Finite Group Databasebeta

← #13072381

Subgroups — #13072381

Order 1408.

696 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×#66947C212yesmaximal, complemented
2C2×#66927C211yesmaximal, characteristic
3C2×C4×D44C211yesmaximal, characteristic, complemented
4C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5#10622604C212yesmaximal, complemented
6#10622552C211yesmaximal, characteristic, complemented
7#10622552C211yesmaximal, characteristic, complemented
8#10622552C211yesmaximal, characteristic, complemented
9#10622541C211yesmaximal, characteristic, complemented
10#10622285C212yesmaximal, complemented
11#10622278C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×D44C2212yes—
14C22×D44C2212yes—
15C22×D44C2211yescharacteristic
16C22×C4×D11C2212yes—
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C42×C11C2211yescharacteristic
20C2×C42×C11C2211yescharacteristic
21C2×C42×C11C2211yescharacteristic
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×Dic11⋊C4C2212yes—
32#66947—28no—
33#66927—24no—
34C4×D44—24no—
35C11×#95C2211yescharacteristic
36C11×#95C2211yescharacteristic
37C11⋊#95C2212yes—
38C23×D11C2312yes—
39C23×D11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C22×Dic11C2312yes—
48C22×Dic11C2312yes—
49C2×D44—24no—
50C2×D44—24no—
51C2×D44—22no—
52C2×D44—24no—
53C2×D44—22no—
54C2×D44—22no—
55C2×D44—24no—
56C2×D44—22no—
57C2×D44—22no—
58C2×D44—42no—
59C2×D44—42no—
60C2×D44D414yes—
61C2×C4×D11—24no—
62C2×C4×D11—24no—
63C2×C4×D11—42no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4D414yescomplemented
66C42×C11—22no—
67C42×C11—22no—
68C42×C11—22no—
69(C2×D11)⋊C4—24no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—24no—
72(C2×D11)⋊C4—24no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—42no—
75(C2×D11)⋊C4—42no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78Dic11⋊C4—24no—
79#2445—111nomaximal, Sylow
80C23×C11C2411yescharacteristic
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—22no—
94C22×D11C2×D414yes—
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—21no—
109C2×C4×C11C2×D412yes—
110C2×C4×C11C2×D412yes—
111C2×C4×C11C2×D412yes—
112C2×C4×C11C2×D412yes—
113C2×C4×C11#4112yes—
114C2×C4×C11#4112yes—
115C2×C4×C11#4112yes—
116C2×Dic11—22no—
117C2×Dic11—22no—
118C2×Dic11—22no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11—22no—
122D44—28no—
123D44—48no—
124D44—48no—
125D44—44no—
126C4×D11—48no—
127C2×#127—111no—
128C2×#123—112no—
129C2×C4×D4—111no—
130#394—112no—
131#394—112no—
132#390—111no—
133#390—111no—
134#390—111no—
135#389—111no—
136#386—112no—
137C4×C4⋊C4D1111yescharacteristic, complemented
138C22×C11C22×D411yescharacteristic
139C22×C11C22×D411yescharacteristic
140C22×C11C2×#4111yescharacteristic
141C22×C11C2×#4111yescharacteristic
142C22×C11C2×#4111yescharacteristic
143C22×C11H(5,𝔽2)11yescharacteristic
144C22×C11H(5,𝔽2)11yescharacteristic
145C2×D11—24no—
146C2×D11—24no—
147C2×D11—24no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—42no—
153C2×D11—42no—
154C2×D11—42no—
155C2×D11—42no—
156C2×D11—42no—
157C2×D11—42no—
158C2×D11—42no—
159C4×C11—22no—
160C4×C11—22no—
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11#12314yescomplemented
166Dic11—42no—
167Dic11—42no—
168C22×D4—111no—
169C22×D4—111no—
170C22×D4—112no—
171C22×D4—112no—
172C23×C4—112no—
173#127—224no—
174#123—228no—
175C4×D4—224no—
176C2×C4⋊C4—111no—
177C2×C4⋊C4—112no—
178C2×C4⋊C4—111no—
179C2×C4⋊C4C2×D1111yescharacteristic
180C2×C4⋊C4C2×D1111yescharacteristic
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4—112no—
