Finite Group Databasebeta

← #13072196

Subgroups — #13072196

Order 1408.

660 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#124C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3C2×#66991C211yesmaximal, characteristic
4C2×D4×Dic11C211yesmaximal, characteristic, complemented
5#10622843C211yesmaximal, characteristic, complemented
6#10622572C212yesmaximal, complemented
7#10622571C212yesmaximal, complemented
8#10622565C212yesmaximal, complemented
9#10622555C212yesmaximal, complemented
10C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11#10622541C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C22×C22⋊D11C2212yes—
15C23×Dic11C2212yes—
16C22×C4×D11C2211yescharacteristic
17C11×#124—24no—
18C2×C11×C22⋊C4C2212yes—
19C2×C11×C22⋊C4C2212yes—
20C2×C42×C11C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23#66999—24no—
24#66991—24no—
25D4×Dic11—24no—
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2212yes—
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×Dic11⋊C4C2212yes—
32C2×Dic11⋊C4C2212yes—
33C2×C4×Dic11C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2211yescharacteristic
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C24×C11C2312yes—
40C23×D11C2311yescharacteristic
41C2×Q8×C11—22no—
42C2×Q8×C11—22no—
43C2×Q8×C11—22no—
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C2×D4×C11D414yes—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2312yes—
49C22×C4×C11C2311yescharacteristic
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—24no—
52C2×C22⋊D11—24no—
53C2×C22⋊D11—42no—
54C22×Dic11—24no—
55C22×Dic11—24no—
56C22×Dic11—42no—
57C22×Dic11C2311yescharacteristic
58C22×Dic11C2312yes—
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2312yes—
61C22×Dic11C2311yescharacteristic
62C2×C4×D11—22no—
63C2×C4×D11—22no—
64C2×C4×D11—22no—
65C11×C22⋊C4—24no—
66C11×C22⋊C4—24no—
67C42×C11—22no—
68C22⋊Dic11—24no—
69C22⋊Dic11—24no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—22no—
73C4⋊Dic11—22no—
74C4⋊Dic11D414yescomplemented
75Dic11⋊C4—24no—
76Dic11⋊C4—42no—
77C4×Dic11—22no—
78#2427—111nomaximal, Sylow
79C23×C11—22no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11C2×D414yes—
86C23×C11C2411yescharacteristic
87C22×D11—21no—
88C22×D11—21no—
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—21no—
92C22×D11—21no—
93C22×D11#4112yes—
94Q8×C11—44no—
95D4×C11—28no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11C2×D412yes—
106C2×C4×C11C2×D412yes—
107C2×C4×C11#4112yes—
108C22⋊D11—48no—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—22no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11—21no—
122C2×Dic11—48no—
123C2×Dic11C2×D414yes—
124C2×Dic11#4112yes—
125C4×D11—44no—
126C2×#124D1111yescharacteristic, complemented
127C2×C22⋊Q8—111no—
128C2×#121—111no—
129C2×C4×D4—111no—
130#397—112no—
131#394—112no—
132#391—111no—
133#389—111no—
134#386—112no—
135#380—112no—
136C4×C22⋊C4—111no—
137C22×C11—24no—
138C22×C11—24no—
139C22×C11—24no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11C22×D411yescharacteristic
145C22×C11C22×D411yescharacteristic
146C22×C11C2×#4111yescharacteristic
147C22×C11C2×#4111yescharacteristic
148C22×C11C2×#4111yescharacteristic
149C22×C11H(5,𝔽2)11yescharacteristic
150C22×C112−1+411yescharacteristic
151C2×D11—22no—
152C2×D11—22no—
153C2×D11—22no—
154C2×D11—41no—
155C2×D11—41no—
156C2×D11—41no—
157C2×D11—41no—
158C4×C11—42no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11#12114yes—
162Dic11—22no—
163Dic11—24no—
164Dic11—41no—
165Dic11—42no—
166Dic11—41no—
