Subgroups — #384×C₁₇₃ #26011007

Order 11072.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₁₇₃	C₂	1	6	yes	maximal
2	C₂×C₄²×C₁₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₁₇₃	C₂²	1	4	yes	—
4	C₂²×C₄×C₁₇₃	C₂²	1	3	yes	—
5	C₄⋊C₄×C₁₇₃	—	2	12	no	—
6	C₄²×C₁₇₃	C₄	1	4	yes	complemented
7	C₂³×C₁₇₃	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₁₇₃	—	2	12	no	—
9	C₂×C₄×C₁₇₃	C₂×C₄	1	6	yes	—
10	C₂×C₄×C₁₇₃	D₄	1	6	yes	—
11	C₂×C₄×C₁₇₃	Q₈	1	6	yes	—
12	C₂²×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
13	C₂²×C₁₇₃	C₂×D₄	1	3	yes	—
14	C₂²×C₁₇₃	C₂×Q₈	1	3	yes	—
15	C₄×C₁₇₃	—	4	4	no	—
16	C₄×C₁₇₃	C₄⋊C₄	1	12	yes	complemented
17	C₂×C₁₇₃	C₂×C₄⋊C₄	1	3	yes	—
18	C₂×C₁₇₃	#127	1	1	yes	characteristic
19	C₂×C₁₇₃	C₄⋊Q₈	1	3	yes	—
20	C₁₇₃	#384	1	1	yes	characteristic, direct product factor, Sylow
21	#384	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂×C₄⋊C₄	C₂×C₁₇₃	1	6	yes	—
23	C₂×C₄²	C₂×C₁₇₃	1	1	yes	characteristic
24	C₂²×C₄	C₂²×C₁₇₃	1	4	yes	—
25	C₂²×C₄	C₂²×C₁₇₃	1	3	yes	—
26	C₄⋊C₄	—	2	12	no	—
27	C₄²	C₄×C₁₇₃	1	4	yes	complemented
28	C₂³	C₂³×C₁₇₃	1	1	yes	characteristic
29	C₂×C₄	—	2	12	no	—
30	C₂×C₄	C₂×C₄×C₁₇₃	1	6	yes	—
31	C₂×C₄	D₄×C₁₇₃	1	6	yes	—
32	C₂×C₄	Q₈×C₁₇₃	1	6	yes	—
33	C₂²	C₂²×C₄×C₁₇₃	1	1	yes	characteristic
34	C₂²	C₂×D₄×C₁₇₃	1	3	yes	—
35	C₂²	C₂×Q₈×C₁₇₃	1	3	yes	—
36	C₄	—	4	4	no	—
37	C₄	C₄⋊C₄×C₁₇₃	1	12	yes	complemented
38	C₂	C₂×C₄⋊C₄×C₁₇₃	1	3	yes	—
39	C₂	#127×C₁₇₃	1	1	yes	characteristic
40	C₂	C₄⋊Q₈×C₁₇₃	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇₃	C₂³
commutator	C₂²	C₂²×C₄×C₁₇₃
Frattini, cosocle	C₂³	C₂³×C₁₇₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄²×C₁₇₃	C₄	semidirect
16. C₄×C₁₇₃	C₄⋊C₄	semidirect
20. C₁₇₃	#384	direct (N × H)
21. #384	C₁₇₃	direct (N × H)
27. C₄²	C₄×C₁₇₃	semidirect
37. C₄	C₄⋊C₄×C₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×C₁₇₃	2
C₂×C₄²×C₁₇₃	2
#384	173

Subgroups — #384×C173 #26011007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #384×C₁₇₃ #26011007