Finite Group Databasebeta

← #13072220

Subgroups — #13072220

Order 1408.

914 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
1C22×C11×#41C211yesmaximal, characteristic, complemented
2C2×#66992C212yesmaximal, complemented
3C2×#66982C211yesmaximal, characteristic, complemented
4#10622844C211yesmaximal, characteristic, complemented
5#10622842C211yesmaximal, characteristic, complemented
6#10622836C211yesmaximal, characteristic, complemented
7#10622835C211yesmaximal, characteristic, complemented
8#10622833C212yesmaximal, complemented
9#10622826C212yesmaximal, complemented
10#10622823C212yesmaximal, complemented
11C2×C11⋊#95C211yesmaximal, characteristic, complemented
12C2×C11×#41—28no—
13C2×C11×#41—24no—
14C22×Q8×C11C2211yescharacteristic
15C22×D4×C11C2211yescharacteristic
16C22×D4×C11C2212yes—
17C23×C4×C11C2212yes—
18C23×C4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2212yes—
21C23×Dic11C2212yes—
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2212yes—
25C2×C22⋊Dic11C2212yes—
26#66992—28no—
27#66982—24no—
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2212yes—
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2211yescharacteristic
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C24×C11C2312yes—
40C24×C11C2311yescharacteristic
41C23×D11C2311yescharacteristic
42C11×#41—232no—
43C2×Q8×C11—24no—
44C2×Q8×C11—22no—
45C2×D4×C11—24no—
46C2×D4×C11—24no—
47C2×D4×C11—24no—
48C2×D4×C11—22no—
49C2×D4×C11D418yescomplemented
50C22×C4×C11—24no—
51C22×C4×C11—24no—
52C22×C4×C11—24no—
53C22×C4×C11—24no—
54C22×C4×C11D414yescomplemented
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2312yes—
57C22×C4×C11C2311yescharacteristic
58C2×C22⋊D11—24no—
59C2×C22⋊D11—22no—
60C2×C22⋊D11—24no—
61C2×C22⋊D11—24no—
62C2×C22⋊D11—42no—
63C22×Dic11—24no—
64C22×Dic11—24no—
65C22×Dic11—42no—
66C22×Dic11C2312yes—
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2312yes—
71C22⋊Dic11—24no—
72C22⋊Dic11—22no—
73C22⋊Dic11—24no—
74C22⋊Dic11—42no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—22no—
77(C2×D11)⋊C4—24no—
78Dic11⋊C4—22no—
79Dic11⋊C4—22no—
80Dic11⋊C4—24no—
81#2430—111nomaximal, Sylow
82C23×C11—22no—
83C23×C11—21no—
84C23×C11—21no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—22no—
91C23×C11C2×D414yes—
92C23×C11C2×D412yes—
93C23×C11C2×D414yes—
94C23×C11C2411yescharacteristic
95C22×D11—21no—
96C22×D11—22no—
97C22×D11—22no—
98C22×D11—21no—
99C22×D11—21no—
100Q8×C11—28no—
101D4×C11—28no—
102D4×C11—216no—
103C2×C4×C11—216no—
104C2×C4×C11—28no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11C2×D412yes—
110C2×C4×C11C2×D414yes—
111C2×C4×C11C2×D412yes—
112C22⋊D11—48no—
113C22⋊D11—44no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11—22no—
122C2×Dic11—22no—
123C2×Dic11—21no—
124C2×Dic11—22no—
125C2×Dic11—21no—
126C2×Dic11—48no—
127C2×Dic11#4114yescomplemented
128C22×#41D1111yescharacteristic, complemented
129C2×#123—111no—
130C2×#121—112no—
131#395—111no—
132#394—111no—
133#393—111no—
134#392—111no—
135#386—112no—
136#386—112no—
137#385—112no—
138C2×#95—111no—
139C22×C11—22no—
140C22×C11—22no—
141C22×C11—24no—
142C22×C11—24no—
143C22×C11—24no—
144C22×C11—24no—
145C22×C11—24no—
146C22×C11—42no—
147C22×C11—42no—
148C22×C11—42no—
149C22×C11—42no—
150C22×C11#12014yes—
151C22×C11C22×D411yescharacteristic
152C22×C11C22×D412yes—
153C22×C11C2×#4112yes—
154C22×C11H(5,𝔽2)11yescharacteristic
155C22×C112−1+411yescharacteristic
156C2×D11—41no—
157C2×D11—41no—
158C2×D11—41no—
159C2×D11—42no—
160C2×D11—42no—
161C4×C11—22no—
162C4×C11—24no—
163C4×C11—22no—
164Dic11—24no—
165Dic11—41no—
166Dic11—41no—
167Dic11—41no—
168Dic11—42no—
169C2×#41—28no—
170C2×#41—24no—
