Finite Group Databasebeta

← #20243321

Subgroups — #20243321

Order 6016.

592 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 125 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×Q8×D47C211yesmaximal, characteristic
2C2×#13093949C211yesmaximal, characteristic, complemented
3C2×#13093948C211yesmaximal, characteristic, complemented
4C2×#13093947C211yesmaximal, characteristic, complemented
5C2×(C2×D47)⋊C8C211yesmaximal, characteristic
6#15688980C211yesmaximal, characteristic
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C22×Dic94—21no—
9C22×Dic94C2211yescharacteristic
10C2×Q8×D47—22no—
11C2×Q8×D47—22no—
12C2×Q8×D47—22no—
13C2×Q8×D47—22no—
14C2×Q8×D47—22no—
15C2×Q8×D47C414yescomplemented
16C22×C4×D47—21no—
17C22×C4×D47C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×(C2×D47)⋊C4—21no—
21#13093949—22no—
22#13093948—22no—
23#13093947—22no—
24(C2×D47)⋊C8—22no—
25C47⋊#95—21no—
26C22×Q8×C47C2211yescharacteristic
27C22×C8×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29#103×C47—22no—
30C23×D47D411yescharacteristic
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×C47—21no—
39C22×C4×C47C2311yescharacteristic
40C22×Dic47—21no—
41C22×Dic47—21no—
42C22×Dic47D411yescharacteristic
43Q8×D47—28no—
44Q8×D47—28no—
45Q8×D47—28no—
46Q8×D47—28no—
47C2×C4×D47—24no—
48C2×C4×D47—24no—
49C2×C4×D47—24no—
50C2×C4×D47—21no—
51C2×C4×D47—21no—
52C2×C4×D47—21no—
53C2×C4×D47—21no—
54C2×C4×D47C2×C412yes—
55C2×C4×D47D412yes—
56C2×Dic94—24no—
57C2×Dic94—24no—
58C2×Dic94—21no—
59C2×Dic94—21no—
60C2×Dic94—21no—
61C2×Dic94—24no—
62C2×Dic94C2×C412yes—
63C2×Dic94D412yes—
64C2×Dic94D412yes—
65C2×C8×C47—21no—
66C2×C8×C47—21no—
67C2×C8×C47—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70(C2×D47)⋊C4—42no—
71C4⋊Dic47—21no—
72C4⋊Dic47—21no—
73C2×C47⋊C8—21no—
74C2×C47⋊C8—21no—
75C2×C47⋊C8—21no—
76C23×C47C2×D411yescharacteristic
77C22×D47—21no—
78C22×D47—21no—
79C22×D47—21no—
80C22×D47—21no—
81C22×D47C22⋊C412yes—
82C22×D47SD1612yes—
83C22×D47Q1612yes—
84Q8×C47—22no—
85Q8×C47—22no—
86Q8×C47—22no—
87Q8×C47C22⋊C414yescomplemented
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—41no—
92C2×C4×C47—41no—
93C2×C4×C47—41no—
94C2×C4×C47C22×C411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D411yescharacteristic
100C2×Dic47—22no—
101C2×Dic47—21no—
102C2×Dic47—21no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—41no—
106C2×Dic47—41no—
107C2×Dic47—41no—
108C2×Dic47C22⋊C412yes—
109C4×D47—216no—
110C4×D47—22no—
111C4×D47—22no—
112C4×D47—22no—
113C4×D47—22no—
114Dic94—216no—
115Dic94—22no—
116Dic94—22no—
117Dic94—22no—
118Dic94C22⋊C414yescomplemented
119C8×C47—41no—
120C47⋊C8—41no—
121C22×C47C2×C22⋊C411yescharacteristic
122C22×C47#12011yescharacteristic
123C22×C47#12011yescharacteristic
124C22×C47C2×SD1611yescharacteristic
125C22×C47C2×Q1611yescharacteristic
126C22×C47#13711yescharacteristic
127C22×C47#13711yescharacteristic
128C2×D47—22no—
129C2×D47—22no—
130C2×D47—22no—
131C2×D47—22no—
132C2×D47—22no—
133C2×D47—22no—
134C2×D47#10314yescomplemented
135C4×C47—24no—
136C4×C47—81no—
137C4×C47C2×C22⋊C411yescharacteristic
138C4×C47C2×C22⋊C411yescharacteristic
139C4×C47#12011yescharacteristic
140C4×C47#12011yescharacteristic
141Dic47—22no—
142Dic47—24no—
143Dic47—81no—
144#1787—471nomaximal, Sylow
145C2×C47#37911yescharacteristic
146C2×C47C2×#10311yescharacteristic
147C2×C47#41911yescharacteristic
148C2×C47#44811yescharacteristic
149C2×C47#44811yescharacteristic
150C2×C47#45111yescharacteristic
