Finite Group Databasebeta

← #22594166

Subgroups — #22594166

Order 9088.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14556127C211yesmaximal, characteristic, complemented
2C2×#14556084C211yesmaximal, characteristic
3#17985939C211yesmaximal, characteristic, complemented
4#17985937C211yesmaximal, characteristic, complemented
5#17985935C211yesmaximal, characteristic
6#17985919C212yesmaximal, complemented
7#17985911C212yesmaximal
8#17985894C212yesmaximal, complemented
9#17985863C211yesmaximal, characteristic, complemented
10#17985857C212yesmaximal
11#399×C71C211yesmaximal, characteristic
12C22×Dic142C2212yes—
13C23×Dic71C2211yescharacteristic
14#14556127—24no—
15#14556084—24no—
16C2×C4⋊Dic71C2211yescharacteristic
17C2×Dic71⋊C4C2212yes—
18C2×Dic71⋊C4C2212yes—
19C2×Dic71⋊C4C2211yescharacteristic
20C2×Dic71⋊C4C2211yescharacteristic
21C2×Dic71⋊C4C2212yes—
22C2×C22⋊Dic71C2211yescharacteristic
23C2×C22⋊Dic71C2212yes—
24C2×C4×Dic71C2211yescharacteristic
25C2×C4×Dic71C2211yescharacteristic
26C71⋊#95C2212yes—
27C71⋊#95C2212yes—
28C71⋊#95C2212yes—
29C71⋊#95C2211yescharacteristic
30C71⋊#95C2212yes—
31C71⋊#95C2212yes—
32C2×C4⋊C4×C71C2211yescharacteristic
33C2×C4⋊C4×C71C2212yes—
34C2×C22⋊C4×C71C2211yescharacteristic
35C2×C22⋊C4×C71C2212yes—
36#95×C71C2211yescharacteristic
37C2×Dic142—24no—
38C2×Dic142—42no—
39C2×Dic142—42no—
40C22×Dic71—22no—
41C22×Dic71—22no—
42C22×Dic71Q814yescomplemented
43C22×Dic71C2312yes—
44C22×Dic71C2311yescharacteristic
45C22×Dic71C2312yes—
46C22×Dic71C2311yescharacteristic
47C22×Dic71C2311yescharacteristic
48C22×Dic71C2311yescharacteristic
49C4⋊Dic71—22no—
50Dic71⋊C4—22no—
51Dic71⋊C4—22no—
52Dic71⋊C4—24no—
53Dic71⋊C4—24no—
54Dic71⋊C4—42no—
55C22⋊Dic71—22no—
56C22⋊Dic71—42no—
57C4×Dic71—22no—
58C4×Dic71D414yes—
59C24×C71C2311yescharacteristic
60C22×C4×C71C2312yes—
61C22×C4×C71C2312yes—
62C22×C4×C71C2311yescharacteristic
63C22×C4×C71C2311yescharacteristic
64C4⋊C4×C71—22no—
65C4⋊C4×C71—42no—
66C22⋊C4×C71—22no—
67C22⋊C4×C71—42no—
68C23×C71—21no—
69C23×C71—21no—
70C23×C71—22no—
71C23×C71—22no—
72C23×C71C2×Q812yes—
73C23×C71C2411yescharacteristic
74C2×C4×C71—22no—
75C2×C4×C71—21no—
76C2×C4×C71—22no—
77C2×C4×C71—22no—
78C2×C4×C71—22no—
79C2×C4×C71—22no—
80C2×C4×C71—22no—
81C2×C4×C71—22no—
82C2×C4×C71—22no—
83C2×C4×C71C2×D412yes—
84C2×Dic71—21no—
85C2×Dic71—21no—
86C2×Dic71—22no—
87C2×Dic71—28no—
88C2×Dic71—21no—
89C2×Dic71—22no—
90C2×Dic71—22no—
91C2×Dic71—22no—
92C2×Dic71—22no—
93C2×Dic71—22no—
94C2×Dic71—22no—
95C2×Dic71—22no—
96C2×Dic71C2×D412yes—
97C2×Dic71C2×D412yes—
98C2×Dic71C2×Q812yes—
99C2×Dic71C2×Q812yes—
100C2×Dic71#4112yes—
101Dic142—48no—
102C22×C71—22no—
103C22×C71—24no—
104C22×C71—41no—
105C22×C71—41no—
106C22×C71—42no—
107C22×C71C22×D411yescharacteristic
108C22×C71C22×Q811yescharacteristic
109C22×C71C2×#4111yescharacteristic
110C22×C71H(5,𝔽2)12yes—
111C22×C712−1+412yes—
112C4×C71—22no—
113C4×C71—42no—
114C4×C71—41no—
115C4×C71—42no—
116Dic71—22no—
