Subgroups — C₄⋊Q₈×D₂₃ #13092958

Order 1472.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₂₃	C₂	1	2	yes	maximal
2	C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#10625115	C₂	1	2	yes	maximal, complemented
4	C₄⋊C₄×D₂₃	C₂	1	4	yes	maximal
5	#10625059	C₂	1	4	yes	maximal, complemented
6	C₄²×D₂₃	C₂	1	1	yes	maximal, characteristic
7	#10625040	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×C₂₃	C₂²	1	2	yes	—
9	Q₈×D₂₃	—	2	8	no	—
10	C₂×C₄×D₂₃	C₂²	1	4	yes	—
11	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₂₃	C₂²	1	2	yes	—
13	C₂×Dic₄₆	C₂²	1	2	yes	—
14	C₂×Dic₄₆	C₂²	1	4	yes	—
15	C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
16	C₄²×C₂₃	C₂²	1	1	yes	characteristic
17	C₄⋊Dic₂₃	C₂²	1	4	yes	—
18	Dic₂₃⋊C₄	C₂²	1	8	yes	—
19	C₄×Dic₂₃	C₂²	1	2	yes	—
20	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
21	C₂²×D₂₃	C₂³	1	1	yes	characteristic
22	Q₈×C₂₃	—	2	4	no	—
23	C₂×C₄×C₂₃	C₂³	1	4	yes	—
24	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₂₃	C₂³	1	2	yes	—
26	C₂×Dic₂₃	C₂³	1	4	yes	—
27	C₂×Dic₂₃	C₂³	1	1	yes	characteristic
28	C₂×Dic₂₃	C₂³	1	2	yes	—
29	C₄×D₂₃	—	2	8	no	—
30	C₄×D₂₃	D₄	1	4	yes	—
31	C₄×D₂₃	Q₈	1	8	yes	complemented
32	Dic₄₆	—	2	4	no	—
33	Dic₄₆	—	2	8	no	—
34	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
35	C₂×D₂₃	C₂×D₄	1	2	yes	—
36	C₂×D₂₃	C₂×Q₈	1	4	yes	—
37	C₄×C₂₃	—	2	4	no	—
38	C₄×C₂₃	C₂×D₄	1	2	yes	—
39	C₄×C₂₃	C₂×Q₈	1	4	yes	complemented
40	Dic₂₃	—	2	4	no	—
41	Dic₂₃	C₂×D₄	1	2	yes	—
42	Dic₂₃	C₂×Q₈	1	4	yes	complemented
43	C₂×C₄⋊Q₈	—	23	1	no	maximal, Sylow
44	C₂×C₂₃	C₂²×D₄	1	1	yes	characteristic
45	C₂×C₂₃	C₂²×Q₈	1	2	yes	—
46	D₂₃	C₄⋊Q₈	1	4	yes	direct product factor
47	C₂²×Q₈	—	23	2	no	—
48	C₄⋊Q₈	—	23	2	no	—
49	C₄⋊Q₈	—	23	4	no	—
50	C₄⋊Q₈	—	23	1	no	—
51	C₄⋊Q₈	D₂₃	1	1	yes	characteristic, direct product factor
52	C₂×C₄⋊C₄	—	23	4	no	—
53	C₂×C₄²	—	23	1	no	—
54	C₂₃	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₈	—	23	4	no	—
56	C₂×Q₈	—	23	2	no	—
57	C₂×Q₈	—	46	8	no	—
58	C₂×Q₈	C₂×D₂₃	1	2	yes	—
59	C₂²×C₄	—	23	2	no	—
60	C₂²×C₄	—	23	1	no	—
61	C₂²×C₄	—	23	4	no	—
62	C₄⋊C₄	—	23	8	no	—
63	C₄⋊C₄	—	23	4	no	—
64	C₄⋊C₄	C₂×D₂₃	1	4	yes	—
65	C₄²	—	23	1	no	—
66	C₄²	—	23	2	no	—
67	C₄²	C₂×D₂₃	1	1	yes	characteristic
68	C₂³	—	23	1	no	—
69	Q₈	—	2	4	no	—
70	Q₈	—	46	8	no	—
71	Q₈	—	46	4	no	—
72	C₂×C₄	—	23	2	no	—
73	C₂×C₄	—	23	1	no	—
74	C₂×C₄	—	23	4	no	—
75	C₂×C₄	—	23	8	no	—
76	C₂×C₄	—	23	4	no	—
77	C₂×C₄	—	46	8	no	—
78	C₂×C₄	C₂²×D₂₃	1	4	yes	—
79	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
80	C₂×C₄	C₂²×D₂₃	1	2	yes	—
81	C₂²	—	23	2	no	—
82	C₂²	—	23	4	no	—
83	C₂²	C₂³×D₂₃	1	1	yes	characteristic
84	C₄	—	2	4	no	—
85	C₄	—	23	2	no	—
86	C₄	—	23	4	no	—
87	C₄	—	46	4	no	—
88	C₄	D₄×D₂₃	1	2	yes	—
89	C₄	Q₈×D₂₃	1	4	yes	complemented
90	C₂	—	23	4	no	—
91	C₂	C₂×D₄×D₂₃	1	1	yes	characteristic
92	C₂	C₂×Q₈×D₂₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁴
Fitting	C₂₃×C₄⋊Q₈	C₂
prime radical	C₂²×D₂₃	C₂³
hypercenter	C₄⋊Q₈	D₂₃
hypocenter	C₂₃	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂₃×C₄⋊Q₈	C₂	semidirect
3. #10625115	C₂	semidirect
5. #10625059	C₂	semidirect
7. #10625040	C₂	semidirect
31. C₄×D₂₃	Q₈	semidirect
39. C₄×C₂₃	C₂×Q₈	semidirect
42. Dic₂₃	C₂×Q₈	semidirect
46. D₂₃	C₄⋊Q₈	direct (N × H)
51. C₄⋊Q₈	D₂₃	direct (N × H)
54. C₂₃	C₂×C₄⋊Q₈	semidirect
89. C₄	Q₈×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₂₃	2
C₂₃×C₄⋊Q₈	2
#10625115	2
C₄⋊C₄×D₂₃	2
#10625059	2
C₄²×D₂₃	2
#10625040	2
C₂×C₄⋊Q₈	23

Subgroups — C4⋊Q8×D23 #13092958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊Q₈×D₂₃ #13092958