Finite Group Databasebeta

← #20251435

Subgroups — #20251435

Order 6016.

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

normal subgroups only

This group has 580 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
1C2×#13094011C211yesmaximal, characteristic, complemented
2C2×#13094010C211yesmaximal, characteristic, complemented
3#15689038C212yesmaximal, complemented
4#15689037C212yesmaximal, complemented
5#15689036C211yesmaximal, characteristic, complemented
6#15689035C211yesmaximal, characteristic, complemented
7#15689035C212yesmaximal, complemented
8#15689031C211yesmaximal, characteristic, complemented
9#15689031C212yesmaximal, complemented
10#15688987C211yesmaximal, characteristic, complemented
11C47×#392C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×Dic94C2211yescharacteristic
14C22×C22⋊D47C2211yescharacteristic
15C22×C22⋊D47C2212yes—
16#13094011—24no—
17#13094010—24no—
18C2×Dic47⋊C4C2212yes—
19C2×C22⋊Dic47C2212yes—
20C2×C22⋊Dic47C2211yescharacteristic
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2212yes—
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×D4×C47C2211yescharacteristic
33C22×D4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2312yes—
38C24×C47C2311yescharacteristic
39C23×D47C2311yescharacteristic
40C2×D4×C47—22no—
41C2×D4×C47—42no—
42C2×D4×C47—42no—
43C2×D4×C47—42no—
44C2×D4×C47—42no—
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2312yes—
47C22×C4×C47C2311yescharacteristic
48C2×C22⋊D47—22no—
49C2×C22⋊D47—42no—
50C2×C22⋊D47—42no—
51C2×C22⋊D47—42no—
52C2×C22⋊D47—42no—
53C22×Dic47C2312yes—
54C22×Dic47C2311yescharacteristic
55C22×Dic47C2312yes—
56C22×Dic47C2311yescharacteristic
57C22×Dic47C2311yescharacteristic
58C2×Dic94—22no—
59C2×Dic94—22no—
60C2×Dic94—42no—
61C2×Dic94—42no—
62C22⋊C4×C47—22no—
63C22⋊C4×C47—42no—
64C22⋊Dic47—22no—
65C22⋊Dic47—24no—
66C22⋊Dic47—24no—
67C22⋊Dic47—42no—
68C22⋊Dic47—42no—
69(C2×D47)⋊C4—22no—
70(C2×D47)⋊C4—22no—
71(C2×D47)⋊C4—42no—
72Dic47⋊C4—42no—
73C4×Dic47D414yescomplemented
74C23×C47—22no—
75C23×C47—21no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47—22no—
83C23×C47—21no—
84C23×C47—22no—
85C23×C47—21no—
86C23×C47C2411yescharacteristic
87C22×D47—21no—
88C22×D47—22no—
89C22×D47—22no—
90C22×D47—21no—
91C22×D47—21no—
92D4×C47—44no—
93D4×C47—48no—
94C2×C4×C47—22no—
95C2×C4×C47—21no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47C2×D412yes—
101C22⋊D47—44no—
102C22⋊D47—48no—
103C2×Dic47—21no—
104C2×Dic47—22no—
105C2×Dic47—21no—
106C2×Dic47—21no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47C2×D412yes—
115C2×Dic47C2×D412yes—
116Dic94—44no—
117Dic94—44no—
118C22×C47—41no—
119C22×C47—42no—
120C22×C47—42no—
121C22×C47—41no—
122C22×C47—42no—
123C22×C47—41no—
124C22×C47—42no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—42no—
129C22×C47—42no—
130C22×C47C22×D411yescharacteristic
131C22×C47H(5,𝔽2)12yes—
132C22×C47H(5,𝔽2)12yes—
133C22×C47H(5,𝔽2)11yescharacteristic
134C22×C472−1+411yescharacteristic
135C2×D47—41no—
136C2×D47—41no—
137C2×D47—41no—
138C2×D47—42no—
139C2×D47—42no—
140C4×C47—22no—
141C4×C47—41no—
142C4×C47—42no—
143Dic47—22no—
144Dic47—22no—
145Dic47—41no—
146Dic47—42no—
147Dic47—42no—
148#2819—471nomaximal, Sylow
149C2×C47—81no—
