Finite Group Databasebeta

← #22595993

Subgroups — #22595993

Order 9088.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17985940C211yesmaximal, characteristic, complemented
2#17985929C211yesmaximal, characteristic, complemented
3#17985923C211yesmaximal, characteristic, complemented
4#17985922C211yesmaximal, characteristic, complemented
5#17985921C211yesmaximal, characteristic, complemented
6#17985899C211yesmaximal, characteristic
7#17985894C211yesmaximal, characteristic, complemented
8#17985880C211yesmaximal, characteristic, complemented
9#17985876C211yesmaximal, characteristic
10#17985875C211yesmaximal, characteristic
11#17985871C211yesmaximal, characteristic, complemented
12#17985870C211yesmaximal, characteristic, complemented
13#17985870C211yesmaximal, characteristic, complemented
14#17985857C211yesmaximal, characteristic, complemented
15#399×C71C211yesmaximal, characteristic, complemented
16C22×C22⋊D71C2211yescharacteristic
17C23×Dic71C2211yescharacteristic
18C22×C4×D71C2211yescharacteristic
19C2×C4⋊Dic71C2211yescharacteristic
20C2×Dic71⋊C4C2211yescharacteristic
21C2×Dic71⋊C4C2211yescharacteristic
22C2×Dic71⋊C4C2211yescharacteristic
23C2×Dic71⋊C4C2211yescharacteristic
24C2×Dic71⋊C4C2211yescharacteristic
25C2×Dic71⋊C4C2211yescharacteristic
26C2×Dic71⋊C4C2211yescharacteristic
27C2×C22⋊Dic71C2211yescharacteristic
28C2×C22⋊Dic71C2211yescharacteristic
29C2×(C2×D71)⋊C4C2211yescharacteristic
30C2×(C2×D71)⋊C4C2211yescharacteristic
31C2×(C2×D71)⋊C4C2211yescharacteristic
32C2×(C2×D71)⋊C4C2211yescharacteristic
33C2×(C2×D71)⋊C4C2211yescharacteristic
34C2×C4×Dic71C2211yescharacteristic
35C71⋊#95C2211yescharacteristic
36C71⋊#95C2211yescharacteristic
37C71⋊#95C2211yescharacteristic
38C71⋊#95C2211yescharacteristic
39C71⋊#95C2211yescharacteristic
40C71⋊#95C2211yescharacteristic
41C71⋊#95C2211yescharacteristic
42C71⋊#95C2211yescharacteristic
43C71⋊#95C2211yescharacteristic
44C2×C4⋊C4×C71C2211yescharacteristic
45C2×C4⋊C4×C71C2211yescharacteristic
46C2×C4⋊C4×C71C2211yescharacteristic
47C2×C22⋊C4×C71C2211yescharacteristic
48C2×C22⋊C4×C71C2211yescharacteristic
49C2×C22⋊C4×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51C23×D71C2311yescharacteristic
52C2×C22⋊D71—41no—
53C2×C22⋊D71—41no—
54C2×C22⋊D71Q814yes—
55C22×Dic71—22no—
56C22×Dic71—41no—
57C22×Dic71—41no—
58C22×Dic71C2311yescharacteristic
59C22×Dic71C2311yescharacteristic
60C22×Dic71C2311yescharacteristic
61C22×Dic71C2311yescharacteristic
62C22×Dic71C2311yescharacteristic
63C22×Dic71C2311yescharacteristic
64C22×Dic71C2311yescharacteristic
65C2×C4×D71—41no—
66C2×C4×D71—41no—
67C2×C4×D71—41no—
68C4⋊Dic71—41no—
69Dic71⋊C4—22no—
70Dic71⋊C4—22no—
71Dic71⋊C4—41no—
72Dic71⋊C4—41no—
73Dic71⋊C4—41no—
74Dic71⋊C4—41no—
75Dic71⋊C4—41no—
76C22⋊Dic71—22no—
77C22⋊Dic71—41no—
78(C2×D71)⋊C4—22no—
79(C2×D71)⋊C4—22no—
80(C2×D71)⋊C4—41no—
81(C2×D71)⋊C4—41no—
82(C2×D71)⋊C4—41no—
83C4×Dic71—41no—
84C24×C71C2311yescharacteristic
85C22×C4×C71C2311yescharacteristic
86C22×C4×C71C2311yescharacteristic
