Subgroups — C₂×#20261857 #27158988

Order 12416.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261857	C₂	1	8	yes	maximal, direct product factor
2	C₂×#15690907	C₂	1	3	yes	maximal, complemented
3	C₂×#15690905	C₂	1	3	yes	maximal, complemented
4	C₂×#15690898	C₂	1	1	yes	maximal, characteristic
5	#15690907	C₂²	1	12	yes	complemented
6	#15690905	C₂²	1	12	yes	complemented
7	C₂×#13095523	C₂²	1	1	yes	characteristic
8	C₂×#13095523	C₂²	1	3	yes	—
9	#15690898	C₄	1	4	yes	—
10	#15690898	C₂²	1	4	yes	—
11	C₂×#13095521	C₄	1	3	yes	—
12	C₂×#13095519	C₂²	1	3	yes	—
13	C₂×#13095512	C₄	1	1	yes	characteristic
14	#13095523	C₂³	1	2	yes	—
15	#13095523	C₂³	1	6	yes	—
16	#13095521	C₂×C₄	1	12	yes	—
17	#13095519	C₂×C₄	1	6	yes	—
18	#13095519	C₂³	1	6	yes	—
19	C₂×#11715897	C₂×C₄	1	3	yes	—
20	C₂×#11715897	C₂³	1	1	yes	characteristic
21	#13095512	C₈	1	4	yes	—
22	#13095512	C₂×C₄	1	4	yes	—
23	C₂×D₃₈₈	C₈	1	3	yes	—
24	C₂×C₄×D₉₇	C₂×C₄	1	3	yes	—
25	C₂×Q₈×C₉₇	C₈	1	1	yes	characteristic
26	C₂²×D₉₇	C₂×C₈	1	3	yes	—
27	Q₈×C₉₇	C₂×C₈	1	4	yes	—
28	C₂×C₄×C₉₇	C₂×C₈	1	3	yes	—
29	C₂×Dic₉₇	C₂²×C₄	1	1	yes	characteristic
30	D₃₈₈	C₂×C₈	1	12	yes	—
31	C₄×D₉₇	C₂×C₈	1	6	yes	—
32	C₄×D₉₇	C₂²×C₄	1	6	yes	—
33	#11715897	C₂²×C₄	1	6	yes	—
34	#11715897	C₂²×C₄	1	1	yes	characteristic
35	#11715897	C₂⁴	1	1	yes	characteristic
36	C₂²×C₉₇	C₂²×C₈	1	1	yes	characteristic
37	C₂×D₉₇	—	2	6	no	—
38	C₂×D₉₇	C₂²×C₈	1	6	yes	—
39	C₄×C₉₇	C₂²×C₈	1	6	yes	—
40	Dic₉₇	C₂²×C₈	1	1	yes	characteristic
41	Dic₉₇	C₂³×C₄	1	1	yes	characteristic
42	C₂×C₉₇	#504	1	2	yes	complemented
43	C₂×C₉₇	C₂³×C₈	1	1	yes	characteristic
44	D₉₇	—	2	6	no	—
45	C₂×#504	—	97	1	no	maximal, Sylow
46	C₉₇	C₂×#504	1	1	yes	characteristic, complemented, Sylow
47	C₂×#131	—	97	1	no	—
48	#504	—	97	8	no	—
49	C₂×M₃₂	—	97	3	no	—
50	C₂²×C₁₆	—	97	3	no	—
51	C₂×#41	—	97	1	no	—
52	#131	—	97	4	no	—
53	#131	—	97	4	no	—
54	C₂×M₁₆	—	97	3	no	—
55	C₂²×C₈	—	97	3	no	—
56	M₃₂	—	97	12	no	—
57	C₂×C₁₆	—	97	1	no	—
58	C₂×C₁₆	—	97	3	no	—
59	C₂×C₁₆	—	97	12	no	—
60	#41	—	97	4	no	—
61	#41	—	97	4	no	—
62	C₂×Q₈	#11715906	1	1	yes	characteristic
63	C₂×D₄	—	97	3	no	—
64	C₂²×C₄	—	97	3	no	—
65	M₁₆	—	97	12	no	—
66	C₂×C₈	—	97	3	no	—
67	C₂×C₈	—	97	1	no	—
68	C₂×C₈	—	97	6	no	—
69	C₂×C₈	—	97	6	no	—
70	C₁₆	—	97	2	no	—
71	C₁₆	—	97	6	no	—
72	C₂³	—	97	3	no	—
73	Q₈	C₂×#11715906	1	4	yes	—
74	D₄	—	97	12	no	—
75	C₂×C₄	—	97	1	no	—
76	C₂×C₄	—	97	6	no	—
77	C₂×C₄	—	97	6	no	—
78	C₂×C₄	C₂×#11715906	1	3	yes	—
79	C₈	—	97	1	no	—
80	C₈	—	97	1	no	—
81	C₈	—	97	6	no	—
82	C₂²	—	97	6	no	—
83	C₂²	—	194	6	no	—
84	C₂²	C₂²×#11715906	1	1	yes	characteristic
85	C₄	—	97	1	no	—
86	C₄	—	97	1	no	—
87	C₄	C₂²×#11715906	1	6	yes	—
88	C₂	—	194	6	no	—
89	C₂	#20261857	1	2	yes	direct product factor
90	C₂	C₂³×#11715906	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#11715906
commutator	C₂×C₉₇	C₂³×C₈
Frattini	C₂	C₂³×#11715906
Fitting	C₂×Q₈×C₉₇	C₈
socle	C₂²×C₉₇	C₂²×C₈
prime radical	C₂×#13095512	C₄
cosocle	#11715897	C₂⁴
hypercenter	C₂×Q₈	#11715906
hypocenter	C₉₇	C₂×#504
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. #20261857	C₂	direct (N × H)
2. C₂×#15690907	C₂	semidirect
3. C₂×#15690905	C₂	semidirect
5. #15690907	C₂²	semidirect
6. #15690905	C₂²	semidirect
42. C₂×C₉₇	#504	semidirect
46. C₉₇	C₂×#504	semidirect
89. C₂	#20261857	direct (N × H)

Maximal subgroups

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

subgroup	index
#20261857	2
C₂×#15690907	2
C₂×#15690905	2
C₂×#15690898	2
C₂×#504	97

Subgroups — C2×#20261857 #27158988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20261857 #27158988