186C2×C22⋊C4—112no—
187C2×C22⋊C4—112no—
188C2×C42C2×D1111yescharacteristic
189C2×C42C2×D1111yescharacteristic
190C2×C42C2×D1111yescharacteristic
191#95—112no—
192#95C2×D1111yescharacteristic
193#95C2×D1111yescharacteristic
194C2×C11C2×#12311yescharacteristic
195C2×C11#53211yescharacteristic
196C2×C11#54011yescharacteristic
197C2×C11D4211yescharacteristic
198C2×C11#54611yescharacteristic
199C2×C11#55011yescharacteristic
200C2×C11#55911yescharacteristic
201D11—44no—
202D11—82no—
203C24—112no—
204C24—112no—
205C2×D4—114no—
206C2×D4—224no—
207C2×D4—224no—
208C2×D4—224no—
209C2×D4—222no—
210C2×D4—224no—
211C2×D4—222no—
212C2×D4—222no—
213C2×D4—222no—
214C2×D4—222no—
215C2×D4—442no—
216C2×D4—442no—
217C22×C4—112no—
218C22×C4—112no—
219C22×C4—224no—
220C22×C4—224no—
221C22×C4—442no—
222C22×C4C22×D1111yescharacteristic
223C22×C4C22×D1111yescharacteristic
224C22×C4C22×D1111yescharacteristic
225C22×C4C22×D1111yescharacteristic
226C22×C4C22×D1111yescharacteristic
227C22×C4C22×D1111yescharacteristic
228C22×C4C22×D1111yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—224no—
231C4⋊C4—222no—
232C4⋊C4—222no—
233C4⋊C4D4414yescomplemented
234C22⋊C4—224no—
235C22⋊C4—224no—
236C22⋊C4—224no—
237C22⋊C4—224no—
238C22⋊C4—442no—
239C22⋊C4—442no—
240C22⋊C4—442no—
241C42—22no—
242C42—22no—
243C42—22no—
244C11#244511yescharacteristic, complemented, Sylow
245C23—114no—
246C23—222no—
247C23—222no—
248C23—222no—
249C23—222no—
250C23—222no—
251C23—222no—
252C23—222no—
253C23—222no—
254C23—222no—
255C23—222no—
256C23—222no—
257C23—222no—
258C23—222no—
259C23C23×D1111yescharacteristic
260D4—228no—
261D4—448no—
262D4—448no—
263D4—444no—
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—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—222no—
279C2×C4—222no—
280C2×C4—222no—
281C2×C4—222no—
282C2×C4—222no—
283C2×C4—222no—
284C2×C4—448no—
285C2×C4C2×D4412yes—
286C2×C4C2×D4412yes—
287C2×C4C2×D4412yes—
288C2×C4#433912yes—
289C2×C4#433912yes—
290C2×C4D4×D1112yes—
291C2×C4#434312yes—
292C22—224no—
293C22—224no—
294C22—224no—
295C22—442no—
296C22—442no—
297C22—442no—
298C22—442no—
299C22—442no—
300C22—442no—
301C22—442no—
302C22—442no—
303C22—442no—
304C22—442no—
305C22—442no—
306C22C22×D4411yescharacteristic
307C22C2×#433911yescharacteristic
308C22C2×#433911yescharacteristic
309C22C2×D4×D1111yescharacteristic
310C22C2×#434311yescharacteristic
311C22#6704211yescharacteristic
312C22#6704211yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—442no—
320C4—442no—
321C4#6694714yescomplemented
322C2—444no—
323C2—882no—
324C2#1062300811yescharacteristic
325C2C2×#6694711yescharacteristic
326C2#1062306611yescharacteristic
327C2D4×D4411yescharacteristic
328C2#1062308111yescharacteristic
329C2#1062310811yescharacteristic
330C2#1062311611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C4⋊C4C2
prime radicalC2×#66927C2
hypercenterC4×C4⋊C4D11
hypocenterC11#2445
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#66947C2semidirect
3. C2×C4×D44C2semidirect
4. C4×C11×C4⋊C4C2semidirect
5. #10622604C2semidirect
6. #10622552C2semidirect
7. #10622552C2semidirect
8. #10622552C2semidirect
9. #10622541C2semidirect
10. #10622285C2semidirect
11. #10622278C2semidirect
65. C11×C4⋊C4D4semidirect
137. C4×C4⋊C4D11semidirect
165. C4×C11#123semidirect
233. C4⋊C4D44semidirect
244. C11#2445semidirect
321. C4#66947semidirect

Maximal subgroups

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

subgroupindex
C2×#669472
C2×#669272
C2×C4×D442
C4×C11×C4⋊C42
#106226042
#106225522
#106225412
#106222852
#106222782
#244511