Finite Group Databasebeta

← #13071632

Subgroups — #13071632

Order 1408.

788 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×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#66983C211yesmaximal, characteristic
3C2×C4×C22⋊D11C212yesmaximal, complemented
4C2×#66946C211yesmaximal, characteristic, complemented
5#10622826C212yesmaximal, complemented
6C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
7#10622603C212yesmaximal, complemented
8#10622602C212yesmaximal, complemented
9#10622601C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
11#10622586C211yesmaximal, characteristic, complemented
12C23×C4×C11C2212yes—
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2212yes—
15C22×D44C2211yescharacteristic
16C22×C4×D11C2212yes—
17C2×C11×C4⋊C4—24no—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2212yes—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23#66983C418yescomplemented
24C4×C22⋊D11—28no—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×C4⋊Dic11C2211yescharacteristic
30C2×Dic11⋊C4C2212yes—
31C2×C4×Dic11C2211yescharacteristic
32C2×C4×Dic11C2212yes—
33C2×C4×Dic11C2211yescharacteristic
34#66946—24no—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2211yescharacteristic
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C24×C11C2311yescharacteristic
40C23×D11C2312yes—
41C22×C4×C11—22no—
42C22×C4×C11—22no—
43C22×C4×C11—24no—
44C22×C4×C11—24no—
45C22×C4×C11—42no—
46C22×C4×C11C2×C414yescomplemented
47C22×C4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2312yes—
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—24no—
52C2×C22⋊D11—24no—
53C2×C22⋊D11C2×C418yescomplemented
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2312yes—
57C22×Dic11C2311yescharacteristic
58C22×Dic11C2311yescharacteristic
59C2×D44—22no—
60C2×D44—22no—
61C2×D44C2×C414yescomplemented
62C2×C4×D11—24no—
63C2×C4×D11—24no—
64C2×C4×D11—42no—
65C11×C4⋊C4—24no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4D414yescomplemented
68C22⋊Dic11—22no—
69C22⋊Dic11D414yescomplemented
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—24no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4C2×C418yescomplemented
74C4⋊Dic11C2×C414yescomplemented
75Dic11⋊C4—24no—
76C4×Dic11—24no—
77C4×Dic11—22no—
78C4×Dic11—22no—
79#2361—111nomaximal, Sylow
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11C22×C412yes—
85C23×C11C2×D412yes—
86C23×C11#4112yes—
87C23×C11C2411yescharacteristic
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—22no—
94C22×D11C22×C414yes—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—28no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—48no—
104C2×C4×C11C22×C412yes—
105C2×C4×C11C22×C412yes—
106C2×C4×C11C2×D414yes—
107C2×C4×C11C2×D412yes—
108C2×C4×C11#4112yes—
109C22⋊D11—216no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11C22×C414yes—
123C2×Dic11C2×D412yes—
124C2×Dic11C2×D412yes—
125D44—28no—
126C4×D11—48no—
127C2×#121—111no—
128C2×C4×D4—112no—
129C2×C4×D4—111no—
130C22×C4⋊C4D1111yescharacteristic, complemented
131#390—111no—
132#389—111no—
133#388—112no—
134#386—112no—
135#385—112no—
136C4×C4⋊C4—111no—
137C4×C22⋊C4—111no—
138C22×C11—22no—
139C22×C11—22no—
140C22×C11—22no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11C4×D414yescomplemented
145C22×C11C23×C411yescharacteristic
146C22×C11C22×D411yescharacteristic
147C22×C11C22×D411yescharacteristic
148C22×C11C2×#4111yescharacteristic
149C22×C11C2×#4111yescharacteristic
150C22×C11H(5,𝔽2)11yescharacteristic
151C22×C112−1+411yescharacteristic
152C2×D11—24no—
153C2×D11—24no—
154C2×D11—24no—
155C2×D11—42no—
156C2×D11—42no—
157C2×D11—42no—
158C2×D11—42no—
159C4×C11—22no—
160C4×C11—24no—
161C4×C11—42no—
162C4×C11C4×D414yescomplemented
163Dic11—24no—
164Dic11—22no—
165Dic11—22no—
166Dic11—41no—
167Dic11—41no—
168C22×D4—112no—
169C22×D4—111no—
170C23×C4—112no—
171C23×C4C2×D1112yes—
172C23×C4C2×D1111yescharacteristic
173#121—118no—
174C4×D4—228no—
175C4×D4—224no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—111no—
