Subgroups — C₂×#11745252 #14271684

Order 1856.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₂₉	C₂	1	2	yes	maximal
3	C₂×C₄⋊Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#90779	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₂₉	C₂	1	1	yes	maximal, characteristic
6	#11745252	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×C₂₉	C₂²	1	2	yes	—
8	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₂₉	C₂²	1	1	yes	characteristic
10	C₂²×Dic₂₉	C₂²	1	1	yes	characteristic
11	C₂²×Dic₂₉	C₂²	1	2	yes	—
12	C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
13	C₄⋊Dic₂₉	C₂²	1	8	yes	—
14	C₄⋊Dic₂₉	C₂²	1	4	yes	—
15	#90779	C₂²	1	8	yes	—
16	C₄×Dic₂₉	C₂²	1	4	yes	—
17	C₂³×C₂₉	C₂³	1	1	yes	characteristic
18	C₂×C₄×C₂₉	—	2	4	no	—
19	C₂×C₄×C₂₉	Q₈	1	4	yes	—
20	C₂×C₄×C₂₉	C₂³	1	4	yes	—
21	C₂×C₄×C₂₉	C₂³	1	2	yes	—
22	C₂×Dic₂₉	—	2	2	no	—
23	C₂×Dic₂₉	—	2	2	no	—
24	C₂×Dic₂₉	—	2	4	no	—
25	C₂×Dic₂₉	C₂³	1	2	yes	—
26	C₂×Dic₂₉	C₂³	1	2	yes	—
27	C₂×Dic₂₉	C₂³	1	4	yes	—
28	C₂²×C₂₉	C₂×Q₈	1	2	yes	—
29	C₂²×C₂₉	#41	1	2	yes	—
30	C₂²×C₂₉	#41	1	2	yes	—
31	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
32	C₄×C₂₉	—	2	4	no	—
33	C₄×C₂₉	C₂×Q₈	1	4	yes	—
34	Dic₂₉	—	2	2	no	—
35	Dic₂₉	—	2	2	no	—
36	Dic₂₉	—	2	4	no	—
37	C₂×#125	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	#125	1	4	yes	complemented
39	C₂×C₂₉	C₂²×Q₈	1	1	yes	characteristic
40	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
41	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
42	#125	—	29	8	no	—
43	C₂×C₄⋊C₄	—	29	2	no	—
44	C₂×C₄⋊C₄	—	29	2	no	—
45	C₂×C₄⋊C₄	—	29	1	no	—
46	C₂×C₄⋊C₄	D₂₉	1	1	yes	characteristic
47	C₂×C₄²	—	29	1	no	—
48	C₂₉	C₂×#125	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₄	—	29	1	no	—
50	C₂²×C₄	—	29	1	no	—
51	C₂²×C₄	—	29	2	no	—
52	C₂²×C₄	C₂×D₂₉	1	2	yes	—
53	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
54	C₄⋊C₄	—	29	8	no	—
55	C₄⋊C₄	—	29	8	no	—
56	C₄⋊C₄	—	29	4	no	—
57	C₄⋊C₄	C₂×D₂₉	1	4	yes	—
58	C₄²	—	29	4	no	—
59	C₂³	C₂²×D₂₉	1	1	yes	characteristic
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	29	2	no	—
62	C₂×C₄	—	29	2	no	—
63	C₂×C₄	—	29	4	no	—
64	C₂×C₄	—	58	2	no	—
65	C₂×C₄	—	58	2	no	—
66	C₂×C₄	—	58	4	no	—
67	C₂×C₄	Dic₅₈	1	4	yes	—
68	C₂×C₄	C₂²×D₂₉	1	4	yes	—
69	C₂×C₄	C₂²×D₂₉	1	2	yes	—
70	C₂²	C₂×Dic₅₈	1	2	yes	—
71	C₂²	#90807	1	2	yes	—
72	C₂²	#90809	1	2	yes	—
73	C₂²	C₂³×D₂₉	1	1	yes	characteristic
74	C₄	—	2	4	no	—
75	C₄	—	58	2	no	—
76	C₄	—	58	2	no	—
77	C₄	—	58	4	no	—
78	C₄	C₂×Dic₅₈	1	4	yes	—
79	C₂	#11745252	1	4	yes	direct product factor
80	C₂	C₂²×Dic₅₈	1	1	yes	characteristic
81	C₂	C₂×#90807	1	1	yes	characteristic
82	C₂	C₂×#90809	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₉
commutator, cosocle	C₂²×C₂₉	C₂⁴
Frattini	C₂²	C₂³×D₂₉
Fitting	C₂×C₄⋊C₄×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₂³
hypercenter	C₂×C₄⋊C₄	D₂₉
hypocenter	C₂₉	C₂×#125
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #11745252	C₂	direct (N × H)
38. C₂×C₂₉	#125	semidirect
48. C₂₉	C₂×#125	semidirect
79. C₂	#11745252	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×C₄⋊C₄×C₂₉	2
C₂×C₄⋊Dic₂₉	2
C₂×#90779	2
C₂×C₄×Dic₂₉	2
#11745252	2
C₂×#125	29

Subgroups — C2×#11745252 #14271684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745252 #14271684