Subgroups — Q₈×#10596927 #18011009

Order 4736.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#10596927	C₂	1	3	yes	maximal
2	C₄×#10596927	C₂	1	3	yes	maximal
3	Q₈×#64436	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596927	C₂²	1	3	yes	—
5	C₂×#10596927	C₂²	1	1	yes	characteristic
6	C₄⋊#64436	C₄	1	3	yes	—
7	C₄×#64436	C₂²	1	3	yes	—
8	C₄×Q₈×C₃₇	C₄	1	1	yes	characteristic
9	C₂×Q₈×C₃₇	C₈	1	1	yes	characteristic
10	C₄⋊C₄×C₃₇	C₈	1	3	yes	—
11	C₄²×C₃₇	C₂×C₄	1	3	yes	—
12	C₂×#64436	C₂×C₄	1	3	yes	—
13	C₂×#64436	C₂³	1	1	yes	characteristic
14	#10596927	—	2	3	no	—
15	#10596927	Q₈	1	2	yes	direct product factor
16	Q₈×C₃₇	C₁₆	1	4	yes	complemented
17	C₂×C₄×C₃₇	C₂×C₈	1	3	yes	—
18	C₂×C₄×C₃₇	C₂×C₈	1	3	yes	—
19	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
20	#64436	—	2	3	no	—
21	#64436	C₂×Q₈	1	1	yes	characteristic
22	#64436	#41	1	1	yes	characteristic
23	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
24	C₄×C₃₇	—	2	3	no	—
25	C₄×C₃₇	C₂×C₁₆	1	6	yes	—
26	C₄×C₃₇	C₄×Q₈	1	1	yes	characteristic
27	C₄×C₃₇	#131	1	1	yes	characteristic
28	Q₈×C₁₆	—	37	1	no	maximal, Sylow
29	C₂×C₃₇	C₈×Q₈	1	1	yes	characteristic
30	C₂×C₃₇	C₂²×C₁₆	1	1	yes	characteristic
31	C₂×C₃₇	#504	1	1	yes	characteristic
32	C₈×Q₈	—	37	1	no	—
33	C₄⋊C₁₆	—	37	3	no	—
34	C₄×C₁₆	—	37	3	no	—
35	C₃₇	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₄×Q₈	#3866	1	1	yes	characteristic
37	C₂×C₁₆	—	37	1	no	—
38	C₂×C₁₆	—	37	3	no	—
39	C₄⋊C₈	—	37	3	no	—
40	C₄×C₈	—	37	3	no	—
41	C₂×Q₈	#64438	1	1	yes	characteristic
42	C₂×C₈	—	37	1	no	—
43	C₂×C₈	—	37	3	no	—
44	C₄⋊C₄	#64438	1	3	yes	—
45	C₄²	C₂×#3866	1	3	yes	—
46	C₁₆	—	37	2	no	—
47	C₁₆	—	74	3	no	—
48	Q₈	#10596927	1	4	yes	direct product factor
49	C₂×C₄	C₂×#64438	1	3	yes	—
50	C₂×C₄	C₂×#64438	1	3	yes	—
51	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
52	C₈	—	37	1	no	—
53	C₈	—	37	1	no	—
54	C₈	—	74	3	no	—
55	C₂²	C₂²×#64438	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×#10596927	1	6	yes	—
58	C₄	Q₈×#3866	1	1	yes	characteristic
59	C₄	#11924624	1	1	yes	characteristic
60	C₂	Q₈×#64438	1	1	yes	characteristic
61	C₂	C₂²×#10596927	1	1	yes	characteristic
62	C₂	#14558591	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3866
commutator	C₂×C₃₇	C₂²×C₁₆
Fitting	C₄×Q₈×C₃₇	C₄
socle, prime radical	C₂²×C₃₇	C₂²×C₈
cosocle	C₂×#64436	C₂³
hypercenter	C₄×Q₈	#3866
hypocenter	C₃₇	Q₈×C₁₆
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
15. #10596927	Q₈	direct (N × H)
16. Q₈×C₃₇	C₁₆	semidirect
35. C₃₇	Q₈×C₁₆	semidirect
48. Q₈	#10596927	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊#10596927	2
C₄×#10596927	2
Q₈×#64436	2
Q₈×C₁₆	37

Subgroups — Q8×#10596927 #18011009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#10596927 #18011009