151C2×C47#45111yescharacteristic
152D47—24no—
153C23×Q8—471no—
154C2×#103—471no—
155C2×#103—471no—
156C2×#103—471no—
157C2×#103D4711yescharacteristic, complemented
158C2×C22⋊C8—471no—
159#380—471no—
160C47#178711yescharacteristic, complemented, Sylow
161C22×Q8—474no—
162C22×Q8—471no—
163C22×Q8—941no—
164C22×Q8—942no—
165C22×Q8—942no—
166C22×Q8—942no—
167C22×Q8—942no—
168C22×Q8—942no—
169C22×Q8C2×D4711yescharacteristic
170C23×C4—471no—
171C23×C4—941no—
172C22×C8—471no—
173C22×C8C2×D4711yescharacteristic
174C2×C4⋊C4—471no—
175C2×C4⋊C4C2×D4711yescharacteristic
176C2×C22⋊C4—941no—
177#103—22no—
178#103—942no—
179#103—942no—
180#103—942no—
181C22⋊C8—942no—
182#95—941no—
183C24—471no—
184C2×Q8—21no—
185C2×Q8—21no—
186C2×Q8—21no—
187C2×Q8—472no—
188C2×Q8—472no—
189C2×Q8—472no—
190C2×Q8—944no—
191C2×Q8—944no—
192C2×Q8—944no—
193C2×Q8—948no—
194C2×Q8—948no—
195C2×Q8—948no—
196C2×Q8—948no—
197C2×Q8—941no—
198C2×Q8—941no—
199C2×Q8—941no—
200C2×Q8C4×D4712yes—
201C2×Q8D18812yes—
202C2×Q8C22⋊D4712yes—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—471no—
206C22×C4—472no—
207C22×C4—472no—
208C22×C4—944no—
209C22×C4—944no—
210C22×C4—944no—
211C22×C4—941no—
212C22×C4—941no—
213C22×C4—941no—
214C22×C4—941no—
215C22×C4—941no—
216C22×C4—941no—
217C22×C4C22×D4711yescharacteristic
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—941no—
222C2×C8—941no—
223C2×C8—941no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—941no—
227C4⋊C4—941no—
228C22⋊C4—1882no—
229C23—472no—
230C23—472no—
231C23—472no—
232C23—941no—
233C23—941no—
234C23—941no—
235C23—941no—
236C23D4×D4711yescharacteristic
237Q8—22no—
238Q8—22no—
239Q8—22no—
240Q8—474no—
241Q8—9416no—
242Q8—942no—
243Q8—942no—
244Q8—942no—
245Q8(C2×D47)⋊C414yescomplemented
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—472no—
253C2×C4—9416no—
254C2×C4—942no—
255C2×C4—941no—
256C2×C4—942no—
257C2×C4—941no—
258C2×C4—942no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—942no—
262C2×C4—942no—
263C2×C4—1881no—
264C2×C4—1881no—
265C2×C4—1881no—
266C2×C4C2×C4×D4711yescharacteristic
267C2×C4C2×D18811yescharacteristic
268C2×C4D4×D4711yescharacteristic
269C2×C4D4×D4711yescharacteristic
270C2×C4D4×D4711yescharacteristic
271C2×C4C2×C22⋊D4711yescharacteristic
272C8—41no—
273C8—1881no—
274C22—474no—
275C22—942no—
276C22—942no—
277C22—942no—
278C22—942no—
279C22—942no—
280C22—942no—
281C22C22⋊C4×D4711yescharacteristic
282C22#1309399211yescharacteristic
283C22#1309399411yescharacteristic
284C22SD16×D4711yescharacteristic
285C22Q16×D4711yescharacteristic
286C22#1309405311yescharacteristic
287C22#1309405611yescharacteristic
288C4—24no—
289C4—81no—
290C4—942no—
291C4—944no—
292C4—3761no—
293C4C22⋊C4×D4711yescharacteristic
294C4C2×(C2×D47)⋊C411yescharacteristic
295C4#1309399211yescharacteristic
296C4#1309399411yescharacteristic
297C2—944no—
298C2#1568897811yescharacteristic
299C2#103×D4711yescharacteristic
300C2#1568913011yescharacteristic
301C2#1568926011yescharacteristic
302C2#1568926311yescharacteristic
303C2#1568927711yescharacteristic
304C2#1568928011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#1787
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#13093949C2semidirect
3. C2×#13093948C2semidirect
4. C2×#13093947C2semidirect
7. C2×#103×C47C2semidirect
15. C2×Q8×D47C4semidirect
87. Q8×C47C22⋊C4semidirect
118. Dic94C22⋊C4semidirect
134. C2×D47#103semidirect
157. C2×#103D47semidirect
160. C47#1787semidirect
245. Q8(C2×D47)⋊C4semidirect