Finite Group Databasebeta

← #22594271

Subgroups — #22594271

Order 9088.

576 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556106C211yesmaximal, characteristic, complemented
2C2×#14556099C211yesmaximal, characteristic
3#17985939C211yesmaximal, characteristic, complemented
4#17985938C211yesmaximal, characteristic, complemented
5#17985927C212yesmaximal, complemented
6#17985913C211yesmaximal, characteristic, complemented
7#17985911C212yesmaximal, complemented
8#17985875C212yesmaximal, complemented
9#17985875C212yesmaximal, complemented
10#95×D71C211yesmaximal, characteristic, complemented
11#394×C71C211yesmaximal, characteristic, complemented
12C22×Dic142C2211yescharacteristic
13C22×C22⋊D71C2212yes—
14C22×C4×D71C2212yes—
15C22×C4×D71C2211yescharacteristic
16#14556106—24no—
17#14556099—24no—
18C2×C4⋊Dic71C2211yescharacteristic
19C2×Dic71⋊C4C2211yescharacteristic
20C2×Dic71⋊C4C2211yescharacteristic
21C2×C22⋊Dic71C2212yes—
22C2×C22⋊Dic71C2212yes—
23C2×C22⋊Dic71C2212yes—
24C2×(C2×D71)⋊C4C2211yescharacteristic
25C2×(C2×D71)⋊C4C2211yescharacteristic
26C71⋊#95C2212yes—
27C71⋊#95C2211yescharacteristic
28C71⋊#95C2212yes—
29C71⋊#95C2212yes—
30C71⋊#95C2212yes—
31C71⋊#95C2212yes—
32C22×D4×C71C2211yescharacteristic
33C2×C4⋊C4×C71C2211yescharacteristic
34C2×C22⋊C4×C71C2212yes—
35C2×C22⋊C4×C71C2212yes—
36#95×C71C2211yescharacteristic
37C23×D71C2311yescharacteristic
38C2×Dic142—22no—
39C2×Dic142—42no—
40C2×C22⋊D71—24no—
41C2×C22⋊D71—24no—
42C2×C22⋊D71—24no—
43C22×Dic71C2312yes—
44C22×Dic71C2312yes—
45C22×Dic71C2311yescharacteristic
46C22×Dic71C2311yescharacteristic
47C22×Dic71C2311yescharacteristic
48C2×C4×D71—24no—
49C2×C4×D71—42no—
50C2×C4×D71—42no—
51C2×C4×D71—42no—
52C2×C4×D71D414yes—
53C4⋊Dic71—22no—
54Dic71⋊C4—22no—
55Dic71⋊C4—22no—
56C22⋊Dic71—24no—
57C22⋊Dic71—42no—
58C22⋊Dic71—42no—
59(C2×D71)⋊C4—22no—
60(C2×D71)⋊C4—22no—
61C24×C71C2312yes—
62C2×D4×C71—22no—
63C2×D4×C71—42no—
64C22×C4×C71C2312yes—
65C22×C4×C71C2311yescharacteristic
66C22×C4×C71C2311yescharacteristic
67C22×C4×C71C2311yescharacteristic
68C4⋊C4×C71—22no—
69C22⋊C4×C71—42no—
70C22⋊C4×C71—42no—
71C23×C71—22no—
72C23×C71—22no—
73C23×C71—22no—
74C23×C71—22no—
75C23×C71—22no—
76C23×C71—22no—
77C23×C71—22no—
78C23×C71C2411yescharacteristic
79C22×D71—22no—
80C22×D71—21no—
81C22×D71—21no—
82C22×D71C2×D412yes—
83C22×D71#4114yes—
84D4×C71—44no—
85C2×C4×C71—22no—
86C2×C4×C71—21no—
87C2×C4×C71—21no—
88C2×C4×C71—22no—
89C2×C4×C71—21no—
90C2×C4×C71—22no—
91C2×C4×C71—22no—
92C2×C4×C71—22no—
93C2×C4×C71—21no—
94C2×C4×C71C2×D412yes—
95C22⋊D71—48no—
96C2×Dic71—22no—
97C2×Dic71—21no—
98C2×Dic71—21no—
99C2×Dic71—22no—
100C2×Dic71—22no—
101C2×Dic71—22no—
102C2×Dic71—22no—
103C2×Dic71—21no—
104C2×Dic71—22no—
105C2×Dic71—22no—
106C2×Dic71—22no—
107C2×Dic71—21no—
108C2×Dic71C2×D412yes—
109C4×D71—44no—
110C4×D71—48no—
111Dic142—44no—
112C22×C71—42no—
113C22×C71—42no—
114C22×C71—42no—
115C22×C71—42no—
116C22×C71—42no—
117C22×C71—42no—
118C22×C71—42no—
119C22×C71C22×D411yescharacteristic
120C22×C71C2×#4112yes—
121C22×C71H(5,𝔽2)12yes—
122C22×C71H(5,𝔽2)11yescharacteristic
123C22×C712−1+411yescharacteristic
124C2×D71—22no—
125C2×D71—22no—
126C2×D71—24no—
127C2×D71—24no—
128C2×D71#12414yes—
129C4×C71—22no—
130C4×C71—41no—
