Subgroups — #13092341

Order 1472.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₂×D₂₃)⋊C₄	C₂	1	3	yes	maximal
2	C₂×Dic₂₃⋊C₄	C₂	1	3	yes	maximal, complemented
3	C₂₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₂₃	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₂₃	C₂²	1	3	yes	—
6	C₂²×Dic₂₃	C₂²	1	3	yes	—
7	(C₂×D₂₃)⋊C₄	—	2	6	no	—
8	Dic₂₃⋊C₄	—	2	6	no	—
9	C₂³×C₂₃	C₂³	1	1	yes	characteristic
10	C₂²×D₂₃	—	2	3	no	—
11	C₂²×D₂₃	—	2	3	no	—
12	C₂²×D₂₃	Q₈	1	2	yes	—
13	C₂×C₄×C₂₃	—	2	3	no	—
14	C₂×C₄×C₂₃	—	2	3	no	—
15	C₂×C₄×C₂₃	—	2	3	no	—
16	C₂×Dic₂₃	—	2	3	no	—
17	C₂×Dic₂₃	—	2	3	no	—
18	C₂×Dic₂₃	D₄	1	6	yes	—
19	C₂²×C₂₃	C₂×D₄	1	3	yes	—
20	C₂²×C₂₃	C₂×Q₈	1	1	yes	characteristic
21	C₂²×C₂₃	#41	1	3	yes	—
22	C₂×D₂₃	—	2	6	no	—
23	C₂×D₂₃	—	4	3	no	—
24	C₂×D₂₃	—	4	1	no	—
25	C₄×C₂₃	—	4	3	no	—
26	Dic₂₃	—	2	6	no	—
27	#396	—	23	1	no	maximal, Sylow
28	C₂×C₂₃	#121	1	3	yes	—
29	C₂×C₂₃	C₂²⋊Q₈	1	3	yes	—
30	C₂×C₂₃	#126	1	1	yes	characteristic
31	D₂₃	—	4	2	no	—
32	C₂×C₄⋊C₄	—	23	3	no	—
33	C₂×C₂²⋊C₄	—	23	3	no	—
34	#95	D₂₃	1	1	yes	characteristic, complemented
35	C₂₃	#396	1	1	yes	characteristic, complemented, Sylow
36	C₂⁴	—	23	1	no	—
37	C₂²×C₄	—	23	3	no	—
38	C₂²×C₄	C₂×D₂₃	1	3	yes	—
39	C₄⋊C₄	—	46	6	no	—
40	C₂²⋊C₄	—	46	6	no	—
41	C₂³	—	23	2	no	—
42	C₂³	—	46	3	no	—
43	C₂³	—	46	3	no	—
44	C₂³	C₂²×D₂₃	1	1	yes	characteristic
45	C₂×C₄	—	2	3	no	—
46	C₂×C₄	—	2	3	no	—
47	C₂×C₄	—	2	3	no	—
48	C₂×C₄	—	23	6	no	—
49	C₂×C₄	—	46	3	no	—
50	C₂×C₄	—	46	3	no	—
51	C₂²	—	46	6	no	—
52	C₂²	—	92	1	no	—
53	C₂²	—	92	3	no	—
54	C₂²	#67288	1	3	yes	—
55	C₂²	D₄×D₂₃	1	3	yes	—
56	C₂²	Q₈×D₂₃	1	1	yes	characteristic
57	C₄	—	4	3	no	—
58	C₄	—	46	6	no	—
59	C₂	—	92	2	no	—
60	C₂	#10625047	1	1	yes	characteristic
61	C₂	#10625055	1	3	yes	—
62	C₂	#10625067	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₂₃
commutator, socle, cosocle	C₂³×C₂₃	C₂³
Fitting	C₂₃×#95	C₂
prime radical	C₂³×D₂₃	C₂²
hypercenter	#95	D₂₃
hypocenter	C₂₃	#396
LCS	G ▷ C₂³×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₂₃⋊C₄	C₂	semidirect
3. C₂₃×#95	C₂	semidirect
34. #95	D₂₃	semidirect
35. C₂₃	#396	semidirect

Maximal subgroups

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

subgroup	index
C₂×(C₂×D₂₃)⋊C₄	2
C₂×Dic₂₃⋊C₄	2
C₂₃×#95	2
#396	23