Subgroups — C₂×#11745151 #14271112

Order 1856.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6597	C₂	1	2	yes	maximal
3	#11745151	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₂₉	C₄	1	2	yes	—
5	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
6	C₄²×C₂₉	C₄	1	2	yes	—
7	C₄²×C₂₉	C₂²	1	2	yes	—
8	C₂×#6597	C₄	1	8	yes	complemented
9	C₂×#6597	C₂²	1	4	yes	—
10	C₂³×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₂₉	—	2	4	no	—
12	C₂×C₄×C₂₉	C₂×C₄	1	4	yes	—
13	C₂×C₄×C₂₉	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
16	#6597	C₂×C₄	1	8	yes	complemented
17	C₂²×C₂₉	C₄²	1	2	yes	—
18	C₂²×C₂₉	M₁₆	1	4	yes	—
19	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
20	C₄×C₂₉	—	2	4	no	—
21	C₄×C₂₉	C₄²	1	2	yes	—
22	C₄×C₂₉	C₂²×C₄	1	2	yes	—
23	C₂×#97	—	29	1	no	maximal, Sylow
24	C₂×C₂₉	#97	1	4	yes	complemented
25	C₂×C₂₉	C₂×C₄²	1	1	yes	characteristic
26	C₂×C₂₉	C₂×M₁₆	1	2	yes	—
27	C₂²×C₈	—	29	2	no	—
28	C₂×C₄²	D₂₉	1	1	yes	characteristic
29	#97	—	29	4	no	—
30	C₂₉	C₂×#97	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₄	Dic₂₉	1	2	yes	—
32	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
33	C₂×C₈	—	29	8	no	—
34	C₂×C₈	—	29	4	no	—
35	C₄²	Dic₂₉	1	2	yes	—
36	C₄²	C₂×D₂₉	1	2	yes	—
37	C₂³	C₂×Dic₂₉	1	1	yes	characteristic
38	C₂×C₄	—	2	4	no	—
39	C₂×C₄	C₄×D₂₉	1	4	yes	—
40	C₂×C₄	C₂×Dic₂₉	1	4	yes	—
41	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
42	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
43	C₈	—	29	8	no	—
44	C₂²	#90777	1	4	yes	—
45	C₂²	C₄×Dic₂₉	1	2	yes	—
46	C₂²	C₂²×Dic₂₉	1	1	yes	characteristic
47	C₄	—	2	4	no	—
48	C₄	C₄×Dic₂₉	1	2	yes	—
49	C₄	C₂×C₄×D₂₉	1	2	yes	—
50	C₂	#11745151	1	4	yes	direct product factor
51	C₂	C₂×#90777	1	2	yes	—
52	C₂	C₂×C₄×Dic₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₉
commutator	C₂×C₂₉	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂×C₄²×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₂×C₄²	D₂₉
hypocenter	C₂₉	C₂×#97
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. #11745151	C₂	direct (N × H)
8. C₂×#6597	C₄	semidirect
16. #6597	C₂×C₄	semidirect
24. C₂×C₂₉	#97	semidirect
30. C₂₉	C₂×#97	semidirect
50. C₂	#11745151	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₂₉	2
C₂²×#6597	2
#11745151	2
C₂×#97	29

Subgroups — C2×#11745151 #14271112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745151 #14271112