Finite Group Databasebeta

← #20249273

Subgroups — #20249273

Order 6016.

620 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×C22⋊D47C211yesmaximal, characteristic, complemented
2#15689061C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689037C211yesmaximal, characteristic, complemented
5#15689037C212yesmaximal, complemented
6#15689031C211yesmaximal, characteristic, complemented
7#15689031C212yesmaximal, complemented
8#15689011C212yesmaximal, complemented
9#15688999C212yesmaximal, complemented
10#15688986C211yesmaximal, characteristic, complemented
11C2×#121×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C22×C22⋊D47C2212yes—
14C22×C4×D47C2211yescharacteristic
15C4×C22⋊D47—24no—
16C2×Dic47⋊C4C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2211yescharacteristic
20C2×C22⋊Dic47C2212yes—
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×C4×Dic47C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2211yescharacteristic
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C22×D4×C47C2212yes—
32C22×D4×C47C2211yescharacteristic
33C23×C4×C47C2211yescharacteristic
34#121×C47—24no—
35C2×C4⋊C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2212yes—
37C24×C47C2312yes—
38C24×C47C2311yescharacteristic
39C23×D47C2311yescharacteristic
40C2×D4×C47—24no—
41C2×D4×C47—22no—
42C2×D4×C47—42no—
43C2×D4×C47—42no—
44C2×D4×C47—42no—
45C22×C4×C47—42no—
46C22×C4×C47D414yescomplemented
47C22×C4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2311yescharacteristic
50C2×C22⋊D47—22no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—24no—
53C2×C22⋊D47—22no—
54C2×C22⋊D47—42no—
55C2×C22⋊D47—42no—
56C22×Dic47C2312yes—
57C22×Dic47C2312yes—
58C22×Dic47C2311yescharacteristic
59C22×Dic47C2311yescharacteristic
60C22×Dic47C2311yescharacteristic
61C2×C4×D47—22no—
62C2×C4×D47—42no—
63C4⋊C4×C47—22no—
64C22⋊C4×C47—24no—
65C22⋊Dic47—22no—
66C22⋊Dic47—24no—
67C22⋊Dic47—42no—
68C22⋊Dic47—42no—
69C22⋊Dic47—42no—
70(C2×D47)⋊C4—22no—
71(C2×D47)⋊C4—42no—
72Dic47⋊C4—22no—
73Dic47⋊C4—42no—
74C4×Dic47—22no—
75C23×C47—21no—
76C23×C47—21no—
77C23×C47—22no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47—22no—
85C23×C47—22no—
86C23×C47C2×D412yes—
87C23×C47C2411yescharacteristic
88C22×D47—21no—
89C22×D47—21no—
90C22×D47—22no—
91C22×D47—22no—
92C22×D47#4112yes—
93D4×C47—44no—
94D4×C47—48no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—44no—
101C2×C4×C47C2×D412yes—
102C2×C4×C47C2×D412yes—
103C22⋊D47—28no—
104C22⋊D47—48no—
105C2×Dic47—21no—
106C2×Dic47—21no—
107C2×Dic47—21no—
108C2×Dic47—21no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47—22no—
115C2×Dic47—22no—
116C2×Dic47—22no—
117C2×Dic47#4112yes—
118C4×D47—44no—
119C22×C47—22no—
120C22×C47—22no—
121C22×C47—22no—
122C22×C47—42no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—42no—
129C22×C47—42no—
130C22×C47—42no—
131C22×C47C22×D411yescharacteristic
132C22×C47C2×#4111yescharacteristic
133C22×C47C2×#4111yescharacteristic
134C22×C47H(5,𝔽2)12yes—
135C22×C47H(5,𝔽2)12yes—
136C2×D47—22no—
137C2×D47—24no—
138C2×D47—41no—
139C2×D47—41no—
140C2×D47—42no—
141C4×C47—22no—
142C4×C47—22no—
143C4×C47—42no—
144Dic47—22no—
145Dic47—41no—
146Dic47—41no—
147Dic47—42no—
148Dic47—42no—
149#2635—471nomaximal, Sylow
150C2×C47—42no—
151C2×C47—82no—