87C22×C4×C71C2311yescharacteristic
88C22×C4×C71C2311yescharacteristic
89C22×C4×C71C2311yescharacteristic
90C22×C4×C71C2311yescharacteristic
91C4⋊C4×C71—41no—
92C4⋊C4×C71—41no—
93C4⋊C4×C71—41no—
94C22⋊C4×C71—41no—
95C22⋊C4×C71—41no—
96C22⋊C4×C71—41no—
97C23×C71—21no—
98C23×C71—21no—
99C23×C71—21no—
100C23×C71—21no—
101C23×C71—21no—
102C23×C71—21no—
103C23×C71C2×Q812yes—
104C23×C71C2411yescharacteristic
105C22×D71—21no—
106C22×D71—21no—
107C22×D71—21no—
108C22×D71—21no—
109C22×D71—21no—
110C22×D71—21no—
111C22×D71C2×Q812yes—
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×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71—21no—
124C2×C4×C71—21no—
125C2×C4×C71—21no—
126C2×C4×C71—21no—
127C2×C4×C71—21no—
128C2×C4×C71—21no—
129C2×C4×C71—21no—
130C22⋊D71—44no—
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×Dic71—21no—
142C2×Dic71—21no—
143C2×Dic71—21no—
144C2×Dic71—21no—
145C2×Dic71—21no—
146C2×Dic71—21no—
147C2×Dic71—21no—
148C2×Dic71—21no—
149C2×Dic71—44no—
150C2×Dic71C2×Q812yes—
151C2×Dic71#4112yes—
152C2×Dic71#4112yes—
153C4×D71—44no—
154C22×C71—22no—
155C22×C71—22no—
156C22×C71—22no—
157C22×C71—41no—
158C22×C71—41no—
159C22×C71—41no—
160C22×C71—41no—
161C22×C71C22×Q811yescharacteristic
162C22×C71C2×#4111yescharacteristic
163C22×C71C2×#4111yescharacteristic
164C22×C71H(5,𝔽2)11yescharacteristic
165C22×C71H(5,𝔽2)11yescharacteristic
166C22×C71H(5,𝔽2)11yescharacteristic
167C22×C71H(5,𝔽2)11yescharacteristic
168C2×D71—22no—
169C2×D71—22no—
170C2×D71—22no—
171C2×D71—41no—
172C2×D71—41no—
173C2×D71—41no—
174C2×D71—41no—
175C4×C71—41no—
176C4×C71—41no—
177C4×C71—41no—
178C4×C71—41no—
179C4×C71—41no—
180C4×C71—41no—
181Dic71—22no—
182Dic71—22no—
183Dic71—22no—
184Dic71—41no—
185Dic71—41no—
186Dic71—41no—
187Dic71—41no—
188C2×C71—42no—
189C2×C71#53811yescharacteristic
190C2×C71#54011yescharacteristic
191C2×C71#54311yescharacteristic
192C2×C71#55311yescharacteristic
193C2×C71#55411yescharacteristic
194C2×C71#55411yescharacteristic
195C2×C71#56011yescharacteristic
196D71—42no—
197#2780—711nomaximal, Sylow
198C71#278011yescharacteristic, complemented, Sylow
199#400—711no—
200#399D7111yescharacteristic, complemented
201#398—711no—
202#396—711no—
203#396—711no—
204#396—711no—
205#390—711no—
206#389—711no—
207#387—711no—
208#386—711no—
209#386—711no—
210#385—711no—
211#385—711no—
212#385—711no—
213#380—711no—
214C22×D4—711no—
215C23×C4—711no—
216C23×C4—711no—
217C2×C4⋊C4—711no—
218C2×C4⋊C4—711no—
219C2×C4⋊C4—711no—
220C2×C4⋊C4—711no—
221C2×C4⋊C4—711no—
222C2×C4⋊C4—711no—
223C2×C4⋊C4—711no—
224C2×C4⋊C4—711no—
225C2×C4⋊C4C2×D7111yescharacteristic
226C2×C4⋊C4C2×D7111yescharacteristic
227C2×C4⋊C4C2×D7111yescharacteristic
228C2×C22⋊C4—711no—
229C2×C22⋊C4—711no—
230C2×C22⋊C4—711no—
231C2×C22⋊C4—711no—
232C2×C22⋊C4—711no—
233C2×C22⋊C4—711no—
234C2×C22⋊C4—711no—
235C2×C22⋊C4C2×D7111yescharacteristic
236C2×C22⋊C4C2×D7111yescharacteristic
237C2×C22⋊C4C2×D7111yescharacteristic
238C2×C42—711no—
239#95—711no—
240#95—711no—
