Finite Group Databasebeta

← #37559593

Subgroups — #37559593

Order 23872.

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#26045839C211yesmaximal, characteristic, complemented
2#26045818C211yesmaximal, characteristic, complemented
3#26045779C211yesmaximal, characteristic, complemented
4#26045719C211yesmaximal, characteristic, complemented
5#26045718C211yesmaximal, characteristic, complemented
6#26045710C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C373C211yesmaximal, characteristic, complemented
8#20238610—21no—
9#20238610C2211yescharacteristic
10#20238609—22no—
11#20238609—21no—
12C2×Dic746—21no—
13C2×Dic746C2211yescharacteristic
14Q8×D373—21no—
15#20238598—21no—
16#20238595—21no—
17#20238594C2211yescharacteristic
18C22⋊Dic373—22no—
19C4×Dic373C2211yescharacteristic
20#41×C373C2211yescharacteristic
21C2×D4×C373C2211yescharacteristic
22SD16×C373—21no—
23D8×C373—21no—
24M16×C373C2211yescharacteristic
25Dic746—22no—
26Dic746—21no—
27Dic746—21no—
28Dic746D411yescharacteristic
29D1492D411yescharacteristic
30C22⋊D373—22no—
31C22⋊D373—21no—
32C2×Dic373—22no—
33C2×Dic373—21no—
34C2×Dic373D412yes—
35C4×D373—22no—
36C4×D373—21no—
37#15688412—21no—
38C23×C373—21no—
39Q8×C373D411yescharacteristic
40D4×C373—21no—
41D4×C373—21no—
42D4×C373—21no—
43D4×C373D411yescharacteristic
44C2×C4×C373—21no—
45C2×C4×C373C2311yescharacteristic
46C8×C373—21no—
47C22×C373—21no—
48C22×C373—42no—
49C22×C373—41no—
50C22×C373C2×D411yescharacteristic
51C2×D373—21no—
52C4×C373—21no—
53C4×C373C2×D411yescharacteristic
54C4×C373C2×D411yescharacteristic
55Dic373—21no—
56Dic373—22no—
57Dic373—41no—
58C2×C373—21no—
59C2×C373—41no—
60C2×C373—81no—
61C2×C373#12011yescharacteristic
62D373—41no—
63C373#45411yescharacteristic, complemented, Sylow
64#454—3731nomaximal, Sylow
652−1+4—3731no—
66AGL(1,ℤ/8)—3731no—
67AGL(1,ℤ/8)D37311yescharacteristic, complemented
68#124—3731no—
69#104—3731no—
70#104—3731no—
71#101—3731no—
72#41—3731no—
73#41—7461no—
74#41—7462no—
75#41—7461no—
76#41C2×D37311yescharacteristic
77C2×Q8—3731no—
78C2×Q8—7461no—
79C2×Q8—7461no—
80C2×D4C2×D37311yescharacteristic
81SD16—21no—
82SD16—7461no—
83D8—21no—
84D8—7461no—
85M16—3731no—
86M16C2×D37311yescharacteristic
87C22⋊C4—7462no—
88C42—3731no—
89C23—21no—
90Q8—3731no—
91Q8—7462no—
92Q8—7461no—
93Q8—7461no—
94Q8C22⋊D37311yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—3731no—
99D4—7462no—
100D4—7461no—
101D4C22⋊D37311yescharacteristic
102C2×C4—21no—
103C2×C4—3732no—
104C2×C4—7462no—
105C2×C4—7461no—
106C2×C4—7462no—
107C2×C4—7461no—
108C2×C4C22×D37311yescharacteristic
109C8—21no—
110C8—7461no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—7461no—
115C22D4×D37311yescharacteristic
116C4—21no—
117C4—14921no—
118C4—7462no—
119C4—7461no—
120C4D4×D37311yescharacteristic
121C4C2×C22⋊D37311yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—14921no—
126C2#2604576011yescharacteristic
subgroupG/H
centerC2#26045760
commutator, cosocleC2×C4×C373C23
FrattiniC2×C4C22×D373
FittingAGL(1,ℤ/8)×C373C2
socleC2×C373#120
hypercenterAGL(1,ℤ/8)D373
hypocenterC373#454
LCSG ▷ C2×C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #26045839C2semidirect
2. #26045818C2semidirect
3. #26045779C2semidirect
4. #26045719C2semidirect
5. #26045718C2semidirect
6. #26045710C2semidirect
7. AGL(1,ℤ/8)×C373C2semidirect
63. C373#454semidirect
67. AGL(1,ℤ/8)D373semidirect

Maximal subgroups

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

subgroupindex
#260458392
#260458182
#260457792
#260457192
#260457182
#260457102
AGL(1,ℤ/8)×C3732
#454373