Subgroups — #1636

Order 128.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#557	C₂	1	1	yes	maximal, characteristic
2	#487	C₂	1	1	yes	maximal, characteristic
3	#477	C₂	1	1	yes	maximal, characteristic
4	#477	C₂	1	1	yes	maximal, characteristic
5	#332	C₂	1	1	yes	maximal, characteristic
6	Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
7	Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₄⋊Q₈	—	2	1	no	—
9	C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	#125	—	2	2	no	—
12	#125	—	2	1	no	—
13	C₄×Q₈	—	2	1	no	—
14	C₄×Q₈	—	2	1	no	—
15	C₄×Q₈	C₂²	1	1	yes	characteristic
16	C₄×Q₈	C₂²	1	1	yes	characteristic
17	#107	—	2	1	no	—
18	#107	—	2	1	no	—
19	C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊C₈	C₂²	1	1	yes	characteristic
21	#103	—	2	1	no	—
22	#103	—	2	1	no	—
23	#103	—	2	2	no	—
24	C₄×C₈	C₂²	1	1	yes	characteristic
25	C₂×Q₈	—	2	1	no	—
26	C₂×Q₈	—	2	1	no	—
27	C₂×Q₈	D₄	1	1	yes	characteristic
28	C₂×Q₈	D₄	1	1	yes	characteristic
29	C₂×C₈	—	2	1	no	—
30	C₂×C₈	—	2	1	no	—
31	C₂×C₈	—	2	1	no	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	2	2	no	—
34	C₄⋊C₄	—	2	2	no	—
35	C₄⋊C₄	—	2	1	no	—
36	C₄⋊C₄	—	2	1	no	—
37	C₄⋊C₄	—	2	1	no	—
38	C₄⋊C₄	—	2	1	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	D₄	1	2	yes	—
41	C₄⋊C₄	D₄	1	1	yes	characteristic
42	C₄⋊C₄	D₄	1	1	yes	characteristic
43	C₄²	—	2	2	no	—
44	C₄²	—	2	1	no	—
45	C₄²	—	2	1	no	—
46	C₄²	C₂³	1	1	yes	characteristic
47	Q₈	—	2	1	no	—
48	Q₈	—	2	1	no	—
49	Q₈	—	2	1	no	—
50	Q₈	—	4	2	no	—
51	Q₈	—	4	1	no	—
52	Q₈	—	4	1	no	—
53	Q₈	Q₁₆	1	2	yes	—
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	4	1	no	—
60	C₂×C₄	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄	C₂×D₄	1	1	yes	characteristic
63	C₈	—	4	1	no	—
64	C₈	—	4	1	no	—
65	C₈	—	4	1	no	—
66	C₂²	#120	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	2	1	no	—
69	C₄	—	4	1	no	—
70	C₄	—	4	2	no	—
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	8	1	no	—
74	C₄	C₂×Q₁₆	1	1	yes	characteristic
75	C₄	#135	1	1	yes	characteristic
76	C₄	#137	1	1	yes	characteristic
77	C₄	#137	1	1	yes	characteristic
78	C₂	#451	1	1	yes	characteristic
79	C₂	#452	1	1	yes	characteristic
80	C₂	#454	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²	#120
commutator, Frattini, cosocle	C₄²	C₂³
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Maximal subgroups

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

subgroup	index
#557	2
#487	2
#477	2
#332	2
Q₈⋊C₈	2