Subgroups — C₁₁×#2104 #13064942

Order 1408.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#342	C₂	1	7	yes	maximal
2	C₂×C₁₁×C₂²⋊C₄	C₂²	1	7	yes	—
3	C₂⁴×C₁₁	C₂³	1	1	yes	characteristic
4	C₂²×C₄×C₁₁	—	2	7	no	—
5	C₁₁×C₂²⋊C₄	—	2	14	no	—
6	#2104	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂³×C₁₁	—	8	1	no	—
8	C₂³×C₁₁	#41	1	7	yes	—
9	C₂×C₄×C₁₁	—	4	7	no	—
10	C₂×C₄×C₁₁	—	8	7	no	—
11	#342	C₂×C₁₁	1	7	yes	—
12	C₂²×C₁₁	—	4	7	no	—
13	C₂²×C₁₁	#126	1	7	yes	—
14	C₄×C₁₁	—	8	7	no	—
15	C₂×C₂²⋊C₄	C₂²×C₁₁	1	7	yes	—
16	C₂×C₁₁	—	2	7	no	—
17	C₂×C₁₁	#401	1	1	yes	characteristic
18	C₂⁴	C₂³×C₁₁	1	1	yes	characteristic
19	C₂²×C₄	—	2	7	no	—
20	C₂²⋊C₄	—	2	14	no	—
21	C₁₁	#2104	1	1	yes	characteristic, direct product factor, Sylow
22	C₂³	—	8	1	no	—
23	C₂³	C₁₁×#41	1	7	yes	—
24	C₂×C₄	—	4	7	no	—
25	C₂×C₄	—	8	7	no	—
26	C₂²	—	4	7	no	—
27	C₂²	C₁₁×#126	1	7	yes	—
28	C₄	—	8	7	no	—
29	C₂	—	2	7	no	—
30	C₂	C₁₁×#401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	#401
commutator, Frattini, cosocle	C₂⁴	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂⁴×C₁₁ ◁ G

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

N	H ≅ G/N	type
6. #2104	C₁₁	direct (N × H)
21. C₁₁	#2104	direct (N × H)

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

subgroup	index
C₁₁×#342	2
#2104	11