Finite Group Databasebeta

← #22595249

Subgroups — #22595249

Order 9088.

448 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556123C211yesmaximal, characteristic
2C2×#14556123C211yesmaximal, characteristic
3#17985932C211yesmaximal, characteristic, complemented
4#17985932C211yesmaximal, characteristic, complemented
5#17985931C211yesmaximal, characteristic, complemented
6#17985928C211yesmaximal, characteristic
7#17985925C211yesmaximal, characteristic
8#17985895C211yesmaximal, characteristic, complemented
9#17985894C211yesmaximal, characteristic, complemented
10#17985886C211yesmaximal, characteristic, complemented
11#17985884C211yesmaximal, characteristic, complemented
12#17985873C211yesmaximal, characteristic
13#17985858C211yesmaximal, characteristic
14#17985856C211yesmaximal, characteristic
15#398×C71C211yesmaximal, characteristic, complemented
16C22×C4×D71C2211yescharacteristic
17#14556123—24no—
18#14556123—24no—
19C2×C4⋊Dic71C2211yescharacteristic
20C2×C4⋊Dic71C2211yescharacteristic
21C2×C4⋊Dic71C2211yescharacteristic
22C2×C4⋊Dic71C2211yescharacteristic
23C2×Dic71⋊C4C2211yescharacteristic
24C2×Dic71⋊C4C2211yescharacteristic
25C2×Dic71⋊C4C2211yescharacteristic
26C2×Dic71⋊C4C2211yescharacteristic
27C2×Dic71⋊C4C2211yescharacteristic
28C2×Dic71⋊C4C2211yescharacteristic
29C2×(C2×D71)⋊C4C2211yescharacteristic
30C2×(C2×D71)⋊C4C2211yescharacteristic
31C2×(C2×D71)⋊C4C2211yescharacteristic
32C2×(C2×D71)⋊C4C2211yescharacteristic
33C2×(C2×D71)⋊C4C2211yescharacteristic
34C2×(C2×D71)⋊C4C2211yescharacteristic
35C2×C4×Dic71C2211yescharacteristic
36C2×C4×Dic71C2211yescharacteristic
37C71⋊#95C2211yescharacteristic
38C71⋊#95C2211yescharacteristic
39C71⋊#95C2211yescharacteristic
40C71⋊#95C2211yescharacteristic
41C71⋊#95C2211yescharacteristic
42C71⋊#95C2211yescharacteristic
43C71⋊#95C2211yescharacteristic
44C71⋊#95C2211yescharacteristic
45C71⋊#95C2211yescharacteristic
46C2×C4⋊C4×C71C2211yescharacteristic
47C2×C4⋊C4×C71C2211yescharacteristic
48C2×C4⋊C4×C71C2211yescharacteristic
49C2×C4⋊C4×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51#95×C71C2211yescharacteristic
52#95×C71C2211yescharacteristic
53C23×D71C2311yescharacteristic
54C22×Dic71C2311yescharacteristic
55C22×Dic71C2311yescharacteristic
56C22×Dic71C2311yescharacteristic
57C22×Dic71C2311yescharacteristic
58C22×Dic71C2311yescharacteristic
59C22×Dic71C2311yescharacteristic
60C22×Dic71C2311yescharacteristic
61C2×C4×D71—22no—
62C2×C4×D71—22no—
63C2×C4×D71—41no—
64C4⋊Dic71—22no—
65C4⋊Dic71—22no—
66C4⋊Dic71—22no—
67C4⋊Dic71—22no—
68Dic71⋊C4—22no—
69Dic71⋊C4—22no—
70Dic71⋊C4—22no—
71Dic71⋊C4—22no—
72Dic71⋊C4—41no—
73Dic71⋊C4—41no—
74(C2×D71)⋊C4—22no—
75(C2×D71)⋊C4—22no—
76(C2×D71)⋊C4—22no—
77(C2×D71)⋊C4—22no—
78(C2×D71)⋊C4—41no—
79(C2×D71)⋊C4D414yes—
80C4×Dic71—22no—
81C4×Dic71—22no—
82C22×C4×C71C2311yescharacteristic
83C22×C4×C71C2311yescharacteristic
