Finite Group Databasebeta

← #13072070

Subgroups — #13072070

Order 1408.

648 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66999C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4C2×C4×D44C211yesmaximal, characteristic
5C11×#391C211yesmaximal, characteristic, complemented
6#10622600C211yesmaximal, characteristic, complemented
7#10622541C211yesmaximal, characteristic, complemented
8#10622289C212yesmaximal, complemented
9#10622280C212yesmaximal, complemented
10#10622278C212yesmaximal
11#10622270C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2212yes—
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C42×C11C2211yescharacteristic
19#66999—24no—
20#66999—24no—
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×Dic11⋊C4C2212yes—
31C2×Dic11⋊C4C2212yes—
32C2×Dic11⋊C4C2212yes—
33C4⋊C4×D11—24no—
34C4×D44—24no—
35C11×#95C2212yes—
36C11×#95C2212yes—
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C23×D11C2311yescharacteristic
40C23×D11C2311yescharacteristic
41C2×Q8×C11—22no—
42C2×Q8×C11—22no—
43C2×Q8×C11—22no—
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2312yes—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C22×Dic11C2312yes—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C2×D44—22no—
54C2×D44—22no—
55C2×D44Q814yescomplemented
56C2×C4×D11—24no—
57C2×C4×D11—24no—
58C2×C4×D11—22no—
59C2×C4×D11—22no—
60C2×C4×D11—22no—
61C2×C4×D11—22no—
62C2×C4×D11—22no—
63C2×C4×D11—42no—
64C2×C4×D11D414yes—
65C11×C4⋊C4—22no—
66C42×C11—22no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—22no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—42no—
72C4⋊Dic11—22no—
73C4⋊Dic11—22no—
74C4⋊Dic11D414yescomplemented
75Dic11⋊C4—24no—
76Dic11⋊C4—24no—
77Dic11⋊C4—24no—
78Dic11⋊C4—42no—
79#2417—111nomaximal, Sylow
80C23×C11C2411yescharacteristic
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—21no—
86C22×D11—21no—
87C22×D11—21no—
88C22×D11—21no—
89C22×D11—21no—
90C22×D11—21no—
91C22×D11C2×D412yes—
92C22×D11C2×Q812yes—
93C22×D11C2×Q812yes—
94C22×D11#4112yes—
95Q8×C11—44no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11C2×D412yes—
108C2×C4×C11C2×D412yes—
109C2×C4×C11C2×Q812yes—
110C2×C4×C11#4112yes—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11—21no—
116C2×Dic11—22no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11C2×D412yes—
122C2×Dic11C2×D414yes—
123D44—28no—
124C4×D11—28no—
125C4×D11—48no—
126C4×D11—44no—
127C2×C22⋊Q8—111no—
128C2×C22⋊Q8—111no—
129C2×C4×D4—111no—
130C22×C4⋊C4—111no—
131#398—112no—
132#396—112no—
133#391D1111yescharacteristic, complemented
134#389—111no—
135#386—112no—
136#380—111no—
137#380—112no—
138C22×C11C22×D411yescharacteristic
139C22×C11C22×D411yescharacteristic
140C22×C11C22×Q811yescharacteristic
141C22×C11C2×#4111yescharacteristic
142C22×C11C2×#4111yescharacteristic
143C22×C11H(5,𝔽2)11yescharacteristic
144C22×C112−1+411yescharacteristic
145C2×D11—22no—
146C2×D11—22no—
147C2×D11—22no—
148C2×D11—22no—
149C2×D11—22no—
150C2×D11—22no—
151C2×D11—22no—
152C2×D11—22no—
153C2×D11—22no—
154C2×D11—41no—
155C2×D11—41no—
156C2×D11—41no—
157C2×D11—41no—
158C2×D11C22⋊Q814yescomplemented
159C4×C11—22no—
160C4×C11—42no—
161C4×C11—41no—
162C4×C11—42no—
163C4×C11#12114yes—
164Dic11—22no—
165Dic11—24no—
166Dic11—41no—
167Dic11—42no—
168C22×Q8C2×D1111yescharacteristic
169C22×D4—111no—
170C23×C4—111no—
171C23×C4—111no—
172C23×C4—112no—
173C22⋊Q8—224no—
174C22⋊Q8—224no—
175C4×D4—224no—
176C2×C4⋊C4—111no—
177C2×C4⋊C4—112no—
178C2×C4⋊C4—111no—
179C2×C4⋊C4—111no—
