Finite Group Databasebeta

← #37560022

Subgroups — #37560022

Order 23872.

240 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 93 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#26045788C211yesmaximal, characteristic, complemented
2#26045782C211yesmaximal, characteristic, complemented
3#26045777C211yesmaximal, characteristic, complemented
4#26045775C211yesmaximal, characteristic, complemented
5#26045774C211yesmaximal, characteristic, complemented
6#26045773C211yesmaximal, characteristic, complemented
7#26045765C211yesmaximal, characteristic, complemented
8#26045764C211yesmaximal, characteristic, complemented
9#26045764C211yesmaximal, characteristic, complemented
10#26045764C211yesmaximal, characteristic, complemented
11#26045763C211yesmaximal, characteristic, complemented
12C4×C22⋊D373C211yesmaximal, characteristic, complemented
13#26045752C211yesmaximal, characteristic, complemented
14#26045748C211yesmaximal, characteristic, complemented
15#121×C373C211yesmaximal, characteristic, complemented
16C2×D1492C2211yescharacteristic
17C2×C22⋊D373C2211yescharacteristic
18C2×C22⋊D373C2211yescharacteristic
19C2×C22⋊D373C2211yescharacteristic
20C2×C22⋊D373C2211yescharacteristic
21C2×C22⋊D373C2211yescharacteristic
22C2×C22⋊D373C2211yescharacteristic
23C22×Dic373C2211yescharacteristic
24C22×Dic373C2211yescharacteristic
25C2×C4×D373C2211yescharacteristic
26C2×C4×D373C2211yescharacteristic
27C4⋊Dic373C2211yescharacteristic
28#20238589C2211yescharacteristic
29#20238589C2211yescharacteristic
30#20238589C2211yescharacteristic
31#20238589C2211yescharacteristic
32#20238589C2211yescharacteristic
33#20238589C2211yescharacteristic
34C22⋊Dic373C2211yescharacteristic
35C22⋊Dic373C2211yescharacteristic
36C22⋊Dic373C2211yescharacteristic
37C22⋊Dic373C2211yescharacteristic
38#20238587C2211yescharacteristic
39#20238587C2211yescharacteristic
40#20238587C2211yescharacteristic
41#20238587C2211yescharacteristic
42C4×Dic373C2211yescharacteristic
43C4×Dic373C2211yescharacteristic
44C2×D4×C373C2211yescharacteristic
45C2×D4×C373C2211yescharacteristic
46C2×D4×C373C2211yescharacteristic
47C22×C4×C373C2211yescharacteristic
48C4⋊C4×C373C2211yescharacteristic
49C22⋊C4×C373C2211yescharacteristic
50C22⋊C4×C373C2211yescharacteristic
51C22×D373C2311yescharacteristic
52C22×D373C2311yescharacteristic
53D1492—41no—
54C22⋊D373—22no—
55C22⋊D373—22no—
56C22⋊D373—41no—
57C22⋊D373—41no—
58C22⋊D373—41no—
59C22⋊D373—41no—
60C2×Dic373—22no—
61C2×Dic373—41no—
62C2×Dic373C2311yescharacteristic
63C2×Dic373C2311yescharacteristic
64C2×Dic373C2311yescharacteristic
65C2×Dic373C2311yescharacteristic
66C2×Dic373C2311yescharacteristic
67C2×Dic373C2311yescharacteristic
68C4×D373—41no—
69C4×D373—41no—
70C23×C373C2311yescharacteristic
71C23×C373C2311yescharacteristic
72C23×C373C2311yescharacteristic
73D4×C373—41no—
74D4×C373—41no—
75D4×C373—41no—
76C2×C4×C373—41no—
77C2×C4×C373C2311yescharacteristic
78C2×C4×C373C2311yescharacteristic
79C2×C4×C373C2311yescharacteristic
80C2×C4×C373C2311yescharacteristic
81C22×C373—21no—
82C22×C373—21no—
83C22×C373—21no—
84C22×C373—21no—
85C22×C373—21no—
86C22×C373—21no—
87C22×C373—21no—
88C22×C373—21no—
89C22×C373—21no—
90C22×C373C2411yescharacteristic
91C2×D373—21no—
92C2×D373—21no—
93C2×D373—21no—
94C2×D373—21no—
95C2×D373—21no—
96C2×D373—21no—
97C4×C373—21no—
98C4×C373—21no—
99C4×C373—21no—
