Finite Group Databasebeta

← #20248198

Subgroups — #20248198

Order 6016.

398 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689064C211yesmaximal, characteristic, complemented
2#15689057C211yesmaximal, characteristic, complemented
3#15689046C211yesmaximal, characteristic
4#15689019C211yesmaximal, characteristic, complemented
5#15689017C211yesmaximal, characteristic
6#15689017C211yesmaximal, characteristic
7#15689017C211yesmaximal, characteristic
8#15689016C211yesmaximal, characteristic
9#15689011C211yesmaximal, characteristic
10#15689009C211yesmaximal, characteristic, complemented
11#15689006C211yesmaximal, characteristic, complemented
12#15688987C211yesmaximal, characteristic, complemented
13#15688974C211yesmaximal, characteristic, complemented
14#15688968C211yesmaximal, characteristic, complemented
15C47×#397C211yesmaximal, characteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C4×Dic47C2211yescharacteristic
29C2×C4×Dic47C2211yescharacteristic
30C2×C4×Dic47C2211yescharacteristic
31C2×C4×Dic47C2211yescharacteristic
32C2×C4×Dic47C2211yescharacteristic
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
48#95×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×Dic47C2311yescharacteristic
59C22×Dic47C2311yescharacteristic
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C4⋊C4×C47—22no—
67C22⋊C4×C47—22no—
68C22⋊C4×C47—41no—
69C22⋊C4×C47—41no—
70C22⋊Dic47—22no—
71C22⋊Dic47—22no—
72C22⋊Dic47—22no—
73C22⋊Dic47—22no—
74C4⋊Dic47—22no—
75C4⋊Dic47—22no—
76Dic47⋊C4—22no—
77Dic47⋊C4—22no—
78Dic47⋊C4—41no—
79Dic47⋊C4—41no—
80Dic47⋊C4—41no—
81Dic47⋊C4—41no—
82C4×Dic47—22no—
83C4×Dic47—22no—
84C4×Dic47—22no—
85C4×Dic47—22no—
86C4×Dic47—22no—
87C23×C47—21no—
88C23×C47—21no—
89C23×C47—21no—
90C23×C47—21no—
91C23×C47—21no—
92C23×C47—21no—
93C23×C47—21no—
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#4112yes—
134C2×Dic47#4112yes—
135C2×Dic47#4112yes—
136C2×Dic47#4112yes—
137C22×C47—41no—
138C22×C47—41no—
139C22×C47—41no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47C2×#4111yescharacteristic
145C22×C47C2×#4111yescharacteristic
146C22×C47C2×#4111yescharacteristic
147C22×C47C2×#4111yescharacteristic
148C22×C47C2×#4111yescharacteristic
149C22×C47H(5,𝔽2)11yescharacteristic
150C22×C472−1+411yescharacteristic
151C4×C47—22no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157Dic47—22no—
158Dic47—22no—
159Dic47—22no—
160Dic47—22no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165#2529—471nomaximal, Sylow
166C2×C47—81no—
167C2×C47#52911yescharacteristic
168C2×C47#52911yescharacteristic
169C2×C47#54211yescharacteristic
170C2×C47#55211yescharacteristic
171C2×C47#55211yescharacteristic
172C2×C47#55311yescharacteristic
173C2×C47#55511yescharacteristic
174#400—471no—
175#398—471no—
176#397D4711yescharacteristic
177#396—471no—
178#389—471no—
179#388—471no—
180#388—471no—
181#388—471no—
182#388—471no—
183#388—471no—
184#387—471no—
185#387—471no—
186#382—471no—
187C4×C4⋊C4—471no—
188#376—471no—
189C47#252911yescharacteristic, complemented, Sylow
190C2×C4⋊C4—471no—
191C2×C4⋊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⋊C4C2×D4711yescharacteristic
199C2×C22⋊C4—471no—
200C2×C22⋊C4—471no—
201C2×C22⋊C4—471no—
202C2×C22⋊C4—471no—
203C2×C22⋊C4C2×D4711yescharacteristic
204C2×C22⋊C4C2×D4711yescharacteristic
205C2×C22⋊C4C2×D4711yescharacteristic
206C2×C42—471no—
207C2×C42—471no—
208C2×C42—471no—
209C2×C42—471no—
210C2×C42—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#95C2×D4711yescharacteristic
223#95C2×D4711yescharacteristic
224#95C2×D4711yescharacteristic
225C24C22×D4711yescharacteristic
226C22×C4—471no—
227C22×C4—471no—
228C22×C4—471no—
229C22×C4—471no—
230C22×C4—471no—
231C22×C4—471no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4C22×D4711yescharacteristic
235C22×C4C22×D4711yescharacteristic
236C22×C4C22×D4711yescharacteristic
237C22×C4C22×D4711yescharacteristic
238C22×C4C22×D4711yescharacteristic
239C22×C4C22×D4711yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—942no—
242C4⋊C4—942no—
243C4⋊C4—942no—
244C4⋊C4—942no—
245C4⋊C4—1881no—
246C4⋊C4—1881no—
247C4⋊C4—1881no—
248C4⋊C4—1881no—
249C22⋊C4—22no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—942no—
253C22⋊C4—942no—
254C22⋊C4—942no—
255C22⋊C4—942no—
256C42—942no—
257C42—942no—
258C42—942no—
259C42—942no—
260C42—942no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C23×D4711yescharacteristic
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—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—472no—
287C2×C4—472no—
288C2×C4—472no—
289C2×C4—472no—
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#1062535212yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#41×D4711yescharacteristic
319C22#41×D4711yescharacteristic
320C22#41×D4711yescharacteristic
321C22#41×D4711yescharacteristic
322C22C2×#1062535211yescharacteristic
323C22#1309406911yescharacteristic
324C22#1309407111yescharacteristic
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—942no—
332C4—942no—
333C4—942no—
334C4—942no—
335C4—1881no—
336C4—1881no—
337C4—1881no—
338C4—1881no—
339C2—81no—
340C2#1568965211yescharacteristic
341C2#1568965611yescharacteristic
342C2#1568974111yescharacteristic
343C2#1568980911yescharacteristic
344C2#1568981011yescharacteristic
345C2#1568981811yescharacteristic
346C2#1568983711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2529
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #15689064C2semidirect
2. #15689057C2semidirect
4. #15689019C2semidirect
10. #15689009C2semidirect
11. #15689006C2semidirect
12. #15688987C2semidirect
13. #15688974C2semidirect
14. #15688968C2semidirect
189. C47#2529semidirect