Subgroups — #16817650

Order 3712.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271553	C₂	1	1	yes	maximal, characteristic
2	#14270958	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#124	C₂²	1	1	yes	characteristic
5	C₂×#90784	—	2	1	no	—
6	C₂×#90782	—	2	1	no	—
7	#11745236	C₄	1	1	yes	characteristic, complemented
8	C₂₉×#101	—	2	1	no	—
9	#11745182	—	2	1	no	—
10	#11745151	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
12	C₂×D₄×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	C₂²⋊C₄×C₂₉	—	4	1	no	—
17	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²⋊Dic₂₉	—	4	1	no	—
19	#90784	—	4	2	no	—
20	#90782	—	4	2	no	—
21	C₂×#6597	—	2	1	no	—
22	C₂³×C₂₉	—	2	1	no	—
23	C₂²×D₂₉	—	4	1	no	—
24	Q₈×C₂₉	—	4	1	no	—
25	D₄×C₂₉	—	4	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	C₂×Dic₂₉	—	8	1	no	—
30	D₁₁₆	—	4	1	no	—
31	D₁₁₆	—	4	1	no	—
32	D₁₁₆	—	8	2	no	—
33	C₈×C₂₉	—	8	1	no	—
34	#6597	—	2	2	no	—
35	#1406	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	—	4	1	no	—
37	C₂²×C₂₉	—	8	1	no	—
38	C₂²×C₂₉	#99	1	1	yes	characteristic
39	C₂×D₂₉	—	8	2	no	—
40	C₂×D₂₉	—	8	1	no	—
41	C₄×C₂₉	—	2	1	no	—
42	C₄×C₂₉	—	4	1	no	—
43	C₄×C₂₉	—	4	1	no	—
44	Dic₂₉	—	16	1	no	—
45	#496	—	29	1	no	—
46	#355	D₂₉	1	1	yes	characteristic, complemented
47	#354	—	29	1	no	—
48	C₂×C₂₉	—	2	1	no	—
49	C₂×C₂₉	—	8	1	no	—
50	C₂×C₂₉	#353	1	1	yes	characteristic
51	D₂₉	—	16	1	no	—
52	C₂×SD₁₆	—	58	1	no	—
53	C₂×D₈	—	58	1	no	—
54	#127	—	29	1	no	—
55	#124	C₂×D₂₉	1	1	yes	characteristic
56	#101	—	2	1	no	—
57	#99	—	58	1	no	—
58	#97	—	29	1	no	—
59	C₂₉	#1406	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	C₂²⋊D₂₉	1	1	yes	characteristic
61	C₂×D₄	—	58	1	no	—
62	C₂×D₄	—	116	1	no	—
63	C₂×D₄	D₁₁₆	1	1	yes	characteristic
64	SD₁₆	—	116	2	no	—
65	D₈	—	116	2	no	—
66	M₁₆	—	4	1	no	—
67	C₂×C₈	—	58	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	116	1	no	—
70	C₄²	C₄×D₂₉	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	116	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	116	1	no	—
76	D₄	—	116	1	no	—
77	D₄	—	232	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	232	1	no	—
81	C₂×C₄	#90781	1	1	yes	characteristic
82	C₈	—	8	1	no	—
83	C₈	—	58	2	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	232	2	no	—
87	C₂²	—	232	1	no	—
88	C₂²	#11745154	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	464	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	464	1	no	—
96	C₂	#14270955	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270955
commutator	C₄²×C₂₉	C₂×C₄
Frattini	#124	C₂×D₂₉
Fitting	C₂₉×#355	C₂
socle	C₂×C₂₉	#353
prime radical	#14271553	C₂
cosocle	C₂₉×#124	C₂²
hypercenter	#355	D₂₉
hypocenter	C₂₉	#1406
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
2. #14270958	C₂	semidirect
3. C₂₉×#355	C₂	semidirect
7. #11745236	C₄	semidirect
10. #11745151	C₄	semidirect
46. #355	D₂₉	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
#14271553	2
#14270958	2
C₂₉×#355	2
#1406	29