Subgroups — C₄×#63216 #11763694

Order 1088.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63216	C₂	1	2	yes	maximal
2	C₄×#3622	C₂	1	1	yes	maximal, characteristic
3	C₄²×C₁₇	C₄	1	1	yes	characteristic
4	C₂×#3622	C₄	1	1	yes	characteristic
5	C₂×#3622	C₂²	1	1	yes	characteristic
6	#63216	C₄	1	4	yes	direct product factor
7	C₂×C₄×C₁₇	C₈	1	2	yes	—
8	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
9	#3622	C₈	1	2	yes	—
10	#3622	C₂×C₄	1	2	yes	—
11	C₂²×C₁₇	C₂×C₈	1	1	yes	characteristic
12	C₄×C₁₇	C₁₆	1	4	yes	complemented
13	C₄×C₁₇	C₄²	1	1	yes	characteristic
14	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₆	—	17	1	no	maximal, Sylow
16	C₂×C₁₇	C₄×C₈	1	1	yes	characteristic
17	C₂×C₁₇	C₂×C₁₆	1	2	yes	—
18	C₂×C₁₆	—	17	2	no	—
19	C₄×C₈	—	17	1	no	—
20	C₁₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₈	—	17	1	no	—
22	C₂×C₈	—	17	1	no	—
23	C₄²	#595	1	1	yes	characteristic
24	C₁₆	—	17	4	no	—
25	C₂×C₄	#3624	1	2	yes	—
26	C₂×C₄	C₂×#595	1	1	yes	characteristic
27	C₈	—	17	2	no	—
28	C₈	—	17	2	no	—
29	C₂²	C₂×#3624	1	1	yes	characteristic
30	C₄	#63216	1	4	yes	direct product factor
31	C₄	#63242	1	1	yes	characteristic
32	C₄	C₄×#595	1	1	yes	characteristic
33	C₂	C₂×#63216	1	2	yes	—
34	C₂	C₄×#3624	1	1	yes	characteristic

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.