Subgroups — C₄×C₄⋊Q₈ #2307

Order 128.

294 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈	C₂	1	2	yes	maximal
3	#391	C₂	1	2	yes	maximal
4	#389	C₂	1	4	yes	maximal
5	#384	C₂	1	1	yes	maximal, characteristic
6	C₄×C₄⋊C₄	C₂	1	4	yes	maximal
7	C₄³	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈	C₂²	1	2	yes	—
9	C₄⋊Q₈	C₄	1	8	yes	direct product factor
10	C₄×Q₈	—	2	8	no	—
11	C₂×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₄⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄	C₂²	1	4	yes	—
15	C₂×C₄²	C₂²	1	2	yes	—
16	C₂×C₄²	C₂²	1	1	yes	characteristic
17	C₂×C₄²	C₂²	1	4	yes	—
18	C₂×C₄²	C₂²	1	1	yes	characteristic
19	C₂×C₄²	C₂²	1	1	yes	characteristic
20	C₂×C₄²	C₂²	1	2	yes	—
21	#95	C₂²	1	8	yes	—
22	C₂×Q₈	—	2	4	no	—
23	C₂×Q₈	—	2	4	no	—
24	C₂×Q₈	C₂×C₄	1	8	yes	—
25	C₂²×C₄	C₂³	1	4	yes	—
26	C₂²×C₄	C₂³	1	4	yes	—
27	C₂²×C₄	C₂³	1	1	yes	characteristic
28	C₂²×C₄	C₂³	1	2	yes	—
29	C₂²×C₄	C₂³	1	1	yes	characteristic
30	C₂²×C₄	C₂³	1	2	yes	—
31	C₂²×C₄	C₂³	1	1	yes	characteristic
32	C₄⋊C₄	—	2	8	no	—
33	C₄⋊C₄	—	2	4	no	—
34	C₄⋊C₄	—	2	8	no	—
35	C₄⋊C₄	C₂×C₄	1	16	yes	—
36	C₄²	—	2	8	no	—
37	C₄²	—	2	2	no	—
38	C₄²	—	2	4	no	—
39	C₄²	C₂×C₄	1	4	yes	—
40	C₄²	D₄	1	4	yes	—
41	C₄²	Q₈	1	8	yes	complemented
42	C₂³	C₂⁴	1	1	yes	characteristic
43	Q₈	—	2	16	no	—
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	—	2	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	2	4	no	—
49	C₂×C₄	—	2	4	no	—
50	C₂×C₄	—	2	8	no	—
51	C₂×C₄	C₂²×C₄	1	8	yes	—
52	C₂×C₄	C₂²×C₄	1	2	yes	—
53	C₂×C₄	C₂²×C₄	1	4	yes	—
54	C₂×C₄	C₂×D₄	1	2	yes	—
55	C₂×C₄	C₂×D₄	1	2	yes	—
56	C₂×C₄	C₂×D₄	1	2	yes	—
57	C₂×C₄	C₂×Q₈	1	4	yes	—
58	C₂×C₄	C₂×Q₈	1	4	yes	—
59	C₂×C₄	C₂×Q₈	1	4	yes	—
60	C₂×C₄	#41	1	2	yes	—
61	C₂×C₄	#41	1	4	yes	—
62	C₂²	C₂³×C₄	1	1	yes	characteristic
63	C₂²	C₂²×D₄	1	1	yes	characteristic
64	C₂²	C₂²×Q₈	1	2	yes	—
65	C₂²	C₂×#41	1	1	yes	characteristic
66	C₂²	C₂×#41	1	2	yes	—
67	C₄	—	2	8	no	—
68	C₄	—	2	2	no	—
69	C₄	—	2	4	no	—
70	C₄	—	4	4	no	—
71	C₄	C₄×D₄	1	4	yes	—
72	C₄	C₄×Q₈	1	8	yes	complemented
73	C₄	C₄⋊Q₈	1	4	yes	direct product factor
74	C₂	C₂×C₄×D₄	1	1	yes	characteristic
75	C₂	C₂×C₄×Q₈	1	2	yes	—
76	C₂	C₂×C₄⋊Q₈	1	1	yes	characteristic
77	C₂	#532	1	1	yes	characteristic
78	C₂	#533	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³
commutator	C₂²	C₂³×C₄
Frattini, socle, prime radical, cosocle	C₂³	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
9. C₄⋊Q₈	C₄	direct (N × H)
41. C₄²	Q₈	semidirect
72. C₄	C₄×Q₈	semidirect
73. C₄	C₄⋊Q₈	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⋊Q₈	2
C₂×C₄×Q₈	2
#391	2
#389	2
#384	2
C₄×C₄⋊C₄	2
C₄³	2

Subgroups — C4×C4⋊Q8 #2307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊Q₈ #2307