Subgroups — Q₈×#88036 #16791490

Order 3328.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#88036	C₂	1	3	yes	maximal
2	C₄×#88036	C₂	1	3	yes	maximal
3	Q₈×#6090	C₂	1	1	yes	maximal, characteristic
4	C₈×Q₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂×#88036	C₂²	1	3	yes	—
6	C₂×#88036	C₂²	1	1	yes	characteristic
7	C₄⋊#6090	C₄	1	3	yes	—
8	C₄×#6090	C₂²	1	3	yes	—
9	C₄×Q₈×C₁₃	C₈	1	1	yes	characteristic
10	C₁₃×C₄⋊C₈	C₈	1	3	yes	—
11	C₄×C₈×C₁₃	C₂×C₄	1	3	yes	—
12	C₂×#6090	C₂×C₄	1	3	yes	—
13	C₂×#6090	C₂³	1	1	yes	characteristic
14	#88036	—	2	3	no	—
15	#88036	Q₈	1	2	yes	direct product factor
16	Q₈×C₃₂	—	13	1	no	maximal, Sylow
17	C₂×Q₈×C₁₃	C₁₆	1	1	yes	characteristic
18	C₂×C₈×C₁₃	C₂×C₈	1	3	yes	—
19	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
20	C₁₃×C₄⋊C₄	C₁₆	1	3	yes	—
21	C₄²×C₁₃	C₂×C₈	1	3	yes	—
22	#6090	—	2	3	no	—
23	#6090	C₂×Q₈	1	1	yes	characteristic
24	#6090	#41	1	1	yes	characteristic
25	Q₈×C₁₆	—	13	1	no	—
26	C₄⋊C₃₂	—	13	3	no	—
27	C₄×C₃₂	—	13	3	no	—
28	Q₈×C₁₃	C₃₂	1	4	yes	complemented
29	C₂×C₄×C₁₃	C₂×C₁₆	1	3	yes	—
30	C₂×C₄×C₁₃	C₂×C₁₆	1	3	yes	—
31	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
32	C₈×C₁₃	—	2	3	no	—
33	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
34	C₈×C₁₃	#131	1	1	yes	characteristic
35	C₈×Q₈	#261	1	1	yes	characteristic
36	C₂×C₃₂	—	13	1	no	—
37	C₂×C₃₂	—	13	3	no	—
38	C₄⋊C₁₆	—	13	3	no	—
39	C₄×C₁₆	—	13	3	no	—
40	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
41	C₄×C₁₃	—	2	3	no	—
42	C₄×C₁₃	C₂×C₃₂	1	6	yes	—
43	C₄×C₁₃	C₈×Q₈	1	1	yes	characteristic
44	C₄×C₁₃	#504	1	1	yes	characteristic
45	C₄×Q₈	#1057	1	1	yes	characteristic
46	C₂×C₁₆	—	13	1	no	—
47	C₂×C₁₆	—	13	3	no	—
48	C₄⋊C₈	#1057	1	3	yes	—
49	C₄×C₈	C₂×#261	1	3	yes	—
50	C₃₂	—	13	2	no	—
51	C₃₂	—	26	3	no	—
52	C₂×C₁₃	Q₈×C₁₆	1	1	yes	characteristic
53	C₂×C₁₃	C₂²×C₃₂	1	1	yes	characteristic
54	C₂×C₁₃	#2258	1	1	yes	characteristic
55	C₂×Q₈	#6092	1	1	yes	characteristic
56	C₂×C₈	C₂×#1057	1	3	yes	—
57	C₂×C₈	C₂²×#261	1	1	yes	characteristic
58	C₄⋊C₄	#6092	1	3	yes	—
59	C₄²	C₂×#1057	1	3	yes	—
60	C₁₆	—	13	1	no	—
61	C₁₆	—	13	1	no	—
62	C₁₆	—	26	3	no	—
63	C₁₃	Q₈×C₃₂	1	1	yes	characteristic, complemented, Sylow
64	Q₈	#88036	1	4	yes	direct product factor
65	C₂×C₄	C₂×#6092	1	3	yes	—
66	C₂×C₄	C₂×#6092	1	3	yes	—
67	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
68	C₈	—	2	3	no	—
69	C₈	#88240	1	1	yes	characteristic
70	C₈	Q₈×#261	1	1	yes	characteristic
71	C₂²	C₂²×#6092	1	1	yes	characteristic
72	C₄	—	2	3	no	—
73	C₄	C₂×#88036	1	6	yes	—
74	C₄	Q₈×#1057	1	1	yes	characteristic
75	C₄	#11719162	1	1	yes	characteristic
76	C₂	Q₈×#6092	1	1	yes	characteristic
77	C₂	C₂²×#88036	1	1	yes	characteristic
78	C₂	#13131259	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#261
commutator	C₂×C₁₃	C₂²×C₃₂
Fitting	C₈×Q₈×C₁₃	C₄
socle, prime radical	C₂²×C₁₃	C₂²×C₁₆
cosocle	C₂×#6090	C₂³
hypercenter	C₈×Q₈	#261
hypocenter	C₁₃	Q₈×C₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
15. #88036	Q₈	direct (N × H)
28. Q₈×C₁₃	C₃₂	semidirect
63. C₁₃	Q₈×C₃₂	semidirect
64. Q₈	#88036	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⋊#88036	2
C₄×#88036	2
Q₈×#6090	2
Q₈×C₃₂	13

Subgroups — Q8×#88036 #16791490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#88036 #16791490