Finite Group Databasebeta

← #20253597

Subgroups — #20253597

Order 6016.

372 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#15689733C211yesmaximal, characteristic, complemented
2#15689604C211yesmaximal, characteristic
3#15689453C211yesmaximal, characteristic, complemented
4#15689429C211yesmaximal, characteristic, complemented
5#15689426C211yesmaximal, characteristic, complemented
6#15689332C211yesmaximal, characteristic, complemented
7#15689327C211yesmaximal, characteristic, complemented
8#15689287C211yesmaximal, characteristic
9#15689283C211yesmaximal, characteristic
10#15689227C211yesmaximal, characteristic, complemented
11#15689222C211yesmaximal, characteristic, complemented
12#15689217C211yesmaximal, characteristic, complemented
13#15689208C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#484C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21#13094022C2211yescharacteristic
22#13094017—21no—
23#13094017—21no—
24#13094015—21no—
25#13094015C2211yescharacteristic
26#13094014—21no—
27#13094003C2211yescharacteristic
28Q8×Dic47C2211yescharacteristic
29#13093989C2211yescharacteristic
30#13093989C2211yescharacteristic
31#13093989C2211yescharacteristic
32#13093986C2211yescharacteristic
33#13093986C2211yescharacteristic
34C4×C22⋊D47—21no—
35C4×C22⋊D47—21no—
36#13093983C2211yescharacteristic
37#13093982—21no—
38C4⋊C4×D47—21no—
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C22×C4×C47—21no—
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63#10625350—22no—
64#10625350—22no—
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×Dic94C2311yescharacteristic
70C2×Dic94C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47D411yescharacteristic
81C22⋊Dic47D411yescharacteristic
82#10625337—22no—
83#10625336—22no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47D411yescharacteristic
89C4⋊Dic47D411yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106Dic188—22no—
107#10625325—22no—
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110Q8×C47—21no—
111Q8×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—81no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—24no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129D188—21no—
130D188#4112yes—
131C4×D47—24no—
132C4×D47—81no—
133C4×D47—81no—
134Dic94—21no—
135Dic94—21no—
136Dic94—21no—
137Dic94#4112yes—
138C8×C47—21no—
139C8×C47—21no—
140C47⋊C8—21no—
141C47⋊C8—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47C22×D411yescharacteristic
146C2×D47—22no—
147C2×D47—41no—
148C2×D47—41no—
149C4×C47—21no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47C2×#4111yescharacteristic
155C4×C47C2×#4111yescharacteristic
156Dic47—22no—
157Dic47—21no—
158Dic47—21no—
159Dic47—21no—
160Dic47—21no—
161Dic47—41no—
162Dic47—41no—
163#3120—471nomaximal, Sylow
164C2×C47—41no—
165C2×C47#52511yescharacteristic
166C2×C47#57711yescharacteristic
167C2×C47#57811yescharacteristic
168D47—42no—
169#541—471no—
170#520—471no—
171#484D4711yescharacteristic, complemented
172#483—471no—
173#479—471no—
174#478—471no—
175#462—471no—
176#461—471no—
177#452—471no—
178#452—471no—
179#441—471no—
180#440—471no—
181C4×Q16—471no—
182C4×SD16—471no—
183#433—471no—
184C47#312011yescharacteristic, complemented, Sylow
185C2×#41—471no—
186C2×Q16—471no—
187C2×Q16—471no—
188C2×SD16—471no—
189C2×SD16—471no—
190C4⋊Q8—471no—
191#126—941no—
192#126—941no—
193#125—471no—
194#125—941no—
195#125—941no—
196C22⋊Q8—471no—
197C22⋊Q8C2×D4711yescharacteristic
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×D4—471no—
203C4×D4—471no—
204C4×D4—941no—
205C4×D4—941no—
206#117—471no—
207#117—941no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4C2×D4711yescharacteristic
210#107C2×D4711yescharacteristic
211#107C2×D4711yescharacteristic
212#106—471no—
213#106—471no—
214C4⋊C8—471no—
215C4⋊C8—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103C2×D4711yescharacteristic
221#103C2×D4711yescharacteristic
222#102—471no—
223#102—471no—
224C22⋊C8—471no—
225C22⋊C8C2×D4711yescharacteristic
226#97—471no—
227C4×C8—471no—
228#41—942no—
229#41—942no—
230C2×Q8—471no—
231C2×Q8—471no—
232C2×Q8C22×D4711yescharacteristic
233C2×D4—471no—
234C2×D4—941no—
235C22×C4—21no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4C22×D4711yescharacteristic
240Q16—942no—
241Q16—942no—
242SD16—942no—
243SD16—942no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
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⋊C4—941no—
262C4⋊C4C22×D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—471no—
267C22⋊C4—471no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C42—471no—
272C42—471no—
273C42—941no—
274C42—941no—
275C42—941no—
276C42—941no—
277C23—941no—
278C23D4×D4711yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—472no—
282Q8—941no—
283Q8—941no—
284Q8—941no—
285D4—472no—
286D4—944no—
287D4—941no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—471no—
298C2×C4—471no—
299C2×C4—944no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—3761no—
304C2×C4—3761no—
305C2×C4D4×D4711yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—21no—
308C8—21no—
309C8—941no—
310C8—941no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—942no—
315C22—1881no—
316C22—1881no—
317C22C2×D4×D4711yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—942no—
324C4—941no—
325C4—941no—
326C4—941no—
327C4—941no—
328C4—1881no—
329C4—1881no—
330C4#41×D4711yescharacteristic
331C4#41×D4711yescharacteristic
332C2—41no—
333C2—1882no—
334C2#1568963111yescharacteristic
335C2#1568993311yescharacteristic
336C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#484C2
socleC22×C47C22×D4
hypercenter#484D47
hypocenterC47#3120
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #15689733C2semidirect
3. #15689453C2semidirect
4. #15689429C2semidirect
5. #15689426C2semidirect
6. #15689332C2semidirect
7. #15689327C2semidirect
10. #15689227C2semidirect
11. #15689222C2semidirect
12. #15689217C2semidirect
13. #15689208C2semidirect
14. #15689181C2semidirect
15. C47×#484C2semidirect
171. #484D47semidirect
184. C47#3120semidirect