Finite Group Databasebeta

← #13072206

Subgroups — #13072206

Order 1408.

832 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C211yesmaximal, characteristic, complemented
2C2×#66993C211yesmaximal, characteristic, complemented
3C2×#66992C212yesmaximal, complemented
4C2×D4×Dic11C211yesmaximal, characteristic, complemented
5C2×#66983C211yesmaximal, characteristic, complemented
6#10622836C212yesmaximal, complemented
7C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
8#10622601C211yesmaximal, characteristic, complemented
9#10622586C211yesmaximal, characteristic, complemented
10#10622572C212yesmaximal, complemented
11#10622571C212yesmaximal, complemented
12C22×D4×C11C2212yes—
13C22×D4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C22×C22⋊D11C2212yes—
16C22×C22⋊D11C2212yes—
17C22×C22⋊D11C2212yes—
18C23×Dic11C2212yes—
19C22×D44C2211yescharacteristic
20C11×#121—24no—
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2212yes—
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26#66993—24no—
27#66992—28no—
28D4×Dic11—24no—
29#66983—24no—
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2212yes—
32C2×(C2×D11)⋊C4C2212yes—
33C2×C4⋊Dic11C2211yescharacteristic
34C2×Dic11⋊C4C2212yes—
35C2×C4×Dic11C2211yescharacteristic
36C2×C4×Dic11C2211yescharacteristic
37C11⋊#95C2211yescharacteristic
38C11⋊#95C2211yescharacteristic
39C11⋊#95C2212yes—
40C24×C11C2311yescharacteristic
41C24×C11C2312yes—
42C23×D11C2312yes—
43C2×D4×C11—24no—
44C2×D4×C11—24no—
45C2×D4×C11—22no—
46C2×D4×C11—22no—
47C2×D4×C11—42no—
48C2×D4×C11D414yescomplemented
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2312yes—
54C22×C4×C11C2311yescharacteristic
55C2×C22⋊D11—24no—
56C2×C22⋊D11—24no—
57C2×C22⋊D11—24no—
58C2×C22⋊D11—24no—
59C2×C22⋊D11—24no—
60C2×C22⋊D11—24no—
61C2×C22⋊D11—42no—
62C2×C22⋊D11—42no—
63C2×C22⋊D11—42no—
64C22×Dic11—24no—
65C22×Dic11—24no—
66C22×Dic11—42no—
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2312yes—
71C22×Dic11C2311yescharacteristic
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—22no—
75C11×C4⋊C4—22no—
76C11×C22⋊C4—24no—
77C22⋊Dic11—24no—
78C22⋊Dic11—22no—
79C22⋊Dic11D414yescomplemented
80(C2×D11)⋊C4—24no—
81(C2×D11)⋊C4—24no—
82(C2×D11)⋊C4—42no—
83C4⋊Dic11D414yescomplemented
84Dic11⋊C4—24no—
85C4×Dic11—22no—
86C4×Dic11—22no—
87#2428—111nomaximal, Sylow
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—22no—
94C23×C11—21no—
95C23×C11—22no—
96C23×C11—22no—
97C23×C11—21no—
98C23×C11—22no—
99C23×C11—21no—
100C23×C11C2×D412yes—
101C23×C11C2×D414yes—
102C23×C11C2411yescharacteristic
103C22×D11—22no—
104C22×D11—22no—
105C22×D11—22no—
106C22×D11—22no—
107C22×D11—22no—
108C22×D11—22no—
109C22×D11—22no—
110D4×C11—28no—
111D4×C11—48no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—44no—
119C2×C4×C11C2×D412yes—
120C2×C4×C11C2×D412yes—
121C2×C4×C11#4112yes—
122C22⋊D11—48no—
123C22⋊D11—48no—
124C22⋊D11—48no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—22no—
129C2×Dic11—21no—
130C2×Dic11—22no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—48no—
137C2×Dic11C2×D412yes—
138C2×Dic11C2×D414yes—
139C2×Dic11C2×D412yes—
140C2×Dic11#4112yes—
141D44—44no—
142C2×#127—111no—
143C2×#121—112no—
144C2×#121—111no—
145C2×#121D1111yescharacteristic, complemented
146C2×C4×D4—111no—
147#394—112no—
148#392—112no—
149#390—111no—
150#389—111no—
151#386—112no—
152C4×C22⋊C4—111no—
153C22×C11—24no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—24no—
157C22×C11—22no—
158C22×C11—24no—
159C22×C11—41no—
160C22×C11—42no—
161C22×C11—41no—
162C22×C11—42no—
163C22×C11—42no—
164C22×C11—41no—
165C22×C11—42no—
166C22×C11—41no—
167C22×C11C22×D411yescharacteristic
168C22×C11C22×D411yescharacteristic
169C22×C11C22×D411yescharacteristic
170C22×C11C2×#4111yescharacteristic
171C22×C11C2×#4111yescharacteristic
172C22×C11H(5,𝔽2)11yescharacteristic
173C22×C11H(5,𝔽2)11yescharacteristic
174C2×D11—42no—
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—42no—
179C2×D11—42no—
180C2×D11—42no—
181C4×C11—41no—
182C4×C11—42no—
183C4×C11#12114yescomplemented
184Dic11—22no—
185Dic11—24no—
186Dic11—22no—
187Dic11—22no—
