Subgroups — C₂×#10597713 #11929159

Order 1248.

98 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	#10597713	C₂	1	2	yes	maximal, direct product factor
3	C₂×#6131	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	Q₈⋊(C₁₃⋊C₃)	C₂²	1	1	yes	characteristic, complemented
5	C₂×Dic₁₃⋊C₃	—	4	1	no	maximal
6	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic
7	#6131	—	3	2	no	—
8	#6131	C₂×C₃	1	2	yes	complemented
9	C₂×D₅₂	—	3	1	no	—
10	C₂×C₄×D₁₃	—	3	1	no	—
11	C₂²×C₁₃⋊C₃	—	4	1	no	—
12	Dic₁₃⋊C₃	—	4	2	no	—
13	C₂²×D₁₃	—	3	1	no	—
14	Q₈×C₁₃	—	3	1	no	—
15	Q₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₄×C₁₃	—	3	1	no	—
17	C₂×Dic₁₃	A₄	1	1	yes	characteristic
18	D₅₂	—	3	2	no	—
19	D₅₂	—	3	2	no	—
20	C₄×D₁₃	—	3	2	no	—
21	C₄×D₁₃	—	3	2	no	—
22	C₂×#41⋊C₃	—	13	1	no	maximal, Hall
23	C₂×C₁₃⋊C₃	—	4	2	no	—
24	C₂×C₁₃⋊C₃	—	4	1	no	—
25	C₂²×C₁₃	C₂×A₄	1	1	yes	characteristic
26	C₂×D₁₃	—	3	2	no	—
27	C₂×D₁₃	—	6	2	no	—
28	C₄×C₁₃	—	3	1	no	—
29	C₄×C₁₃	—	3	1	no	—
30	Dic₁₃	C₂×A₄	1	2	yes	—
31	#41⋊C₃	—	13	2	no	—
32	C₂×SL(2,𝔽₃)	—	13	1	no	—
33	C₁₃⋊C₃	—	4	1	no	Hall
34	C₂×#41	—	13	1	no	Sylow
35	C₂×C₁₃	#41⋊C₃	1	2	yes	complemented
36	C₂×C₁₃	C₂²×A₄	1	1	yes	characteristic
37	D₁₃	—	6	2	no	—
38	C₂×C₃×C₄	—	52	1	no	—
39	SL(2,𝔽₃)	—	13	1	no	—
40	#41	—	13	2	no	—
41	#41	—	39	2	no	—
42	C₂×Q₈	D₁₃⋊C₃	1	1	yes	characteristic
43	C₂×D₄	—	39	1	no	—
44	C₂²×C₄	—	39	1	no	—
45	C₁₃	C₂×#41⋊C₃	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₃	—	52	1	no	—
47	C₃×C₄	—	52	2	no	—
48	C₂³	—	39	1	no	—
49	Q₈	—	3	1	no	—
50	Q₈	C₂×D₁₃⋊C₃	1	1	yes	characteristic
51	D₄	—	39	2	no	—
52	D₄	—	39	2	no	—
53	C₂×C₄	—	3	1	no	—
54	C₂×C₄	—	13	1	no	—
55	C₂×C₄	—	39	2	no	—
56	C₂×C₄	—	39	2	no	—
57	C₂×C₃	—	52	2	no	—
58	C₂×C₃	—	52	1	no	—
59	C₂²	—	39	2	no	—
60	C₂²	—	78	2	no	—
61	C₂²	D₁₃⋊A₄	1	1	yes	characteristic
62	C₄	—	3	1	no	—
63	C₄	—	3	1	no	—
64	C₄	—	13	2	no	—
65	C₃	—	52	1	no	Sylow
66	C₂	—	78	2	no	—
67	C₂	#10597713	1	2	yes	direct product factor
68	C₂	C₂×D₁₃⋊A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₁₃⋊A₄
commutator, cosocle, hypocenter	Q₈×C₁₃	C₂²×C₃
Frattini	C₂	C₂×D₁₃⋊A₄
Fitting	C₂×Q₈×C₁₃	C₂×C₃
socle	C₂²×C₁₃	C₂×A₄
LCS	G ▷ Q₈×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈⋊(C₁₃⋊C₃)	C₂	semidirect
2. #10597713	C₂	direct (N × H)
3. C₂×#6131	C₃	semidirect
4. Q₈⋊(C₁₃⋊C₃)	C₂²	semidirect
8. #6131	C₂×C₃	semidirect
35. C₂×C₁₃	#41⋊C₃	semidirect
45. C₁₃	C₂×#41⋊C₃	semidirect
67. C₂	#10597713	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×Q₈⋊(C₁₃⋊C₃)	2
#10597713	2
C₂×#6131	3
C₂×Dic₁₃⋊C₃	4
C₂×#41⋊C₃	13

Subgroups — C2×#10597713 #11929159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10597713 #11929159