Subgroups — C₄²×#622 #11783011

Order 1152.

666 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#622	C₂	1	6	yes	maximal
2	C₄²×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#622	C₂²	1	4	yes	—
4	C₂×C₃²×C₄²	C₄	1	1	yes	characteristic
5	C₂×C₄×C₃⋊Dic₃	C₄	1	3	yes	—
6	C₂×C₄×C₃⋊Dic₃	C₂²	1	3	yes	—
7	C₄×#622	C₄	1	24	yes	direct product factor
8	C₄²×Dic₃	—	6	2	no	—
9	C₂²×C₃²×C₄	C₂×C₄	1	3	yes	—
10	C₂²×C₃⋊Dic₃	C₂×C₄	1	3	yes	—
11	C₂²×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
12	C₂×#622	C₂×C₄	1	24	yes	—
13	C₃²×C₄²	C₈	1	4	yes	complemented
14	C₄×C₃⋊Dic₃	C₈	1	12	yes	complemented
15	C₄×C₃⋊Dic₃	C₂×C₄	1	12	yes	—
16	C₄²×C₈	—	9	1	no	maximal, Sylow
17	C₂×C₃×C₄²	—	2	2	no	—
18	C₂×C₄×Dic₃	—	6	6	no	—
19	C₂×C₄×Dic₃	—	6	6	no	—
20	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₃²×C₄	C₄²	1	6	yes	—
22	C₂×C₃²×C₄	C₂×C₈	1	6	yes	—
23	C₂×C₃²×C₄	C₂×C₈	1	6	yes	—
24	C₂×C₃⋊Dic₃	C₄²	1	6	yes	—
25	C₂×C₃⋊Dic₃	C₂×C₈	1	12	yes	—
26	C₂×C₃⋊Dic₃	C₂²×C₄	1	6	yes	—
27	#622	C₄²	1	16	yes	direct product factor
28	C₂×C₄×C₈	—	9	6	no	—
29	C₄³	—	9	1	no	—
30	C₂²×C₃×C₄	—	2	6	no	—
31	C₂²×Dic₃	—	6	6	no	—
32	C₂²×Dic₃	—	6	2	no	—
33	C₃×C₄²	—	2	8	no	—
34	C₄×Dic₃	—	6	24	no	—
35	C₄×Dic₃	—	6	24	no	—
36	C₂²×C₃²	C₂×C₄²	1	3	yes	—
37	C₂²×C₃²	C₂²×C₈	1	3	yes	—
38	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
39	C₃²×C₄	C₄×C₈	1	12	yes	complemented
40	C₃⋊Dic₃	C₄×C₈	1	12	yes	complemented
41	C₃⋊Dic₃	C₂×C₄²	1	4	yes	—
42	C₂²×C₈	—	9	4	no	—
43	C₂×C₄²	—	9	3	no	—
44	C₂×C₄²	—	9	3	no	—
45	C₂×C₄²	#157	1	1	yes	characteristic
46	C₄×C₈	—	9	24	no	—
47	C₂³×C₃	—	2	2	no	—
48	C₂×C₃×C₄	—	2	12	no	—
49	C₂×C₃×C₄	—	2	12	no	—
50	C₂×C₃×C₄	—	2	12	no	—
51	C₂×Dic₃	—	6	12	no	—
52	C₂×Dic₃	—	6	24	no	—
53	C₂×Dic₃	—	6	12	no	—
54	C₂×C₃²	C₄³	1	1	yes	characteristic
55	C₂×C₃²	C₂×C₄×C₈	1	3	yes	—
56	C₂×C₃²	C₂×C₄×C₈	1	3	yes	—
57	C₂²×C₄	—	9	1	no	—
58	C₂²×C₄	—	9	3	no	—
59	C₂²×C₄	C₂×#157	1	3	yes	—
60	C₂×C₈	—	9	24	no	—
61	C₄²	—	9	12	no	—
62	C₄²	—	9	12	no	—
63	C₄²	#622	1	4	yes	direct product factor
64	C₂²×C₃	—	2	6	no	—
65	C₂²×C₃	—	2	6	no	—
66	C₂²×C₃	—	2	2	no	—
67	C₃×C₄	—	2	24	no	—
68	Dic₃	—	6	24	no	—
69	Dic₃	—	6	8	no	—
70	C₃²	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
71	C₂³	C₂²×#157	1	1	yes	characteristic
72	C₂×C₄	—	9	12	no	—
73	C₂×C₄	—	9	6	no	—
74	C₂×C₄	—	9	6	no	—
75	C₂×C₄	#3787	1	6	yes	—
76	C₂×C₄	C₄×#157	1	6	yes	—
77	C₂×C₄	C₂×#622	1	6	yes	—
78	C₈	—	9	16	no	—
79	C₂×C₃	—	2	6	no	—
80	C₂×C₃	—	2	6	no	—
81	C₂×C₃	—	2	2	no	—
82	C₂²	C₂×#3787	1	3	yes	—
83	C₂²	C₂×C₄×#157	1	3	yes	—
84	C₂²	C₂²×#622	1	1	yes	characteristic
85	C₄	—	9	12	no	—
86	C₄	—	9	4	no	—
87	C₄	C₄×#622	1	12	yes	direct product factor
88	C₃	—	2	2	no	—
89	C₂	C₄×#3787	1	3	yes	—
90	C₂	C₄²×#157	1	1	yes	characteristic
91	C₂	C₂×C₄×#622	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	#157
commutator, hypocenter	C₃²	C₄²×C₈
Frattini	C₂³	C₂²×#157
Fitting	C₂×C₃²×C₄²	C₄
socle, prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃⋊Dic₃	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
7. C₄×#622	C₄	direct (N × H)
13. C₃²×C₄²	C₈	semidirect
14. C₄×C₃⋊Dic₃	C₈	semidirect
27. #622	C₄²	direct (N × H)
39. C₃²×C₄	C₄×C₈	semidirect
40. C₃⋊Dic₃	C₄×C₈	semidirect
63. C₄²	#622	direct (N × H)
70. C₃²	C₄²×C₈	semidirect
87. C₄	C₄×#622	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×C₄×#622	2
C₄²×C₃⋊Dic₃	2
C₄²×C₈	9

Subgroups — C42×#622 #11783011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#622 #11783011