Finite Group Databasebeta

← #22593056

Subgroups — #22593056

Order 9088.

428 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17985934C211yesmaximal, characteristic
2#17985933C211yesmaximal, characteristic, complemented
3#17985933C211yesmaximal, characteristic, complemented
4#17985923C211yesmaximal, characteristic
5#17985897C211yesmaximal, characteristic, complemented
6#17985894C211yesmaximal, characteristic, complemented
7#17985891C211yesmaximal, characteristic
8#17985891C211yesmaximal, characteristic
9#17985881C211yesmaximal, characteristic, complemented
10#17985880C211yesmaximal, characteristic, complemented
11#17985870C211yesmaximal, characteristic
12#17985858C211yesmaximal, characteristic
13#17985850C211yesmaximal, characteristic, complemented
14C4×(C2×D71)⋊C4C211yesmaximal, characteristic
15#387×C71C211yesmaximal, characteristic, complemented
16C22×C4×D71C2211yescharacteristic
17C2×C4⋊Dic71C2211yescharacteristic
18C2×C4⋊Dic71C2211yescharacteristic
19C2×Dic71⋊C4C2211yescharacteristic
20C2×Dic71⋊C4C2211yescharacteristic
21C2×Dic71⋊C4C2211yescharacteristic
22C2×Dic71⋊C4C2211yescharacteristic
23C2×Dic71⋊C4C2211yescharacteristic
24C2×Dic71⋊C4C2211yescharacteristic
25C2×Dic71⋊C4C2211yescharacteristic
26C2×Dic71⋊C4C2211yescharacteristic
27C2×(C2×D71)⋊C4C2211yescharacteristic
28C2×(C2×D71)⋊C4C2211yescharacteristic
29C2×(C2×D71)⋊C4C2211yescharacteristic
30C2×(C2×D71)⋊C4C2211yescharacteristic
31C2×(C2×D71)⋊C4C2211yescharacteristic
32C2×(C2×D71)⋊C4C2211yescharacteristic
33C2×C4×Dic71C2211yescharacteristic
34C2×C4×Dic71C2211yescharacteristic
35C2×C4×Dic71C2211yescharacteristic
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×C42×C71C2211yescharacteristic
47#95×C71C2211yescharacteristic
48#95×C71C2211yescharacteristic
49#95×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51C23×D71C2311yescharacteristic
52C22×Dic71C2311yescharacteristic
53C22×Dic71C2311yescharacteristic
54C22×Dic71C2311yescharacteristic
55C22×Dic71C2311yescharacteristic
56C22×Dic71C2311yescharacteristic
57C22×Dic71C2311yescharacteristic
58C22×Dic71C2311yescharacteristic
59C2×C4×D71—22no—
60C2×C4×D71—22no—
61C2×C4×D71—41no—
62C4⋊Dic71—22no—
63C4⋊Dic71—41no—
64Dic71⋊C4—22no—
65Dic71⋊C4—22no—
66Dic71⋊C4—22no—
67Dic71⋊C4—22no—
68Dic71⋊C4—22no—
69Dic71⋊C4—41no—
70Dic71⋊C4—41no—
71Dic71⋊C4—41no—
72(C2×D71)⋊C4—22no—
73(C2×D71)⋊C4—22no—
74(C2×D71)⋊C4—41no—
75(C2×D71)⋊C4—41no—
76(C2×D71)⋊C4—41no—
77(C2×D71)⋊C4Q814yes—
78C4×Dic71—22no—
79C4×Dic71—41no—
80C4×Dic71—41no—
81C22×C4×C71C2311yescharacteristic
82C22×C4×C71C2311yescharacteristic
83C22×C4×C71C2311yescharacteristic
84C22×C4×C71C2311yescharacteristic
85C22×C4×C71C2311yescharacteristic
86C22×C4×C71C2311yescharacteristic
87C22×C4×C71C2311yescharacteristic
88C4⋊C4×C71—22no—
89C4⋊C4×C71—41no—
90C42×C71—41no—
91C23×C71C2411yescharacteristic
92C22×D71—21no—
93C22×D71—21no—
94C22×D71—21no—
95C22×D71—21no—
96C22×D71—21no—
97C22×D71—21no—
98C22×D71C2×Q812yes—
99C2×C4×C71—21no—
100C2×C4×C71—21no—
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×C71C2×Q812yes—
119C2×C4×C71#4112yes—
120C2×Dic71—21no—
121C2×Dic71—21no—
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×Dic71C2×Q812yes—
138C2×Dic71#4112yes—
139C2×Dic71#4112yes—
140C2×Dic71#4112yes—
141C4×D71—44no—
142C22×C71C22×Q811yescharacteristic
143C22×C71C2×#4111yescharacteristic
144C22×C71C2×#4111yescharacteristic
145C22×C71C2×#4111yescharacteristic
146C22×C71C2×#4111yescharacteristic
147C22×C71H(5,𝔽2)11yescharacteristic
148C22×C71H(5,𝔽2)11yescharacteristic
149C2×D71—22no—
150C2×D71—22no—
151C2×D71—22no—
152C2×D71—41no—
153C2×D71—41no—
154C2×D71—41no—
155C2×D71—41no—
156C4×C71—22no—
157C4×C71—22no—
158C4×C71—41no—
159C4×C71—41no—
160C4×C71—41no—
161C4×C71—41no—
162C4×C71—41no—
