Finite Group Databasebeta

← #20247607

Subgroups — #20247607

Order 6016.

476 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
1C2×#13094019C211yesmaximal, characteristic
2C2×#13093982C211yesmaximal, characteristic
3#15689053C211yesmaximal, characteristic, complemented
4#15689052C211yesmaximal, characteristic
5#15689049C211yesmaximal, characteristic
6#15689022C211yesmaximal, characteristic, complemented
7#15689020C211yesmaximal, characteristic, complemented
8#15689013C211yesmaximal, characteristic
9#15689010C211yesmaximal, characteristic, complemented
10#15689006C211yesmaximal, characteristic, complemented
11#15689004C211yesmaximal, characteristic, complemented
12#15688997C211yesmaximal, characteristic
13#15688997C211yesmaximal, characteristic
14C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C47×#398C211yesmaximal, characteristic, complemented
16C22×C4×D47C2211yescharacteristic
17#13094019—24no—
18#13093982—24no—
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×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×C4×Dic47C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic
35C2×C4×Dic47C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C23×D47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C2×C4×D47—22no—
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C4⋊C4×C47—22no—
72C4⋊C4×C47—22no—
73C4⋊C4×C47—22no—
74C4⋊C4×C47—22no—
75(C2×D47)⋊C4—22no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—22no—
79(C2×D47)⋊C4—22no—
80(C2×D47)⋊C4D414yes—
81C4⋊Dic47—22no—
82C4⋊Dic47—22no—
83C4⋊Dic47—22no—
84C4⋊Dic47—22no—
85Dic47⋊C4—22no—
86Dic47⋊C4—22no—
87Dic47⋊C4—22no—
88Dic47⋊C4—22no—
89C4×Dic47—22no—
90C4×Dic47—22no—
91C4×Dic47—22no—
92C4×Dic47—22no—
93C23×C47C2411yescharacteristic
94C22×D47—21no—
95C22×D47—21no—
96C22×D47—21no—
97C22×D47—21no—
98C22×D47—21no—
99C22×D47—21no—
100C22×D47C2×D412yes—
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×C47—21no—
119C2×C4×C47C2×D412yes—
120C2×C4×C47#4112yes—
121C2×C4×C47#4112yes—
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×Dic47C2×D412yes—
141C2×Dic47#4112yes—
142C2×Dic47#4112yes—
143C4×D47—28no—
144C22×C47C22×D411yescharacteristic
145C22×C47C2×#4111yescharacteristic
146C22×C47C2×#4111yescharacteristic
147C22×C47C2×#4111yescharacteristic
148C22×C47C2×#4111yescharacteristic
149C22×C472−1+411yescharacteristic
150C22×C472−1+411yescharacteristic
151C2×D47—22no—
152C2×D47—22no—
153C2×D47—22no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C4×C47—22no—
159C4×C47—22no—
160C4×C47—22no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47—41no—
165Dic47—22no—
166Dic47—22no—
167Dic47—22no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172#2478—471nomaximal, Sylow
173C2×C47#52511yescharacteristic
174C2×C47#52911yescharacteristic
175C2×C47#54111yescharacteristic
176C2×C47#54711yescharacteristic
177C2×C47#54711yescharacteristic
178C2×C47#55211yescharacteristic
179C2×C47#55611yescharacteristic
180D47—42no—
181C2×#126—471no—
182C2×#117—471no—
183#398—471no—
184#398D4711yescharacteristic, complemented
185#397—471no—
186#397—471no—
187#389—471no—
188#389—471no—
189#388—471no—
190#387—471no—
191#387—471no—
192#387—471no—
193#385—471no—
194#385—471no—
195C4×C4⋊C4—471no—
196C47#247811yescharacteristic, complemented, Sylow
197C23×C4—471no—
198#126—944no—
199#117—944no—
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×C4⋊C4C2×D4711yescharacteristic
211C2×C4⋊C4C2×D4711yescharacteristic
212C2×C22⋊C4—471no—
213C2×C22⋊C4—471no—
214C2×C22⋊C4—471no—
215C2×C22⋊C4—471no—
216C2×C22⋊C4—471no—
217C2×C22⋊C4—471no—
218C2×C42—471no—
219C2×C42—471no—
220C2×C42—471no—
221C2×C42—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#95C2×D4711yescharacteristic
232#95C2×D4711yescharacteristic
233#95C2×D4711yescharacteristic
234C24—471no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—942no—
243C22×C4—942no—
244C22×C4—942no—
245C22×C4C22×D4711yescharacteristic
246C22×C4C22×D4711yescharacteristic
247C22×C4C22×D4711yescharacteristic
248C22×C4C22×D4711yescharacteristic
249C22×C4C22×D4711yescharacteristic
250C22×C4C22×D4711yescharacteristic
251C22×C4C22×D4711yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—942no—
257C4⋊C4—942no—
258C4⋊C4—942no—
259C4⋊C4—942no—
260C4⋊C4—942no—
261C4⋊C4—942no—
262C4⋊C4—942no—
263C4⋊C4—942no—
264C22⋊C4—474no—
265C22⋊C4—942no—
266C22⋊C4—942no—
267C22⋊C4—942no—
268C22⋊C4—942no—
269C22⋊C4—942no—
270C42—942no—
271C42—942no—
272C42—942no—
273C42—942no—
274C23—472no—
275C23—941no—
276C23—941no—
277C23—941no—
278C23—941no—
279C23—941no—
280C23—941no—
281C23C23×D4711yescharacteristic
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—21no—
300C2×C4—472no—
301C2×C4—472no—
302C2×C4—472no—
303C2×C4—948no—
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—941no—
321C2×C4—941no—
322C2×C4D4×D4712yes—
323C2×C4#1062535212yes—
324C2×C4#1062535412yes—
325C22—942no—
326C22—942no—
327C22—942no—
328C22—1881no—
329C22—1881no—
330C22—1881no—
331C22—1881no—
332C22C2×D4×D4711yescharacteristic
333C22#41×D4711yescharacteristic
334C22#41×D4711yescharacteristic
335C22C2×#1062535211yescharacteristic
336C22C2×#1062535411yescharacteristic
337C22#1309407111yescharacteristic
338C22#1309407211yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—942no—
347C4—942no—
348C4—942no—
349C4—1881no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C2—1882no—
354C2#1568963611yescharacteristic
355C2#1568965011yescharacteristic
356C2#1568973211yescharacteristic
357C2#1568977311yescharacteristic
358C2#1568977511yescharacteristic
359C2#1568981111yescharacteristic
360C2#1568984711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2478
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #15689053C2semidirect
6. #15689022C2semidirect
7. #15689020C2semidirect
9. #15689010C2semidirect
10. #15689006C2semidirect
11. #15689004C2semidirect
14. C4⋊C4×Dic47C2semidirect
15. C47×#398C2semidirect
184. #398D47semidirect
196. C47#2478semidirect