Finite Group Databasebeta

← #22588326

Subgroups — #22588326

Order 9088.

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

normal subgroups only

This group has 380 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
1C2×D4×Dic71C211yesmaximal, characteristic
2C2×#14556043C211yesmaximal, characteristic
3#17985857C212yesmaximal, complemented
4#17985765C212yesmaximal, complemented
5C2×#99×C71C211yesmaximal, characteristic
6C23×Dic71C411yescharacteristic, complemented
7C23×Dic71C2211yescharacteristic
8D4×Dic71—22no—
9D4×Dic71—22no—
10C2×C4⋊Dic71C411yescharacteristic, complemented
11C2×Dic71⋊C4—22no—
12C2×C22⋊Dic71C411yescharacteristic, complemented
13C2×C22⋊Dic71C2212yes—
14C2×C22⋊Dic71C2211yescharacteristic
15C2×C4×Dic71C411yescharacteristic, complemented
16#14556043—22no—
17C71⋊#95—22no—
18C22×D4×C71C2211yescharacteristic
19C2×C22⋊C4×C71C2212yes—
20#99×C71—22no—
21C22×Dic71—21no—
22C22×Dic71—21no—
23C22×Dic71—22no—
24C22×Dic71—42no—
25C22×Dic71—42no—
26C22×Dic71C2×C411yescharacteristic
27C22×Dic71C2×C411yescharacteristic
28C22×Dic71C2×C411yescharacteristic
29C22×Dic71C2×C411yescharacteristic
30C22×Dic71D412yes—
31C22×Dic71D412yes—
32C4⋊Dic71—22no—
33Dic71⋊C4—44no—
34C22⋊Dic71—22no—
35C22⋊Dic71—22no—
36C22⋊Dic71—22no—
37C22⋊Dic71—22no—
38C4×Dic71—21no—
39C4×Dic71—21no—
40C24×C71C2×C411yescharacteristic
41C24×C71C2311yescharacteristic
42C2×D4×C71—22no—
43C2×D4×C71—22no—
44C2×D4×C71D412yes—
45C2×D4×C71Q812yes—
46C22×C4×C71—22no—
47C22×C4×C71C2×C411yescharacteristic
48C22⋊C4×C71—22no—
49C22⋊C4×C71—22no—
50C23×C71—21no—
51C23×C71—21no—
52C23×C71—41no—
53C23×C71—41no—
54C23×C71—41no—
55C23×C71—41no—
56C23×C71C4⋊C412yescomplemented
57C23×C71C22×C411yescharacteristic
58C23×C71C2×D412yes—
59C23×C71C2×D411yescharacteristic
60C23×C71C2×Q811yescharacteristic
61C23×C71#4112yes—
62D4×C71—24no—
63D4×C71—24no—
64C2×C4×C71—21no—
65C2×C4×C71—21no—
66C2×C4×C71—42no—
67C2×C4×C71—42no—
68C2×C4×C71—42no—
69C2×C4×C71C4⋊C412yescomplemented
70C2×Dic71—24no—
71C2×Dic71—22no—
72C2×Dic71—21no—
73C2×Dic71—21no—
74C2×Dic71—41no—
75C2×Dic71—42no—
76C2×Dic71—42no—
77C2×Dic71—42no—
78C2×Dic71—41no—
79C2×Dic71—41no—
80C2×Dic71—42no—
81C2×Dic71—42no—
82C2×Dic71—42no—
83C2×Dic71C22⋊C411yescharacteristic
84C2×Dic71C22⋊C412yes—
85C2×Dic71C22⋊C411yescharacteristic
86C22×C71—22no—
87C22×C71—21no—
88C22×C71—22no—
89C22×C71—21no—
90C22×C71—22no—
91C22×C71—41no—
92C22×C71—41no—
93C22×C71—42no—
94C22×C71—42no—
95C22×C71—42no—
96C22×C71—41no—
97C22×C71—41no—
98C22×C71C2×C22⋊C411yescharacteristic
99C22×C71C2×C4⋊C411yescharacteristic
100C22×C71#11711yescharacteristic
101C22×C71#12112yes—
102C22×C71C22⋊Q812yes—
103C4×C71—22no—
104C4×C71—82no—
105Dic71—21no—
106Dic71—22no—
107Dic71—41no—
108Dic71—41no—
109Dic71—82no—
110Dic71#9912yescomplemented
111C2×C71—22no—
112C2×C71—21no—
113C2×C71—21no—
