Subgroups — #13092411

Order 1472.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#67288	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#10624992	C₂	1	2	yes	maximal, complemented
5	#10624991	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₂₃	—	2	1	no	—
8	#67288	—	2	2	no	—
9	#67288	C₄	1	4	yes	complemented
10	C₂×D₉₂	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₂₃	—	2	1	no	—
12	C₂×Dic₄₆	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
14	C₂²⋊C₄×C₂₃	—	2	1	no	—
15	C₄²×C₂₃	—	2	1	no	—
16	C₂×C₂₃⋊C₈	—	2	2	no	—
17	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
18	C₂³×C₂₃	D₄	1	1	yes	characteristic
19	C₂²×D₂₃	—	2	1	no	—
20	C₂×C₄×C₂₃	—	2	2	no	—
21	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₂₃	D₄	1	2	yes	—
23	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
25	C₂²⋊D₂₃	—	2	4	no	—
26	C₂×Dic₂₃	—	2	1	no	—
27	D₉₂	—	2	1	no	—
28	D₉₂	C₂×C₄	1	2	yes	—
29	C₄×D₂₃	—	2	4	no	—
30	Dic₄₆	—	2	1	no	—
31	Dic₄₆	C₂×C₄	1	2	yes	—
32	C₂₃⋊C₈	—	2	2	no	—
33	C₂²×C₂₃	—	2	2	no	—
34	C₂²×C₂₃	C₂²⋊C₄	1	2	yes	—
35	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
36	C₂×D₂₃	—	2	2	no	—
37	C₂×D₂₃	—	4	2	no	—
38	C₄×C₂₃	—	4	2	no	—
39	C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
40	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
41	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
42	Dic₂₃	—	2	2	no	—
43	#416	—	23	1	no	maximal, Sylow
44	C₂×C₂₃	—	2	2	no	—
45	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₂₃	#135	1	2	yes	—
47	D₂₃	—	4	2	no	—
48	C₂×#41	—	23	1	no	—
49	C₂²×C₈	—	23	1	no	—
50	#117	D₂₃	1	1	yes	characteristic, complemented
51	#103	—	23	2	no	—
52	#102	—	23	2	no	—
53	C₂₃	#416	1	1	yes	characteristic, complemented, Sylow
54	#41	—	23	4	no	—
55	#41	—	46	2	no	—
56	C₂×Q₈	—	23	1	no	—
57	C₂×D₄	—	23	1	no	—
58	C₂×D₄	—	46	1	no	—
59	C₂²×C₄	—	46	1	no	—
60	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
61	C₂×C₈	—	23	2	no	—
62	C₂×C₈	—	46	2	no	—
63	C₄⋊C₄	C₂×D₂₃	1	2	yes	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	—	2	1	no	—
66	C₂³	—	46	1	no	—
67	C₂³	C₂²⋊D₂₃	1	1	yes	characteristic
68	Q₈	—	23	2	no	—
69	Q₈	—	46	1	no	—
70	D₄	—	23	2	no	—
71	D₄	—	46	4	no	—
72	D₄	—	46	1	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	46	1	no	—
75	C₂×C₄	—	46	4	no	—
76	C₂×C₄	C₄×D₂₃	1	2	yes	—
77	C₂×C₄	D₉₂	1	2	yes	—
78	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
79	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
80	C₈	—	46	2	no	—
81	C₂²	—	2	2	no	—
82	C₂²	—	46	2	no	—
83	C₂²	—	92	2	no	—
84	C₂²	(C₂×D₂₃)⋊C₄	1	2	yes	—
85	C₂²	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
86	C₄	—	4	2	no	—
87	C₄	—	46	2	no	—
88	C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
89	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
90	C₄	C₂×D₉₂	1	1	yes	characteristic
91	C₂	—	2	2	no	—
92	C₂	—	92	2	no	—
93	C₂	C₂×(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
94	C₂	#10625121	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₂₃
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#117	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂×#67288	C₂
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#117	D₂₃
hypocenter	C₂₃	#416
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. C₂₃×#117	C₂	semidirect
3. C₂²×C₂₃⋊C₈	C₂	semidirect
4. #10624992	C₂	semidirect
5. #10624991	C₂	semidirect
9. #67288	C₄	semidirect
50. #117	D₂₃	semidirect
53. C₂₃	#416	semidirect

Maximal subgroups

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

subgroup	index
C₂×#67288	2
C₂₃×#117	2
C₂²×C₂₃⋊C₈	2
#10624992	2
#10624991	2
#416	23