Finite Group Databasebeta

← #22591083

Subgroups — #22591083

Order 9088.

460 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556126C211yesmaximal, characteristic
2#17985906C211yesmaximal, characteristic
3#17985903C211yesmaximal, characteristic
4#17985903C211yesmaximal, characteristic
5#17985896C211yesmaximal, characteristic
6#17985894C211yesmaximal, characteristic
7#17985886C211yesmaximal, characteristic
8#17985883C211yesmaximal, characteristic
9#17985881C211yesmaximal, characteristic
10#17985880C211yesmaximal, characteristic
11#17985863C211yesmaximal, characteristic
12C4×Dic71⋊C4C211yesmaximal, characteristic
13#17985850C211yesmaximal, characteristic
14#17985844C211yesmaximal, characteristic
15#391×C71C211yesmaximal, characteristic
16C22×Dic142C2211yescharacteristic
17#14556126C418yescomplemented
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×C4×Dic71C2211yescharacteristic
28C2×C4×Dic71C2211yescharacteristic
29C2×C4×Dic71C2211yescharacteristic
30C2×C4×Dic71C2211yescharacteristic
31C2×C4×Dic71C2211yescharacteristic
32C2×C4×Dic71C2211yescharacteristic
33C71⋊#95C2211yescharacteristic
34C71⋊#95C2211yescharacteristic
35C71⋊#95C2211yescharacteristic
36C71⋊#95C2211yescharacteristic
37C71⋊#95C2211yescharacteristic
38C71⋊#95C2211yescharacteristic
39C71⋊#95C2211yescharacteristic
40C71⋊#95C2211yescharacteristic
41C71⋊#95C2211yescharacteristic
42C71⋊#95C2211yescharacteristic
43C71⋊#95C2211yescharacteristic
44C71⋊#95C2211yescharacteristic
45C22×Q8×C71C2211yescharacteristic
46C2×C4⋊C4×C71C2211yescharacteristic
47C2×C42×C71C2211yescharacteristic
48#95×C71C2211yescharacteristic
49#95×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51#95×C71C2211yescharacteristic
52C2×Dic142—41no—
53C2×Dic142—41no—
54C2×Dic142C2×C414yes—
55C22×Dic71C2311yescharacteristic
56C22×Dic71C2311yescharacteristic
57C22×Dic71C2311yescharacteristic
58C22×Dic71C2311yescharacteristic
59C22×Dic71C2311yescharacteristic
60C22×Dic71C2311yescharacteristic
61C22×Dic71C2311yescharacteristic
62C22×Dic71C2311yescharacteristic
63C4⋊Dic71—41no—
64Dic71⋊C4—22no—
65Dic71⋊C4—22no—
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×Dic71Q814yescomplemented
78C2×Q8×C71—41no—
79C2×Q8×C71—41no—
80C2×Q8×C71C2×C414yes—
81C22×C4×C71C2311yescharacteristic
82C22×C4×C71C2311yescharacteristic
83C22×C4×C71C2311yescharacteristic
84C22×C4×C71C2311yescharacteristic
85C22×C4×C71C2311yescharacteristic
86C22×C4×C71C2311yescharacteristic
87C22×C4×C71C2311yescharacteristic
88C4⋊C4×C71—41no—
89C42×C71—41no—
90C23×C71C2411yescharacteristic
91Q8×C71—44no—
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×C71—21no—
109C2×C4×C71C22×C412yes—
110C2×C4×C71C22×C412yes—
111C2×C4×C71C22×C412yes—
112C2×C4×C71C2×Q812yes—
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×Dic71—21no—
130C2×Dic71C22×C412yes—
131C2×Dic71C22×C412yes—
132C2×Dic71C22×C412yes—
133C2×Dic71C22×C412yes—
134C2×Dic71C2×Q812yes—
135C2×Dic71C2×Q812yes—
136C2×Dic71#4112yes—
137Dic142—44no—
138C22×C71C23×C411yescharacteristic
139C22×C71C22×Q811yescharacteristic
140C22×C71C2×#4111yescharacteristic
141C22×C71H(5,𝔽2)11yescharacteristic
142C22×C71H(5,𝔽2)11yescharacteristic
143C22×C712−1+411yescharacteristic
144C22×C712−1+411yescharacteristic
145C4×C71—22no—
146C4×C71—22no—
147C4×C71—22no—
148C4×C71—22no—
149C4×C71—41no—
150C4×C71—41no—
