Finite Group Databasebeta

← #20246167

Subgroups — #20246167

Order 6016.

476 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689022C211yesmaximal, characteristic, complemented
2#15689022C211yesmaximal, characteristic, complemented
3#15689016C211yesmaximal, characteristic
4#15689016C211yesmaximal, characteristic
5#15689016C211yesmaximal, characteristic
6#15689009C211yesmaximal, characteristic, complemented
7#15689009C211yesmaximal, characteristic, complemented
8#15689009C211yesmaximal, characteristic, complemented
9#15688998C211yesmaximal, characteristic
10#15688998C211yesmaximal, characteristic
11#15688989C211yesmaximal, characteristic, complemented
12C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
13C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic47C211yesmaximal, characteristic
15C2×#126×C47C211yesmaximal, characteristic
16C23×Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×C4⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C4×Dic47C2211yescharacteristic
28C2×C4×Dic47C2211yescharacteristic
29C2×C4×Dic47C2211yescharacteristic
30C2×C4×Dic47C2211yescharacteristic
31C2×C4×Dic47C2211yescharacteristic
32C47⋊#95C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44#126×C47C418yescomplemented
45C2×C4⋊C4×C47C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C42×C47C2211yescharacteristic
52C24×C47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×Dic47—22no—
60C22×Dic47—41no—
61C22×Dic47—41no—
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C4⋊C4×C47C2×C414yescomplemented
71C4⋊C4×C47C2×C414yescomplemented
72C4⋊C4×C47C2×C414yescomplemented
73C22⋊C4×C47C2×C414yes—
74C22⋊C4×C47C2×C414yes—
75C22⋊C4×C47C2×C414yes—
76C42×C47C2×C414yescomplemented
77C22⋊Dic47—22no—
78C22⋊Dic47—41no—
79C22⋊Dic47—41no—
80C4⋊Dic47—22no—
81C4⋊Dic47—22no—
82C4⋊Dic47—22no—
83C4⋊Dic47—41no—
84C4⋊Dic47—41no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87C4×Dic47—22no—
88C4×Dic47—41no—
89C4×Dic47—41no—
90C4×Dic47—41no—
91C4×Dic47—41no—
92C23×C47—21no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47—21no—
98C23×C47C22×C412yes—
99C23×C47C2411yescharacteristic
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×C47C22×C412yes—
113C2×C4×C47C22×C412yes—
114C2×C4×C47C22×C412yes—
115C2×C4×C47C22×C412yes—
116C2×C4×C47C22×C412yes—
117C2×C4×C47C22×C412yes—
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—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—44no—
141C2×Dic47#4112yes—
142C2×Dic47#4112yes—
143C22×C47—22no—
144C22×C47—22no—
145C22×C47—22no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47C23×C411yescharacteristic
151C22×C47C2×#4111yescharacteristic
152C22×C47C2×#4111yescharacteristic
153C22×C47H(5,𝔽2)11yescharacteristic
154C22×C47H(5,𝔽2)11yescharacteristic
155C22×C472−1+411yescharacteristic
156C22×C472−1+411yescharacteristic
157C4×C47—22no—
158C4×C47—22no—
159C4×C47—22no—
160C4×C47—22no—
161C4×C47—22no—
162C4×C47—22no—
163Dic47—22no—
164Dic47—22no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171#2334—471nomaximal, Sylow
172C2×C47—42no—
173C2×C47C4×#4111yescharacteristic
174C2×C47#52011yescharacteristic
175C2×C47#52011yescharacteristic
176C2×C47#53811yescharacteristic
177C2×C47#53911yescharacteristic
178C2×C47#54111yescharacteristic
179C2×C47#54211yescharacteristic
180C2×#126D4711yescharacteristic
181#389—471no—
182#389—471no—
183#388—471no—
184#388—471no—
185#388—471no—
186#387—471no—
187#387—471no—
