Finite Group Databasebeta

← #13072194

Subgroups — #13072194

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×#67000C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3C2×#66948C211yesmaximal, characteristic
4C2×C4×D44C211yesmaximal, characteristic, complemented
5C11×#391C211yesmaximal, characteristic, complemented
6#10622586C211yesmaximal, characteristic, complemented
7C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
8#10622288C212yesmaximal, complemented
9#10622285C212yesmaximal, complemented
10#10622280C212yesmaximal, complemented
11#10622278C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×D44C2212yes—
14C22×D44C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C22×C4×D11C2212yes—
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C42×C11C2211yescharacteristic
19#67000—24no—
20#66999—24no—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×Dic11⋊C4C2212yes—
31C2×C4×Dic11C2211yescharacteristic
32#66948—24no—
33C4×D44—24no—
34C11×#95C2212yes—
35C11×#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2211yescharacteristic
38C11⋊#95C2211yescharacteristic
39C23×D11C2312yes—
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×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2312yes—
53C2×D44—24no—
54C2×D44—24no—
55C2×D44—22no—
56C2×D44—22no—
57C2×D44—42no—
58C2×D44D414yes—
59C2×C4×D11—24no—
60C2×C4×D11—22no—
61C2×C4×D11—22no—
62C2×C4×D11—22no—
63C2×C4×D11—24no—
64C2×C4×D11—42no—
65C11×C4⋊C4—22no—
66C42×C11—22no—
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—24no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—24no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—22no—
74C4⋊Dic11D414yescomplemented
75Dic11⋊C4—24no—
76Dic11⋊C4—42no—
77C4×Dic11—22no—
78#2427—111nomaximal, Sylow
79C23×C11C2411yescharacteristic
80C22×D11—21no—
81C22×D11—22no—
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—21no—
90C22×D11—22no—
91C22×D11—21no—
92C22×D11C2×D414yes—
93C22×D11#4112yes—
94Q8×C11—44no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11C2×D412yes—
107C2×C4×C11C2×D412yes—
108C2×C4×C11#4112yes—
109C2×C4×C11#4112yes—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11C2×D414yes—
122D44—28no—
123D44—48no—
124C4×D11—48no—
125C4×D11—44no—
126C2×#124—111no—
127C2×C22⋊Q8—111no—
128C2×#121—111no—
129C2×C4×D4—111no—
130#397—112no—
131#394—112no—
132#391D1111yescharacteristic, complemented
133#389—111no—
134#386—112no—
135#380—112no—
136C4×C22⋊C4—111no—
137C22×C11C22×D411yescharacteristic
138C22×C11C22×D411yescharacteristic
139C22×C11C2×#4111yescharacteristic
140C22×C11C2×#4111yescharacteristic
141C22×C11C2×#4111yescharacteristic
142C22×C11H(5,𝔽2)11yescharacteristic
143C22×C112−1+411yescharacteristic
144C2×D11—24no—
145C2×D11—22no—
146C2×D11—24no—
147C2×D11—22no—
148C2×D11—24no—
149C2×D11—22no—
150C2×D11—41no—
151C2×D11—42no—
152C2×D11—41no—
153C2×D11—42no—
154C2×D11—41no—
155C2×D11—42no—
156C2×D11—41no—
157C2×D11—42no—
158C4×C11—22no—
159C4×C11—42no—
160C4×C11—42no—
161C4×C11—41no—
162C4×C11#12114yes—
163Dic11—24no—
164Dic11—41no—
165Dic11—41no—
166Dic11—41no—
167C22×Q8C2×D1111yescharacteristic
168C22×D4—111no—
169C22×D4—112no—
170C23×C4—111no—
171C23×C4—112no—
172#124—224no—
173C22⋊Q8—224no—
174#121—224no—
175C4×D4—224no—
176C2×C4⋊C4—111no—
