Subgroups — C₂×#15690881 #20261749

Order 6208.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095521	C₂	1	2	yes	maximal
2	#15690881	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₉₇	C₂	1	1	yes	maximal, characteristic
4	#13095521	—	2	2	no	—
5	#13095521	C₂²	1	4	yes	—
6	C₂×#11715897	—	2	2	no	—
7	C₂×C₄×D₉₇	C₂²	1	1	yes	characteristic
8	C₂×#11715895	C₄	1	1	yes	characteristic
9	C₈×D₉₇	C₄	1	2	yes	—
10	C₈×D₉₇	C₂²	1	2	yes	—
11	C₂×C₈×C₉₇	C₄	1	1	yes	characteristic
12	C₂²×D₉₇	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₉₇	D₄	1	1	yes	characteristic
15	C₄×D₉₇	C₂×C₄	1	1	yes	characteristic
16	C₄×D₉₇	D₄	1	1	yes	characteristic
17	C₄×D₉₇	Q₈	1	1	yes	characteristic
18	C₄×D₉₇	C₂³	1	1	yes	characteristic
19	#11715897	—	2	4	no	—
20	C₈×C₉₇	C₂×C₄	1	2	yes	—
21	#11715895	C₂×C₄	1	2	yes	—
22	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
23	C₂×D₉₇	—	2	2	no	—
24	C₂×D₉₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₉₇	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₉₇	C₄⋊C₄	1	1	yes	characteristic
27	C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
28	Dic₉₇	C₄⋊C₄	1	1	yes	characteristic
29	Dic₉₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₉₇	#108	1	2	yes	complemented
31	C₂×C₉₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	D₉₇	—	2	1	no	—
33	D₉₇	—	2	1	no	—
34	C₉₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
35	C₂×#108	—	97	1	no	maximal, Sylow
36	C₂×M₁₆	—	97	2	no	—
37	C₂²×C₈	—	97	1	no	—
38	#108	—	97	4	no	—
39	C₂²×C₄	—	97	1	no	—
40	M₁₆	—	97	4	no	—
41	M₁₆	—	194	2	no	—
42	C₂×C₈	—	97	1	no	—
43	C₂×C₈	—	97	2	no	—
44	C₂×C₈	—	97	2	no	—
45	C₂×C₈	—	194	2	no	—
46	C₂×C₈	#87604	1	1	yes	characteristic
47	C₂³	—	97	1	no	—
48	C₂×C₄	—	97	1	no	—
49	C₂×C₄	—	97	1	no	—
50	C₂×C₄	—	97	1	no	—
51	C₂×C₄	—	97	1	no	—
52	C₂×C₄	—	97	1	no	—
53	C₂×C₄	C₂×#87604	1	1	yes	characteristic
54	C₈	—	97	2	no	—
55	C₈	—	194	4	no	—
56	C₈	C₂×#87604	1	2	yes	—
57	C₂²	—	97	1	no	—
58	C₂²	—	97	1	no	—
59	C₂²	—	194	2	no	—
60	C₂²	C₄⋊#87604	1	1	yes	characteristic
61	C₄	—	97	1	no	—
62	C₄	—	97	1	no	—
63	C₄	C₄⋊#87604	1	1	yes	characteristic
64	C₄	C₂²×#87604	1	1	yes	characteristic
65	C₂	—	194	1	no	—
66	C₂	—	194	1	no	—
67	C₂	#15690881	1	2	yes	direct product factor
68	C₂	C₂×C₄⋊#87604	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#87604
commutator	C₄×C₉₇	C₂²×C₄
Frattini	C₄	C₂²×#87604
Fitting	C₂×C₈×C₉₇	C₄
socle	C₂²×C₉₇	C₄⋊C₄
hypercenter	C₂×C₈	#87604
hypocenter	C₉₇	C₂×#108
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #15690881	C₂	direct (N × H)
30. C₂×C₉₇	#108	semidirect
34. C₉₇	C₂×#108	semidirect
67. C₂	#15690881	direct (N × H)

Subgroups — C2×#15690881 #20261749

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15690881 #20261749