163Dic71—22no—
164Dic71—22no—
165Dic71—22no—
166Dic71—22no—
167Dic71—41no—
168Dic71—41no—
169Dic71—41no—
170C2×C71#52911yescharacteristic
171C2×C71#53311yescharacteristic
172C2×C71#54011yescharacteristic
173C2×C71#55111yescharacteristic
174C2×C71#55311yescharacteristic
175C2×C71#55411yescharacteristic
176C2×C71#55411yescharacteristic
177D71—42no—
178#2522—711nomaximal, Sylow
179C71#252211yescharacteristic, complemented, Sylow
180#399—711no—
181#398—711no—
182#398—711no—
183#396—711no—
184#389—711no—
185#389—711no—
186#388—711no—
187#388—711no—
188#387—711no—
189#387—711no—
190#387D7111yescharacteristic, complemented
191#385—711no—
192#380—711no—
193C4×C4⋊C4—711no—
194C4×C22⋊C4—711no—
195C23×C4—711no—
196C2×C4⋊C4—711no—
197C2×C4⋊C4—711no—
198C2×C4⋊C4—711no—
199C2×C4⋊C4—711no—
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⋊C4C2×D7111yescharacteristic
207C2×C4⋊C4C2×D7111yescharacteristic
208C2×C22⋊C4—711no—
209C2×C22⋊C4—711no—
210C2×C22⋊C4—711no—
211C2×C22⋊C4—711no—
212C2×C22⋊C4—711no—
213C2×C22⋊C4—711no—
214C2×C42—711no—
215C2×C42—711no—
216C2×C42—711no—
217C2×C42C2×D7111yescharacteristic
218#95—711no—
219#95—711no—
220#95—711no—
221#95—711no—
222#95—711no—
223#95—711no—
224#95—711no—
225#95—711no—
226#95C2×D7111yescharacteristic
227#95C2×D7111yescharacteristic
228#95C2×D7111yescharacteristic
229#95C2×D7111yescharacteristic
230C24—711no—
231C22×C4—2841no—
232C22×C4—711no—
233C22×C4—711no—
234C22×C4—711no—
235C22×C4—711no—
236C22×C4—711no—
237C22×C4—711no—
238C22×C4—711no—
239C22×C4—1422no—
240C22×C4—1422no—
241C22×C4C22×D7111yescharacteristic
242C22×C4C22×D7111yescharacteristic
243C22×C4C22×D7111yescharacteristic
244C22×C4C22×D7111yescharacteristic
245C22×C4C22×D7111yescharacteristic
246C22×C4C22×D7111yescharacteristic
247C22×C4C22×D7111yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—2841no—
251C4⋊C4—2841no—
252C4⋊C4—2841no—
253C4⋊C4—2841no—
254C4⋊C4—1422no—
255C4⋊C4—1422no—
256C4⋊C4—1422no—
257C4⋊C4—1422no—
258C4⋊C4—1422no—
259C4⋊C4—1422no—
260C22⋊C4—2841no—
261C22⋊C4—2841no—
262C22⋊C4—2841no—
263C22⋊C4—714no—
264C22⋊C4—1422no—
265C22⋊C4—1422no—
266C42—41no—
267C42—2841no—
268C42—2841no—
269C42—1422no—
270C23—712no—
271C23—1421no—
272C23—1421no—
273C23—1421no—
274C23—1421no—
275C23—1421no—
276C23—1421no—
277C23C23×D7111yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
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—2844no—
298C2×C4—712no—
299C2×C4—712no—
300C2×C4—712no—
301C2×C4—712no—
302C2×C4—1421no—
303C2×C4—1421no—
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×C4Q8×D7112yes—
320C2×C4#1176586512yes—
321C22—2841no—
322C22—2841no—
323C22—2841no—
324C22—2841no—
325C22—1422no—
326C22—1422no—
327C22—1422no—
328C22C2×Q8×D7111yescharacteristic
329C22#41×D7111yescharacteristic
330C22#41×D7111yescharacteristic
331C22#41×D7111yescharacteristic
332C22C2×#1176586511yescharacteristic
333C22#1455617311yescharacteristic
334C22#1455617411yescharacteristic
335C4—22no—
336C4—22no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—2841no—
343C4—2841no—
344C4—2841no—
345C4—1422no—
346C4—1422no—
347C4—1422no—
348C4—1422no—
349C2—2842no—
350C2#1798652711yescharacteristic
351C2#1798655511yescharacteristic
352C2#1798660111yescharacteristic
353C2#1798667811yescharacteristic
354C2#1798670011yescharacteristic
355C2#1798670311yescharacteristic
356C2#1798670911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#387×C71C2
hypercenter#387D71
hypocenterC71#2522
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #17985933C2semidirect
3. #17985933C2semidirect
5. #17985897C2semidirect
6. #17985894C2semidirect
9. #17985881C2semidirect
10. #17985880C2semidirect
13. #17985850C2semidirect
15. #387×C71C2semidirect
179. C71#2522semidirect
190. #387D71semidirect