Subgroups — #16821743

Order 3712.

176 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	C₂×#11745177	C₂	1	2	yes	maximal
3	#14271541	C₂	1	2	yes	maximal
4	C₁₆×Dic₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₉×Q₃₂	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₂₉	C₂²	1	2	yes	—
7	#11745306	—	2	2	no	—
8	C₂×#90785	—	2	2	no	—
9	C₂×Dic₁₁₆	C₂²	1	2	yes	—
10	C₂₉×Q₃₂	—	2	2	no	—
11	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
12	#11745177	—	2	4	no	—
13	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂×#90768	C₂²	1	1	yes	characteristic
15	Dic₂₃₂	—	2	2	no	—
16	C₂×Q₈×C₂₉	—	2	2	no	—
17	C₂×Dic₅₈	—	2	2	no	—
18	Q₁₆×C₂₉	—	2	2	no	—
19	Q₁₆×C₂₉	—	2	2	no	—
20	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
21	#90785	—	4	4	no	—
22	#90779	—	4	4	no	—
23	C₄×Dic₂₉	D₄	1	1	yes	characteristic
24	C₂×#6597	D₄	1	1	yes	characteristic
25	Dic₁₁₆	—	2	2	no	—
26	Dic₁₁₆	—	2	2	no	—
27	C₁₆×C₂₉	D₄	1	2	yes	—
28	#90768	D₄	1	2	yes	—
29	Q₈×C₂₉	—	4	2	no	—
30	Q₈×C₂₉	—	4	2	no	—
31	C₂×C₄×C₂₉	—	4	2	no	—
32	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₂₉	—	4	2	no	—
34	C₂×Dic₂₉	D₈	1	2	yes	—
35	Dic₅₈	—	4	2	no	—
36	Dic₅₈	—	4	2	no	—
37	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
39	#6597	D₈	1	2	yes	—
40	#2247	—	29	1	no	maximal, Sylow
41	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
42	C₄×C₂₉	—	8	2	no	—
43	C₄×C₂₉	#127	1	1	yes	characteristic
44	C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
45	Dic₂₉	—	8	2	no	—
46	Dic₂₉	Q₃₂	1	4	yes	complemented
47	C₂×Q₃₂	—	29	2	no	—
48	C₂×Q₃₂	—	29	1	no	—
49	C₂×Q₃₂	D₂₉	1	1	yes	characteristic
50	#494	—	29	2	no	—
51	C₄×C₁₆	—	29	1	no	—
52	C₂×C₂₉	#493	1	1	yes	characteristic
53	C₂×C₂₉	C₂×Q₃₂	1	2	yes	—
54	C₂×Q₁₆	—	29	2	no	—
55	C₂×Q₁₆	—	58	2	no	—
56	C₂×Q₁₆	C₂×D₂₉	1	2	yes	—
57	C₄⋊Q₈	—	58	2	no	—
58	Q₃₂	—	2	2	no	—
59	Q₃₂	—	58	4	no	—
60	Q₃₂	—	58	2	no	—
61	C₂×C₁₆	—	29	1	no	—
62	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
63	C₄×C₈	—	29	1	no	—
64	C₂₉	#2247	1	1	yes	characteristic, complemented, Sylow
65	C₂×Q₈	—	2	2	no	—
66	C₂×Q₈	—	58	2	no	—
67	Q₁₆	—	2	2	no	—
68	Q₁₆	—	2	2	no	—
69	Q₁₆	—	58	2	no	—
70	Q₁₆	—	58	2	no	—
71	Q₁₆	—	116	4	no	—
72	C₂×C₈	—	29	1	no	—
73	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
74	C₄⋊C₄	—	116	4	no	—
75	C₄²	—	29	1	no	—
76	C₁₆	—	29	2	no	—
77	C₁₆	C₂²⋊D₂₉	1	2	yes	—
78	Q₈	—	4	2	no	—
79	Q₈	—	4	2	no	—
80	Q₈	—	116	2	no	—
81	Q₈	—	116	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	29	2	no	—
84	C₂×C₄	—	116	2	no	—
85	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
86	C₈	—	29	2	no	—
87	C₈	D₄×D₂₉	1	1	yes	characteristic
88	C₈	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
89	C₂²	D₈×D₂₉	1	1	yes	characteristic
90	C₄	—	8	2	no	—
91	C₄	—	29	4	no	—
92	C₄	—	232	2	no	—
93	C₄	D₈×D₂₉	1	1	yes	characteristic
94	C₄	#11745302	1	1	yes	characteristic
95	C₂	#14271538	1	1	yes	characteristic
96	C₂	Q₃₂×D₂₉	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₂₉
commutator, cosocle	C₂×C₈×C₂₉	C₂³
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂×C₂₉×Q₃₂	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₈
hypercenter	C₂×Q₃₂	D₂₉
hypocenter	C₂₉	#2247
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
46. Dic₂₉	Q₃₂	semidirect
64. C₂₉	#2247	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
C₂×#11745177	2
#14271541	2
C₁₆×Dic₂₉	2
C₂×C₂₉×Q₃₂	2
#2247	29