Finite Group Databasebeta

← #13073771

Subgroups — #13073771

Order 1408.

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

normal subgroups only

This group has 672 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
1C22×C22⋊Dic11C211yesmaximal, characteristic
2C2×#66931C211yesmaximal, characteristic, complemented
3C11×#379C211yesmaximal, characteristic
4#10622860C211yesmaximal, characteristic
5#10622565C212yesmaximal, complemented
6#10622564C212yesmaximal, complemented
7#10622560C212yesmaximal, complemented
8#10622557C212yesmaximal, complemented
9#10622556C211yesmaximal, characteristic, complemented
10#10622556C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C25×C11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C22×Dic22C2211yescharacteristic, complemented
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11—24no—
21C2×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2212yes—
25C2×C22⋊Dic11C2212yes—
26C2×C22⋊Dic11C2212yes—
27C2×C4⋊Dic11C2211yescharacteristic, complemented
28C2×Dic11⋊C4C2211yescharacteristic, complemented
29C2×Dic11⋊C4C2211yescharacteristic, complemented
30C2×C4×Dic11C2212yescomplemented
31#66931—24no—
32C11⋊#95C2212yescomplemented
33C11⋊#95C2212yescomplemented
34C11⋊#95C2212yescomplemented
35C11⋊#95C2212yescomplemented
36C11⋊#95C2212yescomplemented
37C24×C11—22no—
38C24×C11—24no—
39C24×C11—22no—
40C24×C11—22no—
41C24×C11—42no—
42C24×C11C2312yes—
43C24×C11C2311yescharacteristic
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C22×Dic11—22no—
48C22×Dic11—22no—
49C22×Dic11—22no—
50C22×Dic11—42no—
51C22×Dic11D414yes—
52C22×Dic11C2312yes—
53C22×Dic11C2312yes—
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2311yescharacteristic
58C2×Dic22—22no—
59C2×Dic22—42no—
60C11×C22⋊C4—22no—
61C11×C22⋊C4—24no—
62C11×C22⋊C4—22no—
63C11×C22⋊C4—42no—
64C22⋊Dic11—24no—
65C22⋊Dic11—24no—
66C22⋊Dic11—22no—
67C22⋊Dic11—22no—
68C22⋊Dic11—24no—
69C22⋊Dic11—42no—
70C4⋊Dic11—22no—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73C4×Dic11—42no—
74#2561—111nomaximal, Sylow
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—28no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—48no—
85C23×C11—48no—
86C23×C11—44no—
87C23×C11—44no—
88C23×C11C2×D412yes—
89C23×C11#4112yes—
90C23×C11#4114yes—
91C23×C11#4112yes—
92C23×C11C2411yescharacteristic
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—21no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—44no—
113C2×Dic11—44no—
114C2×Dic11C2×D412yes—
115C2×Dic11C2×D412yes—
116Dic22—44no—
117C2×C22⋊Q8—111no—
118C22×C22⋊C4—111no—
119#397—112no—
120#393—112no—
121#388—112no—
122#388—112no—
123#381—111no—
124#381—111no—
125#379—111no—
126#379D1111yescharacteristic
127C4×C22⋊C4—111no—
128C22×C11—22no—
129C22×C11—22no—
130C22×C11—24no—
131C22×C11—24no—
132C22×C11—24no—
133C22×C11—24no—
134C22×C11—24no—
135C22×C11—416no—
136C22×C11—42no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11—42no—
140C22×C11#12414yes—
141C22×C11C22×D411yescharacteristic
142C22×C11C2×#4111yescharacteristic
143C22×C11C2×#4112yes—
144C22×C11C2×#4111yescharacteristic
145C22×C11H(5,𝔽2)12yes—
146C4×C11—41no—
147C4×C11—41no—
148C4×C11—42no—
149Dic11—22no—
150Dic11—22no—
151Dic11—41no—
152Dic11—42no—
153Dic11—41no—
154Dic11—42no—
155C25C2×D1111yescharacteristic
156C22×Q8—111no—
157C23×C4—111no—