171C22×Q8C2×D1111yescharacteristic
172C22×D4—111no—
173C22×D4—112no—
174C22×D4C2×D1111yescharacteristic
175C22×D4C2×D1112yes—
176C23×C4—112no—
177C23×C4C2×D1112yes—
178C23×C4C2×D1111yescharacteristic
179#123—224no—
180#121—228no—
181C2×C4⋊C4—112no—
182C2×C4⋊C4—111no—
183C2×C4⋊C4—111no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4—111no—
186C2×C22⋊C4—112no—
187C2×C22⋊C4—112no—
188C2×C22⋊C4—111no—
189C2×C22⋊C4—111no—
190C2×C22⋊C4—112no—
191#95—112no—
192#95—111no—
193#95—111no—
194#95—112no—
195#95—112no—
196C2×C11—24no—
197C2×C11—44no—
198C2×C11C2×#12011yescharacteristic
199C2×C11#53211yescharacteristic
200C2×C11#53711yescharacteristic
201C2×C11#54612yes—
202C2×C11#54712yes—
203D11—81no—
204C24—111no—
205C24C22×D1112yes—
206C24C22×D1111yescharacteristic
207#41—232no—
208C2×Q8—24no—
209C2×Q8—22no—
210C2×D4—24no—
211C2×D4—24no—
212C2×D4—24no—
213C2×D4—22no—
214C2×D4—224no—
215C2×D4—224no—
216C2×D4—224no—
217C2×D4—222no—
218C2×D4—442no—
219C2×D4C22⋊D1118yescomplemented
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—112no—
225C22×C4—112no—
226C22×C4—111no—
227C22×C4—111no—
228C22×C4—111no—
229C22×C4—224no—
230C22×C4—224no—
231C22×C4—442no—
232C22×C4C22⋊D1114yescomplemented
233C22×C4C22×D1111yescharacteristic
234C22×C4C22×D1112yes—
235C22×C4C22×D1111yescharacteristic
236C4⋊C4—224no—
237C4⋊C4—222no—
238C4⋊C4—222no—
239C22⋊C4—224no—
240C22⋊C4—224no—
241C22⋊C4—222no—
242C22⋊C4—224no—
243C22⋊C4—222no—
244C22⋊C4—222no—
245C22⋊C4—442no—
246C11#243011yescharacteristic, complemented, Sylow
247C23—22no—
248C23—21no—
249C23—21no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—222no—
257C23—221no—
258C23—221no—
259C23—221no—
260C23—222no—
261C23C2×C22⋊D1114yes—
262C23C2×C22⋊D1112yes—
263C23C2×C22⋊D1114yes—
264C23C23×D1111yescharacteristic
265Q8—28no—
266D4—28no—
267D4—216no—
268D4—448no—
269D4—444no—
270C2×C4—216no—
271C2×C4—28no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—114no—
277C2×C4—222no—
278C2×C4—222no—
279C2×C4—222no—
280C2×C4—222no—
281C2×C4—221no—
282C2×C4—222no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—222no—
287C2×C4—222no—
288C2×C4—221no—
289C2×C4—448no—
290C2×C4C2×C22⋊D1112yes—
291C2×C4C2×C22⋊D1114yes—
292C2×C4C2×C22⋊D1112yes—
293C22—24no—
294C22—24no—
295C22—22no—
296C22—22no—
297C22—24no—
298C22—24no—
299C22—24no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—442no—
305C22—442no—
306C22—441no—
307C22—441no—
308C22—441no—
309C22#6700614yes—
310C22#41×D1112yes—
311C22#6704211yescharacteristic
312C22#6704311yescharacteristic
313C22C22×C22⋊D1112yes—
314C22C22×C22⋊D1111yescharacteristic
315C4—22no—
316C4—24no—
317C4—22no—
318C4—224no—
319C4—442no—
320C4—441no—
321C4—441no—
322C4—441no—
323C2—24no—
324C2—44no—
325C2—881no—
326C2#1062335512yes—
327C2#1062336012yes—
328C2#1062336311yescharacteristic
329C2#1062336411yescharacteristic
330C2C2×#6700611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC22×C11×#41C2
hypercenterC22×#41D11
hypocenterC11#2430
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C11×#41C2semidirect
2. C2×#66992C2semidirect
3. C2×#66982C2semidirect
4. #10622844C2semidirect
5. #10622842C2semidirect
6. #10622836C2semidirect
7. #10622835C2semidirect
8. #10622833C2semidirect
9. #10622826C2semidirect
10. #10622823C2semidirect
11. C2×C11⋊#95C2semidirect
49. C2×D4×C11D4semidirect
54. C22×C4×C11D4semidirect
127. C2×Dic11#41semidirect
128. C22×#41D11semidirect
219. C2×D4C22⋊D11semidirect
232. C22×C4C22⋊D11semidirect
246. C11#2430semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#412
C2×#669922
C2×#669822
#106228442
#106228422
#106228362
#106228352
#106228332
#106228262
#106228232
C2×C11⋊#952
#243011