Finite Group Databasebeta

← #37560121

Subgroups — #37560121

Order 23872.

238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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#26045782C211yesmaximal, characteristic, complemented
4#26045777C211yesmaximal, characteristic, complemented
5#26045775C211yesmaximal, characteristic, complemented
6#26045766C211yesmaximal, characteristic, complemented
7#26045765C211yesmaximal, characteristic, complemented
8#26045764C211yesmaximal, characteristic, complemented
9#26045764C211yesmaximal, characteristic, complemented
10C4×C22⋊D373C211yesmaximal, characteristic, complemented
11#26045752C211yesmaximal, characteristic, complemented
12#26045752C211yesmaximal, characteristic, complemented
13#26045749C211yesmaximal, characteristic, complemented
14C2×#20238589C211yesmaximal, characteristic, complemented
15C4×D4×C373C211yesmaximal, characteristic, complemented
16C2×D1492C2211yescharacteristic
17C2×C22⋊D373C2211yescharacteristic
18C2×C22⋊D373C2211yescharacteristic
19C2×C22⋊D373C2211yescharacteristic
20C2×C22⋊D373C2211yescharacteristic
21C22×Dic373C2211yescharacteristic
22C22×Dic373C2211yescharacteristic
23C2×C4×D373C2211yescharacteristic
24C2×C4×D373C2211yescharacteristic
25C4⋊Dic373C2211yescharacteristic
26#20238589C2211yescharacteristic
27#20238589C2211yescharacteristic
28#20238589C2211yescharacteristic
29#20238589C2211yescharacteristic
30#20238589C2211yescharacteristic
31#20238589C2211yescharacteristic
32#20238589C2211yescharacteristic
33#20238589C2211yescharacteristic
34C22⋊Dic373C2211yescharacteristic
35C22⋊Dic373C2211yescharacteristic
36#20238587C2211yescharacteristic
37#20238587C2211yescharacteristic
38#20238587C2211yescharacteristic
39#20238587C2211yescharacteristic
40#20238587C2211yescharacteristic
41#20238587C2211yescharacteristic
42C4×Dic373C2211yescharacteristic
43C4×Dic373C2211yescharacteristic
44C2×D4×C373C2211yescharacteristic
45C22×C4×C373C2211yescharacteristic
46C22×C4×C373C2211yescharacteristic
47C4⋊C4×C373C2211yescharacteristic
48C22⋊C4×C373C2211yescharacteristic
49C22⋊C4×C373C2211yescharacteristic
50C42×C373C2211yescharacteristic
51C22×D373C2311yescharacteristic
52C22×D373C2311yescharacteristic
53D1492—41no—
54C22⋊D373—22no—
55C22⋊D373—22no—
56C22⋊D373—22no—
57C22⋊D373—41no—
58C2×Dic373—22no—
59C2×Dic373—41no—
60C2×Dic373C2311yescharacteristic
61C2×Dic373C2311yescharacteristic
62C2×Dic373C2311yescharacteristic
63C2×Dic373C2311yescharacteristic
64C2×Dic373C2311yescharacteristic
65C2×Dic373C2311yescharacteristic
66C4×D373—22no—
67C4×D373—41no—
68C23×C373C2311yescharacteristic
69C23×C373C2311yescharacteristic
70D4×C373—22no—
71C2×C4×C373—41no—
72C2×C4×C373—41no—
73C2×C4×C373C2311yescharacteristic
74C2×C4×C373C2311yescharacteristic
75C2×C4×C373C2311yescharacteristic
76C2×C4×C373C2311yescharacteristic
77C2×C4×C373C2311yescharacteristic
78C22×C373—21no—
79C22×C373—21no—
80C22×C373—21no—
81C22×C373—21no—
82C22×C373—21no—
83C22×C373#4112yes—
84C22×C373C2411yescharacteristic
85C2×D373—21no—
86C2×D373—21no—
87C2×D373—21no—
88C2×D373—21no—
89C2×D373—21no—
90C2×D373—21no—
91C4×C373—21no—
92C4×C373—21no—
93C4×C373—21no—
94C4×C373—21no—
95C4×C373—21no—
96Dic373—21no—
97Dic373—21no—
98Dic373—21no—