158C23×C4—111no—
159C22⋊Q8—224no—
160C2×C4⋊C4—111no—
161C2×C4⋊C4—111no—
162C2×C4⋊C4—111no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—111no—
166C2×C22⋊C4—111no—
167C2×C22⋊C4—112no—
168C2×C22⋊C4—112no—
169C2×C22⋊C4—224no—
170C2×C22⋊C4C2×D1111yescharacteristic
171C2×C22⋊C4C2×D1111yescharacteristic
172C2×C22⋊C4C2×D1112yes—
173C2×C22⋊C4C2×D1112yes—
174C2×C42—112no—
175#95—112no—
176#95—112no—
177#95—112no—
178#95—112no—
179#95—112no—
180C2×C11—24no—
181C2×C11—44no—
182C2×C11#52511yescharacteristic
183C2×C11C2×#12411yescharacteristic
184C2×C11#53411yescharacteristic
185C2×C11#55112yes—
186C2×C11#55112yes—
187C24—22no—
188C24—24no—
189C24—22no—
190C24—22no—
191C24—42no—
192C24C22×D1112yes—
193C24C22×D1111yescharacteristic
194C2×Q8—222no—
195C2×Q8—442no—
196C22×C4—111no—
197C22×C4—111no—
198C22×C4—114no—
199C22×C4—112no—
200C22×C4—112no—
201C22×C4—111no—
202C22×C4—111no—
203C22×C4—222no—
204C22×C4—222no—
205C22×C4—222no—
206C22×C4—442no—
207C22×C4C22×D1112yes—
208C22×C4C22×D1111yescharacteristic
209C22×C4C22×D1111yescharacteristic
210C4⋊C4—222no—
211C4⋊C4—222no—
212C4⋊C4—222no—
213C22⋊C4—22no—
214C22⋊C4—24no—
215C22⋊C4—22no—
216C22⋊C4—42no—
217C22⋊C4—224no—
218C22⋊C4—224no—
219C22⋊C4—222no—
220C22⋊C4—222no—
221C22⋊C4—224no—
222C22⋊C4—442no—
223C42—442no—
224C11#256111yescharacteristic, complemented, Sylow
225C23—22no—
226C23—22no—
227C23—28no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—48no—
235C23—48no—
236C23—44no—
237C23—44no—
238C23#433912yes—
239C23D4×D1112yes—
240C23#434114yes—
241C23#434112yes—
242C23C23×D1111yescharacteristic
243Q8—444no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—112no—
252C2×C4—112no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—222no—
257C2×C4—222no—
258C2×C4—221no—
259C2×C4—221no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—222no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—444no—
266C2×C4—444no—
267C22—24no—
268C22—22no—
269C22—24no—
270C22—22no—
271C22—24no—
272C22—24no—
273C22—24no—
274C22—416no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22#6693814yes—
280C22C2×#433911yescharacteristic
281C22C2×D4×D1111yescharacteristic
282C22C2×#434111yescharacteristic
283C22C2×#434112yes—
284C22#6703712yes—
285C4—41no—
286C4—42no—
287C4—41no—
288C4—222no—
289C4—222no—
290C4—442no—
291C4—442no—
292C4—441no—
293C4—441no—
294C2—24no—
295C2—44no—
296C2C2×#6693811yescharacteristic
297C2#1062302612yes—
298C2#1062311711yescharacteristic
299C2#1062311812yes—
300C2#1062312011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#379C2
prime radicalC25×C11C22
hypercenter#379D11
hypocenterC11#2561
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#66931C2semidirect
5. #10622565C2semidirect
6. #10622564C2semidirect
7. #10622560C2semidirect
8. #10622557C2semidirect
9. #10622556C2semidirect
10. #10622556C2semidirect
11. C22⋊C4×Dic11C2semidirect
15. C22×Dic22C22semidirect
27. C2×C4⋊Dic11C22semidirect
28. C2×Dic11⋊C4C22semidirect
29. C2×Dic11⋊C4C22semidirect
30. C2×C4×Dic11C22semidirect
32. C11⋊#95C22semidirect
33. C11⋊#95C22semidirect
34. C11⋊#95C22semidirect
35. C11⋊#95C22semidirect
36. C11⋊#95C22semidirect
224. C11#2561semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C22⋊Dic112
C2×#669312
C11×#3792
#106228602
#106225652
#106225642
#106225602
#106225572
#106225562
C22⋊C4×Dic112
#256111