Subgroups — C₂×#29504612 #44486852

Order 30592.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₉₁₂	C₂	1	1	yes	maximal, characteristic
2	#29504612	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₂₃₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂×C₂₃₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₉₅₆	—	2	1	no	—
6	Dic₁₉₁₂	—	2	1	no	—
7	Dic₁₉₁₂	C₂²	1	2	yes	—
8	C₂₃₉⋊C₃₂	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₂₃₉	—	2	1	no	—
10	Q₃₂×C₂₃₉	—	2	1	no	—
11	Q₃₂×C₂₃₉	C₂²	1	2	yes	—
12	C₂×C₁₆×C₂₃₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₇₈	—	4	1	no	—
14	Dic₉₅₆	—	2	2	no	—
15	Dic₉₅₆	—	4	1	no	—
16	C₂×Q₈×C₂₃₉	—	4	1	no	—
17	Q₁₆×C₂₃₉	—	2	2	no	—
18	Q₁₆×C₂₃₉	—	4	1	no	—
19	C₂×C₈×C₂₃₉	D₄	1	1	yes	characteristic
20	C₁₆×C₂₃₉	D₄	1	1	yes	characteristic
21	C₁₆×C₂₃₉	C₂³	1	1	yes	characteristic
22	Dic₄₇₈	—	4	2	no	—
23	Dic₄₇₈	—	8	1	no	—
24	C₂×Dic₂₃₉	—	8	1	no	—
25	Q₈×C₂₃₉	—	4	2	no	—
26	Q₈×C₂₃₉	—	8	1	no	—
27	C₂×C₄×C₂₃₉	—	8	1	no	—
28	C₂×C₄×C₂₃₉	D₈	1	1	yes	characteristic
29	C₈×C₂₃₉	D₈	1	1	yes	characteristic
30	C₈×C₂₃₉	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₂₃₉	D₁₆	1	1	yes	characteristic
32	C₄×C₂₃₉	—	8	2	no	—
33	C₄×C₂₃₉	D₁₆	1	1	yes	characteristic
34	C₄×C₂₃₉	C₂×D₈	1	1	yes	characteristic
35	Dic₂₃₉	—	8	2	no	—
36	C₂×C₂₃₉	Q₆₄	1	2	yes	complemented
37	C₂×C₂₃₉	C₂×D₁₆	1	1	yes	characteristic
38	C₂₃₉	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₆₄	—	239	1	no	maximal, Sylow
40	C₂×Q₃₂	—	239	1	no	—
41	C₂×Q₃₂	D₂₃₉	1	1	yes	characteristic
42	Q₆₄	—	239	4	no	—
43	C₂×C₃₂	—	239	1	no	—
44	C₂×Q₁₆	—	2	1	no	—
45	C₂×Q₁₆	—	478	1	no	—
46	Q₃₂	—	2	1	no	—
47	Q₃₂	—	478	1	no	—
48	Q₃₂	—	239	2	no	—
49	Q₃₂	C₂×D₂₃₉	1	2	yes	—
50	C₂×C₁₆	C₂×D₂₃₉	1	1	yes	characteristic
51	C₃₂	—	239	2	no	—
52	C₂×Q₈	—	4	1	no	—
53	C₂×Q₈	—	956	1	no	—
54	Q₁₆	—	2	2	no	—
55	Q₁₆	—	4	1	no	—
56	Q₁₆	—	956	1	no	—
57	Q₁₆	—	478	2	no	—
58	C₂×C₈	C₂²⋊D₂₃₉	1	1	yes	characteristic
59	C₁₆	C₂²⋊D₂₃₉	1	1	yes	characteristic
60	C₁₆	C₂²×D₂₃₉	1	1	yes	characteristic
61	Q₈	—	4	2	no	—
62	Q₈	—	8	1	no	—
63	Q₈	—	1912	1	no	—
64	Q₈	—	956	2	no	—
65	C₂×C₄	—	8	1	no	—
66	C₂×C₄	—	1912	1	no	—
67	C₂×C₄	#16838533	1	1	yes	characteristic
68	C₈	#16838533	1	1	yes	characteristic
69	C₈	C₂×C₂²⋊D₂₃₉	1	1	yes	characteristic
70	C₂²	#21439901	1	1	yes	characteristic
71	C₄	—	8	2	no	—
72	C₄	—	1912	2	no	—
73	C₄	#21439901	1	1	yes	characteristic
74	C₄	C₂×#16838533	1	1	yes	characteristic
75	C₂	#29504612	1	2	yes	direct product factor
76	C₂	C₂×#21439901	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#21439901
commutator, cosocle	C₁₆×C₂₃₉	C₂³
Frattini	C₁₆	C₂²×D₂₃₉
Fitting	C₂×Q₃₂×C₂₃₉	C₂
socle, prime radical	C₂²×C₂₃₉	D₁₆
hypercenter	C₂×Q₃₂	D₂₃₉
hypocenter	C₂₃₉	C₂×Q₆₄
LCS	G ▷ C₁₆×C₂₃₉ ▷ C₈×C₂₃₉ ▷ C₄×C₂₃₉ ▷ C₂×C₂₃₉ ▷ C₂₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
2. #29504612	C₂	direct (N × H)
36. C₂×C₂₃₉	Q₆₄	semidirect
38. C₂₃₉	C₂×Q₆₄	semidirect
75. C₂	#29504612	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×Dic₁₉₁₂	2
#29504612	2
C₂×C₂₃₉⋊C₃₂	2
C₂×Q₃₂×C₂₃₉	2
C₂×Q₆₄	239

Subgroups — C2×#29504612 #44486852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#29504612 #44486852