Subgroups — #1684

Order 128.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#487	C₂	1	1	yes	maximal, characteristic
2	#477	C₂	1	1	yes	maximal, characteristic
3	#475	C₂	1	1	yes	maximal, characteristic
4	C₈×Q₈	C₂	1	1	yes	maximal, characteristic
5	#335	C₂	1	1	yes	maximal, characteristic
6	#333	C₂	1	1	yes	maximal, characteristic
7	#332	C₂	1	1	yes	maximal, characteristic
8	C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₄×Q₈	C₂²	1	1	yes	characteristic
11	#107	—	2	1	no	—
12	#106	—	2	1	no	—
13	C₄⋊C₈	—	2	1	no	—
14	C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₄⋊C₈	C₂²	1	1	yes	characteristic
17	#103	—	2	1	no	—
18	#103	—	2	1	no	—
19	#103	—	2	1	no	—
20	#103	—	2	1	no	—
21	C₄×C₈	—	2	1	no	—
22	C₄×C₈	C₂²	1	1	yes	characteristic
23	C₂×Q₈	—	2	1	no	—
24	C₂×Q₈	—	2	1	no	—
25	C₂×Q₈	D₄	1	1	yes	characteristic
26	C₂×C₈	—	2	1	no	—
27	C₂×C₈	—	2	1	no	—
28	C₂×C₈	—	2	1	no	—
29	C₂×C₈	D₄	1	1	yes	characteristic
30	C₂×C₈	D₄	1	1	yes	characteristic
31	C₄⋊C₄	—	2	1	no	—
32	C₄⋊C₄	—	2	1	no	—
33	C₄⋊C₄	—	2	1	no	—
34	C₄⋊C₄	—	2	1	no	—
35	C₄⋊C₄	—	2	1	no	—
36	C₄⋊C₄	D₄	1	1	yes	characteristic
37	C₄²	—	2	1	no	—
38	C₄²	C₂³	1	1	yes	characteristic
39	Q₈	—	2	1	no	—
40	Q₈	—	4	1	no	—
41	Q₈	—	4	1	no	—
42	Q₈	—	8	1	no	—
43	Q₈	Q₁₆	1	2	yes	—
44	C₂×C₄	—	2	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄	#41	1	1	yes	characteristic
51	C₈	—	2	1	no	—
52	C₈	—	2	1	no	—
53	C₈	—	4	1	no	—
54	C₈	—	4	1	no	—
55	C₈	—	4	1	no	—
56	C₂²	#121	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2	1	no	—
59	C₄	—	4	1	no	—
60	C₄	—	8	1	no	—
61	C₄	—	8	1	no	—
62	C₄	C₂×Q₁₆	1	1	yes	characteristic
63	C₄	#135	1	1	yes	characteristic
64	C₄	#135	1	1	yes	characteristic
65	C₄	#137	1	1	yes	characteristic
66	C₂	#464	1	1	yes	characteristic
67	C₂	#467	1	1	yes	characteristic
68	C₂	#471	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²	#121
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
#487	2
#477	2
#475	2
C₈×Q₈	2
#335	2
#333	2
#332	2