Finite Group Databasebeta

← #20244620

Subgroups — #20244620

Order 6016.

402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#13094020C211yesmaximal, characteristic
2C2×#13093946C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic, complemented
4C2×#13093944C211yesmaximal, characteristic, complemented
5#15689019C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C22⋊D47—21no—
10C22×C22⋊D47—21no—
11C22×C47⋊C8C2211yescharacteristic
12#13094020—22no—
13#13094020—22no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4—21no—
16C2×C4×Dic47C2211yescharacteristic
17#13093946—22no—
18#13093945—22no—
19#13093944—22no—
20C47⋊#95—21no—
21C22×D4×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#102×C47—22no—
25C24×C47—21no—
26C23×D47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47D412yes—
33C22×C4×C47—21no—
34C22×C4×C47C2311yescharacteristic
35C2×C22⋊D47—24no—
36C2×C22⋊D47—24no—
37C2×C22⋊D47—42no—
38C2×C22⋊D47—42no—
39C2×C22⋊D47—42no—
40C2×C22⋊D47—42no—
41C22×Dic47—21no—
42C22×Dic47D411yescharacteristic
43C22×Dic47D411yescharacteristic
44C2×D188—21no—
45C2×D188—21no—
46C2×D188—21no—
47C2×D188—21no—
48C2×D188—21no—
49C2×D188D412yes—
50C2×C8×C47—21no—
51C2×C8×C47—21no—
52C2×C8×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47D412yescomplemented
57Dic47⋊C4—42no—
58C4×Dic47—21no—
59C4×Dic47—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8—21no—
62C2×C47⋊C8—21no—
63C23×C47—22no—
64C23×C47—41no—
65C23×C47—41no—
66C23×C47—41no—
67C23×C47—41no—
68C23×C47—41no—
69C23×C47—41no—
70C23×C47C2×D411yescharacteristic
71C22×D47—22no—
72C22×D47—41no—
73C22×D47—41no—
74C22×D47—41no—
75C22×D47—41no—
76C22×D47—41no—
77C22×D47—41no—
78D4×C47—22no—
79D4×C47—22no—
80D4×C47—41no—
81D4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47—41no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47#4111yescharacteristic
89C2×C4×C47#4111yescharacteristic
90C2×C4×C47#4111yescharacteristic
91C22⋊D47—48no—
92C22⋊D47—48no—
93C2×Dic47—21no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47—22no—
98C2×Dic47—41no—
99C2×Dic47—41no—
100C2×Dic47D812yes—
101C2×Dic47SD1612yes—
102D188—22no—
103D188—22no—
104D188—41no—
105D188—41no—
106C8×C47—41no—
107C47⋊C8—41no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47—81no—
112C22×C47—81no—
113C22×C47—81no—
114C22×C47—81no—
115C22×C47#12011yescharacteristic
116C22×C47#12111yescharacteristic
117C22×C47#12411yescharacteristic
118C22×C47C2×D811yescharacteristic
119C22×C47C2×SD1611yescharacteristic
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—81no—
130C4×C47#12111yescharacteristic
131C4×C47#12111yescharacteristic
132C4×C47#12311yescharacteristic
133C4×C47#12311yescharacteristic
134Dic47—22no—
135Dic47—22no—
136Dic47—42no—
137#2041—471nomaximal, Sylow
138C2×C47—82no—
139C2×C47#39411yescharacteristic
140C2×C47#44711yescharacteristic
141C2×C47#45011yescharacteristic
142C2×C47#45911yescharacteristic
143C2×C47#46011yescharacteristic
144C2×C47#48611yescharacteristic
145C2×C47#49011yescharacteristic
146D47—82no—
147C2×#127—471no—
148C2×#102—471no—
149C2×#102—471no—
150C2×#102—471no—
151C2×#102D4711yescharacteristic, complemented
152#389—471no—
153#336—471no—
154C47#204111yescharacteristic, complemented, Sylow
155C22×D4—471no—
156C22×D4—941no—
157C22×D4—941no—
158C22×D4C2×D4711yescharacteristic
159C22×C8—471no—
160C22×C8C2×D4711yescharacteristic
161#127—942no—
162#127—942no—
163C2×C4⋊C4—471no—
164C2×C4⋊C4—941no—
165C2×C4⋊C4C2×D4711yescharacteristic
166C2×C42—471no—
167#102—22no—
168#102—942no—
169#102—942no—
170#102—942no—
171#95—941no—
172C24—21no—
173C24—941no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—472no—
180C2×D4—944no—
181C2×D4—944no—
182C2×D4—941no—
183C2×D4—941no—
184C2×D4—941no—
185C2×D4—941no—
186C2×D4—941no—
187C2×D4—1882no—
188C2×D4—1882no—
189C2×D4—1882no—
190C2×D4—1882no—
191C2×D4C22⋊D4712yes—
192C22×C4—21no—
193C22×C4—471no—
194C22×C4—471no—
195C22×C4—941no—
196C22×C4C22×D4711yescharacteristic
197C2×C8—21no—
198C2×C8—21no—
199C2×C8—21no—
200C2×C8—941no—
201C2×C8—941no—
202C2×C8—941no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—472no—
206C4⋊C4—941no—
207C4⋊C4—1882no—
208C42—941no—
209C42—941no—
210C23—22no—
211C23—41no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—942no—
218C23—1881no—
219C23—1881no—
220C23—1881no—
221C23—1881no—
222C23—1881no—
223C23—1881no—
224C23D4×D4711yescharacteristic
225D4—22no—
226D4—22no—
227D4—41no—
228D4—41no—
229D4—942no—
230D4—942no—
231D4—1888no—
232D4—1888no—
233D4—1881no—
234D4—1881no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—472no—
239C2×C4—472no—
240C2×C4—941no—
241C2×C4—941no—
242C2×C4—941no—
243C2×C4—941no—
244C2×C4—942no—
245C2×C4—1881no—
246C2×C4—1881no—
247C2×C4#1062535011yescharacteristic
248C2×C4#1062535011yescharacteristic
249C2×C4D4×D4711yescharacteristic
250C2×C4D4×D4711yescharacteristic
251C2×C4#1062535211yescharacteristic
252C2×C4C2×C22⋊D4711yescharacteristic
253C8—41no—
254C8—1881no—
255C22—42no—
256C22—42no—
257C22—42no—
258C22—81no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22—3761no—
263C22—3761no—
264C22—3761no—
265C22—3761no—
266C22—1882no—
267C22—1882no—
268C22—1882no—
269C22#1309399211yescharacteristic
270C22#1309399711yescharacteristic
271C22#1309401011yescharacteristic
272C22D8×D4711yescharacteristic
273C22SD16×D4711yescharacteristic
274C22#1309404811yescharacteristic
275C22#1309405111yescharacteristic
276C4—81no—
277C4—942no—
278C4—942no—
279C4—1882no—
280C4#1309399611yescharacteristic
281C4#1309399711yescharacteristic
282C4#1309400611yescharacteristic
283C4#1309400711yescharacteristic
284C2—82no—
285C2—3762no—
286C2#1568903811yescharacteristic
287C2#1568925511yescharacteristic
288C2#1568927211yescharacteristic
289C2#1568931711yescharacteristic
290C2#1568932211yescharacteristic
291C2#1568946811yescharacteristic
292C2#1568948611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#2041
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#13093946C2semidirect
3. C2×#13093945C2semidirect
4. C2×#13093944C2semidirect
5. #15689019C2semidirect
6. #15688877C2semidirect
7. C2×#102×C47C2semidirect
56. C4⋊Dic47D4semidirect
151. C2×#102D47semidirect
154. C47#2041semidirect