Finite Group Databasebeta

← #22596035

Subgroups — #22596035

Order 9088.

472 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17985940C211yesmaximal, characteristic, complemented
2#17985923C211yesmaximal, characteristic, complemented
3#17985922C211yesmaximal, characteristic, complemented
4#17985918C211yesmaximal, characteristic, complemented
5#17985910C211yesmaximal, characteristic, complemented
6#17985899C211yesmaximal, characteristic
7#17985884C211yesmaximal, characteristic, complemented
8#17985881C211yesmaximal, characteristic, complemented
9#17985876C211yesmaximal, characteristic
10#17985875C211yesmaximal, characteristic
11#17985873C211yesmaximal, characteristic, complemented
12#17985871C211yesmaximal, characteristic, complemented
13#17985858C211yesmaximal, characteristic, complemented
14#17985857C211yesmaximal, characteristic, complemented
15#393×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
44C22×Q8×C71C2211yescharacteristic
45C2×C22⋊C4×C71C2211yescharacteristic
46C2×C22⋊C4×C71C2211yescharacteristic
47C2×C22⋊C4×C71C2211yescharacteristic
48#95×C71C2211yescharacteristic
49#95×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51C23×D71C2311yescharacteristic
52C2×C22⋊D71—41no—
53C2×C22⋊D71—41no—
54C2×C22⋊D71Q814yescomplemented
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—22no—
66C2×C4×D71—41no—
67C2×C4×D71—41no—
68C4⋊Dic71—22no—
69Dic71⋊C4—22no—
70Dic71⋊C4—41no—
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—41no—
80(C2×D71)⋊C4—41no—
81(C2×D71)⋊C4—41no—
82(C2×D71)⋊C4—41no—
83C4×Dic71—41no—
84C24×C71C2311yescharacteristic
85C2×Q8×C71—41no—
86C2×Q8×C71—41no—
87C2×Q8×C71—41no—
88C22×C4×C71C2311yescharacteristic
89C22×C4×C71C2311yescharacteristic
90C22×C4×C71C2311yescharacteristic
91C22×C4×C71C2311yescharacteristic
92C22×C4×C71C2311yescharacteristic
93C22×C4×C71C2311yescharacteristic
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—
112Q8×C71—44no—
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—
130C2×C4×C71—21no—
131C22⋊D71—44no—
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—21no—
150C2×Dic71—44no—
151C2×Dic71C2×Q812yes—
152C2×Dic71#4112yes—
153C2×Dic71#4112yes—
154C4×D71—44no—
155C22×C71—22no—
156C22×C71—22no—
157C22×C71—22no—
158C22×C71—41no—
159C22×C71—41no—
160C22×C71—41no—
161C22×C71—41no—
162C22×C71C22×Q811yescharacteristic
163C22×C71C2×#4111yescharacteristic
164C22×C71C2×#4111yescharacteristic
165C22×C71H(5,𝔽2)11yescharacteristic
166C22×C71H(5,𝔽2)11yescharacteristic
167C22×C71H(5,𝔽2)11yescharacteristic
168C22×C71H(5,𝔽2)11yescharacteristic
169C2×D71—22no—
170C2×D71—22no—
171C2×D71—22no—
172C2×D71—41no—
173C2×D71—41no—
174C2×D71—41no—
175C2×D71—41no—
176C4×C71—41no—
177C4×C71—41no—
178C4×C71—41no—
179C4×C71—41no—
180C4×C71—41no—
181C4×C71—41no—
182Dic71—22no—
183Dic71—22no—
184Dic71—22no—
185Dic71—41no—
186Dic71—41no—
187Dic71—41no—
188Dic71—41no—
189C2×C71—42no—
190C2×C71#53811yescharacteristic
191C2×C71#53811yescharacteristic
192C2×C71#54311yescharacteristic
193C2×C71#55411yescharacteristic
194C2×C71#55411yescharacteristic
195C2×C71#55511yescharacteristic
196C2×C71#56011yescharacteristic
197D71—42no—
198#2784—711nomaximal, Sylow
199C71#278411yescharacteristic, complemented, Sylow
200#400—711no—
201#396—711no—
202#396—711no—
203#395—711no—
204#393—711no—
205#393D7111yescharacteristic, complemented
206#390—711no—
