Finite Group Databasebeta

← #22592315

Subgroups — #22592315

Order 9088.

452 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×#14556118C211yesmaximal, characteristic
2C2×Q8×Dic71C211yesmaximal, characteristic
3#17985933C211yesmaximal, characteristic
4#17985932C211yesmaximal, characteristic
5#17985918C211yesmaximal, characteristic
6#17985896C211yesmaximal, characteristic
7#17985894C211yesmaximal, characteristic
8#17985885C211yesmaximal, characteristic
9#17985884C211yesmaximal, characteristic
10#17985882C211yesmaximal, characteristic
11#17985882C211yesmaximal, characteristic
12#17985881C211yesmaximal, characteristic
13#17985880C211yesmaximal, characteristic
14C4⋊C4×Dic71C211yesmaximal, characteristic
15#395×C71C211yesmaximal, characteristic
16#14556118—24no—
17Q8×Dic71—24no—
18C2×C4⋊Dic71C2211yescharacteristic
19C2×C4⋊Dic71C2211yescharacteristic
20C2×C4⋊Dic71C2211yescharacteristic
21C2×C4⋊Dic71C2211yescharacteristic
22C2×Dic71⋊C4C2211yescharacteristic
23C2×Dic71⋊C4C2211yescharacteristic
24C2×Dic71⋊C4C2211yescharacteristic
25C2×Dic71⋊C4C2211yescharacteristic
26C2×Dic71⋊C4C2211yescharacteristic
27C2×Dic71⋊C4C2211yescharacteristic
28C2×Dic71⋊C4C2211yescharacteristic
29C2×Dic71⋊C4C2211yescharacteristic
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
45C71⋊#95C2211yescharacteristic
46C22×Q8×C71C2211yescharacteristic
47C2×C4⋊C4×C71C2211yescharacteristic
48C2×C4⋊C4×C71C2211yescharacteristic
49C2×C4⋊C4×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51#95×C71C2211yescharacteristic
52#95×C71C2211yescharacteristic
53C22×Dic71C2311yescharacteristic
54C22×Dic71C2311yescharacteristic
55C22×Dic71C2311yescharacteristic
56C22×Dic71C2311yescharacteristic
57C22×Dic71C2311yescharacteristic
58C22×Dic71C2311yescharacteristic
59C22×Dic71C2311yescharacteristic
60C22×Dic71C2311yescharacteristic
61C4⋊Dic71—22no—
62C4⋊Dic71—22no—
63C4⋊Dic71D414yes—
64C4⋊Dic71Q814yescomplemented
65Dic71⋊C4—22no—
66Dic71⋊C4—22no—
67Dic71⋊C4—22no—
68Dic71⋊C4—22no—
69Dic71⋊C4—22no—
70Dic71⋊C4—22no—
71Dic71⋊C4—22no—
72Dic71⋊C4—22no—
73C4×Dic71—22no—
74C4×Dic71—22no—
75C4×Dic71—22no—
76C4×Dic71—22no—
77C4×Dic71—22no—
78C2×Q8×C71—22no—
79C2×Q8×C71—22no—
80C2×Q8×C71—22no—
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—22no—
90C4⋊C4×C71—22no—
91C23×C71C2411yescharacteristic
92Q8×C71—28no—
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×C71—21no—
110C2×C4×C71C2×D412yes—
111C2×C4×C71C2×Q812yes—
112C2×C4×C71#4112yes—
113C2×C4×C71#4112yes—
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×Dic71—21no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71C2×D412yes—
134C2×Dic71C2×D412yes—
135C2×Dic71C2×Q812yes—
136C2×Dic71C2×Q812yes—
137C2×Dic71#4112yes—
138C22×C71C22×D411yescharacteristic
139C22×C71C22×Q811yescharacteristic
140C22×C71C2×#4111yescharacteristic
141C22×C71C2×#4111yescharacteristic
142C22×C71C2×#4111yescharacteristic
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—22no—
157Dic71—41no—
158Dic71—41no—
159Dic71—41no—
