Finite Group Databasebeta

← #20249128

Subgroups — #20249128

Order 6016.

824 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13093996C211yesmaximal, characteristic, complemented
2C2×#13093994C211yesmaximal, characteristic, complemented
3C2×#13093992C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5#15689052C212yesmaximal, complemented
6#15689041C212yesmaximal, complemented
7#15689038C212yesmaximal, complemented
8#15689032C212yesmaximal, complemented
9#15689002C211yesmaximal, characteristic, complemented
10#15688981C211yesmaximal, characteristic, complemented
11C47×#386C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C22×D188C2212yes—
14C22×C22⋊D47C2211yescharacteristic
15C22×C22⋊D47C2212yes—
16C22×C22⋊D47C2211yescharacteristic, complemented
17C23×Dic47C2211yescharacteristic
18#13093996—24no—
19#13093994—24no—
20#13093992—24no—
21C2×Dic47⋊C4C2211yescharacteristic, complemented
22C2×Dic47⋊C4C2212yescomplemented
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic, complemented
25C2×(C2×D47)⋊C4—24no—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×(C2×D47)⋊C4C2212yes—
29C2×(C2×D47)⋊C4C2212yes—
30C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
31C2×(C2×D47)⋊C4C2212yescomplemented
32C47⋊#95C2212yescomplemented
33C47⋊#95C2212yescomplemented
34C22×D4×C47C2211yescharacteristic
35C23×C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2211yescharacteristic
37C2×C22⋊C4×C47C2212yescomplemented
38#95×C47C2212yescomplemented
39C24×C47C2311yescharacteristic
40C24×C47C2311yescharacteristic
41C23×D47—22no—
42C23×D47—22no—
43C23×D47—42no—
44C23×D47—42no—
45C23×D47D414yescomplemented
46C23×D47C2311yescharacteristic
47C23×D47C2312yes—
48C2×D4×C47—22no—
49C2×D4×C47—22no—
50C2×D4×C47—22no—
51C22×C4×C47—22no—
52C22×C4×C47—42no—
53C22×C4×C47C2312yes—
54C22×C4×C47C2312yes—
55C22×C4×C47C2311yescharacteristic
56C2×C22⋊D47—22no—
57C2×C22⋊D47—22no—
58C2×C22⋊D47—22no—
59C2×C22⋊D47—24no—
60C2×C22⋊D47—22no—
61C2×C22⋊D47—42no—
62C2×C22⋊D47—42no—
63C2×C22⋊D47—42no—
64C22×Dic47—42no—
65C22×Dic47D414yescomplemented
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2312yes—
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C2×D188—24no—
71C2×D188—42no—
72C2×D188—42no—
73C22⋊C4×C47—22no—
74C22⋊C4×C47—42no—
75C22⋊Dic47—22no—
76C22⋊Dic47—22no—
77(C2×D47)⋊C4—24no—
78(C2×D47)⋊C4—24no—
79(C2×D47)⋊C4—24no—
80(C2×D47)⋊C4—24no—
81(C2×D47)⋊C4—22no—
82(C2×D47)⋊C4—42no—
83Dic47⋊C4—22no—
84Dic47⋊C4—42no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—21no—
88C23×C47—21no—
89C23×C47—21no—
90C23×C47—22no—
91C23×C47—22no—
92C23×C47C2×D412yes—
93C23×C47C2×D412yes—
94C23×C47#4112yes—
95C23×C47C2411yescharacteristic
96C22×D47—28no—
97C22×D47—22no—
98C22×D47—22no—
99C22×D47—22no—
100C22×D47—22no—
101C22×D47—22no—
102C22×D47—22no—
103C22×D47—21no—
