Finite Group Databasebeta

← #22591078

Subgroups — #22591078

Order 9088.

444 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556118C211yesmaximal, characteristic
2#17985896C211yesmaximal, characteristic
3#17985895C211yesmaximal, characteristic
4#17985894C211yesmaximal, characteristic
5#17985894C211yesmaximal, characteristic
6#17985894C211yesmaximal, characteristic
7#17985885C211yesmaximal, characteristic
8#17985883C211yesmaximal, characteristic
9#17985882C211yesmaximal, characteristic
10#17985880C211yesmaximal, characteristic
11#17985868C211yesmaximal, characteristic
12C4×Dic71⋊C4C211yesmaximal, characteristic
13#17985850C211yesmaximal, characteristic
14#17985844C211yesmaximal, characteristic
15#389×C71C211yesmaximal, characteristic
16#14556118C418yescomplemented
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×Dic71⋊C4C2211yescharacteristic
28C2×Dic71⋊C4C2211yescharacteristic
29C2×C4×Dic71C2211yescharacteristic
30C2×C4×Dic71C2211yescharacteristic
31C2×C4×Dic71C2211yescharacteristic
32C2×C4×Dic71C2211yescharacteristic
33C2×C4×Dic71C2211yescharacteristic
34C2×C4×Dic71C2211yescharacteristic
35C71⋊#95C2211yescharacteristic
36C71⋊#95C2211yescharacteristic
37C71⋊#95C2211yescharacteristic
38C71⋊#95C2211yescharacteristic
39C71⋊#95C2211yescharacteristic
40C71⋊#95C2211yescharacteristic
41C71⋊#95C2211yescharacteristic
42C71⋊#95C2211yescharacteristic
43C71⋊#95C2211yescharacteristic
44C71⋊#95C2211yescharacteristic
45C2×C4⋊C4×C71C2211yescharacteristic
46C2×C4⋊C4×C71C2211yescharacteristic
47C2×C4⋊C4×C71C2211yescharacteristic
48C2×C4⋊C4×C71C2211yescharacteristic
49C2×C42×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51#95×C71C2211yescharacteristic
52C22×Dic71C2311yescharacteristic
53C22×Dic71C2311yescharacteristic
54C22×Dic71C2311yescharacteristic
55C22×Dic71C2311yescharacteristic
56C22×Dic71C2311yescharacteristic
57C22×Dic71C2311yescharacteristic
58C22×Dic71C2311yescharacteristic
59C22×Dic71C2311yescharacteristic
60C4⋊Dic71—41no—
61C4⋊Dic71C2×C414yes—
62Dic71⋊C4—22no—
63Dic71⋊C4—22no—
64Dic71⋊C4—41no—
65Dic71⋊C4—41no—
66Dic71⋊C4—41no—
67Dic71⋊C4—41no—
68Dic71⋊C4C2×C414yes—
69Dic71⋊C4C2×C414yes—
70Dic71⋊C4C2×C414yes—
71Dic71⋊C4C2×C414yes—
72C4×Dic71—22no—
73C4×Dic71—41no—
74C4×Dic71—41no—
75C4×Dic71—41no—
76C4×Dic71C2×C414yes—
77C4×Dic71Q814yes—
78C22×C4×C71C2311yescharacteristic
79C22×C4×C71C2311yescharacteristic
80C22×C4×C71C2311yescharacteristic
81C22×C4×C71C2311yescharacteristic
82C22×C4×C71C2311yescharacteristic
83C22×C4×C71C2311yescharacteristic
84C22×C4×C71C2311yescharacteristic
85C4⋊C4×C71—41no—
86C4⋊C4×C71—41no—
87C4⋊C4×C71—41no—
88C4⋊C4×C71C2×C414yes—
89C42×C71—41no—
90C23×C71C2411yescharacteristic
91C2×C4×C71—21no—
92C2×C4×C71—21no—
93C2×C4×C71—21no—
94C2×C4×C71—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×C71C22×C412yes—
109C2×C4×C71C22×C412yes—
110C2×C4×C71C22×C412yes—
111C2×C4×C71C2×Q812yes—
112C2×Dic71—21no—
113C2×Dic71—21no—
114C2×Dic71—21no—
115C2×Dic71—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×Dic71C22×C412yes—
130C2×Dic71C22×C412yes—
131C2×Dic71C22×C412yes—
132C2×Dic71C22×C412yes—
133C2×Dic71C2×Q812yes—
134C2×Dic71C2×Q812yes—
135C2×Dic71#4112yes—
136C22×C71C23×C411yescharacteristic
137C22×C71C22×Q811yescharacteristic
138C22×C71C2×#4111yescharacteristic
139C22×C71H(5,𝔽2)11yescharacteristic
140C22×C71H(5,𝔽2)11yescharacteristic
141C22×C712−1+411yescharacteristic
142C22×C712−1+411yescharacteristic
143C4×C71—22no—
144C4×C71—22no—
145C4×C71—22no—
146C4×C71—22no—
147C4×C71—41no—
148C4×C71—41no—
149C4×C71—41no—
150Dic71—22no—
151Dic71—22no—