188#387—471no—
189#385—471no—
190#385—471no—
191#382—471no—
192C4×C4⋊C4—471no—
193C4×C4⋊C4—471no—
194C4×C22⋊C4—471no—
195C47#233411yescharacteristic, complemented, Sylow
196C23×C4—471no—
197#126Dic4718yescomplemented
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4C2×D4711yescharacteristic
206C2×C4⋊C4C2×D4711yescharacteristic
207C2×C4⋊C4C2×D4711yescharacteristic
208C2×C22⋊C4—471no—
209C2×C22⋊C4—471no—
210C2×C22⋊C4—471no—
211C2×C22⋊C4C2×D4711yescharacteristic
212C2×C22⋊C4C2×D4711yescharacteristic
213C2×C22⋊C4C2×D4711yescharacteristic
214C2×C42—471no—
215C2×C42—471no—
216C2×C42—471no—
217C2×C42—471no—
218C2×C42—471no—
219C2×C42C2×D4711yescharacteristic
220#95—471no—
221#95—471no—
222#95—471no—
223#95—471no—
224#95—471no—
225#95—471no—
226#95—471no—
227#95—471no—
228#95—471no—
229#95—471no—
230#95—471no—
231#95—471no—
232C24C22×D4711yescharacteristic
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—942no—
242C22×C4—1881no—
243C22×C4—1881no—
244C22×C4C22×D4711yescharacteristic
245C22×C4C22×D4711yescharacteristic
246C22×C4C22×D4711yescharacteristic
247C22×C4C22×D4711yescharacteristic
248C22×C4C22×D4711yescharacteristic
249C22×C4C22×D4711yescharacteristic
250C4⋊C4—942no—
251C4⋊C4—942no—
252C4⋊C4—942no—
253C4⋊C4—1881no—
254C4⋊C4—1881no—
255C4⋊C4—1881no—
256C4⋊C4—1881no—
257C4⋊C4C2×Dic4714yescomplemented
258C4⋊C4C2×Dic4714yescomplemented
259C4⋊C4C2×Dic4714yescomplemented
260C22⋊C4—942no—
261C22⋊C4—1881no—
262C22⋊C4—1881no—
263C22⋊C4C2×Dic4714yes—
264C22⋊C4C2×Dic4714yes—
265C22⋊C4C2×Dic4714yes—
266C42—942no—
267C42—1881no—
268C42—1881no—
269C42—1881no—
270C42—1881no—
271C42C2×Dic4714yescomplemented
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C22×Dic4712yes—
279C23C23×D4711yescharacteristic
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—472no—
293C2×C4—472no—
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—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—1884no—
317C2×C4C22×Dic4712yes—
318C2×C4C22×Dic4712yes—
319C2×C4C22×Dic4712yes—
320C2×C4C22×Dic4712yes—
321C2×C4C22×Dic4712yes—
322C2×C4C22×Dic4712yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C23×Dic4711yescharacteristic
331C22#41×D4711yescharacteristic
332C22#41×D4711yescharacteristic
333C22#1309407011yescharacteristic
334C22#1309407011yescharacteristic
335C22#1309407111yescharacteristic
336C22#1309407111yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—22no—
343C4—942no—
344C4—942no—
345C4—1881no—
346C4—1881no—
347C4—1881no—
348C4—1881no—
349C4—1881no—
350C4—1881no—
351C2—42no—
352C2#41×Dic4711yescharacteristic
353C2#1568960611yescharacteristic
354C2#1568960611yescharacteristic
355C2#1568971211yescharacteristic
356C2#1568971411yescharacteristic
357C2#1568973011yescharacteristic
358C2#1568973911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC2×#126×C47C2
socleC23×C47C24
hypercenterC2×#126D47
hypocenterC47#2334
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #15689022C2semidirect
2. #15689022C2semidirect
6. #15689009C2semidirect
7. #15689009C2semidirect
8. #15689009C2semidirect
11. #15688989C2semidirect
12. C4⋊C4×Dic47C2semidirect
13. C4×C4⋊Dic47C2semidirect
44. #126×C47C4semidirect
70. C4⋊C4×C47C2×C4semidirect
71. C4⋊C4×C47C2×C4semidirect
72. C4⋊C4×C47C2×C4semidirect
76. C42×C47C2×C4semidirect
195. C47#2334semidirect
197. #126Dic47semidirect
257. C4⋊C4C2×Dic47semidirect
258. C4⋊C4C2×Dic47semidirect
259. C4⋊C4C2×Dic47semidirect
271. C42C2×Dic47semidirect