Finite Group Databasebeta

← #20246243

Subgroups — #20246243

Order 6016.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093982C211yesmaximal, characteristic
2#15689009C211yesmaximal, characteristic, complemented
3#15689008C211yesmaximal, characteristic, complemented
4#15689006C211yesmaximal, characteristic, complemented
5#15688997C211yesmaximal, characteristic
6#15688994C211yesmaximal, characteristic
7#15688990C211yesmaximal, characteristic, complemented
8#15688987C211yesmaximal, characteristic, complemented
9#15688985C211yesmaximal, characteristic
10C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
11C4×(C2×D47)⋊C4C211yesmaximal, characteristic
12#15688970C211yesmaximal, characteristic
13#15688969C211yesmaximal, characteristic, complemented
14#95×D47C211yesmaximal, characteristic
15C47×#387C211yesmaximal, characteristic, complemented
16C22×C4×D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19#13093982C418yescomplemented
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
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
44C47⋊#95C2211yescharacteristic
45C2×C4⋊C4×C47C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C42×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52C23×D47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C2×C4×D47—22no—
68C2×C4×D47—22no—
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C2×C4×D47—22no—
72C2×C4×D47—22no—
73C2×C4×D47—41no—
74C2×C4×D47—41no—
75C2×C4×D47C2×C414yes—
76C4⋊C4×C47—22no—
77C4⋊C4×C47C2×C414yescomplemented
78C42×C47—22no—
79(C2×D47)⋊C4—22no—
80(C2×D47)⋊C4—22no—
81(C2×D47)⋊C4C2×C414yes—
82(C2×D47)⋊C4C2×C414yes—
83C4⋊Dic47—22no—
84C4⋊Dic47C2×C414yescomplemented
85Dic47⋊C4—41no—
86Dic47⋊C4—41no—
87C4×Dic47—22no—
88C4×Dic47—41no—
89C4×Dic47—41no—
90C4×Dic47C2×C414yescomplemented
91C4×Dic47C2×C414yescomplemented
92C23×C47C2411yescharacteristic
93C22×D47—21no—
94C22×D47—21no—
95C22×D47—21no—
96C22×D47—21no—
97C22×D47C22×C412yes—
98C22×D47#4112yes—
99C22×D47#4112yes—
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×C47C22×C412yes—
118C2×C4×C47C22×C412yes—
119C2×C4×C47C22×C412yes—
120C2×C4×C47#4112yes—
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×Dic47C22×C412yes—
139C2×Dic47C22×C412yes—
140C2×Dic47C22×C412yes—
141C2×Dic47#4112yes—
142C4×D47—28no—
143C4×D47—44no—
144C4×D47—44no—
145C22×C47C23×C411yescharacteristic
146C22×C47C2×#4111yescharacteristic
147C22×C47C2×#4111yescharacteristic
148C22×C47C2×#4111yescharacteristic
149C22×C47C2×#4111yescharacteristic
150C22×C47H(5,𝔽2)11yescharacteristic
151C22×C472−1+411yescharacteristic
152C2×D47—22no—
153C2×D47—22no—
154C2×D47—22no—
155C2×D47—22no—
156C2×D47—22no—
157C2×D47—22no—
158C2×D47#11714yes—
159C4×C47—22no—
160C4×C47—22no—
161C4×C47—22no—
162C4×C47—22no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166Dic47—22no—
167Dic47—22no—
168Dic47—22no—
169Dic47—22no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173#2343—471nomaximal, Sylow
174C2×C47C2×#11711yescharacteristic
175C2×C47C4×#4111yescharacteristic
176C2×C47#52011yescharacteristic
177C2×C47#55111yescharacteristic
178C2×C47#55111yescharacteristic
179C2×C47#55211yescharacteristic
180C2×C47#55211yescharacteristic
181D47—24no—
182C2×#117—471no—
183#387—471no—
184#387—471no—
185#387—471no—
186#387D4711yescharacteristic, complemented
187#385—471no—
188#385—471no—
189#383—471no—
190#382—471no—
191#381—471no—
192C4×C4⋊C4—471no—
193C4×C22⋊C4—471no—
194C4×C22⋊C4—471no—
195#376—471no—
196C2×#95—471no—
197C47#234311yescharacteristic, complemented, Sylow
198C23×C4—471no—
199C23×C4—471no—
200C23×C4—471no—
201#117—478no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4C2×D4711yescharacteristic
207C2×C4⋊C4C2×D4711yescharacteristic
208C2×C22⋊C4—471no—
209C2×C22⋊C4—471no—
210C2×C22⋊C4—471no—
211C2×C22⋊C4—471no—
212C2×C42—471no—
213C2×C42—471no—
214C2×C42—471no—
215C2×C42—471no—
216C2×C42—471no—
217C2×C42C2×D4711yescharacteristic
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#95—471no—
228#95—471no—
229#95—471no—
230#95C2×D4711yescharacteristic
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—474no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—942no—
244C22×C4—942no—
245C22×C4—942no—
246C22×C4—942no—
247C22×C4—942no—
248C22×C4—942no—
249C22×C4—1881no—
250C22×C4—1881no—
251C22×C4C22×D4711yescharacteristic
252C22×C4C22×D4711yescharacteristic
253C22×C4C22×D4711yescharacteristic
254C22×C4C22×D4711yescharacteristic
255C22×C4C22×D4711yescharacteristic
256C22×C4C22×D4711yescharacteristic
257C22×C4C22×D4711yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—474no—
260C4⋊C4—942no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C4⋊C4C4×D4714yescomplemented
264C22⋊C4—474no—
265C22⋊C4—474no—
266C22⋊C4—942no—
267C22⋊C4—942no—
268C42—22no—
269C42—474no—
270C42—474no—
271C42—942no—
272C42—1881no—
273C42—1881no—
274C23—472no—
275C23—472no—
276C23—472no—
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—472no—
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—1884no—
322C2×C4—1884no—
323C2×C4C2×C4×D4712yes—
324C2×C4C2×C4×D4712yes—
325C2×C4C2×C4×D4712yes—
326C2×C4#1062535212yes—
327C22—474no—
328C22—942no—
329C22—942no—
330C22—942no—
331C22—942no—
332C22—942no—
333C22—942no—
334C22C22×C4×D4711yescharacteristic
335C22#41×D4711yescharacteristic
336C22#41×D4711yescharacteristic
337C22#41×D4711yescharacteristic
338C22C2×#1062535211yescharacteristic
339C22#1309407011yescharacteristic
340C22#1309407211yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—942no—
349C4—942no—
350C4—942no—
351C4—942no—
352C4—1881no—
353C4—1881no—
354C4—1881no—
355C2—944no—
356C2#117×D4711yescharacteristic
357C2C4×#1062535211yescharacteristic
358C2#1568960511yescharacteristic
359C2#1568979611yescharacteristic
360C2#1568979811yescharacteristic
361C2#1568980511yescharacteristic
362C2#1568980711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#387C2
socleC23×C47C24
hypercenter#387D47
hypocenterC47#2343
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #15689009C2semidirect
3. #15689008C2semidirect
4. #15689006C2semidirect
7. #15688990C2semidirect
8. #15688987C2semidirect
10. C4⋊C4×Dic47C2semidirect
13. #15688969C2semidirect
15. C47×#387C2semidirect
19. #13093982C4semidirect
77. C4⋊C4×C47C2×C4semidirect
84. C4⋊Dic47C2×C4semidirect
90. C4×Dic47C2×C4semidirect
91. C4×Dic47C2×C4semidirect
186. #387D47semidirect
197. C47#2343semidirect
263. C4⋊C4C4×D47semidirect