152Dic71—22no—
153Dic71—22no—
154Dic71—41no—
155Dic71—41no—
156Dic71—41no—
157Dic71C4×Q814yes—
158C2×C71C2×C4×Q811yescharacteristic
159C2×C71#52011yescharacteristic
160C2×C71#52011yescharacteristic
161C2×C71#54011yescharacteristic
162C2×C71#54111yescharacteristic
163C2×C71#54411yescharacteristic
164C2×C71#54411yescharacteristic
165#2330—711nomaximal, Sylow
166C71#233011yescharacteristic, complemented, Sylow
167C2×#125—711no—
168#389—711no—
169#389—711no—
170#389—711no—
171#389—711no—
172#389—711no—
173#389D7111yescharacteristic
174#387—711no—
175#387—711no—
176#387—711no—
177#387—711no—
178#384—711no—
179C4×C4⋊C4—711no—
180C4×C4⋊C4—711no—
181#376—711no—
182#125—718no—
183C2×C4⋊C4—711no—
184C2×C4⋊C4—711no—
185C2×C4⋊C4—711no—
186C2×C4⋊C4—711no—
187C2×C4⋊C4—711no—
188C2×C4⋊C4—711no—
189C2×C4⋊C4—711no—
190C2×C4⋊C4—711no—
191C2×C4⋊C4—711no—
192C2×C4⋊C4—711no—
193C2×C4⋊C4—711no—
194C2×C4⋊C4—711no—
195C2×C4⋊C4C2×D7111yescharacteristic
196C2×C4⋊C4C2×D7111yescharacteristic
197C2×C4⋊C4C2×D7111yescharacteristic
198C2×C4⋊C4C2×D7111yescharacteristic
199C2×C42—711no—
200C2×C42—711no—
201C2×C42—711no—
202C2×C42—711no—
203C2×C42—711no—
204C2×C42—711no—
205C2×C42C2×D7111yescharacteristic
206#95—711no—
207#95—711no—
208#95—711no—
209#95—711no—
210#95—711no—
211#95—711no—
212#95—711no—
213#95—711no—
214#95—711no—
215#95—711no—
216#95C2×D7111yescharacteristic
217#95C2×D7111yescharacteristic
218C22×C4—711no—
219C22×C4—711no—
220C22×C4—711no—
221C22×C4—711no—
222C22×C4—711no—
223C22×C4—711no—
224C22×C4—711no—
225C22×C4—711no—
226C22×C4C22×D7111yescharacteristic
227C22×C4C22×D7111yescharacteristic
228C22×C4C22×D7111yescharacteristic
229C22×C4C22×D7111yescharacteristic
230C22×C4C22×D7111yescharacteristic
231C22×C4C22×D7111yescharacteristic
232C22×C4C22×D7111yescharacteristic
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—2841no—
237C4⋊C4—2841no—
238C4⋊C4—2841no—
239C4⋊C4—2841no—
240C4⋊C4—2841no—
241C4⋊C4—714no—
242C4⋊C4—714no—
243C4⋊C4—714no—
244C4⋊C4—714no—
245C4⋊C4—714no—
246C4⋊C4—1422no—
247C4⋊C4—1422no—
248C4⋊C4C4×D7114yes—
249C42—41no—
250C42—2841no—
251C42—2841no—
252C42—2841no—
253C42—714no—
254C42—714no—
255C42—1422no—
256C23C23×D7111yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—712no—
275C2×C4—712no—
276C2×C4—712no—
277C2×C4—712no—
278C2×C4—712no—
279C2×C4—712no—
280C2×C4—712no—
281C2×C4—1421no—
282C2×C4—1421no—
283C2×C4—1421no—
284C2×C4—1421no—
285C2×C4—1421no—
286C2×C4—1421no—
287C2×C4—1421no—
288C2×C4—1421no—
289C2×C4—1421no—
290C2×C4—1421no—
291C2×C4—1421no—
292C2×C4—1421no—
293C2×C4—1421no—
294C2×C4—1421no—
295C2×C4—1421no—
296C2×C4—1421no—
297C2×C4—1421no—
298C2×C4C2×C4×D7112yes—
299C2×C4C2×C4×D7112yes—
300C2×C4C2×C4×D7112yes—
301C2×C4Q8×D7112yes—
302C22C22×C4×D7111yescharacteristic
303C22C2×Q8×D7111yescharacteristic
304C22#41×D7111yescharacteristic
305C22#1455617311yescharacteristic
306C22#1455617311yescharacteristic
307C22#1455617511yescharacteristic
308C22#1455617611yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—2841no—
317C4—2841no—
318C4—2841no—
319C4—714no—
320C4—1422no—
321C4—1422no—
322C4—1422no—
323C4—1422no—
324C2C4×Q8×D7111yescharacteristic
325C2#1798647811yescharacteristic
326C2#1798648011yescharacteristic
327C2#1798659911yescharacteristic
328C2#1798660811yescharacteristic
329C2#1798662611yescharacteristic
330C2#1798662811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutatorC22×C71C23×C4
Fitting#389×C71C2
socleC23×C71C24
hypercenter#389D71
hypocenterC71#2330
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
16. #14556118C4semidirect
166. C71#2330semidirect