Subgroups — M₁₆×#87604 #20261695

Order 6208.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₇⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#87604	C₂	1	1	yes	maximal, characteristic
3	#15690864	C₂	1	2	yes	maximal, complemented
4	C₈×#87604	C₂	1	2	yes	maximal, complemented
5	M₁₆×D₉₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#87604	C₄	1	2	yes	—
7	#13095521	C₄	1	2	yes	complemented
8	#13095520	C₄	1	2	yes	complemented
9	#13095519	C₂²	1	2	yes	—
10	C₄×#87604	C₄	1	2	yes	—
11	C₄×#87604	C₂²	1	1	yes	characteristic
12	C₄×#87604	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₉₇	C₂²	1	1	yes	characteristic
14	#13095495	C₄	1	1	yes	characteristic, complemented
15	#13095494	C₄	1	2	yes	complemented
16	C₈×D₉₇	C₂²	1	2	yes	—
17	M₁₆×C₉₇	C₄	1	1	yes	characteristic, complemented
18	C₂²×D₉₇	C₂×C₄	1	1	yes	characteristic
19	C₂×#87604	—	2	4	no	—
20	C₂×#87604	C₂×C₄	1	2	yes	—
21	C₂×#87604	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₉₇	C₂×C₄	1	1	yes	characteristic
24	C₄×D₉₇	C₂×C₄	1	1	yes	characteristic
25	C₄×D₉₇	C₂×C₄	1	1	yes	characteristic
26	C₄×D₉₇	C₂×C₄	1	1	yes	characteristic
27	C₄×D₉₇	C₂³	1	1	yes	characteristic
28	#11715897	C₂×C₄	1	4	yes	complemented
29	C₈×C₉₇	C₂×C₄	1	2	yes	complemented
30	#11715895	C₂×C₄	1	2	yes	complemented
31	C₂²×C₉₇	C₄²	1	1	yes	characteristic
32	C₂×D₉₇	—	2	2	no	—
33	C₂×D₉₇	C₄²	1	1	yes	characteristic
34	C₂×D₉₇	C₂²×C₄	1	1	yes	characteristic
35	#87604	—	2	2	no	—
36	#87604	M₁₆	1	4	yes	direct product factor
37	C₄×C₉₇	C₄²	1	1	yes	characteristic
38	C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
39	Dic₉₇	C₄²	1	1	yes	characteristic
40	Dic₉₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₉₇	—	2	1	no	—
42	C₂×C₉₇	C₂×C₄²	1	1	yes	characteristic
43	D₉₇	—	2	1	no	—
44	D₉₇	C₂×M₁₆	1	2	yes	—
45	C₉₇	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
46	C₄×M₁₆	—	97	1	no	maximal, Sylow
47	C₂×M₁₆	—	97	1	no	—
48	C₂×M₁₆	—	97	1	no	—
49	C₂×C₄²	—	97	1	no	—
50	#97	—	97	2	no	—
51	C₄×C₈	—	97	2	no	—
52	C₂²×C₄	—	97	1	no	—
53	C₂²×C₄	—	97	2	no	—
54	M₁₆	—	97	2	no	—
55	M₁₆	—	97	2	no	—
56	M₁₆	—	97	1	no	—
57	M₁₆	—	97	2	no	—
58	M₁₆	#87604	1	1	yes	characteristic, direct product factor
59	C₂×C₈	—	97	2	no	—
60	C₂×C₈	—	97	2	no	—
61	C₄²	—	97	2	no	—
62	C₄²	—	97	1	no	—
63	C₄²	—	97	1	no	—
64	C₂³	—	97	1	no	—
65	C₂×C₄	—	97	2	no	—
66	C₂×C₄	—	97	1	no	—
67	C₂×C₄	—	97	1	no	—
68	C₂×C₄	—	97	1	no	—
69	C₂×C₄	—	97	1	no	—
70	C₂×C₄	—	97	1	no	—
71	C₂×C₄	—	97	2	no	—
72	C₂×C₄	—	194	4	no	—
73	C₂×C₄	C₂×#87604	1	1	yes	characteristic
74	C₈	—	97	4	no	—
75	C₈	—	97	2	no	—
76	C₈	C₂×#87604	1	2	yes	complemented
77	C₂²	—	97	1	no	—
78	C₂²	—	97	1	no	—
79	C₂²	—	194	2	no	—
80	C₂²	C₄×#87604	1	1	yes	characteristic
81	C₄	—	97	4	no	—
82	C₄	—	97	1	no	—
83	C₄	—	97	1	no	—
84	C₄	—	194	2	no	—
85	C₄	C₄×#87604	1	1	yes	characteristic
86	C₄	C₂²×#87604	1	1	yes	characteristic
87	C₂	—	2	1	no	—
88	C₂	—	97	2	no	—
89	C₂	—	194	1	no	—
90	C₂	C₂×C₄×#87604	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#87604
commutator, socle	C₂×C₉₇	C₂×C₄²
Fitting	M₁₆×C₉₇	C₄
hypercenter	M₁₆	#87604
hypocenter	C₉₇	C₄×M₁₆
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
3. #15690864	C₂	semidirect
4. C₈×#87604	C₂	semidirect
7. #13095521	C₄	semidirect
8. #13095520	C₄	semidirect
14. #13095495	C₄	semidirect
15. #13095494	C₄	semidirect
17. M₁₆×C₉₇	C₄	semidirect
28. #11715897	C₂×C₄	semidirect
29. C₈×C₉₇	C₂×C₄	semidirect
30. #11715895	C₂×C₄	semidirect
36. #87604	M₁₆	direct (N × H)
45. C₉₇	C₄×M₁₆	semidirect
58. M₁₆	#87604	direct (N × H)
76. C₈	C₂×#87604	semidirect

Subgroups — M16×#87604 #20261695

Conjugacy classes of subgroups

Complements

Subgroups — M₁₆×#87604 #20261695