Subgroups — C₂×#14272091 #16835845

Order 3712.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745212	C₂	1	2	yes	maximal
2	#14272091	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#90796	—	2	2	no	—
5	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
6	#11745212	—	2	2	no	—
7	#11745212	C₂²	1	4	yes	—
8	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
9	C₂×#90768	C₄	1	1	yes	characteristic
10	C₁₆×D₂₉	C₄	1	2	yes	—
11	C₁₆×D₂₉	C₂²	1	2	yes	—
12	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
13	C₂×#6599	—	4	2	no	—
14	#90796	—	2	4	no	—
15	#90796	—	4	2	no	—
16	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×#6597	Q₈	1	1	yes	characteristic
18	C₈×D₂₉	C₂×C₄	1	1	yes	characteristic
19	C₈×D₂₉	D₄	1	1	yes	characteristic
20	C₈×D₂₉	Q₈	1	1	yes	characteristic
21	C₈×D₂₉	C₂³	1	1	yes	characteristic
22	C₁₆×C₂₉	C₂×C₄	1	2	yes	—
23	#90768	C₂×C₄	1	2	yes	—
24	C₂²×D₂₉	Q₁₆	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂×Dic₂₉	D₈	1	1	yes	characteristic
27	C₄×D₂₉	C₄⋊C₄	1	1	yes	characteristic
28	C₄×D₂₉	D₈	1	1	yes	characteristic
29	C₄×D₂₉	Q₁₆	1	1	yes	characteristic
30	C₄×D₂₉	C₂×D₄	1	1	yes	characteristic
31	#6599	—	4	4	no	—
32	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
33	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	#6597	C₄⋊C₄	1	1	yes	characteristic
35	#6597	C₂×Q₈	1	1	yes	characteristic
36	C₂×#368	—	29	1	no	maximal, Sylow
37	C₂²×C₂₉	#107	1	1	yes	characteristic
38	C₂×D₂₉	—	2	2	no	—
39	C₂×D₂₉	#107	1	1	yes	characteristic
40	C₂×D₂₉	C₂×Q₁₆	1	1	yes	characteristic
41	C₄×C₂₉	#107	1	1	yes	characteristic
42	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
43	Dic₂₉	#107	1	1	yes	characteristic
44	Dic₂₉	C₂×D₈	1	1	yes	characteristic
45	C₂²×C₁₆	—	29	1	no	—
46	C₂×#108	—	29	2	no	—
47	#368	—	29	4	no	—
48	C₂×C₂₉	#368	1	2	yes	complemented
49	C₂×C₂₉	C₂×#107	1	1	yes	characteristic
50	D₂₉	—	2	1	no	—
51	D₂₉	—	2	1	no	—
52	C₂×M₁₆	—	58	2	no	—
53	C₂²×C₈	—	29	1	no	—
54	C₂×C₁₆	—	29	1	no	—
55	C₂×C₁₆	—	29	2	no	—
56	C₂×C₁₆	—	29	2	no	—
57	C₂×C₁₆	#1181	1	1	yes	characteristic
58	#108	—	29	4	no	—
59	#108	—	58	2	no	—
60	C₂₉	C₂×#368	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	—	29	1	no	—
62	M₁₆	—	58	4	no	—
63	M₁₆	—	116	2	no	—
64	C₂×C₈	—	29	1	no	—
65	C₂×C₈	—	29	1	no	—
66	C₂×C₈	—	29	1	no	—
67	C₂×C₈	—	29	1	no	—
68	C₂×C₈	—	29	1	no	—
69	C₂×C₈	—	116	2	no	—
70	C₂×C₈	C₂×#1181	1	1	yes	characteristic
71	C₁₆	—	29	2	no	—
72	C₁₆	C₂×#1181	1	2	yes	—
73	C₂³	—	29	1	no	—
74	C₂×C₄	—	29	1	no	—
75	C₂×C₄	—	29	1	no	—
76	C₂×C₄	—	29	1	no	—
77	C₂×C₄	—	29	1	no	—
78	C₂×C₄	—	29	1	no	—
79	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
80	C₈	—	29	1	no	—
81	C₈	—	29	1	no	—
82	C₈	—	116	4	no	—
83	C₈	C₄⋊#1181	1	1	yes	characteristic
84	C₈	C₂²×#1181	1	1	yes	characteristic
85	C₂²	—	29	1	no	—
86	C₂²	—	29	1	no	—
87	C₂²	—	58	2	no	—
88	C₂²	#11745210	1	1	yes	characteristic
89	C₄	—	29	1	no	—
90	C₄	—	29	1	no	—
91	C₄	#11745210	1	1	yes	characteristic
92	C₄	C₂×C₄⋊#1181	1	1	yes	characteristic
93	C₂	—	58	1	no	—
94	C₂	—	58	1	no	—
95	C₂	#14272091	1	2	yes	direct product factor
96	C₂	C₂×#11745210	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745210
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₈	C₂²×#1181
Fitting	C₂×C₁₆×C₂₉	C₄
socle	C₂²×C₂₉	#107
prime radical	C₂²×D₂₉	Q₁₆
cosocle	C₈×D₂₉	C₂³
hypercenter	C₂×C₁₆	#1181
hypocenter	C₂₉	C₂×#368
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #14272091	C₂	direct (N × H)
48. C₂×C₂₉	#368	semidirect
60. C₂₉	C₂×#368	semidirect
95. C₂	#14272091	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11745212	2
#14272091	2
C₂×C₁₆×D₂₉	2
C₂×#368	29

Subgroups — C2×#14272091 #16835845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14272091 #16835845