Subgroups — #1837

Order 128.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#423	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#341	C₂	1	4	yes	maximal
4	C₂×M₁₆	C₂²	1	4	yes	—
5	C₂²×C₈	C₂²	1	2	yes	—
6	C₂×C₄²	C₂²	1	1	yes	characteristic
7	C₄⋊C₈	—	2	4	no	—
8	C₄×C₈	C₄	1	2	yes	—
9	C₄×C₈	C₄	1	2	yes	—
10	C₂²×C₄	Q₈	1	2	yes	—
11	C₂²×C₄	C₂³	1	1	yes	characteristic
12	M₁₆	—	2	8	no	—
13	C₂×C₈	—	2	4	no	—
14	C₂×C₈	—	2	4	no	—
15	C₂×C₈	C₂×C₄	1	4	yes	—
16	C₄²	C₂×C₄	1	1	yes	characteristic
17	C₄²	C₂×C₄	1	1	yes	characteristic
18	C₄²	D₄	1	2	yes	—
19	C₂³	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄	—	2	4	no	—
21	C₂×C₄	C₄⋊C₄	1	2	yes	—
22	C₂×C₄	C₄⋊C₄	1	2	yes	—
23	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄	#41	1	4	yes	—
26	C₈	—	2	4	no	—
27	C₈	—	4	4	no	—
28	C₂²	—	2	2	no	—
29	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂²	#125	1	2	yes	—
31	C₄	—	2	2	no	—
32	C₄	#108	1	4	yes	—
33	C₄	#117	1	2	yes	—
34	C₄	#124	1	2	yes	—
35	C₂	—	2	2	no	—
36	C₂	#382	1	1	yes	characteristic
37	C₂	C₂×#108	1	2	yes	—

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