Finite Group Databasebeta

← #22594257

Subgroups — #22594257

Order 9088.

520 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556107C211yesmaximal, characteristic, complemented
2#17985929C211yesmaximal, characteristic, complemented
3#17985927C212yesmaximal, complemented
4#17985924C211yesmaximal, characteristic, complemented
5#17985919C211yesmaximal, characteristic, complemented
6#17985913C212yesmaximal
7#17985911C211yesmaximal, characteristic, complemented
8#17985883C212yesmaximal, complemented
9#17985872C212yesmaximal, complemented
10#17985862C211yesmaximal, characteristic, complemented
11C2×C4×D4×C71C211yesmaximal, characteristic
12C22×Dic142C2211yescharacteristic
13#14556107—24no—
14C2×C4⋊Dic71C2211yescharacteristic
15C2×Dic71⋊C4C2212yes—
16C2×Dic71⋊C4C2212yes—
17C2×Dic71⋊C4C2212yes—
18C2×C22⋊Dic71C2212yes—
19C2×C22⋊Dic71C2212yes—
20C2×C22⋊Dic71C2212yes—
21C2×C22⋊Dic71C2212yes—
22C71⋊#95C2212yes—
23C71⋊#95C2211yescharacteristic
24C71⋊#95C2211yescharacteristic
25C71⋊#95C2212yes—
26C71⋊#95C2212yes—
27C71⋊#95C2212yes—
28C71⋊#95C2212yes—
29C22×D4×C71C2211yescharacteristic
30C23×C4×C71C2211yescharacteristic
31C23×C4×C71C2211yescharacteristic
32C4×D4×C71—24no—
33C2×C4⋊C4×C71C2211yescharacteristic
34C2×C22⋊C4×C71C2211yescharacteristic
35C2×C22⋊C4×C71C2211yescharacteristic
36C2×C42×C71C2211yescharacteristic
37C2×Dic142—22no—
38C2×Dic142—42no—
39C22×Dic71C2312yes—
40C22×Dic71C2312yes—
41C22×Dic71C2312yes—
42C22×Dic71C2312yes—
43C4⋊Dic71—22no—
44Dic71⋊C4—24no—
45Dic71⋊C4—24no—
46Dic71⋊C4—42no—
47C22⋊Dic71—24no—
48C22⋊Dic71—24no—
49C22⋊Dic71—42no—
50C22⋊Dic71—42no—
51C24×C71C2311yescharacteristic
52C24×C71C2311yescharacteristic
53C2×D4×C71—22no—
54C2×D4×C71—22no—
55C2×D4×C71—22no—
56C22×C4×C71—22no—
57C22×C4×C71—42no—
58C22×C4×C71—42no—
59C22×C4×C71D414yes—
60C22×C4×C71C2311yescharacteristic
61C22×C4×C71C2311yescharacteristic
62C22×C4×C71C2311yescharacteristic
63C22×C4×C71C2311yescharacteristic
64C22×C4×C71C2311yescharacteristic
65C4⋊C4×C71—22no—
66C22⋊C4×C71—22no—
67C22⋊C4×C71—22no—
68C42×C71—22no—
69C23×C71—21no—
70C23×C71—21no—
71C23×C71—21no—
72C23×C71—21no—
73C23×C71—22no—
74C23×C71—22no—
75C23×C71—22no—
76C23×C71—22no—
77C23×C71C2×D412yes—
78C23×C71#4112yes—
79C23×C71C2411yescharacteristic
80D4×C71—28no—
81C2×C4×C71—21no—
82C2×C4×C71—21no—
83C2×C4×C71—22no—
84C2×C4×C71—22no—
85C2×C4×C71—21no—
86C2×C4×C71—21no—
87C2×C4×C71—22no—
88C2×C4×C71—22no—
89C2×C4×C71—44no—
90C2×C4×C71—44no—
91C2×C4×C71C2×D412yes—
92C2×C4×C71C2×D412yes—
93C2×C4×C71#4112yes—
94C2×Dic71—22no—
95C2×Dic71—22no—
96C2×Dic71—22no—
97C2×Dic71—22no—
98C2×Dic71—22no—
99C2×Dic71—22no—
100C2×Dic71—22no—
101C2×Dic71—22no—
102C2×Dic71—22no—
103C2×Dic71—22no—
104C2×Dic71—22no—
105C2×Dic71—22no—
106Dic142—44no—
107C22×C71—22no—
108C22×C71—22no—
109C22×C71—22no—
110C22×C71—22no—
111C22×C71—24no—
112C22×C71—41no—
113C22×C71—41no—
114C22×C71—42no—
115C22×C71—42no—
116C22×C71—42no—
117C22×C71C22×D411yescharacteristic
118C22×C71C2×#4111yescharacteristic
119C22×C71C2×#4111yescharacteristic
120C22×C71H(5,𝔽2)12yes—
121C22×C712−1+412yes—
122C4×C71—22no—
123C4×C71—22no—
124C4×C71—22no—
125C4×C71—41no—
126C4×C71—41no—
127Dic71—42no—
128Dic71—42no—
