Subgroups — C₂×#330×C₉₇ #27137481

Order 12416.

232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#125×C₉₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#97×C₉₇	C₂	1	2	yes	maximal
3	#330×C₉₇	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₉₇	—	2	2	no	—
5	#125×C₉₇	—	2	2	no	—
6	#125×C₉₇	C₄	1	2	yes	—
7	#125×C₉₇	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₉₇	—	2	2	no	—
9	C₂×C₄⋊C₄×C₉₇	C₄	1	2	yes	—
10	C₂×C₄²×C₉₇	C₂²	1	1	yes	characteristic
11	#97×C₉₇	—	2	2	no	—
12	#97×C₉₇	C₂²	1	4	yes	—
13	C₂²×C₄×C₉₇	—	2	2	no	—
14	C₂²×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₉₇	D₄	1	2	yes	—
16	C₂×C₈×C₉₇	—	2	8	no	—
17	C₂×C₈×C₉₇	—	2	4	no	—
18	C₄⋊C₄×C₉₇	—	2	4	no	—
19	C₄⋊C₄×C₉₇	—	2	2	no	—
20	C₄⋊C₄×C₉₇	—	2	4	no	—
21	C₄⋊C₄×C₉₇	C₂×C₄	1	4	yes	—
22	C₄²×C₉₇	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₉₇	D₄	1	2	yes	—
24	C₄²×C₉₇	C₂³	1	1	yes	characteristic
25	C₂³×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₉₇	—	2	2	no	—
27	C₂×C₄×C₉₇	—	2	4	no	—
28	C₂×C₄×C₉₇	—	2	4	no	—
29	C₂×C₄×C₉₇	—	4	4	no	—
30	C₂×C₄×C₉₇	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₉₇	C₂×D₄	1	2	yes	—
34	C₈×C₉₇	—	2	8	no	—
35	C₂²×C₉₇	#101	1	2	yes	—
36	C₂²×C₉₇	#104	1	4	yes	—
37	C₂²×C₉₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₄×C₉₇	—	2	1	no	—
39	C₄×C₉₇	—	2	1	no	—
40	C₄×C₉₇	—	2	2	no	—
41	C₄×C₉₇	—	2	2	no	—
42	C₄×C₉₇	—	4	4	no	—
43	C₂×C₉₇	#330	1	4	yes	direct product factor
44	C₂×C₉₇	C₂×#101	1	1	yes	characteristic
45	C₂×C₉₇	C₂×#104	1	2	yes	—
46	C₂×#330	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₉₇	C₂×#330	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×#125	C₂×C₉₇	1	1	yes	characteristic
49	C₂×#97	C₂×C₉₇	1	2	yes	—
50	#330	C₂×C₉₇	1	4	yes	direct product factor
51	C₂²×C₈	—	2	2	no	—
52	#125	—	2	2	no	—
53	#125	C₄×C₉₇	1	2	yes	—
54	#125	C₂²×C₉₇	1	2	yes	—
55	C₂×C₄⋊C₄	—	2	2	no	—
56	C₂×C₄⋊C₄	C₄×C₉₇	1	2	yes	—
57	C₂×C₄²	C₂²×C₉₇	1	1	yes	characteristic
58	#97	—	2	2	no	—
59	#97	C₂²×C₉₇	1	4	yes	—
60	C₂²×C₄	—	2	2	no	—
61	C₂²×C₄	C₂×C₄×C₉₇	1	1	yes	characteristic
62	C₂²×C₄	D₄×C₉₇	1	2	yes	—
63	C₂×C₈	—	2	8	no	—
64	C₂×C₈	—	2	4	no	—
65	C₄⋊C₄	—	2	4	no	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	4	no	—
68	C₄⋊C₄	C₂×C₄×C₉₇	1	4	yes	—
69	C₄²	C₂×C₄×C₉₇	1	1	yes	characteristic
70	C₄²	D₄×C₉₇	1	2	yes	—
71	C₄²	C₂³×C₉₇	1	1	yes	characteristic
72	C₂³	C₂²⋊C₄×C₉₇	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	4	4	no	—
77	C₂×C₄	C₂²⋊C₄×C₉₇	1	2	yes	—
78	C₂×C₄	C₂²⋊C₄×C₉₇	1	1	yes	characteristic
79	C₂×C₄	C₂²×C₄×C₉₇	1	1	yes	characteristic
80	C₂×C₄	C₂×D₄×C₉₇	1	2	yes	—
81	C₈	—	2	8	no	—
82	C₂²	#101×C₉₇	1	2	yes	—
83	C₂²	#104×C₉₇	1	4	yes	—
84	C₂²	C₂×C₂²⋊C₄×C₉₇	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	2	1	no	—
87	C₄	—	2	2	no	—
88	C₄	—	2	2	no	—
89	C₄	—	4	4	no	—
90	C₂	#330×C₉₇	1	4	yes	direct product factor
91	C₂	C₂×#101×C₉₇	1	1	yes	characteristic
92	C₂	C₂×#104×C₉₇	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₉₇	C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₉₇
Frattini, cosocle	C₄²	C₂³×C₉₇
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉₇ ◁ C₂×C₄²×C₉₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #330×C₉₇	C₂	direct (N × H)
43. C₂×C₉₇	#330	direct (N × H)
46. C₂×#330	C₉₇	direct (N × H)
47. C₉₇	C₂×#330	direct (N × H)
50. #330	C₂×C₉₇	direct (N × H)
90. C₂	#330×C₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#125×C₉₇	2
C₂×#97×C₉₇	2
#330×C₉₇	2
C₂×#330	97

Subgroups — C2×#330×C97 #27137481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#330×C₉₇ #27137481