167C22×Q8C2×D1111yescharacteristic
168C22×D4—112no—
169C22×D4C2×D1111yescharacteristic
170C23×C4—112no—
171C23×C4—111no—
172#124—24no—
173C22⋊Q8—224no—
174#121—224no—
175C4×D4—224no—
176C2×C4⋊C4—111no—
177C2×C4⋊C4—111no—
178C2×C4⋊C4—112no—
179C2×C4⋊C4—112no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—111no—
184C2×C22⋊C4—111no—
185C2×C22⋊C4C2×D1112yes—
186C2×C22⋊C4C2×D1112yes—
187C2×C42—111no—
188C2×C42C2×D1111yescharacteristic
189#95—111no—
190#95—111no—
191#95—112no—
192#95—112no—
193#95—112no—
194C2×C11—44no—
195C2×C11C2×#12111yescharacteristic
196C2×C11#52911yescharacteristic
197C2×C11#54211yescharacteristic
198C2×C11#54611yescharacteristic
199C2×C11#54611yescharacteristic
200C2×C11#54711yescharacteristic
201C2×C11#54811yescharacteristic
202D11—42no—
203C24—111no—
204C24C22×D1112yes—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—224no—
211C2×D4—224no—
212C2×D4—442no—
213C2×D4C22⋊D1114yes—
214C22×C4—111no—
215C22×C4—112no—
216C22×C4—111no—
217C22×C4—112no—
218C22×C4—111no—
219C22×C4—224no—
220C22×C4—224no—
221C22×C4—222no—
222C22×C4—222no—
223C22×C4—222no—
224C22×C4—442no—
225C22×C4C22×D1111yescharacteristic
226C22×C4C22×D1112yes—
227C22×C4C22×D1111yescharacteristic
228C22×C4C22×D1111yescharacteristic
229C4⋊C4—114no—
230C4⋊C4—224no—
231C4⋊C4—222no—
232C4⋊C4—442no—
233C22⋊C4—24no—
234C22⋊C4—24no—
235C22⋊C4—224no—
236C22⋊C4—222no—
237C22⋊C4—222no—
238C22⋊C4—224no—
239C22⋊C4—224no—
240C42—22no—
241C42—222no—
242C11#242711yescharacteristic, complemented, Sylow
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—112no—
250C23—221no—
251C23—221no—
252C23—221no—
253C23—221no—
254C23—221no—
255C23—221no—
256C23C2×C22⋊D1114yes—
257C23C23×D1111yescharacteristic
258Q8—44no—
259D4—28no—
260D4—448no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—114no—
271C2×C4—112no—
272C2×C4—221no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—222no—
281C2×C4—222no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—222no—
285C2×C4—448no—
286C2×C4—444no—
287C2×C4D4×D1112yes—
288C2×C4#434112yes—
289C2×C4C2×C22⋊D1112yes—
290C22—24no—
291C22—24no—
292C22—24no—
293C22—42no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—222no—
298C22—222no—
299C22—222no—
300C22—441no—
301C22—441no—
302C22—441no—
303C22—441no—
304C22C2×D4×D1111yescharacteristic
305C22C2×#434111yescharacteristic
306C22#41×D1111yescharacteristic
307C22#41×D1111yescharacteristic
308C22#6704211yescharacteristic
309C22#6704311yescharacteristic
310C22C22×C22⋊D1111yescharacteristic
311C4—42no—
312C4—41no—
313C4—41no—
314C4—222no—
315C4—224no—
316C4—441no—
317C4—442no—
318C4—441no—
319C4#6699214yes—
320C2—44no—
321C2—442no—
322C2#1062320711yescharacteristic
323C2#1062320811yescharacteristic
324C2#1062321111yescharacteristic
325C2#1062321311yescharacteristic
326C2C2×#6699211yescharacteristic
327C2#1062335511yescharacteristic
328C2#1062336011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
prime radicalC2×#66991C2
hypercenterC2×#124D11
hypocenterC11#2427
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C11×#124C2semidirect
2. C2×#66999C2semidirect
4. C2×D4×Dic11C2semidirect
5. #10622843C2semidirect
6. #10622572C2semidirect
7. #10622571C2semidirect
8. #10622565C2semidirect
9. #10622555C2semidirect
10. C4×(C2×D11)⋊C4C2semidirect
11. #10622541C2semidirect
74. C4⋊Dic11D4semidirect
126. C2×#124D11semidirect
242. C11#2427semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#669992
C2×#669912
C2×D4×Dic112
#106228432
#106225722
#106225712
#106225652
#106225552
C4×(C2×D11)⋊C42
#106225412
#242711