Subgroups — (C₂×#14523348)⋊C₄ #30657828

Order 16448.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523348	C₂	1	2	yes	maximal
2	C₂×C₄×#11759967	C₂	1	1	yes	maximal, characteristic
3	C₂×#14523348	—	2	2	no	—
4	C₂×#14523348	—	2	2	no	—
5	C₂×#14523348	C₄	1	4	yes	complemented
6	C₂²×#11759967	C₄	1	1	yes	characteristic
7	C₂²×#11759967	C₂²	1	1	yes	characteristic
8	C₄×#11759967	—	2	2	no	—
9	C₂×C₄×D₂₅₇	C₄	1	1	yes	characteristic
10	#14523348	—	2	4	no	—
11	C₂×#11759967	—	2	1	no	—
12	C₂×#11759967	—	2	1	no	—
13	C₂×#11759967	C₈	1	2	yes	complemented
14	C₂×#11759967	C₂×C₄	1	2	yes	—
15	C₂×#11759967	D₄	1	1	yes	characteristic
16	C₂×#11759967	D₄	1	2	yes	—
17	C₂×#11759967	Q₈	1	1	yes	characteristic
18	C₂²×D₂₅₇	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₂₅₇	C₈	1	1	yes	characteristic, complemented
20	C₄×D₂₅₇	—	2	1	no	—
21	C₄×D₂₅₇	—	2	1	no	—
22	C₂×C₄×C₂₅₇	C₈	1	1	yes	characteristic, complemented
23	C₂²×C₂₅₇	C₂×C₈	1	1	yes	characteristic
24	C₂×D₂₅₇	C₄²	1	1	yes	characteristic
25	C₂×D₂₅₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×D₂₅₇	C₄⋊C₄	1	1	yes	characteristic
27	C₂×D₂₅₇	C₂×C₈	1	1	yes	characteristic
28	C₂×D₂₅₇	M₁₆	1	1	yes	characteristic
29	C₂×D₂₅₇	M₁₆	1	1	yes	characteristic
30	#11759967	—	2	2	no	—
31	#11759967	C₂²⋊C₄	1	2	yes	—
32	#11759967	C₄⋊C₄	1	2	yes	—
33	C₄×C₂₅₇	—	2	1	no	—
34	Dic₂₅₇	—	2	1	no	—
35	C₂×C₂₅₇	C₄×C₈	1	1	yes	characteristic
36	C₂×C₂₅₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×C₂₅₇	C₄⋊C₈	1	1	yes	characteristic
38	D₂₅₇	#95	1	1	yes	characteristic
39	D₂₅₇	#97	1	1	yes	characteristic
40	D₂₅₇	C₂²⋊C₈	1	1	yes	characteristic
41	D₂₅₇	C₄⋊C₈	1	1	yes	characteristic
42	C₂₅₇	#336	1	1	yes	characteristic, complemented, Sylow
43	#336	—	257	1	no	maximal, Sylow
44	C₂²×C₈	—	257	2	no	—
45	C₂×C₄²	—	257	1	no	—
46	C₂²×C₄	—	257	1	no	—
47	C₂²×C₄	—	257	1	no	—
48	C₂²×C₄	—	257	1	no	—
49	C₂×C₈	—	257	4	no	—
50	C₂×C₈	—	514	2	no	—
51	C₂×C₈	—	514	2	no	—
52	C₄²	—	514	2	no	—
53	C₂³	—	257	1	no	—
54	C₂×C₄	—	257	2	no	—
55	C₂×C₄	—	257	2	no	—
56	C₂×C₄	—	257	1	no	—
57	C₂×C₄	—	257	1	no	—
58	C₂×C₄	—	257	2	no	—
59	C₂×C₄	—	257	1	no	—
60	C₂×C₄	—	514	1	no	—
61	C₂×C₄	—	514	1	no	—
62	C₂×C₄	—	514	1	no	—
63	C₂×C₄	—	514	1	no	—
64	C₂×C₄	#14523348	1	1	yes	characteristic, complemented
65	C₈	—	514	4	no	—
66	C₂²	—	257	1	no	—
67	C₂²	—	257	1	no	—
68	C₂²	—	257	1	no	—
69	C₂²	—	257	1	no	—
70	C₂²	—	257	1	no	—
71	C₂²	—	257	1	no	—
72	C₂²	C₂×#14523348	1	1	yes	characteristic
73	C₄	—	257	2	no	—
74	C₄	—	257	2	no	—
75	C₄	—	2	1	no	—
76	C₄	—	514	2	no	—
77	C₄	—	514	1	no	—
78	C₂	—	257	1	no	—
79	C₂	—	257	1	no	—
80	C₂	—	257	1	no	—
81	C₂	—	257	1	no	—
82	C₂	C₄×#14523348	1	1	yes	characteristic
83	C₂	C₂²⋊#14523348	1	1	yes	characteristic
84	C₂	C₄⋊#14523348	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#14523348
commutator	C₂×C₂₅₇	C₄×C₈
Fitting	C₂×C₄×C₂₅₇	C₈
socle	C₂²×C₂₅₇	C₂×C₈
prime radical	C₂²×D₂₅₇	C₂×C₄
cosocle	C₂²×#11759967	C₂²
hypercenter	C₂×C₄	#14523348
hypocenter	C₂₅₇	#336
LCS	G ▷ C₂×C₂₅₇ ▷ C₂₅₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
5. C₂×#14523348	C₄	semidirect
13. C₂×#11759967	C₈	semidirect
19. C₂×Dic₂₅₇	C₈	semidirect
22. C₂×C₄×C₂₅₇	C₈	semidirect
42. C₂₅₇	#336	semidirect
64. C₂×C₄	#14523348	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14523348	2
C₂×C₄×#11759967	2
#336	257

Subgroups — (C2×#14523348)⋊C4 #30657828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#14523348)⋊C₄ #30657828