Finite Group Databasebeta

← #20243736

Subgroups — #20243736

Order 6016.

438 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625334C211yesmaximal, characteristic
2C2×#13093945C211yesmaximal, characteristic, complemented
3C2×#13093944C211yesmaximal, characteristic, complemented
4#15689025C211yesmaximal, characteristic, complemented
5#15688885C211yesmaximal, characteristic, complemented
6#15688878C211yesmaximal, characteristic, complemented
7C2×C4×D4×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C2×#10625334—22no—
10C2×#10625334—22no—
11C2×#10625334C414yescomplemented
12C22×C47⋊C8C2211yescharacteristic
13C22×C47⋊C8C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×(C2×D47)⋊C4—21no—
16C2×(C2×D47)⋊C4—21no—
17#13093945—22no—
18#13093944—22no—
19C22×D4×C47C2211yescharacteristic
20C23×C4×C47—21no—
21C4×D4×C47—22no—
22C4×D4×C47—22no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47—21no—
25C2×C42×C47C2211yescharacteristic
26C24×C47—21no—
27C23×D47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47C2×C412yes—
32C2×D4×C47D412yes—
33C2×D4×C47D412yes—
34C22×C4×C47—24no—
35C22×C4×C47—21no—
36C22×C4×C47—42no—
37C22×C4×C47—42no—
38C22×C4×C47D411yescharacteristic
39C22×C4×C47D411yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×Dic47—21no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188—21no—
47C2×D188C2×C412yescomplemented
48C4⋊C4×C47—21no—
49C4⋊C4×C47D412yes—
50C22⋊C4×C47—24no—
51C42×C47—21no—
52C42×C47—21no—
53#10625334—28no—
54(C2×D47)⋊C4—42no—
55(C2×D47)⋊C4—42no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C2×C47⋊C8—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8—21no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8C2×C412yescomplemented
64C23×C47—22no—
65C23×C47—22no—
66C23×C47—22no—
67C23×C47—41no—
68C23×C47—41no—
69C23×C47—41no—
70C23×C47—41no—
71C23×C47C2×D411yescharacteristic
72C22×D47—22no—
73C22×D47—41no—
74C22×D47—41no—
75C22×D47—41no—
76C22×D47—41no—
77C22×D47—41no—
78C22×D47—41no—
79D4×C47—22no—
80D4×C47—22no—
81D4×C47—22no—
82D4×C47C22⋊C414yescomplemented
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—22no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—48no—
90C2×C4×C47—41no—
91C2×C4×C47—41no—
92C2×C4×C47D812yescomplemented
93C2×C4×C47C22×C411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47#4111yescharacteristic
98C2×C4×C47#4111yescharacteristic
99C2×Dic47—41no—
100C2×Dic47—41no—
101C2×Dic47—41no—
102D188—22no—
103D188—22no—
104D188—41no—
105D188—41no—
106C47⋊C8—22no—
107C47⋊C8—41no—
108C22×C47—24no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47—42no—
112C22×C47—42no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47C4×D411yescharacteristic
116C22×C47#12011yescharacteristic
117C22×C47#12111yescharacteristic
118C22×C47C2×D811yescharacteristic
119C22×C47#13511yescharacteristic
120C22×C47AGL(1,ℤ/8)11yescharacteristic
121C22×C47AGL(1,ℤ/8)11yescharacteristic
122C2×D47—42no—
123C2×D47—42no—
124C2×D47—42no—
125C2×D47—81no—
126C2×D47—81no—
127C2×D47—81no—
128C2×D47—81no—
129C4×C47—22no—
130C4×C47—42no—
131C4×C47—41no—
132C4×C47C2×C22⋊C411yescharacteristic
133C4×C47C4×D411yescharacteristic
134C4×C47#12111yescharacteristic
135C4×C47#12311yescharacteristic
136Dic47—81no—
137#1879—471nomaximal, Sylow
138C2×C47—44no—
139C2×C47#38611yescharacteristic
140C2×C47C4×D811yescharacteristic
141C2×C47#44211yescharacteristic
142C2×C47#44711yescharacteristic
143C2×C47#44911yescharacteristic
144C2×C47#45911yescharacteristic
