Subgroups — C₂×#379 #2277

Order 128.

1732 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₄	C₂	1	6	yes	maximal, complemented
3	#379	C₂	1	8	yes	maximal, direct product factor
4	C₂⁵	—	2	24	no	—
5	C₂⁵	C₄	1	8	yes	complemented
6	C₂⁵	C₂²	1	4	yes	—
7	C₂⁵	C₂²	1	3	yes	—
8	C₂³×C₄	C₂²	1	4	yes	complemented
9	C₂×C₂²⋊C₄	—	2	24	no	—
10	C₂×C₂²⋊C₄	C₂²	1	24	yes	complemented
11	C₂⁴	—	2	128	no	—
12	C₂⁴	—	2	96	no	—
13	C₂⁴	—	2	48	no	—
14	C₂⁴	—	2	24	no	—
15	C₂⁴	C₂×C₄	1	12	yes	—
16	C₂⁴	C₂×C₄	1	16	yes	complemented
17	C₂⁴	D₄	1	24	yes	—
18	C₂⁴	C₂³	1	6	yes	—
19	C₂⁴	C₂³	1	1	yes	characteristic
20	C₂²×C₄	—	2	24	no	—
21	C₂²×C₄	C₂³	1	8	yes	complemented
22	C₂²⋊C₄	—	2	48	no	—
23	C₂³	—	2	128	no	—
24	C₂³	—	2	256	no	—
25	C₂³	—	2	48	no	—
26	C₂³	—	2	96	no	—
27	C₂³	—	2	96	no	—
28	C₂³	—	2	24	no	—
29	C₂³	C₂²⋊C₄	1	48	yes	complemented
30	C₂³	C₂²×C₄	1	12	yes	—
31	C₂³	C₂²×C₄	1	2	yes	—
32	C₂³	C₂×D₄	1	24	yes	—
33	C₂³	C₂×D₄	1	12	yes	—
34	C₂³	C₂⁴	1	1	yes	characteristic
35	C₂×C₄	—	2	24	no	—
36	C₂×C₄	—	4	16	no	—
37	C₂²	—	2	128	no	—
38	C₂²	—	2	24	no	—
39	C₂²	—	2	48	no	—
40	C₂²	—	2	96	no	—
41	C₂²	C₂×C₂²⋊C₄	1	12	yes	—
42	C₂²	C₂×C₂²⋊C₄	1	24	yes	complemented
43	C₂²	#120	1	16	yes	—
44	C₂²	C₂³×C₄	1	1	yes	characteristic
45	C₂²	C₂²×D₄	1	6	yes	—
46	C₄	—	4	8	no	—
47	C₂	—	2	24	no	—
48	C₂	#379	1	8	yes	direct product factor
49	C₂	C₂²×C₂²⋊C₄	1	3	yes	—
50	C₂	C₂×#120	1	4	yes	—

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

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