Finite Group Databasebeta

← #20248345

Subgroups — #20248345

Order 6016.

724 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 147 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×#13093999C211yesmaximal, characteristic, complemented
2C2×#13093997C212yesmaximal, complemented
3C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4#15689054C211yesmaximal, characteristic, complemented
5#15689041C211yesmaximal, characteristic, complemented
6#15689032C211yesmaximal, characteristic, complemented
7#15689012C212yesmaximal, complemented
8#15689001C212yesmaximal, complemented
9#15689000C212yesmaximal, complemented
10#95×D47C211yesmaximal, characteristic, complemented
11C47×#397C211yesmaximal, characteristic, complemented
12C22×D188C2212yes—
13C22×D188C2211yescharacteristic
14C22×C22⋊D47C2212yes—
15C22×C22⋊D47C2211yescharacteristic
16C23×Dic47C2211yescharacteristic
17C22×C4×D47C2212yes—
18C22×C4×D47C2211yescharacteristic
19#13093999—24no—
20#13093997—28no—
21(C22⋊D47)⋊C4—24no—
22C2×Dic47⋊C4C2212yes—
23C2×Dic47⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×(C2×D47)⋊C4C2212yes—
29C2×C4×Dic47C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2211yescharacteristic
32C47⋊#95C2212yes—
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35C2×C22⋊C4×C47C2211yescharacteristic
36#95×C47C2211yescharacteristic
37#95×C47C2212yes—
38C24×C47C2311yescharacteristic
39C23×D47C2312yes—
40C23×D47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—24no—
48C2×C22⋊D47—24no—
49C2×C22⋊D47—42no—
50C2×C22⋊D47D414yescomplemented
51C22×Dic47—22no—
52C22×Dic47—42no—
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2311yescharacteristic
55C22×Dic47C2311yescharacteristic
56C22×Dic47C2312yes—
57C2×D188—24no—
58C2×D188—24no—
59C2×D188—24no—
60C2×D188—22no—
61C2×D188—42no—
62C2×C4×D47—24no—
63C2×C4×D47—24no—
64C2×C4×D47—42no—
65C2×C4×D47—42no—
66C2×C4×D47D414yescomplemented
67C4⋊C4×C47—22no—
68C22⋊C4×C47—24no—
69C22⋊C4×C47—22no—
70(C2×D47)⋊C4—22no—
71(C2×D47)⋊C4—24no—
72(C2×D47)⋊C4—24no—
73(C2×D47)⋊C4—24no—
74(C2×D47)⋊C4—42no—
75Dic47⋊C4—22no—
76Dic47⋊C4—24no—
77C4×Dic47—22no—
78C23×C47—21no—
79C23×C47—21no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47C2×D412yes—
83C23×C47C2411yescharacteristic
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—22no—
89C22×D47—22no—
90C22×D47—22no—
91C22×D47—22no—
92C22×D47—22no—
93C22×D47C2×D412yes—
94C22×D47C2×D412yes—
95C22×D47#4112yes—
96C2×C4×C47—22no—
97C2×C4×C47—21no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47—22no—
105C2×C4×C47C2×D412yes—
106C22⋊D47—28no—
107C22⋊D47—48no—
108C2×Dic47—21no—
109C2×Dic47—22no—
110C2×Dic47—21no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—21no—
114C2×Dic47—22no—
115C2×Dic47—44no—
116C2×Dic47C2×D412yes—
117C2×Dic47C2×D412yes—
118C2×Dic47#4114yes—
119D188—44no—
120D188—48no—
121C4×D47—44no—
122C4×D47—48no—
123C22×C47—22no—
124C22×C47—24no—
125C22×C47—41no—
126C22×C47—41no—
127C22×C47—42no—
128C22×C47C22×D411yescharacteristic
129C22×C47C22×D411yescharacteristic
130C22×C47C2×#4111yescharacteristic
131C22×C47C2×#4112yes—
132C22×C47H(5,𝔽2)12yes—
133C2×D47—22no—
134C2×D47—22no—
135C2×D47—24no—
136C2×D47—24no—
137C2×D47—42no—
138C2×D47—42no—
139C2×D47—42no—
140C2×D47—42no—
141C2×D47—42no—
142C2×D47—42no—
143C2×D47—42no—
144C2×D47#12114yes—
145C4×C47—22no—
146C4×C47—42no—
147C4×C47—41no—
148C4×C47—42no—
149Dic47—22no—
150Dic47—22no—
151Dic47—24no—
152Dic47—41no—
153#2543—471nomaximal, Sylow
154C2×C47—42no—
