Subgroups — C₄×C₄⋊#13062438 #36342244

Order 21568.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#13062438	C₂	1	2	yes	maximal
2	C₂×C₄×#13062438	C₂	1	2	yes	maximal
3	(C₂×#13062438)⋊C₄	C₂	1	2	yes	maximal
4	C₄²×D₃₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#13062438	C₂²	1	4	yes	—
6	C₄⋊#13062438	C₄	1	8	yes	direct product factor
7	C₄×#13062438	—	2	4	no	—
8	C₂×C₄×D₃₃₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₃₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃₃₇	C₂²	1	1	yes	characteristic
11	C₄×Dic₃₃₇	C₄	1	1	yes	characteristic, complemented
12	C₄×Dic₃₃₇	C₄	1	1	yes	characteristic, complemented
13	C₄×Dic₃₃₇	C₄	1	1	yes	characteristic, complemented
14	C₄²×C₃₃₇	C₄	1	1	yes	characteristic, complemented
15	C₂×#13062438	—	2	4	no	—
16	C₂×#13062438	—	2	4	no	—
17	C₂×#13062438	C₂×C₄	1	8	yes	—
18	C₂²×D₃₃₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₃₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₃₃₇	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₃₃₇	C₂×C₄	1	1	yes	characteristic
22	C₄×D₃₃₇	—	2	2	no	—
23	C₄×D₃₃₇	C₂×C₄	1	4	yes	—
24	C₄×D₃₃₇	D₄	1	2	yes	—
25	C₄×D₃₃₇	Q₈	1	2	yes	—
26	C₂×C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃₃₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×D₃₃₇	C₂²×C₄	1	2	yes	—
31	C₂×D₃₃₇	C₂×D₄	1	1	yes	characteristic
32	C₂×D₃₃₇	C₂×Q₈	1	1	yes	characteristic
33	C₂×D₃₃₇	#41	1	2	yes	—
34	#13062438	—	2	8	no	—
35	C₄×C₃₃₇	—	2	1	no	—
36	C₄×C₃₃₇	C₄²	1	2	yes	complemented
37	C₄×C₃₃₇	C₄⋊C₄	1	2	yes	complemented
38	Dic₃₃₇	—	2	1	no	—
39	Dic₃₃₇	C₄²	1	2	yes	complemented
40	Dic₃₃₇	C₄⋊C₄	1	2	yes	complemented
41	C₂×C₃₃₇	C₂×C₄²	1	1	yes	characteristic
42	C₂×C₃₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₃₃₇	#117	1	1	yes	characteristic
44	D₃₃₇	C₄×D₄	1	2	yes	—
45	D₃₃₇	C₄×Q₈	1	2	yes	—
46	C₃₃₇	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
47	C₄×C₄⋊C₄	—	337	1	no	maximal, Sylow
48	C₂×C₄⋊C₄	—	337	2	no	—
49	C₂×C₄²	—	337	1	no	—
50	C₂×C₄²	—	337	2	no	—
51	#95	—	337	2	no	—
52	C₂²×C₄	—	337	1	no	—
53	C₂²×C₄	—	337	1	no	—
54	C₂²×C₄	—	337	4	no	—
55	C₂²×C₄	—	337	1	no	—
56	C₄⋊C₄	—	337	8	no	—
57	C₄²	—	337	1	no	—
58	C₄²	—	337	1	no	—
59	C₄²	—	337	1	no	—
60	C₄²	—	674	4	no	—
61	C₄²	#13062438	1	1	yes	characteristic, complemented
62	C₂³	—	337	1	no	—
63	C₂×C₄	—	337	1	no	—
64	C₂×C₄	—	337	1	no	—
65	C₂×C₄	—	337	4	no	—
66	C₂×C₄	—	337	2	no	—
67	C₂×C₄	—	337	2	no	—
68	C₂×C₄	—	337	8	no	—
69	C₂×C₄	—	337	1	no	—
70	C₂×C₄	—	674	2	no	—
71	C₂×C₄	—	674	4	no	—
72	C₂×C₄	—	674	4	no	—
73	C₂×C₄	C₂×#13062438	1	1	yes	characteristic
74	C₂×C₄	C₂×#13062438	1	1	yes	characteristic
75	C₂×C₄	C₂×#13062438	1	1	yes	characteristic
76	C₂²	—	337	2	no	—
77	C₂²	—	337	1	no	—
78	C₂²	—	337	1	no	—
79	C₂²	—	337	2	no	—
80	C₂²	C₂²×#13062438	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	337	2	no	—
83	C₄	—	337	2	no	—
84	C₄	—	674	8	no	—
85	C₄	—	674	1	no	—
86	C₄	C₄×#13062438	1	2	yes	complemented
87	C₄	C₄⋊#13062438	1	2	yes	direct product factor
88	C₂	—	337	2	no	—
89	C₂	—	337	2	no	—
90	C₂	C₂×C₄×#13062438	1	1	yes	characteristic
91	C₂	C₂×C₄⋊#13062438	1	1	yes	characteristic
92	C₂	#24925038	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#13062438
commutator	C₂×C₃₃₇	C₂×C₄²
Frattini	C₂²	C₂²×#13062438
Fitting	C₄²×C₃₃₇	C₄
socle	C₂²×C₃₃₇	C₂²×C₄
prime radical, cosocle	C₂²×D₃₃₇	C₂³
hypercenter	C₄²	#13062438
hypocenter	C₃₃₇	C₄×C₄⋊C₄
LCS	G ▷ C₂×C₃₃₇ ▷ C₃₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
6. C₄⋊#13062438	C₄	direct (N × H)
11. C₄×Dic₃₃₇	C₄	semidirect
12. C₄×Dic₃₃₇	C₄	semidirect
13. C₄×Dic₃₃₇	C₄	semidirect
14. C₄²×C₃₃₇	C₄	semidirect
36. C₄×C₃₃₇	C₄²	semidirect
37. C₄×C₃₃₇	C₄⋊C₄	semidirect
39. Dic₃₃₇	C₄²	semidirect
40. Dic₃₃₇	C₄⋊C₄	semidirect
46. C₃₃₇	C₄×C₄⋊C₄	semidirect
61. C₄²	#13062438	semidirect
86. C₄	C₄×#13062438	semidirect
87. C₄	C₄⋊#13062438	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⋊#13062438	2
C₂×C₄×#13062438	2
(C₂×#13062438)⋊C₄	2
C₄²×D₃₃₇	2
C₄×C₄⋊C₄	337

Subgroups — C4×C4⋊#13062438 #36342244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊#13062438 #36342244