Finite Group Databasebeta

← #13072111

Subgroups — #13072111

Order 1408.

596 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66948C211yesmaximal, characteristic
2C2×#66946C211yesmaximal, characteristic, complemented
3C11×#382C211yesmaximal, characteristic, complemented
4#10622600C211yesmaximal, characteristic, complemented
5#10622586C211yesmaximal, characteristic, complemented
6#10622552C211yesmaximal, characteristic, complemented
7C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
8#10622288C212yesmaximal, complemented
9#10622285C212yesmaximal, complemented
10#10622278C212yesmaximal, complemented
11#10622277C212yesmaximal, complemented
12C22×D44C2212yes—
13C22×D44C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2212yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C42×C11C2211yescharacteristic
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28C2×C4×Dic11C2211yescharacteristic
29#66948—24no—
30#66946—24no—
31C11×#95C2212yes—
32C11×#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C23×D11C2312yes—
38C23×D11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×D44—24no—
49C2×D44—24no—
50C2×D44—22no—
51C2×D44—22no—
52C2×D44—42no—
53C2×D44D414yes—
54C2×C4×D11—24no—
55C2×C4×D11—24no—
56C2×C4×D11—22no—
57C2×C4×D11—22no—
58C2×C4×D11—22no—
59C2×C4×D11—42no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—22no—
62C42×C11—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—42no—
68(C2×D11)⋊C4—42no—
69(C2×D11)⋊C4—42no—
70C4⋊Dic11—22no—
71Dic11⋊C4—42no—
72C4×Dic11—22no—
73#2420—111nomaximal, Sylow
74C23×C11C2411yescharacteristic
75C22×D11—21no—
76C22×D11—21no—
77C22×D11—21no—
78C22×D11—21no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—21no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—21no—
87C22×D11C2×D414yes—
88C22×D11#4112yes—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11C2×D412yes—
102C2×C4×C11#4112yes—
103C2×C4×C11#4112yes—
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—22no—
109C2×Dic11—21no—
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11#4112yes—
116D44—28no—
117D44—48no—
118C4×D11—48no—
119C4×D11—44no—
120C2×#121—111no—
121C2×C4×D4—111no—
122#397—112no—
123#394—112no—
124#390—111no—
125#389—111no—
126#386—112no—
127#382D1111yescharacteristic, complemented
128#381—112no—
129#380—111no—
130C4×C22⋊C4—111no—
131C22×C11C22×D411yescharacteristic
132C22×C11C2×#4111yescharacteristic
133C22×C11C2×#4111yescharacteristic
134C22×C11C2×#4111yescharacteristic
135C22×C11C2×#4111yescharacteristic
136C22×C11H(5,𝔽2)11yescharacteristic
137C22×C11H(5,𝔽2)11yescharacteristic
138C2×D11—24no—
139C2×D11—22no—
140C2×D11—24no—
141C2×D11—24no—
142C2×D11—22no—
143C2×D11—22no—
144C2×D11—41no—
145C2×D11—42no—
146C2×D11—41no—
147C2×D11—42no—
148C2×D11—41no—
149C2×D11—42no—
150C2×D11—41no—
151C2×D11—42no—
152C4×C11—42no—
153C4×C11—42no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11#12314yes—
157Dic11—22no—
158Dic11—41no—
159Dic11—42no—
160Dic11—41no—
161C22×D4—111no—
162C22×D4—112no—
163C23×C4—111no—
164C23×C4—112no—
165#121—224no—
166C4×D4—224no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—112no—
169C2×C4⋊C4C2×D1111yescharacteristic
170C2×C4⋊C4C2×D1111yescharacteristic
171C2×C22⋊C4—112no—
172C2×C22⋊C4—112no—
173C2×C22⋊C4—111no—
