Subgroups — #16827890

Order 3712.

648 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745231	C₂	1	6	yes	maximal
2	#14271033	C₂	1	8	yes	maximal
3	C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₅₈	C₂²	1	4	yes	—
5	C₂×C₄²×C₂₉	C₂²	1	3	yes	—
6	C₂×C₄²×C₂₉	C₂²	1	4	yes	—
7	C₂×C₄⋊Dic₂₉	C₂²	1	24	yes	—
8	#11745231	—	2	24	no	—
9	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₂₉	C₂³	1	6	yes	—
11	C₂²×Dic₂₉	C₂³	1	8	yes	—
12	C₂×Dic₅₈	—	2	24	no	—
13	C₄²×C₂₉	D₄	1	12	yes	—
14	C₄²×C₂₉	Q₈	1	16	yes	complemented
15	C₄⋊Dic₂₉	—	2	48	no	—
16	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂×D₄	1	6	yes	—
18	C₂×C₄×C₂₉	C₂×D₄	1	12	yes	—
19	C₂×C₄×C₂₉	C₂×Q₈	1	24	yes	—
20	C₂×Dic₂₉	—	2	24	no	—
21	Dic₅₈	—	4	16	no	—
22	#2868	—	29	1	no	maximal, Sylow
23	C₂²×C₂₉	C₂²×D₄	1	3	yes	—
24	C₂²×C₂₉	C₂²×Q₈	1	4	yes	—
25	C₄×C₂₉	#127	1	4	yes	—
26	C₄×C₂₉	C₄⋊Q₈	1	24	yes	complemented
27	Dic₂₉	—	4	8	no	—
28	C₂×C₄⋊Q₈	—	29	6	no	—
29	#384	—	29	8	no	—
30	C₄³	D₂₉	1	1	yes	characteristic
31	C₂×C₂₉	C₂×#127	1	1	yes	characteristic
32	C₂×C₂₉	C₂×C₄⋊Q₈	1	6	yes	—
33	C₂²×Q₈	—	29	4	no	—
34	C₄⋊Q₈	—	58	24	no	—
35	C₂×C₄⋊C₄	—	29	24	no	—
36	C₂×C₄²	C₂×D₂₉	1	4	yes	—
37	C₂×C₄²	C₂×D₂₉	1	3	yes	—
38	C₂₉	#2868	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₈	—	58	24	no	—
40	C₂²×C₄	—	29	8	no	—
41	C₂²×C₄	C₂²×D₂₉	1	6	yes	—
42	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
43	C₄⋊C₄	—	58	48	no	—
44	C₄²	Dic₅₈	1	16	yes	complemented
45	C₄²	D₁₁₆	1	12	yes	—
46	C₂³	C₂³×D₂₉	1	1	yes	characteristic
47	Q₈	—	116	16	no	—
48	C₂×C₄	—	58	24	no	—
49	C₂×C₄	C₂×Dic₅₈	1	24	yes	—
50	C₂×C₄	C₂×D₁₁₆	1	12	yes	—
51	C₂×C₄	C₂×D₁₁₆	1	6	yes	—
52	C₂²	C₂²×Dic₅₈	1	4	yes	—
53	C₂²	C₂²×D₁₁₆	1	3	yes	—
54	C₄	—	116	8	no	—
55	C₄	#11745231	1	24	yes	complemented
56	C₄	#11745236	1	4	yes	—
57	C₂	C₂×#11745236	1	1	yes	characteristic
58	C₂	C₂×#11745231	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator, socle, prime radical, cosocle	C₂³×C₂₉	C₂⁴
Fitting	C₄³×C₂₉	C₂
hypercenter	C₄³	D₂₉
hypocenter	C₂₉	#2868
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
14. C₄²×C₂₉	Q₈	semidirect
26. C₄×C₂₉	C₄⋊Q₈	semidirect
38. C₂₉	#2868	semidirect
44. C₄²	Dic₅₈	semidirect
55. C₄	#11745231	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745231	2
#14271033	2
C₄³×C₂₉	2
#2868	29