Subgroups — C₂²×#14583829 #26012544

Order 11072.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583829	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#13063436	C₂	1	1	yes	maximal, characteristic
3	#14583829	C₂²	1	4	yes	direct product factor
4	C₂×#13063436	C₄	1	3	yes	—
5	C₂×#13063436	C₂²	1	3	yes	—
6	C₂²×C₄×C₁₇₃	C₄	1	1	yes	characteristic
7	#13063436	C₂×C₄	1	3	yes	—
8	#13063436	C₂³	1	1	yes	characteristic
9	C₂³×C₁₇₃	C₈	1	1	yes	characteristic
10	C₂×C₄×C₁₇₃	C₈	1	3	yes	—
11	C₂×C₄×C₁₇₃	C₂×C₄	1	3	yes	—
12	C₂²×C₁₇₃	C₁₆	1	4	yes	complemented
13	C₂²×C₁₇₃	C₂×C₈	1	3	yes	—
14	C₄×C₁₇₃	C₂×C₈	1	3	yes	—
15	C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₁₇₃	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
18	C₁₇₃	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	173	1	no	maximal, Sylow
20	C₂²×C₈	—	173	1	no	—
21	C₂×C₁₆	—	173	6	no	—
22	C₂²×C₄	#10621924	1	1	yes	characteristic
23	C₂×C₈	—	173	3	no	—
24	C₂×C₈	—	173	3	no	—
25	C₁₆	—	173	4	no	—
26	C₂³	#13063443	1	1	yes	characteristic
27	C₂×C₄	#13063443	1	3	yes	—
28	C₂×C₄	C₂×#10621924	1	3	yes	—
29	C₈	—	173	3	no	—
30	C₈	—	173	1	no	—
31	C₂²	#14583829	1	4	yes	direct product factor
32	C₂²	C₂×#13063443	1	3	yes	—
33	C₄	C₂×#13063443	1	3	yes	—
34	C₄	C₂²×#10621924	1	1	yes	characteristic
35	C₂	C₂×#14583829	1	6	yes	direct product factor
36	C₂	C₂²×#13063443	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.