Finite Group Databasebeta

← #20256172

Subgroups — #20256172

Order 6016.

340 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689851C211yesmaximal, characteristic, complemented
2#15689829C211yesmaximal, characteristic
3#15689493C211yesmaximal, characteristic, complemented
4#15689490C211yesmaximal, characteristic, complemented
5#15689472C211yesmaximal, characteristic, complemented
6#15689433C211yesmaximal, characteristic, complemented
7#15689417C211yesmaximal, characteristic, complemented
8#15689329C211yesmaximal, characteristic
9#15689327C211yesmaximal, characteristic
10#15689327C211yesmaximal, characteristic
11#15689252C211yesmaximal, characteristic, complemented
12#15689222C211yesmaximal, characteristic
13#15689221C211yesmaximal, characteristic
14#15689210C211yesmaximal, characteristic
15C47×#479C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094022C2211yescharacteristic
22#13094022C2211yescharacteristic
23#13094016—21no—
24#13094015C2211yescharacteristic
25#13094014—21no—
26#13094014—21no—
27#13094004—21no—
28#13094002—21no—
29#13094002—21no—
30C4×Dic94—21no—
31C4×Dic94C2211yescharacteristic
32#13093989C2211yescharacteristic
33#13093989C2211yescharacteristic
34C4×D188C2211yescharacteristic
35#13093986C2211yescharacteristic
36#13093986C2211yescharacteristic
37C4⋊C4×D47—21no—
38#13093957C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D188C2311yescharacteristic
61C2×C4×D47—21no—
62C2×C4×D47—21no—
63C2×C4×D47—21no—
64C2×Dic94—21no—
65C2×Dic94D411yescharacteristic
66C2×Dic94C2311yescharacteristic
67C2×Dic94C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C42×C47—21no—
77C42×C47C2311yescharacteristic
78#10625336—22no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47D411yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87Dic47⋊C4—21no—
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4D411yescharacteristic
96Dic47⋊C4D411yescharacteristic
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47C2311yescharacteristic
100C4×Dic47C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103#10625325—22no—
104#10625325—22no—
105C22×D47—21no—
106Q8×C47—21no—
107Q8×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2411yescharacteristic
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47C2×D411yescharacteristic
119C2×Dic47C2×D411yescharacteristic
120C2×Dic47C2×D411yescharacteristic
121C2×Dic47C2×D411yescharacteristic
122D188—21no—
123D188#4112yes—
124C4×D47—42no—
125C4×D47—81no—
126C4×D47—81no—
127Dic94—22no—
128Dic94—21no—
129Dic94—21no—
130Dic94—21no—
131Dic94—21no—
132Dic94—81no—
133C8×C47—21no—
134C8×C47—21no—
135C47⋊C8—21no—
136C47⋊C8—21no—
137C22×C47C22×D411yescharacteristic
138C2×D47—22no—
139C2×D47—41no—
140C2×D47—41no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47C2×#4111yescharacteristic
148C4×C472−1+411yescharacteristic
149Dic47—21no—
150Dic47—21no—
151Dic47—21no—
152Dic47—41no—
153Dic47—41no—
154Dic47—41no—
155Dic47#13712yes—
156#3372—471nomaximal, Sylow
157C2×C47#54811yescharacteristic
158C2×C47C2×#13711yescharacteristic
159C2×C47#57711yescharacteristic
160D47—42no—
161#557—471no—
162#554—471no—
163#491—471no—
164#491—471no—
165#487—471no—
166#479—471no—
167#479D4711yescharacteristic, complemented
168#477—471no—
169#461—471no—
170#461—471no—
171#461—471no—
172#446—471no—
173#440—471no—
174#440—471no—
175C4×SD16—471no—
176C47#337211yescharacteristic, complemented, Sylow
177C2×SD16—471no—
178C2×SD16—471no—
179C2×SD16—471no—
180C4⋊Q8—471no—
181C4⋊Q8—471no—
182C4⋊Q8—471no—
183C4⋊Q8—471no—
184#125—471no—
185#125—941no—
186#125—941no—
187#125—941no—
188#125C2×D4711yescharacteristic
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191C22⋊Q8—941no—
192C4×Q8—471no—
193C4×Q8—471no—
194C4×Q8—471no—
195C4×Q8—941no—
196C4×Q8C2×D4711yescharacteristic
197C4×D4—471no—
198C4×D4—471no—
199C4×D4—471no—
200C2×C4⋊C4—941no—
201#107—471no—
202#107C2×D4711yescharacteristic
203#106C2×D4711yescharacteristic
204C4⋊C8—471no—
205C4⋊C8—471no—
206C4⋊C8C2×D4711yescharacteristic
207#103—471no—
208#103—471no—
209#103—471no—
210#103—471no—
211#103—471no—
212#103—471no—
213#103—471no—
214#103C2×D4711yescharacteristic
215#103C2×D4711yescharacteristic
216#102—471no—
217#97—471no—
218#97—471no—
219C4×C8—471no—
220C2×Q8—471no—
221C2×Q8—471no—
222C2×Q8—471no—
223C2×Q8—941no—
224C2×Q8C22×D4711yescharacteristic
225C2×D4—471no—
226C22×C4—941no—
227C22×C4—941no—
228C22×C4—941no—
229SD16—942no—
230SD16—942no—
231SD16—942no—
232C2×C8—471no—
233C2×C8—471no—
234C2×C8C22×D4711yescharacteristic
235C2×C8C22×D4711yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C22⋊C4—941no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C42—21no—
261C42—471no—
262C42—471no—
263C42—941no—
264C42—941no—
265C42C22×D4711yescharacteristic
266C23—941no—
267Q8—21no—
268Q8—21no—
269Q8—942no—
270Q8—941no—
271Q8—941no—
272Q8—941no—
273Q8—941no—
274Q8—3761no—
275D4—472no—
276D4—941no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—471no—
282C2×C4—471no—
283C2×C4—471no—
284C2×C4—471no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—3761no—
289C2×C4—3761no—
290C2×C4—1882no—
291C2×C4D4×D4711yescharacteristic
292C2×C4D4×D4711yescharacteristic
293C2×C4C23×D4711yescharacteristic
294C8—21no—
295C8—21no—
296C8—941no—
297C8—941no—
298C22—942no—
299C22—1881no—
300C22—1881no—
301C22C2×D4×D4711yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—472no—
309C4—941no—
310C4—941no—
311C4—941no—
312C4—1881no—
313C4—1881no—
314C4—1881no—
315C4#41×D4711yescharacteristic
316C4#1309407211yescharacteristic
317C2—1882no—
318C2#1568978311yescharacteristic
319C2#137×D4711yescharacteristic
320C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#479C2
socleC22×C47C22×D4
hypercenter#479D47
hypocenterC47#3372
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #15689851C2semidirect
3. #15689493C2semidirect
4. #15689490C2semidirect
5. #15689472C2semidirect
6. #15689433C2semidirect
7. #15689417C2semidirect
11. #15689252C2semidirect
15. C47×#479C2semidirect
167. #479D47semidirect
176. C47#3372semidirect