Subgroups — #2097

Order 128.

119 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#107	C₂	1	1	yes	maximal, characteristic
2	C₂×#106	C₂	1	1	yes	maximal, characteristic
3	C₂×#103	C₂	1	1	yes	maximal, characteristic
4	C₂×#103	C₂	1	1	yes	maximal, characteristic
5	#391	C₂	1	1	yes	maximal, characteristic
6	#382	C₂	1	1	yes	maximal, characteristic
7	#336	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₄²	C₂²	1	1	yes	characteristic
15	#107	—	2	2	no	—
16	#106	—	2	2	no	—
17	#103	—	2	2	no	—
18	#103	—	2	2	no	—
19	#95	—	2	2	no	—
20	#95	—	2	2	no	—
21	C₂×Q₈	—	2	1	no	—
22	C₂×Q₈	—	2	1	no	—
23	C₂×Q₈	—	2	1	no	—
24	C₂×Q₈	—	2	1	no	—
25	C₂×Q₈	—	2	1	no	—
26	C₂×Q₈	Q₈	1	2	yes	—
27	C₂²×C₄	—	2	1	no	—
28	C₂²×C₄	—	2	1	no	—
29	C₂²×C₄	—	2	1	no	—
30	C₂²×C₄	—	2	1	no	—
31	C₂²×C₄	D₄	1	2	yes	—
32	C₂²×C₄	C₂³	1	1	yes	characteristic
33	C₂×C₈	—	2	1	no	—
34	C₂×C₈	—	2	1	no	—
35	C₂×C₈	—	2	1	no	—
36	C₂×C₈	—	2	1	no	—
37	C₂×C₈	D₄	1	2	yes	—
38	C₂×C₈	D₄	1	2	yes	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	2	1	no	—
41	C₄⋊C₄	—	2	1	no	—
42	C₄⋊C₄	—	2	1	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	2	1	no	—
45	C₄²	—	2	1	no	—
46	C₄²	—	2	1	no	—
47	C₂³	C₂×D₄	1	1	yes	characteristic
48	Q₈	—	2	2	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	4	1	no	—
51	Q₈	—	4	1	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	4	1	no	—
57	C₂×C₄	—	4	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	—	4	1	no	—
60	C₂×C₄	—	4	1	no	—
61	C₂×C₄	—	4	2	no	—
62	C₂×C₄	—	4	2	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
67	C₂×C₄	#41	1	1	yes	characteristic
68	C₂×C₄	#41	1	1	yes	characteristic
69	C₂×C₄	#41	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	2	2	no	—
72	C₂²	C₂²⋊Q₈	1	1	yes	characteristic
73	C₂²	#123	1	1	yes	characteristic
74	C₂²	#127	1	1	yes	characteristic
75	C₂²	#135	1	2	yes	—
76	C₂²	#137	1	2	yes	—
77	C₄	—	4	2	no	—
78	C₄	—	4	2	no	—
79	C₄	—	8	1	no	—
80	C₄	—	8	1	no	—
81	C₄	—	8	1	no	—
82	C₄	C₂²⋊Q₈	1	1	yes	characteristic
83	C₄	C₂²⋊Q₈	1	1	yes	characteristic
84	C₄	#123	1	1	yes	characteristic
85	C₄	#123	1	1	yes	characteristic
86	C₂	#399	1	1	yes	characteristic
87	C₂	#479	1	2	yes	—
88	C₂	#485	1	2	yes	—
89	C₂	#495	1	1	yes	characteristic
90	C₂	#497	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ 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
C₂×#107	2
C₂×#106	2
C₂×#103	2
#391	2
#382	2
#336	2