Finite Group Databasebeta

← #13071634

Subgroups — #13071634

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
1C2×#66948C211yesmaximal, characteristic
2C2×#66946C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4C2×C4×D44C212yesmaximal, complemented
5C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6#10622598C211yesmaximal, characteristic, complemented
7#10622553C212yesmaximal, complemented
8#10622552C211yesmaximal, characteristic, complemented
9C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
10#10622281C212yesmaximal, complemented
11#10622278C212yesmaximal, complemented
12C22×D44C2212yes—
13C22×D44C2211yescharacteristic
14C22×C4×D11C2212yes—
15C22×C4×D11C2212yes—
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C42×C11C2212yes—
20C2×C42×C11C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×C4⋊Dic11C2212yes—
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31#66948C418yescomplemented
32#66946—24no—
33C4⋊C4×D11—24no—
34C4×D44—28no—
35C11×#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2211yescharacteristic
38C11⋊#95C2211yescharacteristic
39C23×D11C2312yes—
40C23×D11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2312yes—
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C2×D44—24no—
51C2×D44—24no—
52C2×D44—22no—
53C2×D44—22no—
54C2×D44C2×C418yescomplemented
55C2×D44C2×C414yescomplemented
56C2×C4×D11—24no—
57C2×C4×D11—24no—
58C2×C4×D11—22no—
59C2×C4×D11—24no—
60C2×C4×D11—24no—
61C2×C4×D11—22no—
62C2×C4×D11—42no—
63C2×C4×D11—42no—
64C2×C4×D11C2×C414yescomplemented
65C11×C4⋊C4C2×C414yescomplemented
66C11×C4⋊C4D414yescomplemented
67C42×C11—24no—
68C42×C11—22no—
69(C2×D11)⋊C4—22no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—24no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4C2×C418yescomplemented
74(C2×D11)⋊C4D414yescomplemented
75C4⋊Dic11—24no—
76C4⋊Dic11—22no—
77Dic11⋊C4—24no—
78C4×Dic11—22no—
79#2361—111nomaximal, Sylow
80C23×C11C2411yescharacteristic
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11C22×C414yes—
92C22×D11C22×C412yes—
93C22×D11C2×D412yes—
94C22×D11#4112yes—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11C22×C414yes—
105C2×C4×C11C22×C412yes—
106C2×C4×C11C2×D414yes—
107C2×C4×C11C2×D412yes—
108C2×C4×C11C2×D412yes—
109C2×C4×C11#4112yes—
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—21no—
118C2×Dic11—22no—
119C2×Dic11—21no—
120C2×Dic11C22×C412yes—
121C2×Dic11C2×D412yes—
122D44—216no—
123D44—28no—
124C4×D11—28no—
125C4×D11—48no—
126C4×D11—48no—
127C2×#121—111no—
128C2×C4×D4—111no—
129C2×C4×D4—112no—
130C22×C4⋊C4—111no—
131#390—111no—
132#389—111no—
133#388—112no—
134#386—112no—
135#385—112no—
136C4×C4⋊C4D1111yescharacteristic, complemented
137C4×C22⋊C4—111no—
138C22×C11C23×C411yescharacteristic
139C22×C11C22×D411yescharacteristic
140C22×C11C22×D411yescharacteristic
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—24no—
152C2×D11—24no—
153C2×D11—24no—
154C2×D11—42no—
155C2×D11—42no—
156C2×D11—42no—
157C2×D11—42no—
158C2×D11C4×D414yescomplemented
159C4×C11—24no—
160C4×C11—24no—
161C4×C11—22no—
162C4×C11—41no—
163C4×C11C4×D414yescomplemented
164Dic11—22no—
165Dic11—22no—
166Dic11—42no—
167Dic11—41no—
168C22×D4—112no—
169C22×D4—111no—
170C23×C4—111no—
171C23×C4—112no—
172C23×C4—112no—
173#121—118no—
174C4×D4—228no—
175C4×D4—224no—
176C2×C4⋊C4—112no—
177C2×C4⋊C4—111no—
178C2×C4⋊C4—112no—
179C2×C4⋊C4—224no—
180C2×C4⋊C4C2×D1111yescharacteristic
181C2×C4⋊C4C2×D1111yescharacteristic
182C2×C22⋊C4—111no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4—112no—
186C2×C22⋊C4—111no—
187C2×C22⋊C4—112no—
188C2×C42—111no—
189C2×C42C2×D1112yes—
190C2×C42C2×D1111yescharacteristic
