Finite Group Databasebeta

← #22596024

Subgroups — #22596024

Order 9088.

378 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17985941C211yesmaximal, characteristic, complemented
2#17985929C211yesmaximal, characteristic, complemented
3#17985926C211yesmaximal, characteristic
4#17985926C211yesmaximal, characteristic
5#17985923C211yesmaximal, characteristic
6#17985923C211yesmaximal, characteristic
7#17985896C211yesmaximal, characteristic, complemented
8#17985895C211yesmaximal, characteristic, complemented
9#17985890C211yesmaximal, characteristic
10#17985889C211yesmaximal, characteristic
11#17985889C211yesmaximal, characteristic
12#17985883C211yesmaximal, characteristic, complemented
13#17985881C211yesmaximal, characteristic, complemented
14#17985863C211yesmaximal, characteristic, complemented
15#387×C71C211yesmaximal, characteristic, complemented
16C2×C4⋊Dic71C2211yescharacteristic
17C2×C4⋊Dic71C2211yescharacteristic
18C2×Dic71⋊C4C2211yescharacteristic
19C2×Dic71⋊C4C2211yescharacteristic
20C2×Dic71⋊C4C2211yescharacteristic
21C2×Dic71⋊C4C2211yescharacteristic
22C2×Dic71⋊C4C2211yescharacteristic
23C2×Dic71⋊C4C2211yescharacteristic
24C2×Dic71⋊C4C2211yescharacteristic
25C2×(C2×D71)⋊C4C2211yescharacteristic
26C2×(C2×D71)⋊C4C2211yescharacteristic
27C2×(C2×D71)⋊C4C2211yescharacteristic
28C2×(C2×D71)⋊C4C2211yescharacteristic
29C2×(C2×D71)⋊C4C2211yescharacteristic
30C2×(C2×D71)⋊C4C2211yescharacteristic
31C2×(C2×D71)⋊C4C2211yescharacteristic
32C2×C4×Dic71C2211yescharacteristic
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
52C22×Dic71C2311yescharacteristic
53C22×Dic71C2311yescharacteristic
54C22×Dic71C2311yescharacteristic
55C22×Dic71C2311yescharacteristic
56C22×Dic71C2311yescharacteristic
57C22×Dic71C2311yescharacteristic
58C22×Dic71C2311yescharacteristic
59C4⋊Dic71—22no—
60C4⋊Dic71—41no—
61Dic71⋊C4—22no—
62Dic71⋊C4—22no—
63Dic71⋊C4—22no—
64Dic71⋊C4—41no—
65Dic71⋊C4—41no—
66Dic71⋊C4—41no—
67Dic71⋊C4—41no—
68(C2×D71)⋊C4—22no—
69(C2×D71)⋊C4—22no—
70(C2×D71)⋊C4—22no—
71(C2×D71)⋊C4—41no—
72(C2×D71)⋊C4—41no—
73(C2×D71)⋊C4—41no—
74(C2×D71)⋊C4—41no—
75C4×Dic71—22no—
76C4×Dic71—41no—
77C22×C4×C71C2311yescharacteristic
78C22×C4×C71C2311yescharacteristic
79C22×C4×C71C2311yescharacteristic
80C22×C4×C71C2311yescharacteristic
81C22×C4×C71C2311yescharacteristic
82C22×C4×C71C2311yescharacteristic
83C22×C4×C71C2311yescharacteristic
84C4⋊C4×C71—22no—
85C4⋊C4×C71—41no—
86C42×C71—41no—
87C23×C71C2411yescharacteristic
88C22×D71—21no—
89C22×D71—21no—
90C22×D71—21no—
91C22×D71—21no—
92C22×D71—21no—
93C22×D71—21no—
94C22×D71—21no—
95C2×C4×C71—21no—
96C2×C4×C71—21no—
97C2×C4×C71—21no—
98C2×C4×C71—21no—
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#4112yes—
116C2×Dic71—21no—
117C2×Dic71—21no—
118C2×Dic71—21no—
119C2×Dic71—21no—
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#4112yes—
136C2×Dic71#4112yes—
137C22×C71C2×#4111yescharacteristic
138C22×C71C2×#4111yescharacteristic
139C22×C71C2×#4111yescharacteristic
140C22×C71H(5,𝔽2)11yescharacteristic
141C22×C71H(5,𝔽2)11yescharacteristic
142C22×C712−1+411yescharacteristic
143C22×C712−1+411yescharacteristic
144C2×D71—41no—
145C2×D71—41no—
146C2×D71—41no—
147C2×D71—41no—
148C2×D71—41no—
149C2×D71—41no—
150C2×D71—41no—
151C4×C71—22no—
152C4×C71—41no—
153C4×C71—41no—
154C4×C71—41no—
155C4×C71—41no—
156C4×C71—41no—
157C4×C71—41no—
158Dic71—22no—
159Dic71—22no—
160Dic71—41no—
161Dic71—41no—
162Dic71—41no—
163Dic71—41no—
164Dic71—41no—
165C2×C71#53911yescharacteristic
166C2×C71#53911yescharacteristic
167C2×C71#54111yescharacteristic
168C2×C71#55311yescharacteristic
