Subgroups — #16817658

Order 3712.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271537	C₂	1	1	yes	maximal, characteristic
2	#14270962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
5	C₂×#90784	—	2	1	no	—
6	C₂×#90784	—	2	1	no	—
7	#11745236	C₄	1	1	yes	characteristic
8	C₂₉×#101	—	2	1	no	—
9	#11745184	—	2	1	no	—
10	C₄×#6597	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
12	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
13	C₂×D₁₁₆	—	2	1	no	—
14	C₂×D₁₁₆	—	4	1	no	—
15	M₁₆×C₂₉	—	4	1	no	—
16	C₄⋊C₄×C₂₉	—	4	1	no	—
17	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
18	#90784	—	4	2	no	—
19	#90784	—	4	2	no	—
20	#90777	—	4	1	no	—
21	C₂×#6597	—	2	1	no	—
22	C₂²×D₂₉	—	4	1	no	—
23	Q₈×C₂₉	—	4	1	no	—
24	Q₈×C₂₉	—	4	1	no	—
25	C₂×C₄×C₂₉	—	2	1	no	—
26	C₂×C₄×C₂₉	—	2	1	no	—
27	C₂×C₄×C₂₉	—	2	1	no	—
28	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
29	D₁₁₆	—	4	1	no	—
30	D₁₁₆	—	4	1	no	—
31	D₁₁₆	—	8	2	no	—
32	C₈×C₂₉	—	8	1	no	—
33	#6597	—	2	2	no	—
34	#6597	—	8	1	no	—
35	#1410	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	#99	1	1	yes	characteristic
37	C₂×D₂₉	—	8	2	no	—
38	C₂×D₂₉	—	8	1	no	—
39	C₄×C₂₉	—	2	2	no	—
40	C₄×C₂₉	—	2	1	no	—
41	C₄×C₂₉	—	4	1	no	—
42	C₄×C₂₉	—	4	1	no	—
43	#492	—	29	1	no	—
44	#356	—	29	1	no	—
45	#356	D₂₉	1	1	yes	characteristic, complemented
46	C₂×C₂₉	—	2	1	no	—
47	C₂×C₂₉	#353	1	1	yes	characteristic
48	D₂₉	—	16	1	no	—
49	C₂×SD₁₆	—	58	1	no	—
50	C₂×SD₁₆	—	58	1	no	—
51	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
52	#127	—	29	1	no	—
53	#101	—	2	1	no	—
54	#101	—	58	1	no	—
55	C₄×C₈	—	29	1	no	—
56	C₂₉	#1410	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	D₁₁₆	1	1	yes	characteristic
58	C₂×Q₈	C₂²⋊D₂₉	1	1	yes	characteristic
59	C₂×D₄	—	58	1	no	—
60	C₂×D₄	—	116	1	no	—
61	SD₁₆	—	116	2	no	—
62	SD₁₆	—	116	2	no	—
63	M₁₆	—	4	1	no	—
64	M₁₆	—	116	1	no	—
65	C₂×C₈	—	58	1	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄²	C₄×D₂₉	1	1	yes	characteristic
68	C₂³	—	116	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	D₄	—	116	1	no	—
72	D₄	—	116	1	no	—
73	D₄	—	232	2	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	#90781	1	1	yes	characteristic
78	C₈	—	8	1	no	—
79	C₈	—	58	2	no	—
80	C₈	—	232	1	no	—
81	C₂²	—	232	2	no	—
82	C₂²	—	232	1	no	—
83	C₂²	#11745154	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	—	2	1	no	—
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	464	1	no	—
90	C₂	#14270955	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270955
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₂₉
Fitting	C₂₉×#356	C₂
socle	C₂×C₂₉	#353
prime radical	#11745236	C₄
cosocle	C₂₉×C₄⋊Q₈	C₂²
hypercenter	#356	D₂₉
hypocenter	C₂₉	#1410
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
2. #14270962	C₂	semidirect
3. C₂₉×#356	C₂	semidirect
45. #356	D₂₉	semidirect
56. C₂₉	#1410	semidirect

Maximal subgroups

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

subgroup	index
#14271537	2
#14270962	2
C₂₉×#356	2
#1410	29