Finite Group Databasebeta

← #20256301

Subgroups — #20256301

Order 6016.

340 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic94C211yesmaximal, characteristic, complemented
2#15689829C211yesmaximal, characteristic
3#15689533C211yesmaximal, characteristic, complemented
4#15689530C211yesmaximal, characteristic, complemented
5#15689527C211yesmaximal, characteristic, complemented
6#15689432C211yesmaximal, characteristic, complemented
7#15689416C211yesmaximal, characteristic, complemented
8#15689412C211yesmaximal, characteristic
9#15689404C211yesmaximal, characteristic
10#15689402C211yesmaximal, characteristic
11#15689252C211yesmaximal, characteristic, complemented
12#15689226C211yesmaximal, characteristic
13#15689221C211yesmaximal, characteristic
14#15689208C211yesmaximal, characteristic
15C47×#479C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17#13094024—21no—
18#13094024C2211yescharacteristic
19#13094023—21no—
20#13094023—21no—
21#13094023C2211yescharacteristic
22#13094023C2211yescharacteristic
23#13094023C2211yescharacteristic
24#13094015C2211yescharacteristic
25#13094004—21no—
26#13094002—21no—
27#13094002—21no—
28Q8×Dic47C2211yescharacteristic
29Q8×Dic47C2211yescharacteristic
30C4×Dic94—21no—
31C4×Dic94C2211yescharacteristic
32C4×D188C2211yescharacteristic
33#13093986C2211yescharacteristic
34#13093986C2211yescharacteristic
35C4⋊C4×D47—21no—
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
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×Dic94—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×Dic94D411yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C42×C47—21no—
78C42×C47C2311yescharacteristic
79#10625336Q814yescomplemented
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47D411yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
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
103C22×D47—21no—
104Q8×C47—21no—
105Q8×C47C2×Q812yes—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2411yescharacteristic
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47C2×D411yescharacteristic
117C2×Dic47C2×D411yescharacteristic
118C2×Dic47C2×D411yescharacteristic
119C2×Dic47C2×D411yescharacteristic
120D188—21no—
121D188C2×Q812yes—
122C4×D47—42no—
123C4×D47—81no—
124C4×D47—81no—
125Dic94—22no—
126Dic94—81no—
127Dic94—81no—
128Dic94—81no—
129Dic94—81no—
130C8×C47—21no—
131C8×C47—21no—
132C47⋊C8—21no—
133C47⋊C8C2×Q812yes—
134C22×C47C22×D411yescharacteristic
135C2×D47—22no—
136C2×D47—41no—
137C2×D47—41no—
138C4×C47—22no—
139C4×C47—21no—
140C4×C47—21no—
141C4×C47—41no—
142C4×C47—41no—
143C4×C47—41no—
144C4×C47C22×Q811yescharacteristic
145C4×C472−1+411yescharacteristic
146Dic47—21no—
147Dic47—21no—
148Dic47—21no—
149Dic47—41no—
150Dic47—41no—
151Dic47—41no—
152Dic47#13712yes—
153#3385—471nomaximal, Sylow
154C2×C47D4×Q811yescharacteristic
155C2×C47C2×#13711yescharacteristic
156C2×C47#57611yescharacteristic
157D47—42no—
158Q82—471no—
159#554—471no—
160#501—471no—
161#501—471no—
162#500—471no—
163#479—471no—
164#479D4711yescharacteristic, complemented
165#477—471no—
166#476—471no—
167#474—471no—
168#474—471no—
169#446—471no—
170#440—471no—
171#440—471no—
172C4×SD16—471no—
173C47#338511yescharacteristic, complemented, Sylow
174C2×SD16—471no—
175C4⋊Q8—471no—
176C4⋊Q8—471no—
177C4⋊Q8—471no—
178C4⋊Q8—471no—
179C4⋊Q8—941no—
180C4⋊Q8—941no—
181C4⋊Q8—941no—
182#125—471no—
183#125C2×D4711yescharacteristic
184C22⋊Q8—941no—
185C22⋊Q8—941no—
186C22⋊Q8—941no—
187C4×Q8—471no—
188C4×Q8—471no—
189C4×Q8—471no—
190C4×Q8—941no—
191C4×Q8C2×D4711yescharacteristic
192C4×D4—471no—
193C4×D4—471no—
194C4×D4—471no—
195C2×C4⋊C4—941no—
196#107—471no—
197#107—471no—
198#107—471no—
199#107—471no—
200#107—471no—
201#107C2×D4711yescharacteristic
202#106—471no—
203#106—471no—
204#106C2×D4711yescharacteristic
205C4⋊C8—471no—
206C4⋊C8—471no—
207C4⋊C8C2×D4711yescharacteristic
208#103—471no—
209#103C2×D4711yescharacteristic
210#103C2×D4711yescharacteristic
211#102—471no—
212#102—471no—
213#102—471no—
214#97—471no—
215#97—471no—
216C4×C8—471no—
217C2×Q8—471no—
218C2×Q8—941no—
219C2×Q8—941no—
220C2×Q8—941no—
221C2×Q8—941no—
222C2×Q8C22×D4711yescharacteristic
223C2×D4—471no—
224C22×C4—941no—
225C22×C4—941no—
226C22×C4—941no—
227SD16—474no—
228C2×C8—471no—
229C2×C8—471no—
230C2×C8C22×D4711yescharacteristic
231C2×C8C22×D4711yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—471no—
236C4⋊C4—471no—
237C4⋊C4—471no—
238C4⋊C4—471no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4C22×D4711yescharacteristic
250C4⋊C4C22×D4711yescharacteristic
251C4⋊C4C22×D4711yescharacteristic
252C22⋊C4—941no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C42—21no—
256C42—471no—
257C42—471no—
258C42—941no—
259C42—941no—
260C42C22×D4711yescharacteristic
261C23—941no—
262Q8—21no—
263Q8—942no—
264Q8—3761no—
265Q8—3761no—
266Q8—3761no—
267Q8—3761no—
268Q8Q8×D4712yes—
269D4—472no—
270D4—941no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—471no—
276C2×C4—471no—
277C2×C4—471no—
278C2×C4—471no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—3761no—
283C2×C4—3761no—
284C2×C4—1882no—
285C2×C4D4×D4711yescharacteristic
286C2×C4D4×D4711yescharacteristic
287C2×C4C23×D4711yescharacteristic
288C8—21no—
289C8—21no—
290C8—472no—
291C8—941no—
292C22—942no—
293C22—1881no—
294C22—1881no—
295C22C2×D4×D4711yescharacteristic
296C4—22no—
297C4—21no—
298C4—21no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—472no—
303C4—941no—
304C4—941no—
305C4—941no—
306C4—1881no—
307C4—1881no—
308C4—1881no—
309C4C2×Q8×D4711yescharacteristic
310C4#1309407111yescharacteristic
311C2—1882no—
312C2#1568978611yescharacteristic
313C2#137×D4711yescharacteristic
314C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#479C2
socleC22×C47C22×D4
hypercenter#479D47
hypocenterC47#3385
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. Q8×Dic94C2semidirect
3. #15689533C2semidirect
4. #15689530C2semidirect
5. #15689527C2semidirect
6. #15689432C2semidirect
7. #15689416C2semidirect
11. #15689252C2semidirect
15. C47×#479C2semidirect
79. #10625336Q8semidirect
164. #479D47semidirect
173. C47#3385semidirect