Subgroups — #6881⋊Q₈ #14516005

Order 1944.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6881	C₂	1	1	yes	maximal, characteristic
2	#6881⋊C₄	C₂	1	2	yes	maximal
3	#733⋊Q₈	C₃	1	1	yes	maximal, characteristic, complemented
4	Dic₁₈⋊C₉	—	3	1	no	maximal
5	C₂×#6881	C₂²	1	1	yes	characteristic
6	C₄×#733	C₂×C₃	1	1	yes	characteristic
7	C₄×#732	—	2	1	no	—
8	C₄×C₉⋊C₉	D₃	1	1	yes	characteristic
9	#733⋊C₄	C₂×C₃	1	2	yes	—
10	Dic₉⋊C₉	—	3	2	no	—
11	#6881	Q₈	1	1	yes	characteristic, complemented, Sylow
12	3₋¹⁺²⋊Q₈	—	9	1	no	—
13	C₉×Dic₆	—	9	1	no	—
14	C₃×Dic₁₈	—	3	1	no	—
15	C₂×#733	C₂²×C₃	1	1	yes	characteristic
16	C₂×#732	—	2	1	no	—
17	C₂×C₉⋊C₉	C₂×D₃	1	1	yes	characteristic
18	C₄×3₋¹⁺²	—	3	1	no	—
19	C₄×H(3,𝔽₃)	—	6	1	no	—
20	C₃×C₄×C₉	—	3	1	no	—
21	C₃×C₄×C₉	C₃×D₃	1	1	yes	characteristic
22	3₋¹⁺²⋊C₄	—	9	2	no	—
23	C₉×Dic₃	—	9	2	no	—
24	C₃×Dic₉	—	3	2	no	—
25	#733	C₃×Q₈	1	1	yes	characteristic
26	#732	—	2	1	no	—
27	C₉⋊C₉	Dic₆	1	1	yes	characteristic
28	C₃×Dic₆	—	9	1	no	—
29	Q₈×C₉	—	27	1	no	—
30	Dic₁₈	—	3	1	no	—
31	Dic₁₈	—	9	1	no	—
32	C₂×3₋¹⁺²	—	3	1	no	—
33	C₂×H(3,𝔽₃)	—	6	1	no	—
34	C₂×C₃×C₉	—	3	1	no	—
35	C₂×C₃×C₉	C₂×C₃×D₃	1	1	yes	characteristic
36	C₃²×C₄	—	18	1	no	—
37	C₃²×C₄	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
38	C₃×Dic₃	—	9	2	no	—
39	C₄×C₉	—	3	1	no	—
40	C₄×C₉	—	9	1	no	—
41	C₄×C₉	—	9	1	no	—
42	C₄×C₉	—	27	2	no	—
43	Dic₉	—	3	2	no	—
44	Dic₉	—	9	2	no	—
45	3₋¹⁺²	—	3	1	no	—
46	H(3,𝔽₃)	—	6	1	no	—
47	C₃×C₉	—	3	1	no	—
48	C₃×C₉	C₃×Dic₆	1	1	yes	characteristic
49	C₃×Q₈	—	27	1	no	—
50	Dic₆	—	9	1	no	—
51	C₂×C₃²	—	18	1	no	—
52	C₂×C₃²	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
53	C₂×C₉	—	3	1	no	—
54	C₂×C₉	—	9	1	no	—
55	C₂×C₉	—	9	1	no	—
56	C₃×C₄	—	3	1	no	—
57	C₃×C₄	—	27	2	no	—
58	C₃×C₄	—	54	1	no	—
59	C₃×C₄	#4178	1	1	yes	characteristic
60	Dic₃	—	9	2	no	—
61	C₃²	—	18	1	no	—
62	C₃²	#634⋊C₃	1	1	yes	characteristic
63	C₉	—	3	1	no	—
64	C₉	—	9	1	no	—
65	C₉	—	9	1	no	—
66	Q₈	—	27	1	no	Sylow
67	C₂×C₃	—	3	1	no	—
68	C₂×C₃	—	54	1	no	—
69	C₂×C₃	C₂×#4178	1	1	yes	characteristic
70	C₄	—	27	2	no	—
71	C₄	#6881⋊C₂	1	1	yes	characteristic
72	C₃	—	3	1	no	—
73	C₃	—	54	1	no	—
74	C₃	#10619619	1	1	yes	characteristic
75	C₂	C₂×#6881⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#6881⋊C₂
commutator, cosocle	C₂×#733	C₂²×C₃
Frattini	C₂×C₃×C₉	C₂×C₃×D₃
Fitting	C₄×#6881	C₂
socle	C₂×C₃	C₂×#4178
prime radical	C₂×#6881	C₂²
hypercenter	C₄	#6881⋊C₂
hypocenter	#733	C₃×Q₈
LCS	G ▷ C₂×#733 ▷ #733
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
3. #733⋊Q₈	C₃	semidirect
11. #6881	Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6881	2
#6881⋊C₄	2
#733⋊Q₈	3
Dic₁₈⋊C₉	3

Subgroups — #6881⋊Q8 #14516005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #6881⋊Q₈ #14516005