Subgroups — #16821748

Order 3712.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745148	C₂	1	4	yes	maximal, complemented
2	#14271543	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271540	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₁₁₆	—	2	1	no	—
6	C₂×Dic₁₁₆	C₂²	1	2	yes	—
7	C₂×D₂₃₂	—	2	1	no	—
8	C₂×D₂₃₂	C₂²	1	2	yes	—
9	#11745236	—	2	1	no	—
10	#11745231	—	2	1	no	—
11	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
12	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
13	#11745148	—	2	8	no	—
14	C₂×D₁₁₆	—	2	2	no	—
15	C₂×D₁₁₆	—	4	2	no	—
16	C₂×Dic₅₈	—	2	2	no	—
17	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
19	C₄²×C₂₉	D₄	1	1	yes	characteristic
20	C₄⋊Dic₂₉	—	4	2	no	—
21	Dic₁₁₆	—	2	4	no	—
22	Dic₁₁₆	—	4	2	no	—
23	D₂₃₂	—	2	4	no	—
24	D₂₃₂	—	4	2	no	—
25	C₁₆×C₂₉	D₄	1	4	yes	complemented
26	C₂²×D₂₉	—	4	2	no	—
27	C₂×C₄×C₂₉	D₈	1	2	yes	—
28	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₂₉	—	4	2	no	—
30	D₁₁₆	—	4	2	no	—
31	D₁₁₆	—	4	2	no	—
32	D₁₁₆	—	8	4	no	—
33	Dic₅₈	—	4	2	no	—
34	Dic₅₈	—	4	2	no	—
35	C₈×C₂₉	D₈	1	2	yes	—
36	C₈×C₂₉	C₂×D₄	1	2	yes	—
37	#2248	—	29	1	no	maximal, Sylow
38	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
39	C₂×D₂₉	—	8	2	no	—
40	C₂×D₂₉	—	8	4	no	—
41	C₄×C₂₉	SD₃₂	1	4	yes	complemented
42	C₄×C₂₉	#127	1	1	yes	characteristic
43	C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
44	Dic₂₉	—	8	2	no	—
45	C₂×SD₃₂	—	29	4	no	—
46	#494	—	29	1	no	—
47	#493	—	29	1	no	—
48	C₄×C₁₆	D₂₉	1	1	yes	characteristic, complemented
49	C₂×C₂₉	#493	1	1	yes	characteristic
50	C₂×C₂₉	C₂×SD₃₂	1	2	yes	—
51	D₂₉	—	16	2	no	—
52	C₂×Q₁₆	—	29	2	no	—
53	C₂×Q₁₆	—	58	1	no	—
54	C₂×D₈	—	29	2	no	—
55	C₂×D₈	—	58	1	no	—
56	C₄⋊Q₈	—	58	1	no	—
57	#127	—	58	1	no	—
58	SD₃₂	—	58	8	no	—
59	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
60	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
61	C₂₉	#2248	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	58	2	no	—
63	C₂×D₄	—	58	2	no	—
64	C₂×D₄	—	116	2	no	—
65	Q₁₆	—	58	4	no	—
66	Q₁₆	—	116	2	no	—
67	D₈	—	58	4	no	—
68	D₈	—	116	2	no	—
69	C₂×C₈	D₁₁₆	1	1	yes	characteristic
70	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
71	C₄⋊C₄	—	116	2	no	—
72	C₄²	D₁₁₆	1	1	yes	characteristic
73	C₁₆	D₁₁₆	1	4	yes	complemented
74	C₂³	—	116	2	no	—
75	Q₈	—	116	2	no	—
76	Q₈	—	116	2	no	—
77	D₄	—	116	2	no	—
78	D₄	—	116	2	no	—
79	D₄	—	232	4	no	—
80	C₂×C₄	—	116	2	no	—
81	C₂×C₄	D₂₃₂	1	2	yes	—
82	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
83	C₈	D₂₃₂	1	2	yes	—
84	C₈	C₂×D₁₁₆	1	2	yes	—
85	C₂²	—	232	2	no	—
86	C₂²	—	232	4	no	—
87	C₂²	C₂×D₂₃₂	1	1	yes	characteristic
88	C₄	—	232	2	no	—
89	C₄	#11745148	1	4	yes	complemented
90	C₄	#11745236	1	1	yes	characteristic
91	C₄	C₂×D₂₃₂	1	1	yes	characteristic
92	C₂	—	464	2	no	—
93	C₂	#14271540	1	1	yes	characteristic
94	C₂	C₂×#11745148	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₃₂
commutator, cosocle	C₂×C₈×C₂₉	C₂³
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₄×C₁₆×C₂₉	C₂
socle	C₂²×C₂₉	C₂×D₈
prime radical	#14271540	C₂
hypercenter	C₄×C₁₆	D₂₉
hypocenter	C₂₉	#2248
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#11745148	C₂	semidirect
2. #14271543	C₂	semidirect
4. C₄×C₁₆×C₂₉	C₂	semidirect
25. C₁₆×C₂₉	D₄	semidirect
41. C₄×C₂₉	SD₃₂	semidirect
48. C₄×C₁₆	D₂₉	semidirect
61. C₂₉	#2248	semidirect
73. C₁₆	D₁₁₆	semidirect
89. C₄	#11745148	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745148	2
#14271543	2
#14271540	2
C₄×C₁₆×C₂₉	2
#2248	29