100C4×C373—21no—
101Dic373—21no—
102Dic373—21no—
103Dic373—21no—
104Dic373—21no—
105Dic373—21no—
106Dic373#4112yes—
107C2×C373—41no—
108C2×C373—41no—
109C2×C373—41no—
110C2×C373C2×#4111yescharacteristic
111C2×C373H(5,𝔽2)11yescharacteristic
112C2×C373H(5,𝔽2)11yescharacteristic
113D373—41no—
114D373—41no—
115C373#54011yescharacteristic, complemented, Sylow
116#540—3731nomaximal, Sylow
117#127—3731no—
118#125—3731no—
119#123—3731no—
120#123—3731no—
121#123—3731no—
122#123—3731no—
123#121—3731no—
124#121—3731no—
125#121—3731no—
126#121—3731no—
127#121—3731no—
128#121D37311yescharacteristic, complemented
129C4×D4—3731no—
130C4×D4—3731no—
131#117—3731no—
132C2×D4—3731no—
133C2×D4—3731no—
134C2×D4—3731no—
135C2×D4—3731no—
136C2×D4—3731no—
137C2×D4—3731no—
138C2×D4—3731no—
139C2×D4C2×D37311yescharacteristic
140C2×D4C2×D37311yescharacteristic
141C2×D4C2×D37311yescharacteristic
142C22×C4—3731no—
143C22×C4—3731no—
144C22×C4—3731no—
145C22×C4—3731no—
146C22×C4C2×D37311yescharacteristic
147C4⋊C4—3731no—
148C4⋊C4—3731no—
149C4⋊C4—3731no—
150C4⋊C4—3731no—
151C4⋊C4—3731no—
152C4⋊C4—3731no—
153C4⋊C4—3731no—
154C4⋊C4C2×D37311yescharacteristic
155C22⋊C4—3731no—
156C22⋊C4—3731no—
157C22⋊C4—3731no—
158C22⋊C4—3731no—
159C22⋊C4—3731no—
160C22⋊C4—3731no—
161C22⋊C4—3731no—
162C22⋊C4—3731no—
163C22⋊C4C2×D37311yescharacteristic
164C22⋊C4C2×D37311yescharacteristic
165C42—3731no—
166C42—3731no—
167C23—3731no—
168C23—3731no—
169C23C22×D37311yescharacteristic
170C23C22×D37311yescharacteristic
171C23C22×D37311yescharacteristic
172D4—41no—
173D4—41no—
174D4—41no—
175D4—14921no—
176D4—14921no—
177D4—14921no—
178D4—14921no—
179D4—14921no—
180D4—7462no—
181D4—7462no—
182C2×C4—41no—
183C2×C4—3731no—
184C2×C4—3731no—
185C2×C4—3731no—
186C2×C4—3731no—
187C2×C4—3731no—
188C2×C4—3731no—
189C2×C4—14921no—
190C2×C4—14921no—
191C2×C4—14921no—
192C2×C4—7462no—
193C2×C4C22×D37311yescharacteristic
194C2×C4C22×D37311yescharacteristic
195C2×C4C22×D37311yescharacteristic
196C2×C4C22×D37311yescharacteristic
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—7461no—
207C22—7461no—
208C22—7461no—
209C22—7461no—
210C22—7461no—
211C22—7461no—
212C22C23×D37311yescharacteristic
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—3732no—
218C4—7461no—
219C4—7461no—
220C4—7461no—
221C4—7461no—
222C4—7461no—
223C2—41no—
224C2—41no—
225C2—41no—
226C2—14921no—
227C2—14921no—
228C2#41×D37311yescharacteristic
229C2#2604583711yescharacteristic
230C2#2604583711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D373
commutator, socle, cosocleC22×C373C24
Fitting#121×C373C2
hypercenter#121D373
hypocenterC373#540
LCSG ▷ C22×C373 ▷ C373
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #26045788C2semidirect
2. #26045782C2semidirect
3. #26045777C2semidirect
4. #26045775C2semidirect
5. #26045774C2semidirect
6. #26045773C2semidirect
7. #26045765C2semidirect
8. #26045764C2semidirect
9. #26045764C2semidirect
10. #26045764C2semidirect
11. #26045763C2semidirect
12. C4×C22⋊D373C2semidirect
13. #26045752C2semidirect
14. #26045748C2semidirect
15. #121×C373C2semidirect
115. C373#540semidirect
128. #121D373semidirect

Maximal subgroups

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

subgroupindex
#260457882
#260457822
#260457772
#260457752
#260457742
#260457732
#260457652
#260457642
#260457632
C4×C22⋊D3732
#260457522
#260457482
#121×C3732
#540373