Subgroups — #13092675

Order 1472.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625095	C₂	1	2	yes	maximal
3	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#10624999	C₂	1	1	yes	maximal, characteristic, complemented
5	#10624998	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₄₆	C₂²	1	2	yes	—
8	M₁₆×C₂₃	—	2	2	no	—
9	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²⋊Dic₂₃	—	2	2	no	—
12	C₄⋊Dic₂₃	C₂²	1	2	yes	—
13	Dic₂₃⋊C₄	—	2	2	no	—
14	Dic₉₂	—	2	2	no	—
15	C₂³×C₂₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₃	—	2	1	no	—
17	C₂×C₄×C₂₃	—	2	1	no	—
18	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₂₃	—	2	2	no	—
21	C₂×Dic₂₃	—	2	2	no	—
22	Dic₄₆	—	2	2	no	—
23	Dic₄₆	—	2	2	no	—
24	C₈×C₂₃	—	2	1	no	—
25	C₈×C₂₃	D₄	1	2	yes	—
26	C₂²×C₂₃	—	2	1	no	—
27	C₂²×C₂₃	—	2	2	no	—
28	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
29	C₄×C₂₃	—	2	1	no	—
30	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₂₃	#41	1	1	yes	characteristic
32	Dic₂₃	—	4	2	no	—
33	Dic₂₃	—	4	2	no	—
34	#470	—	23	1	no	maximal, Sylow
35	C₂×C₂₃	—	4	1	no	—
36	C₂×C₂₃	#121	1	1	yes	characteristic
37	C₂×C₂₃	#137	1	2	yes	—
38	C₂×Q₁₆	—	23	1	no	—
39	C₂×M₁₆	D₂₃	1	1	yes	characteristic
40	C₂²⋊Q₈	—	23	2	no	—
41	#106	—	23	1	no	—
42	#103	—	23	2	no	—
43	C₂₃	#470	1	1	yes	characteristic, complemented, Sylow
44	C₂×Q₈	—	23	2	no	—
45	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
46	Q₁₆	—	46	2	no	—
47	M₁₆	—	2	2	no	—
48	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
49	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
50	C₄⋊C₄	—	23	2	no	—
51	C₄⋊C₄	—	46	2	no	—
52	C₂²⋊C₄	—	46	2	no	—
53	C₂³	D₉₂	1	1	yes	characteristic
54	Q₈	—	46	2	no	—
55	Q₈	—	46	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	46	2	no	—
59	C₂×C₄	—	46	2	no	—
60	C₂×C₄	D₉₂	1	1	yes	characteristic
61	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
62	C₈	—	2	1	no	—
63	C₈	C₂²⋊D₂₃	1	2	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	—	2	1	no	—
66	C₂²	C₂×D₉₂	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	92	2	no	—
69	C₄	—	92	2	no	—
70	C₄	#67288	1	1	yes	characteristic
71	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
72	C₂	—	4	1	no	—
73	C₂	#10625080	1	2	yes	—
74	C₂	#10625101	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₉₂
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×M₁₆×C₂₃	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂³×C₂₃	D₄
hypercenter	C₂×M₁₆	D₂₃
hypocenter	C₂₃	#470
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₉₂	C₂	semidirect
4. #10624999	C₂	semidirect
5. #10624998	C₂	semidirect
43. C₂₃	#470	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₂₃	2
#10625095	2
C₂×Dic₉₂	2
#10624999	2
#10624998	2
#470	23