Finite Group Databasebeta

← #20255875

Subgroups — #20255875

Order 6016.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689830C211yesmaximal, characteristic, complemented
2#15689819C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689465C211yesmaximal, characteristic, complemented
5#15689459C211yesmaximal, characteristic, complemented
6#15689442C211yesmaximal, characteristic, complemented
7#15689437C211yesmaximal, characteristic, complemented
8#15689431C211yesmaximal, characteristic, complemented
9#15689404C211yesmaximal, characteristic, complemented
10#15689369C211yesmaximal, characteristic, complemented
11#15689352C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13#15689165C211yesmaximal, characteristic, complemented
14C2×#13093958C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094019—21no—
19#13094016C2211yescharacteristic
20#13094015—21no—
21#13094006—21no—
22#13094003C2211yescharacteristic
23#13094003C2211yescharacteristic
24#13094001—21no—
25#13094001—21no—
26#13093998C2211yescharacteristic
27#13093998C2211yescharacteristic
28#13093996—21no—
29C4×Dic94C2211yescharacteristic
30C4×D188C2211yescharacteristic
31D4×Dic47—21no—
32(C22⋊D47)⋊C4—21no—
33#13093983C2211yescharacteristic
34C2×C4⋊Dic47C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36C2×C4⋊Dic47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093958C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093956C2211yescharacteristic
45#13093956C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47D411yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×Dic94—21no—
70C2×Dic94C2311yescharacteristic
71M16×C47—22no—
72C2×C8×C47—22no—
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47D411yescharacteristic
78C22⋊C4×C47D411yescharacteristic
79C22⋊C4×C47D411yescharacteristic
80C42×C47C2311yescharacteristic
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104#10625325—22no—
105C23×C47C2×D411yescharacteristic
106C23×C47C2×D411yescharacteristic
107C22×D47—21no—
108D4×C47—22no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C22⋊D47—42no—
119C22⋊D47—81no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—81no—
128C2×Dic47—81no—
129C2×Dic47—81no—
130D188—21no—
131D188—21no—
132C4×D47—81no—
133Dic94—21no—
134Dic94—21no—
135Dic94—81no—
136C8×C47—21no—
137C8×C47—21no—
138C8×C47—21no—
139C8×C47#4112yes—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47#13712yes—
146C22×C47C22×D411yescharacteristic
147C2×D47—41no—
148C2×D47—41no—
149C2×D47—41no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47C2×#4111yescharacteristic
155C4×C472−1+411yescharacteristic
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163#3346—471nomaximal, Sylow
164C2×C47—22no—
165C2×C47—41no—
166C2×C47#54711yescharacteristic
167C2×C47C2×#13711yescharacteristic
168C2×C47#57611yescharacteristic
169D47—81no—
170#554—471no—
171#553—471no—
172#501—471no—
173#485—471no—
174#484—471no—
175#481—471no—
176#480—471no—
177#479—471no—
178#474—471no—
179#468—471no—
180#465—471no—
181#440—471no—
182#435D4711yescharacteristic, complemented
183#428—471no—
184C2×#107—471no—
185C47#334611yescharacteristic, complemented, Sylow
186C2×SD16—471no—
187C2×M16C2×D4711yescharacteristic
188C22×C8C2×D4711yescharacteristic
189C4⋊Q8—471no—
190#126—941no—
191#125—471no—
192#125—941no—
193#123—941no—
194C22⋊Q8—471no—
195C22⋊Q8—471no—
196C22⋊Q8—941no—
197C22⋊Q8—941no—
198#121—471no—
199#121—471no—
200#121—941no—
201C4×Q8—471no—
202C4×D4—471no—
203C4×D4—941no—
204C4×D4—941no—
205C4×D4C2×D4711yescharacteristic
206#117—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210#107—471no—
211#107—471no—
212#107—471no—
213#107—471no—
214#107—471no—
215#107—471no—
216#106—471no—
217#106—471no—
218#106—471no—
219C4⋊C8C2×D4711yescharacteristic
220#103—471no—
221#103—471no—
222#103—471no—
223#102—471no—
224#102—471no—
225#102—471no—
226C22⋊C8C2×D4711yescharacteristic
227C22⋊C8C2×D4711yescharacteristic
228#97C2×D4711yescharacteristic
229C2×Q8—471no—
230C2×Q8—941no—
231C2×D4—471no—
232C2×D4—941no—
233C2×D4—941no—
234C2×D4D18811yescharacteristic
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4C22×D4711yescharacteristic
240C22×C4C22×D4711yescharacteristic
241SD16—942no—
242M16—22no—
243C2×C8—22no—
244C2×C8C22×D4711yescharacteristic
245C2×C8C22×D4711yescharacteristic
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—471no—
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⋊C4—941no—
263C4⋊C4D18811yescharacteristic
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4D18811yescharacteristic
271C22⋊C4D18811yescharacteristic
272C42—941no—
273C42—941no—
274C42C22×D4711yescharacteristic
275C23—941no—
276C23C2×D18811yescharacteristic
277C23C2×D18811yescharacteristic
278Q8—941no—
279Q8—941no—
280Q8—3761no—
281D4—22no—
282D4—941no—
283D4—941no—
284D4—3761no—
285D4—1882no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—3761no—
298C2×C4—3761no—
299C2×C4—3761no—
300C2×C4—3761no—
301C2×C4C2×D18811yescharacteristic
302C2×C4C2×D18811yescharacteristic
303C2×C4C2×D18811yescharacteristic
304C2×C4C2×D18811yescharacteristic
305C2×C4C23×D4711yescharacteristic
306C8—21no—
307C8—21no—
308C8—21no—
309C8#1062535212yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—1881no—
316C22—1881no—
317C22—1881no—
318C22#1309405712yes—
319C22C22×D18811yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—1881no—
325C4—1881no—
326C4—1881no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C4—1881no—
331C4C2×#1062535211yescharacteristic
332C4#1309407111yescharacteristic
333C2—22no—
334C2—41no—
335C2—3761no—
336C2#1568977711yescharacteristic
337C2C2×#1309405711yescharacteristic
338C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3346
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #15689830C2semidirect
3. #15689532C2semidirect
4. #15689465C2semidirect
5. #15689459C2semidirect
6. #15689442C2semidirect
7. #15689437C2semidirect
8. #15689431C2semidirect
9. #15689404C2semidirect
10. #15689369C2semidirect
11. #15689352C2semidirect
12. #15689225C2semidirect
13. #15689165C2semidirect
14. C2×#13093958C2semidirect
15. C47×#435C2semidirect
182. #435D47semidirect
185. C47#3346semidirect