207#387—711no—
208#387—711no—
209#386—711no—
210#386—711no—
211#385—711no—
212#385—711no—
213#380—711no—
214#380—711no—
215C22×Q8C2×D7111yescharacteristic
216C22×D4—711no—
217C23×C4—711no—
218C23×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⋊C4—711no—
226C2×C4⋊C4—711no—
227C2×C22⋊C4—711no—
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⋊C4C2×D7111yescharacteristic
235C2×C22⋊C4C2×D7111yescharacteristic
236C2×C22⋊C4C2×D7111yescharacteristic
237C2×C42—711no—
238#95—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#95C2×D7111yescharacteristic
248#95C2×D7111yescharacteristic
249#95C2×D7111yescharacteristic
250C24—711no—
251C24C22×D7111yescharacteristic
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×D4—2841no—
256C2×D4—2841no—
257C2×D4—714no—
258C22×C4—2841no—
259C22×C4—2841no—
260C22×C4—2841no—
261C22×C4—2841no—
262C22×C4—711no—
263C22×C4—711no—
264C22×C4—711no—
265C22×C4—711no—
266C22×C4—711no—
267C22×C4—711no—
268C22×C4—711no—
269C22×C4—1422no—
270C22×C4—1422no—
271C22×C4C22×D7111yescharacteristic
272C22×C4C22×D7111yescharacteristic
273C22×C4C22×D7111yescharacteristic
274C22×C4C22×D7111yescharacteristic
275C22×C4C22×D7111yescharacteristic
276C22×C4C22×D7111yescharacteristic
277C4⋊C4—2841no—
278C4⋊C4—2841no—
279C4⋊C4—2841no—
280C4⋊C4—2841no—
281C4⋊C4—2841no—
282C4⋊C4—2841no—
283C4⋊C4—1422no—
284C4⋊C4—1422no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—2841no—
289C22⋊C4—2841no—
290C22⋊C4—2841no—
291C22⋊C4—2841no—
292C22⋊C4—2841no—
293C22⋊C4—1422no—
294C22⋊C4—1422no—
295C42—2841no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—712no—
303C23—1421no—
304C23—1421no—
305C23—1421no—
306C23—1421no—
307C23—1421no—
308C23—1421no—
309C23Q8×D7112yes—
310C23C23×D7111yescharacteristic
311Q8—44no—
312D4—2844no—
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—21no—
330C2×C4—21no—
331C2×C4—2844no—
332C2×C4—2844no—
333C2×C4—712no—
334C2×C4—712no—
335C2×C4—712no—
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—
352C2×C4—1421no—
353C2×C4—1421no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—2841no—
362C22—2841no—
363C22—2841no—
364C22—2841no—
365C22—1422no—
366C22—1422no—
367C22—1422no—
368C22C2×Q8×D7111yescharacteristic
369C22#41×D7111yescharacteristic
370C22#41×D7111yescharacteristic
371C22#1455617311yescharacteristic
372C22#1455617311yescharacteristic
373C22#1455617311yescharacteristic
374C22#1455617411yescharacteristic
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—2841no—
382C4—2841no—
383C4—2841no—
384C4—2841no—
385C4—1422no—
386C4—1422no—
387C4—1422no—
388C2—42no—
389C2—2842no—
390C2#1798658311yescharacteristic
391C2#1798658311yescharacteristic
392C2#1798662411yescharacteristic
393C2#1798670311yescharacteristic
394C2#1798670311yescharacteristic
395C2#1798671111yescharacteristic
396C2#1798673811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#393×C71C2
hypercenter#393D71
hypocenterC71#2784
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #17985940C2semidirect
2. #17985923C2semidirect
3. #17985922C2semidirect
4. #17985918C2semidirect
5. #17985910C2semidirect
7. #17985884C2semidirect
8. #17985881C2semidirect
11. #17985873C2semidirect
12. #17985871C2semidirect
13. #17985858C2semidirect
14. #17985857C2semidirect
15. #393×C71C2semidirect
54. C2×C22⋊D71Q8semidirect
199. C71#2784semidirect
205. #393D71semidirect