151C4×C71—41no—
152Dic71—22no—
153Dic71—22no—
154Dic71—22no—
155Dic71—22no—
156Dic71—41no—
157Dic71—41no—
158Dic71—41no—
159Dic71C4×Q814yes—
160C2×C71C2×C4×Q811yescharacteristic
161C2×C71#51811yescharacteristic
162C2×C71#51911yescharacteristic
163C2×C71#54211yescharacteristic
164C2×C71#54211yescharacteristic
165C2×C71#54411yescharacteristic
166C2×C71#54411yescharacteristic
167#2331—711nomaximal, Sylow
168C71#233111yescharacteristic, complemented, Sylow
169C2×C4⋊Q8—711no—
170#391—711no—
171#391—711no—
172#391—711no—
173#391D7111yescharacteristic
174#389—711no—
175#389—711no—
176#387—711no—
177#387—711no—
178#387—711no—
179#387—711no—
180#382—711no—
181C4×C4⋊C4—711no—
182C4×C4⋊C4—711no—
183#376—711no—
184C22×Q8—711no—
185C22×Q8C2×D7111yescharacteristic
186C4⋊Q8—718no—
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⋊C4—711no—
196C2×C4⋊C4C2×D7111yescharacteristic
197C2×C42—711no—
198C2×C42—711no—
199C2×C42—711no—
200C2×C42—711no—
201C2×C42—711no—
202C2×C42—711no—
203C2×C42C2×D7111yescharacteristic
204#95—711no—
205#95—711no—
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
218#95C2×D7111yescharacteristic
219#95C2×D7111yescharacteristic
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—2841no—
223C2×Q8—2841no—
224C2×Q8—714no—
225C2×Q8C4×D7114yes—
226C22×C4—711no—
227C22×C4—711no—
228C22×C4—711no—
229C22×C4—711no—
230C22×C4—711no—
231C22×C4—711no—
232C22×C4—711no—
233C22×C4—711no—
234C22×C4C22×D7111yescharacteristic
235C22×C4C22×D7111yescharacteristic
236C22×C4C22×D7111yescharacteristic
237C22×C4C22×D7111yescharacteristic
238C22×C4C22×D7111yescharacteristic
239C22×C4C22×D7111yescharacteristic
240C22×C4C22×D7111yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—2841no—
243C4⋊C4—2841no—
244C4⋊C4—2841no—
245C4⋊C4—714no—
246C4⋊C4—714no—
247C4⋊C4—714no—
248C4⋊C4—714no—
249C4⋊C4—1422no—
250C4⋊C4—1422no—
251C42—41no—
252C42—2841no—
253C42—2841no—
254C42—2841no—
255C42—714no—
256C42—714no—
257C42—1422no—
258C23C23×D7111yescharacteristic
259Q8—44no—
260Q8—2844no—
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—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—712no—
279C2×C4—712no—
280C2×C4—712no—
281C2×C4—712no—
282C2×C4—712no—
283C2×C4—712no—
284C2×C4—712no—
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×C4—1421no—
299C2×C4—1421no—
300C2×C4—1421no—
301C2×C4—1421no—
302C2×C4C2×C4×D7112yes—
303C2×C4C2×C4×D7112yes—
304C2×C4C2×C4×D7112yes—
305C2×C4Q8×D7112yes—
306C22C22×C4×D7111yescharacteristic
307C22C2×Q8×D7111yescharacteristic
308C22#41×D7111yescharacteristic
309C22#1455617311yescharacteristic
310C22#1455617311yescharacteristic
311C22#1455617511yescharacteristic
312C22#1455617611yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—2841no—
321C4—2841no—
322C4—2841no—
323C4—714no—
324C4—1422no—
325C4—1422no—
326C4—1422no—
327C4—1422no—
328C2C4×Q8×D7111yescharacteristic
329C2#1798647211yescharacteristic
330C2#1798647511yescharacteristic
331C2#1798661311yescharacteristic
332C2#1798661911yescharacteristic
333C2#1798662611yescharacteristic
334C2#1798662811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutatorC22×C71C23×C4
Fitting#391×C71C2
socleC23×C71C24
hypercenter#391D71
hypocenterC71#2331
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
17. #14556126C4semidirect
77. C4×Dic71Q8semidirect
168. C71#2331semidirect