188Dic11—41no—
189C22×D4—112no—
190C22×D4—112no—
191C22×D4—112no—
192C22×D4—111no—
193C22×D4C2×D1112yes—
194C22×D4C2×D1111yescharacteristic
195C23×C4—112no—
196C23×C4C2×D1111yescharacteristic
197#127—224no—
198#121—24no—
199#121—228no—
200#121—224no—
201C4×D4—224no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—112no—
204C2×C4⋊C4C2×D1111yescharacteristic
205C2×C22⋊C4—111no—
206C2×C22⋊C4—112no—
207C2×C22⋊C4—111no—
208C2×C22⋊C4—112no—
209C2×C22⋊C4—112no—
210C2×C22⋊C4—112no—
211C2×C22⋊C4C2×D1112yes—
212C2×C42—111no—
213C2×C42—111no—
214#95—111no—
215#95—111no—
216#95—112no—
217C2×C11—44no—
218C2×C11—42no—
219C2×C11C2×#12111yescharacteristic
220C2×C11#53211yescharacteristic
221C2×C11#54011yescharacteristic
222C2×C11D4211yescharacteristic
223C2×C11D4211yescharacteristic
224C2×C11#54611yescharacteristic
225C2×C11#55011yescharacteristic
226D11—82no—
227C24—112no—
228C24C22×D1111yescharacteristic
229C24C22×D1112yes—
230C2×D4—24no—
231C2×D4—24no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—42no—
235C2×D4—224no—
236C2×D4—224no—
237C2×D4—224no—
238C2×D4—224no—
239C2×D4—224no—
240C2×D4—224no—
241C2×D4—222no—
242C2×D4—222no—
243C2×D4—222no—
244C2×D4—442no—
245C2×D4—442no—
246C2×D4—442no—
247C2×D4C22⋊D1114yescomplemented
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—111no—
252C22×C4—111no—
253C22×C4—111no—
254C22×C4—112no—
255C22×C4—111no—
256C22×C4—224no—
257C22×C4—224no—
258C22×C4—442no—
259C22×C4C22×D1111yescharacteristic
260C22×C4C22×D1112yes—
261C22×C4C22×D1111yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—114no—
264C4⋊C4—224no—
265C22⋊C4—24no—
266C22⋊C4—114no—
267C22⋊C4—224no—
268C22⋊C4—224no—
269C22⋊C4—224no—
270C22⋊C4—222no—
271C22⋊C4—442no—
272C42—222no—
273C42—222no—
274C11#242811yescharacteristic, complemented, Sylow
275C23—22no—
276C23—21no—
277C23—22no—
278C23—21no—
279C23—22no—
280C23—21no—
281C23—22no—
282C23—21no—
283C23—22no—
284C23—22no—
285C23—21no—
286C23—21no—
287C23—222no—
288C23—222no—
289C23—222no—
290C23—222no—
291C23—222no—
292C23—222no—
293C23—222no—
294C23D4×D1112yes—
295C23C2×C22⋊D1114yes—
296C23C23×D1111yescharacteristic
297D4—28no—
298D4—48no—
299D4—448no—
300D4—448no—
301D4—448no—
302D4—444no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—44no—
310C2×C4—112no—
311C2×C4—112no—
312C2×C4—114no—
313C2×C4—112no—
314C2×C4—221no—
315C2×C4—222no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—222no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—448no—
326C2×C4D4×D1112yes—
327C2×C4#434112yes—
328C2×C4C2×C22⋊D1112yes—
329C22—22no—
330C22—24no—
331C22—24no—
332C22—24no—
333C22—22no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—42no—
339C22—41no—
340C22—42no—
341C22—41no—
342C22—42no—
343C22—442no—
344C22—442no—
345C22—442no—
346C22—442no—
347C22—442no—
348C22—442no—
349C22—442no—
350C22C2×D4×D1111yescharacteristic
351C22C2×D4×D1111yescharacteristic
352C22C2×#434111yescharacteristic
353C22#6703711yescharacteristic
354C22#41×D1111yescharacteristic
355C22#6704211yescharacteristic
356C22C22×C22⋊D1111yescharacteristic
357C4—42no—
358C4—41no—
359C4—222no—
360C4—222no—
361C4—222no—
362C4—224no—
363C4—441no—
364C4#6699214yescomplemented
365C2—42no—
366C2—44no—
367C2—882no—
368C2#1062312711yescharacteristic
369C2#1062313011yescharacteristic
370C2#1062314011yescharacteristic
371C2#1062315011yescharacteristic
372C2D4×C22⋊D1111yescharacteristic
373C2C2×#6699211yescharacteristic
374C2#1062336011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×#66993C2semidirect
3. C2×#66992C2semidirect
4. C2×D4×Dic11C2semidirect
5. C2×#66983C2semidirect
6. #10622836C2semidirect
7. C4×C22⋊Dic11C2semidirect
8. #10622601C2semidirect
9. #10622586C2semidirect
10. #10622572C2semidirect
11. #10622571C2semidirect
48. C2×D4×C11D4semidirect
79. C22⋊Dic11D4semidirect
83. C4⋊Dic11D4semidirect
145. C2×#121D11semidirect
183. C4×C11#121semidirect
247. C2×D4C22⋊D11semidirect
274. C11#2428semidirect
364. C4#66992semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669932
C2×#669922
C2×D4×Dic112
C2×#669832
#106228362
C4×C22⋊Dic112
#106226012
#106225862
#106225722
#106225712
#242811