Finite Group Databasebeta

← #20243360

Subgroups — #20243360

Order 6016.

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13094072C211yesmaximal, characteristic
2#15689141C211yesmaximal, characteristic, complemented
3#15689139C211yesmaximal, characteristic, complemented
4#15689132C211yesmaximal, characteristic, complemented
5#15689105C211yesmaximal, characteristic, complemented
6#15689096C211yesmaximal, characteristic, complemented
7C47×#419C211yesmaximal, characteristic, complemented
8#13094072—22no—
9#13094072—22no—
10#13094072—22no—
11#13094072—22no—
12C2×#10625354—21no—
13C2×#10625354C412yescomplemented
14C2×#10625350—22no—
15C2×#10625350C2211yescharacteristic
16C2×#10625350C2211yescharacteristic
17C2×Q8×D47—21no—
18C2×Q8×D47C412yescomplemented
19C2×#10625329C2211yescharacteristic
20#13093983C2211yescharacteristic
21#13093952—22no—
22#13093950—22no—
23#13093948—22no—
24#13093942—21no—
25#13093940—21no—
26#13093938—22no—
27C22×Q8×C47C2211yescharacteristic
28C2×M16×C47C2211yescharacteristic
29#117×C47C2211yescharacteristic
30#103×C47—22no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47C2×C412yes—
35C2×Q8×C47D412yes—
36C2×Q8×C47D412yes—
37C22×C4×C47—21no—
38C22×C4×C47C2311yescharacteristic
39C2×C22⋊D47—21no—
40C2×C22⋊D47D412yes—
41#10625354—24no—
42#10625354—24no—
43#10625354—24no—
44#10625354—24no—
45Q8×D47—24no—
46Q8×D47—24no—
47Q8×D47—24no—
48Q8×D47—24no—
49#10625350—28no—
50#10625350—28no—
51#10625350—21no—
52#10625350—21no—
53#10625350—21no—
54#10625350—21no—
55#10625350—21no—
56#10625350—21no—
57#10625350D412yes—
58#10625350D412yes—
59C2×D188—22no—
60C2×D188C2×C411yescharacteristic
61C2×D188D411yescharacteristic
62C2×C4×D47—22no—
63C2×C4×D47—21no—
64C2×C4×D47—22no—
65C2×C4×D47C2×C412yes—
66C2×Dic94—22no—
67C2×Dic94C2×C411yescharacteristic
68C2×Dic94D411yescharacteristic
69M16×C47—21no—
70M16×C47—21no—
71C2×C8×C47—21no—
72C4⋊C4×C47—21no—
73C22⋊C4×C47—21no—
74C42×C47—21no—
75C22⋊Dic47—21no—
76C4⋊Dic47—21no—
77C4×Dic47—21no—
78#10625329—21no—
79#10625329—21no—
80C2×C47⋊C8—21no—
81C23×C47C2×D411yescharacteristic
82C22×D47—21no—
83C22×D47C22⋊C412yes—
84Q8×C47—22no—
85Q8×C47—22no—
86Q8×C47—22no—
87Q8×C47C22⋊C414yes—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—41no—
92C2×C4×C47C22×C411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47C2×D411yescharacteristic
98C22⋊D47—22no—
99C22⋊D47—22no—
100C22⋊D47—22no—
101C22⋊D47—22no—
102C2×Dic47—21no—
103C2×Dic47—41no—
104C2×Dic47C22⋊C412yes—
105D188—28no—
106D188—21no—
107D188—21no—
108D188—21no—
109D188C22⋊C412yes—
110C4×D47—28no—
111C4×D47—28no—
112C4×D47—22no—
113C4×D47—22no—
114C4×D47—22no—
115C4×D47—22no—
116Dic94—28no—
117Dic94—21no—
118Dic94—21no—
119Dic94—21no—
120Dic94C22⋊C412yes—
121C8×C47—41no—
122C47⋊C8—41no—
123C22×C47—41no—
124C22×C47C2×C22⋊C411yescharacteristic
125C22×C47#12011yescharacteristic
126C22×C47#12011yescharacteristic
127C2×D47—22no—
128C2×D47—22no—
129C2×D47—42no—
130C2×D47—42no—
131C4×C47—24no—
132C4×C47—81no—
133C4×C47C2×C22⋊C411yescharacteristic
134C4×C47C2×C22⋊C411yescharacteristic
135C4×C47#12011yescharacteristic
136C4×C47#12011yescharacteristic
137Dic47—22no—
138Dic47—22no—
139Dic47—81no—
140#1796—471nomaximal, Sylow
