Subgroups — #1696

Order 128.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500	C₂	1	1	yes	maximal, characteristic
2	#477	C₂	1	2	yes	maximal
3	#446	C₂	1	1	yes	maximal, characteristic
4	#334	C₂	1	1	yes	maximal, characteristic
5	#333	C₂	1	2	yes	maximal
6	C₄⋊Q₈	C₂²	1	2	yes	—
7	C₄×Q₈	C₂²	1	1	yes	characteristic
8	#107	—	2	1	no	—
9	#107	—	2	1	no	—
10	#107	—	2	2	no	—
11	C₄⋊C₈	—	2	1	no	—
12	C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₄⋊C₈	C₂²	1	2	yes	—
14	#103	—	2	2	no	—
15	#97	—	2	1	no	—
16	C₄×C₈	C₂²	1	1	yes	characteristic
17	C₂×Q₈	—	2	2	no	—
18	C₂×Q₈	D₄	1	1	yes	characteristic
19	C₂×C₈	—	2	1	no	—
20	C₂×C₈	—	2	2	no	—
21	C₂×C₈	D₄	1	1	yes	characteristic
22	C₂×C₈	D₄	1	1	yes	characteristic
23	C₄⋊C₄	—	2	1	no	—
24	C₄⋊C₄	—	2	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄⋊C₄	D₄	1	1	yes	characteristic
27	C₄²	—	2	1	no	—
28	C₄²	C₂³	1	1	yes	characteristic
29	Q₈	—	2	2	no	—
30	Q₈	—	8	2	no	—
31	C₂×C₄	—	2	1	no	—
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	—	4	2	no	—
34	C₂×C₄	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄	#41	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	—	4	1	no	—
39	C₈	—	4	2	no	—
40	C₈	Q₁₆	1	2	yes	—
41	C₂²	#121	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	4	1	no	—
44	C₄	—	4	1	no	—
45	C₄	—	8	2	no	—
46	C₄	C₂×Q₁₆	1	1	yes	characteristic
47	C₄	#137	1	1	yes	characteristic
48	C₄	#137	1	2	yes	—
49	C₂	#462	1	1	yes	characteristic
50	C₂	#470	1	1	yes	characteristic
51	C₂	#472	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

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