Finite Group Databasebeta

← #20253596

Subgroups — #20253596

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#15689603C211yesmaximal, characteristic
2#15689456C211yesmaximal, characteristic, complemented
3#15689451C211yesmaximal, characteristic, complemented
4#15689427C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689330C211yesmaximal, characteristic, complemented
7#15689325C211yesmaximal, characteristic, complemented
8#15689283C211yesmaximal, characteristic
9#15689283C211yesmaximal, characteristic
10#15689228C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12C4×#10625337C211yesmaximal, characteristic, complemented
13C4×#10625336C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#541C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21C4×Dic94C2211yescharacteristic
22C4×Dic94C2211yescharacteristic
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25(C22⋊D47)⋊C4—21no—
26(C22⋊D47)⋊C4—21no—
27#13093982—21no—
28C2×C4⋊Dic47C2211yescharacteristic
29C4⋊C4×D47—21no—
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#126×C47—21no—
50#126×C47—21no—
51#125×C47—21no—
52#125×C47—21no—
53#125×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×Q8×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C22×Dic47—21no—
64#10625350—22no—
65#10625350—22no—
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×Dic94C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47D411yescharacteristic
80C4⋊C4×C47D411yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47D411yescharacteristic
86C22⋊C4×C47D411yescharacteristic
87C42×C47—21no—
88C42×C47—21no—
89C42×C47C2311yescharacteristic
90C42×C47C2311yescharacteristic
91#10625337—22no—
92#10625337—22no—
93#10625336—22no—
94#10625336—22no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47—21no—
114C2×C4×C47—21no—
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×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—24no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—81no—
131D188—21no—
132D188#4112yes—
133C4×D47—24no—
134C4×D47—81no—
135C4×D47—81no—
136Dic94—21no—
137Dic94#4112yes—
138C47⋊C8—21no—
139C47⋊C8—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—21no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C2×#4111yescharacteristic
159C4×C47C2×#4111yescharacteristic
160Dic47—22no—
161Dic47—41no—
162Dic47—41no—
163#3120—471nomaximal, Sylow
164C2×C47—41no—
165C2×C47#52511yescharacteristic
166C2×C47#57711yescharacteristic
167C2×C47#57811yescharacteristic
168D47—42no—
169#541D4711yescharacteristic, complemented
170#520—471no—
171#484—471no—
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⋊Q8C2×D4711yescharacteristic
191#126—21no—
192#126—21no—
193#125—21no—
194#125—21no—
195#125C2×D4711yescharacteristic
196C22⋊Q8C2×D4711yescharacteristic
197C22⋊Q8C2×D4711yescharacteristic
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8C2×D4711yescharacteristic
201C4×Q8C2×D4711yescharacteristic
202C4×D4—471no—
203C4×D4—471no—
204C4×D4—941no—
205C4×D4—941no—
206#117—941no—
207#117C2×D4711yescharacteristic
208C2×C4⋊C4—471no—
209C2×C4⋊C4—941no—
210#107—471no—
211#107—471no—
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#103—471no—
221#103—471no—
222#102—471no—
223#102—471no—
224C22⋊C8—471no—
225C22⋊C8—471no—
226#97—471no—
227C4×C8—471no—
228#41—942no—
229#41—942no—
230C2×Q8—471no—
231C2×Q8C22×D4711yescharacteristic
232C2×Q8C22×D4711yescharacteristic
233C2×D4—471no—
234C2×D4—941no—
235C22×C4—941no—
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×C8—471no—
247C2×C8—471no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4C22⋊D4711yescharacteristic
262C4⋊C4C22⋊D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4C22⋊D4711yescharacteristic
270C22⋊C4C22⋊D4711yescharacteristic
271C42—21no—
272C42—21no—
273C42—941no—
274C42—941no—
275C42C22×D4711yescharacteristic
276C42C22×D4711yescharacteristic
277C23—941no—
278C23C2×C22⋊D4711yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—472no—
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—944no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—3761no—
299C2×C4—3761no—
300C2×C4—3761no—
301C2×C4C2×C22⋊D4711yescharacteristic
302C2×C4C2×C22⋊D4711yescharacteristic
303C2×C4C2×C22⋊D4711yescharacteristic
304C2×C4C2×C22⋊D4711yescharacteristic
305C2×C4C2×C22⋊D4711yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—941no—
308C8—941no—
309C8—941no—
310C8—941no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—942no—
315C22—1881no—
316C22—1881no—
317C22C22×C22⋊D4711yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—942no—
328C4—1881no—
329C4—1881no—
330C4#41×D4711yescharacteristic
331C4#41×D4711yescharacteristic
332C2—41no—
333C2—1882no—
334C2#1568963011yescharacteristic
335C2#1568993111yescharacteristic
336C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#541C2
socleC22×C47C22×D4
hypercenter#541D47
hypocenterC47#3120
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #15689456C2semidirect
3. #15689451C2semidirect
4. #15689427C2semidirect
5. #15689420C2semidirect
6. #15689330C2semidirect
7. #15689325C2semidirect
10. #15689228C2semidirect
11. #15689221C2semidirect
12. C4×#10625337C2semidirect
13. C4×#10625336C2semidirect
14. #15689184C2semidirect
15. C47×#541C2semidirect
169. #541D47semidirect
184. C47#3120semidirect