Finite Group Databasebeta

← #20244394

Subgroups — #20244394

Order 6016.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10625325C211yesmaximal, characteristic, complemented
2C2×#13094004C211yesmaximal, characteristic, complemented
3C2×#13093999C211yesmaximal, characteristic
4C2×#13093947C211yesmaximal, characteristic, complemented
5C2×#13093944C211yesmaximal, characteristic, complemented
6C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
7C47×#340C211yesmaximal, characteristic, complemented
8C22×Dic94C2211yescharacteristic
9C22×D188—21no—
10C22×D188C2211yescharacteristic
11C22×C4×D47C2211yescharacteristic
12C2×#10625325—22no—
13C2×#10625325—22no—
14C2×#10625325—22no—
15C22×C47⋊C8C2211yescharacteristic
16#13094004—22no—
17#13094004—22no—
18#13093999—22no—
19#13093999—22no—
20C2×C4⋊Dic47—21no—
21C2×(C2×D47)⋊C4—21no—
22C2×(C2×D47)⋊C4—21no—
23#13093947—22no—
24#13093944—22no—
25(C2×D47)⋊C8—22no—
26C22×C8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C23×D47—21no—
30C23×D47D411yescharacteristic
31C22×C4×C47—21no—
32C22×C4×C47—21no—
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—21no—
35C22×Dic47D411yescharacteristic
36C2×D188—21no—
37C2×D188—21no—
38C2×D188—21no—
39C2×D188—21no—
40C2×D188—24no—
41C2×D188—21no—
42C2×D188—42no—
43C2×D188—42no—
44C2×D188D412yes—
45C2×C4×D47—21no—
46C2×C4×D47—21no—
47C2×C4×D47—21no—
48C2×C4×D47—21no—
49C2×C4×D47—21no—
50C2×C4×D47—21no—
51C2×Dic94—21no—
52C2×Dic94—21no—
53C2×Dic94—21no—
54C2×Dic94—21no—
55C2×Dic94—21no—
56C2×Dic94D412yescomplemented
57C2×C8×C47—21no—
58C2×C8×C47—21no—
59C2×C8×C47D412yescomplemented
60C4⋊C4×C47—21no—
61C4⋊C4×C47—21no—
62C4⋊C4×C47D412yes—
63C4⋊C4×C47D412yescomplemented
64(C2×D47)⋊C4—24no—
65(C2×D47)⋊C4—24no—
66C4⋊Dic47—24no—
67C2×C47⋊C8—21no—
68C2×C47⋊C8—21no—
69C2×C47⋊C8—21no—
70#10625325—28no—
71C23×C47C2×D411yescharacteristic
72C22×D47—21no—
73C22×D47—21no—
74C22×D47—21no—
75C22×D47—21no—
76C22×D47—21no—
77C22×D47—21no—
78C22×D47—22no—
79C22×D47—41no—
80C22×D47—41no—
81C22×D47—41no—
82C22×D47—41no—
83C22×D47—41no—
84C22×D47—41no—
85C22×D47SD1612yescomplemented
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—41no—
89C2×C4×C47—41no—
90C2×C4×C47—41no—
91C2×C4×C47—41no—
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47#4111yescharacteristic
98C2×Dic47—21no—
99C2×Dic47—22no—
100C2×Dic47—21no—
101C2×Dic47—21no—
102C2×Dic47—41no—
103C2×Dic47—41no—
104D188—22no—
105D188—22no—
106D188—48no—
107D188—41no—
108D188—41no—
109C4×D47—41no—
110C4×D47—41no—
111C4×D47—41no—
112C4×D47—41no—
113Dic94—22no—
114Dic94—22no—
115Dic94—41no—
116Dic94—41no—
117C8×C47—22no—
118C47⋊C8—41no—
119C22×C47#12011yescharacteristic
120C22×C47#12011yescharacteristic
121C22×C47#12111yescharacteristic
122C22×C47C2×SD1611yescharacteristic
123C22×C47#13511yescharacteristic
124C22×C47AGL(1,ℤ/8)11yescharacteristic
125C22×C47#13711yescharacteristic
126C2×D47—22no—
127C2×D47—22no—
128C2×D47—22no—
129C2×D47—41no—
130C2×D47—41no—
131C2×D47—41no—
132C2×D47—41no—
133C2×D47—42no—
134C2×D47—42no—
135C2×D47—42no—
136C2×D47—81no—
137C2×D47—81no—
138C2×D47—81no—
139C2×D47—81no—
140C4×C47—42no—
141C4×C47—42no—
142C4×C47#12011yescharacteristic
143C4×C47#12111yescharacteristic
144C4×C47#12111yescharacteristic
145C4×C47#12711yescharacteristic
146Dic47—42no—
147Dic47—41no—
148#2000—471nomaximal, Sylow
149C2×C47#39211yescharacteristic
150C2×C47#44811yescharacteristic
151C2×C47#44911yescharacteristic
152C2×C47#45011yescharacteristic
153C2×C47#45211yescharacteristic
154C2×C47#46511yescharacteristic
155C2×C47#46811yescharacteristic
156D47—42no—
157D47—82no—