178C2×C4⋊C4—112no—
179C2×C4⋊C4C2×D1112yes—
180C2×C4⋊C4C2×D1111yescharacteristic
181C2×C4⋊C4C2×D1111yescharacteristic
182C2×C22⋊C4—111no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4—111no—
185C2×C22⋊C4—112no—
186C2×C22⋊C4—112no—
187C2×C22⋊C4—112no—
188C2×C42—111no—
189C2×C42—112no—
190C2×C42—111no—
191#95—111no—
192#95—111no—
193#95—112no—
194#95—112no—
195C2×C11—24no—
196C2×C11C2×C4×D411yescharacteristic
197C2×C11C2×C4×D411yescharacteristic
198C2×C11#52011yescharacteristic
199C2×C11D4211yescharacteristic
200C2×C11#54711yescharacteristic
201C2×C11#54811yescharacteristic
202C2×C11#55311yescharacteristic
203D11—44no—
204C24—112no—
205C24C22×D1111yescharacteristic
206C2×D4—118no—
207C2×D4—114no—
208C2×D4—224no—
209C2×D4—224no—
210C2×D4—222no—
211C2×D4—222no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—42no—
217C22×C4—112no—
218C22×C4—111no—
219C22×C4—111no—
220C22×C4—111no—
221C22×C4—111no—
222C22×C4—224no—
223C22×C4—224no—
224C22×C4—442no—
225C22×C4C4×D1114yescomplemented
226C22×C4C22×D1112yes—
227C22×C4C22×D1111yescharacteristic
228C22×C4C22×D1112yes—
229C22×C4C22×D1111yescharacteristic
230C4⋊C4—24no—
231C4⋊C4—22no—
232C4⋊C4—114no—
233C4⋊C4—224no—
234C4⋊C4C22⋊D1114yescomplemented
235C22⋊C4—114no—
236C22⋊C4—118no—
237C22⋊C4—224no—
238C22⋊C4—222no—
239C22⋊C4—224no—
240C22⋊C4—442no—
241C42—224no—
242C42—222no—
243C42—222no—
244C11#236111yescharacteristic, complemented, Sylow
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—114no—
250C23—222no—
251C23—222no—
252C23—222no—
253C23—222no—
254C23—222no—
255C23—222no—
256C23C2×C4×D1112yes—
257C23D4×D1112yes—
258C23#434312yes—
259C23C23×D1111yescharacteristic
260D4—2216no—
261D4—228no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—28no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—48no—
271C2×C4—114no—
272C2×C4—112no—
273C2×C4—112no—
274C2×C4—221no—
275C2×C4—222no—
276C2×C4—221no—
277C2×C4—222no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—448no—
287C2×C4C2×C4×D1112yes—
288C2×C4C2×C4×D1112yes—
289C2×C4#433912yes—
290C2×C4C2×C22⋊D1114yes—
291C2×C4C2×C22⋊D1112yes—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—224no—
299C22—224no—
300C22—224no—
301C22—442no—
302C22—442no—
303C22—442no—
304C22—442no—
305C22#6694614yescomplemented
306C22C22×C4×D1111yescharacteristic
307C22C2×#433911yescharacteristic
308C22C2×D4×D1111yescharacteristic
309C22#6703711yescharacteristic
310C22C2×#434311yescharacteristic
311C22#6704011yescharacteristic
312C22C22×C22⋊D1111yescharacteristic
313C4—22no—
314C4—24no—
315C4—42no—
316C4—224no—
317C4—222no—
318C4—222no—
319C4—441no—
320C4—441no—
321C4C4×C22⋊D1114yescomplemented
322C2—24no—
323C2—444no—
324C2C2×#6694611yescharacteristic
325C2#1062303511yescharacteristic
326C2#1062303811yescharacteristic
327C2#1062304511yescharacteristic
328C2C2×C4×C22⋊D1111yescharacteristic
329C2D4×C22⋊D1111yescharacteristic
330C2#1062334811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC22×C11×C4⋊C4C2
socle, cosocleC23×C11C24
prime radicalC2×#66983C2
hypercenterC22×C4⋊C4D11
hypocenterC11#2361
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊C4C2semidirect
3. C2×C4×C22⋊D11C2semidirect
4. C2×#66946C2semidirect
5. #10622826C2semidirect
6. C4×C22⋊Dic11C2semidirect
7. #10622603C2semidirect
8. #10622602C2semidirect
9. #10622601C2semidirect
10. C4⋊C4×Dic11C2semidirect
11. #10622586C2semidirect
23. #66983C4semidirect
46. C22×C4×C11C2×C4semidirect
53. C2×C22⋊D11C2×C4semidirect
61. C2×D44C2×C4semidirect
67. C11×C4⋊C4D4semidirect
69. C22⋊Dic11D4semidirect
73. (C2×D11)⋊C4C2×C4semidirect
74. C4⋊Dic11C2×C4semidirect
130. C22×C4⋊C4D11semidirect
144. C22×C11C4×D4semidirect
162. C4×C11C4×D4semidirect
225. C22×C4C4×D11semidirect
234. C4⋊C4C22⋊D11semidirect
244. C11#2361semidirect
305. C22#66946semidirect
321. C4C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊C42
C2×#669832
C2×C4×C22⋊D112
C2×#669462
#106228262
C4×C22⋊Dic112
#106226032
#106226022
#106226012
C4⋊C4×Dic112
#106225862
#236111