152C2×C47#52511yescharacteristic
153C2×C47#53411yescharacteristic
154C2×C47#53511yescharacteristic
155C2×C47#53812yes—
156C2×C47#54012yes—
157D47—42no—
158C2×#121D4711yescharacteristic, complemented
159C2×C4×D4—471no—
160#400—471no—
161#399—471no—
162#394—471no—
163#394—472no—
164#392—471no—
165#392—472no—
166#388—472no—
167#386—472no—
168#381—471no—
169C47#263511yescharacteristic, complemented, Sylow
170C22×D4—471no—
171C22×D4—472no—
172C22×D4C2×D4712yes—
173C22×D4C2×D4711yescharacteristic
174C23×C4—471no—
175C23×C4C2×D4711yescharacteristic
176#121—24no—
177C4×D4—944no—
178C2×C4⋊C4—471no—
179C2×C4⋊C4—472no—
180C2×C4⋊C4C2×D4711yescharacteristic
181C2×C22⋊C4—471no—
182C2×C22⋊C4—472no—
183C2×C22⋊C4—471no—
184C2×C22⋊C4—472no—
185C2×C22⋊C4—472no—
186C2×C22⋊C4—472no—
187C2×C22⋊C4—472no—
188C2×C22⋊C4C2×D4712yes—
189C2×C42—471no—
190#95—472no—
191#95—471no—
192#95—471no—
193#95—472no—
194#95—472no—
195C24—471no—
196C24C22×D4712yes—
197C24C22×D4711yescharacteristic
198C2×D4—24no—
199C2×D4—22no—
200C2×D4—42no—
201C2×D4—42no—
202C2×D4—42no—
203C2×D4—942no—
204C2×D4—942no—
205C2×D4—942no—
206C2×D4—944no—
207C2×D4—1882no—
208C2×D4—1882no—
209C22×C4—42no—
210C22×C4—471no—
211C22×C4—472no—
212C22×C4—472no—
213C22×C4—471no—
214C22×C4—471no—
215C22×C4—942no—
216C22×C4—1882no—
217C22×C4C22⋊D4714yescomplemented
218C22×C4C22×D4712yes—
219C22×C4C22×D4711yescharacteristic
220C22×C4C22×D4711yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—942no—
223C4⋊C4—1882no—
224C22⋊C4—24no—
225C22⋊C4—944no—
226C22⋊C4—942no—
227C22⋊C4—942no—
228C22⋊C4—1882no—
229C22⋊C4—1882no—
230C22⋊C4—1882no—
231C22⋊C4—1882no—
232C42—942no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—472no—
245C23—941no—
246C23—941no—
247C23—942no—
248C23—942no—
249C23C2×C22⋊D4712yes—
250C23C23×D4711yescharacteristic
251D4—44no—
252D4—48no—
253D4—948no—
254D4—1888no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—44no—
261C2×C4—472no—
262C2×C4—941no—
263C2×C4—941no—
264C2×C4—941no—
265C2×C4—941no—
266C2×C4—942no—
267C2×C4—942no—
268C2×C4—942no—
269C2×C4—942no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—942no—
273C2×C4—942no—
274C2×C4—1884no—
275C2×C4C2×C22⋊D4712yes—
276C2×C4C2×C22⋊D4712yes—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—942no—
290C22—944no—
291C22—1881no—
292C22—1881no—
293C22—1882no—
294C22C22×C22⋊D4711yescharacteristic
295C22#41×D4711yescharacteristic
296C22#41×D4711yescharacteristic
297C22#1309406912yes—
298C22#1309406912yes—
299C4—22no—
300C4—22no—
301C4—42no—
302C4—942no—
303C4—1881no—
304C4—1881no—
305C4—1882no—
306C4—1882no—
307C2—42no—
308C2—82no—
309C2—1882no—
310C2#1568963011yescharacteristic
311C2#1568968211yescharacteristic
312C2#1568969011yescharacteristic
313C2#1568970512yes—
314C2#1568972312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#121×C47C2
hypercenterC2×#121D47
hypocenterC47#2635
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D47C2semidirect
2. #15689061C2semidirect
3. #15689058C2semidirect
4. #15689037C2semidirect
5. #15689037C2semidirect
6. #15689031C2semidirect
7. #15689031C2semidirect
8. #15689011C2semidirect
9. #15688999C2semidirect
10. #15688986C2semidirect
11. C2×#121×C47C2semidirect
46. C22×C4×C47D4semidirect
158. C2×#121D47semidirect
169. C47#2635semidirect
217. C22×C4C22⋊D47semidirect