Finite Group Databasebeta

← #20254688

Subgroups — #20254688

Order 6016.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689751C211yesmaximal, characteristic, complemented
2#15689744C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689521C211yesmaximal, characteristic, complemented
5#15689483C211yesmaximal, characteristic, complemented
6#15689478C211yesmaximal, characteristic, complemented
7#15689465C211yesmaximal, characteristic, complemented
8#15689454C211yesmaximal, characteristic, complemented
9#15689448C211yesmaximal, characteristic
10#15689442C211yesmaximal, characteristic
11#15689431C211yesmaximal, characteristic, complemented
12#15689424C211yesmaximal, characteristic, complemented
13#15689414C211yesmaximal, characteristic, complemented
14#15689409C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic, complemented
16#13094024C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094023—21no—
20#13094019—21no—
21#13094016C2211yescharacteristic
22#13094016C2211yescharacteristic
23#13094015—21no—
24#13094012C2211yescharacteristic
25#13094010—21no—
26#13094006—21no—
27#13094003C2211yescharacteristic
28#13094002—21no—
29#13094001—21no—
30#13094001—21no—
31#13093998C2211yescharacteristic
32C4×Dic94C2211yescharacteristic
33C4×D188C2211yescharacteristic
34#13093983C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52#117×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic
54C4⋊C8×C47C2211yescharacteristic
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C2×C22⋊D47—21no—
61C22×Dic47—21no—
62C2×D188C2311yescharacteristic
63C2×C4×D47—21no—
64C2×Dic94—21no—
65C2×Dic94—21no—
66C2×Dic94—21no—
67C2×Dic94C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47D411yescharacteristic
73C4⋊C4×C47D411yescharacteristic
74C22⋊C4×C47D411yescharacteristic
75C22⋊C4×C47D411yescharacteristic
76C42×C47C2311yescharacteristic
77C42×C47C2311yescharacteristic
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C23×C47C2×D411yescharacteristic
103C22×D47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47C2×D411yescharacteristic
107C2×C4×C47C2×D411yescharacteristic
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2411yescharacteristic
112C22⋊D47—81no—
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—81no—
121D188—21no—
122D188—21no—
123C4×D47—81no—
124Dic94—21no—
125Dic94—21no—
126Dic94—81no—
127Dic94—81no—
128Dic94—81no—
129C8×C47—21no—
130C8×C47—21no—
131C8×C47—21no—
132C8×C47—21no—
133C22×C47—21no—
134C22×C47—21no—
135C22×C47—21no—
136C22×C47C22×D411yescharacteristic
137C2×D47—41no—
138C2×D47—41no—
139C2×D47—41no—
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C472−1+411yescharacteristic
146C4×C472−1+411yescharacteristic
147Dic47—41no—
148Dic47—41no—
149Dic47—41no—
150Dic47—41no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154#3244—471nomaximal, Sylow
155C2×C47—41no—
156C2×C47#53611yescharacteristic
157C2×C47#57711yescharacteristic
158C2×C47#57711yescharacteristic
159D47—81no—
160#544—471no—
161#542—471no—
162#501—471no—
163#498—471no—
164#489—471no—
165#488—471no—
166#485—471no—
167#483—471no—
168#482—471no—
169#481—471no—
170#479—471no—
171#478—471no—
172#476—471no—
173#475—471no—
174#433D4711yescharacteristic, complemented
175C47#324411yescharacteristic, complemented, Sylow
176C4⋊Q8—471no—
177C4⋊Q8—471no—
178C4⋊Q8—471no—
179C4⋊Q8—941no—
180#126—941no—
181#125—471no—
182#125—471no—
183#125—941no—
184#124—471no—
185#124—941no—
186#123—941no—
187C22⋊Q8—471no—
188C22⋊Q8—941no—
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191#121—471no—
192C4×Q8—471no—
193C4×D4—471no—
194#117—471no—
195#117C2×D4711yescharacteristic
196C2×C4⋊C4—471no—
197#107—471no—
198#107—471no—
199#106—471no—
200#106—471no—
201#106—471no—
202#106—471no—
203#106—471no—
204#106—471no—
205C4⋊C8C2×D4711yescharacteristic
206C4⋊C8C2×D4711yescharacteristic
207#103—471no—
208#103—471no—
209#103—471no—
210#103—471no—
211#102—471no—
212#102—471no—
213#102—471no—
214#102—471no—
215C22⋊C8C2×D4711yescharacteristic
216C22⋊C8C2×D4711yescharacteristic
217#97C2×D4711yescharacteristic
218C4×C8C2×D4711yescharacteristic
219C2×Q8—471no—
220C2×Q8—941no—
221C2×Q8—941no—
222C2×Q8—941no—
223C2×D4—471no—
224C2×D4—941no—
225C22×C4—941no—
226C22×C4—941no—
227C22×C4C22×D4711yescharacteristic
228C2×C8C22×D4711yescharacteristic
229C2×C8C22×D4711yescharacteristic
230C2×C8C22×D4711yescharacteristic
231C2×C8C22×D4711yescharacteristic
232C4⋊C4—471no—
233C4⋊C4—471no—
234C4⋊C4—471no—
235C4⋊C4—471no—
236C4⋊C4—471no—
237C4⋊C4—471no—
238C4⋊C4—941no—
239C4⋊C4—941no—
240C4⋊C4—941no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4D18811yescharacteristic
249C4⋊C4D18811yescharacteristic
250C22⋊C4—941no—
251C22⋊C4—941no—
252C22⋊C4—941no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C22⋊C4—941no—
256C22⋊C4D18811yescharacteristic
257C22⋊C4D18811yescharacteristic
258C42—941no—
259C42—941no—
260C42C22×D4711yescharacteristic
261C42C22×D4711yescharacteristic
262C23—941no—
263C23C2×D18811yescharacteristic
264Q8—941no—
265Q8—941no—
266Q8—3761no—
267Q8—3761no—
268Q8—3761no—
269D4—941no—
270D4—941no—
271D4—3761no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—941no—
275C2×C4—941no—
276C2×C4—941no—
277C2×C4—941no—
278C2×C4—941no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—3761no—
282C2×C4—3761no—
283C2×C4C2×D18811yescharacteristic
284C2×C4C2×D18811yescharacteristic
285C2×C4C2×D18811yescharacteristic
286C2×C4C2×D18811yescharacteristic
287C2×C4C2×D18811yescharacteristic
288C2×C4C23×D4711yescharacteristic
289C8—21no—
290C8—21no—
291C8—21no—
292C8—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—1881no—
297C22—1881no—
298C22—1881no—
299C22C22×D18811yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—1881no—
306C4—1881no—
307C4—1881no—
308C4—1881no—
309C4—1881no—
310C4—1881no—
311C4—1881no—
312C4#1309407111yescharacteristic
313C4#1309407111yescharacteristic
314C2—41no—
315C2—3761no—
316C2#1568969911yescharacteristic
317C2#1568993511yescharacteristic
318C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3244
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #15689751C2semidirect
3. #15689532C2semidirect
4. #15689521C2semidirect
5. #15689483C2semidirect
6. #15689478C2semidirect
7. #15689465C2semidirect
8. #15689454C2semidirect
11. #15689431C2semidirect
12. #15689424C2semidirect
13. #15689414C2semidirect
14. #15689409C2semidirect
15. C47×#433C2semidirect
174. #433D47semidirect
175. C47#3244semidirect