84C22×C4×C71C2311yescharacteristic
85C22×C4×C71C2311yescharacteristic
86C22×C4×C71C2311yescharacteristic
87C22×C4×C71C2311yescharacteristic
88C22×C4×C71C2311yescharacteristic
89C4⋊C4×C71—22no—
90C4⋊C4×C71—22no—
91C4⋊C4×C71—41no—
92C4⋊C4×C71—41no—
93C23×C71C2411yescharacteristic
94C22×D71—21no—
95C22×D71—21no—
96C22×D71—21no—
97C22×D71—21no—
98C22×D71—21no—
99C22×D71—21no—
100C22×D71C2×D412yes—
101C2×C4×C71—21no—
102C2×C4×C71—21no—
103C2×C4×C71—21no—
104C2×C4×C71—21no—
105C2×C4×C71—21no—
106C2×C4×C71—21no—
107C2×C4×C71—21no—
108C2×C4×C71—21no—
109C2×C4×C71—21no—
110C2×C4×C71—21no—
111C2×C4×C71—21no—
112C2×C4×C71—21no—
113C2×C4×C71—21no—
114C2×C4×C71—21no—
115C2×C4×C71—21no—
116C2×C4×C71—21no—
117C2×C4×C71—21no—
118C2×C4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71C2×D412yes—
121C2×C4×C71#4112yes—
122C2×Dic71—21no—
123C2×Dic71—21no—
124C2×Dic71—21no—
125C2×Dic71—21no—
126C2×Dic71—21no—
127C2×Dic71—21no—
128C2×Dic71—21no—
129C2×Dic71—21no—
130C2×Dic71—21no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—21no—
134C2×Dic71—21no—
135C2×Dic71—21no—
136C2×Dic71—21no—
137C2×Dic71—21no—
138C2×Dic71—21no—
139C2×Dic71—21no—
140C2×Dic71—21no—
141C2×Dic71C2×D412yes—
142C2×Dic71#4112yes—
143C4×D71—44no—
144C22×C71C22×D411yescharacteristic
145C22×C71C2×#4111yescharacteristic
146C22×C71C2×#4111yescharacteristic
147C22×C71H(5,𝔽2)11yescharacteristic
148C22×C712−1+411yescharacteristic
149C22×C712−1+411yescharacteristic
150C22×C712−1+411yescharacteristic
151C2×D71—22no—
152C2×D71—22no—
153C2×D71—22no—
154C2×D71—41no—
155C2×D71—41no—
156C2×D71—41no—
157C2×D71—41no—
158C4×C71—22no—
159C4×C71—22no—
160C4×C71—41no—
161C4×C71—41no—
162C4×C71—41no—
163C4×C71—41no—
164C4×C71—41no—
165Dic71—22no—
166Dic71—22no—
167Dic71—41no—
168Dic71—41no—
169Dic71—41no—
170Dic71—41no—
171Dic71—41no—
172C2×C71#53711yescharacteristic
173C2×C71#54111yescharacteristic
174C2×C71#54111yescharacteristic
175C2×C71#54711yescharacteristic
176C2×C71#54711yescharacteristic
177C2×C71#55111yescharacteristic
178C2×C71#56311yescharacteristic
179D71—42no—
180#2722—711nomaximal, Sylow
181C71#272211yescharacteristic, complemented, Sylow
182C2×#126—711no—
183C2×#126—711no—
184#398—711no—
185#398—711no—
186#398—711no—
187#398D7111yescharacteristic, complemented
188#397—711no—
189#397—711no—
190#389—711no—
191#389—711no—
192#387—711no—
193#387—711no—
194#385—711no—
195#380—711no—
196#380—711no—
197C23×C4—711no—
198#126—1424no—
199#126—1424no—
200C2×C4⋊C4—711no—
201C2×C4⋊C4—711no—
202C2×C4⋊C4—711no—
203C2×C4⋊C4—711no—
204C2×C4⋊C4—711no—
205C2×C4⋊C4—711no—
206C2×C4⋊C4—711no—
207C2×C4⋊C4—711no—
208C2×C4⋊C4—711no—
209C2×C4⋊C4—711no—
210C2×C4⋊C4C2×D7111yescharacteristic
211C2×C4⋊C4C2×D7111yescharacteristic
212C2×C4⋊C4C2×D7111yescharacteristic
213C2×C4⋊C4C2×D7111yescharacteristic
214C2×C22⋊C4—711no—
215C2×C22⋊C4—711no—