241#95—711no—
242#95—711no—
243#95—711no—
244#95—711no—
245#95—711no—
246#95—711no—
247#95—711no—
248#95C2×D7111yescharacteristic
249C24—711no—
250C24C22×D7111yescharacteristic
251C2×D4—2841no—
252C2×D4—2841no—
253C2×D4—714no—
254C22×C4—2841no—
255C22×C4—2841no—
256C22×C4—2841no—
257C22×C4—2841no—
258C22×C4—2841no—
259C22×C4—711no—
260C22×C4—711no—
261C22×C4—711no—
262C22×C4—711no—
263C22×C4—711no—
264C22×C4—711no—
265C22×C4—711no—
266C22×C4—1422no—
267C22×C4C22×D7111yescharacteristic
268C22×C4C22×D7111yescharacteristic
269C22×C4C22×D7111yescharacteristic
270C22×C4C22×D7111yescharacteristic
271C22×C4C22×D7111yescharacteristic
272C22×C4C22×D7111yescharacteristic
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—2841no—
277C4⋊C4—2841no—
278C4⋊C4—2841no—
279C4⋊C4—2841no—
280C4⋊C4—2841no—
281C4⋊C4—2841no—
282C4⋊C4—1422no—
283C4⋊C4—1422no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—2841no—
288C22⋊C4—2841no—
289C22⋊C4—2841no—
290C22⋊C4—2841no—
291C22⋊C4—1422no—
292C22⋊C4—1422no—
293C22⋊C4—1422no—
294C42—2841no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—712no—
302C23—1421no—
303C23—1421no—
304C23—1421no—
305C23—1421no—
306C23—1421no—
307C23—1421no—
308C23Q8×D7112yes—
309C23C23×D7111yescharacteristic
310D4—2844no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—2844no—
330C2×C4—2844no—
331C2×C4—712no—
332C2×C4—712no—
333C2×C4—712no—
334C2×C4—1421no—
335C2×C4—1421no—
336C2×C4—1421no—
337C2×C4—1421no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4—1421no—
341C2×C4—1421no—
342C2×C4—1421no—
343C2×C4—1421no—
344C2×C4—1421no—
345C2×C4—1421no—
346C2×C4—1421no—
347C2×C4—1421no—
348C2×C4—1421no—
349C2×C4—1421no—
350C2×C4—1421no—
351C2×C4—1421no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—2841no—
360C22—2841no—
361C22—2841no—
362C22—2841no—
363C22—1422no—
364C22—1422no—
365C22—1422no—
366C22C2×Q8×D7111yescharacteristic
367C22#41×D7111yescharacteristic
368C22#41×D7111yescharacteristic
369C22#1455617311yescharacteristic
370C22#1455617311yescharacteristic
371C22#1455617311yescharacteristic
372C22#1455617411yescharacteristic
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—2841no—
380C4—2841no—
381C4—2841no—
382C4—2841no—
383C4—1422no—
384C4—1422no—
385C4—1422no—
386C2—42no—
387C2—2842no—
388C2#1798658511yescharacteristic
389C2#1798660111yescharacteristic
390C2#1798662411yescharacteristic
391C2#1798669411yescharacteristic
392C2#1798670311yescharacteristic
393C2#1798670311yescharacteristic
394C2#1798673611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#399×C71C2
hypercenter#399D71
hypocenterC71#2780
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #17985940C2semidirect
2. #17985929C2semidirect
3. #17985923C2semidirect
4. #17985922C2semidirect
5. #17985921C2semidirect
7. #17985894C2semidirect
8. #17985880C2semidirect
11. #17985871C2semidirect
12. #17985870C2semidirect
13. #17985870C2semidirect
14. #17985857C2semidirect
15. #399×C71C2semidirect
198. C71#2780semidirect
200. #399D71semidirect