Subgroups — #88198⋊C₃ #11928306

Order 1248.

136 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
2	C₂×(C₁₃⋊C₃)⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	#6101⋊C₃	C₂	1	4	yes	maximal
4	C₄×Dic₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
5	#88198	C₃	1	1	yes	maximal, characteristic, complemented, Hall
6	Q₈×C₁₃⋊C₃	—	2	2	no	—
7	C₂×C₄×C₁₃⋊C₃	C₂²	1	2	yes	—
8	C₂×C₄×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₃⋊C₃	C₂²	1	2	yes	—
10	C₂×Dic₁₃⋊C₃	C₂²	1	2	yes	—
11	(C₁₃⋊C₃)⋊Q₈	—	2	2	no	—
12	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic
13	C₂×Dic₂₆	C₂×C₃	1	1	yes	characteristic
14	#6101	C₂×C₃	1	4	yes	—
15	C₄×Dic₁₃	C₂×C₃	1	1	yes	characteristic
16	C₂²×C₁₃⋊C₃	C₂³	1	1	yes	characteristic
17	C₄×C₁₃⋊C₃	—	2	2	no	—
18	C₄×C₁₃⋊C₃	D₄	1	2	yes	—
19	Dic₁₃⋊C₃	—	2	2	no	—
20	Dic₁₃⋊C₃	Q₈	1	4	yes	complemented
21	Q₈×C₁₃	—	2	2	no	—
22	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
23	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
24	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
25	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
26	Dic₂₆	—	2	2	no	—
27	C₃×C₄⋊Q₈	—	13	1	no	maximal, Hall
28	C₂×C₁₃⋊C₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₁₃⋊C₃	C₂×Q₈	1	2	yes	—
30	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
31	C₄×C₁₃	—	2	2	no	—
32	C₄×C₁₃	C₃×D₄	1	2	yes	—
33	Dic₁₃	—	2	2	no	—
34	Dic₁₃	C₃×Q₈	1	4	yes	complemented
35	C₂×C₃×Q₈	—	13	1	no	—
36	C₂×C₃×Q₈	—	13	1	no	—
37	C₃×C₄⋊C₄	—	13	4	no	—
38	C₃×C₄²	—	13	1	no	—
39	C₁₃⋊C₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
40	C₄⋊Q₈	—	13	1	no	Sylow
41	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
42	C₂×C₁₃	C₂×C₃×Q₈	1	2	yes	—
43	C₃×Q₈	—	26	2	no	—
44	C₃×Q₈	—	26	2	no	—
45	C₂×C₃×C₄	—	13	2	no	—
46	C₂×C₃×C₄	—	13	2	no	—
47	C₂×C₃×C₄	—	13	1	no	—
48	C₂×C₃×C₄	—	13	2	no	—
49	C₂×Q₈	—	13	1	no	—
50	C₂×Q₈	D₁₃⋊C₃	1	1	yes	characteristic
51	C₄⋊C₄	—	13	4	no	—
52	C₄²	—	13	1	no	—
53	C₁₃	C₃×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₃	—	13	1	no	—
55	C₃×C₄	—	13	4	no	—
56	C₃×C₄	—	13	2	no	—
57	C₃×C₄	—	26	2	no	—
58	C₃×C₄	—	26	2	no	—
59	Q₈	—	2	2	no	—
60	Q₈	—	26	2	no	—
61	C₂×C₄	—	13	2	no	—
62	C₂×C₄	—	13	2	no	—
63	C₂×C₄	C₂×D₁₃⋊C₃	1	2	yes	—
64	C₂×C₄	C₂×D₁₃⋊C₃	1	1	yes	characteristic
65	C₂×C₃	—	13	2	no	—
66	C₂×C₃	—	13	1	no	—
67	C₂²	C₂²×D₁₃⋊C₃	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	—	13	4	no	—
70	C₄	—	26	2	no	—
71	C₄	(C₂²⋊D₁₃)⋊C₃	1	2	yes	—
72	C₃	—	13	1	no	Sylow
73	C₂	Q₈×D₁₃⋊C₃	1	2	yes	—
74	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	C₂²×C₁₃⋊C₃	C₂³
hypercenter	C₂×Q₈	D₁₃⋊C₃
hypocenter	C₁₃	C₃×C₄⋊Q₈
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
5. #88198	C₃	semidirect
20. Dic₁₃⋊C₃	Q₈	semidirect
34. Dic₁₃	C₃×Q₈	semidirect
39. C₁₃⋊C₃	C₄⋊Q₈	semidirect
53. C₁₃	C₃×C₄⋊Q₈	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×(C₁₃⋊C₃)⋊Q₈	2
#6101⋊C₃	2
C₄×Dic₁₃⋊C₃	2
#88198	3
C₃×C₄⋊Q₈	13

Subgroups — #88198⋊C3 #11928306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #88198⋊C₃ #11928306