	D₄	1	2	yes	—
14	C₄²×C₂₃	Q₈	1	2	yes	—
15	C₂×C₂₃⋊C₈	—	2	4	no	—
16	C₂×C₂₃⋊C₈	—	2	8	no	—
17	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₃	—	2	4	no	—
19	C₂×C₄×C₂₃	—	2	4	no	—
20	C₂×C₄×C₂₃	—	2	8	no	—
21	C₂×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₂₃	#41	1	4	yes	—
25	C₂₃⋊C₈	—	4	4	no	—
26	#1832	—	23	1	no	maximal, Sylow
27	C₂²×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₂₃	#117	1	2	yes	—
29	C₂²×C₂₃	#131	1	4	yes	—
30	C₄×C₂₃	—	2	4	no	—
31	C₄×C₂₃	—	4	4	no	—
32	C₄×C₂₃	#124	1	2	yes	—
33	C₄×C₂₃	#125	1	2	yes	—
34	C₂×C₄⋊C₈	—	23	2	no	—
35	#376	D₂₃	1	1	yes	characteristic
36	#336	—	23	4	no	—
37	C₂×C₂₃	#382	1	1	yes	characteristic
38	C₂×C₂₃	#424	1	2	yes	—
39	C₂×C₂₃	#433	1	4	yes	—
40	C₂²×C₈	—	23	4	no	—
41	C₂×C₄²	C₂×D₂₃	1	2	yes	—
42	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
43	C₄⋊C₈	—	46	4	no	—
44	#95	Dic₂₃	1	4	yes	—
45	C₂₃	#1832	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	C₂×Dic₂₃	1	4	yes	—
47	C₂²×C₄	C₂×Dic₂₃	1	2	yes	—
48	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
49	C₂×C₈	—	46	4	no	—
50	C₂×C₈	—	46	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	Dic₄₆	1	2	yes	—
53	C₄²	D₉₂	1	2	yes	—
54	C₂³	C₂²×Dic₂₃	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	2	8	no	—
58	C₂×C₄	C₄⋊Dic₂₃	1	4	yes	—
59	C₂×C₄	C₂×Dic₄₆	1	1	yes	characteristic
60	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
61	C₂×C₄	#67288	1	4	yes	—
62	C₈	—	92	4	no	—
63	C₂²	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
64	C₂²	#10625097	1	2	yes	—
65	C₂²	#10625119	1	4	yes	—
66	C₄	—	2	4	no	—
67	C₄	—	4	4	no	—
68	C₄	#10625041	1	2	yes	—
69	C₄	#10625046	1	2	yes	—
70	C₂	#13092283	1	1	yes	characteristic
71	C₂	#13092444	1	2	yes	—
72	C₂	#13092478	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₃
commutator, socle, prime radical	C₂³×C₂₃	C₂²×C₄
Fitting	C₂₃×#376	C₂
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	#376	D₂₃
hypocenter	C₂₃	#1832
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
45. C₂₃	#1832	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊(C₂₃⋊C₈)	2
#13092172	2
C₂₃×#376	2
#1832	23