99Dic373—21no—
100Dic373—21no—
101Dic373#4112yes—
102C2×C373—22no—
103C2×C373—41no—
104C2×C373C2×#4111yescharacteristic
105C2×C373C2×#4111yescharacteristic
106C2×C373H(5,𝔽2)11yescharacteristic
107D373—41no—
108D373—41no—
109C373#55311yescharacteristic, complemented, Sylow
110#553—3731nomaximal, Sylow
111#126—3731no—
112#126—3731no—
113#125—3731no—
114#123—3731no—
115#123—3731no—
116#121—3731no—
117#121—3731no—
118#121—3731no—
119#121—3731no—
120C4×D4—3731no—
121C4×D4—3731no—
122C4×D4—3731no—
123C4×D4D37311yescharacteristic, complemented
124#117—3731no—
125C2×C4⋊C4—3731no—
126C2×D4—3731no—
127C2×D4—3731no—
128C2×D4—3731no—
129C2×D4—3731no—
130C2×D4—3731no—
131C2×D4C2×D37311yescharacteristic
132C22×C4—3731no—
133C22×C4—3731no—
134C22×C4—3731no—
135C22×C4—3731no—
136C22×C4C2×D37311yescharacteristic
137C22×C4C2×D37311yescharacteristic
138C4⋊C4—3731no—
139C4⋊C4—3731no—
140C4⋊C4—3731no—
141C4⋊C4—3731no—
142C4⋊C4—3731no—
143C4⋊C4—3731no—
144C4⋊C4—3731no—
145C4⋊C4—3731no—
146C4⋊C4—3731no—
147C4⋊C4C2×D37311yescharacteristic
148C22⋊C4—3731no—
149C22⋊C4—3731no—
150C22⋊C4—3731no—
151C22⋊C4—3731no—
152C22⋊C4—3731no—
153C22⋊C4—3731no—
154C22⋊C4—3731no—
155C22⋊C4—3731no—
156C22⋊C4C2×D37311yescharacteristic
157C22⋊C4C2×D37311yescharacteristic
158C42—3731no—
159C42—3731no—
160C42C2×D37311yescharacteristic
161C23—3731no—
162C23—3731no—
163C23C22×D37311yescharacteristic
164C23C22×D37311yescharacteristic
165D4—22no—
166D4—14921no—
167D4—14921no—
168D4—7462no—
169D4—7462no—
170D4—7462no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3731no—
174C2×C4—3731no—
175C2×C4—3731no—
176C2×C4—3731no—
177C2×C4—3731no—
178C2×C4—3731no—
179C2×C4—14921no—
180C2×C4—14921no—
181C2×C4—7462no—
182C2×C4—7462no—
183C2×C4C22×D37311yescharacteristic
184C2×C4C22×D37311yescharacteristic
185C2×C4C22×D37311yescharacteristic
186C2×C4C22×D37311yescharacteristic
187C2×C4C22×D37311yescharacteristic
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—7461no—
194C22—7461no—
195C22—7461no—
196C22—7461no—
197C22—7461no—
198C22—7461no—
199C22#2023861012yes—
200C22C23×D37311yescharacteristic
201C4—21no—
202C4—21no—
203C4—21no—
204C4—21no—
205C4—21no—
206C4—3732no—
207C4—7461no—
208C4—7461no—
209C4—7461no—
210C4—7461no—
211C4—7461no—
212C2—22no—
213C2—41no—
214C2—14921no—
215C2—14921no—
216C2#41×D37311yescharacteristic
217C2C2×#2023861011yescharacteristic
218C2#2604583711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D373
commutator, socle, cosocleC22×C373C24
FittingC4×D4×C373C2
hypercenterC4×D4D373
hypocenterC373#553
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. #26045782C2semidirect
4. #26045777C2semidirect
5. #26045775C2semidirect
6. #26045766C2semidirect
7. #26045765C2semidirect
8. #26045764C2semidirect
9. #26045764C2semidirect
10. C4×C22⋊D373C2semidirect
11. #26045752C2semidirect
12. #26045752C2semidirect
13. #26045749C2semidirect
14. C2×#20238589C2semidirect
15. C4×D4×C373C2semidirect
109. C373#553semidirect
123. C4×D4D373semidirect

Maximal subgroups

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

subgroupindex
#260457862
#260457852
#260457822
#260457772
#260457752
#260457662
#260457652
#260457642
C4×C22⋊D3732
#260457522
#260457492
C2×#202385892
C4×D4×C3732
#553373