Finite Group Databasebeta

← #22596503

Subgroups — #22596503

Order 9088.

366 conjugacy classes of subgroups.

The subgroup lattice has 350 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#17985937C211yesmaximal, characteristic, complemented
4#17985929C211yesmaximal, characteristic, complemented
5#17985928C211yesmaximal, characteristic
6#17985925C211yesmaximal, characteristic
7#17985925C211yesmaximal, characteristic
8#17985923C211yesmaximal, characteristic
9#17985921C211yesmaximal, characteristic
10#17985919C211yesmaximal, characteristic, complemented
11#17985912C211yesmaximal, characteristic
12#17985903C211yesmaximal, characteristic, complemented
13#17985889C211yesmaximal, characteristic
14#17985880C211yesmaximal, characteristic, complemented
15#398×C71C211yesmaximal, characteristic, complemented
16C22×Dic142C2211yescharacteristic
17C2×C4⋊Dic71C2211yescharacteristic
18C2×Dic71⋊C4C2211yescharacteristic
19C2×Dic71⋊C4C2211yescharacteristic
20C2×Dic71⋊C4C2211yescharacteristic
21C2×Dic71⋊C4C2211yescharacteristic
22C2×Dic71⋊C4C2211yescharacteristic
23C2×(C2×D71)⋊C4C2211yescharacteristic
24C2×(C2×D71)⋊C4C2211yescharacteristic
25C2×(C2×D71)⋊C4C2211yescharacteristic
26C2×(C2×D71)⋊C4C2211yescharacteristic
27C2×(C2×D71)⋊C4C2211yescharacteristic
28C2×(C2×D71)⋊C4C2211yescharacteristic
29C2×(C2×D71)⋊C4C2211yescharacteristic
30C2×C4×Dic71C2211yescharacteristic
31C71⋊#95C2211yescharacteristic
32C71⋊#95C2211yescharacteristic
33C71⋊#95C2211yescharacteristic
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×C4⋊C4×C71C2211yescharacteristic
47C2×C4⋊C4×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
62C4⋊Dic71—41no—
63Dic71⋊C4—22no—
64Dic71⋊C4—41no—
65Dic71⋊C4—41no—
66Dic71⋊C4—41no—
67Dic71⋊C4—41no—
68(C2×D71)⋊C4—22no—
69(C2×D71)⋊C4—41no—
70(C2×D71)⋊C4—41no—
71(C2×D71)⋊C4—41no—
72(C2×D71)⋊C4—41no—
73(C2×D71)⋊C4—41no—
74(C2×D71)⋊C4—41no—
75C4×Dic71—41no—
76C22×C4×C71C2311yescharacteristic
77C22×C4×C71C2311yescharacteristic
78C22×C4×C71C2311yescharacteristic
79C22×C4×C71C2311yescharacteristic
80C22×C4×C71C2311yescharacteristic
81C22×C4×C71C2311yescharacteristic
82C22×C4×C71C2311yescharacteristic
83C4⋊C4×C71—41no—
84C4⋊C4×C71—41no—
85C4⋊C4×C71—41no—
86C4⋊C4×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—21no—
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—21no—
136C2×Dic71#4112yes—
137Dic142—44no—
138C22×C71C2×#4111yescharacteristic
139C22×C71H(5,𝔽2)11yescharacteristic
140C22×C71H(5,𝔽2)11yescharacteristic
141C22×C71H(5,𝔽2)11yescharacteristic
142C22×C712−1+411yescharacteristic
143C22×C712−1+411yescharacteristic
144C22×C712−1+411yescharacteristic
145C2×D71—41no—
146C2×D71—41no—
147C2×D71—41no—
148C2×D71—41no—
149C2×D71—41no—
150C2×D71—41no—
151C2×D71—41no—
152C4×C71—41no—
153C4×C71—41no—
154C4×C71—41no—
155C4×C71—41no—
156C4×C71—41no—
157C4×C71—41no—
158C4×C71—41no—
159Dic71—22no—
160Dic71—41no—
161Dic71—41no—
162Dic71—41no—
163Dic71—41no—
164Dic71—41no—
165Dic71—41no—
166C2×C71#53811yescharacteristic
167C2×C71#54111yescharacteristic
168C2×C71#54211yescharacteristic
169C2×C71#56211yescharacteristic
170C2×C71#56211yescharacteristic
