Finite Group Databasebeta

← #20254049

Subgroups — #20254049

Order 6016.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689740C211yesmaximal, characteristic
2#15689733C211yesmaximal, characteristic, complemented
3#15689531C211yesmaximal, characteristic, complemented
4#15689514C211yesmaximal, characteristic, complemented
5#15689476C211yesmaximal, characteristic, complemented
6#15689472C211yesmaximal, characteristic, complemented
7#15689381C211yesmaximal, characteristic, complemented
8#15689362C211yesmaximal, characteristic, complemented
9#15689350C211yesmaximal, characteristic
10#15689227C211yesmaximal, characteristic, complemented
11#15689220C211yesmaximal, characteristic, complemented
12#15689217C211yesmaximal, characteristic, complemented
13SD16×Dic47C211yesmaximal, characteristic, complemented
14#15689081C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic
16C2×Dic188C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C22×C47⋊C8C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094022C2211yescharacteristic
22#13094017—21no—
23#13094017—21no—
24#13094017—21no—
25#13094015—21no—
26#13094015C2211yescharacteristic
27#13094014—21no—
28#13094011—21no—
29#13094011C2211yescharacteristic
30#13094005—21no—
31#13094003C2211yescharacteristic
32#13094003C2211yescharacteristic
33#13094001—21no—
34Q8×Dic47C2211yescharacteristic
35#13093989C2211yescharacteristic
36#13093989C2211yescharacteristic
37D4×Dic47C2211yescharacteristic
38#13093983C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093934C2211yescharacteristic
49#13093934C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×Dic47—21no—
64C2×Dic94—21no—
65C2×Dic94C2311yescharacteristic
66C2×Dic94C2311yescharacteristic
67SD16×C47—22no—
68M16×C47—22no—
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C22⋊C4×C47—21no—
75C22⋊C4×C47—21no—
76C22⋊Dic47—21no—
77C22⋊Dic47—21no—
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47D411yescharacteristic
82C22⋊Dic47D411yescharacteristic
83#10625337—22no—
84#10625335—22no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47D411yescharacteristic
88C4⋊Dic47D411yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8—22no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107Dic188—22no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112D4×C47—21no—
113D4×C47—21no—
114D4×C47—81no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—81no—
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131Dic94—21no—
132Dic94—21no—
133Dic94—21no—
134Dic94—21no—
135Dic94—81no—
136C8×C47—21no—
137C8×C47#4112yes—
138C47⋊C8—21no—
139C47⋊C8#4112yes—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47C22×D411yescharacteristic
147C4×C47—21no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47C2×#4111yescharacteristic
152C4×C47C2×#4111yescharacteristic
153Dic47—21no—
154Dic47—21no—
155Dic47—21no—
156Dic47—21no—
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3178—471nomaximal, Sylow
162C2×C47—41no—
163C2×C47—81no—
164C2×C47#53211yescharacteristic
165C2×C47#57711yescharacteristic
166C2×C47#57811yescharacteristic
167#542—471no—
168#541—471no—
169#501—471no—
170#497—471no—
171#488—471no—
172#487—471no—
173#470—471no—
174#468D4711yescharacteristic
175#467—471no—
176#465—471no—
177#441—471no—
178#440—471no—
179C4×Q16—471no—
180C4×SD16—471no—
181#405—471no—
182C47#317811yescharacteristic, complemented, Sylow
183C2×Q16—471no—
184C2×Q16—471no—
185C2×SD16—471no—
186C2×SD16C2×D4711yescharacteristic
187C2×M16C2×D4711yescharacteristic
188C22×C8—471no—
189C4⋊Q8—471no—
190C4⋊Q8—471no—
191#126—941no—
192#126—941no—
193#126—941no—
194#125—471no—
195#125—941no—
196#125—941no—
197#124—471no—
198#124—941no—
199#123—941no—
200C22⋊Q8—471no—
201C22⋊Q8—471no—
202C22⋊Q8—941no—
203C22⋊Q8C2×D4711yescharacteristic
204#121C2×D4711yescharacteristic
205C4×Q8—471no—
206C4×Q8—471no—
207C4×Q8—471no—
208C4×D4—471no—
209#117—471no—
210#107—471no—
211#107C2×D4711yescharacteristic
212#106—471no—
213#106—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103C2×D4711yescharacteristic
220#102—471no—
221#102C2×D4711yescharacteristic
222#97—471no—
223#97—471no—
224C4×C8—471no—
225C4×C8—471no—
226C2×Q8—471no—
227C2×Q8—471no—
228C2×Q8—941no—
229C2×Q8C22×D4711yescharacteristic
230C2×D4—21no—
231C2×D4C22×D4711yescharacteristic
232C22×C4—941no—
233C22×C4C22×D4711yescharacteristic
234Q16—942no—
235Q16—942no—
236SD16—22no—
237SD16—942no—
238M16—22no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—942no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4C22×D4711yescharacteristic
260C4⋊C4C22×D4711yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—471no—
264C22⋊C4—471no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—471no—
271C42—471no—
272C42—941no—
273C42—941no—
274C42—941no—
275C23—21no—
276C23D4×D4711yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—941no—
280Q8—941no—
281Q8—941no—
282Q8—941no—
283Q8—3761no—
284D4—21no—
285D4—21no—
286D4—81no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—3761no—
301C2×C4D4×D4711yescharacteristic
302C2×C4C23×D4711yescharacteristic
303C8—21no—
304C8—472no—
305C8—941no—
306C8#1062535212yes—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22C2×D4×D4711yescharacteristic
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—941no—
319C4—941no—
320C4—941no—
321C4—941no—
322C4—1881no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4#41×D4711yescharacteristic
327C4C2×#1062535211yescharacteristic
328C2—41no—
329C2—81no—
330C2#1568966811yescharacteristic
331C2#1568993311yescharacteristic
332C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3178
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #15689733C2semidirect
3. #15689531C2semidirect
4. #15689514C2semidirect
5. #15689476C2semidirect
6. #15689472C2semidirect
7. #15689381C2semidirect
8. #15689362C2semidirect
10. #15689227C2semidirect
11. #15689220C2semidirect
12. #15689217C2semidirect
13. SD16×Dic47C2semidirect
14. #15689081C2semidirect
182. C47#3178semidirect