Subgroups — #16819163

Order 3712.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271568	C₂	1	2	yes	maximal, complemented
2	#14271543	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271536	C₂	1	1	yes	maximal, characteristic
4	#14271510	C₂	1	2	yes	maximal
5	C₂₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₁₆	—	2	2	no	—
7	C₂×#90773	—	2	2	no	—
8	#11745236	C₂²	1	1	yes	characteristic
9	#11745231	C₂²	1	2	yes	—
10	#11745231	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₂₉	C₂²	1	2	yes	—
12	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
13	#11745169	—	2	4	no	—
14	#11745166	—	2	4	no	—
15	C₂×D₁₁₆	—	2	2	no	—
16	C₂×D₁₁₆	—	2	1	no	—
17	C₂×Dic₅₈	—	2	1	no	—
18	C₂×Dic₅₈	—	2	2	no	—
19	C₂×C₈×C₂₉	D₄	1	4	yes	—
20	C₂×C₈×C₂₉	D₄	1	2	yes	—
21	C₄²×C₂₉	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₂₉	—	2	2	no	—
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄⋊Dic₂₉	—	2	2	no	—
25	Dic₁₁₆	—	4	4	no	—
26	#90773	—	4	4	no	—
27	C₂²×D₂₉	—	4	1	no	—
28	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
30	C₂×Dic₂₉	—	4	1	no	—
31	C₂×Dic₂₉	—	4	2	no	—
32	D₁₁₆	—	4	2	no	—
33	D₁₁₆	—	4	4	no	—
34	Dic₅₈	—	4	2	no	—
35	Dic₅₈	—	4	4	no	—
36	C₈×C₂₉	—	2	4	no	—
37	C₈×C₂₉	D₈	1	4	yes	—
38	#1722	—	29	1	no	maximal, Sylow
39	C₂²×C₂₉	#127	1	1	yes	characteristic
40	C₂×D₂₉	—	8	1	no	—
41	C₂×D₂₉	—	8	2	no	—
42	C₄×C₂₉	C₂×D₈	1	2	yes	—
43	C₄×C₂₉	#137	1	4	yes	—
44	Dic₂₉	—	8	1	no	—
45	Dic₂₉	—	8	2	no	—
46	#500	—	29	2	no	—
47	#494	—	29	1	no	—
48	#492	—	29	1	no	—
49	#486	—	29	2	no	—
50	#322	D₂₉	1	1	yes	characteristic, complemented
51	C₂×C₂₉	#493	1	1	yes	characteristic
52	C₂×C₂₉	#497	1	2	yes	—
53	D₂₉	—	16	1	no	—
54	C₂×Q₁₆	—	58	2	no	—
55	C₂×SD₁₆	—	58	2	no	—
56	C₄⋊Q₈	—	29	2	no	—
57	C₄⋊Q₈	—	29	1	no	—
58	#127	—	29	1	no	—
59	#107	—	58	4	no	—
60	#102	—	58	4	no	—
61	C₄×C₈	C₂×D₂₉	1	2	yes	—
62	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
63	C₂₉	#1722	1	1	yes	characteristic, complemented, Sylow
64	C₂×Q₈	—	58	1	no	—
65	C₂×Q₈	—	58	2	no	—
66	C₂×D₄	—	58	2	no	—
67	C₂×D₄	—	58	1	no	—
68	Q₁₆	—	116	4	no	—
69	SD₁₆	—	116	4	no	—
70	C₂×C₈	D₁₁₆	1	4	yes	—
71	C₂×C₈	D₁₁₆	1	2	yes	—
72	C₄⋊C₄	—	58	2	no	—
73	C₄⋊C₄	—	58	2	no	—
74	C₄⋊C₄	—	58	2	no	—
75	C₄²	C₂²×D₂₉	1	1	yes	characteristic
76	C₂³	—	116	1	no	—
77	Q₈	—	116	2	no	—
78	Q₈	—	116	4	no	—
79	D₄	—	116	2	no	—
80	D₄	—	116	4	no	—
81	C₂×C₄	—	116	2	no	—
82	C₂×C₄	—	116	1	no	—
83	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
84	C₂×C₄	C₂×D₁₁₆	1	2	yes	—
85	C₈	—	2	4	no	—
86	C₈	D₂₃₂	1	4	yes	—
87	C₂²	—	232	1	no	—
88	C₂²	—	232	2	no	—
89	C₂²	#11745236	1	1	yes	characteristic
90	C₄	—	232	1	no	—
91	C₄	—	232	2	no	—
92	C₄	C₂×D₂₃₂	1	2	yes	—
93	C₄	#11745271	1	4	yes	—
94	C₂	—	464	1	no	—
95	C₂	#14271540	1	1	yes	characteristic
96	C₂	#14271557	1	2	yes	—

	subgroup	G/H
center	C₂²	#11745236
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#322	C₂
socle	C₂²×C₂₉	#127
prime radical	#11745236	C₂²
hypercenter	#322	D₂₉
hypocenter	C₂₉	#1722
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
1. #14271568	C₂	semidirect
2. #14271543	C₂	semidirect
5. C₂₉×#322	C₂	semidirect
50. #322	D₂₉	semidirect
63. C₂₉	#1722	semidirect

Maximal subgroups

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

subgroup	index
#14271568	2
#14271543	2
#14271536	2
#14271510	2
C₂₉×#322	2
#1722	29