Subgroups — #2082

Order 128.

92 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	#419	C₂	1	1	yes	maximal, characteristic
3	#419	C₂	1	1	yes	maximal, characteristic
4	C₂×#101	C₂	1	1	yes	maximal, characteristic
5	#344	C₂	1	1	yes	maximal, characteristic
6	#344	C₂	1	1	yes	maximal, characteristic
7	H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈	C₂²	1	1	yes	characteristic
9	C₂×M₁₆	C₂²	1	1	yes	characteristic
10	C₂×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×M₁₆	C₂²	1	1	yes	characteristic
13	#117	C₂²	1	1	yes	characteristic
14	#117	C₂²	1	1	yes	characteristic
15	#108	—	2	2	no	—
16	#103	—	2	2	no	—
17	#103	—	2	2	no	—
18	#101	—	2	2	no	—
19	C₂×Q₈	—	2	1	no	—
20	C₂×Q₈	—	2	1	no	—
21	C₂×Q₈	—	2	1	no	—
22	C₂×Q₈	—	2	1	no	—
23	C₂×Q₈	—	2	1	no	—
24	C₂×Q₈	D₄	1	2	yes	—
25	C₂²×C₄	—	2	1	no	—
26	C₂²×C₄	C₂³	1	1	yes	characteristic
27	M₁₆	—	2	1	no	—
28	M₁₆	—	2	1	no	—
29	M₁₆	—	2	1	no	—
30	M₁₆	—	2	1	no	—
31	M₁₆	—	2	1	no	—
32	M₁₆	—	2	1	no	—
33	M₁₆	—	2	1	no	—
34	M₁₆	—	2	1	no	—
35	C₂×C₈	—	2	1	no	—
36	C₂×C₈	—	2	1	no	—
37	C₂×C₈	—	2	1	no	—
38	C₂×C₈	D₄	1	2	yes	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	2	1	no	—
41	C₂²⋊C₄	—	2	1	no	—
42	C₂²⋊C₄	—	2	1	no	—
43	C₄²	—	2	1	no	—
44	C₄²	—	2	1	no	—
45	C₂³	#41	1	1	yes	characteristic
46	Q₈	—	2	2	no	—
47	Q₈	—	2	2	no	—
48	Q₈	—	4	1	no	—
49	Q₈	—	4	1	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	—	4	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	4	1	no	—
55	C₂×C₄	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄	#41	1	1	yes	characteristic
58	C₂×C₄	#41	1	1	yes	characteristic
59	C₂×C₄	#41	1	1	yes	characteristic
60	C₂×C₄	#41	1	1	yes	characteristic
61	C₈	—	2	2	no	—
62	C₈	—	4	1	no	—
63	C₈	—	4	1	no	—
64	C₈	—	4	1	no	—
65	C₂²	—	4	1	no	—
66	C₂²	#123	1	1	yes	characteristic
67	C₂²	#124	1	1	yes	characteristic
68	C₂²	#126	1	1	yes	characteristic
69	C₄	—	4	2	no	—
70	C₄	—	8	1	no	—
71	C₄	—	8	1	no	—
72	C₄	#121	1	1	yes	characteristic
73	C₄	#123	1	1	yes	characteristic
74	C₄	#123	1	1	yes	characteristic
75	C₄	#126	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	2	1	no	—
78	C₂	—	2	1	no	—
79	C₂	#397	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#397
commutator, Frattini, cosocle	C₂²×C₄	C₂³
prime radical	C₂³	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Maximal subgroups

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

subgroup	index
#430	2
#419	2
C₂×#101	2
#344	2
H(3,ℤ/4)	2