Finite Group Databasebeta

← #13073530

Subgroups — #13073530

Order 1408.

788 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C211yesmaximal, characteristic, complemented
2C2×#66992C212yesmaximal, complemented
3C2×#66991C211yesmaximal, characteristic, complemented
4C2×D4×Dic11C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
6#10622835C212yesmaximal, complemented
7#10622825C211yesmaximal, characteristic, complemented
8#10622600C211yesmaximal, characteristic, complemented
9#10622589C211yesmaximal, characteristic, complemented
10#10622572C212yesmaximal, complemented
11#10622555C212yesmaximal, complemented
12C22×D4×C11C2212yes—
13C22×D4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C22×C22⋊D11C2212yes—
16C22×C22⋊D11C2211yescharacteristic
17C23×Dic11C2212yes—
18C22×C4×D11C2211yescharacteristic
19C11×#121—24no—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2212yes—
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2212yes—
25C2×C22⋊Dic11C2212yes—
26#66992—28no—
27#66991—24no—
28D4×Dic11—24no—
29C4×C22⋊D11—24no—
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2212yes—
32C2×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2212yes—
36C2×Dic11⋊C4C2212yes—
37C2×C4×Dic11C2211yescharacteristic
38C11⋊#95C2212yes—
39C11⋊#95C2212yes—
40C24×C11C2311yescharacteristic
41C24×C11C2312yes—
42C23×D11C2311yescharacteristic
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—22no—
56C2×C22⋊D11—22no—
57C2×C22⋊D11—24no—
58C2×C22⋊D11—24no—
59C2×C22⋊D11—42no—
60C2×C22⋊D11D414yescomplemented
61C22×Dic11—24no—
62C22×Dic11—24no—
63C22×Dic11—24no—
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2312yes—
66C22×Dic11C2312yes—
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C2×C4×D11—22no—
70C2×C4×D11—22no—
71C2×C4×D11—22no—
72C11×C4⋊C4—22no—
73C11×C22⋊C4—24no—
74C22⋊Dic11—22no—
75C22⋊Dic11—24no—
76C22⋊Dic11—24no—
77C22⋊Dic11—24no—
78(C2×D11)⋊C4—22no—
79(C2×D11)⋊C4—24no—
80C4⋊Dic11—22no—
81C4⋊Dic11—22no—
82Dic11⋊C4—22no—
83Dic11⋊C4—24no—
84Dic11⋊C4—42no—
85C4×Dic11D414yescomplemented
86#2537—111nomaximal, Sylow
87C23×C11—22no—
88C23×C11—21no—
89C23×C11—22no—
90C23×C11—21no—
91C23×C11—22no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—22no—
95C23×C11—22no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—22no—
99C23×C11C2×D412yes—
100C23×C11C2×D414yes—
101C23×C11C2411yescharacteristic
102C22×D11—21no—
103C22×D11—21no—
104C22×D11—21no—
105C22×D11—21no—
106C22×D11—21no—
107C22×D11—21no—
108C22×D11C2×D412yes—
109D4×C11—28no—
110D4×C11—48no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—44no—
118C2×C4×C11C2×D412yes—
119C2×C4×C11C2×D412yes—
120C2×C4×C11#4112yes—
121C22⋊D11—28no—
122C22⋊D11—48no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—22no—
133C2×Dic11—22no—
134C2×Dic11—48no—
135C2×Dic11C2×D412yes—
136C2×Dic11C2×D412yes—
137C2×Dic11C2×D412yes—
138C2×Dic11#4112yes—
139C4×D11—44no—
140C2×#121—111no—
141C2×#121—112no—
142C2×#121D1111yescharacteristic, complemented
143C2×C4×D4—111no—
144C2×C4×D4—111no—
145#394—112no—
146#394—112no—
147#384—111no—
148#380—111no—
149#380—111no—
150#380—112no—
151C22×C11—24no—
152C22×C11—22no—
153C22×C11—22no—
154C22×C11—24no—
155C22×C11—24no—
156C22×C11—22no—
157C22×C11—41no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—42no—
163C22×C11—42no—
164C22×C11—41no—
165C22×C11C22×D411yescharacteristic
166C22×C11C22×D411yescharacteristic
167C22×C11C22×D411yescharacteristic
168C22×C11C2×#4111yescharacteristic
169C22×C11C2×#4111yescharacteristic
170C22×C11H(5,𝔽2)11yescharacteristic
171C22×C112−1+411yescharacteristic
172C2×D11—22no—
173C2×D11—22no—
174C2×D11—22no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C4×C11—41no—
180C4×C11—42no—
181C4×C11#12114yescomplemented
182Dic11—22no—
183Dic11—41no—
184Dic11—42no—
185Dic11—42no—
186Dic11#12114yescomplemented
187C22×D4—111no—
188C22×D4—112no—
189C22×D4C2×D1112yes—
190C22×D4C2×D1111yescharacteristic
191C23×C4—112no—
192C23×C4—111no—
193C23×C4C2×D1111yescharacteristic
194#121—24no—
195#121—228no—
196#121—224no—
