Subgroups — (C₂×#16861969)⋊C₄ #45688523

Order 33344.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16861969	C₂	1	2	yes	maximal
2	C₂×C₄×#14523438	C₂	1	1	yes	maximal, characteristic
3	C₂×#16861969	—	2	2	no	—
4	C₂×#16861969	—	2	2	no	—
5	C₂×#16861969	C₄	1	4	yes	complemented
6	C₂²×#14523438	C₄	1	1	yes	characteristic
7	C₂²×#14523438	C₂²	1	1	yes	characteristic
8	C₄×#14523438	—	2	2	no	—
9	C₂×C₄×D₅₂₁	C₄	1	1	yes	characteristic
10	#16861969	—	2	4	no	—
11	C₂×#14523438	—	2	1	no	—
12	C₂×#14523438	—	2	1	no	—
13	C₂×#14523438	C₈	1	2	yes	complemented
14	C₂×#14523438	C₂×C₄	1	2	yes	—
15	C₂×#14523438	D₄	1	1	yes	characteristic
16	C₂×#14523438	D₄	1	2	yes	—
17	C₂×#14523438	Q₈	1	1	yes	characteristic
18	C₂²×D₅₂₁	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₅₂₁	C₈	1	1	yes	characteristic, complemented
20	C₄×D₅₂₁	—	2	1	no	—
21	C₄×D₅₂₁	—	2	1	no	—
22	C₂×C₄×C₅₂₁	C₈	1	1	yes	characteristic, complemented
23	C₂²×C₅₂₁	C₂×C₈	1	1	yes	characteristic
24	C₂×D₅₂₁	C₄²	1	1	yes	characteristic
25	C₂×D₅₂₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×D₅₂₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂×D₅₂₁	C₂×C₈	1	1	yes	characteristic
28	C₂×D₅₂₁	M₁₆	1	1	yes	characteristic
29	C₂×D₅₂₁	M₁₆	1	1	yes	characteristic
30	#14523438	—	2	2	no	—
31	#14523438	C₂²⋊C₄	1	2	yes	—
32	#14523438	C₄⋊C₄	1	2	yes	—
33	C₄×C₅₂₁	—	2	1	no	—
34	Dic₅₂₁	—	2	1	no	—
35	C₂×C₅₂₁	C₄×C₈	1	1	yes	characteristic
36	C₂×C₅₂₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×C₅₂₁	C₄⋊C₈	1	1	yes	characteristic
38	D₅₂₁	#95	1	1	yes	characteristic
39	D₅₂₁	#97	1	1	yes	characteristic
40	D₅₂₁	C₂²⋊C₈	1	1	yes	characteristic
41	D₅₂₁	C₄⋊C₈	1	1	yes	characteristic
42	C₅₂₁	#336	1	1	yes	characteristic, complemented, Sylow
43	#336	—	521	1	no	maximal, Sylow
44	C₂²×C₈	—	521	2	no	—
45	C₂×C₄²	—	521	1	no	—
46	C₂²×C₄	—	521	1	no	—
47	C₂²×C₄	—	521	1	no	—
48	C₂²×C₄	—	521	1	no	—
49	C₂×C₈	—	521	4	no	—
50	C₂×C₈	—	1042	2	no	—
51	C₂×C₈	—	1042	2	no	—
52	C₄²	—	1042	2	no	—
53	C₂³	—	521	1	no	—
54	C₂×C₄	—	521	2	no	—
55	C₂×C₄	—	521	2	no	—
56	C₂×C₄	—	521	1	no	—
57	C₂×C₄	—	521	1	no	—
58	C₂×C₄	—	521	2	no	—
59	C₂×C₄	—	521	1	no	—
60	C₂×C₄	—	1042	1	no	—
61	C₂×C₄	—	1042	1	no	—
62	C₂×C₄	—	1042	1	no	—
63	C₂×C₄	—	1042	1	no	—
64	C₂×C₄	#16861969	1	1	yes	characteristic, complemented
65	C₈	—	1042	4	no	—
66	C₂²	—	521	1	no	—
67	C₂²	—	521	1	no	—
68	C₂²	—	521	1	no	—
69	C₂²	—	521	1	no	—
70	C₂²	—	521	1	no	—
71	C₂²	—	521	1	no	—
72	C₂²	C₂×#16861969	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	—	521	2	no	—
75	C₄	—	521	2	no	—
76	C₄	—	1042	2	no	—
77	C₄	—	1042	1	no	—
78	C₂	—	521	1	no	—
79	C₂	—	521	1	no	—
80	C₂	—	521	1	no	—
81	C₂	—	521	1	no	—
82	C₂	C₄×#16861969	1	1	yes	characteristic
83	C₂	C₂²⋊#16861969	1	1	yes	characteristic
84	C₂	C₄⋊#16861969	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#16861969
commutator	C₂×C₅₂₁	C₄×C₈
Fitting	C₂×C₄×C₅₂₁	C₈
socle	C₂²×C₅₂₁	C₂×C₈
prime radical	C₂²×D₅₂₁	C₂×C₄
cosocle	C₂²×#14523438	C₂²
hypercenter	C₂×C₄	#16861969
hypocenter	C₅₂₁	#336
LCS	G ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
5. C₂×#16861969	C₄	semidirect
13. C₂×#14523438	C₈	semidirect
19. C₂×Dic₅₂₁	C₈	semidirect
22. C₂×C₄×C₅₂₁	C₈	semidirect
42. C₅₂₁	#336	semidirect
64. C₂×C₄	#16861969	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#16861969	2
C₂×C₄×#14523438	2
#336	521

Subgroups — (C2×#16861969)⋊C4 #45688523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#16861969)⋊C₄ #45688523