Subgroups — #1836

Order 128.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#97	C₂	1	1	yes	maximal, characteristic
2	#384	C₂	1	1	yes	maximal, characteristic
3	#382	C₂	1	1	yes	maximal, characteristic
4	#340	C₂	1	4	yes	maximal
5	C₂²×C₈	C₂²	1	2	yes	—
6	C₂×C₄⋊C₄	—	2	2	no	—
7	C₂×C₄⋊C₄	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₄²	C₂²	1	1	yes	characteristic
10	#97	C₄	1	4	yes	complemented
11	#95	—	2	2	no	—
12	C₂²×C₄	—	2	2	no	—
13	C₂²×C₄	—	2	2	no	—
14	C₂²×C₄	D₄	1	2	yes	—
15	C₂²×C₄	C₂³	1	1	yes	characteristic
16	C₂×C₈	—	2	2	no	—
17	C₂×C₈	—	2	2	no	—
18	C₂×C₈	C₂×C₄	1	4	yes	—
19	C₄⋊C₄	—	2	4	no	—
20	C₄⋊C₄	—	2	4	no	—
21	C₄⋊C₄	—	4	4	no	—
22	C₄²	C₂×C₄	1	2	yes	—
23	C₄²	Q₈	1	2	yes	—
24	C₂³	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	—	2	2	no	—
27	C₂×C₄	—	4	2	no	—
28	C₂×C₄	—	4	2	no	—
29	C₂×C₄	—	4	4	no	—
30	C₂×C₄	—	4	2	no	—
31	C₂×C₄	—	4	2	no	—
32	C₂×C₄	C₄⋊C₄	1	4	yes	—
33	C₂×C₄	C₂²×C₄	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	4	no	—
38	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂²	#124	1	1	yes	characteristic
40	C₂²	#124	1	1	yes	characteristic
41	C₂²	AGL(1,ℤ/8)	1	2	yes	—
42	C₂²	#137	1	2	yes	—
43	C₄	—	2	4	no	—
44	C₄	—	8	2	no	—
45	C₄	—	8	2	no	—
46	C₄	#117	1	2	yes	—
47	C₄	#125	1	2	yes	—
48	C₂	#382	1	1	yes	characteristic
49	C₂	#428	1	2	yes	—
50	C₂	#489	1	2	yes	—
51	C₂	#490	1	1	yes	characteristic
52	C₂	#491	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. #97	C₄	semidirect

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