Subgroups — #88201⋊C₃ #11928312

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄⋊(D₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic
3	#6103⋊C₃	C₂	1	4	yes	maximal, complemented
4	C₄×Dic₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#88201	C₃	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂²×D₁₃⋊C₃	C₂²	1	2	yes	—
7	Q₈×C₁₃⋊C₃	—	2	2	no	—
8	C₂×C₄×C₁₃⋊C₃	C₂²	1	2	yes	—
9	C₂×C₄×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₃⋊C₃	C₂²	1	2	yes	—
11	C₄⋊(D₁₃⋊C₃)	—	2	2	no	—
12	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×D₅₂	C₂×C₃	1	1	yes	characteristic
14	#6103	C₂×C₃	1	4	yes	complemented
15	C₄×Dic₁₃	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂²×C₁₃⋊C₃	C₂³	1	1	yes	characteristic
17	C₂×D₁₃⋊C₃	—	2	2	no	—
18	C₂×D₁₃⋊C₃	—	2	4	no	—
19	C₄×C₁₃⋊C₃	—	2	2	no	—
20	C₄×C₁₃⋊C₃	D₄	1	2	yes	—
21	Dic₁₃⋊C₃	—	2	2	no	—
22	C₂²×D₁₃	C₂²×C₃	1	2	yes	—
23	Q₈×C₁₃	—	2	2	no	—
24	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
25	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
26	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
27	D₅₂	—	2	2	no	—
28	C₃×#124	—	13	1	no	maximal, Hall
29	C₂×C₁₃⋊C₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₁₃⋊C₃	#41	1	2	yes	—
31	D₁₃⋊C₃	—	4	2	no	—
32	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
33	C₂×D₁₃	—	2	2	no	—
34	C₂×D₁₃	—	2	4	no	—
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	C₃×D₄	1	2	yes	—
37	Dic₁₃	—	2	2	no	—
38	C₂×C₃×Q₈	—	13	1	no	—
39	C₂×C₃×D₄	—	13	1	no	—
40	C₃×C₂²⋊C₄	—	13	4	no	—
41	C₃×C₄²	—	13	1	no	—
42	C₁₃⋊C₃	#124	1	1	yes	characteristic, complemented, Hall
43	#124	—	13	1	no	Sylow
44	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
45	C₂×C₁₃	C₃×#41	1	2	yes	—
46	D₁₃	—	4	2	no	—
47	C₂³×C₃	—	13	2	no	—
48	C₃×Q₈	—	26	2	no	—
49	C₃×D₄	—	26	2	no	—
50	C₂×C₃×C₄	—	13	2	no	—
51	C₂×C₃×C₄	—	13	1	no	—
52	C₂×C₃×C₄	—	13	2	no	—
53	C₂×Q₈	D₁₃⋊C₃	1	1	yes	characteristic, complemented
54	C₂×D₄	—	13	1	no	—
55	C₂²⋊C₄	—	13	4	no	—
56	C₄²	—	13	1	no	—
57	C₁₃	C₃×#124	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	—	13	1	no	—
59	C₂²×C₃	—	26	2	no	—
60	C₂²×C₃	—	26	4	no	—
61	C₃×C₄	—	13	2	no	—
62	C₃×C₄	—	26	2	no	—
63	C₃×C₄	—	26	2	no	—
64	C₂³	—	13	2	no	—
65	Q₈	—	2	2	no	—
66	D₄	—	26	2	no	—
67	C₂×C₄	—	13	2	no	—
68	C₂×C₄	C₂×D₁₃⋊C₃	1	2	yes	—
69	C₂×C₄	C₂×D₁₃⋊C₃	1	1	yes	characteristic
70	C₂×C₃	—	13	2	no	—
71	C₂×C₃	—	13	1	no	—
72	C₂×C₃	—	52	2	no	—
73	C₂²	—	26	4	no	—
74	C₂²	—	26	2	no	—
75	C₂²	C₂²×D₁₃⋊C₃	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	26	2	no	—
78	C₄	(C₂²⋊D₁₃)⋊C₃	1	2	yes	—
79	C₃	—	13	1	no	Sylow
80	C₂	—	52	2	no	—
81	C₂	#10597707	1	2	yes	—
82	C₂	C₂×(C₂²⋊D₁₃)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₃⋊C₃
commutator, socle, cosocle	C₂²×C₁₃	C₂³×C₃
Fitting	C₂×Q₈×C₁₃	C₂×C₃
prime radical	C₂×C₄⋊(D₁₃⋊C₃)	C₂
hypercenter	C₂×Q₈	D₁₃⋊C₃
hypocenter	C₁₃	C₃×#124
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₁₃⋊C₃	C₂	semidirect
3. #6103⋊C₃	C₂	semidirect
4. C₄×Dic₁₃⋊C₃	C₂	semidirect
5. #88201	C₃	semidirect
12. C₂×Q₈×C₁₃	C₂×C₃	semidirect
14. #6103	C₂×C₃	semidirect
15. C₄×Dic₁₃	C₂×C₃	semidirect
42. C₁₃⋊C₃	#124	semidirect
53. C₂×Q₈	D₁₃⋊C₃	semidirect
57. C₁₃	C₃×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₁₃⋊C₃	2
C₂×C₄⋊(D₁₃⋊C₃)	2
#6103⋊C₃	2
C₄×Dic₁₃⋊C₃	2
#88201	3
C₃×#124	13

Subgroups — #88201⋊C3 #11928312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #88201⋊C₃ #11928312