Subgroups — #14271224

Order 1856.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#117	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#6597	C₂	1	2	yes	maximal
3	C₄⋊#6597	C₂	1	2	yes	maximal, complemented
4	#11745151	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#6597	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₂₉	C₄	1	2	yes	—
8	C₂²⋊C₄×C₂₉	C₄	1	2	yes	—
9	C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×#6597	C₂²	1	2	yes	—
12	C₂×#6597	C₂²	1	2	yes	—
13	C₂³×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₉	—	2	2	no	—
15	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	#6597	—	2	2	no	—
20	#6597	—	2	2	no	—
21	C₂²×C₂₉	—	2	1	no	—
22	C₂²×C₂₉	—	2	2	no	—
23	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₉	—	2	1	no	—
25	C₄×C₂₉	—	2	2	no	—
26	C₄×C₂₉	—	2	2	no	—
27	C₄×C₂₉	#41	1	2	yes	—
28	#433	—	29	1	no	maximal, Sylow
29	C₂×C₂₉	—	4	1	no	—
30	C₂×C₂₉	#117	1	1	yes	characteristic
31	C₂×C₂₉	#131	1	2	yes	—
32	#117	D₂₉	1	1	yes	characteristic
33	C₄⋊C₈	—	29	2	no	—
34	C₂²⋊C₈	—	29	2	no	—
35	#97	—	29	1	no	—
36	C₄×C₈	—	29	1	no	—
37	C₂₉	#433	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
39	C₂×C₈	—	29	2	no	—
40	C₂×C₈	—	29	2	no	—
41	C₄⋊C₄	Dic₂₉	1	2	yes	—
42	C₂²⋊C₄	Dic₂₉	1	2	yes	—
43	C₄²	C₂×D₂₉	1	1	yes	characteristic
44	C₄²	C₂×D₂₉	1	1	yes	characteristic
45	C₂³	C₂×Dic₂₉	1	1	yes	characteristic
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	C₂×Dic₂₉	1	2	yes	—
48	C₂×C₄	C₂×Dic₂₉	1	2	yes	—
49	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
51	C₈	—	58	2	no	—
52	C₈	—	58	2	no	—
53	C₂²	—	2	1	no	—
54	C₂²	—	2	2	no	—
55	C₂²	C₂²×Dic₂₉	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	2	no	—
58	C₄	—	2	2	no	—
59	C₄	#90805	1	2	yes	—
60	C₂	—	4	1	no	—
61	C₂	#11745288	1	1	yes	characteristic
62	C₂	#11745310	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂²×C₄
Fitting	C₂₉×#117	C₂
prime radical	C₂³×C₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	#117	D₂₉
hypocenter	C₂₉	#433
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. C₄⋊#6597	C₂	semidirect
4. #11745151	C₂	semidirect
5. C₄×#6597	C₂	semidirect
37. C₂₉	#433	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#117	2
C₂²⋊#6597	2
C₄⋊#6597	2
#11745151	2
C₄×#6597	2
#433	29