Subgroups — C₄×C₄⋊#11757210 #29508656

Order 15424.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#11757210	C₂	1	2	yes	maximal
2	C₂×C₄×#11757210	C₂	1	2	yes	maximal
3	(C₂×#11757210)⋊C₄	C₂	1	2	yes	maximal
4	C₄²×D₂₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11757210	C₂²	1	4	yes	—
6	C₄⋊#11757210	C₄	1	8	yes	direct product factor
7	C₄×#11757210	—	2	4	no	—
8	C₂×C₄×D₂₄₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₂₄₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₂₄₁	C₂²	1	1	yes	characteristic
11	C₄×Dic₂₄₁	C₄	1	1	yes	characteristic, complemented
12	C₄×Dic₂₄₁	C₄	1	1	yes	characteristic, complemented
13	C₄×Dic₂₄₁	C₄	1	1	yes	characteristic, complemented
14	C₄²×C₂₄₁	C₄	1	1	yes	characteristic, complemented
15	C₂×#11757210	—	2	4	no	—
16	C₂×#11757210	—	2	4	no	—
17	C₂×#11757210	C₂×C₄	1	8	yes	—
18	C₂²×D₂₄₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
22	C₄×D₂₄₁	—	2	2	no	—
23	C₄×D₂₄₁	C₂×C₄	1	4	yes	—
24	C₄×D₂₄₁	D₄	1	2	yes	—
25	C₄×D₂₄₁	Q₈	1	2	yes	—
26	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×D₂₄₁	C₂²×C₄	1	2	yes	—
31	C₂×D₂₄₁	C₂×D₄	1	1	yes	characteristic
32	C₂×D₂₄₁	C₂×Q₈	1	1	yes	characteristic
33	C₂×D₂₄₁	#41	1	2	yes	—
34	#11757210	—	2	8	no	—
35	C₄×C₂₄₁	—	2	1	no	—
36	C₄×C₂₄₁	C₄²	1	2	yes	complemented
37	C₄×C₂₄₁	C₄⋊C₄	1	2	yes	complemented
38	Dic₂₄₁	—	2	1	no	—
39	Dic₂₄₁	C₄²	1	2	yes	complemented
40	Dic₂₄₁	C₄⋊C₄	1	2	yes	complemented
41	C₂×C₂₄₁	C₂×C₄²	1	1	yes	characteristic
42	C₂×C₂₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₂₄₁	#117	1	1	yes	characteristic
44	D₂₄₁	C₄×D₄	1	2	yes	—
45	D₂₄₁	C₄×Q₈	1	2	yes	—
46	C₂₄₁	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
47	C₄×C₄⋊C₄	—	241	1	no	maximal, Sylow
48	C₂×C₄⋊C₄	—	241	2	no	—
49	C₂×C₄²	—	241	2	no	—
50	C₂×C₄²	—	241	1	no	—
51	#95	—	241	2	no	—
52	C₂²×C₄	—	241	4	no	—
53	C₂²×C₄	—	241	1	no	—
54	C₂²×C₄	—	241	1	no	—
55	C₂²×C₄	—	241	1	no	—
56	C₄⋊C₄	—	241	8	no	—
57	C₄²	—	482	4	no	—
58	C₄²	—	241	1	no	—
59	C₄²	—	241	1	no	—
60	C₄²	—	241	1	no	—
61	C₄²	#11757210	1	1	yes	characteristic, complemented
62	C₂³	—	241	1	no	—
63	C₂×C₄	—	482	2	no	—
64	C₂×C₄	—	482	4	no	—
65	C₂×C₄	—	482	4	no	—
66	C₂×C₄	—	241	8	no	—
67	C₂×C₄	—	241	1	no	—
68	C₂×C₄	—	241	1	no	—
69	C₂×C₄	—	241	1	no	—
70	C₂×C₄	—	241	4	no	—
71	C₂×C₄	—	241	2	no	—
72	C₂×C₄	—	241	2	no	—
73	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
74	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
75	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
76	C₂²	—	241	2	no	—
77	C₂²	—	241	1	no	—
78	C₂²	—	241	1	no	—
79	C₂²	—	241	2	no	—
80	C₂²	C₂²×#11757210	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	482	8	no	—
83	C₄	—	482	1	no	—
84	C₄	—	241	2	no	—
85	C₄	—	241	2	no	—
86	C₄	C₄×#11757210	1	2	yes	complemented
87	C₄	C₄⋊#11757210	1	2	yes	direct product factor
88	C₂	—	241	2	no	—
89	C₂	—	241	2	no	—
90	C₂	C₂×C₄×#11757210	1	1	yes	characteristic
91	C₂	C₂×C₄⋊#11757210	1	1	yes	characteristic
92	C₂	#21440721	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#11757210
commutator	C₂×C₂₄₁	C₂×C₄²
Frattini	C₂²	C₂²×#11757210
Fitting	C₄²×C₂₄₁	C₄
socle	C₂²×C₂₄₁	C₂²×C₄
prime radical, cosocle	C₂²×D₂₄₁	C₂³
hypercenter	C₄²	#11757210
hypocenter	C₂₄₁	C₄×C₄⋊C₄
LCS	G ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
6. C₄⋊#11757210	C₄	direct (N × H)
11. C₄×Dic₂₄₁	C₄	semidirect
12. C₄×Dic₂₄₁	C₄	semidirect
13. C₄×Dic₂₄₁	C₄	semidirect
14. C₄²×C₂₄₁	C₄	semidirect
36. C₄×C₂₄₁	C₄²	semidirect
37. C₄×C₂₄₁	C₄⋊C₄	semidirect
39. Dic₂₄₁	C₄²	semidirect
40. Dic₂₄₁	C₄⋊C₄	semidirect
46. C₂₄₁	C₄×C₄⋊C₄	semidirect
61. C₄²	#11757210	semidirect
86. C₄	C₄×#11757210	semidirect
87. C₄	C₄⋊#11757210	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⋊#11757210	2
C₂×C₄×#11757210	2
(C₂×#11757210)⋊C₄	2
C₄²×D₂₄₁	2
C₄×C₄⋊C₄	241

Subgroups — C4×C4⋊#11757210 #29508656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊#11757210 #29508656