Finite Group Databasebeta

← #37560014

Subgroups — #37560014

Order 23872.

218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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#26045786C211yesmaximal, characteristic, complemented
2#26045785C211yesmaximal, characteristic, complemented
3#26045784C211yesmaximal, characteristic, complemented
4#26045782C211yesmaximal, characteristic, complemented
5#26045776C211yesmaximal, characteristic, complemented
6#26045775C211yesmaximal, characteristic, complemented
7#26045774C211yesmaximal, characteristic, complemented
8#26045773C211yesmaximal, characteristic, complemented
9#26045771C211yesmaximal, characteristic, complemented
10#26045770C211yesmaximal, characteristic, complemented
11#26045769C211yesmaximal, characteristic, complemented
12#26045764C211yesmaximal, characteristic
13C4×C22⋊D373C211yesmaximal, characteristic, complemented
14C2×#20238589C211yesmaximal, characteristic, complemented
15C4×D4×C373C211yesmaximal, characteristic, complemented
16C2×Dic746C2211yescharacteristic
17C2×C22⋊D373C2211yescharacteristic
18C2×C22⋊D373C2211yescharacteristic
19C22×Dic373C2211yescharacteristic
20C22×Dic373C2211yescharacteristic
21C2×C4×D373C2211yescharacteristic
22C4⋊Dic373C2211yescharacteristic
23C4⋊Dic373C2211yescharacteristic
24C4⋊Dic373C2211yescharacteristic
25#20238589C2211yescharacteristic
26#20238589C2211yescharacteristic
27#20238589C2211yescharacteristic
28#20238589C2211yescharacteristic
29#20238589C2211yescharacteristic
30#20238589C2211yescharacteristic
31#20238589C2211yescharacteristic
32#20238589C2211yescharacteristic
33#20238589C2211yescharacteristic
34#20238589C2211yescharacteristic
35C22⋊Dic373C2211yescharacteristic
36C22⋊Dic373C2211yescharacteristic
37C22⋊Dic373C2211yescharacteristic
38C22⋊Dic373C2211yescharacteristic
39#20238587C2211yescharacteristic
40#20238587C2211yescharacteristic
41#20238587C2211yescharacteristic
42#20238587C2211yescharacteristic
43C4×Dic373C2211yescharacteristic
44C2×D4×C373C2211yescharacteristic
45C22×C4×C373C2211yescharacteristic
46C22×C4×C373C2211yescharacteristic
47C4⋊C4×C373C2211yescharacteristic
48C22⋊C4×C373C2211yescharacteristic
49C22⋊C4×C373C2211yescharacteristic
50C42×C373C2211yescharacteristic
51C22×D373C2311yescharacteristic
52Dic746—41no—
53C22⋊D373—22no—
54C22⋊D373—41no—
55C2×Dic373—22no—
56C2×Dic373—41no—
57C2×Dic373C2311yescharacteristic
58C2×Dic373C2311yescharacteristic
59C2×Dic373C2311yescharacteristic
60C2×Dic373C2311yescharacteristic
61C2×Dic373C2311yescharacteristic
62C2×Dic373C2311yescharacteristic
63C2×Dic373C2311yescharacteristic
64C4×D373—41no—
65C23×C373C2311yescharacteristic
66C23×C373C2311yescharacteristic
67D4×C373—22no—
68C2×C4×C373—41no—
69C2×C4×C373—41no—
70C2×C4×C373C2311yescharacteristic
71C2×C4×C373C2311yescharacteristic
72C2×C4×C373C2311yescharacteristic
73C2×C4×C373C2311yescharacteristic
74C2×C4×C373C2311yescharacteristic
75C22×C373—21no—
76C22×C373—21no—
77C22×C373—21no—
78C22×C373—21no—
79C22×C373—21no—
80C22×C373#4112yes—
81C22×C373C2411yescharacteristic
82C2×D373—21no—
83C2×D373—21no—
84C2×D373—21no—
85C4×C373—21no—
86C4×C373—21no—
87C4×C373—21no—
88C4×C373—21no—
89C4×C373—21no—
90Dic373—21no—
91Dic373—21no—
