Finite Group Databasebeta

← #20251436

Subgroups — #20251436

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×#13094013C211yesmaximal, characteristic, complemented
2C2×#13094010C211yesmaximal, characteristic, complemented
3#15689041C212yesmaximal, complemented
4#15689038C212yesmaximal, complemented
5#15689036C212yesmaximal, complemented
6#15689034C211yesmaximal, characteristic, complemented
7#15689033C211yesmaximal, characteristic, complemented
8#15689032C211yesmaximal, characteristic, complemented
9#15689032C212yesmaximal, complemented
10#15688987C211yesmaximal, characteristic, complemented
11C47×#393C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×D188C2211yescharacteristic
14C22×D188C2212yes—
15C22×C22⋊D47C2211yescharacteristic
16C22×C22⋊D47C2212yes—
17#13094013—24no—
18#13094010—24no—
19C2×Dic47⋊C4C2212yes—
20C2×C22⋊Dic47C2211yescharacteristic
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×C4×Dic47C2211yescharacteristic
29C47⋊#95C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2312yes—
39C23×D47C2311yescharacteristic
40C2×Q8×C47—22no—
41C2×Q8×C47—42no—
42C22×C4×C47C2312yes—
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—22no—
47C2×C22⋊D47—42no—
48C2×C22⋊D47—42no—
49C2×C22⋊D47—42no—
50C2×C22⋊D47—42no—
51C22×Dic47C2312yes—
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2311yescharacteristic
55C2×D188—22no—
56C2×D188—42no—
57C2×D188—42no—
58C2×D188—42no—
59C2×D188—42no—
60C2×Dic94—22no—
61C2×Dic94—42no—
62C22⋊C4×C47—22no—
63C22⋊C4×C47—42no—
64C22⋊Dic47—22no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—24no—
68(C2×D47)⋊C4—24no—
69(C2×D47)⋊C4—42no—
70(C2×D47)⋊C4—42no—
71(C2×D47)⋊C4—42no—
72Dic47⋊C4—42no—
73C4×Dic47D414yescomplemented
74C23×C47—21no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47—21no—
78C23×C47—21no—
79C23×C47C2411yescharacteristic
80C22×D47—22no—
81C22×D47—21no—
82C22×D47—22no—
83C22×D47—22no—
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—21no—
87C22×D47—22no—
88C22×D47—22no—
89C22×D47—22no—
90C22×D47—22no—
91C22×D47—21no—
92Q8×C47—44no—
93C2×C4×C47—22no—
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×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47C2×D412yes—
103C22⋊D47—44no—
104C22⋊D47—48no—
105C2×Dic47—21no—
106C2×Dic47—22no—
107C2×Dic47—21no—
108C2×Dic47—21no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47C2×D412yes—
114C2×Dic47C2×D412yes—
115D188—44no—
116D188—48no—
117Dic94—44no—
118C22×C47—41no—
119C22×C47—41no—
120C22×C47—41no—
121C22×C47—42no—
122C22×C47—42no—
123C22×C47C22×D411yescharacteristic
124C22×C47H(5,𝔽2)12yes—
125C22×C47H(5,𝔽2)12yes—
126C22×C47H(5,𝔽2)11yescharacteristic
127C22×C472−1+411yescharacteristic
128C2×D47—42no—
129C2×D47—41no—
130C2×D47—41no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—41no—
134C2×D47—42no—
135C2×D47—42no—
136C2×D47—42no—
137C2×D47—42no—
138C2×D47—42no—
139C2×D47—42no—
140C4×C47—22no—
141C4×C47—41no—
142C4×C47—42no—
143C4×C47—42no—
144Dic47—22no—
145Dic47—22no—
146Dic47—41no—
147Dic47—42no—
148#2819—471nomaximal, Sylow
149C2×C47—81no—
150C2×C47#53511yescharacteristic
151C2×C47#53511yescharacteristic
