Finite Group Databasebeta

← #20249137

Subgroups — #20249137

Order 6016.

728 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13094020C211yesmaximal, characteristic, complemented
2C2×#13093996C212yesmaximal, complemented
3C2×#13093980C211yesmaximal, characteristic, complemented
4#15689041C211yesmaximal, characteristic, complemented
5#15689038C212yesmaximal, complemented
6#15689037C211yesmaximal, characteristic, complemented
7#15689032C211yesmaximal, characteristic, complemented
8#15689031C212yesmaximal, complemented
9#15689023C212yesmaximal, complemented
10#15688987C211yesmaximal, characteristic, complemented
11C47×#392C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C22⋊D47C2212yes—
14C22×C22⋊D47C2212yes—
15C22×C22⋊D47C2212yes—
16C23×Dic47C2211yescharacteristic
17#13094020—24no—
18#13093996—28no—
19#13093980—24no—
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2212yes—
25C2×C22⋊Dic47C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×(C2×D47)⋊C4C2212yes—
29C2×C4×Dic47C2211yescharacteristic
30C2×C4×Dic47C2211yescharacteristic
31C47⋊#95C2212yes—
32C47⋊#95C2211yescharacteristic
33C22×D4×C47C2212yes—
34C22×D4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2212yes—
37#95×C47C2211yescharacteristic
38C24×C47C2312yes—
39C24×C47C2311yescharacteristic
40C23×D47C2312yes—
41C2×D4×C47—24no—
42C2×D4×C47—22no—
43C2×D4×C47—42no—
44C2×D4×C47—42no—
45C2×D4×C47—42no—
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C2×C22⋊D47—24no—
50C2×C22⋊D47—24no—
51C2×C22⋊D47—24no—
52C2×C22⋊D47—24no—
53C2×C22⋊D47—24no—
54C2×C22⋊D47—42no—
55C2×C22⋊D47—42no—
56C2×C22⋊D47—42no—
57C2×C22⋊D47—42no—
58C22×Dic47—22no—
59C22×Dic47—22no—
60C22×Dic47D414yescomplemented
61C22×Dic47C2312yes—
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C2×D188—22no—
67C2×D188—42no—
68C22⋊C4×C47—22no—
69C22⋊C4×C47—42no—
70C22⋊Dic47—22no—
71C22⋊Dic47—24no—
72C22⋊Dic47—42no—
73(C2×D47)⋊C4—24no—
74(C2×D47)⋊C4—42no—
75(C2×D47)⋊C4—42no—
76Dic47⋊C4—22no—
77Dic47⋊C4—22no—
78Dic47⋊C4—24no—
79C4×Dic47—22no—
80C4×Dic47D414yescomplemented
81C23×C47—21no—
82C23×C47—21no—
83C23×C47—22no—
84C23×C47—22no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—22no—
88C23×C47—22no—
89C23×C47—22no—
90C23×C47—22no—
91C23×C47—22no—
92C23×C47C2×D412yes—
93C23×C47C2411yescharacteristic
94C22×D47—22no—
95C22×D47—22no—
96C22×D47—22no—
97C22×D47—22no—
98C22×D47—22no—
99C22×D47—22no—
100C22×D47—22no—
101D4×C47—44no—
102D4×C47—48no—
103C2×C4×C47—22no—
104C2×C4×C47—21no—
105C2×C4×C47—22no—
106C2×C4×C47—22no—
107C2×C4×C47—22no—
108C2×C4×C47—22no—
109C2×C4×C47C2×D412yes—
110C22⋊D47—48no—
111C22⋊D47—48no—
112C22⋊D47—48no—
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47—22no—
116C2×Dic47—28no—
117C2×Dic47—21no—
118C2×Dic47—22no—
119C2×Dic47—22no—
120C2×Dic47—22no—
121C2×Dic47—22no—
122C2×Dic47C2×D412yes—
123C2×Dic47C2×D412yes—
124C2×Dic47C2×D412yes—
125C2×Dic47C2×D412yes—
126C2×Dic47#4112yes—
127D188—44no—
128C22×C47—22no—
129C22×C47—24no—
130C22×C47—41no—
131C22×C47—41no—
132C22×C47—42no—
133C22×C47—42no—
134C22×C47—42no—
135C22×C47—42no—
136C22×C47—42no—
137C22×C47—42no—
138C22×C47—42no—
139C22×C47—42no—
140C22×C47C22×D411yescharacteristic
141C22×C47C22×D411yescharacteristic
142C22×C47C2×#4111yescharacteristic
143C22×C47H(5,𝔽2)12yes—
144C22×C47H(5,𝔽2)12yes—
145C2×D47—42no—
146C2×D47—42no—
147C2×D47—42no—
148C2×D47—42no—
149C2×D47—42no—
150C2×D47—42no—
151C2×D47—42no—
152C4×C47—22no—
153C4×C47—41no—
154C4×C47—42no—
155Dic47—22no—
156Dic47—22no—
157Dic47—41no—
158Dic47—42no—