169C2×C71#55511yescharacteristic
170C2×C71#55611yescharacteristic
171C2×C71#56211yescharacteristic
172D71—81no—
173#2783—711nomaximal, Sylow
174C71#278311yescharacteristic, complemented, Sylow
175#400—711no—
176#398—711no—
177#397—711no—
178#397—711no—
179#396—711no—
180#396—711no—
181#389—711no—
182#389—711no—
183#388—711no—
184#388—711no—
185#388—711no—
186#387—711no—
187#387—711no—
188#387D7111yescharacteristic, complemented
189#382—711no—
190C2×C4⋊C4—711no—
191C2×C4⋊C4—711no—
192C2×C4⋊C4—711no—
193C2×C4⋊C4—711no—
194C2×C4⋊C4—711no—
195C2×C4⋊C4—711no—
196C2×C4⋊C4—711no—
197C2×C4⋊C4—711no—
198C2×C4⋊C4—711no—
199C2×C4⋊C4C2×D7111yescharacteristic
200C2×C4⋊C4C2×D7111yescharacteristic
201C2×C22⋊C4—711no—
202C2×C22⋊C4—711no—
203C2×C22⋊C4—711no—
204C2×C22⋊C4—711no—
205C2×C22⋊C4—711no—
206C2×C22⋊C4—711no—
207C2×C22⋊C4—711no—
208C2×C42—711no—
209C2×C42—711no—
210C2×C42C2×D7111yescharacteristic
211#95—711no—
212#95—711no—
213#95—711no—
214#95—711no—
215#95—711no—
216#95—711no—
217#95—711no—
218#95—711no—
219#95—711no—
220#95—711no—
221#95C2×D7111yescharacteristic
222#95C2×D7111yescharacteristic
223#95C2×D7111yescharacteristic
224#95C2×D7111yescharacteristic
225C24—711no—
226C22×C4—711no—
227C22×C4—711no—
228C22×C4—711no—
229C22×C4—711no—
230C22×C4—711no—
231C22×C4—711no—
232C22×C4—711no—
233C22×C4C22×D7111yescharacteristic
234C22×C4C22×D7111yescharacteristic
235C22×C4C22×D7111yescharacteristic
236C22×C4C22×D7111yescharacteristic
237C22×C4C22×D7111yescharacteristic
238C22×C4C22×D7111yescharacteristic
239C22×C4C22×D7111yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—41no—
242C4⋊C4—2841no—
243C4⋊C4—2841no—
244C4⋊C4—2841no—
245C4⋊C4—2841no—
246C4⋊C4—2841no—
247C4⋊C4—1422no—
248C4⋊C4—1422no—
249C4⋊C4—1422no—
250C4⋊C4—1422no—
251C22⋊C4—2841no—
252C22⋊C4—2841no—
253C22⋊C4—2841no—
254C22⋊C4—2841no—
255C22⋊C4—1422no—
256C22⋊C4—1422no—
257C22⋊C4—1422no—
258C42—41no—
259C42—2841no—
260C42—1422no—
261C23—1421no—
262C23—1421no—
263C23—1421no—
264C23—1421no—
265C23—1421no—
266C23—1421no—
267C23—1421no—
268C23C23×D7111yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
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—712no—
290C2×C4—712no—
291C2×C4—1421no—
292C2×C4—1421no—
293C2×C4—1421no—
294C2×C4—1421no—
295C2×C4—1421no—
296C2×C4—1421no—
297C2×C4—1421no—
298C2×C4—1421no—
299C2×C4—1421no—
300C2×C4—1421no—
301C2×C4—1421no—
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#1176586512yes—
311C22—2841no—
312C22—2841no—
313C22—2841no—
314C22—2841no—
315C22—2841no—
316C22—2841no—
317C22—2841no—
318C22#41×D7111yescharacteristic
319C22#41×D7111yescharacteristic
320C22C2×#1176586511yescharacteristic
321C22#1455617311yescharacteristic
322C22#1455617411yescharacteristic
323C22#1455617511yescharacteristic
324C22#1455617611yescharacteristic
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—2841no—
333C4—2841no—
334C4—2841no—
335C4—2841no—
336C4—2841no—
337C4—1422no—
338C4—1422no—
339C2—5681no—
340C2#1798659011yescharacteristic
341C2#1798659111yescharacteristic
342C2#1798660811yescharacteristic
343C2#1798669411yescharacteristic
344C2#1798671211yescharacteristic
345C2#1798672111yescharacteristic
346C2#1798674511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#387×C71C2
hypercenter#387D71
hypocenterC71#2783
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. #17985941C2semidirect
2. #17985929C2semidirect
7. #17985896C2semidirect
8. #17985895C2semidirect
12. #17985883C2semidirect
13. #17985881C2semidirect
14. #17985863C2semidirect
15. #387×C71C2semidirect
174. C71#2783semidirect
188. #387D71semidirect