Subgroups — C₄×#14583801 #26011265

Order 11072.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583801	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₇₃	C₂	1	1	yes	maximal, characteristic
3	#14583801	C₄	1	4	yes	direct product factor
4	C₂×C₈×C₁₇₃	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₇₃	C₂²	1	1	yes	characteristic
6	C₄²×C₁₇₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₇₃	C₈	1	2	yes	—
8	C₂×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₇₃	C₈	1	2	yes	—
10	C₈×C₁₇₃	C₂×C₄	1	2	yes	—
11	C₂²×C₁₇₃	C₂×C₈	1	1	yes	characteristic
12	C₄×C₁₇₃	C₁₆	1	4	yes	complemented
13	C₄×C₁₇₃	C₄²	1	1	yes	characteristic
14	C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
15	C₂×C₁₇₃	C₄×C₈	1	1	yes	characteristic
16	C₂×C₁₇₃	C₂×C₁₆	1	2	yes	—
17	C₁₇₃	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₁₆	—	173	1	no	maximal, Sylow
19	C₂×C₁₆	—	173	2	no	—
20	C₄×C₈	D₁₇₃	1	1	yes	characteristic
21	C₂×C₈	Dic₁₇₃	1	1	yes	characteristic
22	C₂×C₈	C₂×D₁₇₃	1	1	yes	characteristic
23	C₄²	Dic₁₇₃	1	1	yes	characteristic
24	C₁₆	—	173	4	no	—
25	C₂×C₄	#13063436	1	2	yes	—
26	C₂×C₄	C₂×Dic₁₇₃	1	1	yes	characteristic
27	C₈	#13063436	1	2	yes	—
28	C₈	C₄×D₁₇₃	1	2	yes	—
29	C₂²	C₂×#13063436	1	1	yes	characteristic
30	C₄	#14583801	1	4	yes	direct product factor
31	C₄	C₄×Dic₁₇₃	1	1	yes	characteristic
32	C₄	C₂×#13063436	1	1	yes	characteristic
33	C₂	C₄×#13063436	1	1	yes	characteristic
34	C₂	C₂×#14583801	1	2	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.