Subgroups — C₂×#20261864 #27159028

Order 12416.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261864	C₂	1	4	yes	maximal, direct product factor
2	C₂×#15690909	C₂	1	2	yes	maximal, complemented
3	C₂×#15690905	C₂	1	1	yes	maximal, characteristic
4	#15690909	C₂²	1	4	yes	complemented
5	#15690905	C₄	1	2	yes	—
6	#15690905	C₂²	1	2	yes	—
7	C₂×#13095523	C₄	1	1	yes	characteristic
8	C₂×#13095523	C₂²	1	1	yes	characteristic
9	C₂×#13095519	C₄	1	1	yes	characteristic
10	#13095523	C₂×C₄	1	2	yes	—
11	#13095523	C₂×C₄	1	1	yes	characteristic
12	#13095523	C₂³	1	1	yes	characteristic
13	#13095519	C₈	1	2	yes	—
14	#13095519	C₂×C₄	1	2	yes	—
15	C₂×#11715897	C₈	1	1	yes	characteristic
16	C₂×#11715897	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₉₇	C₈	1	1	yes	characteristic
18	C₂²×D₉₇	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₉₇	C₁₆	1	1	yes	characteristic
20	C₂×Dic₉₇	C₂×C₈	1	1	yes	characteristic
21	C₄×D₉₇	C₁₆	1	2	yes	—
22	C₄×D₉₇	C₂×C₈	1	2	yes	—
23	#11715897	C₂×C₈	1	2	yes	—
24	#11715897	C₂×C₈	1	1	yes	characteristic
25	#11715897	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₉₇	C₂×C₁₆	1	1	yes	characteristic
27	C₂×D₉₇	C₃₂	1	4	yes	complemented
28	C₂×D₉₇	C₂×C₁₆	1	2	yes	—
29	C₄×C₉₇	C₂×C₁₆	1	2	yes	—
30	Dic₉₇	C₂×C₁₆	1	1	yes	characteristic
31	Dic₉₇	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₉₇	C₂×C₃₂	1	2	yes	complemented
33	C₂×C₉₇	C₂²×C₁₆	1	1	yes	characteristic
34	D₉₇	C₂×C₃₂	1	4	yes	complemented
35	C₂²×C₃₂	—	97	1	no	maximal, Sylow
36	C₉₇	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₁₆	—	97	1	no	—
38	C₂×C₃₂	—	97	2	no	—
39	C₂×C₃₂	—	97	4	no	—
40	C₂²×C₈	—	97	1	no	—
41	C₂×C₁₆	—	97	1	no	—
42	C₂×C₁₆	—	97	2	no	—
43	C₂×C₁₆	—	97	1	no	—
44	C₂×C₁₆	—	97	2	no	—
45	C₃₂	—	97	4	no	—
46	C₂²×C₄	—	97	1	no	—
47	C₂×C₈	—	97	1	no	—
48	C₂×C₈	—	97	1	no	—
49	C₂×C₈	—	97	2	no	—
50	C₂×C₈	—	97	2	no	—
51	C₁₆	—	97	1	no	—
52	C₁₆	—	97	2	no	—
53	C₁₆	—	97	1	no	—
54	C₂³	—	97	1	no	—
55	C₂×C₄	—	97	1	no	—
56	C₂×C₄	—	97	2	no	—
57	C₂×C₄	—	97	2	no	—
58	C₂×C₄	#13095525	1	1	yes	characteristic
59	C₈	—	97	1	no	—
60	C₈	—	97	2	no	—
61	C₈	—	97	1	no	—
62	C₂²	—	97	4	no	—
63	C₂²	—	97	2	no	—
64	C₂²	C₂×#13095525	1	1	yes	characteristic
65	C₄	—	97	1	no	—
66	C₄	—	97	1	no	—
67	C₄	C₂×#13095525	1	2	yes	—
68	C₂	—	97	4	no	—
69	C₂	#20261864	1	2	yes	direct product factor
70	C₂	C₂²×#13095525	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	#13095525
commutator, hypocenter	C₉₇	C₂²×C₃₂
Frattini	C₂	C₂²×#13095525
Fitting	C₂×C₄×C₉₇	C₁₆
socle	C₂²×C₉₇	C₂×C₁₆
prime radical	C₂²×D₉₇	C₁₆
cosocle	#13095523	C₂³
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #20261864	C₂	direct (N × H)
2. C₂×#15690909	C₂	semidirect
4. #15690909	C₂²	semidirect
27. C₂×D₉₇	C₃₂	semidirect
32. C₂×C₉₇	C₂×C₃₂	semidirect
34. D₉₇	C₂×C₃₂	semidirect
36. C₉₇	C₂²×C₃₂	semidirect
69. C₂	#20261864	direct (N × H)

Maximal subgroups

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

subgroup	index
#20261864	2
C₂×#15690909	2
C₂×#15690905	2
C₂²×C₃₂	97

Subgroups — C2×#20261864 #27159028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20261864 #27159028