Finite Group Databasebeta

← #20246169

Subgroups — #20246169

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
1C2×#13094019C211yesmaximal, characteristic
2#15689020C211yesmaximal, characteristic, complemented
3#15689019C211yesmaximal, characteristic, complemented
4#15689014C211yesmaximal, characteristic
5#15689012C211yesmaximal, characteristic
6#15689012C211yesmaximal, characteristic
7#15689008C211yesmaximal, characteristic, complemented
8#15689005C211yesmaximal, characteristic, complemented
9#15688997C211yesmaximal, characteristic
10#15688994C211yesmaximal, characteristic
11#15688987C211yesmaximal, characteristic, complemented
12C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
13C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic
15C47×#387C211yesmaximal, characteristic, complemented
16C22×C4×D47C2211yescharacteristic
17#13094019C418yescomplemented
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×C4×Dic47C2211yescharacteristic
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
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—41no—
69C2×C4×D47—41no—
70C4⋊C4×C47—41no—
71C4⋊C4×C47C2×C414yescomplemented
72C42×C47—41no—
73(C2×D47)⋊C4—22no—
74(C2×D47)⋊C4—41no—
75(C2×D47)⋊C4—41no—
76(C2×D47)⋊C4C2×C414yes—
77(C2×D47)⋊C4C2×C414yes—
78(C2×D47)⋊C4C2×C414yes—
79C4⋊Dic47—22no—
80C4⋊Dic47C2×C414yescomplemented
81Dic47⋊C4—22no—
82Dic47⋊C4—22no—
83Dic47⋊C4—41no—
84Dic47⋊C4—41no—
85Dic47⋊C4—41no—
86Dic47⋊C4C2×C414yescomplemented
87C4×Dic47—22no—
88C4×Dic47—41no—
89C4×Dic47—41no—
90C4×Dic47—41no—
91C4×Dic47C2×C414yescomplemented
92C23×C47C2411yescharacteristic
93C22×D47—21no—
94C22×D47—21no—
95C22×D47—21no—
96C22×D47—21no—
97C22×D47—21no—
98C22×D47—21no—
99C22×D47C22×C412yes—
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×C47C22×C412yes—
119C2×C4×C47C22×C412yes—
120C2×C4×C47C22×C412yes—
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×Dic47C22×C412yes—
138C2×Dic47C22×C412yes—
139C2×Dic47C22×C412yes—
140C2×Dic47#4112yes—
141C2×Dic47#4112yes—
142C4×D47—44no—
143C22×C47C23×C411yescharacteristic
144C22×C47C2×#4111yescharacteristic
145C22×C47C2×#4111yescharacteristic
146C22×C47H(5,𝔽2)11yescharacteristic
147C22×C47H(5,𝔽2)11yescharacteristic
148C22×C472−1+411yescharacteristic
149C22×C472−1+411yescharacteristic
150C2×D47—22no—
151C2×D47—22no—
152C2×D47—22no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C4×C47—22no—
158C4×C47—22no—
159C4×C47—22no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47—41no—
164Dic47—22no—
165Dic47—22no—
166Dic47—22no—
167Dic47—22no—
168Dic47—22no—
169Dic47—41no—
170Dic47—41no—
171#2334—471nomaximal, Sylow
172C2×C47C4×#4111yescharacteristic
173C2×C47#52011yescharacteristic
174C2×C47#52011yescharacteristic
175C2×C47#53811yescharacteristic
176C2×C47#53911yescharacteristic
177C2×C47#54111yescharacteristic
178C2×C47#54211yescharacteristic
179D47—42no—
180C2×#126—471no—
181#389—471no—
182#389—471no—
183#388—471no—
184#388—471no—
185#388—471no—
186#387—471no—
187#387—471no—
188#387D4711yescharacteristic, complemented
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#126—478no—
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⋊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×C22⋊C4—471no—
213C2×C22⋊C4—471no—
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#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—1881no—
242C22×C4—1881no—
243C22×C4C22×D4711yescharacteristic
244C22×C4C22×D4711yescharacteristic
245C22×C4C22×D4711yescharacteristic
246C22×C4C22×D4711yescharacteristic
247C22×C4C22×D4711yescharacteristic
248C22×C4C22×D4711yescharacteristic
249C22×C4C22×D4711yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—474no—
252C4⋊C4—474no—
253C4⋊C4—942no—
254C4⋊C4—942no—
255C4⋊C4—942no—
256C4⋊C4—1881no—
257C4⋊C4—1881no—
258C4⋊C4—1881no—
259C4⋊C4C4×D4714yescomplemented
260C22⋊C4—474no—
261C22⋊C4—474no—
262C22⋊C4—474no—
263C22⋊C4—942no—
264C22⋊C4—1881no—
265C22⋊C4—1881no—
266C42—41no—
267C42—474no—
268C42—942no—
269C42—1881no—
270C42—1881no—
271C42—1881no—
272C23—472no—
273C23—941no—
274C23—941no—
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—472no—
299C2×C4—472no—
300C2×C4—472no—
301C2×C4—472no—
302C2×C4—472no—
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—1884no—
320C2×C4C2×C4×D4712yes—
321C2×C4C2×C4×D4712yes—
322C2×C4C2×C4×D4712yes—
323C22—942no—
324C22—942no—
325C22—942no—
326C22—1881no—
327C22—1881no—
328C22—1881no—
329C22—1881no—
330C22C22×C4×D4711yescharacteristic
331C22#41×D4711yescharacteristic
332C22#41×D4711yescharacteristic
333C22#1309406911yescharacteristic
334C22#1309407011yescharacteristic
335C22#1309407111yescharacteristic
336C22#1309407211yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—942no—
345C4—942no—
346C4—942no—
347C4—942no—
348C4—942no—
349C4—1881no—
350C4—1881no—
351C2—1882no—
352C2#1568959111yescharacteristic
353C2#1568960211yescharacteristic
354C2#1568960511yescharacteristic
355C2#1568970911yescharacteristic
356C2#1568971911yescharacteristic
357C2#1568973211yescharacteristic
358C2#1568973911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#387C2
socleC23×C47C24
hypercenter#387D47
hypocenterC47#2334
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #15689020C2semidirect
3. #15689019C2semidirect
7. #15689008C2semidirect
8. #15689005C2semidirect
11. #15688987C2semidirect
12. C4⋊C4×Dic47C2semidirect
13. C4×Dic47⋊C4C2semidirect
15. C47×#387C2semidirect
17. #13094019C4semidirect
71. C4⋊C4×C47C2×C4semidirect
80. C4⋊Dic47C2×C4semidirect
86. Dic47⋊C4C2×C4semidirect
91. C4×Dic47C2×C4semidirect
188. #387D47semidirect
195. C47#2334semidirect
259. C4⋊C4C4×D47semidirect