Finite Group Databasebeta

← #20254643

Subgroups — #20254643

Order 6016.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689751C211yesmaximal, characteristic, complemented
2#15689728C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689525C211yesmaximal, characteristic, complemented
5#15689488C211yesmaximal, characteristic, complemented
6#15689470C211yesmaximal, characteristic, complemented
7#15689448C211yesmaximal, characteristic, complemented
8#15689448C211yesmaximal, characteristic, complemented
9#15689442C211yesmaximal, characteristic, complemented
10#15689437C211yesmaximal, characteristic, complemented
11#15689424C211yesmaximal, characteristic, complemented
12#15689424C211yesmaximal, characteristic, complemented
13#15689414C211yesmaximal, characteristic, complemented
14#15689404C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic, complemented
16#13094024C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094023—21no—
19#13094021C2211yescharacteristic
20#13094016C2211yescharacteristic
21#13094016C2211yescharacteristic
22#13094016C2211yescharacteristic
23#13094015—21no—
24#13094009—21no—
25#13094009—21no—
26#13094001—21no—
27#13094001—21no—
28#13093998C2211yescharacteristic
29#13093998C2211yescharacteristic
30#13093997—21no—
31#13093997—21no—
32C4×D188C2211yescharacteristic
33C4×D188C2211yescharacteristic
34#13093983C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
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—
61C2×C22⋊D47—21no—
62C22×Dic47—21no—
63C2×D188—21no—
64C2×D188—21no—
65C2×D188C2311yescharacteristic
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×Dic94—21no—
70C2×Dic94—21no—
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C22⋊C4×C47D411yescharacteristic
78C22⋊C4×C47D411yescharacteristic
79C42×C47C2311yescharacteristic
80C42×C47C2311yescharacteristic
81C22⋊Dic47—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86C4⋊Dic47—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—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C23×C47C2×D411yescharacteristic
103C22×D47—21no—
104C22×D47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47C2×D411yescharacteristic
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2411yescharacteristic
113C22⋊D47—81no—
114C22⋊D47—81no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—81no—
122D188—21no—
123D188—21no—
124D188—21no—
125D188—21no—
126D188—81no—
127D188—81no—
128C4×D47—81no—
129C4×D47—81no—
130Dic94—81no—
131Dic94—81no—
132C8×C47—21no—
133C8×C47—21no—
134C8×C47—21no—
135C8×C47—21no—
136C22×C47—21no—
137C22×C47—21no—
138C22×C47—21no—
139C22×C47C22×D411yescharacteristic
140C2×D47—41no—
141C2×D47—41no—
142C2×D47—41no—
143C2×D47—41no—
144C2×D47—41no—
145C2×D47—41no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C472−1+411yescharacteristic
152C4×C472−1+411yescharacteristic
153Dic47—41no—
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159#3241—471nomaximal, Sylow
160C2×C47—41no—
161C2×C47#53611yescharacteristic
162C2×C47#57611yescharacteristic
163C2×C47#57711yescharacteristic
164D47—81no—
165D47—81no—
166#544—471no—
167#540—471no—
168#501—471no—
169#499—471no—
170#490—471no—
171#486—471no—
172#482—471no—
173#482—471no—
174#481—471no—
175#480—471no—
176#478—471no—
177#478—471no—
178#476—471no—
179#474—471no—
180#433D4711yescharacteristic, complemented
181C47#324111yescharacteristic, complemented, Sylow
182C4⋊Q8—471no—
183C4⋊Q8—471no—
184C4⋊Q8—941no—
185#127—471no—
186#125—471no—
187#125—471no—
188#125—471no—
189#125—941no—
190#123—941no—
191#123—941no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194#121—471no—
195#121—471no—
196#121—941no—
197#121—941no—
198C4×D4—471no—
199C4×D4—471no—
200#117—471no—
201#117C2×D4711yescharacteristic
202C2×C4⋊C4—471no—
203#107—471no—
204#107—471no—
205#107—471no—
206#107—471no—
207#106—471no—
208#106—471no—
209#106—471no—
210#106—471no—
211C4⋊C8C2×D4711yescharacteristic
212C4⋊C8C2×D4711yescharacteristic
213#102—471no—
214#102—471no—
215#102—471no—
216#102—471no—
217#102—471no—
218#102—471no—
219#102—471no—
220#102—471no—
221C22⋊C8C2×D4711yescharacteristic
222C22⋊C8C2×D4711yescharacteristic
223#97C2×D4711yescharacteristic
224C4×C8C2×D4711yescharacteristic
225C2×Q8—941no—
226C2×Q8—941no—
227C2×D4—471no—
228C2×D4—471no—
229C2×D4—941no—
230C2×D4—941no—
231C2×D4—941no—
232C2×D4—941no—
233C22×C4—941no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4C22×D4711yescharacteristic
237C2×C8C22×D4711yescharacteristic
238C2×C8C22×D4711yescharacteristic
239C2×C8C22×D4711yescharacteristic
240C2×C8C22×D4711yescharacteristic
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4D18811yescharacteristic
257C4⋊C4D18811yescharacteristic
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4D18811yescharacteristic
264C22⋊C4D18811yescharacteristic
265C42—941no—
266C42C22×D4711yescharacteristic
267C42C22×D4711yescharacteristic
268C23—941no—
269C23—941no—
270C23C2×D18811yescharacteristic
271Q8—3761no—
272Q8—3761no—
273D4—941no—
274D4—941no—
275D4—941no—
276D4—941no—
277D4—3761no—
278D4—3761no—
279D4—3761no—
280D4—3761no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—3761no—
290C2×C4—3761no—
291C2×C4—3761no—
292C2×C4C2×D18811yescharacteristic
293C2×C4C2×D18811yescharacteristic
294C2×C4C2×D18811yescharacteristic
295C2×C4C2×D18811yescharacteristic
296C2×C4C2×D18811yescharacteristic
297C2×C4C23×D4711yescharacteristic
298C8—21no—
299C8—21no—
300C8—21no—
301C8—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—1881no—
306C22—1881no—
307C22—1881no—
308C22—1881no—
309C22—1881no—
310C22—1881no—
311C22C22×D18811yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—1881no—
318C4—1881no—
319C4—1881no—
320C4—1881no—
321C4—1881no—
322C4—1881no—
323C4#1309407111yescharacteristic
324C4#1309407111yescharacteristic
325C2—41no—
326C2—3761no—
327C2—3761no—
328C2#1568969911yescharacteristic
329C2#1568992811yescharacteristic
330C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3241
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. #15689525C2semidirect
5. #15689488C2semidirect
6. #15689470C2semidirect
7. #15689448C2semidirect
8. #15689448C2semidirect
9. #15689442C2semidirect
10. #15689437C2semidirect
11. #15689424C2semidirect
12. #15689424C2semidirect
13. #15689414C2semidirect
14. #15689404C2semidirect
15. C47×#433C2semidirect
180. #433D47semidirect
181. C47#3241semidirect