Finite Group Databasebeta

← #20255905

Subgroups — #20255905

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#15689838C211yesmaximal, characteristic
2#15689813C211yesmaximal, characteristic, complemented
3#15689532C211yesmaximal, characteristic, complemented
4#15689465C211yesmaximal, characteristic, complemented
5#15689465C211yesmaximal, characteristic, complemented
6#15689448C211yesmaximal, characteristic, complemented
7#15689442C211yesmaximal, characteristic, complemented
8#15689424C211yesmaximal, characteristic, complemented
9#15689409C211yesmaximal, characteristic, complemented
10#15689369C211yesmaximal, characteristic, complemented
11#15689352C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13#15689165C211yesmaximal, characteristic, complemented
14#15689161C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094017—21no—
19#13094016C2211yescharacteristic
20#13094014—21no—
21#13094010—21no—
22#13094010—21no—
23#13094005—21no—
24#13094003C2211yescharacteristic
25#13094003C2211yescharacteristic
26#13093998C2211yescharacteristic
27#13093998C2211yescharacteristic
28#13093995—21no—
29C4×Dic94C2211yescharacteristic
30C4×D188C2211yescharacteristic
31#13093983C2211yescharacteristic
32#13093983C2211yescharacteristic
33#13093983C2211yescharacteristic
34#13093982—21no—
35#13093980—21no—
36C2×C4⋊Dic47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093956C2211yescharacteristic
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—
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×Dic94—21no—
68C2×Dic94C2311yescharacteristic
69M16×C47—22no—
70C2×C8×C47—22no—
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47D411yescharacteristic
76C22⋊C4×C47D411yescharacteristic
77C22⋊C4×C47D411yescharacteristic
78C42×C47C2311yescharacteristic
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
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⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104#10625325—22no—
105C23×C47C2×D411yescharacteristic
106C23×C47C2×D411yescharacteristic
107C22×D47—21no—
108D4×C47—41no—
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—81no—
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—42no—
128D188—21no—
129D188—21no—
130C4×D47—42no—
131Dic94—21no—
132Dic94—21no—
133Dic94—81no—
134C8×C47—21no—
135C8×C47—21no—
136C8×C47—21no—
137C8×C47#4112yes—
138C22×C47—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47C22×D411yescharacteristic
145C2×D47—41no—
146C2×D47—41no—
147C2×D47—41no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47C2×#4111yescharacteristic
153C4×C472−1+411yescharacteristic
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3348—471nomaximal, Sylow
162C2×C47—41no—
163C2×C47—41no—
164C2×C47#54711yescharacteristic
165C2×C47#57511yescharacteristic
166C2×C47#57711yescharacteristic
167D47—81no—
168#555—471no—
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#435D4711yescharacteristic, complemented
181#428—471no—
182#427—471no—
183C47#334811yescharacteristic, complemented, Sylow
184C2×SD16—471no—
185C2×M16C2×D4711yescharacteristic
186C22×C8C2×D4711yescharacteristic
187C4⋊Q8—471no—
188#126—941no—
189#125—471no—
190#125—941no—
191#124—941no—
192#124—941no—
193#123—941no—
194C22⋊Q8—471no—
195C22⋊Q8—471no—
196#121—471no—
197#121—471no—
198#121—941no—
199C4×Q8—471no—
200C4×D4—471no—
201C4×D4C2×D4711yescharacteristic
202#117—471no—
203#117—471no—
204#117—471no—
205#117—941no—
206#117—941no—
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⋊C8C2×D4711yescharacteristic
218#103—471no—
219#103—471no—
220#103—471no—
221#102—471no—
222#102—471no—
223#102—471no—
224C22⋊C8C2×D4711yescharacteristic
225C22⋊C8C2×D4711yescharacteristic
226#97C2×D4711yescharacteristic
227C2×Q8—471no—
228C2×Q8—941no—
229C2×D4—471no—
230C2×D4—941no—
231C2×D4—941no—
232C2×D4D18811yescharacteristic
233C22×C4—941no—
234C22×C4—941no—
235C22×C4C22×D4711yescharacteristic
236C22×C4C22×D4711yescharacteristic
237SD16—942no—
238M16—22no—
239C2×C8—22no—
240C2×C8C22×D4711yescharacteristic
241C2×C8C22×D4711yescharacteristic
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—471no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4D18811yescharacteristic
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4D18811yescharacteristic
267C22⋊C4D18811yescharacteristic
268C42—941no—
269C42—941no—
270C42—941no—
271C42—941no—
272C42C22×D4711yescharacteristic
273C23—941no—
274C23C2×D18811yescharacteristic
275C23C2×D18811yescharacteristic
276Q8—941no—
277Q8—941no—
278Q8—3761no—
279D4—41no—
280D4—941no—
281D4—941no—
282D4—3761no—
283D4—3761no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—1882no—
296C2×C4—1882no—
297C2×C4C2×D18811yescharacteristic
298C2×C4C2×D18811yescharacteristic
299C2×C4C2×D18811yescharacteristic
300C2×C4C2×D18811yescharacteristic
301C2×C4C23×D4711yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8#1062535212yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—1881no—
313C22—1881no—
314C22—1881no—
315C22C22×D18811yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—1881no—
321C4—1881no—
322C4—1881no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4—1881no—
327C4C2×#1062535211yescharacteristic
328C4#1309407111yescharacteristic
329C2—41no—
330C2—41no—
331C2—3761no—
332C2#1568977711yescharacteristic
333C2#1568992311yescharacteristic
334C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3348
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
2. #15689813C2semidirect
3. #15689532C2semidirect
4. #15689465C2semidirect
5. #15689465C2semidirect
6. #15689448C2semidirect
7. #15689442C2semidirect
8. #15689424C2semidirect
9. #15689409C2semidirect
10. #15689369C2semidirect
11. #15689352C2semidirect
12. #15689225C2semidirect
13. #15689165C2semidirect
14. #15689161C2semidirect
15. C47×#435C2semidirect
180. #435D47semidirect
183. C47#3348semidirect