Finite Group Databasebeta

← #20256299

Subgroups — #20256299

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#15689832C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689531C211yesmaximal, characteristic, complemented
5#15689527C211yesmaximal, characteristic, complemented
6#15689430C211yesmaximal, characteristic, complemented
7#15689428C211yesmaximal, characteristic, complemented
8#15689416C211yesmaximal, characteristic, complemented
9#15689411C211yesmaximal, characteristic
10#15689403C211yesmaximal, characteristic
11#15689401C211yesmaximal, characteristic
12#15689251C211yesmaximal, characteristic, complemented
13#15689224C211yesmaximal, characteristic
14SD16×Dic47C211yesmaximal, characteristic
15C47×#440C211yesmaximal, characteristic
16#13094024—21no—
17#13094024C2211yescharacteristic
18#13094023—21no—
19#13094023—21no—
20#13094023C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094023C2211yescharacteristic
23#13094016C2211yescharacteristic
24#13094015C2211yescharacteristic
25#13094003—21no—
26#13094001—21no—
27#13094001—21no—
28Q8×Dic47C2211yescharacteristic
29Q8×Dic47C2211yescharacteristic
30C4×Dic94—21no—
31C4×Dic94C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34C2×Dic47⋊C4—21no—
35#13093958C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×Dic47—21no—
63C22×Dic47—21no—
64C2×Dic94—21no—
65C2×Dic94—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×Dic94D411yescharacteristic
69SD16×C47Q814yescomplemented
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C22⋊C4×C47—21no—
76C42×C47—21no—
77C42×C47C2311yescharacteristic
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47D411yescharacteristic
85C4⋊Dic47C2311yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
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
103C23×C47—21no—
104Q8×C47—21no—
105Q8×C47C2×Q812yes—
106D4×C47—21no—
107D4×C47C2×Q812yes—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—81no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2411yescharacteristic
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—42no—
120C2×Dic47—81no—
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125Dic94—22no—
126Dic94—81no—
127Dic94—81no—
128Dic94—81no—
129Dic94—81no—
130C8×C47—21no—
131C8×C47C2×Q812yes—
132C47⋊C8—21no—
133C47⋊C8—21no—
134C22×C47—22no—
135C22×C47—41no—
136C22×C47—41no—
137C22×C47C22×D411yescharacteristic
138C4×C47—22no—
139C4×C47—21no—
140C4×C47—21no—
141C4×C47—41no—
142C4×C47—41no—
143C4×C47C22×Q811yescharacteristic
144C4×C472−1+411yescharacteristic
145Dic47—21no—
146Dic47—21no—
147Dic47—21no—
148Dic47—41no—
149Dic47—41no—
150Dic47—41no—
151Dic47—41no—
152Dic47#13712yes—
153#3385—471nomaximal, Sylow
154C2×C47—42no—
155C2×C47D4×Q811yescharacteristic
156C2×C47C2×#13711yescharacteristic
157C2×C47#57611yescharacteristic
158Q82—471no—
159#554—471no—
160#501—471no—
161#501—471no—
162#500—471no—
163#479—471no—
164#479—471no—
165#477—471no—
166#476—471no—
167#474—471no—
168#474—471no—
169#446—471no—
170#440—471no—
171#440D4711yescharacteristic
172C4×SD16—471no—
173C47#338511yescharacteristic, complemented, Sylow
174C2×SD16C2×D4711yescharacteristic
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#125—471no—
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×D4C2×D4711yescharacteristic
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#106—471no—
205C4⋊C8—471no—
206C4⋊C8—471no—
207C4⋊C8—471no—
208#103—471no—
209#103—471no—
210#103C2×D4711yescharacteristic
211#102—471no—
212#102—471no—
213#102C2×D4711yescharacteristic
214#97—471no—
215#97C2×D4711yescharacteristic
216C4×C8—471no—
217C2×Q8—471no—
218C2×Q8—941no—
219C2×Q8—941no—
220C2×Q8—941no—
221C2×Q8—941no—
222C2×Q8C22×D4711yescharacteristic
223C2×D4C22×D4711yescharacteristic
224C22×C4—21no—
225C22×C4—941no—
226C22×C4—941no—
227SD16Dic9414yescomplemented
228C2×C8—471no—
229C2×C8—471no—
230C2×C8C22×D4711yescharacteristic
231C2×C8C22×D4711yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—471no—
234C4⋊C4—471no—
235C4⋊C4—471no—
236C4⋊C4—471no—
237C4⋊C4—471no—
238C4⋊C4—471no—
239C4⋊C4—471no—
240C4⋊C4—941no—
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⋊C4—941no—
250C4⋊C4C22×D4711yescharacteristic
251C4⋊C4C22×D4711yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C42—21no—
256C42—471no—
257C42—471no—
258C42—941no—
259C42—941no—
260C42C22×D4711yescharacteristic
261C23—21no—
262Q8—21no—
263Q8—942no—
264Q8—3761no—
265Q8—3761no—
266Q8—3761no—
267Q8—3761no—
268Q8C2×Dic9412yes—
269D4—21no—
270D4C2×Dic9412yes—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—81no—
275C2×C4—471no—
276C2×C4—471no—
277C2×C4—471no—
278C2×C4—471no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—3761no—
284C2×C4—1882no—
285C2×C4D4×D4711yescharacteristic
286C2×C4D4×D4711yescharacteristic
287C2×C4C23×D4711yescharacteristic
288C8—21no—
289C8—941no—
290C8—941no—
291C8C2×Dic9412yes—
292C22—22no—
293C22—41no—
294C22—41no—
295C22C2×D4×D4711yescharacteristic
296C4—22no—
297C4—21no—
298C4—21no—
299C4—41no—
300C4—41no—
301C4—472no—
302C4—941no—
303C4—941no—
304C4—941no—
305C4—1881no—
306C4—1881no—
307C4—1881no—
308C4—1881no—
309C4C22×Dic9411yescharacteristic
310C4#1309407111yescharacteristic
311C2—42no—
312C2D4×Dic9411yescharacteristic
313C2#137×D4711yescharacteristic
314C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3385
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. Q8×Dic94C2semidirect
3. #15689532C2semidirect
4. #15689531C2semidirect
5. #15689527C2semidirect
6. #15689430C2semidirect
7. #15689428C2semidirect
8. #15689416C2semidirect
12. #15689251C2semidirect
69. SD16×C47Q8semidirect
173. C47#3385semidirect
227. SD16Dic94semidirect