216C2×C22⋊C4—711no—
217C2×C22⋊C4—711no—
218C2×C22⋊C4—711no—
219C2×C22⋊C4—711no—
220C2×C42—711no—
221C2×C42—711no—
222#95—711no—
223#95—711no—
224#95—711no—
225#95—711no—
226#95—711no—
227#95—711no—
228#95—711no—
229#95—711no—
230#95—711no—
231#95C2×D7111yescharacteristic
232#95C2×D7111yescharacteristic
233#95C2×D7111yescharacteristic
234C24—711no—
235C22×C4—2841no—
236C22×C4—711no—
237C22×C4—711no—
238C22×C4—711no—
239C22×C4—711no—
240C22×C4—711no—
241C22×C4—711no—
242C22×C4—711no—
243C22×C4—1422no—
244C22×C4—1422no—
245C22×C4C22×D7111yescharacteristic
246C22×C4C22×D7111yescharacteristic
247C22×C4C22×D7111yescharacteristic
248C22×C4C22×D7111yescharacteristic
249C22×C4C22×D7111yescharacteristic
250C22×C4C22×D7111yescharacteristic
251C22×C4C22×D7111yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—2841no—
257C4⋊C4—2841no—
258C4⋊C4—1422no—
259C4⋊C4—1422no—
260C4⋊C4—1422no—
261C4⋊C4—1422no—
262C4⋊C4—1422no—
263C4⋊C4—1422no—
264C4⋊C4—1422no—
265C4⋊C4—1422no—
266C22⋊C4—2841no—
267C22⋊C4—714no—
268C22⋊C4—1422no—
269C22⋊C4—1422no—
270C22⋊C4—1422no—
271C22⋊C4—1422no—
272C42—1422no—
273C42—1422no—
274C23—712no—
275C23—1421no—
276C23—1421no—
277C23—1421no—
278C23—1421no—
279C23—1421no—
280C23—1421no—
281C23C23×D7111yescharacteristic
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2844no—
302C2×C4—712no—
303C2×C4—712no—
304C2×C4—1421no—
305C2×C4—1421no—
306C2×C4—1421no—
307C2×C4—1421no—
308C2×C4—1421no—
309C2×C4—1421no—
310C2×C4—1421no—
311C2×C4—1421no—
312C2×C4—1421no—
313C2×C4—1421no—
314C2×C4—1421no—
315C2×C4—1421no—
316C2×C4—1421no—
317C2×C4—1421no—
318C2×C4—1421no—
319C2×C4—1421no—
320C2×C4—1421no—
321C2×C4—1421no—
322C2×C4—1421no—
323C2×C4D4×D7112yes—
324C2×C4#1176586612yes—
325C22—2841no—
326C22—2841no—
327C22—2841no—
328C22—2841no—
329C22—1422no—
330C22—1422no—
331C22—1422no—
332C22C2×D4×D7111yescharacteristic
333C22#41×D7111yescharacteristic
334C22C2×#1176586611yescharacteristic
335C22#1455617311yescharacteristic
336C22#1455617511yescharacteristic
337C22#1455617511yescharacteristic
338C22#1455617611yescharacteristic
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—2841no—
347C4—2841no—
348C4—2841no—
349C4—2841no—
350C4—2841no—
351C4—1422no—
352C4—1422no—
353C2—2842no—
354C2#1798657811yescharacteristic
355C2#1798660811yescharacteristic
356C2#1798661211yescharacteristic
357C2#1798664711yescharacteristic
358C2#1798665211yescharacteristic
359C2#1798667611yescharacteristic
360C2#1798675011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#398×C71C2
hypercenter#398D71
hypocenterC71#2722
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #17985932C2semidirect
4. #17985932C2semidirect
5. #17985931C2semidirect
8. #17985895C2semidirect
9. #17985894C2semidirect
10. #17985886C2semidirect
11. #17985884C2semidirect
15. #398×C71C2semidirect
181. C71#2722semidirect
187. #398D71semidirect