Finite Group Databasebeta

← #20251417

Subgroups — #20251417

Order 6016.

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

normal subgroups only

This group has 528 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×#13094004C211yesmaximal, characteristic, complemented
2C2×#13093997C211yesmaximal, characteristic
3#15689058C211yesmaximal, characteristic, complemented
4#15689056C212yesmaximal, complemented
5#15689040C212yesmaximal, complemented
6#15689039C212yesmaximal, complemented
7#15689038C212yesmaximal, complemented
8#15689036C211yesmaximal, characteristic, complemented
9#15689035C211yesmaximal, characteristic, complemented
10#15688985C211yesmaximal, characteristic, complemented
11C47×#399C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×D188C2211yescharacteristic
14C22×C22⋊D47C2211yescharacteristic
15C22×C22⋊D47C2211yescharacteristic
16C22×C4×D47C2211yescharacteristic
17#13094004—24no—
18#13093997—24no—
19C2×C4⋊Dic47C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C23×D47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—22no—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—42no—
47C2×C22⋊D47—42no—
48C22×Dic47C2312yes—
49C22×Dic47C2312yes—
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2311yescharacteristic
52C2×D188—22no—
53C2×D188—42no—
54C2×C4×D47—42no—
55C2×C4×D47D414yes—
56C2×Dic94—22no—
57C2×Dic94—42no—
58C4⋊C4×C47—22no—
59C4⋊C4×C47—42no—
60C22⋊C4×C47—22no—
61C22⋊C4×C47—42no—
62C22⋊Dic47—42no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—42no—
66(C2×D47)⋊C4—42no—
67(C2×D47)⋊C4—42no—
68C4⋊Dic47—24no—
69Dic47⋊C4—22no—
70Dic47⋊C4—42no—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—21no—
75C23×C47—21no—
76C23×C47C2411yescharacteristic
77C22×D47—22no—
78C22×D47—22no—
79C22×D47—21no—
80C22×D47—21no—
81C22×D47—21no—
82C22×D47—22no—
83C22×D47—22no—
84C22×D47—21no—
85C22×D47—21no—
86C22×D47C2×D412yes—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47C2×D412yes—
97C22⋊D47—44no—
98C22⋊D47—44no—
99C2×Dic47—22no—
100C2×Dic47—21no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47C2×D412yes—
109D188—44no—
110C4×D47—44no—
111Dic94—44no—
112C22×C47—41no—
113C22×C47—41no—
114C22×C47—41no—
115C22×C47—42no—
116C22×C47—42no—
117C22×C47C22×D411yescharacteristic
118C22×C47H(5,𝔽2)12yes—
119C22×C47H(5,𝔽2)12yes—
120C22×C472−1+411yescharacteristic
121C22×C472−1+411yescharacteristic
122C2×D47—22no—
123C2×D47—22no—
124C2×D47—22no—
125C2×D47—42no—
126C2×D47—42no—
127C2×D47—41no—
128C2×D47—41no—
129C2×D47—41no—
130C2×D47—42no—
131C2×D47—42no—
132C4×C47—22no—
133C4×C47—41no—
134C4×C47—42no—
135C4×C47—42no—
136Dic47—22no—
137Dic47—42no—
138Dic47—41no—
139Dic47—42no—
140#2816—471nomaximal, Sylow
141C2×C47—81no—
142C2×C47#53411yescharacteristic
143C2×C47#53511yescharacteristic
144C2×C47#53611yescharacteristic
145C2×C47#56212yes—
146C2×C47#56212yes—
147D47—42no—
148D47—81no—
149C2×C22⋊Q8—471no—
150C2×#121—471no—
151#399—471no—
152#399D4711yescharacteristic, complemented
153#398—472no—
154#394—472no—
155#394—472no—
156#394—472no—
157#393—471no—
158#393—471no—
159#381—471no—
160C47#281611yescharacteristic, complemented, Sylow
161C22×Q8—471no—
162C22×D4—471no—
163C22×D4—471no—
164C22×D4—471no—
165C23×C4—471no—
166C22⋊Q8—944no—
167#121—944no—
168C2×C4⋊C4—471no—
169C2×C4⋊C4—472no—
170C2×C4⋊C4—472no—
171C2×C4⋊C4C2×D4711yescharacteristic
172C2×C4⋊C4C2×D4712yes—
173C2×C22⋊C4—471no—
174C2×C22⋊C4—472no—
175C2×C22⋊C4—472no—
176C2×C22⋊C4—472no—
177C2×C22⋊C4—472no—
178C2×C22⋊C4—472no—
179C2×C22⋊C4C2×D4711yescharacteristic
180C2×C22⋊C4C2×D4712yes—
181#95—471no—
182#95—472no—
183#95—472no—
184#95—472no—
185#95C2×D4711yescharacteristic
186C24—471no—
187C24—471no—
188C24C22×D4711yescharacteristic
189C2×Q8—942no—
190C2×Q8—1882no—
191C2×D4—942no—
192C2×D4—942no—
193C2×D4—942no—
194C2×D4—1882no—
195C2×D4—1882no—
196C2×D4—1882no—
197C22×C4—471no—
198C22×C4—474no—
199C22×C4—472no—
200C22×C4—472no—
201C22×C4—471no—
202C22×C4—1882no—
203C22×C4C22×D4712yes—
204C22×C4C22×D4711yescharacteristic
205C22×C4C22×D4712yes—
206C22×C4C22×D4711yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—42no—
209C4⋊C4—942no—
210C4⋊C4—944no—
211C4⋊C4—1882no—
212C22⋊C4—22no—
213C22⋊C4—42no—
214C22⋊C4—944no—
215C22⋊C4—942no—
216C22⋊C4—1882no—
217C22⋊C4—1882no—
218C22⋊C4—1882no—
219C22⋊C4—1882no—
220C23—21no—
221C23—22no—
222C23—22no—
223C23—21no—
224C23—21no—
225C23—472no—
226C23—942no—
227C23—942no—
228C23—941no—
229C23—941no—
230C23—941no—
231C23—942no—
232C23—942no—
233C23—941no—
234C23—941no—
235C23C23×D4711yescharacteristic
236Q8—1884no—
237D4—1884no—
238D4—1884no—
239D4—1884no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—472no—
250C2×C4—942no—
251C2×C4—941no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—1884no—
260C2×C4D4×D4712yes—
261C22—42no—
262C22—42no—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—942no—
267C22—942no—
268C22—942no—
269C22—1882no—
270C22—1882no—
271C22—1881no—
272C22—1881no—
273C22—1881no—
274C22—1882no—
275C22—1882no—
276C22C2×D4×D4711yescharacteristic
277C22#1309406912yes—
278C22#1309407012yes—
279C22#1309407111yescharacteristic
280C22#1309407211yescharacteristic
281C4—22no—
282C4—42no—
283C4—41no—
284C4—42no—
285C4—942no—
286C4—1882no—
287C4—1882no—
288C4—1881no—
289C2—81no—
290C2—3761no—
291C2—1882no—
292C2#1568968411yescharacteristic
293C2#1568968611yescharacteristic
294C2#1568969611yescharacteristic
295C2#1568986912yes—
296C2#1568987012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47#2816
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13094004C2semidirect
3. #15689058C2semidirect
4. #15689056C2semidirect
5. #15689040C2semidirect
6. #15689039C2semidirect
7. #15689038C2semidirect
8. #15689036C2semidirect
9. #15689035C2semidirect
10. #15688985C2semidirect
11. C47×#399C2semidirect
152. #399D47semidirect
160. C47#2816semidirect