150C2×C47—82no—
151C2×C47#53511yescharacteristic
152C2×C47#53511yescharacteristic
153C2×C47#53711yescharacteristic
154C2×C47H(3,𝔽4)12yes—
155C2×C47#56212yes—
156D47—81no—
157C2×#124—471no—
158C2×#124—471no—
159#394—472no—
160#394—472no—
161#393—472no—
162#393—471no—
163#393—471no—
164#392—472no—
165#392—471no—
166#392D4711yescharacteristic, complemented
167#382—471no—
168C47#281911yescharacteristic, complemented, Sylow
169C22×Q8—471no—
170C22×Q8—471no—
171C22×D4—471no—
172C22×D4—472no—
173C22×D4C2×D4711yescharacteristic
174C22×D4C2×D4712yes—
175#124—944no—
176#124—944no—
177C2×C4⋊C4—472no—
178C2×C22⋊C4—472no—
179C2×C22⋊C4—472no—
180C2×C22⋊C4—471no—
181C2×C22⋊C4—471no—
182C2×C22⋊C4—471no—
183C2×C22⋊C4—472no—
184C2×C22⋊C4—472no—
185C2×C22⋊C4—472no—
186C2×C22⋊C4C2×D4711yescharacteristic
187C2×C22⋊C4C2×D4712yes—
188C2×C42—471no—
189#95—472no—
190#95—471no—
191#95—472no—
192#95—472no—
193#95C2×D4711yescharacteristic
194C24—471no—
195C24C22×D4711yescharacteristic
196C24C22×D4712yes—
197C2×Q8—942no—
198C2×Q8—942no—
199C2×Q8—1882no—
200C2×Q8—1882no—
201C2×D4—22no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—942no—
207C2×D4—1882no—
208C2×D4—1882no—
209C2×D4—1882no—
210C2×D4—1882no—
211C22×C4—471no—
212C22×C4—471no—
213C22×C4—472no—
214C22×C4—472no—
215C22×C4—471no—
216C22×C4C22×D4712yes—
217C22×C4C22×D4711yescharacteristic
218C22×C4C22×D4711yescharacteristic
219C4⋊C4—1882no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—942no—
223C22⋊C4—942no—
224C22⋊C4—944no—
225C22⋊C4—944no—
226C22⋊C4—942no—
227C22⋊C4—1882no—
228C22⋊C4—1882no—
229C22⋊C4—1882no—
230C42—474no—
231C23—21no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—21no—
243C23—941no—
244C23—942no—
245C23—941no—
246C23—942no—
247C23—941no—
248C23C23×D4711yescharacteristic
249Q8—1884no—
250Q8—1884no—
251D4—44no—
252D4—48no—
253D4—1884no—
254D4—1888no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—472no—
262C2×C4—472no—
263C2×C4—941no—
264C2×C4—942no—
265C2×C4—941no—
266C2×C4—941no—
267C2×C4—942no—
268C2×C4—942no—
269C2×C4—942no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—942no—
273C2×C4—942no—
274C2×C4D4×D4712yes—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—42no—
283C22—42no—
284C22—41no—
285C22—41no—
286C22—42no—
287C22—1882no—
288C22—1882no—
289C22—1881no—
290C22—1881no—
291C22—1881no—
292C22C2×D4×D4711yescharacteristic
293C22#1309406911yescharacteristic
294C22#1309406912yes—
295C22#1309406912yes—
296C22#1309407111yescharacteristic
297C4—22no—
298C4—42no—
299C4—41no—
300C4—942no—
301C4—942no—
302C4—1882no—
303C4—1881no—
304C4—1882no—
305C2—81no—
306C2—82no—
307C2—3761no—
308C2#1568968611yescharacteristic
309C2#1568968811yescharacteristic
310C2#1568970211yescharacteristic
311C2#1568986612yes—
312C2#1568986812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2819
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13094011C2semidirect
2. C2×#13094010C2semidirect
3. #15689038C2semidirect
4. #15689037C2semidirect
5. #15689036C2semidirect
6. #15689035C2semidirect
7. #15689035C2semidirect
8. #15689031C2semidirect
9. #15689031C2semidirect
10. #15688987C2semidirect
11. C47×#392C2semidirect
73. C4×Dic47D4semidirect
166. #392D47semidirect
168. C47#2819semidirect