114C2×C71—22no—
115C2×C71—42no—
116C2×C71#38011yescharacteristic
117C2×C71C2×#9911yescharacteristic
118C2×C71#41011yescharacteristic
119#1799—711nomaximal, Sylow
120C71#179911yescharacteristic, complemented, Sylow
121C2×C4×D4—711no—
122C2×#99—711no—
123C2×#99D7111yescharacteristic
124#380—712no—
125#342—712no—
126C22×D4C2×D7111yescharacteristic
127C23×C4—711no—
128C23×C4—711no—
129C4×D4—1422no—
130C4×D4—1422no—
131C2×C4⋊C4—711no—
132C2×C4⋊C4—1422no—
133C2×C22⋊C4—711no—
134C2×C22⋊C4—711no—
135C2×C22⋊C4—712no—
136C2×C22⋊C4C2×D7112yes—
137C2×C42—711no—
138#99—22no—
139#99—1422no—
140#95—1422no—
141C24C4×D7111yescharacteristic
142C24C22×D7111yescharacteristic
143C2×D4—22no—
144C2×D4—22no—
145C2×D4Dic14212yes—
146C2×D4C22⋊D7112yes—
147C22×C4—22no—
148C22×C4—2842no—
149C22×C4—2842no—
150C22×C4—711no—
151C22×C4—712no—
152C22×C4—711no—
153C22×C4—711no—
154C22×C4—711no—
155C22×C4—712no—
156C22×C4—1422no—
157C22×C4—1421no—
158C22×C4—1421no—
159C22×C4C4×D7111yescharacteristic
160C4⋊C4—2844no—
161C4⋊C4—1422no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—1422no—
165C22⋊C4—1422no—
166C22⋊C4—1422no—
167C22⋊C4—1422no—
168C42—1421no—
169C42—1421no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23Dic71⋊C412yescomplemented
177C23C2×C4×D7111yescharacteristic
178C23D4×D7112yes—
179C23C2×C22⋊D7111yescharacteristic
180C23C2×Dic14211yescharacteristic
181C23#1176586412yes—
182D4—24no—
183D4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—2842no—
190C2×C4—2842no—
191C2×C4—2841no—
192C2×C4—2841no—
193C2×C4—2842no—
194C2×C4—2842no—
195C2×C4—2842no—
196C2×C4—2842no—
197C2×C4—2841no—
198C2×C4—711no—
199C2×C4—711no—
200C2×C4—712no—
201C2×C4—1421no—
202C2×C4—1421no—
203C2×C4—1424no—
204C2×C4—1422no—
205C2×C4Dic71⋊C412yescomplemented
206C22—22no—
207C22—21no—
208C22—22no—
209C22—21no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22C22⋊C4×D7111yescharacteristic
219C22C2×Dic71⋊C411yescharacteristic
220C22#1455608411yescharacteristic
221C22#1455610012yes—
222C22#1455610512yes—
223C4—22no—
224C4—82no—
225C4—2841no—
226C4—2841no—
227C4—5682no—
228C4—712no—
229C4—1421no—
230C4—1422no—
231C2—22no—
232C2—21no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2#1798585711yescharacteristic
237C2#99×D7111yescharacteristic
238C2#1798597111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC23×C71C22×C4
FrattiniC24C22×D71
FittingC2×#99×C71C2
socleC22×C71C2×C22⋊C4
hypercenterC2×#99D71
hypocenterC71#1799
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #17985857C2semidirect
4. #17985765C2semidirect
6. C23×Dic71C4semidirect
10. C2×C4⋊Dic71C4semidirect
12. C2×C22⋊Dic71C4semidirect
15. C2×C4×Dic71C4semidirect
56. C23×C71C4⋊C4semidirect
69. C2×C4×C71C4⋊C4semidirect
110. Dic71#99semidirect
120. C71#1799semidirect
176. C23Dic71⋊C4semidirect
205. C2×C4Dic71⋊C4semidirect