Subgroups — C₂×#14270993 #16821284

Order 3712.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745167	C₂	1	2	yes	maximal
2	#14270993	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×#90777	—	2	2	no	—
6	C₂×C₁₆×C₂₉	C₄	1	2	yes	—
7	C₂×C₁₆×C₂₉	C₄	1	2	yes	—
8	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
9	#11745167	—	2	2	no	—
10	#11745167	C₂²	1	4	yes	—
11	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
12	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
15	C₂×C₈×C₂₉	Q₈	1	1	yes	characteristic
16	C₂×C₈×C₂₉	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
18	#90777	—	2	4	no	—
19	#90777	—	4	2	no	—
20	C₂×#6597	—	4	2	no	—
21	C₁₆×C₂₉	C₂×C₄	1	4	yes	—
22	C₂³×C₂₉	Q₁₆	1	1	yes	characteristic
23	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
26	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
27	C₂×C₄×C₂₉	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
29	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
30	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
31	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
33	#6597	—	4	4	no	—
34	C₂×#368	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	—	2	2	no	—
36	C₂²×C₂₉	#107	1	1	yes	characteristic
37	C₂²×C₂₉	#107	1	1	yes	characteristic
38	C₂²×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
39	C₄×C₂₉	#107	1	1	yes	characteristic
40	C₄×C₂₉	#107	1	1	yes	characteristic
41	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
43	C₂²×C₁₆	D₂₉	1	1	yes	characteristic
44	C₂×#108	—	29	2	no	—
45	#368	—	29	4	no	—
46	C₂×C₂₉	—	2	1	no	—
47	C₂×C₂₉	—	2	1	no	—
48	C₂×C₂₉	#368	1	2	yes	complemented
49	C₂×C₂₉	C₂×#107	1	1	yes	characteristic
50	C₂×M₁₆	—	58	2	no	—
51	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
52	C₂×C₁₆	Dic₂₉	1	2	yes	—
53	C₂×C₁₆	Dic₂₉	1	2	yes	—
54	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
55	#108	—	29	4	no	—
56	#108	—	58	2	no	—
57	C₂₉	C₂×#368	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
59	M₁₆	—	58	4	no	—
60	M₁₆	—	116	2	no	—
61	C₂×C₈	—	116	2	no	—
62	C₂×C₈	Dic₅₈	1	1	yes	characteristic
63	C₂×C₈	Dic₅₈	1	1	yes	characteristic
64	C₂×C₈	D₁₁₆	1	1	yes	characteristic
65	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
66	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
67	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
68	C₁₆	C₂×Dic₂₉	1	4	yes	—
69	C₂³	Dic₁₁₆	1	1	yes	characteristic
70	C₂×C₄	D₂₃₂	1	1	yes	characteristic
71	C₂×C₄	D₂₃₂	1	1	yes	characteristic
72	C₂×C₄	Dic₁₁₆	1	1	yes	characteristic
73	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
74	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
75	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
76	C₈	—	116	4	no	—
77	C₈	C₄⋊Dic₂₉	1	1	yes	characteristic
78	C₈	C₄⋊Dic₂₉	1	1	yes	characteristic
79	C₈	C₂×Dic₅₈	1	1	yes	characteristic
80	C₈	C₂²×Dic₂₉	1	1	yes	characteristic
81	C₂²	—	2	2	no	—
82	C₂²	#11745166	1	1	yes	characteristic
83	C₂²	#11745166	1	1	yes	characteristic
84	C₂²	C₂×Dic₁₁₆	1	1	yes	characteristic
85	C₄	#11745166	1	1	yes	characteristic
86	C₄	#11745166	1	1	yes	characteristic
87	C₄	C₂×D₂₃₂	1	1	yes	characteristic
88	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	2	1	no	—
91	C₂	#14270993	1	2	yes	direct product factor
92	C₂	C₂×#11745166	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₂₃₂
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂²×C₁₆×C₂₉	C₂
socle	C₂²×C₂₉	#107
prime radical	C₂³×C₂₉	Q₁₆
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	C₂²×C₁₆	D₂₉
hypocenter	C₂₉	C₂×#368
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #14270993	C₂	direct (N × H)
48. C₂×C₂₉	#368	semidirect
57. C₂₉	C₂×#368	semidirect
91. C₂	#14270993	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×#11745167	2
#14270993	2
C₂²×C₁₆×C₂₉	2
C₂×#368	29

Subgroups — C2×#14270993 #16821284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14270993 #16821284