155C2×C47C2×#12111yescharacteristic
156C2×C47#53211yescharacteristic
157C2×C47#53411yescharacteristic
158C2×C47#54612yes—
159C2×C47#55312yes—
160D47—24no—
161D47—82no—
162C2×#121—471no—
163C2×#121—472no—
164C2×C4×D4—471no—
165#398—471no—
166#397D4711yescharacteristic, complemented
167#394—471no—
168#392—471no—
169#388—472no—
170#386—472no—
171#386—472no—
172C2×#95—471no—
173C47#254311yescharacteristic, complemented, Sylow
174C22×D4—471no—
175C22×D4—472no—
176C22×D4—472no—
177C22×D4—471no—
178C23×C4—471no—
179C23×C4—471no—
180C23×C4—472no—
181#121—948no—
182#121—944no—
183C4×D4—944no—
184C2×C4⋊C4—471no—
185C2×C4⋊C4—472no—
186C2×C4⋊C4C2×D4711yescharacteristic
187C2×C22⋊C4—471no—
188C2×C22⋊C4—472no—
189C2×C22⋊C4—472no—
190C2×C22⋊C4—472no—
191C2×C22⋊C4—472no—
192C2×C22⋊C4C2×D4711yescharacteristic
193C2×C22⋊C4C2×D4712yes—
194C2×C42—471no—
195#95—472no—
196#95—471no—
197#95—472no—
198#95C2×D4711yescharacteristic
199#95C2×D4712yes—
200C24—471no—
201C24—472no—
202C24C22×D4711yescharacteristic
203C2×D4—474no—
204C2×D4—944no—
205C2×D4—944no—
206C2×D4—944no—
207C2×D4—944no—
208C2×D4—942no—
209C2×D4—942no—
210C2×D4—944no—
211C2×D4—942no—
212C2×D4—1882no—
213C2×D4—1882no—
214C22×C4—472no—
215C22×C4—471no—
216C22×C4—471no—
217C22×C4—474no—
218C22×C4—471no—
219C22×C4—944no—
220C22×C4—944no—
221C22×C4—942no—
222C22×C4—1882no—
223C22×C4—1882no—
224C22×C4—1882no—
225C22×C4C22×D4712yes—
226C22×C4C22×D4712yes—
227C22×C4C22×D4711yescharacteristic
228C22×C4C22×D4711yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—944no—
231C4⋊C4—942no—
232C22⋊C4—24no—
233C22⋊C4—22no—
234C22⋊C4—944no—
235C22⋊C4—944no—
236C22⋊C4—944no—
237C22⋊C4—942no—
238C22⋊C4—1882no—
239C42—942no—
240C23—21no—
241C23—22no—
242C23—21no—
243C23—22no—
244C23—472no—
245C23—472no—
246C23—472no—
247C23—942no—
248C23—942no—
249C23—942no—
250C23—942no—
251C23—942no—
252C23—942no—
253C23—942no—
254C23—942no—
255C23—942no—
256C23D4×D4712yes—
257C23C23×D4711yescharacteristic
258D4—948no—
259D4—1884no—
260D4—1888no—
261D4—1888no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—472no—
272C2×C4—472no—
273C2×C4—474no—
274C2×C4—941no—
275C2×C4—942no—
276C2×C4—941no—
277C2×C4—942no—
278C2×C4—942no—
279C2×C4—941no—
280C2×C4—942no—
281C2×C4—1884no—
282C2×C4—1888no—
283C2×C4—1884no—
284C2×C4D4×D4712yes—
285C22—24no—
286C22—22no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—474no—
291C22—944no—
292C22—944no—
293C22—942no—
294C22—942no—
295C22—1882no—
296C22—1882no—
297C22—1882no—
298C22—1882no—
299C22—1882no—
300C22—1882no—
301C22—1882no—
302C22C2×D4×D4711yescharacteristic
303C22C2×D4×D4711yescharacteristic
304C22#41×D4712yes—
305C22#41×D4711yescharacteristic
306C22#1309407012yes—
307C4—22no—
308C4—42no—
309C4—42no—
310C4—41no—
311C4—944no—
312C4—942no—
313C4—942no—
314C4—1881no—
315C2—42no—
316C2—944no—
317C2—3762no—
318C2#121×D4711yescharacteristic
319C2#1568967211yescharacteristic
320C2#1568968411yescharacteristic
321C2#1568976512yes—
322C2#1568982412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2543
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13093999C2semidirect
2. C2×#13093997C2semidirect
3. C2×(C22⋊D47)⋊C4C2semidirect
4. #15689054C2semidirect
5. #15689041C2semidirect
6. #15689032C2semidirect
7. #15689012C2semidirect
8. #15689001C2semidirect
9. #15689000C2semidirect
10. #95×D47C2semidirect
11. C47×#397C2semidirect
50. C2×C22⋊D47D4semidirect
66. C2×C4×D47D4semidirect
166. #397D47semidirect
173. C47#2543semidirect