Subgroups — C₂×#14272221 #16836456

Order 3712.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272221	C₂	1	8	yes	maximal, direct product factor
2	C₂×#11745214	C₂	1	3	yes	maximal, complemented
3	C₂²×#90770	C₂	1	3	yes	maximal, complemented
4	C₂×#11745310	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₂₉	C₄	1	1	yes	characteristic
6	#11745310	C₄	1	4	yes	—
7	#11745310	C₂²	1	4	yes	—
8	C₂×#90777	C₄	1	3	yes	—
9	C₂²×#6597	C₂²	1	3	yes	—
10	#11745214	C₂²	1	12	yes	complemented
11	C₂×#90770	C₂²	1	1	yes	characteristic
12	C₂×#90770	C₂²	1	3	yes	—
13	C₂×#90770	C₂²	1	12	yes	complemented
14	#41×C₂₉	C₈	1	4	yes	—
15	#41×C₂₉	C₂×C₄	1	4	yes	—
16	C₂×Q₈×C₂₉	C₈	1	1	yes	characteristic
17	C₂×D₄×C₂₉	C₈	1	3	yes	—
18	C₂²×C₄×C₂₉	C₂×C₄	1	3	yes	—
19	#90777	C₂×C₄	1	12	yes	—
20	C₂×#6597	C₂×C₄	1	3	yes	—
21	C₂×#6597	C₂×C₄	1	6	yes	—
22	C₂×#6597	C₂³	1	1	yes	characteristic
23	C₂×#6597	C₂³	1	6	yes	—
24	#90770	C₂³	1	2	yes	—
25	#90770	C₂³	1	6	yes	—
26	C₂³×C₂₉	C₂×C₈	1	3	yes	—
27	Q₈×C₂₉	C₂×C₈	1	4	yes	—
28	D₄×C₂₉	C₂×C₈	1	12	yes	—
29	C₂×C₄×C₂₉	C₂×C₈	1	3	yes	—
30	C₂×C₄×C₂₉	C₂×C₈	1	6	yes	—
31	C₂×C₄×C₂₉	C₂²×C₄	1	6	yes	—
32	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
33	#6597	C₂²×C₄	1	1	yes	characteristic
34	#6597	C₂²×C₄	1	6	yes	—
35	#6597	C₂⁴	1	1	yes	characteristic
36	C₂×#504	—	29	1	no	maximal, Sylow
37	C₂²×C₂₉	—	2	6	no	—
38	C₂²×C₂₉	C₂²×C₈	1	6	yes	—
39	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
41	C₄×C₂₉	C₂²×C₈	1	6	yes	—
42	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
43	C₂×#131	—	29	1	no	—
44	#504	—	29	8	no	—
45	C₂×M₃₂	—	29	3	no	—
46	C₂²×C₁₆	—	29	3	no	—
47	C₂×C₂₉	—	2	6	no	—
48	C₂×C₂₉	#504	1	2	yes	complemented
49	C₂×C₂₉	C₂³×C₈	1	1	yes	characteristic
50	C₂×#41	#1181	1	1	yes	characteristic
51	#131	—	29	4	no	—
52	#131	—	29	4	no	—
53	C₂×M₁₆	—	29	3	no	—
54	C₂²×C₈	—	29	3	no	—
55	M₃₂	—	29	12	no	—
56	C₂×C₁₆	—	29	1	no	—
57	C₂×C₁₆	—	29	3	no	—
58	C₂×C₁₆	—	29	12	no	—
59	C₂₉	C₂×#504	1	1	yes	characteristic, complemented, Sylow
60	#41	#6599	1	4	yes	—
61	#41	C₂×#1181	1	4	yes	—
62	C₂×Q₈	#6599	1	1	yes	characteristic
63	C₂×D₄	#6599	1	3	yes	—
64	C₂²×C₄	C₂×#1181	1	3	yes	—
65	M₁₆	—	29	12	no	—
66	C₂×C₈	—	29	6	no	—
67	C₂×C₈	—	29	6	no	—
68	C₂×C₈	—	29	1	no	—
69	C₂×C₈	—	29	3	no	—
70	C₁₆	—	29	2	no	—
71	C₁₆	—	29	6	no	—
72	C₂³	C₂×#6599	1	3	yes	—
73	Q₈	C₂×#6599	1	4	yes	—
74	D₄	C₂×#6599	1	12	yes	—
75	C₂×C₄	C₂×#6599	1	3	yes	—
76	C₂×C₄	C₂×#6599	1	6	yes	—
77	C₂×C₄	C₂²×#1181	1	6	yes	—
78	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
79	C₈	—	29	1	no	—
80	C₈	—	29	1	no	—
81	C₈	—	29	6	no	—
82	C₂²	—	2	6	no	—
83	C₂²	C₂²×#6599	1	6	yes	—
84	C₂²	C₂²×#6599	1	1	yes	characteristic
85	C₄	C₂²×#6599	1	1	yes	characteristic
86	C₄	C₂²×#6599	1	6	yes	—
87	C₄	C₂³×#1181	1	1	yes	characteristic
88	C₂	—	2	6	no	—
89	C₂	#14272221	1	2	yes	direct product factor
90	C₂	C₂³×#6599	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#1181
commutator	C₂×C₂₉	C₂³×C₈
Frattini	C₄	C₂³×#1181
Fitting, prime radical	C₂×#41×C₂₉	C₄
socle	C₂²×C₂₉	C₂²×C₈
cosocle	#6597	C₂⁴
hypercenter	C₂×#41	#1181
hypocenter	C₂₉	C₂×#504
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #14272221	C₂	direct (N × H)
2. C₂×#11745214	C₂	semidirect
3. C₂²×#90770	C₂	semidirect
10. #11745214	C₂²	semidirect
13. C₂×#90770	C₂²	semidirect
48. C₂×C₂₉	#504	semidirect
59. C₂₉	C₂×#504	semidirect
89. C₂	#14272221	direct (N × H)

Maximal subgroups

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

subgroup	index
#14272221	2
C₂×#11745214	2
C₂²×#90770	2
C₂×#11745310	2
C₂×#504	29

Subgroups — C2×#14272221 #16836456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14272221 #16836456