Finite Group Databasebeta

← #20253923

Subgroups — #20253923

Order 6016.

340 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689753C211yesmaximal, characteristic
2#15689750C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689531C211yesmaximal, characteristic, complemented
5#15689530C211yesmaximal, characteristic, complemented
6#15689527C211yesmaximal, characteristic, complemented
7#15689526C211yesmaximal, characteristic, complemented
8#15689523C211yesmaximal, characteristic, complemented
9#15689522C211yesmaximal, characteristic, complemented
10#15689164C211yesmaximal, characteristic
11#15689162C211yesmaximal, characteristic
12#15689158C211yesmaximal, characteristic
13#107×D47C211yesmaximal, characteristic
14#15689080C211yesmaximal, characteristic
15C47×#501C211yesmaximal, characteristic, complemented
16C2×#10625324C2211yescharacteristic
17C2×C8×D47C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094023—21no—
20#13094023C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094022—21no—
23#13094016C2211yescharacteristic
24#13094015C2211yescharacteristic
25#13094015C2211yescharacteristic
26#13094014—21no—
27#13094014—21no—
28#13094004—21no—
29#13094002—21no—
30#13094002—21no—
31#13094000—21no—
32#13093982C2211yescharacteristic
33#13093982C2211yescharacteristic
34#13093981C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093957C2211yescharacteristic
43#13093957C2211yescharacteristic
44#13093957C2211yescharacteristic
45#13093956C2211yescharacteristic
46#13093956C2211yescharacteristic
47#13093955C2211yescharacteristic
48#13093955C2211yescharacteristic
49#13093934C2211yescharacteristic
50C4×C47⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×C4×D47—21no—
61C2×C4×D47—21no—
62C2×C4×D47C2311yescharacteristic
63C2×Dic94—21no—
64C2×Dic94—21no—
65C2×Dic94—21no—
66C2×C8×C47C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C42×C47C2311yescharacteristic
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—21no—
78(C2×D47)⋊C4D411yescharacteristic
79(C2×D47)⋊C4D411yescharacteristic
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47C2311yescharacteristic
84C4⋊Dic47C2311yescharacteristic
85C4⋊Dic47C2311yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87Dic47⋊C4—21no—
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4D411yescharacteristic
96Dic47⋊C4D411yescharacteristic
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102#10625324Q814yescomplemented
103C8×D47Q814yescomplemented
104C22×D47C2×D411yescharacteristic
105Q8×C47—81no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2411yescharacteristic
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47C2×D411yescharacteristic
118C2×Dic47C2×D411yescharacteristic
119C2×Dic47C2×D411yescharacteristic
120C4×D47—81no—
121C4×D47—81no—
122C4×D47C2×Q812yes—
123C4×D47C2×Q812yes—
124Dic94—81no—
125Dic94—81no—
126Dic94—81no—
127C8×C47C2×Q812yes—
128C8×C47C2×Q812yes—
129C47⋊C8C2×Q812yes—
130C47⋊C8C2×Q812yes—
131C22×C47C22×D411yescharacteristic
132C2×D47—21no—
133C2×D47—21no—
134C2×D47C4⋊Q812yes—
135C4×C47—21no—
136C4×C47—21no—
137C4×C47—41no—
138C4×C47—41no—
139C4×C47—41no—
140C4×C47—41no—
141C4×C47C22×Q811yescharacteristic
142C4×C47C22×Q811yescharacteristic
143Dic47—21no—
144Dic47—21no—
145Dic47—41no—
146Dic47—41no—
147Dic47—41no—
