Subgroups — Q₁₆×#87604 #20261773

Order 6208.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#87604	C₂	1	2	yes	maximal
2	#15690879	C₂	1	1	yes	maximal, characteristic
3	#15690873	C₂	1	2	yes	maximal
4	C₈×#87604	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×D₉₇	C₂	1	1	yes	maximal, characteristic
6	#13095519	C₂²	1	1	yes	characteristic
7	C₄⋊#87604	—	2	2	no	—
8	C₄⋊#87604	C₂²	1	2	yes	—
9	C₄×#87604	—	2	2	no	—
10	C₄×#87604	C₂²	1	1	yes	characteristic
11	Q₈×D₉₇	C₂²	1	2	yes	—
12	Dic₃₈₈	C₄	1	1	yes	characteristic, complemented
13	#13095501	C₄	1	2	yes	complemented
14	C₈×D₉₇	C₂²	1	1	yes	characteristic
15	Q₁₆×C₉₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#87604	—	2	2	no	—
17	C₂×#87604	D₄	1	1	yes	characteristic
18	C₂×#87604	D₄	1	1	yes	characteristic
19	Q₈×C₉₇	C₂×C₄	1	2	yes	—
20	C₄×D₉₇	—	2	2	no	—
21	C₄×D₉₇	C₂³	1	1	yes	characteristic
22	Dic₁₉₄	—	2	2	no	—
23	Dic₁₉₄	C₂×C₄	1	2	yes	—
24	#11715897	—	2	1	no	—
25	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
26	#11715895	C₂×C₄	1	1	yes	characteristic
27	C₂×D₉₇	C₂×D₄	1	1	yes	characteristic
28	#87604	—	2	1	no	—
29	#87604	—	4	2	no	—
30	#87604	Q₁₆	1	2	yes	direct product factor
31	C₄×C₉₇	—	2	2	no	—
32	C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
33	Dic₉₇	—	2	2	no	—
34	Dic₉₇	#41	1	1	yes	characteristic
35	C₂×C₉₇	C₄×D₄	1	1	yes	characteristic
36	D₉₇	C₂×Q₁₆	1	1	yes	characteristic
37	D₉₇	#135	1	1	yes	characteristic
38	C₉₇	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₄×Q₁₆	—	97	1	no	maximal, Sylow
40	C₂×Q₁₆	—	97	1	no	—
41	C₄×Q₈	—	97	2	no	—
42	#107	—	97	1	no	—
43	#103	—	97	2	no	—
44	C₄×C₈	—	97	1	no	—
45	C₂×Q₈	—	97	2	no	—
46	Q₁₆	—	97	2	no	—
47	Q₁₆	—	97	1	no	—
48	Q₁₆	#87604	1	1	yes	characteristic, direct product factor
49	C₂×C₈	—	97	1	no	—
50	C₂×C₈	—	97	1	no	—
51	C₄⋊C₄	—	97	2	no	—
52	C₄⋊C₄	—	194	2	no	—
53	C₄²	—	97	1	no	—
54	C₄²	—	194	2	no	—
55	Q₈	—	97	2	no	—
56	Q₈	—	194	2	no	—
57	Q₈	C₂×#87604	1	2	yes	—
58	C₂×C₄	—	97	1	no	—
59	C₂×C₄	—	97	1	no	—
60	C₂×C₄	—	97	1	no	—
61	C₂×C₄	—	194	2	no	—
62	C₂×C₄	—	194	2	no	—
63	C₈	—	97	1	no	—
64	C₈	—	194	1	no	—
65	C₈	C₂×#87604	1	1	yes	characteristic
66	C₂²	—	97	1	no	—
67	C₄	—	2	2	no	—
68	C₄	—	97	2	no	—
69	C₄	—	97	1	no	—
70	C₄	—	388	2	no	—
71	C₄	—	194	1	no	—
72	C₄	—	194	2	no	—
73	C₄	C₂²×#87604	1	1	yes	characteristic
74	C₂	—	97	1	no	—
75	C₂	—	97	1	no	—
76	C₂	D₄×#87604	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#87604
commutator	C₄×C₉₇	C₂²×C₄
Frattini	C₄	C₂²×#87604
Fitting	Q₁₆×C₉₇	C₄
socle	C₂×C₉₇	C₄×D₄
hypercenter	Q₁₆	#87604
hypocenter	C₉₇	C₄×Q₁₆
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
12. Dic₃₈₈	C₄	semidirect
13. #13095501	C₄	semidirect
15. Q₁₆×C₉₇	C₄	semidirect
30. #87604	Q₁₆	direct (N × H)
38. C₉₇	C₄×Q₁₆	semidirect
48. Q₁₆	#87604	direct (N × H)

Subgroups — Q16×#87604 #20261773

Conjugacy classes of subgroups

Complements

Subgroups — Q₁₆×#87604 #20261773