Finite Group Databasebeta

← #14682922

Subgroups — #14682922

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066865C214yesmaximal, complemented
2#13066857C212yesmaximal
3#13066853C214yesmaximal, complemented
4#13066848C212yesmaximal, complemented
5#13066843C212yesmaximal, complemented
6C2×C11×#390C211yesmaximal, characteristic
7C23×D4×C11C2211yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C11×C22⋊C4C2214yes—
10C22×C42×C11C2211yescharacteristic
11C22×C22⋊Dic11C2212yes—
12C22×C22⋊Dic11C2214yes—
13C22×C22⋊Dic11C2212yes—
14C22×C4×Dic11C2212yes—
15C11×#390C418yescomplemented
16C2×C11⋊#95C2214yes—
17C2×C11⋊#95C2214yes—
18C2×C11⋊#95C2212yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2214yes—
21C2×C11⋊#95C2212yes—
22C25×C11C2312yes—
23C22×D4×C11—24no—
24C22×D4×C11—42no—
25C22×D4×C11—41no—
26C22×D4×C11—41no—
27C22×D4×C11C2×C414yes—
28C23×C4×C11C2312yes—
29C23×C4×C11C2312yes—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11C2314yes—
32C23×Dic11C2314yes—
33C2×C11×C4⋊C4—41no—
34C2×C11×C4⋊C4—41no—
35C2×C11×C4⋊C4C2×C414yes—
36C2×C11×C22⋊C4—44no—
37C2×C11×C22⋊C4—44no—
38C2×C11×C22⋊C4C2×C4116yes—
39C2×C42×C11—42no—
40C2×C42×C11C2×C414yes—
41C2×C22⋊Dic11—28no—
42C2×C22⋊Dic11—28no—
43C2×C22⋊Dic11—42no—
44C2×C22⋊Dic11—44no—
45C2×C22⋊Dic11—44no—
46C2×C22⋊Dic11—42no—
47C2×C22⋊Dic11—44no—
48C2×C4×Dic11—44no—
49C2×C4×Dic11—42no—
50C11⋊#95—28no—
51C11⋊#95—28no—
52C11⋊#95—44no—
53C11⋊#95—42no—
54C11⋊#95—42no—
55C11⋊#95—42no—
56#14503—111nomaximal, Sylow
57C24×C11—24no—
58C24×C11—24no—
59C24×C11—24no—
60C24×C11—24no—
61C24×C11—24no—
62C24×C11—24no—
63C24×C11—22no—
64C24×C11—22no—
65C24×C11C22×C414yes—
66C24×C11C2411yescharacteristic
67C2×D4×C11—28no—
68C2×D4×C11—44no—
69C2×D4×C11—44no—
70C2×D4×C11—48no—
71C2×D4×C11—48no—
72C22×C4×C11—22no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—24no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—24no—
79C22×C4×C11—22no—
80C22×C4×C11—24no—
81C22×C4×C11—22no—
82C22×C4×C11—24no—
83C22×C4×C11C22×C414yes—
84C22×C4×C11C22×C414yes—
85C22×C4×C11C22×C412yes—
86C22×C4×C11#4114yes—
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—24no—
93C22×Dic11—24no—
94C22×Dic11—24no—
95C22×Dic11—24no—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11#4118yes—
101C11×C4⋊C4—44no—
102C11×C22⋊C4—416no—
103C42×C11—44no—
104C22⋊Dic11—48no—
105C22⋊Dic11—416no—
106C22⋊Dic11—48no—
107C4×Dic11—48no—
108C2×#390D1111yescharacteristic
109#1440—114no—
110#1438—112no—
111#1437—114no—
112#1436—112no—
113#1434—112no—
114C23×C11—24no—
115C23×C11—28no—
116C23×C11—28no—
117C23×C11—24no—
118C23×C11—24no—
119C23×C11—44no—
120C23×C11—44no—
121C23×C11—44no—
122C23×C11—44no—
123C23×C11—44no—
124C23×C11—44no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11—44no—
128C23×C11—44no—
129C23×C11—44no—
130C23×C11—44no—
131C23×C11—44no—
132C23×C11—42no—
133C23×C11—44no—
134C23×C11—42no—
135C23×C11C23×C411yescharacteristic
136C23×C11C2×#4112yes—
137C23×C11C2×#4114yes—
138C23×C11H(5,𝔽2)12yes—
139C23×C11H(5,𝔽2)11yescharacteristic
140C23×C11H(5,𝔽2)11yescharacteristic
141C23×C11H(5,𝔽2)14yes—
142D4×C11—416no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—28no—
151C2×C4×C11—24no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—44no—
157C2×C4×C11#11714yes—
158C2×Dic11—28no—
159C2×Dic11—28no—
160C2×Dic11—28no—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C2×Dic11—44no—
165C2×Dic11—44no—
166C2×Dic11—44no—
167C2×Dic11—44no—
168C2×Dic11—44no—
169C2×Dic11—44no—
170C2×Dic11—44no—
171C2×Dic11—44no—
172C23×D4C2×D1111yescharacteristic
173C22×C4⋊C4C2×D1111yescharacteristic
174C22×C22⋊C4—112no—
175C22×C22⋊C4—114no—
176C22×C22⋊C4—112no—
177C22×C22⋊C4C2×D1114yes—
178C22×C42—112no—
179C22×C42C2×D1111yescharacteristic
180#390Dic1118yescomplemented
181C2×#95—114no—
182C2×#95—114no—
183C2×#95—112no—
184C2×#95—112no—
185C2×#95—114no—
186C2×#95—112no—
187C22×C11—44no—
188C22×C11—48no—
189C22×C11—48no—
190C22×C11—44no—
191C22×C11—44no—
192C22×C11—84no—
193C22×C11—84no—
194C22×C11—84no—
195C22×C11—84no—
196C22×C11C2×#11711yescharacteristic
197C22×C11C4×#4112yes—