148Dic47—41no—
149Dic47C4⋊Q812yes—
150#3164—471nomaximal, Sylow
151C2×C47C2×C4⋊Q811yescharacteristic
152C2×C47#57611yescharacteristic
153C2×C47#57811yescharacteristic
154D47—22no—
155#544—471no—
156#544—471no—
157#501—471no—
158#501—471no—
159#501—471no—
160#501D4711yescharacteristic, complemented
161#500—471no—
162#500—471no—
163#499—471no—
164#499—471no—
165#428—471no—
166#428—471no—
167#427—471no—
168C2×#107—471no—
169#405—471no—
170C47#316411yescharacteristic, complemented, Sylow
171C2×M16—471no—
172C22×C8—471no—
173C4⋊Q8—471no—
174C4⋊Q8—471no—
175C4⋊Q8—471no—
176C4⋊Q8—941no—
177C4⋊Q8—941no—
178C4⋊Q8C2×D4711yescharacteristic
179#125—471no—
180#125—471no—
181#125—471no—
182#125—941no—
183#125—941no—
184#125C2×D4711yescharacteristic
185C22⋊Q8—941no—
186C22⋊Q8—941no—
187C22⋊Q8—941no—
188C22⋊Q8—941no—
189#117—471no—
190#117—471no—
191#117—471no—
192C2×C4⋊C4—471no—
193C2×C4⋊C4—471no—
194#107—471no—
195#107—471no—
196#107—471no—
197#107—471no—
198#107—471no—
199#107—471no—
200#107—471no—
201#107—471no—
202#107C2×D4711yescharacteristic
203#107C2×D4711yescharacteristic
204#106—471no—
205#106—471no—
206#106—471no—
207#106—471no—
208#106C2×D4711yescharacteristic
209#106C2×D4711yescharacteristic
210#97—471no—
211#97C2×D4711yescharacteristic
212C4×C8—471no—
213C4×C8—471no—
214C2×Q8—21no—
215C2×Q8—941no—
216C2×Q8—941no—
217C2×Q8—941no—
218C22×C4—471no—
219C22×C4—941no—
220C22×C4—941no—
221M16—474no—
222C2×C8—471no—
223C2×C8—471no—
224C2×C8—474no—
225C2×C8C22×D4711yescharacteristic
226C2×C8C22×D4711yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—471no—
231C4⋊C4—471no—
232C4⋊C4—471no—
233C4⋊C4—471no—
234C4⋊C4—471no—
235C4⋊C4—471no—
236C4⋊C4—941no—
237C4⋊C4—941no—
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⋊C4C22×D4711yescharacteristic
248C4⋊C4C22×D4711yescharacteristic
249C4⋊C4C22×D4711yescharacteristic
250C4⋊C4C22×D4711yescharacteristic
251C22⋊C4—471no—
252C22⋊C4—471no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C42—471no—
256C42—941no—
257C42—941no—
258C42C22×D4711yescharacteristic
259C23—471no—
260Q8—81no—
261Q8—3761no—
262Q8—3761no—
263Q8—3761no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—471no—
269C2×C4—472no—
270C2×C4—472no—
271C2×C4—471no—
272C2×C4—471no—
273C2×C4—941no—
274C2×C4—941no—
275C2×C4—941no—
276C2×C4—941no—
277C2×C4—3761no—
278C2×C4—3761no—
279C2×C4D4×D4711yescharacteristic
280C2×C4D4×D4711yescharacteristic
281C2×C4C23×D4711yescharacteristic
282C8—472no—
283C8—472no—
284C8Q8×D4712yes—
285C8Q8×D4712yes—
286C22—472no—
287C22—941no—
288C22—941no—
289C22C2×D4×D4711yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—472no—
297C4—941no—
298C4—941no—
299C4—1881no—
300C4—1881no—
301C4—1881no—
302C4—1881no—
303C4C2×Q8×D4711yescharacteristic
304C4C2×Q8×D4711yescharacteristic
305C2—942no—
306C2C4⋊Q8×D4711yescharacteristic
307C2#1568992711yescharacteristic
308C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3164
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #15689532C2semidirect
4. #15689531C2semidirect
5. #15689530C2semidirect
6. #15689527C2semidirect
7. #15689526C2semidirect
8. #15689523C2semidirect
9. #15689522C2semidirect
15. C47×#501C2semidirect
102. #10625324Q8semidirect
103. C8×D47Q8semidirect
160. #501D47semidirect
170. C47#3164semidirect