Finite Group Databasebeta

← #37560073

Subgroups — #37560073

Order 23872.

292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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×#20238610C212yesmaximal, complemented
2#26045791C211yesmaximal, characteristic, complemented
3#26045777C212yesmaximal, complemented
4#26045775C212yesmaximal, complemented
5#26045770C212yesmaximal, complemented
6#26045767C211yesmaximal, characteristic, complemented
7#26045766C211yesmaximal, characteristic, complemented
8#26045754C211yesmaximal, characteristic, complemented
9C4×C22⋊D373C211yesmaximal, characteristic, complemented
10C4⋊C4×D373C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×C373C211yesmaximal, characteristic, complemented
12#20238610—28no—
13C2×Dic746C2212yes—
14C2×D1492C2211yescharacteristic
15C2×D1492C2212yes—
16C2×C22⋊D373C2212yes—
17C2×C22⋊D373C2211yescharacteristic
18C2×C4×D373C2211yescharacteristic
19C2×C4×D373C2212yes—
20C2×C4×D373C2212yes—
21C4⋊Dic373C2211yescharacteristic
22#20238589C2212yes—
23#20238589C2211yescharacteristic
24#20238589C2212yes—
25C22⋊Dic373C2211yescharacteristic
26#20238587C2211yescharacteristic
27#20238587C2212yes—
28#20238587C2212yes—
29#20238587C2212yes—
30C4×Dic373C2211yescharacteristic
31C22×C4×C373C2211yescharacteristic
32C22×C4×C373C2212yes—
33C4⋊C4×C373C2211yescharacteristic
34C4⋊C4×C373C2211yescharacteristic
35C4⋊C4×C373C2212yes—
36C22×D373C2312yes—
37C22×D373C2311yescharacteristic
38Dic746—24no—
39D1492—24no—
40D1492—22no—
41C22⋊D373—24no—
42C22⋊D373D414yescomplemented
43C2×Dic373C2312yes—
44C2×Dic373C2311yescharacteristic
45C2×Dic373C2311yescharacteristic
46C2×Dic373C2311yescharacteristic
47C4×D373—24no—
48C4×D373—22no—
49C4×D373—24no—
50C23×C373C2311yescharacteristic
51C2×C4×C373—24no—
52C2×C4×C373—22no—
53C2×C4×C373C2312yes—
54C2×C4×C373C2312yes—
55C2×C4×C373C2311yescharacteristic
56C2×C4×C373C2311yescharacteristic
57C22×C373—21no—
58C22×C373—21no—
59C22×C373C2×D412yes—
60C22×C373C2411yescharacteristic
61C2×D373—21no—
62C2×D373—21no—
63C2×D373—22no—
64C2×D373—22no—
65C2×D373—22no—
66C2×D373C2×D412yes—
67C4×C373—22no—
68C4×C373—22no—
69C4×C373—21no—
70C4×C373#4112yescomplemented
71Dic373—22no—
72Dic373—21no—
73Dic373—21no—
74Dic373C2×D412yes—
75C2×C373—22no—
76C2×C373C22×D411yescharacteristic
77C2×C373C2×#4111yescharacteristic
78C2×C3732−1+411yescharacteristic
79D373—22no—
80D373—42no—
81C373#54711yescharacteristic, complemented, Sylow
82#547—3731nomaximal, Sylow
83C2×#41—3732no—
84C4⋊Q8—3731no—
85#123—3732no—
86#123—3732no—
87C22⋊Q8—3732no—
88#121—3731no—
89#121—3731no—
90C4×D4—3731no—
91C4×D4—3731no—
92C2×C4⋊C4—3731no—
93C2×C4⋊C4D37311yescharacteristic, complemented
94#41—7468no—
95C2×Q8—3732no—
96C2×D4—3731no—
97C2×D4—3732no—
98C2×D4—3731no—
99C2×D4—3732no—
100C22×C4—3731no—
101C22×C4—3732no—
102C22×C4—3732no—
103C22×C4C2×D37311yescharacteristic
104C22×C4C2×D37312yes—
105C4⋊C4—3731no—
106C4⋊C4—3732no—
107C4⋊C4—3731no—
108C4⋊C4—3732no—
109C4⋊C4C2×D37311yescharacteristic
110C4⋊C4C2×D37311yescharacteristic
111C4⋊C4C2×D37312yes—
112C22⋊C4—3731no—
113C22⋊C4—3731no—
114C22⋊C4—3732no—
115C22⋊C4—3732no—
116C22⋊C4—3732no—
117C42—3731no—
118C23—3731no—
119C23—3732no—
120C23C22×D37311yescharacteristic
121Q8—7464no—
122D4—3734no—
123D4—7464no—
124D4—7464no—
125D4—7462no—
126C2×C4—24no—
127C2×C4—22no—
128C2×C4—3731no—
129C2×C4—3731no—
130C2×C4—3731no—
131C2×C4—3732no—
132C2×C4—7464no—
133C2×C4—7464no—
134C2×C4—7462no—
135C2×C4C22×D37311yescharacteristic
136C2×C4C22×D37312yes—
137C2×C4C22×D37312yes—
138C2×C4C22×D37311yescharacteristic
139C22—21no—
140C22—21no—
141C22—3732no—
142C22—7462no—
143C22—7462no—
144C22—7462no—
145C22—7461no—
146C22—7461no—
147C22D4×D37312yes—
148C22C23×D37311yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—3732no—
153C4—7462no—
154C4—7461no—
155C4—7461no—
156C4#2023861012yescomplemented
157C2—22no—
158C2—14922no—
159C2—7462no—
160C2C2×D4×D37311yescharacteristic
161C2C2×#2023861011yescharacteristic
162C2#2604584011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D373
commutator, socle, cosocleC22×C373C24
FittingC2×C4⋊C4×C373C2
hypercenterC2×C4⋊C4D373
hypocenterC373#547
LCSG ▷ C22×C373 ▷ C373
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#20238610C2semidirect
2. #26045791C2semidirect
3. #26045777C2semidirect
4. #26045775C2semidirect
5. #26045770C2semidirect
6. #26045767C2semidirect
7. #26045766C2semidirect
8. #26045754C2semidirect
9. C4×C22⋊D373C2semidirect
10. C4⋊C4×D373C2semidirect
11. C2×C4⋊C4×C373C2semidirect
42. C22⋊D373D4semidirect
70. C4×C373#41semidirect
81. C373#547semidirect
93. C2×C4⋊C4D373semidirect
156. C4#20238610semidirect

Maximal subgroups

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

subgroupindex
C2×#202386102
#260457912
#260457772
#260457752
#260457702
#260457672
#260457662
#260457542
C4×C22⋊D3732
C4⋊C4×D3732
C2×C4⋊C4×C3732
#547373