Finite Group Databasebeta

← #20260933

Subgroups — #20260933

Order 6208.

128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13095498C211yesmaximal, characteristic, complemented
2#15690806C211yesmaximal, characteristic
3Q8×Dic97C211yesmaximal, characteristic, complemented
4#15690739C211yesmaximal, characteristic, complemented
5#15690732C211yesmaximal, characteristic, complemented
6#15690731C211yesmaximal, characteristic, complemented
7C2×SD16×C97C211yesmaximal, characteristic, complemented
8C2×D388C2211yescharacteristic
9C2×C22⋊D97—21no—
10C2×C22⋊D97—21no—
11#13095498—22no—
12C2×#11715895C2211yescharacteristic
13C4⋊Dic97—21no—
14C4⋊Dic97C2211yescharacteristic
15C4×Dic97—21no—
16C4×Dic97C2211yescharacteristic
17C2×Q8×C97C2211yescharacteristic
18C2×D4×C97C2211yescharacteristic
19SD16×C97—22no—
20C2×C8×C97C2211yescharacteristic
21C23×C97—21no—
22C22×D97—21no—
23Q8×C97—21no—
24Q8×C97D412yescomplemented
25D4×C97—21no—
26D4×C97—21no—
27C2×C4×C97—21no—
28C2×C4×C97C2311yescharacteristic
29C22⋊D97—42no—
30C22⋊D97—42no—
31C2×Dic97—21no—
32C2×Dic97D411yescharacteristic
33C2×Dic97D411yescharacteristic
34D388—21no—
35D388—21no—
36C8×C97—21no—
37#11715895—21no—
38C22×C97—41no—
39C22×C97—41no—
40C22×C97—41no—
41C22×C97C2×D411yescharacteristic
42C2×D97—41no—
43C2×D97—41no—
44C2×D97—41no—
45C4×C97—22no—
46C4×C97C2×D411yescharacteristic
47C4×C97#4111yescharacteristic
48Dic97—21no—
49Dic97—41no—
50Dic97SD1612yescomplemented
51C2×C97—81no—
52C2×C97#12111yescharacteristic
53C2×C97C2×SD1611yescharacteristic
54C2×C97AGL(1,ℤ/8)11yescharacteristic
55D97—81no—
56C97#46011yescharacteristic, complemented, Sylow
57#460—971nomaximal, Sylow
58C2×SD16—971no—
59C2×SD16D9711yescharacteristic, complemented
60#127—971no—
61C4×Q8—971no—
62C4⋊C8—971no—
63#102—971no—
64#102—971no—
65C2×Q8C2×D9711yescharacteristic
66C2×D4—971no—
67C2×D4—1941no—
68C2×D4—1941no—
69C2×D4C2×D9711yescharacteristic
70SD16—22no—
71SD16—1942no—
72C2×C8—971no—
73C2×C8C2×D9711yescharacteristic
74C4⋊C4—971no—
75C4⋊C4—1941no—
76C42—971no—
77C42—1941no—
78C23—21no—
79C23—1941no—
80Q8—21no—
81Q8C22⋊D9712yescomplemented
82D4—21no—
83D4—21no—
84D4—3882no—
85D4—3882no—
86D4—1941no—
87D4—1941no—
88C2×C4—21no—
89C2×C4—971no—
90C2×C4—971no—
91C2×C4—1941no—
92C2×C4C22×D9711yescharacteristic
93C8—21no—
94C8—1941no—
95C22—41no—
96C22—41no—
97C22—41no—
98C22—3881no—
99C22—3881no—
100C22—3881no—
101C22D4×D9711yescharacteristic
102C4—22no—
103C4—972no—
104C4—3881no—
105C4—1941no—
106C4C2×C22⋊D9711yescharacteristic
107C4#1309551011yescharacteristic
108C2—81no—
109C2—7761no—
110C2#1569078211yescharacteristic
111C2SD16×D9711yescharacteristic
112C2#1569083711yescharacteristic
subgroupG/H
centerC22D4×D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×SD16×C97C2
socleC22×C97C2×D4
hypercenterC2×SD16D97
hypocenterC97#460
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13095498C2semidirect
3. Q8×Dic97C2semidirect
4. #15690739C2semidirect
5. #15690732C2semidirect
6. #15690731C2semidirect
7. C2×SD16×C97C2semidirect
24. Q8×C97D4semidirect
50. Dic97SD16semidirect
56. C97#460semidirect
59. C2×SD16D97semidirect
81. Q8C22⋊D97semidirect