141C2×C47—21no—
142C2×C47—21no—
143C2×C47—21no—
144C2×C47#37911yescharacteristic
145D47—42no—
146D47—42no—
147C2×2−1+4—471no—
148#421—471no—
149#421—471no—
150#419—471no—
151#419D4711yescharacteristic, complemented
152#413—471no—
153#410—471no—
154C47#179611yescharacteristic, complemented, Sylow
1552−1+4—942no—
1562−1+4—942no—
1572−1+4—942no—
1582−1+4—942no—
159C2×#41—471no—
160C2×#41—472no—
161C2×#41—471no—
162C2×#41—942no—
163C2×#41—941no—
164C22×Q8—472no—
165C22×Q8—941no—
166C22×Q8C2×D4711yescharacteristic
167C2×M16—471no—
168C2×M16C2×D4711yescharacteristic
169#117—471no—
170#117C2×D4711yescharacteristic
171#104—942no—
172#104—942no—
173#103—22no—
174#103—942no—
175#101—941no—
176#100—941no—
177#99—942no—
178#41—472no—
179#41—472no—
180#41—948no—
181#41—948no—
182#41—944no—
183#41—944no—
184#41—944no—
185#41—944no—
186#41—941no—
187#41—941no—
188#41—941no—
189#41—941no—
190#41—941no—
191#41—941no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8—21no—
195C2×Q8—471no—
196C2×Q8—471no—
197C2×Q8—942no—
198C2×Q8—944no—
199C2×Q8—944no—
200C2×Q8—944no—
201C2×Q8—944no—
202C2×Q8C4×D4712yes—
203C2×Q8D18812yes—
204C2×Q8C22⋊D4712yes—
205C2×D4—472no—
206C2×D4—471no—
207C2×D4—471no—
208C2×D4—942no—
209C2×D4—941no—
210C22×C4—21no—
211C22×C4—472no—
212C22×C4—942no—
213C22×C4—942no—
214C22×C4—941no—
215C22×C4C22×D4711yescharacteristic
216M16—21no—
217M16—21no—
218M16—941no—
219M16—941no—
220C2×C8—21no—
221C2×C8—941no—
222C4⋊C4—21no—
223C4⋊C4—941no—
224C22⋊C4—21no—
225C22⋊C4—941no—
226C42—21no—
227C42—941no—
228C23—472no—
229C23—941no—
230C23D4×D4711yescharacteristic
231Q8—22no—
232Q8—22no—
233Q8—22no—
234Q8—472no—
235Q8—948no—
236Q8—941no—
237Q8—941no—
238Q8—941no—
239Q8(C2×D47)⋊C414yes—
240D4—472no—
241D4—948no—
242D4—942no—
243D4—942no—
244D4—942no—
245D4—942no—
246D4—941no—
247D4—941no—
248D4—941no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—472no—
254C2×C4—948no—
255C2×C4—948no—
256C2×C4—941no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—1881no—
262C2×C4C2×C4×D4711yescharacteristic
263C2×C4C2×D18811yescharacteristic
264C2×C4D4×D4711yescharacteristic
265C2×C4D4×D4711yescharacteristic
266C2×C4D4×D4711yescharacteristic
267C2×C4C2×C22⋊D4711yescharacteristic
268C8—41no—
269C8—1881no—
270C22—41no—
271C22—942no—
272C22—942no—
273C22—1882no—
274C22—1882no—
275C22C22⋊C4×D4711yescharacteristic
276C22#1309399211yescharacteristic
277C22#1309399411yescharacteristic
278C4—24no—
279C4—81no—
280C4—942no—
281C4—942no—
282C4—3761no—
283C4C22⋊C4×D4711yescharacteristic
284C4C2×(C2×D47)⋊C411yescharacteristic
285C4#1309399211yescharacteristic
286C4#1309399411yescharacteristic
287C2—21no—
288C2—21no—
289C2—21no—
290C2—1882no—
291C2—1882no—
292C2#1568897811yescharacteristic
subgroupG/H
centerC2#15688978
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#419C2
socleC2×C47#379
hypercenter#419D47
hypocenterC47#1796
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. #15689141C2semidirect
3. #15689139C2semidirect
4. #15689132C2semidirect
5. #15689105C2semidirect
6. #15689096C2semidirect
7. C47×#419C2semidirect
13. C2×#10625354C4semidirect
18. C2×Q8×D47C4semidirect
151. #419D47semidirect
154. C47#1796semidirect