Finite Group Databasebeta

← #20247882

Subgroups — #20247882

Order 6016.

456 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689065C211yesmaximal, characteristic, complemented
2#15689063C211yesmaximal, characteristic, complemented
3#15689057C211yesmaximal, characteristic, complemented
4#15689022C211yesmaximal, characteristic, complemented
5#15689009C211yesmaximal, characteristic, complemented
6#15689006C211yesmaximal, characteristic, complemented
7#15688997C211yesmaximal, characteristic
8#15688997C211yesmaximal, characteristic
9#15688997C211yesmaximal, characteristic
10#15688994C211yesmaximal, characteristic
11#15688987C211yesmaximal, characteristic, complemented
12#15688980C211yesmaximal, characteristic
13#15688970C211yesmaximal, characteristic
14#95×D47C211yesmaximal, characteristic
15C47×#400C211yesmaximal, characteristic, complemented
16C22×C4×D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
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×C4⋊C4×C47C2211yescharacteristic
46#95×C47C2211yescharacteristic
47#95×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C23×D47C2311yescharacteristic
52C22×C4×C47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×Dic47C2311yescharacteristic
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C2×C4×D47—22no—
67C2×C4×D47—22no—
68C2×C4×D47—22no—
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C2×C4×D47—41no—
72C2×C4×D47—41no—
73C2×C4×D47—41no—
74C2×C4×D47—41no—
75C4⋊C4×C47—22no—
76C4⋊C4×C47—22no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—22no—
79(C2×D47)⋊C4—22no—
80(C2×D47)⋊C4Q814yes—
81C4⋊Dic47—22no—
82C4⋊Dic47—41no—
83C4⋊Dic47—41no—
84C4⋊Dic47—41no—
85Dic47⋊C4—41no—
86Dic47⋊C4—41no—
87Dic47⋊C4—41no—
88Dic47⋊C4—41no—
89C4×Dic47—22no—
90C4×Dic47—41no—
91C23×C47C2411yescharacteristic
92C22×D47—21no—
93C22×D47—21no—
94C22×D47—21no—
95C22×D47—21no—
96C22×D47C2×Q812yes—
97C22×D47#4112yes—
98C22×D47#4112yes—
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—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47C2×Q812yes—
119C2×C4×C47#4112yes—
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×Dic47C2×Q812yes—
140C2×Dic47#4112yes—
141C4×D47—44no—
142C4×D47—44no—
143C4×D47—44no—
144C22×C47C22×Q811yescharacteristic
145C22×C47C2×#4111yescharacteristic
146C22×C47C2×#4111yescharacteristic
147C22×C47C2×#4111yescharacteristic
148C22×C47C2×#4111yescharacteristic
149C22×C47H(5,𝔽2)11yescharacteristic
150C22×C47H(5,𝔽2)11yescharacteristic
151C2×D47—22no—
152C2×D47—22no—
153C2×D47—22no—
154C2×D47—22no—
155C2×D47—22no—
156C2×D47—22no—
157C2×D47#12514yes—
158C4×C47—22no—
159C4×C47—22no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47—41no—
165Dic47—22no—
166Dic47—22no—
167Dic47—41no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172#2505—471nomaximal, Sylow
173C2×C47C2×#12511yescharacteristic
174C2×C47#52911yescharacteristic
175C2×C47#53811yescharacteristic
176C2×C47#55111yescharacteristic
177C2×C47#55111yescharacteristic
178C2×C47#55411yescharacteristic
179C2×C47#55411yescharacteristic
180D47—24no—
181#400—471no—
182#400—471no—
183#400D4711yescharacteristic, complemented
184#398—471no—
185#389—471no—
186#387—471no—
187#387—471no—
188#385—471no—
189#385—471no—
190#385—471no—
191#385—471no—
192#382—471no—
193#380—471no—
194C4×C22⋊C4—471no—
195C2×#95—471no—
196C47#250511yescharacteristic, complemented, Sylow
197C23×C4—471no—
198C23×C4—471no—
199C23×C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4C2×D4711yescharacteristic
209C2×C4⋊C4C2×D4711yescharacteristic
210C2×C22⋊C4—471no—
211C2×C22⋊C4—471no—
212C2×C22⋊C4—471no—
213C2×C22⋊C4—471no—
214C2×C42—471no—
215C2×C42—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#95—471no—
225#95—471no—
226#95—471no—
227#95C2×D4711yescharacteristic
228#95C2×D4711yescharacteristic
229#95C2×D4711yescharacteristic
230#95C2×D4711yescharacteristic
231#95C2×D4711yescharacteristic
232C24—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—942no—
241C22×C4—942no—
242C22×C4—942no—
243C22×C4—942no—
244C22×C4—942no—
245C22×C4—1881no—
246C22×C4—1881no—
247C22×C4—1881no—
248C22×C4—1881no—
249C22×C4C22×D4711yescharacteristic
250C22×C4C22×D4711yescharacteristic
251C22×C4C22×D4711yescharacteristic
252C22×C4C22×D4711yescharacteristic
253C22×C4C22×D4711yescharacteristic
254C22×C4C22×D4711yescharacteristic
255C22×C4C22×D4711yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—942no—
259C4⋊C4—1881no—
260C4⋊C4—1881no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C4⋊C4—1881no—
265C4⋊C4—1881no—
266C22⋊C4—474no—
267C22⋊C4—942no—
268C22⋊C4—942no—
269C22⋊C4—942no—
270C42—942no—
271C42—1881no—
272C23—472no—
273C23—472no—
274C23—472no—
275C23—941no—
276C23—941no—
277C23—941no—
278C23—941no—
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—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—472no—
300C2×C4—472no—
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—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—1884no—
321C2×C4—1884no—
322C2×C4—1884no—
323C2×C4#1062535212yes—
324C2×C4Q8×D4712yes—
325C22—474no—
326C22—942no—
327C22—942no—
328C22—942no—
329C22—942no—
330C22—942no—
331C22—942no—
332C22C2×Q8×D4711yescharacteristic
333C22#41×D4711yescharacteristic
334C22#41×D4711yescharacteristic
335C22#41×D4711yescharacteristic
336C22C2×#1062535211yescharacteristic
337C22#1309407011yescharacteristic
338C22#1309407011yescharacteristic
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—942no—
347C4—942no—
348C4—1881no—
349C4—1881no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C2—944no—
354C2#125×D4711yescharacteristic
355C2#1568965211yescharacteristic
356C2#1568971211yescharacteristic
357C2#1568979611yescharacteristic
358C2#1568979811yescharacteristic
359C2#1568982911yescharacteristic
360C2#1568983111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2505
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #15689065C2semidirect
2. #15689063C2semidirect
3. #15689057C2semidirect
4. #15689022C2semidirect
5. #15689009C2semidirect
6. #15689006C2semidirect
11. #15688987C2semidirect
15. C47×#400C2semidirect
183. #400D47semidirect
196. C47#2505semidirect