Finite Group Databasebeta

← #37560071

Subgroups — #37560071

Order 23872.

292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 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×#20238609C211yesmaximal, characteristic, complemented
2#26045790C211yesmaximal, characteristic, complemented
3#26045775C212yesmaximal, complemented
4#26045773C212yesmaximal, complemented
5#26045771C211yesmaximal, characteristic, complemented
6#26045768C211yesmaximal, characteristic, complemented
7#26045764C212yesmaximal, complemented
8D4×Dic373C211yesmaximal, characteristic, complemented
9C4×C22⋊D373C211yesmaximal, characteristic, complemented
10C2×#20238589C212yesmaximal, complemented
11C2×#41×C373C211yesmaximal, characteristic, complemented
12#20238609—24no—
13C2×Dic746C2211yescharacteristic
14C2×C22⋊D373C2211yescharacteristic
15C2×C22⋊D373C2212yes—
16C22×Dic373C2212yes—
17C22×Dic373C2212yes—
18C2×C4×D373C2211yescharacteristic
19C4⋊Dic373C2211yescharacteristic
20#20238589C2211yescharacteristic
21#20238589C2212yes—
22#20238589C2212yes—
23#20238589C2212yes—
24#20238589C2212yes—
25C22⋊Dic373C2211yescharacteristic
26C22⋊Dic373C2212yes—
27C22⋊Dic373C2212yes—
28#20238587C2211yescharacteristic
29#20238587C2212yes—
30C4×Dic373C2211yescharacteristic
31#41×C373—24no—
32C2×Q8×C373C2211yescharacteristic
33C2×D4×C373C2212yes—
34C2×D4×C373C2211yescharacteristic
35C22×C4×C373C2212yes—
36C22×C4×C373C2211yescharacteristic
37C22×D373C2311yescharacteristic
38Dic746—22no—
39C22⋊D373—24no—
40C22⋊D373—22no—
41C2×Dic373—24no—
42C2×Dic373—24no—
43C2×Dic373C2311yescharacteristic
44C2×Dic373C2312yes—
45C2×Dic373C2312yes—
46C2×Dic373C2311yescharacteristic
47C2×Dic373C2311yescharacteristic
48C4×D373—22no—
49C23×C373C2311yescharacteristic
50C23×C373C2312yes—
51Q8×C373—22no—
52D4×C373—24no—
53D4×C373D414yescomplemented
54C2×C4×C373—24no—
55C2×C4×C373—22no—
56C2×C4×C373C2311yescharacteristic
57C2×C4×C373C2312yes—
58C2×C4×C373C2311yescharacteristic
59C22×C373—22no—
60C22×C373—22no—
61C22×C373—21no—
62C22×C373—21no—
63C22×C373—21no—
64C22×C373C2×D414yes—
65C22×C373C2411yescharacteristic
66C2×D373—21no—
67C2×D373—21no—
68C2×D373—21no—
69C4×C373—21no—
70C4×C373—22no—
71C4×C373C2×D412yes—
72Dic373—21no—
73Dic373—22no—
74Dic373—22no—
75Dic373—21no—
76Dic373#4112yescomplemented
77C2×C373—24no—
78C2×C373—41no—
79C2×C373C22×D411yescharacteristic
80C2×C373C2×#4111yescharacteristic
81C2×C3732−1+411yescharacteristic
82D373—41no—
83C373#54711yescharacteristic, complemented, Sylow
84#547—3731nomaximal, Sylow
85C2×#41—3731no—
86C2×#41D37311yescharacteristic, complemented
87C4⋊Q8—3731no—
88#123—3732no—
89#123—3732no—
90C22⋊Q8—3731no—
91C22⋊Q8—3731no—
92#121—3732no—
93C4×D4—3731no—
94C4×D4—3731no—
95C2×C4⋊C4—3732no—
96#41—24no—
97#41—7464no—
98C2×Q8—3731no—
99C2×Q8C2×D37311yescharacteristic
100C2×D4—3731no—
101C2×D4—3732no—
102C2×D4C2×D37312yes—
103C2×D4C2×D37311yescharacteristic
104C22×C4—3732no—
105C22×C4—3732no—
106C22×C4—3731no—
107C22×C4C2×D37312yes—
108C22×C4C2×D37311yescharacteristic
109C4⋊C4—3731no—
110C4⋊C4—3732no—
111C4⋊C4—3732no—
112C4⋊C4—3732no—
113C4⋊C4—3731no—
114C4⋊C4—3732no—
115C22⋊C4—3732no—
116C22⋊C4—3731no—
117C22⋊C4—3732no—
118C22⋊C4—3731no—
119C22⋊C4—3732no—
120C42—3731no—
121C23—3731no—
122C23C22×D37311yescharacteristic
123C23C22×D37312yes—
124Q8—22no—
125Q8—7462no—
126D4—24no—
127D4—7462no—
128D4—7464no—
129D4C22⋊D37314yescomplemented
130C2×C4—24no—
131C2×C4—22no—
132C2×C4—3731no—
133C2×C4—3731no—
134C2×C4—3732no—
135C2×C4—3731no—
136C2×C4—3732no—
137C2×C4—7464no—
138C2×C4—7464no—
139C2×C4—7462no—
140C2×C4C22×D37311yescharacteristic
141C2×C4C22×D37312yes—
142C2×C4C22×D37311yescharacteristic
143C22—22no—
144C22—22no—
145C22—21no—
146C22—21no—
147C22—21no—
148C22—7461no—
149C22—7461no—
150C22—7461no—
151C22C2×C22⋊D37314yes—
152C22C23×D37311yescharacteristic
153C4—21no—
154C4—22no—
155C4—3732no—
156C4—7461no—
157C4—7462no—
158C4—7462no—
159C4—7461no—
160C4C2×C22⋊D37312yes—
161C2—24no—
162C2—41no—
163C2—14921no—
164C2C22×C22⋊D37311yescharacteristic
165C2#41×D37311yescharacteristic
166C2#2604583911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D373
commutator, socle, cosocleC22×C373C24
FittingC2×#41×C373C2
hypercenterC2×#41D373
hypocenterC373#547
LCSG ▷ C22×C373 ▷ C373
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20238609C2semidirect
2. #26045790C2semidirect
3. #26045775C2semidirect
4. #26045773C2semidirect
5. #26045771C2semidirect
6. #26045768C2semidirect
7. #26045764C2semidirect
8. D4×Dic373C2semidirect
9. C4×C22⋊D373C2semidirect
10. C2×#20238589C2semidirect
11. C2×#41×C373C2semidirect
53. D4×C373D4semidirect
76. Dic373#41semidirect
83. C373#547semidirect
86. C2×#41D373semidirect
129. D4C22⋊D373semidirect

Maximal subgroups

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

subgroupindex
C2×#202386092
#260457902
#260457752
#260457732
#260457712
#260457682
#260457642
D4×Dic3732
C4×C22⋊D3732
C2×#202385892
C2×#41×C3732
#547373