Subgroups — #2245

Order 128.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#499	C₂	1	1	yes	maximal, characteristic
2	#494	C₂	1	1	yes	maximal, characteristic
3	#358	C₂	1	4	yes	maximal
4	#346	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆	—	2	1	no	—
6	C₂×Q₁₆	C₂²	1	2	yes	—
7	C₄⋊Q₈	—	2	1	no	—
8	#125	—	2	1	no	—
9	C₂×C₁₆	C₂²	1	2	yes	—
10	#107	C₂²	1	2	yes	—
11	#106	—	2	1	no	—
12	C₄×C₈	C₂²	1	1	yes	characteristic
13	C₂×Q₈	—	2	2	no	—
14	Q₁₆	—	2	4	no	—
15	Q₁₆	—	4	2	no	—
16	C₂×C₈	D₄	1	1	yes	characteristic
17	C₂×C₈	C₂³	1	1	yes	characteristic
18	C₄⋊C₄	—	2	2	no	—
19	C₄⋊C₄	—	4	2	no	—
20	C₄⋊C₄	—	4	2	no	—
21	C₄²	D₄	1	1	yes	characteristic
22	C₁₆	—	2	2	no	—
23	Q₈	—	4	2	no	—
24	Q₈	—	4	2	no	—
25	C₂×C₄	—	4	2	no	—
26	C₂×C₄	—	4	2	no	—
27	C₂×C₄	D₈	1	2	yes	—
28	C₂×C₄	C₂×D₄	1	1	yes	characteristic
29	C₈	SD₁₆	1	2	yes	—
30	C₈	#41	1	2	yes	—
31	C₂²	C₂×D₈	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	—	8	2	no	—
34	C₄	—	8	2	no	—
35	C₄	#124	1	1	yes	characteristic
36	C₄	C₂×SD₁₆	1	1	yes	characteristic
37	C₂	#486	1	1	yes	characteristic
38	C₂	#510	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

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