Subgroups — #14271434

Order 1856.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745270	C₂	1	2	yes	maximal, complemented
2	C₂×D₂₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745263	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745171	C₂	1	2	yes	maximal, complemented
6	#90805	C₂²	1	1	yes	characteristic
7	C₂×D₁₁₆	C₂²	1	2	yes	—
8	M₁₆×C₂₉	C₂²	1	2	yes	—
9	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	#90777	C₂²	1	1	yes	characteristic
11	D₂₃₂	—	2	2	no	—
12	D₂₃₂	—	2	1	no	—
13	D₂₃₂	—	2	1	no	—
14	#90773	—	2	2	no	—
15	#90772	—	2	1	no	—
16	C₈×D₂₉	—	2	1	no	—
17	C₂²×D₂₉	—	2	2	no	—
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂²⋊D₂₉	—	2	1	no	—
20	D₁₁₆	—	2	2	no	—
21	D₁₁₆	—	2	2	no	—
22	D₁₁₆	D₄	1	1	yes	characteristic
23	C₄×D₂₉	—	2	1	no	—
24	Dic₅₈	D₄	1	1	yes	characteristic
25	C₈×C₂₉	—	2	2	no	—
26	C₈×C₂₉	D₄	1	1	yes	characteristic
27	C₈×C₂₉	D₄	1	1	yes	characteristic
28	#6597	—	2	1	no	—
29	C₂²×C₂₉	#41	1	1	yes	characteristic
30	C₂×D₂₉	—	2	1	no	—
31	C₂×D₂₉	—	4	2	no	—
32	C₂×D₂₉	—	8	2	no	—
33	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
35	Dic₂₉	—	2	1	no	—
36	#472	—	29	1	no	maximal, Sylow
37	C₂×C₂₉	—	2	1	no	—
38	C₂×C₂₉	#121	1	1	yes	characteristic
39	D₂₉	—	4	1	no	—
40	D₂₉	—	8	2	no	—
41	AGL(1,ℤ/8)	—	29	2	no	—
42	C₂×D₈	—	29	1	no	—
43	#131	—	29	1	no	—
44	#108	D₂₉	1	1	yes	characteristic, complemented
45	#100	—	29	2	no	—
46	C₂₉	#472	1	1	yes	characteristic, complemented, Sylow
47	#41	—	29	1	no	—
48	C₂×D₄	—	29	2	no	—
49	SD₁₆	—	58	2	no	—
50	D₈	—	58	2	no	—
51	D₈	—	58	1	no	—
52	D₈	—	58	1	no	—
53	M₁₆	—	29	1	no	—
54	M₁₆	—	58	1	no	—
55	M₁₆	C₂×D₂₉	1	2	yes	—
56	C₂×C₈	—	58	1	no	—
57	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
58	C₂³	—	58	2	no	—
59	Q₈	—	29	1	no	—
60	D₄	—	29	1	no	—
61	D₄	—	58	1	no	—
62	D₄	—	58	2	no	—
63	D₄	—	58	2	no	—
64	C₂×C₄	—	58	1	no	—
65	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	58	1	no	—
68	C₈	D₁₁₆	1	1	yes	characteristic
69	C₈	D₁₁₆	1	1	yes	characteristic
70	C₂²	—	58	1	no	—
71	C₂²	—	116	2	no	—
72	C₂²	—	232	2	no	—
73	C₂²	#90809	1	1	yes	characteristic
74	C₄	—	58	1	no	—
75	C₄	C₂×D₁₁₆	1	1	yes	characteristic
76	C₄	D₄×D₂₉	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	116	1	no	—
79	C₂	—	232	2	no	—
80	C₂	#11745257	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11745257
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#108	C₂
socle	C₂×C₂₉	#121
hypercenter	#108	D₂₉
hypocenter	C₂₉	#472
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
1. #11745270	C₂	semidirect
2. C₂×D₂₃₂	C₂	semidirect
3. #11745263	C₂	semidirect
4. C₂₉×#108	C₂	semidirect
5. #11745171	C₂	semidirect
44. #108	D₂₉	semidirect
46. C₂₉	#472	semidirect

Maximal subgroups

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

subgroup	index
#11745270	2
C₂×D₂₃₂	2
#11745263	2
C₂₉×#108	2
#11745171	2
#472	29