104C22×D47—21no—
105C22×D47—21no—
106C22×D47—22no—
107C22×D47—22no—
108C22×D47—48no—
109C22×D47—44no—
110C22×D47—44no—
111C22×D47—48no—
112C22×D47C2×D414yes—
113D4×C47—44no—
114C2×C4×C47—21no—
115C2×C4×C47—22no—
116C2×C4×C47—21no—
117C2×C4×C47—22no—
118C2×C4×C47—21no—
119C2×C4×C47—22no—
120C2×C4×C47—22no—
121C2×C4×C47—22no—
122C2×C4×C47—22no—
123C2×C4×C47—44no—
124C22⋊D47—44no—
125C22⋊D47—48no—
126C22⋊D47—44no—
127C2×Dic47—22no—
128C2×Dic47—22no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—22no—
132C2×Dic47—21no—
133C2×Dic47—22no—
134C2×Dic47—22no—
135C2×Dic47—44no—
136C2×Dic47C2×D412yes—
137C2×Dic47C2×D412yes—
138D188—48no—
139C22×C47—22no—
140C22×C47—24no—
141C22×C47—22no—
142C22×C47—24no—
143C22×C47—41no—
144C22×C47—42no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—42no—
148C22×C47#12114yes—
149C22×C47C22×D411yescharacteristic
150C22×C47C22×D411yescharacteristic
151C22×C47C2×#4111yescharacteristic
152C22×C47H(5,𝔽2)12yes—
153C22×C47H(5,𝔽2)12yes—
154C2×D47—24no—
155C2×D47—24no—
156C2×D47—24no—
157C2×D47—416no—
158C2×D47—42no—
159C2×D47—42no—
160C2×D47—42no—
161C2×D47—42no—
162C2×D47—41no—
163C2×D47—42no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—42no—
167C4×C47—41no—
168C4×C47—42no—
169C4×C47—42no—
170Dic47—22no—
171Dic47—22no—
172Dic47—41no—
173Dic47—42no—
174#2617—471nomaximal, Sylow
175C2×C47—24no—
176C2×C47—81no—
177C2×C47C2×#12111yescharacteristic
178C2×C47#53412yes—
179C2×C47#53411yescharacteristic
180C2×C47#53511yescharacteristic
181C2×C47#53812yes—
182D47—44no—
183D47—81no—
184C2×#121—471no—
185C2×#120—471no—
186C2×#120—471no—
187C22×C22⋊C4—471no—
188#397—472no—
189#394—472no—
190#394—472no—
191#392—472no—
192#386—471no—
193#386D4711yescharacteristic, complemented
194#380—471no—
195C47#261711yescharacteristic, complemented, Sylow
196C25—471no—
197C22×D4—471no—
198C22×D4—472no—
199C22×D4—471no—
200C22×D4—472no—
201C22×D4C2×D4711yescharacteristic
202C23×C4—471no—
203C23×C4C2×D4711yescharacteristic
204#121—944no—
205#120—944no—
206#120—944no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—472no—
209C2×C22⋊C4—471no—
210C2×C22⋊C4—471no—
211C2×C22⋊C4—472no—
212C2×C22⋊C4—472no—
213C2×C22⋊C4—472no—
214C2×C22⋊C4—472no—
215C2×C22⋊C4—471no—
216C2×C22⋊C4—472no—
217C2×C22⋊C4—944no—
218C2×C22⋊C4C2×D4711yescharacteristic
219C2×C22⋊C4C2×D4712yescomplemented
220#95—472no—
221#95—472no—
222#95C2×D4712yescomplemented
223C24—472no—
224C24—474no—
225C24—471no—
226C24—942no—
227C24—942no—
228C24—1882no—
229C24—1882no—
230C24C22×D4711yescharacteristic
231C24C22×D4711yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—944no—
236C2×D4—942no—
237C2×D4—944no—
238C2×D4—942no—
239C2×D4—942no—
240C2×D4—942no—
241C2×D4—1882no—
242C2×D4—1882no—
243C2×D4—1882no—
244C2×D4—1882no—
245C2×D4—1882no—
246C22×C4—22no—
247C22×C4—42no—
