Finite Group Databasebeta

← #22595268

Subgroups — #22595268

Order 9088.

504 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14556109C211yesmaximal, characteristic
2#17985932C212yesmaximal, complemented
3#17985927C212yesmaximal, complemented
4#17985927C212yesmaximal, complemented
5#17985902C211yesmaximal, characteristic
6#17985894C212yesmaximal, complemented
7#17985872C212yesmaximal, complemented
8#17985871C212yesmaximal, complemented
9C2×#123×C71C211yesmaximal, characteristic
10C23×Dic71C2211yescharacteristic
11#14556109—24no—
12C2×C4⋊Dic71C2211yescharacteristic
13C2×Dic71⋊C4C2212yes—
14C2×Dic71⋊C4C2212yes—
15C2×Dic71⋊C4C2212yes—
16C2×Dic71⋊C4C2212yes—
17C2×C22⋊Dic71C2212yes—
18C2×C22⋊Dic71C2212yes—
19C2×C22⋊Dic71C2212yes—
20C2×C22⋊Dic71C2211yescharacteristic
21C2×C4×Dic71C2211yescharacteristic
22C71⋊#95C2212yes—
23C71⋊#95C2212yes—
24C71⋊#95C2212yes—
25C71⋊#95C2212yes—
26C71⋊#95C2212yes—
27C22×D4×C71C2211yescharacteristic
28C23×C4×C71C2211yescharacteristic
29#123×C71—24no—
30C2×C4⋊C4×C71C2212yes—
31C2×C22⋊C4×C71C2212yes—
32C2×C22⋊C4×C71C2211yescharacteristic
33C22×Dic71—22no—
34C22×Dic71—41no—
35C22×Dic71—41no—
36C22×Dic71C2312yes—
37C22×Dic71C2312yes—
38C22×Dic71C2312yes—
39C22×Dic71C2312yes—
40C4⋊Dic71—41no—
41Dic71⋊C4—24no—
42Dic71⋊C4—24no—
43Dic71⋊C4—42no—
44Dic71⋊C4—42no—
45C22⋊Dic71—22no—
46C22⋊Dic71—24no—
47C22⋊Dic71—24no—
48C22⋊Dic71—24no—
49C4×Dic71—41no—
50C24×C71C2311yescharacteristic
51C24×C71C2311yescharacteristic
52C2×D4×C71—41no—
53C2×D4×C71—41no—
54C2×D4×C71D414yes—
55C22×C4×C71—22no—
56C22×C4×C71—41no—
57C22×C4×C71—41no—
58C22×C4×C71C2312yes—
59C22×C4×C71C2312yes—
60C22×C4×C71C2311yescharacteristic
61C4⋊C4×C71—24no—
62C22⋊C4×C71—22no—
63C22⋊C4×C71—24no—
64C23×C71—22no—
65C23×C71—22no—
66C23×C71—21no—
67C23×C71—21no—
68C23×C71—21no—
69C23×C71—21no—
70C23×C71—22no—
71C23×C71—22no—
72C23×C71C2×D412yes—
73C23×C71C2×D412yes—
74C23×C71C2411yescharacteristic
75D4×C71—44no—
76C2×C4×C71—21no—
77C2×C4×C71—21no—
78C2×C4×C71—22no—
79C2×C4×C71—22no—
80C2×C4×C71—22no—
81C2×C4×C71—22no—
82C2×C4×C71—22no—
83C2×C4×C71—22no—
84C2×C4×C71—44no—
85C2×C4×C71C2×D412yes—
86C2×Dic71—22no—
87C2×Dic71—22no—
88C2×Dic71—22no—
89C2×Dic71—22no—
90C2×Dic71—22no—
91C2×Dic71—22no—
92C2×Dic71—22no—
93C2×Dic71—22no—
94C2×Dic71—22no—
95C2×Dic71—22no—
96C2×Dic71—22no—
97C2×Dic71—44no—
98C2×Dic71#4114yes—
99C22×C71—22no—
100C22×C71—22no—
101C22×C71—24no—
102C22×C71—24no—
103C22×C71—42no—
104C22×C71—42no—
105C22×C71—41no—
106C22×C71—41no—
107C22×C71—41no—
108C22×C71—41no—
109C22×C71C22×D411yescharacteristic
110C22×C71C2×#4112yes—
111C22×C71H(5,𝔽2)11yescharacteristic
112C22×C71H(5,𝔽2)11yescharacteristic
113C22×C712−1+412yes—
114C4×C71—22no—
115C4×C71—42no—
116C4×C71—42no—
117Dic71—24no—
118Dic71—42no—
119Dic71—42no—
120Dic71—42no—
121C2×C71—42no—
122C2×C71—42no—
