Subgroups — #2102

Order 128.

79 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#430	C₂	1	1	yes	maximal, characteristic
2	#423	C₂	1	1	yes	maximal, characteristic
3	#344	C₂	1	2	yes	maximal
4	#339	C₂	1	2	yes	maximal
5	H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆	C₂²	1	2	yes	—
7	C₂×M₁₆	C₂²	1	1	yes	characteristic
8	C₂×M₁₆	C₂²	1	1	yes	characteristic
9	#117	C₂²	1	2	yes	—
10	C₂×C₄²	C₂²	1	1	yes	characteristic
11	#108	—	2	2	no	—
12	C₄⋊C₈	—	2	2	no	—
13	C₂²×C₄	—	2	1	no	—
14	C₂²×C₄	C₂³	1	1	yes	characteristic
15	M₁₆	—	2	2	no	—
16	M₁₆	—	2	2	no	—
17	M₁₆	—	2	2	no	—
18	M₁₆	—	2	2	no	—
19	C₂×C₈	—	2	1	no	—
20	C₂×C₈	—	2	2	no	—
21	C₂×C₈	D₄	1	2	yes	—
22	C₄⋊C₄	—	2	2	no	—
23	C₂²⋊C₄	—	2	2	no	—
24	C₄²	—	2	1	no	—
25	C₄²	—	2	2	no	—
26	C₄²	Q₈	1	1	yes	characteristic
27	C₄²	Q₈	1	1	yes	characteristic
28	C₂³	#41	1	1	yes	characteristic
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	—	2	1	no	—
31	C₂×C₄	—	4	2	no	—
32	C₂×C₄	—	4	2	no	—
33	C₂×C₄	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄	#41	1	2	yes	—
36	C₂×C₄	#41	1	2	yes	—
37	C₈	—	2	2	no	—
38	C₈	—	4	1	no	—
39	C₈	—	4	2	no	—
40	C₂²	—	4	1	no	—
41	C₂²	C₂²⋊Q₈	1	1	yes	characteristic
42	C₂²	#126	1	2	yes	—
43	C₄	—	2	2	no	—
44	C₄	—	4	1	no	—
45	C₄	—	8	2	no	—
46	C₄	#123	1	1	yes	characteristic
47	C₄	#124	1	1	yes	characteristic
48	C₄	#125	1	2	yes	—
49	C₂	—	2	1	no	—
50	C₂	—	2	2	no	—
51	C₂	#400	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³
socle	C₂	#400
prime radical	C₂³	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

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