Finite Group Databasebeta

← #20254658

Subgroups — #20254658

Order 6016.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689751C211yesmaximal, characteristic
2#15689735C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689525C211yesmaximal, characteristic, complemented
5#15689492C211yesmaximal, characteristic, complemented
6#15689474C211yesmaximal, characteristic, complemented
7#15689465C211yesmaximal, characteristic
8#15689465C211yesmaximal, characteristic
9#15689459C211yesmaximal, characteristic
10#15689454C211yesmaximal, characteristic
11#15689431C211yesmaximal, characteristic, complemented
12#15689431C211yesmaximal, characteristic, complemented
13#15689419C211yesmaximal, characteristic, complemented
14#15689409C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic
16#13094024C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094023—21no—
20#13094017—21no—
21#13094017—21no—
22#13094016C2211yescharacteristic
23#13094016C2211yescharacteristic
24#13094016C2211yescharacteristic
25#13094015—21no—
26#13094014—21no—
27#13094014—21no—
28#13094003C2211yescharacteristic
29#13094003C2211yescharacteristic
30#13094001—21no—
31#13094001—21no—
32C4×Dic94C2211yescharacteristic
33C4×Dic94C2211yescharacteristic
34#13093983C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093949C2211yescharacteristic
50#13093949C2211yescharacteristic
51#13093949C2211yescharacteristic
52#117×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic
54C4⋊C8×C47C2211yescharacteristic
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×Dic47—21no—
61C2×Dic94—21no—
62C2×Dic94—21no—
63C2×Dic94C2311yescharacteristic
64C2×Dic94C2311yescharacteristic
65C2×C8×C47C2311yescharacteristic
66C2×C8×C47C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C4⋊C4×C47D411yescharacteristic
70C4⋊C4×C47D411yescharacteristic
71C22⋊C4×C47D411yescharacteristic
72C22⋊C4×C47D411yescharacteristic
73C42×C47C2311yescharacteristic
74C42×C47C2311yescharacteristic
75C22⋊Dic47—21no—
76C22⋊Dic47—21no—
77C22⋊Dic47—21no—
78C4⋊Dic47—21no—
79C4⋊Dic47—21no—
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47C2311yescharacteristic
84C4⋊Dic47C2311yescharacteristic
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⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C23×C47C2×D411yescharacteristic
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47C2×D411yescharacteristic
106C2×C4×C47C2×D411yescharacteristic
107C2×C4×C47C2×D411yescharacteristic
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2411yescharacteristic
111C2×Dic47—21no—
112C2×Dic47—21no—
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—81no—
120Dic94—21no—
121Dic94—21no—
122Dic94—21no—
123Dic94—21no—
124Dic94—81no—
125Dic94—81no—
126C8×C47—21no—
127C8×C47—21no—
128C8×C47—21no—
129C8×C47—21no—
130C22×C47—21no—
131C22×C47—21no—
132C22×C47—21no—
133C22×C47C22×D411yescharacteristic
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—21no—
137C4×C47—21no—
138C4×C47—21no—
139C4×C472−1+411yescharacteristic
140C4×C472−1+411yescharacteristic
141Dic47—41no—
142Dic47—41no—
143Dic47—41no—
144Dic47—41no—
145Dic47—41no—
146Dic47—41no—
147Dic47—41no—
148Dic47—41no—
149#3242—471nomaximal, Sylow
150C2×C47—41no—
151C2×C47#53611yescharacteristic
152C2×C47#57711yescharacteristic
