Subgroups — C₄×#365 #12669

Order 256.

165 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#365	C₂	1	2	yes	maximal
2	C₄×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₄×#108	C₂	1	1	yes	maximal, characteristic
4	C₄×#106	C₂	1	1	yes	maximal, characteristic
5	#1383	C₂	1	2	yes	maximal
6	C₂×M₃₂	C₂²	1	1	yes	characteristic
7	C₂×M₃₂	C₂²	1	1	yes	characteristic
8	C₂×#108	C₂²	1	2	yes	—
9	C₂×#106	C₂²	1	2	yes	—
10	C₄×M₁₆	—	2	1	no	—
11	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
12	C₄×C₄⋊C₄	—	2	1	no	—
13	#365	C₄	1	8	yes	direct product factor
14	#346	C₄	1	2	yes	complemented
15	C₄×C₁₆	C₄	1	2	yes	complemented
16	#341	—	2	1	no	—
17	#340	—	2	1	no	—
18	C₂×M₁₆	—	2	2	no	—
19	C₂²×C₈	D₄	1	1	yes	characteristic
20	C₂²×C₈	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊C₄	—	2	2	no	—
22	C₂×C₄²	—	4	1	no	—
23	C₂×C₄²	D₄	1	1	yes	characteristic
24	M₃₂	—	2	2	no	—
25	M₃₂	C₂×C₄	1	4	yes	—
26	C₂×C₁₆	C₂×C₄	1	2	yes	—
27	C₂×C₁₆	C₂×C₄	1	2	yes	—
28	#108	—	2	2	no	—
29	#108	C₂×C₄	1	4	yes	—
30	#106	—	2	2	no	—
31	#106	C₂×C₄	1	4	yes	—
32	#97	—	4	1	no	—
33	C₄×C₈	—	4	1	no	—
34	C₄×C₈	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈	Q₈	1	1	yes	characteristic
37	C₄×C₈	Q₈	1	1	yes	characteristic
38	#95	—	4	1	no	—
39	C₂²×C₄	—	4	2	no	—
40	C₂²×C₄	SD₁₆	1	1	yes	characteristic
41	C₂²×C₄	SD₁₆	1	1	yes	characteristic
42	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
43	M₁₆	—	2	4	no	—
44	M₁₆	—	4	2	no	—
45	C₂×C₈	—	2	2	no	—
46	C₂×C₈	—	4	2	no	—
47	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₈	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₈	C₂²×C₄	1	2	yes	—
51	C₂×C₈	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₈	#41	1	2	yes	—
53	C₄⋊C₄	—	2	4	no	—
54	C₄⋊C₄	—	4	2	no	—
55	C₄²	—	8	2	no	—
56	C₄²	C₄⋊C₄	1	1	yes	characteristic
57	C₄²	C₄⋊C₄	1	1	yes	characteristic
58	C₄²	SD₁₆	1	1	yes	characteristic
59	C₄²	SD₁₆	1	1	yes	characteristic
60	C₁₆	—	2	2	no	—
61	C₁₆	C₄²	1	4	yes	complemented
62	C₂³	C₂×SD₁₆	1	1	yes	characteristic
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	4	1	no	—
65	C₂×C₄	—	4	4	no	—
66	C₂×C₄	—	8	2	no	—
67	C₂×C₄	—	8	2	no	—
68	C₂×C₄	#106	1	1	yes	characteristic
69	C₂×C₄	#106	1	1	yes	characteristic
70	C₂×C₄	#106	1	1	yes	characteristic
71	C₂×C₄	#106	1	1	yes	characteristic
72	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄	C₄×D₄	1	2	yes	—
74	C₂×C₄	C₂×SD₁₆	1	1	yes	characteristic
75	C₂×C₄	#135	1	2	yes	—
76	C₈	—	2	1	no	—
77	C₈	—	2	1	no	—
78	C₈	—	4	4	no	—
79	C₈	C₂×C₄²	1	1	yes	characteristic
80	C₈	#117	1	1	yes	characteristic
81	C₈	C₄×Q₈	1	2	yes	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	1	no	—
84	C₂²	C₂×#106	1	1	yes	characteristic
85	C₂²	C₄×SD₁₆	1	2	yes	—
86	C₄	—	2	1	no	—
87	C₄	—	2	1	no	—
88	C₄	—	2	1	no	—
89	C₄	—	8	4	no	—
90	C₄	#365	1	2	yes	direct product factor
91	C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
92	C₄	#427	1	1	yes	characteristic
93	C₄	C₄×SD₁₆	1	2	yes	—
94	C₂	—	2	2	no	—
95	C₂	C₄×#106	1	1	yes	characteristic
96	C₂	C₂×#365	1	1	yes	characteristic
97	C₂	#2155	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#106
commutator	C₈	C₂×C₄²
Frattini, cosocle	C₂²×C₈	C₂³
socle	C₂²	C₂×#106
prime radical	C₂³	C₂×SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
13. #365	C₄	direct (N × H)
14. #346	C₄	semidirect
15. C₄×C₁₆	C₄	semidirect
61. C₁₆	C₄²	semidirect
90. C₄	#365	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×#365	2
C₄×M₃₂	2
C₄×#108	2
C₄×#106	2
#1383	2

Subgroups — C4×#365 #12669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#365 #12669