Subgroups — C₄×#6897⋊C₂ #14517551

Order 1944.

244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6897⋊C₂	C₂	1	1	yes	maximal, characteristic
2	C₄×#6897	C₂	1	1	yes	maximal, characteristic, complemented
3	#11757614	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₉⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₄×#4169	—	3	4	no	maximal
6	C₂×#6897	C₂²	1	1	yes	characteristic
7	#6897⋊C₂	C₄	1	2	yes	direct product factor
8	C₂×C₉⋊D₉	C₂×C₃	1	1	yes	characteristic
9	C₂×#4169	—	3	4	no	—
10	C₄×C₉⋊C₉	—	2	4	no	—
11	C₄×C₃²⋊C₉	D₃	1	4	yes	—
12	C₄×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
13	C₉⋊Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
14	#66316	—	3	4	no	—
15	#6897	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₃×C₄×C₃⋊D₃	—	9	1	no	—
17	C₄×C₃⋊D₉	—	3	4	no	—
18	C₂×C₉⋊C₉	—	2	4	no	—
19	C₂×C₃²⋊C₉	C₂×D₃	1	4	yes	—
20	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
21	C₉⋊D₉	C₃×C₄	1	2	yes	complemented
22	#4169	—	3	8	no	—
23	C₂×C₃×C₃⋊D₃	—	9	1	no	—
24	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
25	C₃×C₃⋊Dic₃	—	9	1	no	—
26	C₂×C₃⋊D₉	—	3	4	no	—
27	C₃×C₄×C₉	—	2	4	no	—
28	C₃×C₄×C₉	C₃×D₃	1	4	yes	—
29	C₃⋊Dic₉	—	3	4	no	—
30	C₉⋊C₉	—	2	4	no	—
31	C₃²⋊C₉	C₄×D₃	1	4	yes	—
32	C₉²	C₂×C₃×C₄	1	1	yes	characteristic, complemented
33	C₄×C₃⋊D₃	—	9	1	no	—
34	C₃×C₄×D₃	—	27	4	no	—
35	C₄×D₉	—	27	4	no	—
36	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
37	C₃×C₃⋊D₃	—	9	2	no	—
38	C₂×C₃×C₉	—	2	4	no	—
39	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
40	C₃⋊D₉	—	3	8	no	—
41	C₂×C₃⋊D₃	—	9	1	no	—
42	C₂×C₃×D₃	—	27	4	no	—
43	C₃²×C₄	—	3	4	no	—
44	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
45	C₃⋊Dic₃	—	9	1	no	—
46	C₃×Dic₃	—	27	4	no	—
47	C₂×D₉	—	27	4	no	—
48	C₄×C₉	—	3	4	no	—
49	C₄×C₉	—	6	4	no	—
50	Dic₉	—	27	4	no	—
51	C₃³	C₄×C₃⋊D₃	1	1	yes	characteristic
52	C₃×C₉	—	2	4	no	—
53	C₃×C₉	C₃×C₄×D₃	1	4	yes	—
54	C₂×C₃×C₄	—	81	1	no	—
55	C₄×D₃	—	27	4	no	—
56	C₂×C₃²	—	3	4	no	—
57	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
58	C₃⋊D₃	—	9	2	no	—
59	C₃×D₃	—	27	8	no	—
60	C₂×C₉	—	3	4	no	—
61	C₂×C₉	—	6	4	no	—
62	D₉	—	27	8	no	—
63	C₂²×C₃	—	81	1	no	—
64	C₂×D₃	—	27	4	no	—
65	C₃×C₄	—	9	1	no	—
66	C₃×C₄	—	81	1	no	—
67	C₃×C₄	#4207	1	4	yes	—
68	Dic₃	—	27	4	no	—
69	C₃²	—	3	4	no	—
70	C₃²	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
71	C₉	—	3	4	no	—
72	C₉	—	6	4	no	—
73	C₂×C₄	—	81	1	no	Sylow
74	C₂×C₃	—	9	1	no	—
75	C₂×C₃	—	81	2	no	—
76	C₂×C₃	C₂×#4207	1	4	yes	—
77	D₃	—	27	8	no	—
78	C₂²	—	81	1	no	—
79	C₄	—	81	1	no	—
80	C₄	#6897⋊C₂	1	1	yes	characteristic, direct product factor
81	C₃	—	9	1	no	—
82	C₃	C₄×#4207	1	4	yes	—
83	C₂	—	81	2	no	—
84	C₂	C₂×#6897⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	#6897⋊C₂
commutator, hypocenter	C₉²	C₂×C₃×C₄
Frattini, socle	C₂×C₃²	C₂×C₃×C₃⋊D₃
Fitting	C₄×#6897	C₂
prime radical	C₂×#6897⋊C₂	C₂
cosocle	C₂×C₉²	C₂²×C₃
LCS	G ▷ C₉²
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₄×#6897	C₂	semidirect
3. #11757614	C₂	semidirect
4. C₄×C₉⋊D₉	C₃	semidirect
7. #6897⋊C₂	C₄	direct (N × H)
12. C₄×C₉²	C₂×C₃	semidirect
13. C₉⋊Dic₉	C₂×C₃	semidirect
15. #6897	C₂×C₄	semidirect
21. C₉⋊D₉	C₃×C₄	semidirect
32. C₉²	C₂×C₃×C₄	semidirect
80. C₄	#6897⋊C₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#6897⋊C₂	2
C₄×#6897	2
#11757614	2
C₄×C₉⋊D₉	3
C₄×#4169	3

Subgroups — C4×#6897⋊C2 #14517551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#6897⋊C₂ #14517551