Subgroups — C₂²⋊C₄×D₆₇ #14523993

Order 2144.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₆₇	C₂	1	2	yes	maximal, complemented
3	C₂²⋊Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₆₇)⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₆₇	C₂²	1	1	yes	characteristic
7	C₂²×D₆₇	—	2	4	no	—
8	C₂²×D₆₇	C₄	1	4	yes	complemented
9	C₂²×D₆₇	C₂²	1	1	yes	characteristic
10	C₂²×D₆₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₆₇	C₂²	1	2	yes	complemented
12	C₂×Dic₆₇	C₂²	1	2	yes	complemented
13	C₄×D₆₇	—	2	4	no	—
14	C₂²×C₆₇	—	2	2	no	—
15	C₂²×C₆₇	C₂×C₄	1	2	yes	complemented
16	C₂²×C₆₇	C₂³	1	1	yes	characteristic
17	C₂×D₆₇	—	2	2	no	—
18	C₂×D₆₇	—	2	8	no	—
19	C₂×D₆₇	C₂×C₄	1	2	yes	—
20	C₂×D₆₇	C₂×C₄	1	2	yes	complemented
21	C₂×D₆₇	D₄	1	4	yes	—
22	C₄×C₆₇	—	2	2	no	—
23	Dic₆₇	—	2	2	no	—
24	C₂×C₆₇	—	2	2	no	—
25	C₂×C₆₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₆₇	C₂×D₄	1	2	yes	—
27	D₆₇	—	2	2	no	—
28	D₆₇	C₂²⋊C₄	1	4	yes	direct product factor
29	C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₂²⋊C₄	—	67	1	no	maximal, Sylow
31	C₂⁴	—	67	1	no	—
32	C₂²×C₄	—	67	2	no	—
33	C₂²⋊C₄	—	67	1	no	—
34	C₂²⋊C₄	—	67	2	no	—
35	C₂²⋊C₄	D₆₇	1	1	yes	characteristic, direct product factor
36	C₂³	—	67	1	no	—
37	C₂³	—	67	4	no	—
38	C₂³	—	67	1	no	—
39	C₂³	—	134	4	no	—
40	C₂³	C₂×D₆₇	1	1	yes	characteristic
41	C₂×C₄	—	67	2	no	—
42	C₂×C₄	—	134	4	no	—
43	C₂×C₄	C₂×D₆₇	1	2	yes	complemented
44	C₂²	—	2	2	no	—
45	C₂²	—	67	2	no	—
46	C₂²	—	67	4	no	—
47	C₂²	—	67	2	no	—
48	C₂²	—	134	8	no	—
49	C₂²	—	134	2	no	—
50	C₂²	C₄×D₆₇	1	2	yes	complemented
51	C₂²	C₂²×D₆₇	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	—	134	2	no	—
54	C₂	—	2	2	no	—
55	C₂	—	67	4	no	—
56	C₂	—	134	2	no	—
57	C₂	C₂×C₄×D₆₇	1	1	yes	characteristic
58	C₂	D₄×D₆₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₆₇
commutator	C₂×C₆₇	C₂²×C₄
Fitting	C₂²⋊C₄×C₆₇	C₂
socle, cosocle	C₂²×C₆₇	C₂³
prime radical	C₂³×D₆₇	C₂
hypercenter	C₂²⋊C₄	D₆₇
hypocenter	C₆₇	C₂×C₂²⋊C₄
LCS	G ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₆₇	C₂	semidirect
3. C₂²⋊Dic₆₇	C₂	semidirect
4. (C₂×D₆₇)⋊C₄	C₂	semidirect
5. C₂²⋊C₄×C₆₇	C₂	semidirect
8. C₂²×D₆₇	C₄	semidirect
11. C₂×C₄×C₆₇	C₂²	semidirect
12. C₂×Dic₆₇	C₂²	semidirect
15. C₂²×C₆₇	C₂×C₄	semidirect
20. C₂×D₆₇	C₂×C₄	semidirect
28. D₆₇	C₂²⋊C₄	direct (N × H)
29. C₆₇	C₂×C₂²⋊C₄	semidirect
35. C₂²⋊C₄	D₆₇	direct (N × H)
43. C₂×C₄	C₂×D₆₇	semidirect
50. C₂²	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₆₇	2
C₂×C₄×D₆₇	2
C₂²⋊Dic₆₇	2
(C₂×D₆₇)⋊C₄	2
C₂²⋊C₄×C₆₇	2
C₂×C₂²⋊C₄	67

Subgroups — C22⋊C4×D67 #14523993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊C₄×D₆₇ #14523993