Finite Group Databasebeta

← #13074842

Subgroups — #13074842

Order 1408.

796 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 796 conjugacy classes of subgroups — too many to draw. Only its 141 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×#67006C212yesmaximal, complemented
2C2×#66938C212yesmaximal, complemented
3C11×#379C211yesmaximal, characteristic, complemented
4#10622573C211yesmaximal, characteristic, complemented
5#10622573C212yesmaximal, complemented
6#10622572C212yesmaximal, complemented
7#10622570C212yesmaximal, complemented
8#10622560C211yesmaximal, characteristic, complemented
9#10622558C212yesmaximal, complemented
10C25×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×C22⋊D11C2212yes—
13C22×C22⋊D11C2212yes—
14C22×D44C2211yescharacteristic, complemented
15C22×Dic22C2211yescharacteristic, complemented
16C2×C11×C22⋊C4C2212yes—
17C2×C11×C22⋊C4C2212yes—
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20#67006—28no—
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2212yes—
24C2×(C2×D11)⋊C4C2212yescomplemented
25C2×(C2×D11)⋊C4C2212yescomplemented
26C2×(C2×D11)⋊C4C2212yescomplemented
27C2×Dic11⋊C4C2212yescomplemented
28C2×C4×Dic11C2212yescomplemented
29#66938—28no—
30C11⋊#95C2211yescharacteristic, complemented
31C11⋊#95C2212yescomplemented
32C11⋊#95C2211yescharacteristic, complemented
33C24×C11—24no—
34C24×C11—22no—
35C24×C11—41no—
36C24×C11—42no—
37C24×C11—41no—
38C24×C11C2312yes—
39C24×C11C2311yescharacteristic
40C23×D11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C2×C22⋊D11—24no—
45C2×C22⋊D11—24no—
46C2×C22⋊D11—24no—
47C2×C22⋊D11—24no—
48C2×C22⋊D11—24no—
49C2×C22⋊D11—42no—
50C2×C22⋊D11—42no—
51C2×C22⋊D11—42no—
52C2×C22⋊D11—42no—
53C22×Dic11C2312yes—
54C22×Dic11C2312yes—
55C22×Dic11C2312yes—
56C2×D44—42no—
57C2×D44—41no—
58C2×Dic22—24no—
59C2×Dic22—41no—
60C11×C22⋊C4—24no—
61C11×C22⋊C4—42no—
62C11×C22⋊C4—41no—
63C11×C22⋊C4—41no—
64C22⋊Dic11—24no—
65C22⋊Dic11—24no—
66C22⋊Dic11D418yescomplemented
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—42no—
70Dic11⋊C4—42no—
71C4×Dic11—24no—
72#2670—111nomaximal, Sylow
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—44no—
84C23×C11—48no—
85C23×C11—48no—
86C23×C11—44no—
87C23×C11—44no—
88C23×C11C2×D414yes—
89C23×C11#4112yes—
90C23×C11C2411yescharacteristic
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—22no—
94C22×D11—22no—
95C22×D11—22no—
96C22×D11—22no—
97C22×D11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C22⋊D11—48no—
106C22⋊D11—48no—
107C22⋊D11—48no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11C2×D414yes—
116C2×Dic11C2×D414yes—
117D44—44no—
118Dic22—44no—
119C2×#124—112no—
120C2×#120—112no—
121#394—112no—
122#393—111no—
123#392—111no—
124#392—112no—
125#390—112no—
126#388—112no—
127#379D1111yescharacteristic, complemented
128C22×C11—24no—
129C22×C11—22no—
130C22×C11—24no—
131C22×C11—24no—
132C22×C11—24no—
133C22×C11—416no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11—41no—
138C22×C11—42no—
139C22×C11—42no—
140C22×C11—41no—
141C22×C11C22×D412yes—
142C22×C11C2×#4111yescharacteristic
143C22×C11H(5,𝔽2)11yescharacteristic
144C22×C11H(5,𝔽2)12yes—
145C22×C11H(5,𝔽2)11yescharacteristic
146C2×D11—42no—
147C2×D11—42no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—42no—
153C4×C11—42no—
154C4×C11—41no—
155C4×C11—41no—
156Dic11—24no—
157Dic11—24no—
158Dic11—42no—
159C25C2×D1111yescharacteristic
160C22×Q8—111no—
161C22×D4—112no—
162C22×D4—112no—