171C2×C71#56311yescharacteristic
172C2×C71#56311yescharacteristic
173D71—81no—
174#2831—711nomaximal, Sylow
175C71#283111yescharacteristic, complemented, Sylow
176#400—711no—
177#400—711no—
178#400—711no—
179#398—711no—
180#398D7111yescharacteristic, complemented
181#397—711no—
182#397—711no—
183#397—711no—
184#396—711no—
185#396—711no—
186#395—711no—
187#393—711no—
188#391—711no—
189#388—711no—
190#387—711no—
191C22×Q8—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⋊C4C2×D7111yescharacteristic
199C2×C4⋊C4C2×D7111yescharacteristic
200C2×C4⋊C4C2×D7111yescharacteristic
201C2×C4⋊C4C2×D7111yescharacteristic
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×C22⋊C4—711no—
209C2×C42—711no—
210#95—711no—
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#95—711no—
222#95—711no—
223#95C2×D7111yescharacteristic
224#95C2×D7111yescharacteristic
225#95C2×D7111yescharacteristic
226C24—711no—
227C2×Q8—2841no—
228C2×Q8—2841no—
229C2×Q8—1422no—
230C22×C4—711no—
231C22×C4—711no—
232C22×C4—711no—
233C22×C4—711no—
234C22×C4—711no—
235C22×C4—711no—
236C22×C4—711no—
237C22×C4C22×D7111yescharacteristic
238C22×C4C22×D7111yescharacteristic
239C22×C4C22×D7111yescharacteristic
240C22×C4C22×D7111yescharacteristic
241C22×C4C22×D7111yescharacteristic
242C22×C4C22×D7111yescharacteristic
243C22×C4C22×D7111yescharacteristic
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—2841no—
249C4⋊C4—2841no—
250C4⋊C4—2841no—
251C4⋊C4—2841no—
252C4⋊C4—2841no—
253C4⋊C4—1422no—
254C22⋊C4—2841no—
255C22⋊C4—2841no—
256C22⋊C4—2841no—
257C22⋊C4—2841no—
258C22⋊C4—2841no—
259C22⋊C4—2841no—
260C22⋊C4—1422no—
261C42—2841no—
262C23—1421no—
263C23—1421no—
264C23—1421no—
265C23—1421no—
266C23—1421no—
267C23—1421no—
268C23—1421no—
269C23C23×D7111yescharacteristic
270Q8—2844no—
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—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—712no—
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—1421no—
311C2×C4—1421no—
312C2×C4—1421no—
313C22—2841no—
314C22—2841no—
315C22—2841no—
316C22—2841no—
317C22—2841no—
318C22—2841no—
319C22—2841no—
320C22#41×D7111yescharacteristic
321C22#1455617311yescharacteristic
322C22#1455617311yescharacteristic
323C22#1455617411yescharacteristic
324C22#1455617511yescharacteristic
325C22#1455617611yescharacteristic
326C22#1455617611yescharacteristic
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—2841no—
335C4—2841no—
336C4—2841no—
337C4—2841no—
338C4—2841no—
339C4—2841no—
340C4—1422no—
341C2—5681no—
342C2#1798658511yescharacteristic
343C2#1798660811yescharacteristic
344C2#1798661911yescharacteristic
345C2#1798674411yescharacteristic
346C2#1798674511yescharacteristic
347C2#1798674811yescharacteristic
348C2#1798675311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#398×C71C2
hypercenter#398D71
hypocenterC71#2831
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #17985941C2semidirect
2. #17985940C2semidirect
3. #17985937C2semidirect
4. #17985929C2semidirect
10. #17985919C2semidirect
12. #17985903C2semidirect
14. #17985880C2semidirect
15. #398×C71C2semidirect
175. C71#2831semidirect
180. #398D71semidirect