Finite Group Databasebeta

← #20250901

Subgroups — #20250901

Order 6016.

392 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#15689064C211yesmaximal, characteristic, complemented
2#15689064C211yesmaximal, characteristic, complemented
3#15689063C211yesmaximal, characteristic, complemented
4#15689062C211yesmaximal, characteristic, complemented
5#15689059C211yesmaximal, characteristic
6#15689051C211yesmaximal, characteristic
7#15689021C211yesmaximal, characteristic, complemented
8#15689020C211yesmaximal, characteristic, complemented
9#15689011C211yesmaximal, characteristic
10#15689009C211yesmaximal, characteristic, complemented
11#15689007C211yesmaximal, characteristic, complemented
12#15688998C211yesmaximal, characteristic
13#15688995C211yesmaximal, characteristic
14#15688984C211yesmaximal, characteristic
15C47×#388C211yesmaximal, characteristic
16C23×Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C4×Dic47C2211yescharacteristic
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2211yescharacteristic
32C47⋊#95C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C2×C4⋊C4×C47C2211yescharacteristic
45C2×C22⋊C4×C47C2211yescharacteristic
46C2×C22⋊C4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C42×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C24×C47C2311yescharacteristic
52C22×C4×C47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×Dic47—22no—
59C22×Dic47—41no—
60C22×Dic47—41no—
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C4⋊C4×C47—22no—
70C22⋊C4×C47—22no—
71C22⋊C4×C47—22no—
72C22⋊C4×C47—41no—
73C42×C47—41no—
74C22⋊Dic47—22no—
75C22⋊Dic47—22no—
76C22⋊Dic47—41no—
77C4⋊Dic47—22no—
78C4⋊Dic47—41no—
79C4⋊Dic47—41no—
80Dic47⋊C4—22no—
81Dic47⋊C4—22no—
82Dic47⋊C4—41no—
83Dic47⋊C4—41no—
84Dic47⋊C4—41no—
85Dic47⋊C4—41no—
86C4×Dic47—41no—
87C23×C47—21no—
88C23×C47—21no—
89C23×C47—21no—
90C23×C47—21no—
91C23×C47—21no—
92C23×C47—21no—
93C23×C47#4112yes—
94C23×C47C2411yescharacteristic
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47#4112yes—
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—44no—
137C2×Dic47#4112yes—
138C22×C47—22no—
139C22×C47—22no—
140C22×C47—22no—
141C22×C47—41no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47C2×#4111yescharacteristic
146C22×C47C2×#4111yescharacteristic
147C22×C47C2×#4111yescharacteristic
148C22×C47H(5,𝔽2)11yescharacteristic
149C22×C47H(5,𝔽2)11yescharacteristic
150C22×C472−1+411yescharacteristic
151C22×C472−1+411yescharacteristic
152C4×C47—22no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158Dic47—22no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#2771—471nomaximal, Sylow
167C2×C47—42no—
168C2×C47#53811yescharacteristic
169C2×C47#53911yescharacteristic
170C2×C47#53911yescharacteristic
171C2×C47#55211yescharacteristic
172C2×C47#55211yescharacteristic
173C2×C47#55911yescharacteristic
174C2×C47#56311yescharacteristic
175#400—471no—
176#400—471no—
177#400—471no—
178#400—471no—
179#399—471no—
180#397—471no—
181#389—471no—
182#389—471no—
183#388—471no—
184#388D4711yescharacteristic
185#387—471no—
186#387—471no—
187#385—471no—
188#385—471no—
189#381—471no—
190C47#277111yescharacteristic, complemented, Sylow
191C23×C4—471no—
192C2×C4⋊C4—471no—
193C2×C4⋊C4—471no—
194C2×C4⋊C4—471no—
195C2×C4⋊C4—471no—
196C2×C4⋊C4—471no—
197C2×C4⋊C4—471no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4C2×D4711yescharacteristic
202C2×C22⋊C4—471no—
203C2×C22⋊C4—471no—
204C2×C22⋊C4—471no—
205C2×C22⋊C4C2×D4711yescharacteristic
206C2×C22⋊C4C2×D4711yescharacteristic
207C2×C22⋊C4C2×D4711yescharacteristic
208C2×C42—471no—
209C2×C42C2×D4711yescharacteristic
210#95—471no—
211#95—471no—
212#95—471no—
213#95—471no—
214#95—471no—
215#95—471no—
216#95—471no—
217#95—471no—
218#95—471no—
219#95—471no—
220#95—471no—
221#95—471no—
222#95—471no—
223#95—471no—
224#95C2×D4711yescharacteristic
225#95C2×D4711yescharacteristic
226C24C22×D4711yescharacteristic
227C22×C4—471no—
228C22×C4—471no—
229C22×C4—471no—
230C22×C4—471no—
231C22×C4—471no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—942no—
236C22×C4—1881no—
237C22×C4—1881no—
238C22×C4C22×D4711yescharacteristic
239C22×C4C22×D4711yescharacteristic
240C22×C4C22×D4711yescharacteristic
241C22×C4C22×D4711yescharacteristic
242C22×C4C22×D4711yescharacteristic
243C22×C4C22×D4711yescharacteristic
244C4⋊C4—22no—
245C4⋊C4—942no—
246C4⋊C4—942no—
247C4⋊C4—942no—
248C4⋊C4—1881no—
249C4⋊C4—1881no—
250C4⋊C4—1881no—
251C4⋊C4—1881no—
252C4⋊C4—1881no—
253C4⋊C4—1881no—
254C22⋊C4—22no—
255C22⋊C4—22no—
256C22⋊C4—41no—
257C22⋊C4—942no—
258C22⋊C4—942no—
259C22⋊C4—1881no—
260C42—41no—
261C42—1881no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#1062535012yes—
269C23C23×D4711yescharacteristic
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—472no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—1884no—
312C2×C4#1062535212yes—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#41×D4711yescharacteristic
321C22C2×#1062535211yescharacteristic
322C22C2×#1062535011yescharacteristic
323C22#1309406911yescharacteristic
324C22#1309407011yescharacteristic
325C22#1309407111yescharacteristic
326C22#1309407111yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—942no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4—1881no—
338C4—1881no—
339C4—1881no—
340C4—1881no—
341C2—42no—
342C2#1568970611yescharacteristic
343C2#1568971611yescharacteristic
344C2#1568971811yescharacteristic
345C2#1568980611yescharacteristic
346C2#1568981311yescharacteristic
347C2#1568985511yescharacteristic
348C2#1568987511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#388C2
hypercenter#388D47
hypocenterC47#2771
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #15689064C2semidirect
2. #15689064C2semidirect
3. #15689063C2semidirect
4. #15689062C2semidirect
7. #15689021C2semidirect
8. #15689020C2semidirect
10. #15689009C2semidirect
11. #15689007C2semidirect
190. C47#2771semidirect