Finite Group Databasebeta

← #20254754

Subgroups — #20254754

Order 6016.

348 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689675C211yesmaximal, characteristic, complemented
2#15689654C211yesmaximal, characteristic
3#15689429C211yesmaximal, characteristic, complemented
4#15689428C211yesmaximal, characteristic, complemented
5#15689417C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689381C211yesmaximal, characteristic, complemented
8#15689379C211yesmaximal, characteristic, complemented
9#15689367C211yesmaximal, characteristic
10#15689344C211yesmaximal, characteristic, complemented
11#15689343C211yesmaximal, characteristic, complemented
12#15689332C211yesmaximal, characteristic, complemented
13#15689326C211yesmaximal, characteristic, complemented
14#15689146C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic
16C2×Dic188C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094022C2211yescharacteristic
22#13094017—21no—
23#13094015C2211yescharacteristic
24#13094014—21no—
25#13094011C2211yescharacteristic
26#13094005—21no—
27#13094003C2211yescharacteristic
28#13094003C2211yescharacteristic
29#13094001—21no—
30Q8×Dic47C2211yescharacteristic
31#13093989—21no—
32#13093989C2211yescharacteristic
33#13093989C2211yescharacteristic
34D4×Dic47—21no—
35D4×Dic47C2211yescharacteristic
36#13093980—21no—
37#13093980—21no—
38C2×C4×Dic47C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093947C2211yescharacteristic
50#13093947C2211yescharacteristic
51#13093945C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×Dic47—21no—
64C22×Dic47D411yescharacteristic
65C22×Dic47D411yescharacteristic
66C2×Dic94—21no—
67C2×Dic94C2311yescharacteristic
68C2×Dic94C2311yescharacteristic
69SD16×C47—41no—
70M16×C47—41no—
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83#10625337—41no—
84#10625335—41no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
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—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47D411yescharacteristic
101C4×Dic47D411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104#10625329—41no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107Dic188—41no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112D4×C47—21no—
113D4×C47—21no—
114D4×C47—42no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C2×Dic47—22no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—41no—
128C2×Dic47—42no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133Dic94—21no—
134Dic94—21no—
135Dic94—21no—
136Dic94—21no—
137Dic94—42no—
138C8×C47—21no—
139C8×C47—21no—
140C47⋊C8—21no—
141C47⋊C8—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47C22×D411yescharacteristic
149C4×C47—21no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47H(5,𝔽2)11yescharacteristic
154C4×C472−1+411yescharacteristic
155Dic47—21no—
156Dic47—21no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47#13712yes—
163#3252—471nomaximal, Sylow
164C2×C47—41no—
165C2×C47—81no—
166C2×C47#53711yescharacteristic
167C2×C47C2×#13711yescharacteristic
168C2×C47#57511yescharacteristic
169#533—471no—
170#529—471no—
171#479—471no—
172#479—471no—
173#477—471no—
174#476—471no—
175#470—471no—
176#470—471no—
177#468—471no—
178#468D4711yescharacteristic
179#464—471no—
180#464—471no—
181#462—471no—
182#461—471no—
183#423—471no—
184C47#325211yescharacteristic, complemented, Sylow
185C2×Q16—471no—
186C2×Q16—471no—
187C2×SD16—471no—
188C2×SD16C2×D4711yescharacteristic
189C2×M16—471no—
190C2×M16C2×D4711yescharacteristic
191C4⋊Q8—471no—
192C4⋊Q8—471no—
193#126—941no—
194#125—471no—
195#125—941no—
196#124—471no—
197#123—941no—
198C22⋊Q8—471no—
199C22⋊Q8—471no—
200C22⋊Q8—941no—
201C22⋊Q8C2×D4711yescharacteristic
202#121C2×D4711yescharacteristic
203C4×Q8—471no—
204C4×Q8—471no—
205C4×Q8—471no—
206C4×Q8—941no—
207C4×D4—471no—
208C4×D4—941no—
209#117—941no—
210#117—941no—
211C2×C42—471no—
212#107—471no—
213#107C2×D4711yescharacteristic
214#106—471no—
215#106—471no—
216C4⋊C8—471no—
217C4⋊C8—471no—
218C4⋊C8—471no—
219C4⋊C8—471no—
220#103—471no—
221#103—471no—
222#103—471no—
223#103—471no—
224#103—471no—
225#103C2×D4711yescharacteristic
226#102—471no—
227#102C2×D4711yescharacteristic
228C2×Q8—471no—
229C2×Q8—471no—
230C2×Q8—941no—
231C2×Q8C22×D4711yescharacteristic
232C2×D4—21no—
233C2×D4C22×D4711yescharacteristic
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—941no—
237C22×C4C22×D4711yescharacteristic
238Q16—1881no—
239Q16—1881no—
240SD16—41no—
241SD16—1881no—
242M16—41no—
243M16—1881no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4C22×D4711yescharacteristic
262C4⋊C4C22×D4711yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—471no—
271C42—471no—
272C42—471no—
273C42—471no—
274C42—941no—
275C42—941no—
276C42—941no—
277C23—21no—
278C23D4×D4711yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—941no—
282Q8—941no—
283Q8—941no—
284Q8—941no—
285Q8—1882no—
286D4—21no—
287D4—21no—
288D4—42no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—471no—
298C2×C4—942no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—1882no—
304C2×C4—1881no—
305C2×C4D4×D4711yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—21no—
308C8—21no—
309C8—941no—
310C8—941no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C2×D4×D4711yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—472no—
323C4—941no—
324C4—941no—
325C4—941no—
326C4—1881no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C4#1309406911yescharacteristic
331C4#1309407111yescharacteristic
332C2—41no—
333C2—81no—
334C2#1568970011yescharacteristic
335C2#137×D4711yescharacteristic
336C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3252
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #15689675C2semidirect
3. #15689429C2semidirect
4. #15689428C2semidirect
5. #15689417C2semidirect
6. #15689411C2semidirect
7. #15689381C2semidirect
8. #15689379C2semidirect
10. #15689344C2semidirect
11. #15689343C2semidirect
12. #15689332C2semidirect
13. #15689326C2semidirect
14. #15689146C2semidirect
184. C47#3252semidirect