197C4×D4—224no—
198C4×D4—224no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—112no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—112no—
204C2×C4⋊C4C2×D1111yescharacteristic
205C2×C22⋊C4—111no—
206C2×C22⋊C4—112no—
207C2×C22⋊C4—112no—
208C2×C22⋊C4—112no—
209C2×C22⋊C4—111no—
210C2×C22⋊C4—112no—
211C2×C22⋊C4C2×D1112yes—
212C2×C42—111no—
213#95—112no—
214#95—112no—
215C2×C11—44no—
216C2×C11—42no—
217C2×C11C2×#12111yescharacteristic
218C2×C11C2×#12111yescharacteristic
219C2×C11#53711yescharacteristic
220C2×C11D4211yescharacteristic
221C2×C11#54711yescharacteristic
222C2×C11#54711yescharacteristic
223C2×C11#55511yescharacteristic
224D11—42no—
225C24—111no—
226C24C22×D1111yescharacteristic
227C24C22×D1112yes—
228C2×D4—24no—
229C2×D4—24no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—42no—
233C2×D4—114no—
234C2×D4—222no—
235C2×D4—222no—
236C2×D4—224no—
237C2×D4—224no—
238C2×D4—442no—
239C2×D4C22⋊D1114yescomplemented
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—112no—
246C22×C4—111no—
247C22×C4—112no—
248C22×C4—224no—
249C22×C4—224no—
250C22×C4—224no—
251C22×C4—222no—
252C22×C4—222no—
253C22×C4—222no—
254C22×C4C22×D1111yescharacteristic
255C22×C4C22×D1112yes—
256C22×C4C22×D1111yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—222no—
259C4⋊C4—224no—
260C4⋊C4—222no—
261C4⋊C4—222no—
262C4⋊C4—442no—
263C22⋊C4—24no—
264C22⋊C4—222no—
265C22⋊C4—224no—
266C22⋊C4—222no—
267C22⋊C4—224no—
268C22⋊C4—224no—
269C22⋊C4—224no—
270C42—114no—
271C11#253711yescharacteristic, complemented, Sylow
272C23—21no—
273C23—22no—
274C23—22no—
275C23—21no—
276C23—22no—
277C23—21no—
278C23—22no—
279C23—22no—
280C23—21no—
281C23—22no—
282C23—21no—
283C23—21no—
284C23—112no—
285C23—221no—
286C23—221no—
287C23—221no—
288C23—221no—
289C23—221no—
290C23—221no—
291C23D4×D1112yes—
292C23C2×C22⋊D1114yes—
293C23C23×D1111yescharacteristic
294D4—28no—
295D4—48no—
296D4—228no—
297D4—448no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—44no—
305C2×C4—112no—
306C2×C4—112no—
307C2×C4—112no—
308C2×C4—112no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—222no—
312C2×C4—221no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—221no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4—221no—
319C2×C4—222no—
320C2×C4—448no—
321C2×C4—444no—
322C2×C4D4×D1112yes—
323C2×C4#434112yes—
324C2×C4C2×C22⋊D1112yes—
325C22—22no—
326C22—24no—
327C22—24no—
328C22—24no—
329C22—22no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—42no—
334C22—41no—
335C22—42no—
336C22—42no—
337C22—41no—
338C22—42no—
339C22—222no—
340C22—222no—
341C22—222no—
342C22—441no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22C2×D4×D1111yescharacteristic
347C22C2×D4×D1111yescharacteristic
348C22C2×#434111yescharacteristic
349C22#6703711yescharacteristic
350C22#41×D1111yescharacteristic
351C22#6704311yescharacteristic
352C22C22×C22⋊D1111yescharacteristic
353C4—42no—
354C4—41no—
355C4—114no—
356C4—222no—
357C4—442no—
358C4—441no—
359C4—442no—
360C4#6699214yescomplemented
361C2—42no—
362C2—44no—
363C2—442no—
364C2D11×#12111yescharacteristic
365C2#1062313911yescharacteristic
366C2#1062314211yescharacteristic
367C2#1062314711yescharacteristic
368C2D4×C22⋊D1111yescharacteristic
369C2C2×#6699211yescharacteristic
370C2#1062335511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2537
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×#66992C2semidirect
3. C2×#66991C2semidirect
4. C2×D4×Dic11C2semidirect
5. C2×C4×C22⋊D11C2semidirect
6. #10622835C2semidirect
7. #10622825C2semidirect
8. #10622600C2semidirect
9. #10622589C2semidirect
10. #10622572C2semidirect
11. #10622555C2semidirect
48. C2×D4×C11D4semidirect
60. C2×C22⋊D11D4semidirect
85. C4×Dic11D4semidirect
142. C2×#121D11semidirect
181. C4×C11#121semidirect
186. Dic11#121semidirect
239. C2×D4C22⋊D11semidirect
271. C11#2537semidirect
360. 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×#669922
C2×#669912
C2×D4×Dic112
C2×C4×C22⋊D112
#106228352
#106228252
#106226002
#106225892
#106225722
#106225552
#253711