Subgroups — C₂²×#11758202 #16840538

Order 3904.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₂₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#11758202	C₂	1	12	yes	maximal, direct product factor
3	C₂²×#92418	C₂	1	1	yes	maximal, characteristic
4	C₂²×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₆₁	—	2	3	no	—
6	C₂×Q₈×C₆₁	C₂²	1	6	yes	—
7	C₂²×C₄×C₆₁	—	2	1	no	—
8	C₂²×C₄×C₆₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₆₁	—	2	1	no	—
10	C₂×Dic₁₂₂	—	2	3	no	—
11	C₂×Dic₁₂₂	C₂²	1	6	yes	—
12	#11758202	C₂²	1	16	yes	direct product factor
13	C₂×#92418	C₂²	1	6	yes	—
14	C₂³×C₆₁	D₄	1	1	yes	characteristic
15	Q₈×C₆₁	—	2	6	no	—
16	Q₈×C₆₁	C₂³	1	4	yes	—
17	C₂×C₄×C₆₁	—	2	6	no	—
18	C₂×C₄×C₆₁	D₄	1	3	yes	—
19	C₂×C₄×C₆₁	C₂³	1	3	yes	—
20	C₂×Dic₆₁	—	2	6	no	—
21	Dic₁₂₂	—	2	6	no	—
22	Dic₁₂₂	C₂³	1	4	yes	—
23	#92418	C₂³	1	4	yes	—
24	C₂²×C₆₁	Q₁₆	1	4	yes	complemented
25	C₂²×C₆₁	C₂×D₄	1	3	yes	—
26	C₄×C₆₁	—	2	4	no	—
27	C₄×C₆₁	C₂×D₄	1	3	yes	—
28	C₄×C₆₁	C₂⁴	1	1	yes	characteristic
29	Dic₆₁	—	2	4	no	—
30	C₂×C₆₁	C₂×Q₁₆	1	6	yes	complemented
31	C₂×C₆₁	C₂²×D₄	1	1	yes	characteristic
32	C₂²×Q₁₆	—	61	1	no	maximal, Sylow
33	C₆₁	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂²×Q₈	—	61	1	no	—
35	C₂²×Q₈	D₆₁	1	1	yes	characteristic
36	C₂×Q₁₆	—	61	12	no	—
37	C₂²×C₈	—	61	1	no	—
38	C₂×Q₈	—	2	3	no	—
39	C₂×Q₈	—	61	6	no	—
40	C₂×Q₈	—	122	3	no	—
41	C₂×Q₈	C₂×D₆₁	1	6	yes	—
42	C₂²×C₄	—	2	1	no	—
43	C₂²×C₄	—	122	1	no	—
44	C₂²×C₄	C₂×D₆₁	1	1	yes	characteristic
45	Q₁₆	—	61	16	no	—
46	C₂×C₈	—	61	6	no	—
47	C₂³	C₂²⋊D₆₁	1	1	yes	characteristic
48	Q₈	—	2	6	no	—
49	Q₈	—	61	4	no	—
50	Q₈	—	122	6	no	—
51	Q₈	C₂²×D₆₁	1	4	yes	—
52	C₂×C₄	—	2	6	no	—
53	C₂×C₄	—	122	6	no	—
54	C₂×C₄	C₂²⋊D₆₁	1	3	yes	—
55	C₂×C₄	C₂²×D₆₁	1	3	yes	—
56	C₈	—	61	4	no	—
57	C₂²	#11758202	1	4	yes	direct product factor
58	C₂²	C₂×C₂²⋊D₆₁	1	3	yes	—
59	C₄	—	2	4	no	—
60	C₄	—	122	4	no	—
61	C₄	C₂×C₂²⋊D₆₁	1	3	yes	—
62	C₄	C₂³×D₆₁	1	1	yes	characteristic
63	C₂	C₂×#11758202	1	6	yes	direct product factor
64	C₂	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₆₁
commutator, cosocle	C₄×C₆₁	C₂⁴
Frattini	C₄	C₂³×D₆₁
Fitting	C₂²×Q₈×C₆₁	C₂
socle, prime radical	C₂³×C₆₁	D₄
hypercenter	C₂²×Q₈	D₆₁
hypocenter	C₆₁	C₂²×Q₁₆
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×#11758202	C₂	direct (N × H)
12. #11758202	C₂²	direct (N × H)
24. C₂²×C₆₁	Q₁₆	semidirect
30. C₂×C₆₁	C₂×Q₁₆	semidirect
33. C₆₁	C₂²×Q₁₆	semidirect
57. C₂²	#11758202	direct (N × H)
63. C₂	C₂×#11758202	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₁₂₂	2
C₂×#11758202	2
C₂²×#92418	2
C₂²×Q₈×C₆₁	2
C₂²×Q₁₆	61

Subgroups — C22×#11758202 #16840538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11758202 #16840538