129Dic71—42no—
130Dic71—42no—
131C2×C71—42no—
132C2×C71—42no—
133C2×C71#52511yescharacteristic
134C2×C71#53411yescharacteristic
135C2×C71#53611yescharacteristic
136C2×C71#53912yes—
137C2×C71#54212yes—
138#2638—711nomaximal, Sylow
139C71#263811yescharacteristic, complemented, Sylow
140C2×C22⋊Q8—711no—
141C2×C4×D4D7111yescharacteristic
142#398—711no—
143#397—711no—
144#397—712no—
145#395—711no—
146#394—712no—
147#393—711no—
148#387—712no—
149#385—712no—
150#381—711no—
151C22×Q8—711no—
152C22×D4C2×D7111yescharacteristic
153C23×C4C2×D7111yescharacteristic
154C23×C4C2×D7111yescharacteristic
155C22⋊Q8—1424no—
156C4×D4—24no—
157C2×C4⋊C4—712no—
158C2×C4⋊C4—712no—
159C2×C4⋊C4—711no—
160C2×C4⋊C4—712no—
161C2×C4⋊C4C2×D7111yescharacteristic
162C2×C22⋊C4—712no—
163C2×C22⋊C4—712no—
164C2×C22⋊C4—712no—
165C2×C22⋊C4—712no—
166C2×C22⋊C4C2×D7111yescharacteristic
167C2×C22⋊C4C2×D7111yescharacteristic
168C2×C42C2×D7111yescharacteristic
169#95—712no—
170#95—711no—
171#95—711no—
172#95—712no—
173#95—712no—
174#95—712no—
175#95—712no—
176C24C22×D7111yescharacteristic
177C24C22×D7111yescharacteristic
178C2×Q8—2842no—
179C2×Q8—1422no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—22no—
183C22×C4—22no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—712no—
187C22×C4—712no—
188C22×C4—712no—
189C22×C4—712no—
190C22×C4C22⋊D7114yes—
191C22×C4C22×D7111yescharacteristic
192C22×C4C22×D7111yescharacteristic
193C22×C4C22×D7111yescharacteristic
194C22×C4C22×D7111yescharacteristic
195C22×C4C22×D7111yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—2842no—
198C4⋊C4—1424no—
199C4⋊C4—1422no—
200C4⋊C4—1424no—
201C22⋊C4—22no—
202C22⋊C4—22no—
203C22⋊C4—2842no—
204C22⋊C4—2842no—
205C22⋊C4—1424no—
206C22⋊C4—1424no—
207C42—22no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23C2×C22⋊D7112yes—
217C23#1176586512yes—
218C23C23×D7111yescharacteristic
219Q8—2844no—
220D4—28no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—1422no—
232C2×C4—1422no—
233C2×C4—1422no—
234C2×C4—1422no—
235C2×C4—1422no—
236C2×C4—1422no—
237C2×C4—1422no—
238C2×C4—1422no—
239C2×C4—1422no—
240C2×C4—1422no—
241C2×C4—1422no—
242C2×C4—1422no—
243C2×C4C2×C22⋊D7112yes—
244C2×C4C2×C22⋊D7112yes—
245C2×C4#1176586512yes—
246C22—22no—
247C22—24no—
248C22—22no—
249C22—22no—
250C22—22no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—41no—
256C22C22×C22⋊D7111yescharacteristic
257C22C2×#1176586511yescharacteristic
258C22C2×#1176586511yescharacteristic
259C22#1455617312yes—
260C22#1455617512yes—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—2842no—
267C4—2842no—
268C4—2842no—
269C4—2842no—
270C2—42no—
271C2—42no—
272C2#1798651011yescharacteristic
273C2#1798655811yescharacteristic
274C2#1798657011yescharacteristic
275C2#1798659112yes—
276C2#1798661412yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
FittingC2×C4×D4×C71C2
hypercenterC2×C4×D4D71
hypocenterC71#2638
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14556107C2semidirect
2. #17985929C2semidirect
3. #17985927C2semidirect
4. #17985924C2semidirect
5. #17985919C2semidirect
7. #17985911C2semidirect
8. #17985883C2semidirect
9. #17985872C2semidirect
10. #17985862C2semidirect
139. C71#2638semidirect