Subgroups — Dic₁₁×#89204 #34084635

Order 19404.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#89204	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇²×Dic₁₁	C₃	1	1	yes	maximal, characteristic
3	C₁₁×#89204	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₁	C₂×C₃	1	1	yes	characteristic
5	Dic₁₁×C₇⋊C₉	—	7	8	no	maximal
6	C₇²×Dic₁₁	C₉	1	1	yes	characteristic, complemented, Hall
7	C₄×#89204	—	11	1	no	maximal, Hall
8	C₃×C₇²×C₁₁	C₃×C₄	1	1	yes	characteristic
9	C₂×C₁₁×C₇⋊C₉	—	7	8	no	—
10	C₂×C₇²×C₁₁	C₂×C₉	1	1	yes	characteristic
11	C₃×C₇×Dic₁₁	ΓL(1,𝔽₈)	1	8	yes	—
12	C₂×#89204	D₁₁	1	1	yes	characteristic
13	C₁₁×C₇⋊C₉	—	7	8	no	—
14	C₃×C₄×C₇²	—	11	1	no	—
15	C₇²×C₁₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₇×C₁₁	C₂×ΓL(1,𝔽₈)	1	8	yes	—
17	#89204	Dic₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₉×Dic₁₁	—	49	1	no	Hall
19	C₇×Dic₁₁	C₇⋊C₉	1	8	yes	complemented
20	C₂×C₃×C₇²	C₃×D₁₁	1	1	yes	characteristic
21	C₄×C₇⋊C₉	—	77	8	no	—
22	C₃×C₇×C₁₁	C₄×ΓL(1,𝔽₈)	1	8	yes	—
23	C₂×C₉×C₁₁	—	49	1	no	—
24	C₄×C₇²	—	11	1	no	Hall
25	C₂×C₇×C₁₁	C₂×C₇⋊C₉	1	8	yes	—
26	C₃×C₇²	C₃×Dic₁₁	1	1	yes	characteristic
27	C₃×Dic₁₁	#3861	1	1	yes	characteristic
28	C₂×C₇⋊C₉	—	7	8	no	—
29	C₉×C₁₁	—	49	1	no	Hall
30	C₂×C₇²	C₉×D₁₁	1	1	yes	characteristic
31	C₃×C₄×C₇	—	11	8	no	—
32	C₇×C₁₁	C₄×C₇⋊C₉	1	8	yes	complemented
33	C₂×C₃×C₁₁	C₂×#3861	1	1	yes	characteristic
34	C₇⋊C₉	—	7	8	no	—
35	C₇²	C₉×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
36	Dic₁₁	#89204	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₃×C₇	ΓL(1,𝔽₈)×D₁₁	1	8	yes	—
38	C₄×C₉	—	539	1	no	Hall
39	C₃×C₁₁	C₄×#3861	1	1	yes	characteristic
40	C₄×C₇	—	11	8	no	—
41	C₂×C₁₁	C₂×#89204	1	1	yes	characteristic
42	C₃×C₇	ΓL(1,𝔽₈)×Dic₁₁	1	8	yes	—
43	C₂×C₉	—	49	1	no	—
44	C₂×C₇	D₁₁×C₇⋊C₉	1	8	yes	—
45	C₃×C₄	—	11	1	no	—
46	C₁₁	C₄×#89204	1	1	yes	characteristic, complemented, Sylow
47	C₉	—	49	1	no	Sylow
48	C₇	Dic₁₁×C₇⋊C₉	1	8	yes	complemented
49	C₂×C₃	D₁₁×#3861	1	1	yes	characteristic
50	C₄	—	11	1	no	Sylow
51	C₃	Dic₁₁×#3861	1	1	yes	characteristic
52	C₂	D₁₁×#89204	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₁₁×#3861
commutator, hypocenter	C₇²×C₁₁	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇²×C₁₁	C₂×C₃
LCS	G ▷ C₇²×C₁₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₁₁×#89204	C₄	semidirect
6. C₇²×Dic₁₁	C₉	semidirect
15. C₇²×C₁₁	C₄×C₉	semidirect
17. #89204	Dic₁₁	direct (N × H)
19. C₇×Dic₁₁	C₇⋊C₉	semidirect
32. C₇×C₁₁	C₄×C₇⋊C₉	semidirect
35. C₇²	C₉×Dic₁₁	semidirect
36. Dic₁₁	#89204	direct (N × H)
46. C₁₁	C₄×#89204	semidirect
48. C₇	Dic₁₁×C₇⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#89204	2
C₃×C₇²×Dic₁₁	3
Dic₁₁×C₇⋊C₉	7
C₄×#89204	11

Subgroups — Dic11×#89204 #34084635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₁×#89204 #34084635