152C2×C47#53711yescharacteristic
153C2×C47H(3,𝔽4)12yes—
154C2×C47#56212yes—
155D47—82no—
156D47—81no—
157C2×#124—471no—
158C2×#124—471no—
159#394—472no—
160#394—472no—
161#393—471no—
162#393—472no—
163#393D4711yescharacteristic, complemented
164#392—472no—
165#392—471no—
166#392—471no—
167#382—471no—
168C47#281911yescharacteristic, complemented, Sylow
169C22×Q8—471no—
170C22×Q8C2×D4711yescharacteristic
171C22×D4—471no—
172C22×D4—472no—
173C22×D4—471no—
174C22×D4—472no—
175#124—944no—
176#124—944no—
177C2×C4⋊C4—472no—
178C2×C22⋊C4—471no—
179C2×C22⋊C4—472no—
180C2×C22⋊C4—471no—
181C2×C22⋊C4—472no—
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#95C2×D4711yescharacteristic
193#95C2×D4712yes—
194C24—471no—
195C24—472no—
196C24C22×D4711yescharacteristic
197C2×Q8—22no—
198C2×Q8—42no—
199C2×Q8—942no—
200C2×Q8—1882no—
201C2×D4—942no—
202C2×D4—942no—
203C2×D4—1882no—
204C2×D4—1882no—
205C2×D4—1882no—
206C2×D4—1882no—
207C2×D4—1882no—
208C2×D4—1882no—
209C2×D4—1882no—
210C2×D4—1882no—
211C22×C4—471no—
212C22×C4—471no—
213C22×C4—472no—
214C22×C4—471no—
215C22×C4C22×D4712yes—
216C22×C4C22×D4712yes—
217C22×C4C22×D4711yescharacteristic
218C22×C4C22×D4711yescharacteristic
219C4⋊C4—1882no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—942no—
223C22⋊C4—944no—
224C22⋊C4—944no—
225C22⋊C4—942no—
226C22⋊C4—942no—
227C22⋊C4—1882no—
228C22⋊C4—1882no—
229C22⋊C4—1882no—
230C42—474no—
231C23—21no—
232C23—22no—
233C23—21no—
234C23—22no—
235C23—21no—
236C23—942no—
237C23—941no—
238C23—942no—
239C23—942no—
240C23—942no—
241C23—942no—
242C23—942no—
243C23—941no—
244C23—942no—
245C23—942no—
246C23—941no—
247C23—942no—
248C23C23×D4711yescharacteristic
249Q8—44no—
250Q8—1884no—
251D4—1884no—
252D4—1888no—
253D4—1884no—
254D4—1888no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—472no—
265C2×C4—472no—
266C2×C4—941no—
267C2×C4—942no—
268C2×C4—941no—
269C2×C4—941no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—942no—
273C2×C4—942no—
274C2×C4D4×D4712yes—
275C22—42no—
276C22—42no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—1882no—
281C22—1882no—
282C22—1882no—
283C22—1882no—
284C22—1882no—
285C22—1882no—
286C22—1882no—
287C22—1881no—
288C22—1881no—
289C22—1882no—
290C22—1882no—
291C22—1881no—
292C22C2×D4×D4711yescharacteristic
293C22#1309406912yes—
294C22#1309407011yescharacteristic
295C22#1309407012yes—
296C22#1309407211yescharacteristic
297C4—22no—
298C4—42no—
299C4—42no—
300C4—41no—
301C4—942no—
302C4—942no—
303C4—1882no—
304C4—1881no—
305C2—81no—
306C2—3762no—
307C2—3761no—
308C2#1568968811yescharacteristic
309C2#1568969111yescharacteristic
310C2#1568970311yescharacteristic
311C2#1568986512yes—
312C2#1568986912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2819
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13094013C2semidirect
2. C2×#13094010C2semidirect
3. #15689041C2semidirect
4. #15689038C2semidirect
5. #15689036C2semidirect
6. #15689034C2semidirect
7. #15689033C2semidirect
8. #15689032C2semidirect
9. #15689032C2semidirect
10. #15688987C2semidirect
11. C47×#393C2semidirect
73. C4×Dic47D4semidirect
163. #393D47semidirect
168. C47#2819semidirect