Finite Group Databasebeta

← #22596080

Subgroups — #22596080

Order 9088.

416 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17985941C211yesmaximal, characteristic, complemented
2#17985940C211yesmaximal, characteristic, complemented
3#17985932C211yesmaximal, characteristic, complemented
4#17985923C211yesmaximal, characteristic
5#17985920C211yesmaximal, characteristic, complemented
6#17985912C211yesmaximal, characteristic
7#17985903C211yesmaximal, characteristic, complemented
8#17985897C211yesmaximal, characteristic, complemented
9#17985894C211yesmaximal, characteristic, complemented
10#17985891C211yesmaximal, characteristic
11#17985890C211yesmaximal, characteristic
12#17985873C211yesmaximal, characteristic
13#17985870C211yesmaximal, characteristic
14#17985856C211yesmaximal, characteristic
15#387×C71C211yesmaximal, characteristic, complemented
16C22×Dic142C2211yescharacteristic
17C22×C4×D71C2211yescharacteristic
18C2×C4⋊Dic71C2211yescharacteristic
19C2×C4⋊Dic71C2211yescharacteristic
20C2×C4⋊Dic71C2211yescharacteristic
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
34C71⋊#95C2211yescharacteristic
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×C42×C71C2211yescharacteristic
47#95×C71C2211yescharacteristic
48#95×C71C2211yescharacteristic
49#95×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51C23×D71C2311yescharacteristic
52C2×Dic142—22no—
53C2×Dic142—41no—
54C2×Dic142—41no—
55C22×Dic71C2311yescharacteristic
56C22×Dic71C2311yescharacteristic
57C22×Dic71C2311yescharacteristic
58C22×Dic71C2311yescharacteristic
59C22×Dic71C2311yescharacteristic
60C22×Dic71C2311yescharacteristic
61C22×Dic71C2311yescharacteristic
62C2×C4×D71—22no—
63C2×C4×D71—41no—
64C2×C4×D71—41no—
65C4⋊Dic71—22no—
66C4⋊Dic71—41no—
67C4⋊Dic71—41no—
68Dic71⋊C4—22no—
69Dic71⋊C4—41no—
70Dic71⋊C4—41no—
71Dic71⋊C4—41no—
72Dic71⋊C4—41no—
73Dic71⋊C4—41no—
74(C2×D71)⋊C4—22no—
75(C2×D71)⋊C4—41no—
76(C2×D71)⋊C4—41no—
77(C2×D71)⋊C4—41no—
78(C2×D71)⋊C4—41no—
79(C2×D71)⋊C4Q814yescomplemented
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×Dic71—21no—
138C2×Dic71—21no—
139C2×Dic71C2×Q812yes—
140C2×Dic71#4112yes—
141C4×D71—44no—
142Dic142—44no—
143C22×C71C22×Q811yescharacteristic
144C22×C71C2×#4111yescharacteristic
145C22×C71C2×#4111yescharacteristic
146C22×C71H(5,𝔽2)11yescharacteristic
147C22×C71H(5,𝔽2)11yescharacteristic
148C22×C71H(5,𝔽2)11yescharacteristic
149C22×C712−1+411yescharacteristic
150C2×D71—22no—
151C2×D71—22no—
152C2×D71—22no—
153C2×D71—41no—
154C2×D71—41no—
155C2×D71—41no—
156C2×D71—41no—
157C4×C71—22no—
158C4×C71—22no—
159C4×C71—41no—
160C4×C71—41no—
161C4×C71—41no—
162C4×C71—41no—
163C4×C71—41no—
164Dic71—22no—
165Dic71—22no—
166Dic71—41no—
167Dic71—41no—
168Dic71—41no—
169Dic71—41no—
170Dic71—41no—
171C2×C71#53811yescharacteristic
172C2×C71#53811yescharacteristic
173C2×C71#54411yescharacteristic
174C2×C71#55411yescharacteristic
175C2×C71#55411yescharacteristic
176C2×C71#55611yescharacteristic
177C2×C71#56211yescharacteristic
