Subgroups — #16818781

Order 3712.

262 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271553	C₂	1	3	yes	maximal, complemented
2	#14270903	C₂	1	3	yes	maximal, complemented
3	C₂₉×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#124	—	2	3	no	—
5	C₂₉×#124	C₂²	1	3	yes	—
6	C₂₉×#120	—	2	3	no	—
7	C₂×#90784	—	2	3	no	—
8	C₂×#90782	—	2	3	no	—
9	#11745236	C₂²	1	1	yes	characteristic, complemented
10	#11745151	C₂²	1	3	yes	complemented
11	C₂⁴×C₂₉	—	2	1	no	—
12	C₂×Q₈×C₂₉	D₄	1	3	yes	—
13	C₂×D₄×C₂₉	—	2	3	no	—
14	C₂×D₄×C₂₉	D₄	1	3	yes	—
15	C₂×D₁₁₆	—	2	3	no	—
16	C₂²⋊C₄×C₂₉	—	2	3	no	—
17	C₂²⋊C₄×C₂₉	—	2	6	no	—
18	C₄²×C₂₉	—	2	1	no	—
19	C₄²×C₂₉	C₂³	1	1	yes	characteristic
20	#90784	—	4	6	no	—
21	#90782	—	4	6	no	—
22	C₂×#6597	—	2	3	no	—
23	C₂³×C₂₉	—	2	3	no	—
24	C₂³×C₂₉	—	8	3	no	—
25	C₂²×D₂₉	—	4	1	no	—
26	Q₈×C₂₉	—	4	3	no	—
27	D₄×C₂₉	—	4	3	no	—
28	D₄×C₂₉	—	8	3	no	—
29	C₂×C₄×C₂₉	—	2	3	no	—
30	C₂×C₄×C₂₉	C₂×D₄	1	3	yes	—
31	D₁₁₆	—	4	3	no	—
32	D₁₁₆	—	4	3	no	—
33	#6597	—	2	6	no	—
34	#1655	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	—	4	3	no	—
36	C₂²×C₂₉	—	4	6	no	—
37	C₂²×C₂₉	—	8	4	no	—
38	C₂²×C₂₉	#120	1	1	yes	characteristic
39	C₂×D₂₉	—	8	3	no	—
40	C₄×C₂₉	—	2	3	no	—
41	C₄×C₂₉	—	4	3	no	—
42	H(3,𝔽₄)	D₂₉	1	1	yes	characteristic, complemented
43	#496	—	29	3	no	—
44	#329	—	29	3	no	—
45	C₂×C₂₉	—	8	3	no	—
46	C₂×C₂₉	#453	1	3	yes	—
47	D₂₉	—	16	1	no	—
48	C₂×SD₁₆	—	58	3	no	—
49	C₂×D₈	—	58	3	no	—
50	#127	—	29	1	no	—
51	#124	—	2	3	no	—
52	#124	C₂×D₂₉	1	3	yes	—
53	#120	—	2	3	no	—
54	#97	—	29	3	no	—
55	C₂₉	#1655	1	1	yes	characteristic, complemented, Sylow
56	C₂⁴	—	2	1	no	—
57	C₂×Q₈	C₂²⋊D₂₉	1	3	yes	—
58	C₂×D₄	—	2	3	no	—
59	C₂×D₄	—	58	3	no	—
60	C₂×D₄	C₂²⋊D₂₉	1	3	yes	—
61	SD₁₆	—	116	6	no	—
62	D₈	—	116	6	no	—
63	C₂×C₈	—	58	3	no	—
64	C₂²⋊C₄	—	2	3	no	—
65	C₂²⋊C₄	—	2	6	no	—
66	C₄²	—	2	1	no	—
67	C₄²	C₂²×D₂₉	1	1	yes	characteristic
68	C₂³	—	2	3	no	—
69	C₂³	—	8	3	no	—
70	C₂³	—	116	1	no	—
71	Q₈	—	4	3	no	—
72	D₄	—	4	3	no	—
73	D₄	—	8	3	no	—
74	D₄	—	116	3	no	—
75	D₄	—	116	3	no	—
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	C₂×C₂²⋊D₂₉	1	3	yes	—
78	C₈	—	58	6	no	—
79	C₂²	—	4	3	no	—
80	C₂²	—	4	6	no	—
81	C₂²	—	8	4	no	—
82	C₂²	—	232	3	no	—
83	C₂²	#11745315	1	1	yes	characteristic
84	C₄	—	2	3	no	—
85	C₄	—	4	3	no	—
86	C₂	—	8	3	no	—
87	C₂	—	464	1	no	—
88	C₂	#14271331	1	3	yes	—

	subgroup	G/H
center	C₂²	#11745315
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×H(3,𝔽₄)	C₂
socle	C₂²×C₂₉	#120
hypercenter	H(3,𝔽₄)	D₂₉
hypocenter	C₂₉	#1655
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. #14271553	C₂	semidirect
2. #14270903	C₂	semidirect
3. C₂₉×H(3,𝔽₄)	C₂	semidirect
9. #11745236	C₂²	semidirect
10. #11745151	C₂²	semidirect
42. H(3,𝔽₄)	D₂₉	semidirect
55. C₂₉	#1655	semidirect

Maximal subgroups

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

subgroup	index
#14271553	2
#14270903	2
C₂₉×H(3,𝔽₄)	2
#1655	29