92Dic373—21no—
93Dic373—21no—
94Dic373—21no—
95Dic373—21no—
96Dic373—21no—
97C2×C373—22no—
98C2×C373—41no—
99C2×C373C2×#4111yescharacteristic
100C2×C373H(5,𝔽2)11yescharacteristic
101C2×C3732−1+411yescharacteristic
102D373—41no—
103C373#53911yescharacteristic, complemented, Sylow
104#539—3731nomaximal, Sylow
105#126—3731no—
106#126—3731no—
107#125—3731no—
108#125—3731no—
109#123—3731no—
110#123—3731no—
111#123—3731no—
112#123—3731no—
113C22⋊Q8—3731no—
114C22⋊Q8—3731no—
115C22⋊Q8—3731no—
116#121—3731no—
117C4×D4—3731no—
118C4×D4D37311yescharacteristic, complemented
119C2×C4⋊C4—3731no—
120C2×Q8—3731no—
121C2×D4—3731no—
122C2×D4—3731no—
123C2×D4C2×D37311yescharacteristic
124C22×C4—3731no—
125C22×C4—3731no—
126C22×C4—3731no—
127C22×C4C2×D37311yescharacteristic
128C22×C4C2×D37311yescharacteristic
129C4⋊C4—3731no—
130C4⋊C4—3731no—
131C4⋊C4—3731no—
132C4⋊C4—3731no—
133C4⋊C4—3731no—
134C4⋊C4—3731no—
135C4⋊C4—3731no—
136C4⋊C4—3731no—
137C4⋊C4—3731no—
138C4⋊C4—3731no—
139C4⋊C4—3731no—
140C4⋊C4—3731no—
141C4⋊C4—3731no—
142C4⋊C4C2×D37311yescharacteristic
143C22⋊C4—3731no—
144C22⋊C4—3731no—
145C22⋊C4—3731no—
146C22⋊C4—3731no—
147C22⋊C4—3731no—
148C22⋊C4—3731no—
149C22⋊C4—3731no—
150C22⋊C4—3731no—
151C22⋊C4C2×D37311yescharacteristic
152C22⋊C4C2×D37311yescharacteristic
153C42—3731no—
154C42C2×D37311yescharacteristic
155C23—3731no—
156C23C22×D37311yescharacteristic
157C23C22×D37311yescharacteristic
158Q8—14921no—
159D4—22no—
160D4—14921no—
161D4—7462no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—3731no—
165C2×C4—3731no—
166C2×C4—3731no—
167C2×C4—3731no—
168C2×C4—3731no—
169C2×C4—3731no—
170C2×C4—3731no—
171C2×C4—14921no—
172C2×C4—14921no—
173C2×C4—7462no—
174C2×C4C22×D37311yescharacteristic
175C2×C4C22×D37311yescharacteristic
176C2×C4C22×D37311yescharacteristic
177C2×C4C22×D37311yescharacteristic
178C2×C4C22×D37311yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—7461no—
185C22—7461no—
186C22—7461no—
187C22#2023861012yes—
188C22C23×D37311yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—7461no—
195C4—7461no—
196C4—7461no—
197C4—7461no—
198C4—7461no—
199C4—7461no—
200C4—7461no—
201C2—22no—
202C2—41no—
203C2—14921no—
204C2C2×#2023861011yescharacteristic
205C2#2604583711yescharacteristic
206C2#2604583911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D373
commutator, socle, cosocleC22×C373C24
FittingC4×D4×C373C2
prime radical#26045764C2
hypercenterC4×D4D373
hypocenterC373#539
LCSG ▷ C22×C373 ▷ C373
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26045786C2semidirect
2. #26045785C2semidirect
3. #26045784C2semidirect
4. #26045782C2semidirect
5. #26045776C2semidirect
6. #26045775C2semidirect
7. #26045774C2semidirect
8. #26045773C2semidirect
9. #26045771C2semidirect
10. #26045770C2semidirect
11. #26045769C2semidirect
13. C4×C22⋊D373C2semidirect
14. C2×#20238589C2semidirect
15. C4×D4×C373C2semidirect
103. C373#539semidirect
118. C4×D4D373semidirect

Maximal subgroups

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

subgroupindex
#260457862
#260457852
#260457842
#260457822
#260457762
#260457752
#260457742
#260457732
#260457712
#260457702
#260457692
#260457642
C4×C22⋊D3732
C2×#202385892
C4×D4×C3732
#539373