Subgroups — #376×D₉₇ #27144061

Order 12416.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₉₇	C₂	1	3	yes	maximal
2	#20260581	C₂	1	3	yes	maximal, complemented
3	#20260580	C₂	1	4	yes	maximal, complemented
4	#95×D₉₇	C₂	1	4	yes	maximal
5	#376×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₉₇	C₂²	1	6	yes	—
7	C₂²×C₄×D₉₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₉₇	C₂²	1	6	yes	—
9	C₂×C₄×Dic₉₇	C₂²	1	3	yes	—
10	C₄²×D₉₇	C₄	1	24	yes	complemented
11	#15690717	C₂²	1	12	yes	—
12	C₂×C₄²×C₉₇	C₂²	1	3	yes	—
13	#95×C₉₇	C₂²	1	4	yes	—
14	C₂³×D₉₇	C₂³	1	1	yes	characteristic
15	C₂²×Dic₉₇	C₂³	1	6	yes	—
16	C₂²×Dic₉₇	C₂³	1	1	yes	characteristic
17	C₂×C₄×D₉₇	—	2	24	no	—
18	C₂×C₄×D₉₇	C₂×C₄	1	24	yes	—
19	C₂×C₄×D₉₇	C₂×C₄	1	12	yes	—
20	C₄×Dic₉₇	C₂×C₄	1	12	yes	complemented
21	C₄×Dic₉₇	C₂×C₄	1	24	yes	complemented
22	C₂²×C₄×C₉₇	C₂³	1	6	yes	—
23	C₂²×C₄×C₉₇	C₂³	1	1	yes	characteristic
24	C₄²×C₉₇	C₂×C₄	1	12	yes	complemented
25	C₂³×C₉₇	C₂⁴	1	1	yes	characteristic
26	C₂²×D₉₇	C₂²×C₄	1	6	yes	—
27	C₂²×D₉₇	#41	1	8	yes	—
28	C₂×C₄×C₉₇	—	2	12	no	—
29	C₂×C₄×C₉₇	C₂²×C₄	1	12	yes	—
30	C₂×C₄×C₉₇	C₂²×C₄	1	6	yes	—
31	C₂×Dic₉₇	—	2	12	no	—
32	C₂×Dic₉₇	C₂²×C₄	1	12	yes	—
33	C₂×Dic₉₇	C₂²×C₄	1	6	yes	—
34	C₄×D₉₇	—	2	48	no	—
35	C₄×D₉₇	C₄²	1	16	yes	—
36	C₂²×C₉₇	C₂³×C₄	1	3	yes	—
37	C₂²×C₉₇	C₂×#41	1	4	yes	—
38	C₂×D₉₇	C₂×C₄²	1	4	yes	—
39	C₂×D₉₇	#117	1	24	yes	—
40	C₄×C₉₇	—	2	12	no	—
41	C₄×C₉₇	C₂×C₄²	1	4	yes	—
42	Dic₉₇	—	2	12	no	—
43	Dic₉₇	C₂×C₄²	1	4	yes	—
44	C₂×C₉₇	C₂²×C₄²	1	1	yes	characteristic
45	C₂×C₉₇	C₂×#117	1	6	yes	—
46	D₉₇	#376	1	8	yes	direct product factor
47	C₂×#376	—	97	1	no	maximal, Sylow
48	C₉₇	C₂×#376	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₄²	—	97	3	no	—
50	#376	—	97	3	no	—
51	#376	—	97	4	no	—
52	#376	D₉₇	1	1	yes	characteristic, direct product factor
53	C₂×#95	—	97	4	no	—
54	C₂³×C₄	—	97	1	no	—
55	C₂³×C₄	—	97	6	no	—
56	C₂×C₄²	—	97	6	no	—
57	C₂×C₄²	—	97	3	no	—
58	C₂×C₄²	—	97	24	no	—
59	C₂×C₄²	C₂×D₉₇	1	3	yes	—
60	#95	—	97	12	no	—
61	#95	C₂×D₉₇	1	4	yes	—
62	C₂⁴	—	97	1	no	—
63	C₂²×C₄	—	97	1	no	—
64	C₂²×C₄	—	97	12	no	—
65	C₂²×C₄	—	97	6	no	—
66	C₂²×C₄	—	97	24	no	—
67	C₂²×C₄	—	194	24	no	—
68	C₂²×C₄	C₂²×D₉₇	1	6	yes	—
69	C₂²×C₄	C₂²×D₉₇	1	1	yes	characteristic
70	C₄²	—	97	24	no	—
71	C₄²	—	97	12	no	—
72	C₄²	C₄×D₉₇	1	12	yes	complemented
73	C₂³	—	97	6	no	—
74	C₂³	—	97	8	no	—
75	C₂³	C₂³×D₉₇	1	1	yes	characteristic
76	C₂×C₄	—	2	12	no	—
77	C₂×C₄	—	97	6	no	—
78	C₂×C₄	—	97	16	no	—
79	C₂×C₄	—	97	12	no	—
80	C₂×C₄	—	194	48	no	—
81	C₂×C₄	—	194	12	no	—
82	C₂×C₄	C₂×C₄×D₉₇	1	12	yes	—
83	C₂×C₄	C₂×C₄×D₉₇	1	6	yes	—
84	C₂²	—	97	4	no	—
85	C₂²	—	97	24	no	—
86	C₂²	C₂²×C₄×D₉₇	1	3	yes	—
87	C₂²	#41×D₉₇	1	4	yes	—
88	C₄	—	2	12	no	—
89	C₄	—	97	4	no	—
90	C₄	—	194	12	no	—
91	C₄	C₄²×D₉₇	1	4	yes	—
92	C₂	—	97	8	no	—
93	C₂	C₂×C₄²×D₉₇	1	1	yes	characteristic
94	C₂	#117×D₉₇	1	6	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉₇
commutator	C₂×C₉₇	C₂²×C₄²
Frattini	C₂³	C₂³×D₉₇
Fitting	#376×C₉₇	C₂
socle, cosocle	C₂³×C₉₇	C₂⁴
prime radical	C₂³×D₉₇	C₂³
hypercenter	#376	D₉₇
hypocenter	C₉₇	C₂×#376
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
2. #20260581	C₂	semidirect
3. #20260580	C₂	semidirect
5. #376×C₉₇	C₂	semidirect
10. C₄²×D₉₇	C₄	semidirect
20. C₄×Dic₉₇	C₂×C₄	semidirect
21. C₄×Dic₉₇	C₂×C₄	semidirect
24. C₄²×C₉₇	C₂×C₄	semidirect
46. D₉₇	#376	direct (N × H)
48. C₉₇	C₂×#376	semidirect
52. #376	D₉₇	direct (N × H)
72. C₄²	C₄×D₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₉₇	2
#20260581	2
#20260580	2
#95×D₉₇	2
#376×C₉₇	2
C₂×#376	97

Subgroups — #376×D97 #27144061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #376×D₉₇ #27144061