158C22×SD16—471no—
159C2×C22⋊Q8—471no—
160C2×#121—471no—
161C2×#103—471no—
162C2×#102—471no—
163C2×C22⋊C8—471no—
164#340D4711yescharacteristic, complemented
165C47#200011yescharacteristic, complemented, Sylow
166C22×Q8—471no—
167C22×D4—471no—
168C22×D4—941no—
169C23×C4—471no—
170C2×SD16—942no—
171C2×SD16—942no—
172C2×SD16—942no—
173C22×C8—471no—
174C22×C8C2×D4711yescharacteristic
175C22⋊Q8—942no—
176C22⋊Q8—942no—
177#121—942no—
178#121—942no—
179C2×C4⋊C4—941no—
180C2×C4⋊C4C2×D4711yescharacteristic
181C2×C4⋊C4C2×D4711yescharacteristic
182C2×C22⋊C4—941no—
183C2×C22⋊C4—941no—
184#103—942no—
185#102—942no—
186C22⋊C8—942no—
187C24—471no—
188C24—941no—
189C2×Q8—472no—
190C2×Q8—941no—
191C2×Q8—941no—
192C2×Q8—941no—
193C2×Q8—941no—
194C2×Q8—941no—
195C2×D4—472no—
196C2×D4—944no—
197C2×D4—941no—
198C2×D4—941no—
199C2×D4—941no—
200C2×D4—941no—
201C2×D4—941no—
202C2×D4—1882no—
203C2×D4—1882no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—471no—
207C22×C4—941no—
208C22×C4—941no—
209C22×C4—941no—
210C22×C4—941no—
211C22×C4—941no—
212C22×C4—941no—
213C22×C4—941no—
214C22×C4C22×D4711yescharacteristic
215SD16—948no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—941no—
219C2×C8—941no—
220C2×C8—941no—
221C2×C8D18812yescomplemented
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—944no—
225C4⋊C4D18812yes—
226C4⋊C4D18812yescomplemented
227C22⋊C4—944no—
228C22⋊C4—944no—
229C23—472no—
230C23—941no—
231C23—941no—
232C23—941no—
233C23—941no—
234C23—941no—
235C23—941no—
236C23—942no—
237C23—1881no—
238C23—1881no—
239C23—1881no—
240C23—1881no—
241C23—1881no—
242C23—1881no—
243C23D4×D4711yescharacteristic
244Q8—942no—
245Q8—942no—
246Q8—1881no—
247Q8—1881no—
248D4—942no—
249D4—942no—
250D4—1888no—
251D4—1881no—
252D4—1881no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—941no—
260C2×C4—942no—
261C2×C4—941no—
262C2×C4—941no—
263C2×C4—1881no—
264C2×C4—1881no—
265C2×C4—1881no—
266C2×C4—1881no—
267C2×C4—1881no—
268C2×C4—1881no—
269C2×C4C2×D18811yescharacteristic
270C2×C4C2×D18811yescharacteristic
271C2×C4C2×D18811yescharacteristic
272C2×C4D4×D4711yescharacteristic
273C2×C4D4×D4711yescharacteristic
274C2×C4#1062535411yescharacteristic
275C8—22no—
276C8—1881no—
277C22—942no—
278C22—942no—
279C22—942no—
280C22—3761no—
281C22—3761no—
282C22—3761no—
283C22—3761no—
284C22—1882no—
285C22—1882no—
286C22—1882no—
287C22—1881no—
288C22—1881no—
289C22—1881no—
290C22—1881no—
291C22#1309399411yescharacteristic
292C22#1309399411yescharacteristic
293C22#1309399911yescharacteristic
294C22SD16×D4711yescharacteristic
295C22#1309404511yescharacteristic
296C22#1309404811yescharacteristic
297C22#1309405611yescharacteristic
298C4—42no—
299C4—42no—
300C4—1881no—
301C4—1882no—
302C4#1309399411yescharacteristic
303C4#1309399911yescharacteristic
304C4#1309399911yescharacteristic
305C4#1309402111yescharacteristic
306C2—3762no—
307C2—1882no—
308C2#1568903311yescharacteristic
309C2#1568926311yescharacteristic
310C2#1568926911yescharacteristic
311C2#1568927511yescharacteristic
312C2#1568928811yescharacteristic
313C2#1568935311yescharacteristic
314C2#1568937011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2000
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C22×#10625325C2semidirect
2. C2×#13094004C2semidirect
4. C2×#13093947C2semidirect
5. C2×#13093944C2semidirect
6. C2×(C2×D47)⋊C8C2semidirect
7. C47×#340C2semidirect
56. C2×Dic94D4semidirect
59. C2×C8×C47D4semidirect
63. C4⋊C4×C47D4semidirect
85. C22×D47SD16semidirect
164. #340D47semidirect
165. C47#2000semidirect
221. C2×C8D188semidirect
226. C4⋊C4D188semidirect