Subgroups — #16834522

Order 3712.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#90770	C₂	1	2	yes	maximal
2	C₈×#6597	C₂	1	1	yes	maximal, characteristic
3	C₂×#90770	—	2	2	no	—
4	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
5	C₄×#6597	C₄	1	1	yes	characteristic
6	C₄×#6597	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₂₉	—	2	1	no	—
8	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₂×#6597	C₈	1	1	yes	characteristic
10	C₂×#6597	C₈	1	1	yes	characteristic
11	C₂×#6597	D₄	1	1	yes	characteristic
12	C₂×#6597	Q₈	1	1	yes	characteristic
13	#90770	—	4	2	no	—
14	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
17	C₈×C₂₉	—	2	2	no	—
18	#6597	—	2	1	no	—
19	#6597	—	2	1	no	—
20	#6597	C₁₆	1	2	yes	complemented
21	#6597	D₈	1	1	yes	characteristic
22	#6597	Q₁₆	1	1	yes	characteristic
23	#1370	—	29	1	no	maximal, Sylow
24	C₂²×C₂₉	C₄⋊C₈	1	1	yes	characteristic
25	C₄×C₂₉	—	2	1	no	—
26	C₄×C₂₉	#107	1	1	yes	characteristic
27	C₄×C₂₉	#108	1	1	yes	characteristic
28	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
29	C₄×C₂₉	M₃₂	1	1	yes	characteristic
30	C₄⋊C₁₆	—	29	2	no	—
31	C₈²	—	29	1	no	—
32	C₂×C₂₉	#335	1	1	yes	characteristic
33	C₂×C₂₉	C₄⋊C₁₆	1	1	yes	characteristic
34	C₂×C₂₉	#364	1	1	yes	characteristic
35	C₂×C₁₆	—	58	2	no	—
36	C₄×C₈	—	29	1	no	—
37	C₄×C₈	—	29	1	no	—
38	C₄×C₈	#1181	1	1	yes	characteristic
39	C₂₉	#1370	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₈	—	2	1	no	—
41	C₂×C₈	—	29	1	no	—
42	C₂×C₈	—	29	1	no	—
43	C₂×C₈	—	29	1	no	—
44	C₂×C₈	—	29	1	no	—
45	C₄²	C₂×#1181	1	1	yes	characteristic
46	C₁₆	—	116	2	no	—
47	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
48	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
49	C₂×C₄	#90800	1	1	yes	characteristic
50	C₈	—	2	2	no	—
51	C₈	—	29	2	no	—
52	C₈	—	29	1	no	—
53	C₈	—	29	1	no	—
54	C₈	—	58	1	no	—
55	C₈	—	58	1	no	—
56	C₂²	#11745220	1	1	yes	characteristic
57	C₄	—	2	1	no	—
58	C₄	D₂₉⋊C₁₆	1	1	yes	characteristic
59	C₄	#11745206	1	1	yes	characteristic
60	C₄	#11745210	1	1	yes	characteristic
61	C₄	#11745211	1	1	yes	characteristic
62	C₂	#14272027	1	1	yes	characteristic
63	C₂	#14272084	1	1	yes	characteristic
64	C₂	#14272086	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#1181
commutator	C₄×C₂₉	C₂×C₁₆
Frattini	C₄²	C₂×#1181
Fitting	C₄×C₈×C₂₉	C₄
socle, prime radical	C₂²×C₂₉	C₄⋊C₈
cosocle	C₄×#6597	C₂²
hypercenter	C₄×C₈	#1181
hypocenter	C₂₉	#1370
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
20. #6597	C₁₆	semidirect
39. C₂₉	#1370	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#90770	2
C₈×#6597	2
#1370	29