Subgroups — #16835895

Order 3712.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272207	C₂	1	2	yes	maximal, complemented
2	#14272092	C₂	1	1	yes	maximal, characteristic, complemented
3	#14272078	C₂	1	2	yes	maximal, complemented
4	#14272050	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271596	C₂	1	1	yes	maximal, characteristic
6	#11745348	—	2	2	no	—
7	#11745281	C₂²	1	2	yes	—
8	#11745226	—	2	2	no	—
9	#11745212	C₂²	1	2	yes	—
10	C₈×#1181	C₂²	1	1	yes	characteristic
11	D₂₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₂₉×Q₃₂	C₄	1	1	yes	characteristic, complemented
13	#11745176	C₄	1	2	yes	complemented
14	D₄₆₄	C₄	1	1	yes	characteristic, complemented
15	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
16	#90809	—	2	2	no	—
17	C₄×#1181	D₄	1	1	yes	characteristic
18	#90796	—	2	2	no	—
19	#90796	—	4	2	no	—
20	D₂₉⋊C₈	—	4	2	no	—
21	D₂₉⋊C₈	D₄	1	1	yes	characteristic
22	Q₁₆×C₂₉	C₂×C₄	1	2	yes	—
23	#90784	—	2	2	no	—
24	D₂₃₂	C₂×C₄	1	2	yes	—
25	C₈×D₂₉	C₂³	1	1	yes	characteristic
26	#90770	—	2	1	no	—
27	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
28	#90768	C₂×C₄	1	1	yes	characteristic
29	C₂×#1181	—	2	1	no	—
30	Q₈×C₂₉	—	2	2	no	—
31	D₁₁₆	—	2	2	no	—
32	D₁₁₆	—	4	2	no	—
33	C₄×D₂₉	—	4	2	no	—
34	C₄×D₂₉	C₂×D₄	1	1	yes	characteristic
35	#6599	—	4	2	no	—
36	#6599	D₈	1	2	yes	—
37	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
38	#6597	#41	1	1	yes	characteristic
39	#2179	—	29	1	no	maximal, Sylow
40	C₂×D₂₉	—	4	2	no	—
41	C₂×D₂₉	#135	1	1	yes	characteristic
42	#1181	—	4	1	no	—
43	C₄×C₂₉	—	4	2	no	—
44	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
45	Dic₂₉	C₂×D₈	1	1	yes	characteristic
46	#508	—	29	1	no	—
47	#443	—	29	2	no	—
48	#368	—	29	1	no	—
49	#359	—	29	2	no	—
50	#346	—	29	1	no	—
51	C₂×C₂₉	C₄×D₈	1	1	yes	characteristic
52	D₂₉	—	2	1	no	—
53	D₂₉	—	8	2	no	—
54	#135	—	29	2	no	—
55	#131	—	58	2	no	—
56	Q₃₂	#1181	1	1	yes	characteristic, complemented
57	SD₃₂	—	29	2	no	—
58	D₁₆	—	29	1	no	—
59	C₂×C₁₆	—	29	1	no	—
60	C₂×C₁₆	—	29	1	no	—
61	#108	—	29	2	no	—
62	#104	—	58	2	no	—
63	C₄×C₈	—	29	1	no	—
64	C₂₉	#2179	1	1	yes	characteristic, complemented, Sylow
65	#41	—	58	2	no	—
66	Q₁₆	C₂×#1181	1	2	yes	—
67	SD₁₆	—	58	2	no	—
68	D₈	—	29	2	no	—
69	M₁₆	—	58	2	no	—
70	M₁₆	—	116	2	no	—
71	C₂×C₈	—	29	1	no	—
72	C₂×C₈	—	29	1	no	—
73	C₂×C₈	—	116	2	no	—
74	C₄²	—	29	1	no	—
75	C₁₆	—	29	1	no	—
76	C₁₆	—	58	1	no	—
77	C₁₆	C₂×#1181	1	1	yes	characteristic
78	Q₈	—	2	2	no	—
79	D₄	—	58	2	no	—
80	D₄	—	116	2	no	—
81	C₂×C₄	—	29	1	no	—
82	C₂×C₄	—	58	1	no	—
83	C₂×C₄	—	116	2	no	—
84	C₈	—	29	2	no	—
85	C₈	—	29	1	no	—
86	C₈	—	116	2	no	—
87	C₈	C₂²×#1181	1	1	yes	characteristic
88	C₂²	—	29	1	no	—
89	C₂²	—	116	2	no	—
90	C₄	—	4	2	no	—
91	C₄	—	29	1	no	—
92	C₄	—	116	1	no	—
93	C₄	D₄×#1181	1	1	yes	characteristic
94	C₂	—	58	1	no	—
95	C₂	—	232	2	no	—
96	C₂	D₈×#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×#1181
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₈	C₂²×#1181
Fitting	C₂₉×Q₃₂	C₄
socle	C₂×C₂₉	C₄×D₈
prime radical	#14271596	C₂
cosocle	C₈×D₂₉	C₂³
hypercenter	Q₃₂	#1181
hypocenter	C₂₉	#2179
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #14272207	C₂	semidirect
2. #14272092	C₂	semidirect
3. #14272078	C₂	semidirect
4. #14272050	C₂	semidirect
12. C₂₉×Q₃₂	C₄	semidirect
13. #11745176	C₄	semidirect
14. D₄₆₄	C₄	semidirect
56. Q₃₂	#1181	semidirect
64. C₂₉	#2179	semidirect

Maximal subgroups

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

subgroup	index
#14272207	2
#14272092	2
#14272078	2
#14272050	2
#14271596	2
#2179	29