Subgroups — #16821362

Order 3712.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₃₂	C₂	1	1	yes	maximal, characteristic
2	#14271257	C₂	1	2	yes	maximal
3	#14270966	C₂	1	2	yes	maximal
4	#14270938	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#367	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₆	C₂²	1	2	yes	—
7	#11745249	—	2	2	no	—
8	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
9	C₂₉×#107	C₂²	1	2	yes	—
10	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
11	C₂×#90768	C₂²	1	1	yes	characteristic
12	#11745158	—	2	2	no	—
13	Dic₂₃₂	C₄	1	4	yes	complemented
14	C₂×Dic₅₈	—	2	2	no	—
15	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₂₉	—	2	2	no	—
17	#90779	—	4	2	no	—
18	C₄×Dic₂₉	—	4	2	no	—
19	C₄×Dic₂₉	D₄	1	1	yes	characteristic
20	C₂×#6597	D₄	1	1	yes	characteristic
21	Dic₁₁₆	—	2	2	no	—
22	Dic₁₁₆	C₂×C₄	1	4	yes	—
23	C₁₆×C₂₉	C₂×C₄	1	2	yes	—
24	#90768	—	2	1	no	—
25	C₂×C₄×C₂₉	—	4	2	no	—
26	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₂₉	—	4	2	no	—
28	C₂×Dic₂₉	D₈	1	2	yes	—
29	Dic₅₈	—	2	4	no	—
30	Dic₅₈	—	4	2	no	—
31	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₂₉	#41	1	1	yes	characteristic
33	#6597	—	2	1	no	—
34	#2176	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
36	C₄×C₂₉	—	8	2	no	—
37	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
38	C₄×C₂₉	#135	1	1	yes	characteristic
39	Dic₂₉	—	2	2	no	—
40	Dic₂₉	—	4	4	no	—
41	C₂×Q₃₂	—	29	1	no	—
42	C₄×Q₁₆	—	29	2	no	—
43	#367	D₂₉	1	1	yes	characteristic
44	#358	—	29	2	no	—
45	#346	—	29	1	no	—
46	C₂×C₂₉	C₄×D₈	1	1	yes	characteristic
47	C₂×C₂₉	#510	1	2	yes	—
48	C₂×Q₁₆	—	29	2	no	—
49	C₄×Q₈	—	58	2	no	—
50	Q₃₂	—	29	4	no	—
51	C₂×C₁₆	—	29	1	no	—
52	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
53	#107	C₂×D₂₉	1	2	yes	—
54	#103	—	58	2	no	—
55	C₄×C₈	—	29	1	no	—
56	C₂₉	#2176	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	58	2	no	—
58	Q₁₆	—	29	4	no	—
59	Q₁₆	—	58	2	no	—
60	C₂×C₈	—	29	1	no	—
61	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
62	C₄⋊C₄	—	2	2	no	—
63	C₄⋊C₄	—	116	2	no	—
64	C₄²	—	29	1	no	—
65	C₄²	—	116	2	no	—
66	C₁₆	—	58	1	no	—
67	C₁₆	C₄×D₂₉	1	2	yes	—
68	Q₈	—	58	4	no	—
69	Q₈	—	116	2	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	29	2	no	—
72	C₂×C₄	—	116	2	no	—
73	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
74	C₈	—	58	1	no	—
75	C₈	C₂×C₄×D₂₉	1	1	yes	characteristic
76	C₈	#90809	1	1	yes	characteristic
77	C₂²	D₈×D₂₉	1	1	yes	characteristic
78	C₄	—	8	2	no	—
79	C₄	—	58	2	no	—
80	C₄	—	116	4	no	—
81	C₄	#11745255	1	1	yes	characteristic
82	C₄	#11745281	1	1	yes	characteristic
83	C₂	#14271245	1	1	yes	characteristic
84	C₂	#14271602	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₂₉
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂₉×#367	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₈
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	#367	D₂₉
hypocenter	C₂₉	#2176
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
13. Dic₂₃₂	C₄	semidirect
56. C₂₉	#2176	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₂₃₂	2
#14271257	2
#14270966	2
#14270938	2
C₂₉×#367	2
#2176	29