180C2×C4⋊C4—112no—
181C2×C4⋊C4—112no—
182C2×C4⋊C4—112no—
183C2×C4⋊C4—224no—
184C2×C4⋊C4C2×D1111yescharacteristic
185C2×C22⋊C4—111no—
186C2×C22⋊C4—111no—
187C2×C22⋊C4—112no—
188C2×C22⋊C4—112no—
189C2×C22⋊C4—112no—
190C2×C42C2×D1111yescharacteristic
191#95—112no—
192#95—112no—
193#95C2×D1112yes—
194#95C2×D1112yes—
195C2×C11C2×#12111yescharacteristic
196C2×C11C2×C22⋊Q811yescharacteristic
197C2×C11#53711yescharacteristic
198C2×C11#54611yescharacteristic
199C2×C11D4×Q811yescharacteristic
200C2×C11#55211yescharacteristic
201C2×C11#55411yescharacteristic
202D11—24no—
203D11—42no—
204C24—111no—
205C24—111no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—22no—
209C2×D4—114no—
210C2×D4—222no—
211C2×D4—222no—
212C22×C4—112no—
213C22×C4—111no—
214C22×C4—114no—
215C22×C4—112no—
216C22×C4—111no—
217C22×C4—224no—
218C22×C4—224no—
219C22×C4—222no—
220C22×C4—222no—
221C22×C4—222no—
222C22×C4—222no—
223C22×C4—222no—
224C22×C4—442no—
225C22×C4C22×D1112yes—
226C22×C4C22×D1111yescharacteristic
227C22×C4C22×D1112yes—
228C22×C4C22×D1111yescharacteristic
229C22×C4C22×D1111yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—114no—
232C4⋊C4—224no—
233C4⋊C4—222no—
234C4⋊C4—224no—
235C4⋊C4—224no—
236C4⋊C4—222no—
237C4⋊C4—442no—
238C22⋊C4—222no—
239C22⋊C4—224no—
240C22⋊C4—222no—
241C22⋊C4—224no—
242C22⋊C4—442no—
243C42—22no—
244C11#241711yescharacteristic, complemented, Sylow
245C23—112no—
246C23—112no—
247C23—112no—
248C23—112no—
249C23—221no—
250C23—221no—
251C23—221no—
252C23—221no—
253C23—221no—
254C23—221no—
255C23—221no—
256C23—221no—
257C23—221no—
258C23—221no—
259C23C23×D1111yescharacteristic
260Q8—44no—
261D4—228no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—114no—
274C2×C4—112no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—222no—
278C2×C4—222no—
279C2×C4—228no—
280C2×C4—221no—
281C2×C4—222no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—222no—
285C2×C4—222no—
286C2×C4—448no—
287C2×C4—444no—
288C2×C4#433912yes—
289C2×C4D4×D1112yes—
290C2×C4D4×D1112yes—
291C2×C4Q8×D1112yes—
292C22—114no—
293C22—222no—
294C22—222no—
295C22—222no—
296C22—222no—
297C22—222no—
298C22—222no—
299C22—222no—
300C22—222no—
301C22—222no—
302C22—441no—
303C22—441no—
304C22—441no—
305C22—441no—
306C22C2×#433911yescharacteristic
307C22C2×D4×D1111yescharacteristic
308C22C2×D4×D1111yescharacteristic
309C22C2×Q8×D1111yescharacteristic
310C22#6704011yescharacteristic
311C22#41×D1111yescharacteristic
312C22#6704211yescharacteristic
313C4—22no—
314C4—42no—
315C4—41no—
316C4—42no—
317C4—222no—
318C4—224no—
319C4—441no—
320C4—442no—
321C4#6693714yes—
322C2—224no—
323C2—442no—
324C2C2×#6693711yescharacteristic
325C2#1062311011yescharacteristic
326C2#1062311211yescharacteristic
327C2D11×C22⋊Q811yescharacteristic
328C2#1062316011yescharacteristic
329C2#1062320711yescharacteristic
330C2#1062325811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC22×D44C22
hypercenter#391D11
hypocenterC11#2417
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#66999C2semidirect
2. C2×#66999C2semidirect
3. C2×C4⋊C4×D11C2semidirect
5. C11×#391C2semidirect
6. #10622600C2semidirect
7. #10622541C2semidirect
8. #10622289C2semidirect
9. #10622280C2semidirect
11. #10622270C2semidirect
55. C2×D44Q8semidirect
74. C4⋊Dic11D4semidirect
133. #391D11semidirect
158. C2×D11C22⋊Q8semidirect
244. C11#2417semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×C4⋊C4×D112
C2×C4×D442
C11×#3912
#106226002
#106225412
#106222892
#106222802
#106222782
#106222702
#241711