159Dic47#12114yes—
160#2619—471nomaximal, Sylow
161C2×C47—42no—
162C2×C47—82no—
163C2×C47C2×#12111yescharacteristic
164C2×C47#53511yescharacteristic
165C2×C47#53511yescharacteristic
166C2×C47#53512yes—
167C2×C47#54012yes—
168D47—82no—
169C2×#127—471no—
170C2×#121—472no—
171C2×#117—471no—
172#394—471no—
173#394—472no—
174#394—471no—
175#392—472no—
176#392—471no—
177#392D4711yescharacteristic, complemented
178#390—472no—
179#382—471no—
180C47#261911yescharacteristic, complemented, Sylow
181C22×D4—472no—
182C22×D4—472no—
183C22×D4—472no—
184C22×D4—471no—
185C22×D4C2×D4712yes—
186C22×D4C2×D4711yescharacteristic
187C23×C4—471no—
188#127—944no—
189#121—948no—
190#117—944no—
191C2×C4⋊C4—471no—
192C2×C4⋊C4—471no—
193C2×C4⋊C4—472no—
194C2×C22⋊C4—471no—
195C2×C22⋊C4—472no—
196C2×C22⋊C4—472no—
197C2×C22⋊C4—472no—
198C2×C22⋊C4—472no—
199C2×C22⋊C4—472no—
200C2×C22⋊C4C2×D4711yescharacteristic
201C2×C22⋊C4C2×D4712yes—
202C2×C42—471no—
203C2×C42—471no—
204#95—472no—
205#95—471no—
206#95C2×D4711yescharacteristic
207C24—472no—
208C24C22×D4712yes—
209C24C22×D4711yescharacteristic
210C2×D4—24no—
211C2×D4—22no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—944no—
216C2×D4—944no—
217C2×D4—944no—
218C2×D4—944no—
219C2×D4—944no—
220C2×D4—942no—
221C2×D4—1882no—
222C2×D4—1882no—
223C2×D4—1882no—
224C2×D4—1882no—
225C2×D4—1882no—
226C22×C4—471no—
227C22×C4—474no—
228C22×C4—471no—
229C22×C4—471no—
230C22×C4—472no—
231C22×C4—471no—
232C22×C4—942no—
233C22×C4—942no—
234C22×C4C22×D4712yes—
235C22×C4C22×D4711yescharacteristic
236C22×C4C22×D4711yescharacteristic
237C4⋊C4—942no—
238C4⋊C4—944no—
239C4⋊C4—942no—
240C22⋊C4—22no—
241C22⋊C4—42no—
242C22⋊C4—944no—
243C22⋊C4—942no—
244C22⋊C4—944no—
245C22⋊C4—1882no—
246C22⋊C4—1882no—
247C22⋊C4—1882no—
248C42—474no—
249C42—942no—
250C23—21no—
251C23—21no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—942no—
262C23—942no—
263C23—942no—
264C23—942no—
265C23—942no—
266C23—942no—
267C23—942no—
268C23D4×D4712yes—
269C23C23×D4711yescharacteristic
270D4—44no—
271D4—48no—
272D4—1884no—
273D4—1888no—
274D4—1888no—
275D4—1888no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—472no—
283C2×C4—472no—
284C2×C4—472no—
285C2×C4—472no—
286C2×C4—472no—
287C2×C4—948no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—942no—
291C2×C4—941no—
292C2×C4—942no—
293C2×C4—942no—
294C2×C4—942no—
295C2×C4—942no—
296C2×C4D4×D4712yes—
297C22—22no—
298C22—24no—
299C22—41no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—1882no—
310C22—1882no—
311C22—1882no—
312C22—1882no—
313C22—1882no—
314C22—1882no—
315C22—1882no—
316C22C2×D4×D4711yescharacteristic
317C22C2×D4×D4711yescharacteristic
318C22#41×D4711yescharacteristic
319C22#1309406912yes—
320C22#1309406912yes—
321C4—22no—
322C4—41no—
323C4—42no—
324C4—474no—
325C4—942no—
326C4—942no—
327C4—1882no—
328C4—1881no—
329C2—42no—
330C2—82no—
331C2—3762no—
332C2#121×D4711yescharacteristic
333C2#1568968611yescharacteristic
334C2#1568968811yescharacteristic
335C2#1568968812yes—
336C2#1568972312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2619
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13094020C2semidirect
2. C2×#13093996C2semidirect
3. C2×#13093980C2semidirect
4. #15689041C2semidirect
5. #15689038C2semidirect
6. #15689037C2semidirect
7. #15689032C2semidirect
8. #15689031C2semidirect
9. #15689023C2semidirect
10. #15688987C2semidirect
11. C47×#392C2semidirect
60. C22×Dic47D4semidirect
80. C4×Dic47D4semidirect
177. #392D47semidirect
180. C47#2619semidirect