198C22×C11#51811yescharacteristic
199C22×C11#51811yescharacteristic
200C22×C11#51812yes—
201C22×C11#53812yes—
202C22×C11#53812yes—
203C22×C11#53814yes—
204C22×C11#54014yes—
205C22×C11#55112yes—
206C22×C11#55314yes—
207C22×C11#55512yes—
208C22×C11#55914yes—
209C22×C11#56012yes—
210C22×C11#56012yes—
211C4×C11—24no—
212C4×C11—44no—
213C4×C11—44no—
214Dic11—48no—
215Dic11—84no—
216C25C22×D1112yes—
217C22×D4—24no—
218C22×D4—42no—
219C22×D4—41no—
220C22×D4—41no—
221C22×D4C2×Dic1114yes—
222C23×C4—114no—
223C23×C4—114no—
224C23×C4C22×D1112yes—
225C23×C4C22×D1112yes—
226C23×C4C22×D1111yescharacteristic
227C2×C4⋊C4—41no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4C2×Dic1114yes—
230C2×C22⋊C4—44no—
231C2×C22⋊C4—44no—
232C2×C22⋊C4—228no—
233C2×C22⋊C4—228no—
234C2×C22⋊C4—442no—
235C2×C22⋊C4—444no—
236C2×C22⋊C4—444no—
237C2×C22⋊C4—442no—
238C2×C22⋊C4—444no—
239C2×C22⋊C4C2×Dic11116yes—
240C2×C42—42no—
241C2×C42—444no—
242C2×C42—442no—
243C2×C42C2×Dic1114yes—
244#95—228no—
245#95—228no—
246#95—442no—
247#95—442no—
248#95—444no—
249#95—442no—
250C2×C11—84no—
251C2×C11#231211yescharacteristic
252C2×C11#233312yes—
253C2×C11#235712yes—
254C2×C11#237211yescharacteristic
255C2×C11#238011yescharacteristic
256C2×C11#279714yes—
257C2×C11#280314yes—
258C24—24no—
259C24—24no—
260C24—24no—
261C24—22no—
262C24—22no—
263C24—24no—
264C24—24no—
265C24—24no—
266C24C22×Dic1114yes—
267C24C23×D1111yescharacteristic
268C2×D4—28no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—48no—
272C2×D4—48no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—118no—
285C22×C4—224no—
286C22×C4—224no—
287C22×C4—224no—
288C22×C4—224no—
289C22×C4—224no—
290C22×C4—224no—
291C22×C4—224no—
292C22×C4—224no—
293C22×C4—224no—
294C22×C4—224no—
295C22×C4—224no—
296C22×C4—224no—
297C22×C4—224no—
298C22×C4#433914yes—
299C22×C4C22×Dic1114yes—
300C22×C4C22×Dic1114yes—
301C22×C4C22×Dic1112yes—
302C4⋊C4—44no—
303C22⋊C4—416no—
304C22⋊C4—448no—
305C22⋊C4—4416no—
306C22⋊C4—448no—
307C42—44no—
308C42—448no—
309C11#1450311yescharacteristic, complemented, Sylow
310C23—24no—
311C23—28no—
312C23—24no—
313C23—24no—
314C23—28no—
315C23—42no—
316C23—42no—
317C23—44no—
318C23—44no—
319C23—44no—
320C23—44no—
321C23—44no—
322C23—44no—
323C23—44no—
324C23—44no—
325C23—44no—
326C23—44no—
327C23—44no—
328C23—44no—
329C23—42no—
330C23—42no—
331C23C2×#433912yes—
332C23#6703711yescharacteristic
333C23#6703711yescharacteristic
334C23#6703714yes—
335C23#6703712yes—
336C23#41×D1114yes—
337C23C23×Dic1111yescharacteristic
338D4—416no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—28no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—228no—
354C2×C4—228no—
355C2×C4—228no—
356C2×C4—444no—
357C2×C4—444no—
358C2×C4—444no—
359C2×C4—444no—
360C2×C4—444no—
361C2×C4—444no—
362C2×C4—444no—
363C2×C4—444no—
364C2×C4—444no—
365C2×C4—444no—
366C2×C4—444no—
367C2×C4#6697914yes—
368C22—48no—
369C22—44no—
370C22—44no—
371C22—44no—
372C22—48no—
373C22—84no—
374C22—84no—
375C22—84no—
376C22—84no—
377C22#1062302512yes—
378C22#1062302512yes—
379C22#1062308914yes—
380C22#1062309014yes—
381C22#1062314414yes—
382C22#1062314614yes—
383C22#1062320112yes—
384C22#1062321012yes—
385C22#1062325112yes—
386C22#1062325112yes—
387C22C2×#6697911yescharacteristic
388C22#1062332911yescharacteristic
389C22#1062332912yes—
390C22#1062332911yescharacteristic
391C22#41×Dic1112yes—
392C4—24no—
393C4—44no—
394C4—44no—
395C4—448no—
396C4—884no—
397C2—84no—
398C2#1307121411yescharacteristic
399C2#1307138312yes—
400C2#1307158912yes—
401C2#1307172811yescharacteristic
402C2#1307179311yescharacteristic
403C2#1307647014yes—
404C2#1307654514yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14503
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. #13066865C2semidirect
3. #13066853C2semidirect
4. #13066848C2semidirect
5. #13066843C2semidirect
15. C11×#390C4semidirect
180. #390Dic11semidirect
309. C11#14503semidirect

Maximal subgroups

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

subgroupindex
#130668652
#130668572
#130668532
#130668482
#130668432
C2×C11×#3902
#1450311