191#95—111no—
192#95—111no—
193#95—112no—
194#95C2×D1112yes—
195C2×C11C2×C4×D411yescharacteristic
196C2×C11C2×C4×D411yescharacteristic
197C2×C11#52011yescharacteristic
198C2×C11D4211yescharacteristic
199C2×C11#54711yescharacteristic
200C2×C11#54811yescharacteristic
201C2×C11#55311yescharacteristic
202D11—24no—
203D11—44no—
204C24—111no—
205C24—112no—
206C2×D4—118no—
207C2×D4—114no—
208C2×D4—224no—
209C2×D4—224no—
210C2×D4—222no—
211C2×D4—222no—
212C22×C4—111no—
213C22×C4—111no—
214C22×C4—114no—
215C22×C4—111no—
216C22×C4—112no—
217C22×C4—224no—
218C22×C4—224no—
219C22×C4—222no—
220C22×C4—222no—
221C22×C4—224no—
222C22×C4—224no—
223C22×C4—442no—
224C22×C4—442no—
225C22×C4C22×D1111yescharacteristic
226C22×C4C22×D1112yes—
227C22×C4C22×D1112yes—
228C22×C4C22×D1111yescharacteristic
229C22×C4C22×D1111yescharacteristic
230C4⋊C4—224no—
231C4⋊C4—224no—
232C4⋊C4—222no—
233C4⋊C4C4×D1114yescomplemented
234C4⋊C4D4414yescomplemented
235C22⋊C4—118no—
236C22⋊C4—114no—
237C22⋊C4—222no—
238C22⋊C4—224no—
239C22⋊C4—224no—
240C22⋊C4—442no—
241C42—22no—
242C42—24no—
243C42—222no—
244C11#236111yescharacteristic, complemented, Sylow
245C23—112no—
246C23—112no—
247C23—112no—
248C23—114no—
249C23—221no—
250C23—221no—
251C23—221no—
252C23—221no—
253C23—222no—
254C23—222no—
255C23—222no—
256C23—222no—
257C23—222no—
258C23—222no—
259C23C23×D1111yescharacteristic
260D4—2216no—
261D4—228no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—112no—
272C2×C4—112no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—228no—
278C2×C4—221no—
279C2×C4—222no—
280C2×C4—222no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—222no—
284C2×C4—448no—
285C2×C4—448no—
286C2×C4C2×C4×D1114yes—
287C2×C4C2×C4×D1112yes—
288C2×C4C2×D4414yes—
289C2×C4C2×D4412yes—
290C2×C4#433912yes—
291C2×C4D4×D1112yes—
292C22—114no—
293C22—222no—
294C22—222no—
295C22—222no—
296C22—222no—
297C22—222no—
298C22—222no—
299C22—224no—
300C22—224no—
301C22—224no—
302C22—442no—
303C22—442no—
304C22—442no—
305C22—442no—
306C22C22×C4×D1111yescharacteristic
307C22C22×D4411yescharacteristic
308C22C2×#433911yescharacteristic
309C22C2×D4×D1111yescharacteristic
310C22#6704011yescharacteristic
311C22#41×D1111yescharacteristic
312C22#6704211yescharacteristic
313C4—22no—
314C4—24no—
315C4—24no—
316C4—41no—
317C4—222no—
318C4—222no—
319C4—442no—
320C4—441no—
321C4C4×D4414yescomplemented
322C2—224no—
323C2—444no—
324C2C2×C4×D4411yescharacteristic
325C2#1062303811yescharacteristic
326C2#1062306111yescharacteristic
327C2C4×D4×D1111yescharacteristic
328C2D4×D4411yescharacteristic
329C2#1062310511yescharacteristic
330C2#1062310711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC4×C11×C4⋊C4C2
socle, cosocleC23×C11C24
prime radicalC2×#66948C2
hypercenterC4×C4⋊C4D11
hypocenterC11#2361
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#66946C2semidirect
3. C2×C4⋊C4×D11C2semidirect
4. C2×C4×D44C2semidirect
5. C4×C11×C4⋊C4C2semidirect
6. #10622598C2semidirect
7. #10622553C2semidirect
8. #10622552C2semidirect
9. C4×(C2×D11)⋊C4C2semidirect
10. #10622281C2semidirect
11. #10622278C2semidirect
31. #66948C4semidirect
54. C2×D44C2×C4semidirect
55. C2×D44C2×C4semidirect
64. C2×C4×D11C2×C4semidirect
65. C11×C4⋊C4C2×C4semidirect
66. C11×C4⋊C4D4semidirect
73. (C2×D11)⋊C4C2×C4semidirect
74. (C2×D11)⋊C4D4semidirect
136. C4×C4⋊C4D11semidirect
158. C2×D11C4×D4semidirect
163. C4×C11C4×D4semidirect
233. C4⋊C4C4×D11semidirect
234. C4⋊C4D44semidirect
244. C11#2361semidirect
321. C4C4×D44semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669462
C2×C4⋊C4×D112
C2×C4×D442
C4×C11×C4⋊C42
#106225982
#106225532
#106225522
C4×(C2×D11)⋊C42
#106222812
#106222782
#236111