123C2×C71#53411yescharacteristic
124C2×C71#53912yes—
125C2×C71#54712yes—
126C2×C71#55911yescharacteristic
127C2×C71#56311yescharacteristic
128#2724—711nomaximal, Sylow
129C71#272411yescharacteristic, complemented, Sylow
130C2×#123—711no—
131C2×#123D7111yescharacteristic
132#398—712no—
133#397—712no—
134#397—712no—
135#390—711no—
136#389—712no—
137#385—712no—
138#385—712no—
139C22×D4C2×D7111yescharacteristic
140C23×C4—711no—
141C23×C4C2×D7111yescharacteristic
142#123—24no—
143#123—1424no—
144C2×C4⋊C4—712no—
145C2×C4⋊C4—712no—
146C2×C4⋊C4—711no—
147C2×C4⋊C4—712no—
148C2×C4⋊C4—712no—
149C2×C4⋊C4C2×D7112yes—
150C2×C22⋊C4—712no—
151C2×C22⋊C4—711no—
152C2×C22⋊C4—712no—
153C2×C22⋊C4—712no—
154C2×C22⋊C4C2×D7112yes—
155C2×C22⋊C4C2×D7111yescharacteristic
156C2×C42—711no—
157#95—712no—
158#95—712no—
159#95—712no—
160#95—712no—
161#95—712no—
162C24C22×D7111yescharacteristic
163C24C22×D7111yescharacteristic
164C2×D4—41no—
165C2×D4—41no—
166C2×D4C22⋊D7114yes—
167C22×C4—22no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—2841no—
171C22×C4—2841no—
172C22×C4—712no—
173C22×C4—712no—
174C22×C4—712no—
175C22×C4—712no—
176C22×C4—1422no—
177C22×C4C22×D7112yes—
178C22×C4C22×D7112yes—
179C22×C4C22×D7111yescharacteristic
180C4⋊C4—24no—
181C4⋊C4—2842no—
182C4⋊C4—2842no—
183C4⋊C4—2841no—
184C4⋊C4—1424no—
185C4⋊C4—1424no—
186C22⋊C4—22no—
187C22⋊C4—24no—
188C22⋊C4—1424no—
189C22⋊C4—1424no—
190C22⋊C4—1422no—
191C22⋊C4—1424no—
192C42—2841no—
193C23—22no—
194C23—22no—
195C23—21no—
196C23—21no—
197C23—21no—
198C23—21no—
199C23—22no—
200C23—22no—
201C23C2×C22⋊D7112yes—
202C23C2×C22⋊D7112yes—
203C23C23×D7111yescharacteristic
204D4—44no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—44no—
214C2×C4—2844no—
215C2×C4—714no—
216C2×C4—1422no—
217C2×C4—1422no—
218C2×C4—1422no—
219C2×C4—1422no—
220C2×C4—1422no—
221C2×C4—1422no—
222C2×C4—1422no—
223C2×C4—1422no—
224C2×C4—1422no—
225C2×C4—1422no—
226C2×C4—1422no—
227C2×C4C2×C22⋊D7112yes—
228C22—24no—
229C22—24no—
230C22—22no—
231C22—22no—
232C22—42no—
233C22—42no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22C22×C22⋊D7111yescharacteristic
239C22#41×D7112yes—
240C22#1455617311yescharacteristic
241C22#1455617311yescharacteristic
242C22#1455617512yes—
243C4—22no—
244C4—42no—
245C4—42no—
246C4—2842no—
247C4—2842no—
248C4—2842no—
249C4—1424no—
250C2—42no—
251C2—42no—
252C2#1798655811yescharacteristic
253C2#1798659212yes—
254C2#1798664812yes—
255C2#1798673311yescharacteristic
256C2#1798675211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
FittingC2×#123×C71C2
hypercenterC2×#123D71
hypocenterC71#2724
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. #17985932C2semidirect
3. #17985927C2semidirect
4. #17985927C2semidirect
6. #17985894C2semidirect
7. #17985872C2semidirect
8. #17985871C2semidirect
129. C71#2724semidirect