248C22×C4—471no—
249C22×C4—471no—
250C22×C4—474no—
251C22×C4—471no—
252C22×C4—472no—
253C22×C4—1882no—
254C22×C4C22×D4712yes—
255C22×C4C22×D4712yes—
256C22×C4C22×D4711yescharacteristic
257C4⋊C4—942no—
258C4⋊C4—1882no—
259C22⋊C4—22no—
260C22⋊C4—42no—
261C22⋊C4—944no—
262C22⋊C4—944no—
263C22⋊C4—942no—
264C22⋊C4—944no—
265C22⋊C4—944no—
266C22⋊C4—942no—
267C22⋊C4—942no—
268C22⋊C4—1882no—
269C23—22no—
270C23—22no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—22no—
275C23—22no—
276C23—474no—
277C23—948no—
278C23—942no—
279C23—942no—
280C23—942no—
281C23—942no—
282C23—942no—
283C23—942no—
284C23—941no—
285C23—941no—
286C23—941no—
287C23—942no—
288C23—942no—
289C23—1888no—
290C23—1884no—
291C23—1884no—
292C23—1888no—
293C23#1062535012yes—
294C23D4×D4712yes—
295C23D4×D4712yes—
296C23C23×D4711yescharacteristic
297D4—44no—
298D4—1888no—
299D4—1884no—
300D4—1888no—
301D4—1884no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—44no—
312C2×C4—472no—
313C2×C4—472no—
314C2×C4—942no—
315C2×C4—942no—
316C2×C4—941no—
317C2×C4—942no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—942no—
321C2×C4—942no—
322C2×C4—1884no—
323C22—24no—
324C22—22no—
325C22—22no—
326C22—24no—
327C22—41no—
328C22—42no—
329C22—41no—
330C22—41no—
331C22—42no—
332C22—944no—
333C22—944no—
334C22—944no—
335C22—18816no—
336C22—1881no—
337C22—1882no—
338C22—1881no—
339C22—1881no—
340C22—1882no—
341C22—1882no—
342C22—1882no—
343C22—1882no—
344C22—1882no—
345C22#1309399714yes—
346C22C2×D4×D4711yescharacteristic
347C22C2×D4×D4711yescharacteristic
348C22C2×#1062535011yescharacteristic
349C22#1309406912yes—
350C22#1309407012yes—
351C4—41no—
352C4—42no—
353C4—42no—
354C4—942no—
355C4—942no—
356C4—1881no—
357C4—1882no—
358C2—24no—
359C2—81no—
360C2—3761no—
361C2—1884no—
362C2C2×#1309399711yescharacteristic
363C2#1568968112yes—
364C2#1568968411yescharacteristic
365C2#1568968811yescharacteristic
366C2#1568970612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#386C2
hypercenter#386D47
hypocenterC47#2617
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#13093996C2semidirect
2. C2×#13093994C2semidirect
3. C2×#13093992C2semidirect
4. C22×(C2×D47)⋊C4C2semidirect
5. #15689052C2semidirect
6. #15689041C2semidirect
7. #15689038C2semidirect
8. #15689032C2semidirect
9. #15689002C2semidirect
10. #15688981C2semidirect
11. C47×#386C2semidirect
16. C22×C22⋊D47C22semidirect
21. C2×Dic47⋊C4C22semidirect
22. C2×Dic47⋊C4C22semidirect
24. C2×C22⋊Dic47C22semidirect
30. C2×(C2×D47)⋊C4C22semidirect
31. C2×(C2×D47)⋊C4C22semidirect
32. C47⋊#95C22semidirect
33. C47⋊#95C22semidirect
37. C2×C22⋊C4×C47C22semidirect
38. #95×C47C22semidirect
45. C23×D47D4semidirect
65. C22×Dic47D4semidirect
193. #386D47semidirect
195. C47#2617semidirect
219. C2×C22⋊C4C2×D47semidirect
222. #95C2×D47semidirect