Subgroups — C₂×C₉₇⋊#401 #27145032

Order 12416.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉₇⋊#401	C₂	1	8	yes	maximal, direct product factor
2	C₂×#15690717	C₂	1	3	yes	maximal
3	C₂×#15690717	C₂	1	3	yes	maximal
4	C₂×#95×C₉₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₉₇	C₂²	1	3	yes	—
6	C₂³×Dic₉₇	C₂²	1	1	yes	characteristic
7	#15690717	C₂²	1	12	yes	—
8	#15690717	C₂²	1	12	yes	—
9	C₂³×C₄×C₉₇	C₂²	1	3	yes	—
10	#95×C₉₇	C₂²	1	4	yes	—
11	C₂²×Dic₉₇	—	2	6	no	—
12	C₂²×Dic₉₇	—	2	6	no	—
13	C₂²×Dic₉₇	—	2	6	no	—
14	C₂²×Dic₉₇	—	2	6	no	—
15	C₂²×Dic₉₇	C₂³	1	6	yes	—
16	C₂²×Dic₉₇	C₂³	1	2	yes	—
17	C₂⁴×C₉₇	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₉₇	—	2	12	no	—
19	C₂²×C₄×C₉₇	—	2	6	no	—
20	C₂²×C₄×C₉₇	C₂³	1	6	yes	—
21	C₂³×C₉₇	#41	1	6	yes	—
22	C₂³×C₉₇	#41	1	6	yes	—
23	C₂³×C₉₇	#41	1	2	yes	—
24	C₂³×C₉₇	C₂⁴	1	1	yes	characteristic
25	C₂×C₄×C₉₇	—	2	12	no	—
26	C₂×C₄×C₉₇	—	2	6	no	—
27	C₂×C₄×C₉₇	—	4	12	no	—
28	C₂×Dic₉₇	—	2	6	no	—
29	C₂×Dic₉₇	—	2	6	no	—
30	C₂×Dic₉₇	—	2	6	no	—
31	C₂×Dic₉₇	—	2	6	no	—
32	C₂×Dic₉₇	—	4	4	no	—
33	C₂×Dic₉₇	—	4	12	no	—
34	C₂²×C₉₇	#126	1	12	yes	—
35	C₂²×C₉₇	#126	1	4	yes	—
36	C₂²×C₉₇	#126	1	12	yes	—
37	C₂²×C₉₇	C₂×#41	1	3	yes	—
38	C₂²×C₉₇	C₂×#41	1	3	yes	—
39	C₂²×C₉₇	C₂×#41	1	1	yes	characteristic
40	C₄×C₉₇	—	4	6	no	—
41	Dic₉₇	—	4	2	no	—
42	Dic₉₇	—	4	6	no	—
43	C₂×C₉₇	#401	1	8	yes	complemented
44	C₂×C₉₇	C₂×#126	1	3	yes	—
45	C₂×C₉₇	C₂×#126	1	1	yes	characteristic
46	C₂×C₉₇	C₂×#126	1	3	yes	—
47	C₂×#401	—	97	1	no	maximal, Sylow
48	C₉₇	C₂×#401	1	1	yes	characteristic, complemented, Sylow
49	#401	—	97	8	no	—
50	C₂×#95	—	97	3	no	—
51	C₂×#95	—	97	3	no	—
52	C₂×#95	D₉₇	1	1	yes	characteristic
53	C₂³×C₄	—	97	3	no	—
54	C₂³×C₄	—	97	1	no	—
55	C₂³×C₄	C₂×D₉₇	1	3	yes	—
56	#95	—	97	12	no	—
57	#95	—	97	12	no	—
58	#95	C₂×D₉₇	1	4	yes	—
59	C₂⁴	C₂²×D₉₇	1	1	yes	characteristic
60	C₂²×C₄	—	2	12	no	—
61	C₂²×C₄	—	2	6	no	—
62	C₂²×C₄	—	97	6	no	—
63	C₂²×C₄	—	97	2	no	—
64	C₂²×C₄	—	194	6	no	—
65	C₂²×C₄	—	194	6	no	—
66	C₂²×C₄	—	194	6	no	—
67	C₂²×C₄	—	194	6	no	—
68	C₂²×C₄	C₂²×D₉₇	1	6	yes	—
69	C₂³	#13095510	1	6	yes	—
70	C₂³	#13095511	1	6	yes	—
71	C₂³	#13095512	1	2	yes	—
72	C₂³	C₂³×D₉₇	1	1	yes	characteristic
73	C₂×C₄	—	2	12	no	—
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	4	12	no	—
76	C₂×C₄	—	388	4	no	—
77	C₂×C₄	—	388	12	no	—
78	C₂×C₄	—	194	6	no	—
79	C₂×C₄	—	194	6	no	—
80	C₂×C₄	—	194	6	no	—
81	C₂×C₄	—	194	6	no	—
82	C₂²	#15690803	1	12	yes	—
83	C₂²	#15690804	1	4	yes	—
84	C₂²	#15690805	1	12	yes	—
85	C₂²	C₂×#13095510	1	3	yes	—
86	C₂²	C₂×#13095511	1	3	yes	—
87	C₂²	C₂×#13095512	1	1	yes	characteristic
88	C₄	—	4	6	no	—
89	C₄	—	388	2	no	—
90	C₄	—	388	6	no	—
91	C₂	C₉₇⋊#401	1	8	yes	direct product factor
92	C₂	C₂×#15690803	1	3	yes	—
93	C₂	C₂×#15690804	1	1	yes	characteristic
94	C₂	C₂×#15690805	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₉₇
commutator, cosocle	C₂³×C₉₇	C₂⁴
Frattini	C₂³	C₂³×D₉₇
Fitting	C₂×#95×C₉₇	C₂
socle, prime radical	C₂⁴×C₉₇	C₂³
hypercenter	C₂×#95	D₉₇
hypocenter	C₉₇	C₂×#401
LCS	G ▷ C₂³×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
1. C₉₇⋊#401	C₂	direct (N × H)
43. C₂×C₉₇	#401	semidirect
48. C₉₇	C₂×#401	semidirect
91. C₂	C₉₇⋊#401	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉₇⋊#401	2
C₂×#15690717	2
C₂×#95×C₉₇	2
C₂×#401	97

Subgroups — C2×C97⋊#401 #27145032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉₇⋊#401 #27145032