Subgroups — #1315

Order 128.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#408	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×#41	C₄	1	1	yes	characteristic
4	C₂×M₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₁₆	—	2	2	no	—
7	C₂²⋊C₈	—	2	2	no	—
8	#41	—	4	1	no	—
9	#41	—	4	1	no	—
10	C₂×Q₈	C₈	1	1	yes	characteristic
11	C₂×D₄	—	2	1	no	—
12	C₂×D₄	C₈	1	1	yes	characteristic
13	C₂²×C₄	—	2	1	no	—
14	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
15	M₁₆	—	4	1	no	—
16	C₂×C₈	—	2	1	no	—
17	C₂×C₈	—	4	1	no	—
18	C₂×C₈	D₄	1	2	yes	—
19	C₁₆	—	4	2	no	—
20	C₂³	—	2	1	no	—
21	C₂³	M₁₆	1	1	yes	characteristic
22	Q₈	—	4	1	no	—
23	D₄	—	4	1	no	—
24	D₄	—	4	2	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	—	4	1	no	—
30	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄	C₂×C₈	1	1	yes	characteristic
32	C₈	—	2	2	no	—
33	C₈	—	4	1	no	—
34	C₂²	—	2	1	no	—
35	C₂²	—	2	2	no	—
36	C₂²	—	4	1	no	—
37	C₂²	—	4	2	no	—
38	C₂²	C₂²⋊C₈	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	4	1	no	—
41	C₄	#99	1	1	yes	characteristic
42	C₄	#100	1	1	yes	characteristic
43	C₂	—	4	1	no	—
44	C₂	—	8	1	no	—
45	C₂	#323	1	1	yes	characteristic
46	C₂	#350	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²⋊C₁₆	C₂	semidirect

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

subgroup	index
#408	2
C₂²⋊C₁₆	2