174C2×C22⋊C4—111no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4—112no—
178C2×C42—111no—
179C2×C42C2×D1111yescharacteristic
180#95—111no—
181#95—111no—
182#95—112no—
183#95—112no—
184#95C2×D1112yes—
185#95C2×D1112yes—
186C2×C11C2×#12311yescharacteristic
187C2×C11#52911yescharacteristic
188C2×C11#54011yescharacteristic
189C2×C11#54611yescharacteristic
190C2×C11#54611yescharacteristic
191C2×C11#55311yescharacteristic
192C2×C11#55511yescharacteristic
193D11—44no—
194D11—42no—
195C24—112no—
196C24—111no—
197C2×D4—114no—
198C2×D4—224no—
199C2×D4—224no—
200C2×D4—222no—
201C2×D4—222no—
202C2×D4—442no—
203C22×C4—111no—
204C22×C4—111no—
205C22×C4—112no—
206C22×C4—111no—
207C22×C4—224no—
208C22×C4—224no—
209C22×C4—222no—
210C22×C4—222no—
211C22×C4—222no—
212C22×C4—442no—
213C22×C4C22×D1111yescharacteristic
214C22×C4C22×D1111yescharacteristic
215C22×C4C22×D1112yes—
216C22×C4C22×D1112yes—
217C22×C4C22×D1111yescharacteristic
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—222no—
221C4⋊C4—442no—
222C22⋊C4—222no—
223C22⋊C4—224no—
224C22⋊C4—224no—
225C22⋊C4—222no—
226C22⋊C4—442no—
227C22⋊C4—442no—
228C22⋊C4—442no—
229C42—22no—
230C42—222no—
231C11#242011yescharacteristic, complemented, Sylow
232C23—114no—
233C23—112no—
234C23—221no—
235C23—222no—
236C23—221no—
237C23—221no—
238C23—222no—
239C23—221no—
240C23—222no—
241C23—222no—
242C23—221no—
243C23—222no—
244C23—222no—
245C23—221no—
246C23C23×D1111yescharacteristic
247D4—228no—
248D4—448no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—112no—
262C2×C4—221no—
263C2×C4—221no—
264C2×C4—221no—
265C2×C4—221no—
266C2×C4—221no—
267C2×C4—222no—
268C2×C4—221no—
269C2×C4—221no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—221no—
273C2×C4—448no—
274C2×C4—444no—
275C2×C4#433912yes—
276C2×C4D4×D1112yes—
277C2×C4#434312yes—
278C22—224no—
279C22—222no—
280C22—224no—
281C22—222no—
282C22—224no—
283C22—222no—
284C22—441no—
285C22—442no—
286C22—441no—
287C22—442no—
288C22—441no—
289C22—442no—
290C22—441no—
291C22—442no—
292C22C2×#433911yescharacteristic
293C22C2×D4×D1111yescharacteristic
294C22C2×#434311yescharacteristic
295C22#41×D1111yescharacteristic
296C22#41×D1111yescharacteristic
297C22#6704211yescharacteristic
298C22#6704211yescharacteristic
299C4—41no—
300C4—41no—
301C4—42no—
302C4—42no—
303C4—222no—
304C4—441no—
305C4—441no—
306C4—442no—
307C4#6694714yes—
308C2—444no—
309C2—442no—
310C2C2×#6694711yescharacteristic
311C2#1062306111yescharacteristic
312C2#1062306311yescharacteristic
313C2#1062320711yescharacteristic
314C2#1062320711yescharacteristic
315C2#1062322211yescharacteristic
316C2#1062322911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#382C2
prime radicalC2×#66948C2
hypercenter#382D11
hypocenterC11#2420
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#66946C2semidirect
3. C11×#382C2semidirect
4. #10622600C2semidirect
5. #10622586C2semidirect
6. #10622552C2semidirect
7. C4×(C2×D11)⋊C4C2semidirect
8. #10622288C2semidirect
9. #10622285C2semidirect
10. #10622278C2semidirect
11. #10622277C2semidirect
127. #382D11semidirect
231. C11#2420semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669462
C11×#3822
#106226002
#106225862
#106225522
C4×(C2×D11)⋊C42
#106222882
#106222852
#106222782
#106222772
#242011