Subgroups — #14272213

Order 1856.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745249	C₂	1	1	yes	maximal, characteristic
2	#11745218	C₂	1	2	yes	maximal
3	C₄⋊#6599	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#6599	C₂	1	2	yes	maximal
5	C₄×#6599	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₅₈	C₄	1	1	yes	characteristic
7	C₂×#6599	C₂²	1	1	yes	characteristic
8	C₂×#6599	C₂²	1	2	yes	—
9	C₂×#6599	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
11	#90779	C₄	1	2	yes	—
12	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₄×Dic₂₉	C₂²	1	2	yes	—
14	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₂₉	C₂×C₄	1	2	yes	—
18	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
19	Dic₅₈	—	2	2	no	—
20	#6599	—	2	1	no	—
21	#6599	—	2	2	no	—
22	#6599	Q₈	1	2	yes	complemented
23	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₉	—	2	2	no	—
25	C₄×C₂₉	M₁₆	1	2	yes	—
26	Dic₂₉	—	2	2	no	—
27	Dic₂₉	—	2	1	no	—
28	Dic₂₉	C₂×Q₈	1	1	yes	characteristic
29	Dic₂₉	#41	1	1	yes	characteristic
30	#446	—	29	1	no	maximal, Sylow
31	C₂×C₂₉	C₄×Q₈	1	1	yes	characteristic
32	C₂×C₂₉	C₂×M₁₆	1	1	yes	characteristic
33	C₂×C₂₉	#131	1	1	yes	characteristic
34	C₄×Q₈	—	29	1	no	—
35	C₄⋊C₈	—	29	1	no	—
36	C₄⋊C₈	—	29	2	no	—
37	#97	—	29	2	no	—
38	C₄×C₈	—	29	1	no	—
39	C₂₉	#446	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	29	1	no	—
41	C₂×C₈	—	29	1	no	—
42	C₂×C₈	—	29	1	no	—
43	C₂×C₈	—	29	2	no	—
44	C₄⋊C₄	—	29	2	no	—
45	C₄⋊C₄	#1181	1	1	yes	characteristic
46	C₄²	—	29	1	no	—
47	C₄²	—	29	2	no	—
48	Q₈	—	58	2	no	—
49	C₂×C₄	—	29	1	no	—
50	C₂×C₄	—	29	1	no	—
51	C₂×C₄	—	29	2	no	—
52	C₂×C₄	C₂×#1181	1	2	yes	—
53	C₂×C₄	C₂×#1181	1	1	yes	characteristic
54	C₈	—	29	2	no	—
55	C₈	—	58	1	no	—
56	C₈	—	58	2	no	—
57	C₂²	C₂²×#1181	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	29	1	no	—
60	C₄	—	29	1	no	—
61	C₄	—	58	2	no	—
62	C₄	—	58	1	no	—
63	C₄	#90796	1	2	yes	—
64	C₂	C₂×#90796	1	1	yes	characteristic
65	C₂	#11745346	1	1	yes	characteristic
66	C₂	Q₈×#1181	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#1181
commutator, socle, prime radical	C₂²×C₂₉	C₂²×C₄
Fitting	C₄⋊C₄×C₂₉	C₄
cosocle	C₂×Dic₂₉	C₂³
hypercenter	C₄⋊C₄	#1181
hypocenter	C₂₉	#446
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
22. #6599	Q₈	semidirect
39. C₂₉	#446	semidirect

Maximal subgroups

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

subgroup	index
#11745249	2
#11745218	2
C₄⋊#6599	2
C₄×#6599	2
#446	29