131C4×C71—41no—
132C4×C71—42no—
133Dic71—22no—
134Dic71—42no—
135Dic71—41no—
136Dic71—41no—
137Dic71—42no—
138C2×C71—82no—
139C2×C71C2×#12411yescharacteristic
140C2×C71#53411yescharacteristic
141C2×C71#53711yescharacteristic
142C2×C71#53812yes—
143C2×C71#53912yes—
144D71—24no—
145#2639—711nomaximal, Sylow
146C71#263911yescharacteristic, complemented, Sylow
147C2×C22⋊Q8—711no—
148C2×#121—711no—
149#400—711no—
150#400—711no—
151#397—712no—
152#394—711no—
153#394D7111yescharacteristic, complemented
154#393—712no—
155#386—712no—
156#386—712no—
157C2×#95—711no—
158C22×Q8—711no—
159C22×D4—712no—
160C22×D4C2×D7111yescharacteristic
161C23×C4—711no—
162C23×C4—712no—
163C22⋊Q8—1424no—
164#121—1424no—
165C2×C4⋊C4—711no—
166C2×C4⋊C4—711no—
167C2×C4⋊C4—711no—
168C2×C4⋊C4C2×D7111yescharacteristic
169C2×C22⋊C4—712no—
170C2×C22⋊C4—712no—
171C2×C22⋊C4—712no—
172C2×C22⋊C4—711no—
173C2×C22⋊C4—711no—
174C2×C22⋊C4C2×D7112yes—
175C2×C22⋊C4C2×D7112yes—
176#95—712no—
177#95—711no—
178#95—712no—
179#95—712no—
180#95—712no—
181#95—712no—
182#95C2×D7111yescharacteristic
183C24—711no—
184C24C22×D7112yes—
185C2×Q8—2842no—
186C2×Q8—1422no—
187C2×D4—22no—
188C2×D4—42no—
189C2×D4—1424no—
190C2×D4—1424no—
191C2×D4—1424no—
192C22×C4—2842no—
193C22×C4—2842no—
194C22×C4—2842no—
195C22×C4—714no—
196C22×C4—711no—
197C22×C4—712no—
198C22×C4—712no—
199C22×C4—711no—
200C22×C4—711no—
201C22×C4—1424no—
202C22×C4C22×D7112yes—
203C22×C4C22×D7111yescharacteristic
204C22×C4C22×D7111yescharacteristic
205C22×C4C22×D7111yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—1422no—
208C4⋊C4—1422no—
209C4⋊C4—1422no—
210C22⋊C4—42no—
211C22⋊C4—42no—
212C22⋊C4—2842no—
213C22⋊C4—2842no—
214C22⋊C4—1422no—
215C22⋊C4—1422no—
216C22⋊C4—1424no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—712no—
225C23—714no—
226C23—1421no—
227C23—1422no—
228C23—1421no—
229C23C23×D7111yescharacteristic
230Q8—2844no—
231D4—44no—
232D4—2848no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—2844no—
243C2×C4—2848no—
244C2×C4—712no—
245C2×C4—1421no—
246C2×C4—1422no—
247C2×C4—1421no—
248C2×C4—1422no—
249C2×C4—1422no—
250C2×C4—1422no—
251C2×C4—1421no—
252C2×C4—1422no—
253C2×C4—1422no—
254C2×C4—1422no—
255C2×C4—1421no—
256C2×C4—1422no—
257C2×C4D4×D7112yes—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—714no—
266C22—1422no—
267C22—1424no—
268C22—1424no—
269C22—1422no—
270C22C2×D4×D7111yescharacteristic
271C22#41×D7112yes—
272C22#1455617311yescharacteristic
273C22#1455617312yes—
274C22#1455617511yescharacteristic
275C4—22no—
276C4—41no—
277C4—42no—
278C4—41no—
279C4—2841no—
280C4—2842no—
281C4—2842no—
282C4—2841no—
283C4—1422no—
284C2—82no—
285C2—1424no—
286C2#124×D7111yescharacteristic
287C2#1798655911yescharacteristic
288C2#1798657811yescharacteristic
289C2#1798658112yes—
290C2#1798659212yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#394×C71C2
hypercenter#394D71
hypocenterC71#2639
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14556106C2semidirect
3. #17985939C2semidirect
4. #17985938C2semidirect
5. #17985927C2semidirect
6. #17985913C2semidirect
7. #17985911C2semidirect
8. #17985875C2semidirect
9. #17985875C2semidirect
10. #95×D71C2semidirect
11. #394×C71C2semidirect
146. C71#2639semidirect
153. #394D71semidirect