Finite Group Databasebeta

← #20260906

Subgroups — #20260906

Order 6208.

146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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
1#15690857C211yesmaximal, characteristic, complemented
2#15690836C211yesmaximal, characteristic, complemented
3#15690797C211yesmaximal, characteristic, complemented
4#15690737C211yesmaximal, characteristic, complemented
5#15690736C211yesmaximal, characteristic, complemented
6#15690728C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C97C211yesmaximal, characteristic, complemented
8#13095511—21no—
9#13095511C2211yescharacteristic
10#13095510—21no—
11#13095510—22no—
12C2×Dic194—21no—
13C2×Dic194C2211yescharacteristic
14Q8×D97—21no—
15#13095499—21no—
16#13095496—21no—
17#13095495C2211yescharacteristic
18C22⋊Dic97—22no—
19C4×Dic97C2211yescharacteristic
20#41×C97C2211yescharacteristic
21C2×D4×C97C2211yescharacteristic
22SD16×C97—21no—
23D8×C97—21no—
24M16×C97C2211yescharacteristic
25C23×C97—21no—
26Q8×C97D411yescharacteristic
27D4×C97—21no—
28D4×C97—21no—
29D4×C97—21no—
30D4×C97D411yescharacteristic
31C2×C4×C97—21no—
32C2×C4×C97C2311yescharacteristic
33C22⋊D97—22no—
34C22⋊D97—21no—
35C2×Dic97—22no—
36C2×Dic97—21no—
37C2×Dic97D412yes—
38D388D411yescharacteristic
39C4×D97—22no—
40C4×D97—21no—
41Dic194—22no—
42Dic194—21no—
43Dic194—21no—
44Dic194D411yescharacteristic
45C8×C97—21no—
46#11715895—21no—
47C22×C97—21no—
48C22×C97—42no—
49C22×C97—41no—
50C22×C97C2×D411yescharacteristic
51C2×D97—21no—
52C4×C97—21no—
53C4×C97C2×D411yescharacteristic
54C4×C97C2×D411yescharacteristic
55Dic97—22no—
56Dic97—21no—
57Dic97—41no—
58C2×C97—21no—
59C2×C97—41no—
60C2×C97—81no—
61C2×C97#12011yescharacteristic
62D97—41no—
63C97#45411yescharacteristic, complemented, Sylow
64#454—971nomaximal, Sylow
652−1+4—971no—
66AGL(1,ℤ/8)—971no—
67AGL(1,ℤ/8)D9711yescharacteristic, complemented
68#124—971no—
69#104—971no—
70#104—971no—
71#101—971no—
72#41—971no—
73#41—1941no—
74#41—1942no—
75#41—1941no—
76#41C2×D9711yescharacteristic
77C2×Q8—971no—
78C2×Q8—1941no—
79C2×Q8—1941no—
80C2×D4C2×D9711yescharacteristic
81SD16—21no—
82SD16—1941no—
83D8—21no—
84D8—1941no—
85M16—971no—
86M16C2×D9711yescharacteristic
87C22⋊C4—1942no—
88C42—971no—
89C23—21no—
90Q8—971no—
91Q8—1942no—
92Q8—1941no—
93Q8—1941no—
94Q8C22⋊D9711yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—971no—
99D4—1942no—
100D4—1941no—
101D4C22⋊D9711yescharacteristic
102C2×C4—21no—
103C2×C4—972no—
104C2×C4—1942no—
105C2×C4—1941no—
106C2×C4—1942no—
107C2×C4—1941no—
108C2×C4C22×D9711yescharacteristic
109C8—21no—
110C8—1941no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—1941no—
115C22D4×D9711yescharacteristic
116C4—21no—
117C4—3881no—
118C4—1942no—
119C4—1941no—
120C4D4×D9711yescharacteristic
121C4C2×C22⋊D9711yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—3881no—
126C2#1569077811yescharacteristic
subgroupG/H
centerC2#15690778
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingAGL(1,ℤ/8)×C97C2
socleC2×C97#120
hypercenterAGL(1,ℤ/8)D97
hypocenterC97#454
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #15690857C2semidirect
2. #15690836C2semidirect
3. #15690797C2semidirect
4. #15690737C2semidirect
5. #15690736C2semidirect
6. #15690728C2semidirect
7. AGL(1,ℤ/8)×C97C2semidirect
63. C97#454semidirect
67. AGL(1,ℤ/8)D97semidirect