160C2×C71#52511yescharacteristic
161C2×C71#53311yescharacteristic
162C2×C71#54111yescharacteristic
163C2×C71#54711yescharacteristic
164C2×C71D4×Q811yescharacteristic
165C2×C71#55211yescharacteristic
166C2×C71#55711yescharacteristic
167#2462—711nomaximal, Sylow
168C71#246211yescharacteristic, complemented, Sylow
169C2×#125—711no—
170C2×C4×Q8—711no—
171#398—711no—
172#398—711no—
173#395—711no—
174#395D7111yescharacteristic
175#389—711no—
176#389—711no—
177#387—711no—
178#387—711no—
179#387—711no—
180#387—711no—
181#387—711no—
182#387—711no—
183C4×C4⋊C4—711no—
184C22×Q8C2×D7111yescharacteristic
185#125—1424no—
186C4×Q8—1424no—
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⋊C4—711no—
197C2×C4⋊C4—711no—
198C2×C4⋊C4—711no—
199C2×C4⋊C4C2×D7111yescharacteristic
200C2×C4⋊C4C2×D7111yescharacteristic
201C2×C4⋊C4C2×D7111yescharacteristic
202C2×C42—711no—
203C2×C42—711no—
204C2×C42—711no—
205C2×C42—711no—
206C2×C42—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#95—711no—
217#95—711no—
218#95C2×D7111yescharacteristic
219#95C2×D7111yescharacteristic
220#95C2×D7111yescharacteristic
221C2×Q8—22no—
222C2×Q8—22no—
223C2×Q8—22no—
224C22×C4—711no—
225C22×C4—711no—
226C22×C4—711no—
227C22×C4—711no—
228C22×C4—711no—
229C22×C4—711no—
230C22×C4—711no—
231C22×C4—711no—
232C22×C4C22×D7111yescharacteristic
233C22×C4C22×D7111yescharacteristic
234C22×C4C22×D7111yescharacteristic
235C22×C4C22×D7111yescharacteristic
236C22×C4C22×D7111yescharacteristic
237C22×C4C22×D7111yescharacteristic
238C22×C4C22×D7111yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—714no—
243C4⋊C4—714no—
244C4⋊C4—1422no—
245C4⋊C4—1422no—
246C4⋊C4—1422no—
247C4⋊C4—1422no—
248C4⋊C4—1422no—
249C4⋊C4—1422no—
250C4⋊C4—1422no—
251C4⋊C4—1422no—
252C4⋊C4—1422no—
253C4⋊C4—1422no—
254C42—1422no—
255C42—1422no—
256C42—1422no—
257C42—1422no—
258C42—1422no—
259C23C23×D7111yescharacteristic
260Q8—28no—
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—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×C4—1421no—
299C2×C4—1421no—
300C2×C4—1421no—
301C2×C4—1421no—
302C2×C4D4×D7112yes—
303C2×C4Q8×D7112yes—
304C2×C4#1176586412yes—
305C2×C4#1176586412yes—
306C22C2×D4×D7111yescharacteristic
307C22C2×Q8×D7111yescharacteristic
308C22#41×D7111yescharacteristic
309C22C2×#1176586411yescharacteristic
310C22C2×#1176586411yescharacteristic
311C22#1455617611yescharacteristic
312C22#1455617611yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—2841no—
321C4—2841no—
322C4—2841no—
323C4—1422no—
324C4—1422no—
325C4—1422no—
326C4—1422no—
327C4—1422no—
328C2#1798650511yescharacteristic
329C2#1798655111yescharacteristic
330C2#1798661011yescharacteristic
331C2#1798665111yescharacteristic
332C2#1798666411yescharacteristic
333C2#1798668311yescharacteristic
334C2#1798672411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#395×C71C2
hypercenter#395D71
hypocenterC71#2462
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
64. C4⋊Dic71Q8semidirect
168. C71#2462semidirect