178D71—42no—
179#2788—711nomaximal, Sylow
180C71#278811yescharacteristic, complemented, Sylow
181#400—711no—
182#400—711no—
183#398—711no—
184#396—711no—
185#395—711no—
186#393—711no—
187#391—711no—
188#389—711no—
189#389—711no—
190#388—711no—
191#388—711no—
192#387D7111yescharacteristic, complemented
193#385—711no—
194#385—711no—
195#380—711no—
196C22×Q8—711no—
197C23×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⋊C4—711no—
207C2×C4⋊C4C2×D7111yescharacteristic
208C2×C4⋊C4C2×D7111yescharacteristic
209C2×C22⋊C4—711no—
210C2×C22⋊C4—711no—
211C2×C22⋊C4—711no—
212C2×C22⋊C4—711no—
213C2×C22⋊C4—711no—
214C2×C22⋊C4—711no—
215C2×C42—711no—
216C2×C42C2×D7111yescharacteristic
217#95—711no—
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#95—711no—
227#95C2×D7111yescharacteristic
228#95C2×D7111yescharacteristic
229#95C2×D7111yescharacteristic
230#95C2×D7111yescharacteristic
231C24—711no—
232C2×Q8—2841no—
233C2×Q8—2841no—
234C2×Q8—1422no—
235C22×C4—2841no—
236C22×C4—2841no—
237C22×C4—711no—
238C22×C4—711no—
239C22×C4—711no—
240C22×C4—711no—
241C22×C4—711no—
242C22×C4—711no—
243C22×C4—711no—
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—41no—
254C4⋊C4—2841no—
255C4⋊C4—2841no—
256C4⋊C4—2841no—
257C4⋊C4—2841no—
258C4⋊C4—2841no—
259C4⋊C4—2841no—
260C4⋊C4—2841no—
261C4⋊C4—1422no—
262C4⋊C4—1422no—
263C22⋊C4—2841no—
264C22⋊C4—2841no—
265C22⋊C4—2841no—
266C22⋊C4—2841no—
267C22⋊C4—714no—
268C22⋊C4—1422no—
269C42—41no—
270C42—2841no—
271C23—712no—
272C23—1421no—
273C23—1421no—
274C23—1421no—
275C23—1421no—
276C23—1421no—
277C23—1421no—
278C23C23×D7111yescharacteristic
279Q8—2844no—
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—21no—
298C2×C4—21no—
299C2×C4—2844no—
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×C4—1421no—
320C2×C4—1421no—
321C2×C4Q8×D7112yes—
322C2×C4#1176586512yes—
323C22—2841no—
324C22—2841no—
325C22—2841no—
326C22—2841no—
327C22—1422no—
328C22—1422no—
329C22—1422no—
330C22C2×Q8×D7111yescharacteristic
331C22#41×D7111yescharacteristic
332C22C2×#1176586511yescharacteristic
333C22#1455617311yescharacteristic
334C22#1455617411yescharacteristic
335C22#1455617411yescharacteristic
336C22#1455617511yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—2841no—
345C4—2841no—
346C4—2841no—
347C4—2841no—
348C4—2841no—
349C4—1422no—
350C4—1422no—
351C2—2842no—
352C2#1798658211yescharacteristic
353C2#1798658811yescharacteristic
354C2#1798662911yescharacteristic
355C2#1798670311yescharacteristic
356C2#1798670911yescharacteristic
357C2#1798671711yescharacteristic
358C2#1798674611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#387×C71C2
hypercenter#387D71
hypocenterC71#2788
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. #17985941C2semidirect
2. #17985940C2semidirect
3. #17985932C2semidirect
5. #17985920C2semidirect
7. #17985903C2semidirect
8. #17985897C2semidirect
9. #17985894C2semidirect
15. #387×C71C2semidirect
79. (C2×D71)⋊C4Q8semidirect
180. C71#2788semidirect
192. #387D71semidirect