Subgroups — C₄×#67292 #13092887

Order 1472.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#67292	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625064	C₂	1	3	yes	maximal, complemented
5	#10625063	C₂	1	3	yes	maximal, complemented
6	C₄×D₉₂	C₂	1	3	yes	maximal, complemented
7	C₄²×D₂₃	C₂	1	3	yes	maximal, complemented
8	C₂×Q₈×C₂₃	C₂²	1	1	yes	characteristic
9	#67292	C₄	1	8	yes	direct product factor
10	C₂×D₉₂	C₂²	1	3	yes	—
11	C₂×C₄×D₂₃	C₂²	1	3	yes	—
12	C₂×C₄×D₂₃	C₂²	1	3	yes	—
13	C₂×C₄×D₂₃	C₂²	1	3	yes	—
14	C₄⋊C₄×C₂₃	C₂²	1	3	yes	—
15	C₄²×C₂₃	C₂²	1	3	yes	—
16	(C₂×D₂₃)⋊C₄	C₂²	1	6	yes	—
17	C₄⋊Dic₂₃	C₂²	1	3	yes	—
18	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
19	C₄×Dic₂₃	C₂²	1	3	yes	—
20	C₄×Dic₂₃	C₂²	1	3	yes	—
21	C₂²×D₂₃	C₂³	1	3	yes	—
22	Q₈×C₂₃	C₂×C₄	1	4	yes	complemented
23	C₂×C₄×C₂₃	C₂³	1	3	yes	—
24	C₂×C₄×C₂₃	C₂³	1	3	yes	—
25	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
26	C₂×Dic₂₃	C₂³	1	3	yes	—
27	C₂×Dic₂₃	C₂³	1	1	yes	characteristic
28	C₂×Dic₂₃	C₂³	1	1	yes	characteristic
29	D₉₂	C₂×C₄	1	12	yes	complemented
30	C₄×D₂₃	—	2	6	no	—
31	C₄×D₂₃	—	2	6	no	—
32	C₄×D₂₃	C₂×C₄	1	12	yes	complemented
33	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
34	C₂×D₂₃	—	2	3	no	—
35	C₂×D₂₃	—	2	3	no	—
36	C₂×D₂₃	C₂²×C₄	1	6	yes	—
37	C₄×C₂₃	—	2	3	no	—
38	C₄×C₂₃	C₂²×C₄	1	6	yes	—
39	C₄×C₂₃	#41	1	2	yes	complemented
40	Dic₂₃	—	2	3	no	—
41	Dic₂₃	C₂²×C₄	1	2	yes	—
42	Dic₂₃	#41	1	2	yes	complemented
43	C₄×#41	—	23	1	no	maximal, Sylow
44	C₂×C₂₃	C₂³×C₄	1	1	yes	characteristic
45	C₂×C₂₃	C₂×#41	1	1	yes	characteristic
46	C₂×C₂₃	C₂×#41	1	1	yes	characteristic
47	D₂₃	—	2	6	no	—
48	C₂×#41	—	23	1	no	—
49	C₄×Q₈	—	23	1	no	—
50	C₄×Q₈	D₂₃	1	1	yes	characteristic, complemented
51	C₄×D₄	—	23	3	no	—
52	C₄×D₄	—	23	3	no	—
53	#117	—	23	3	no	—
54	C₂×C₄²	—	23	3	no	—
55	C₂₃	C₄×#41	1	1	yes	characteristic, complemented, Sylow
56	#41	—	23	8	no	—
57	C₂×Q₈	C₂×D₂₃	1	1	yes	characteristic
58	C₂×D₄	—	23	3	no	—
59	C₂²×C₄	—	23	3	no	—
60	C₂²×C₄	—	23	3	no	—
61	C₂²×C₄	—	23	3	no	—
62	C₄⋊C₄	—	23	3	no	—
63	C₄⋊C₄	C₂×D₂₃	1	3	yes	—
64	C₂²⋊C₄	—	23	6	no	—
65	C₄²	—	23	3	no	—
66	C₄²	—	23	3	no	—
67	C₄²	—	23	1	no	—
68	C₄²	C₂×D₂₃	1	3	yes	—
69	C₂³	—	23	3	no	—
70	Q₈	C₄×D₂₃	1	4	yes	complemented
71	D₄	—	23	12	no	—
72	C₂×C₄	—	23	1	no	—
73	C₂×C₄	—	23	1	no	—
74	C₂×C₄	—	23	12	no	—
75	C₂×C₄	—	23	3	no	—
76	C₂×C₄	—	46	6	no	—
77	C₂×C₄	—	46	6	no	—
78	C₂×C₄	C₂²×D₂₃	1	3	yes	—
79	C₂×C₄	C₂²×D₂₃	1	3	yes	—
80	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
81	C₂²	—	23	6	no	—
82	C₂²	—	46	3	no	—
83	C₂²	—	46	3	no	—
84	C₂²	C₂³×D₂₃	1	1	yes	characteristic
85	C₄	—	2	3	no	—
86	C₄	—	23	2	no	—
87	C₄	—	23	2	no	—
88	C₄	—	46	3	no	—
89	C₄	C₂×C₄×D₂₃	1	6	yes	—
90	C₄	#67292	1	2	yes	direct product factor
91	C₂	—	46	6	no	—
92	C₂	C₂²×C₄×D₂₃	1	1	yes	characteristic
93	C₂	C₂×#67292	1	1	yes	characteristic
94	C₂	#41×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₃
commutator	C₂×C₂₃	C₂³×C₄
Frattini	C₂²	C₂³×D₂₃
Fitting	C₄×Q₈×C₂₃	C₂
socle, cosocle	C₂²×C₂₃	C₂⁴
prime radical	C₂×#67292	C₂
hypercenter	C₄×Q₈	D₂₃
hypocenter	C₂₃	C₄×#41
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×C₂₃	C₂	semidirect
3. Q₈×Dic₂₃	C₂	semidirect
4. #10625064	C₂	semidirect
5. #10625063	C₂	semidirect
6. C₄×D₉₂	C₂	semidirect
7. C₄²×D₂₃	C₂	semidirect
9. #67292	C₄	direct (N × H)
22. Q₈×C₂₃	C₂×C₄	semidirect
29. D₉₂	C₂×C₄	semidirect
32. C₄×D₂₃	C₂×C₄	semidirect
39. C₄×C₂₃	#41	semidirect
42. Dic₂₃	#41	semidirect
50. C₄×Q₈	D₂₃	semidirect
55. C₂₃	C₄×#41	semidirect
70. Q₈	C₄×D₂₃	semidirect
90. C₄	#67292	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#67292	2
C₄×Q₈×C₂₃	2
Q₈×Dic₂₃	2
#10625064	2
#10625063	2
C₄×D₉₂	2
C₄²×D₂₃	2
C₄×#41	23

Subgroups — C4×#67292 #13092887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#67292 #13092887