153C2×C47#57811yescharacteristic
154#544—471no—
155#541—471no—
156#501—471no—
157#499—471no—
158#491—471no—
159#487—471no—
160#485—471no—
161#485—471no—
162#484—471no—
163#483—471no—
164#479—471no—
165#479—471no—
166#477—471no—
167#475—471no—
168#433D4711yescharacteristic
169C47#324211yescharacteristic, complemented, Sylow
170C4⋊Q8—471no—
171C4⋊Q8—471no—
172C4⋊Q8—471no—
173C4⋊Q8—941no—
174#126—941no—
175#126—941no—
176#125—471no—
177#125—471no—
178#125—471no—
179#125—941no—
180#125—941no—
181#125—941no—
182C22⋊Q8—471no—
183C22⋊Q8—471no—
184C22⋊Q8—941no—
185C22⋊Q8—941no—
186C4×Q8—471no—
187C4×Q8—471no—
188#117—471no—
189#117C2×D4711yescharacteristic
190C2×C4⋊C4—471no—
191#107—471no—
192#107—471no—
193#107—471no—
194#107—471no—
195#106—471no—
196#106—471no—
197#106—471no—
198#106—471no—
199C4⋊C8C2×D4711yescharacteristic
200C4⋊C8C2×D4711yescharacteristic
201#103—471no—
202#103—471no—
203#103—471no—
204#103—471no—
205#103—471no—
206#103—471no—
207#103—471no—
208#103—471no—
209C22⋊C8C2×D4711yescharacteristic
210C22⋊C8C2×D4711yescharacteristic
211#97C2×D4711yescharacteristic
212C4×C8C2×D4711yescharacteristic
213C2×Q8—471no—
214C2×Q8—471no—
215C2×Q8—941no—
216C2×Q8—941no—
217C22×C4—941no—
218C22×C4C22×D4711yescharacteristic
219C2×C8C22×D4711yescharacteristic
220C2×C8C22×D4711yescharacteristic
221C2×C8C22×D4711yescharacteristic
222C2×C8C22×D4711yescharacteristic
223C4⋊C4—471no—
224C4⋊C4—471no—
225C4⋊C4—471no—
226C4⋊C4—471no—
227C4⋊C4—471no—
228C4⋊C4—471no—
229C4⋊C4—941no—
230C4⋊C4—941no—
231C4⋊C4—941no—
232C4⋊C4—941no—
233C4⋊C4—941no—
234C4⋊C4—941no—
235C4⋊C4—941no—
236C4⋊C4—941no—
237C4⋊C4—941no—
238C4⋊C4—941no—
239C4⋊C4—941no—
240C4⋊C4—941no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4D18811yescharacteristic
245C4⋊C4D18811yescharacteristic
246C22⋊C4—941no—
247C22⋊C4—941no—
248C22⋊C4—941no—
249C22⋊C4D18811yescharacteristic
250C22⋊C4D18811yescharacteristic
251C42—941no—
252C42—941no—
253C42—941no—
254C42C22×D4711yescharacteristic
255C42C22×D4711yescharacteristic
256C23C2×D18811yescharacteristic
257Q8—941no—
258Q8—941no—
259Q8—941no—
260Q8—941no—
261Q8—3761no—
262Q8—3761no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—941no—
266C2×C4—941no—
267C2×C4—941no—
268C2×C4—941no—
269C2×C4—941no—
270C2×C4—941no—
271C2×C4—941no—
272C2×C4—941no—
273C2×C4—3761no—
274C2×C4C2×D18811yescharacteristic
275C2×C4C2×D18811yescharacteristic
276C2×C4C2×D18811yescharacteristic
277C2×C4C2×D18811yescharacteristic
278C2×C4C2×D18811yescharacteristic
279C2×C4C23×D4711yescharacteristic
280C8—21no—
281C8—21no—
282C8—21no—
283C8—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×D18811yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—1881no—
294C4—1881no—
295C4—1881no—
296C4—1881no—
297C4—1881no—
298C4—1881no—
299C4—1881no—
300C4—1881no—
301C4#1309407111yescharacteristic
302C4#1309407111yescharacteristic
303C2—41no—
304C2#1568969911yescharacteristic
305C2#1568993511yescharacteristic
306C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3242
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
3. #15689532C2semidirect
4. #15689525C2semidirect
5. #15689492C2semidirect
6. #15689474C2semidirect
11. #15689431C2semidirect
12. #15689431C2semidirect
13. #15689419C2semidirect
14. #15689409C2semidirect
169. C47#3242semidirect