Subgroups — #16834619

Order 3712.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272072	C₂	1	1	yes	maximal, characteristic, complemented
2	#14272070	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271550	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#127	C₄	1	1	yes	characteristic, complemented
5	C₂×#90783	—	2	1	no	—
6	C₂×#90782	—	2	1	no	—
7	#11745237	C₂²	1	1	yes	characteristic
8	#11745221	—	2	1	no	—
9	#11745215	—	2	1	no	—
10	#11745151	C₄	1	1	yes	characteristic, complemented
11	C₂×D₄×C₂₉	—	2	1	no	—
12	C₂×D₄×C₂₉	—	4	1	no	—
13	C₂×D₁₁₆	D₄	1	1	yes	characteristic
14	C₂×Dic₅₈	D₄	1	1	yes	characteristic
15	C₂²⋊#1181	—	4	1	no	—
16	#90800	—	4	1	no	—
17	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
18	#90783	—	4	2	no	—
19	#90782	—	4	2	no	—
20	#90781	—	4	1	no	—
21	C₂×#6597	—	2	1	no	—
22	C₂³×C₂₉	—	4	1	no	—
23	C₂²×D₂₉	—	2	1	no	—
24	C₂×#1181	—	8	1	no	—
25	D₄×C₂₉	—	4	1	no	—
26	D₄×C₂₉	—	4	1	no	—
27	D₄×C₂₉	—	8	2	no	—
28	C₂×C₄×C₂₉	—	2	1	no	—
29	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×Dic₂₉	—	2	1	no	—
31	D₁₁₆	—	4	1	no	—
32	Dic₅₈	—	4	1	no	—
33	#6599	—	8	1	no	—
34	#6597	—	2	2	no	—
35	#1406	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	—	8	2	no	—
37	C₂²×C₂₉	—	8	1	no	—
38	C₂²×C₂₉	#99	1	1	yes	characteristic
39	C₂×D₂₉	—	4	1	no	—
40	C₂×D₂₉	—	8	1	no	—
41	#1181	—	16	1	no	—
42	C₄×C₂₉	—	2	1	no	—
43	C₄×C₂₉	—	4	1	no	—
44	Dic₂₉	—	4	1	no	—
45	#496	—	29	1	no	—
46	#355	—	29	1	no	—
47	#354	—	29	1	no	—
48	C₂×C₂₉	—	2	1	no	—
49	C₂×C₂₉	—	16	1	no	—
50	C₂×C₂₉	#353	1	1	yes	characteristic
51	D₂₉	—	8	1	no	—
52	C₂×SD₁₆	—	58	1	no	—
53	C₂×D₈	—	58	1	no	—
54	#127	#1181	1	1	yes	characteristic, complemented
55	#124	—	29	1	no	—
56	#101	—	58	1	no	—
57	#99	—	58	1	no	—
58	#97	—	29	1	no	—
59	C₂₉	#1406	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	29	1	no	—
61	C₂×D₄	—	2	1	no	—
62	C₂×D₄	—	4	1	no	—
63	C₂×D₄	—	29	1	no	—
64	SD₁₆	—	116	2	no	—
65	D₈	—	116	2	no	—
66	M₁₆	—	116	1	no	—
67	C₂×C₈	—	58	1	no	—
68	C₂²⋊C₄	—	116	1	no	—
69	C₂²⋊C₄	—	116	1	no	—
70	C₄²	C₂×#1181	1	1	yes	characteristic
71	C₂³	—	4	1	no	—
72	C₂³	—	58	1	no	—
73	Q₈	—	116	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	4	1	no	—
76	D₄	—	8	2	no	—
77	D₄	—	116	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	58	1	no	—
80	C₂×C₄	—	232	1	no	—
81	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
82	C₈	—	58	2	no	—
83	C₈	—	232	1	no	—
84	C₂²	—	8	2	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	116	1	no	—
87	C₂²	—	232	1	no	—
88	C₂²	#11745227	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	116	1	no	—
92	C₄	—	464	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	16	1	no	—
95	C₂	—	232	1	no	—
96	C₂	#14272067	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272067
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄²	C₂×#1181
Fitting	C₂₉×#127	C₄
socle	C₂×C₂₉	#353
prime radical	#14271550	C₂
cosocle	#11745237	C₂²
hypercenter	#127	#1181
hypocenter	C₂₉	#1406
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #14272072	C₂	semidirect
2. #14272070	C₂	semidirect
4. C₂₉×#127	C₄	semidirect
10. #11745151	C₄	semidirect
54. #127	#1181	semidirect
59. C₂₉	#1406	semidirect

Maximal subgroups

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

subgroup	index
#14272072	2
#14272070	2
#14271550	2
#1406	29