177C2×C4⋊C4—112no—
178C2×C4⋊C4—112no—
179C2×C4⋊C4C2×D1111yescharacteristic
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4—111no—
186C2×C22⋊C4—111no—
187C2×C42—111no—
188C2×C42C2×D1111yescharacteristic
189#95—111no—
190#95—111no—
191#95—112no—
192#95C2×D1112yes—
193#95C2×D1112yes—
194C2×C11C2×#12111yescharacteristic
195C2×C11#52911yescharacteristic
196C2×C11#54211yescharacteristic
197C2×C11#54611yescharacteristic
198C2×C11#54611yescharacteristic
199C2×C11#54711yescharacteristic
200C2×C11#54811yescharacteristic
201D11—44no—
202D11—42no—
203C24—112no—
204C24—111no—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×D4—114no—
209C2×D4—224no—
210C2×D4—224no—
211C2×D4—222no—
212C2×D4—222no—
213C2×D4—442no—
214C22×C4—112no—
215C22×C4—111no—
216C22×C4—111no—
217C22×C4—111no—
218C22×C4—224no—
219C22×C4—222no—
220C22×C4—222no—
221C22×C4—222no—
222C22×C4—224no—
223C22×C4—442no—
224C22×C4C22×D1111yescharacteristic
225C22×C4C22×D1112yes—
226C22×C4C22×D1112yes—
227C22×C4C22×D1111yescharacteristic
228C22×C4C22×D1111yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—114no—
231C4⋊C4—224no—
232C4⋊C4—442no—
233C22⋊C4—224no—
234C22⋊C4—224no—
235C22⋊C4—224no—
236C22⋊C4—224no—
237C22⋊C4—224no—
238C22⋊C4—222no—
239C22⋊C4—222no—
240C42—22no—
241C42—222no—
242C11#242711yescharacteristic, complemented, Sylow
243C23—114no—
244C23—112no—
245C23—221no—
246C23—222no—
247C23—221no—
248C23—222no—
249C23—221no—
250C23—221no—
251C23—222no—
252C23—222no—
253C23—221no—
254C23—222no—
255C23—222no—
256C23—221no—
257C23C23×D1111yescharacteristic
258Q8—44no—
259D4—228no—
260D4—448no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—114no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—448no—
285C2×C4—444no—
286C2×C4#433912yes—
287C2×C4D4×D1112yes—
288C2×C4D4×D1112yes—
289C2×C4#434312yes—
290C22—224no—
291C22—224no—
292C22—222no—
293C22—222no—
294C22—222no—
295C22—224no—
296C22—441no—
297C22—441no—
298C22—442no—
299C22—441no—
300C22—442no—
301C22—442no—
302C22—441no—
303C22—442no—
304C22C2×#433911yescharacteristic
305C22C2×D4×D1111yescharacteristic
306C22C2×D4×D1111yescharacteristic
307C22C2×#434311yescharacteristic
308C22#6704011yescharacteristic
309C22#41×D1111yescharacteristic
310C22#6704211yescharacteristic
311C4—22no—
312C4—42no—
313C4—41no—
314C4—42no—
315C4—224no—
316C4—441no—
317C4—441no—
318C4—441no—
319C4#6693714yes—
320C2—444no—
321C2—442no—
322C2C2×#6693711yescharacteristic
323C2#1062311111yescharacteristic
324C2#1062311311yescharacteristic
325C2#1062316111yescharacteristic
326C2#1062316411yescharacteristic
327C2#1062320711yescharacteristic
328C2#1062325711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC2×#66948C2
hypercenter#391D11
hypocenterC11#2427
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#67000C2semidirect
2. C2×#66999C2semidirect
4. C2×C4×D44C2semidirect
5. C11×#391C2semidirect
6. #10622586C2semidirect
7. C4×(C2×D11)⋊C4C2semidirect
8. #10622288C2semidirect
9. #10622285C2semidirect
10. #10622280C2semidirect
11. #10622278C2semidirect
74. C4⋊Dic11D4semidirect
132. #391D11semidirect
242. C11#2427semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669992
C2×#669482
C2×C4×D442
C11×#3912
#106225862
C4×(C2×D11)⋊C42
#106222882
#106222852
#106222802
#106222782
#242711