163C22×D4—112no—
164C22×D4—111no—
165#124—228no—
166#120—228no—
167C2×C4⋊C4—112no—
168C2×C22⋊C4—112no—
169C2×C22⋊C4—112no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—112no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4C2×D1112yes—
175C2×C22⋊C4C2×D1112yes—
176C2×C22⋊C4C2×D1111yescharacteristic
177C2×C22⋊C4C2×D1111yescharacteristic
178C2×C42—112no—
179#95—111no—
180#95—112no—
181#95—111no—
182C2×C11—44no—
183C2×C11—42no—
184C2×C11#53512yes—
185C2×C11#53811yescharacteristic
186C2×C11D4211yescharacteristic
187C2×C11#54612yes—
188C2×C11H(3,𝔽4)11yescharacteristic
189D11—82no—
190C24—22no—
191C24—24no—
192C24—42no—
193C24—41no—
194C24—41no—
195C24—112no—
196C24C22×D1111yescharacteristic
197C24C22×D1112yes—
198C2×Q8—224no—
199C2×Q8—441no—
200C2×D4—224no—
201C2×D4—224no—
202C2×D4—224no—
203C2×D4—224no—
204C2×D4—224no—
205C2×D4—442no—
206C2×D4—441no—
207C2×D4—442no—
208C2×D4—442no—
209C2×D4—442no—
210C2×D4—442no—
211C22×C4—112no—
212C22×C4—112no—
213C22×C4—112no—
214C22×C4C22×D1111yescharacteristic
215C22×C4C22×D1111yescharacteristic
216C22×C4C22×D1112yes—
217C4⋊C4—442no—
218C22⋊C4—24no—
219C22⋊C4—41no—
220C22⋊C4—42no—
221C22⋊C4—41no—
222C22⋊C4—118no—
223C22⋊C4—224no—
224C22⋊C4—224no—
225C22⋊C4—224no—
226C22⋊C4—224no—
227C22⋊C4—442no—
228C42—224no—
229C11#267011yescharacteristic, complemented, Sylow
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—21no—
235C23—21no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—48no—
241C23—44no—
242C23—44no—
243C23—48no—
244C23—44no—
245C23—222no—
246C23—222no—
247C23—222no—
248C23—222no—
249C23—222no—
250C23—222no—
251C23—222no—
252C23#433912yes—
253C23D4×D1114yes—
254C23C23×D1111yescharacteristic
255Q8—444no—
256D4—444no—
257D4—448no—
258D4—448no—
259D4—448no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—114no—
268C2×C4—114no—
269C2×C4—222no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—222no—
276C22—24no—
277C22—24no—
278C22—22no—
279C22—24no—
280C22—24no—
281C22—416no—
282C22—42no—
283C22—42no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—42no—
289C22—442no—
290C22—442no—
291C22—442no—
292C22—442no—
293C22—442no—
294C22—442no—
295C22—442no—
296C22C2×#433911yescharacteristic
297C22C2×D4×D1112yes—
298C22#6703712yes—
299C22#6703711yescharacteristic
300C22#6703711yescharacteristic
301C4—41no—
302C4—42no—
303C4—41no—
304C4—224no—
305C4—224no—
306C4—442no—
307C2—42no—
308C2—44no—
309C2—882no—
310C2#1062302112yes—
311C2#1062302511yescharacteristic
312C2#1062312111yescharacteristic
313C2#1062312312yes—
314C2#1062312511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#379C2
hypercenter#379D11
hypocenterC11#2670
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#67006C2semidirect
2. C2×#66938C2semidirect
3. C11×#379C2semidirect
4. #10622573C2semidirect
5. #10622573C2semidirect
6. #10622572C2semidirect
7. #10622570C2semidirect
8. #10622560C2semidirect
9. #10622558C2semidirect
14. C22×D44C22semidirect
15. C22×Dic22C22semidirect
24. C2×(C2×D11)⋊C4C22semidirect
25. C2×(C2×D11)⋊C4C22semidirect
26. C2×(C2×D11)⋊C4C22semidirect
27. C2×Dic11⋊C4C22semidirect
28. C2×C4×Dic11C22semidirect
30. C11⋊#95C22semidirect
31. C11⋊#95C22semidirect
32. C11⋊#95C22semidirect
66. C22⋊Dic11D4semidirect
127. #379D11semidirect
229. C11#2670semidirect

Maximal subgroups

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

subgroupindex
C2×#670062
C2×#669382
C11×#3792
#106225732
#106225722
#106225702
#106225602
#106225582
#267011