Subgroups — C₂²×#11745206 #16836455

Order 3712.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745206	C₂	1	12	yes	maximal, direct product factor
2	C₂²×#90770	C₂	1	2	yes	maximal, complemented
3	C₂²×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×D₂₉	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₂₉	C₄	1	1	yes	characteristic
6	C₂²×#6597	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₂₉	C₄	1	6	yes	—
8	C₂×C₈×D₂₉	C₂²	1	6	yes	—
9	C₂×#90770	C₂²	1	12	yes	complemented
10	#11745206	C₂²	1	16	yes	direct product factor
11	C₂³×D₂₉	C₈	1	1	yes	characteristic
12	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₂₉	C₈	1	1	yes	characteristic
14	C₂×C₄×D₂₉	C₈	1	6	yes	—
15	C₂×C₄×D₂₉	C₂×C₄	1	6	yes	—
16	C₂×C₈×C₂₉	C₂×C₄	1	6	yes	—
17	C₂×#6597	C₂×C₄	1	3	yes	—
18	C₂×#6597	C₂³	1	3	yes	—
19	C₈×D₂₉	C₂×C₄	1	12	yes	—
20	C₈×D₂₉	C₂³	1	4	yes	—
21	#90770	C₂³	1	8	yes	complemented
22	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
23	C₂²×D₂₉	—	2	4	no	—
24	C₂²×D₂₉	C₂×C₈	1	6	yes	—
25	C₂×C₄×C₂₉	C₂×C₈	1	3	yes	—
26	C₂×C₄×C₂₉	C₂²×C₄	1	3	yes	—
27	C₂×Dic₂₉	C₂×C₈	1	6	yes	—
28	C₄×D₂₉	C₂×C₈	1	12	yes	—
29	C₄×D₂₉	C₂²×C₄	1	4	yes	—
30	C₈×C₂₉	C₂²×C₄	1	4	yes	—
31	#6597	C₂²×C₄	1	3	yes	—
32	#6597	C₂⁴	1	1	yes	characteristic
33	C₂²×M₃₂	—	29	1	no	maximal, Sylow
34	C₂²×C₂₉	M₃₂	1	4	yes	complemented
35	C₂²×C₂₉	C₂²×C₈	1	3	yes	—
36	C₂×D₂₉	—	2	12	no	—
37	C₂×D₂₉	C₂²×C₈	1	4	yes	—
38	C₄×C₂₉	C₂²×C₈	1	3	yes	—
39	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
40	Dic₂₉	C₂²×C₈	1	4	yes	—
41	C₂³×C₈	—	29	1	no	—
42	C₂×M₃₂	—	29	12	no	—
43	C₂²×C₁₆	—	29	2	no	—
44	C₂×C₂₉	C₂×M₃₂	1	6	yes	complemented
45	C₂×C₂₉	C₂³×C₈	1	1	yes	characteristic
46	D₂₉	—	2	4	no	—
47	C₂³×C₄	—	29	1	no	—
48	C₂²×C₈	—	29	1	no	—
49	C₂²×C₈	—	29	6	no	—
50	C₂²×C₈	—	29	6	no	—
51	C₂²×C₈	#1181	1	1	yes	characteristic
52	M₃₂	—	29	16	no	—
53	C₂×C₁₆	—	29	12	no	—
54	C₂₉	C₂²×M₃₂	1	1	yes	characteristic, complemented, Sylow
55	C₂⁴	—	29	1	no	—
56	C₂²×C₄	—	29	1	no	—
57	C₂²×C₄	—	29	6	no	—
58	C₂²×C₄	—	29	6	no	—
59	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
60	C₂×C₈	—	29	3	no	—
61	C₂×C₈	—	29	3	no	—
62	C₂×C₈	—	29	4	no	—
63	C₂×C₈	—	29	12	no	—
64	C₂×C₈	C₂×#1181	1	6	yes	—
65	C₁₆	—	29	8	no	—
66	C₂³	—	29	6	no	—
67	C₂³	—	58	4	no	—
68	C₂³	D₂₉⋊C₈	1	1	yes	characteristic
69	C₂×C₄	—	29	6	no	—
70	C₂×C₄	—	29	12	no	—
71	C₂×C₄	—	29	4	no	—
72	C₂×C₄	D₂₉⋊C₈	1	3	yes	—
73	C₂×C₄	C₂²×#1181	1	3	yes	—
74	C₈	—	29	1	no	—
75	C₈	—	29	3	no	—
76	C₈	C₂²×#1181	1	4	yes	—
77	C₂²	—	29	4	no	—
78	C₂²	—	58	12	no	—
79	C₂²	#11745206	1	4	yes	direct product factor
80	C₂²	C₂×D₂₉⋊C₈	1	3	yes	—
81	C₄	—	29	4	no	—
82	C₄	C₂×D₂₉⋊C₈	1	3	yes	—
83	C₄	C₂³×#1181	1	1	yes	characteristic
84	C₂	—	58	4	no	—
85	C₂	C₂×#11745206	1	6	yes	direct product factor
86	C₂	C₂²×D₂₉⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×#1181
commutator	C₂×C₂₉	C₂³×C₈
Frattini	C₄	C₂³×#1181
Fitting	C₂²×C₈×C₂₉	C₄
socle	C₂³×C₂₉	C₂×C₈
prime radical	C₂³×D₂₉	C₈
cosocle	#6597	C₂⁴
hypercenter	C₂²×C₈	#1181
hypocenter	C₂₉	C₂²×M₃₂
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11745206	C₂	direct (N × H)
2. C₂²×#90770	C₂	semidirect
9. C₂×#90770	C₂²	semidirect
10. #11745206	C₂²	direct (N × H)
21. #90770	C₂³	semidirect
34. C₂²×C₂₉	M₃₂	semidirect
44. C₂×C₂₉	C₂×M₃₂	semidirect
54. C₂₉	C₂²×M₃₂	semidirect
79. C₂²	#11745206	direct (N × H)
85. C₂	C₂×#11745206	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×#11745206	2
C₂²×#90770	2
C₂²×C₈×D₂₉	2
C₂²×M₃₂	29

Subgroups — C22×#11745206 #16836455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11745206 #16836455