Finite Group Databasebeta

← #20255903

Subgroups — #20255903

Order 6016.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689813C211yesmaximal, characteristic, complemented
2#15689529C211yesmaximal, characteristic, complemented
3#15689464C211yesmaximal, characteristic, complemented
4#15689464C211yesmaximal, characteristic, complemented
5#15689444C211yesmaximal, characteristic, complemented
6#15689439C211yesmaximal, characteristic, complemented
7#15689423C211yesmaximal, characteristic, complemented
8#15689405C211yesmaximal, characteristic, complemented
9#15689367C211yesmaximal, characteristic, complemented
10#15689350C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689166C211yesmaximal, characteristic, complemented
14#15689159C211yesmaximal, characteristic, complemented
15C47×#555C211yesmaximal, characteristic
16C2×#10625335C2211yescharacteristic
17C2×#10625329C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13094017—21no—
20#13094016C2211yescharacteristic
21#13094014—21no—
22#13094005—21no—
23#13094003C2211yescharacteristic
24#13094003C2211yescharacteristic
25C4×Dic94C2211yescharacteristic
26#13093983C2211yescharacteristic
27#13093980—21no—
28C2×C4⋊Dic47C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093955C2211yescharacteristic
34#13093955C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093955C2211yescharacteristic
37#13093955C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093945C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#124×C47—21no—
50#124×C47—21no—
51#121×C47—21no—
52#121×C47C2211yescharacteristic
53#121×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56#117×C47—21no—
57#117×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47D411yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×Dic47—21no—
68C2×Dic94C2311yescharacteristic
69C4⋊C4×C47—21no—
70C4⋊C4×C47D411yescharacteristic
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C22⋊C4×C47—21no—
75C22⋊C4×C47—21no—
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C22⋊C4×C47D411yescharacteristic
80C22⋊C4×C47D411yescharacteristic
81C42×C47—21no—
82C42×C47—21no—
83C42×C47C2311yescharacteristic
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87#10625335—22no—
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99#10625329—22no—
100C2×C47⋊C8—22no—
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47—21no—
106C23×C47C2×D411yescharacteristic
107C23×C47C2×D411yescharacteristic
108Q8×C47—81no—
109D4×C47—21no—
110D4×C47—21no—
111D4×C47—41no—
112D4×C47—81no—
113D4×C47—81no—
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×C47—21no—
121C2×C4×C47—42no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—42no—
132Dic94—21no—
133Dic94—21no—
134C47⋊C8—21no—
135C47⋊C8—21no—
136C47⋊C8—21no—
137C47⋊C8#4112yes—
138C22×C47—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47C22×D411yescharacteristic
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47C2×#4111yescharacteristic
156C4×C472−1+411yescharacteristic
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3348—471nomaximal, Sylow
162C2×C47—41no—
163C2×C47—41no—
164C2×C47—81no—
165C2×C47#54711yescharacteristic
166C2×C47#57511yescharacteristic
167C2×C47#57711yescharacteristic
168#555D4711yescharacteristic
169#552—471no—
170#501—471no—
171#485—471no—
172#485—471no—
173#482—471no—
174#481—471no—
175#478—471no—
176#475—471no—
177#468—471no—
178#465—471no—
179#440—471no—
180#435—471no—
181#428—471no—
182#427—471no—
183C47#334811yescharacteristic, complemented, Sylow
184C2×SD16—471no—
185C2×M16—471no—
186C22×C8—471no—
187C4⋊Q8C2×D4711yescharacteristic
188#126—941no—
189#125—471no—
190#125—941no—
191#124—21no—
192#124—21no—
193#123—941no—
194C22⋊Q8—471no—
195C22⋊Q8—471no—
196#121—21no—
197#121C2×D4711yescharacteristic
198#121C2×D4711yescharacteristic
199C4×Q8—471no—
200C4×D4C2×D4711yescharacteristic
201C4×D4C2×D4711yescharacteristic
202#117—21no—
203#117—471no—
204#117—941no—
205#117C2×D4711yescharacteristic
206#117C2×D4711yescharacteristic
207C2×C4⋊C4—471no—
208#107—471no—
209#107—471no—
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214#106—471no—
215#106—471no—
216#106—471no—
217C4⋊C8—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#102—471no—
222#102—471no—
223#102—471no—
224C22⋊C8—471no—
225C22⋊C8—471no—
226#97—471no—
227C2×Q8—21no—
228C2×Q8—471no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4C22⋊D4711yescharacteristic
232C2×D4C22×D4711yescharacteristic
233C22×C4—21no—
234C22×C4—941no—
235C22×C4C22×D4711yescharacteristic
236C22×C4C22×D4711yescharacteristic
237SD16—942no—
238M16—942no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—471no—
242C2×C8—471no—
243C2×C8—942no—
244C4⋊C4—21no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4C22⋊D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4C22⋊D4711yescharacteristic
267C22⋊C4C22⋊D4711yescharacteristic
268C42—21no—
269C42—21no—
270C42—941no—
271C42—941no—
272C42C22×D4711yescharacteristic
273C23—21no—
274C23C2×C22⋊D4711yescharacteristic
275C23C2×C22⋊D4711yescharacteristic
276Q8—81no—
277Q8—941no—
278Q8—941no—
279D4—21no—
280D4—21no—
281D4—41no—
282D4—81no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—1882no—
297C2×C4C2×C22⋊D4711yescharacteristic
298C2×C4C2×C22⋊D4711yescharacteristic
299C2×C4C2×C22⋊D4711yescharacteristic
300C2×C4C2×C22⋊D4711yescharacteristic
301C2×C4C23×D4711yescharacteristic
302C8—472no—
303C8—941no—
304C8—941no—
305C8—941no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C22×C22⋊D4711yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4—1881no—
327C4#41×D4711yescharacteristic
328C4#1309407111yescharacteristic
329C2—41no—
330C2—41no—
331C2—81no—
332C2#1568977211yescharacteristic
333C2#1568992111yescharacteristic
334C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#555C2
socleC22×C47C22×D4
hypercenter#555D47
hypocenterC47#3348
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #15689813C2semidirect
2. #15689529C2semidirect
3. #15689464C2semidirect
4. #15689464C2semidirect
5. #15689444C2semidirect
6. #15689439C2semidirect
7. #15689423C2semidirect
8. #15689405C2semidirect
9. #15689367C2semidirect
10. #15689350C2semidirect
11. #15689223C2semidirect
12. #15689195C2semidirect
13. #15689166C2semidirect
14. #15689159C2semidirect
183. C47#3348semidirect