Finite Group Databasebeta

← #13072193

Subgroups — #13072193

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×#66983C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic, complemented
3C2×#66928C211yesmaximal, characteristic, complemented
4C2×C4×D44C211yesmaximal, characteristic, complemented
5C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6#10622572C212yesmaximal, complemented
7#10622569C212yesmaximal, complemented
8#10622542C211yesmaximal, characteristic, complemented
9#10622541C211yesmaximal, characteristic, complemented
10#10622288C212yesmaximal, complemented
11#10622280C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×D44C2211yescharacteristic
15C22×C4×D11C2212yes—
16C22×Dic22C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C42×C11C2211yescharacteristic
20C2×C42×C11C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22#66983—24no—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29#66977—24no—
30C2×Dic11⋊C4C2212yes—
31C2×Dic11⋊C4C2212yes—
32#66928—24no—
33C4×D44—24no—
34C11×#95C2211yescharacteristic
35C11×#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C24×C11C2311yescharacteristic
40C23×D11C2312yes—
41C22×C4×C11—22no—
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—24no—
51C2×C22⋊D11—24no—
52C2×C22⋊D11—42no—
53C22×Dic11C2312yes—
54C22×Dic11C2312yes—
55C22×Dic11C2312yes—
56C2×D44—22no—
57C2×D44—22no—
58C2×D44D414yes—
59C2×C4×D11—24no—
60C2×C4×D11—24no—
61C2×C4×D11—42no—
62C2×Dic22—22no—
63C2×Dic22—22no—
64C2×Dic22—22no—
65C11×C22⋊C4—22no—
66C11×C22⋊C4—22no—
67C42×C11—22no—
68C42×C11—22no—
69C22⋊Dic11—24no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—24no—
72(C2×D11)⋊C4—24no—
73(C2×D11)⋊C4—24no—
74C4⋊Dic11—22no—
75C4⋊Dic11D414yescomplemented
76Dic11⋊C4—24no—
77Dic11⋊C4—42no—
78#2427—111nomaximal, Sylow
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11—21no—
85C23×C11#4112yes—
86C23×C11C2411yescharacteristic
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11—22no—
93C22×D11C2×D414yes—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—44no—
109C2×C4×C11C2×D412yes—
110C2×C4×C11C2×D412yes—
111C2×C4×C11#4112yes—
112C2×C4×C11#4112yes—
113C22⋊D11—48no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—22no—
118C2×Dic11—22no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11—22no—
122C2×Dic11C2×D414yes—
123D44—28no—
124C4×D11—48no—
125Dic22—44no—
126C2×#124—111no—
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⋊C4D1111yescharacteristic, complemented
137C22×C11—22no—
138C22×C11—22no—
139C22×C11—22no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11—41no—
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—24no—
152C2×D11—24no—
153C2×D11—24no—
154C2×D11—42no—
155C2×D11—42no—
156C2×D11—42no—
157C2×D11—42no—
158C4×C11—22no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11#12114yes—
164Dic11—24no—
165Dic11—42no—
166Dic11—42no—
167C22×Q8—111no—
168C22×D4—112no—
169C22×D4—111no—
170C23×C4—112no—
171C23×C4C2×D1111yescharacteristic
172#124—224no—
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—112no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4C2×D1111yescharacteristic
186C2×C22⋊C4C2×D1111yescharacteristic
187C2×C42C2×D1111yescharacteristic
188C2×C42C2×D1111yescharacteristic
189#95—112no—
190#95—112no—
191#95—112no—
192#95C2×D1111yescharacteristic
193#95C2×D1111yescharacteristic
194C2×C11—42no—
195C2×C11C2×#12111yescharacteristic
196C2×C11#52911yescharacteristic
197C2×C11#54211yescharacteristic
198C2×C11#54611yescharacteristic
199C2×C11#54611yescharacteristic
200C2×C11#54711yescharacteristic
201C2×C11#54811yescharacteristic
202D11—44no—
203C24—112no—
204C24C22×D1111yescharacteristic
205C2×Q8—222no—
206C2×Q8—222no—
207C2×Q8—222no—
208C2×D4—114no—
209C2×D4—224no—
210C2×D4—224no—
211C2×D4—222no—
212C2×D4—222no—
213C2×D4—442no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—112no—
218C22×C4—112no—
219C22×C4—112no—
220C22×C4—224no—
221C22×C4—224no—
222C22×C4—442no—
223C22×C4C22×D1111yescharacteristic
224C22×C4C22×D1111yescharacteristic
225C22×C4C22×D1111yescharacteristic
226C22×C4C22×D1111yescharacteristic
227C22×C4C22×D1111yescharacteristic
228C22×C4C22×D1111yescharacteristic
229C4⋊C4—114no—
230C4⋊C4—224no—
231C4⋊C4—222no—
232C4⋊C4—442no—
233C22⋊C4—22no—
234C22⋊C4—22no—
235C22⋊C4—224no—
236C22⋊C4—224no—
237C22⋊C4—224no—
238C22⋊C4—224no—
239C22⋊C4—224no—
240C42—22no—
241C42—22no—
242C11#242711yescharacteristic, complemented, Sylow
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—114no—
250C23—222no—
251C23—222no—
252C23—222no—
253C23—222no—
254C23—222no—
255C23—222no—
256C23#433912yes—
257C23C23×D1111yescharacteristic
258Q8—444no—
259D4—228no—
260D4—448no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—44no—
276C2×C4—114no—
277C2×C4—222no—
278C2×C4—222no—
279C2×C4—222no—
280C2×C4—222no—
281C2×C4—222no—
282C2×C4—222no—
283C2×C4—222no—
284C2×C4—222no—
285C2×C4—448no—
286C2×C4#433912yes—
287C2×C4#433912yes—
288C2×C4D4×D1112yes—
289C2×C4D4×D1112yes—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—224no—
298C22—224no—
299C22—224no—
300C22—442no—
301C22—442no—
302C22—442no—
303C22—442no—
304C22C2×#433911yescharacteristic
305C22C2×#433911yescharacteristic
306C22C2×#433911yescharacteristic
307C22C2×D4×D1111yescharacteristic
308C22C2×D4×D1111yescharacteristic
309C22#6704211yescharacteristic
310C22#6704311yescharacteristic
311C4—22no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—224no—
317C4—442no—
318C4—442no—
319C4#6693714yes—
320C2—42no—
321C2—444no—
322C2#1062301011yescharacteristic
323C2C2×#6693711yescharacteristic
324C2#1062306511yescharacteristic
325C2#1062308111yescharacteristic
326C2#1062308111yescharacteristic
327C2#1062308211yescharacteristic
328C2#1062308311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C22⋊C4C2
prime radicalC2×#66983C2
hypercenterC4×C22⋊C4D11
hypocenterC11#2427
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#66977C2semidirect
3. C2×#66928C2semidirect
4. C2×C4×D44C2semidirect
5. C4×C11×C22⋊C4C2semidirect
6. #10622572C2semidirect
7. #10622569C2semidirect
8. #10622542C2semidirect
9. #10622541C2semidirect
10. #10622288C2semidirect
11. #10622280C2semidirect
75. C4⋊Dic11D4semidirect
136. C4×C22⋊C4D11semidirect
242. C11#2427semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C2×#669772
C2×#669282
C2×C4×D442
C4×C11×C22⋊C42
#106225722
#106225692
#106225422
#106225412
#106222882
#106222802
#242711