145C2×C47#46311yescharacteristic
146D47—82no—
147C22×D8—471no—
148C2×C4×D4D4711yescharacteristic, complemented
149C2×#102—471no—
150C2×#102—471no—
151#390—471no—
152#340—471no—
153#336—471no—
154C47#187911yescharacteristic, complemented, Sylow
155C22×D4—471no—
156C22×D4C2×D4711yescharacteristic
157C23×C4—21no—
158C2×D8—474no—
159C2×D8—942no—
160C2×D8—942no—
161C22×C8—471no—
162C22×C8—471no—
163C4×D4—22no—
164C4×D4—22no—
165C2×C4⋊C4—471no—
166C2×C4⋊C4C2×D4711yescharacteristic
167C2×C22⋊C4—21no—
168C2×C22⋊C4—941no—
169C2×C22⋊C4—941no—
170C2×C42C2×D4711yescharacteristic
171#102—942no—
172#102—942no—
173C24—21no—
174C24—941no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—472no—
179C2×D4—941no—
180C2×D4—941no—
181C2×D4—941no—
182C2×D4—941no—
183C2×D4—941no—
184C2×D4C4×D4712yes—
185C2×D4D18812yes—
186C2×D4C22⋊D4712yes—
187C22×C4—24no—
188C22×C4—21no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—941no—
192C22×C4C22⋊D4711yescharacteristic
193C22×C4C22⋊D4711yescharacteristic
194C22×C4C22×D4711yescharacteristic
195D8—948no—
196C2×C8—472no—
197C2×C8—941no—
198C2×C8—941no—
199C2×C8—941no—
200C2×C8—941no—
201C2×C8—941no—
202C4⋊C4—21no—
203C4⋊C4—941no—
204C4⋊C4—941no—
205C4⋊C4C22⋊D4712yes—
206C22⋊C4—24no—
207C22⋊C4—1882no—
208C22⋊C4—1882no—
209C42—21no—
210C42—21no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—942no—
219C23—1881no—
220C23—1881no—
221C23—1881no—
222C23—1881no—
223C23—1881no—
224C23—1881no—
225C23C2×C22⋊D4711yescharacteristic
226D4—22no—
227D4—22no—
228D4—22no—
229D4—942no—
230D4—942no—
231D4—1881no—
232D4—1881no—
233D4(C2×D47)⋊C414yescomplemented
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—48no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—1881no—
244C2×C4—1881no—
245C2×C4—1881no—
246C2×C4#1062533412yescomplemented
247C2×C4C2×C4×D4711yescharacteristic
248C2×C4C2×D18811yescharacteristic
249C2×C4#1062535011yescharacteristic
250C2×C4#1062535011yescharacteristic
251C2×C4C2×C22⋊D4711yescharacteristic
252C2×C4C2×C22⋊D4711yescharacteristic
253C8—942no—
254C8—1881no—
255C22—24no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—3761no—
263C22—3761no—
264C22—3761no—
265C22—3761no—
266C22—1882no—
267C22—1882no—
268C22—1882no—
269C22C4×C22⋊D4711yescharacteristic
270C22#1309399311yescharacteristic
271C22#1309399811yescharacteristic
272C22C2×#1062533411yescharacteristic
273C22#1309404411yescharacteristic
274C22#1309404911yescharacteristic
275C22#1309405011yescharacteristic
276C4—22no—
277C4—42no—
278C4—41no—
279C4—3761no—
280C4C2×(C2×D47)⋊C411yescharacteristic
281C4C4×C22⋊D4711yescharacteristic
282C4#1309399811yescharacteristic
283C4#1309400711yescharacteristic
284C2—44no—
285C2—3762no—
286C2#1568900211yescharacteristic
287C2C4×#1062533411yescharacteristic
288C2#1568923311yescharacteristic
289C2#1568925711yescharacteristic
290C2#1568926811yescharacteristic
291C2#1568931811yescharacteristic
292C2#1568933811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C4×D4×C47C2
socleC23×C47C2×D4
hypercenterC2×C4×D4D47
hypocenterC47#1879
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#13093945C2semidirect
3. C2×#13093944C2semidirect
4. #15689025C2semidirect
5. #15688885C2semidirect
6. #15688878C2semidirect
7. C2×C4×D4×C47C2semidirect
11. C2×#10625334C4semidirect
47. C2×D188C2×C4semidirect
63. C2×C47⋊C8C2×C4semidirect
82. D4×C47C22⋊C4semidirect
92. C2×C4×C47D8semidirect
148. C2×C4×D4D47semidirect
154. C47#1879semidirect
233. D4(C2×D47)⋊C4semidirect
246. C2×C4#10625334semidirect