117Dic71—22no—
118Dic71—42no—
119Dic71—41no—
120Dic71—42no—
121Dic71C22⋊Q814yes—
122C2×C71—42no—
123C2×C71C2×C22⋊Q811yescharacteristic
124C2×C71#53511yescharacteristic
125C2×C71#53611yescharacteristic
126C2×C71#54212yes—
127C2×C71#54412yes—
128#2628—711nomaximal, Sylow
129C71#262811yescharacteristic, complemented, Sylow
130C2×C4⋊Q8—711no—
131C2×#117—711no—
132#400—711no—
133#400—711no—
134#399—711no—
135#399D7111yescharacteristic
136#395—712no—
137#393—712no—
138#389—712no—
139#382—711no—
140#380—712no—
141C22×Q8—712no—
142C23×C4—711no—
143C4⋊Q8—1424no—
144#117—1424no—
145C2×C4⋊C4—712no—
146C2×C4⋊C4—711no—
147C2×C4⋊C4—711no—
148C2×C4⋊C4—712no—
149C2×C4⋊C4—711no—
150C2×C4⋊C4—712no—
151C2×C4⋊C4C2×D7111yescharacteristic
152C2×C4⋊C4C2×D7112yes—
153C2×C22⋊C4—712no—
154C2×C22⋊C4—711no—
155C2×C22⋊C4C2×D7111yescharacteristic
156C2×C22⋊C4C2×D7112yes—
157C2×C42—711no—
158C2×C42—711no—
159#95—712no—
160#95—712no—
161#95—712no—
162#95—711no—
163#95—712no—
164#95—712no—
165#95C2×D7111yescharacteristic
166C24C22×D7111yescharacteristic
167C2×Q8—2842no—
168C2×Q8—2842no—
169C2×Q8—1424no—
170C22×C4—711no—
171C22×C4—714no—
172C22×C4—711no—
173C22×C4—711no—
174C22×C4—711no—
175C22×C4—712no—
176C22×C4—712no—
177C22×C4—1422no—
178C22×C4—1422no—
179C22×C4C22×D7112yes—
180C22×C4C22×D7112yes—
181C22×C4C22×D7111yescharacteristic
182C22×C4C22×D7111yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—42no—
185C4⋊C4—2842no—
186C4⋊C4—1424no—
187C4⋊C4—1422no—
188C4⋊C4—1424no—
189C4⋊C4—1422no—
190C4⋊C4—1422no—
191C22⋊C4—22no—
192C22⋊C4—42no—
193C22⋊C4—2842no—
194C22⋊C4—1422no—
195C42—714no—
196C42—1422no—
197C23—21no—
198C23—21no—
199C23—22no—
200C23—22no—
201C23Q8×D7112yes—
202C23C23×D7111yescharacteristic
203Q8—2848no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—712no—
214C2×C4—712no—
215C2×C4—712no—
216C2×C4—712no—
217C2×C4—712no—
218C2×C4—1421no—
219C2×C4—1422no—
220C2×C4—1422no—
221C2×C4—1422no—
222C2×C4—1422no—
223C2×C4—1422no—
224C2×C4—1422no—
225C2×C4—1422no—
226C2×C4—1428no—
227C2×C4—1421no—
228C2×C4—1421no—
229C2×C4—1422no—
230C2×C4D4×D7112yes—
231C22—24no—
232C22—22no—
233C22—41no—
234C22—41no—
235C22—42no—
236C22C2×D4×D7111yescharacteristic
237C22C2×Q8×D7111yescharacteristic
238C22#41×D7111yescharacteristic
239C22#1455617312yes—
240C22#1455617512yes—
241C4—22no—
242C4—42no—
243C4—41no—
244C4—42no—
245C4—2842no—
246C4—2841no—
247C4—2842no—
248C4—714no—
249C4—1422no—
250C4—1422no—
251C2—42no—
252C2C22⋊Q8×D7111yescharacteristic
253C2#1798656211yescharacteristic
254C2#1798657111yescharacteristic
255C2#1798661712yes—
256C2#1798662812yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#399×C71C2
hypercenter#399D71
hypocenterC71#2628
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14556127C2semidirect
3. #17985939C2semidirect
4. #17985937C2semidirect
6. #17985919C2semidirect
8. #17985894C2semidirect
9. #17985863C2semidirect
42. C22×Dic71Q8semidirect
129. C71#2628semidirect