Finite Group Databasebeta

← #14643565

Subgroups — #14643565

Order 2816.

634 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077249C211yesmaximal, characteristic
2C2×#10622549C211yesmaximal, characteristic
3#13066475C214yesmaximal, complemented
4C11×#2920C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C22×C4⋊Dic11—21no—
7C11×#432—21no—
8C11×#432—21no—
9C11×#431C412yescomplemented
10C11×#431C2212yes—
11C11×#423—21no—
12C11×#407—21no—
13C4×C11×M16C412yescomplemented
14C2×C11⋊#95—21no—
15C2×C11⋊#95C412yes—
16#10622820—21no—
17#10622549—21no—
18#10622549—21no—
19#10622549C412yes—
20#10622549C2212yes—
21#10622539—21no—
22#10622539C412yescomplemented
23#10622538—21no—
24#10622538C412yescomplemented
25#10622537C2212yes—
26C4×#4318—21no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×Dic11—22no—
31C2×C11×M16—22no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11Q811yescharacteristic
42C2×C42×C11Q811yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×C4⋊Dic11—22no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—44no—
47C2×#4318—22no—
48C11×C4⋊C8—22no—
49C11×C4⋊C8—22no—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—22no—
52C11×#97—22no—
53C4×C8×C11C2×C414yescomplemented
54C11⋊#95—22no—
55C11⋊#95—22no—
56C11⋊#95—22no—
57C11⋊#95C2×C414yes—
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)—22no—
60C4⋊(C11⋊C8)—22no—
61C4⋊(C11⋊C8)C2×C414yescomplemented
62#66867—22no—
63C4×C11⋊C8—22no—
64#7959—111nomaximal, Sylow
65C24×C11C22⋊C411yescharacteristic
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11C4211yescharacteristic
71C22×C4×C11C4211yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C4⋊C411yescharacteristic
80C22×C4×C11C4⋊C411yescharacteristic
81C22×C4×C11C4⋊C411yescharacteristic
82C22×C4×C11C4⋊C411yescharacteristic
83C22×C4×C11C4⋊C411yescharacteristic
84C22×C4×C11C4⋊C411yescharacteristic
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—24no—
89C22×Dic11—44no—
90C22×Dic11—44no—
91C22×Dic11—44no—
92C11×M16—44no—
93C2×C8×C11—24no—
94C42×C11C4211yescharacteristic
95C42×C11C4211yescharacteristic
96C42×C11C22⋊C411yescharacteristic
97C42×C11C22⋊C411yescharacteristic
98C42×C11C22⋊C411yescharacteristic
99C42×C11C22⋊C411yescharacteristic
100C42×C11C4⋊C411yescharacteristic
101C42×C11C4⋊C411yescharacteristic
102C42×C11C4⋊C411yescharacteristic
103C42×C11C4⋊C411yescharacteristic
104C42×C11C4⋊C411yescharacteristic
105C42×C11C4⋊C411yescharacteristic
106C42×C11C22×C411yescharacteristic
107C42×C11C22×C411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×Q811yescharacteristic
110C4⋊Dic11—44no—
111C4⋊Dic11—44no—
112#4318—42no—
113#4318—42no—
114C2×C11⋊C8—24no—
115#2920—111no—
116#2920D1111yescharacteristic
117C2×#382—111no—
118#1286—114no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11#9511yescharacteristic
124C23×C11#9511yescharacteristic
125C23×C11C2×C22⋊C411yescharacteristic
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11#9511yescharacteristic
145C2×C4×C11#9511yescharacteristic
146C2×C4×C11#9511yescharacteristic
147C2×C4×C11#9511yescharacteristic
148C2×C4×C11#9511yescharacteristic
149C2×C4×C11#9511yescharacteristic
150C2×C4×C11C2×C4211yescharacteristic
151C2×C4×C11C2×C22⋊C411yescharacteristic
152C2×C4×C11C2×C22⋊C411yescharacteristic
153C2×C4×C11C2×C4⋊C411yescharacteristic
154C2×C4×C11C2×C4⋊C411yescharacteristic
155C2×C4×C11C2×C4⋊C411yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)12yes—
157C2×C4×C11#13712yes—
158C2×Dic11—44no—
159C2×Dic11—44no—
160C2×Dic11—44no—
161C2×Dic11—88no—
162C8×C11—44no—
163C11⋊C8—44no—
164C22×C4⋊C4—221no—
165C22×C42C2×D1111yescharacteristic
166#432—21no—
167#432—21no—
168#432—112no—
169#432—221no—
170#431—112no—
171#431—221no—
172#431Dic1112yescomplemented
173#431C2×D1112yes—
174#423—21no—
175#423—112no—
176#407—21no—
177#407—221no—
178C4×M16—221no—
179C4×M16Dic1112yescomplemented
180#382—112no—
181#382—112no—
182#382—221no—
183#382—221no—
184C2×#95—112no—
185C2×#95—221no—
186C22×C11—24no—
187C22×C11—24no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11H(3,ℤ/4)12yes—
195C22×C11#34412yes—
196C22×C11C2×#9511yescharacteristic
197C22×C11#41811yescharacteristic
198C22×C11#41911yescharacteristic
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11#41712yes—
210C4×C11#42812yes—
211Dic11—84no—
212C23×C4—222no—
213C23×C4C4×D1111yescharacteristic
214C23×C4D4411yescharacteristic
215C23×C4C22⋊D1111yescharacteristic
216C2×M16—22no—
217C2×M16—222no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—444no—
221C2×C42Dic2211yescharacteristic
222C2×C42Dic2211yescharacteristic
223C2×C42C4×D1111yescharacteristic
224C2×C42C4×D1111yescharacteristic
225C2×C42C4×D1111yescharacteristic
226C2×C42D4411yescharacteristic
227C2×C42C2×Dic1111yescharacteristic
228C2×C42C2×Dic1111yescharacteristic
229C2×C42C22⋊D1111yescharacteristic
230C2×C42C22⋊D1111yescharacteristic
231C2×C42C22⋊D1111yescharacteristic
232C2×C42C22×D1111yescharacteristic
233C4⋊C8—22no—
234C4⋊C8—22no—
235C4⋊C8—114no—
236C4⋊C8—222no—
237C22⋊C8—22no—
238C22⋊C8—22no—
239C22⋊C8—222no—
240C22⋊C8—222no—
241#97—22no—
242#97—222no—
243C4×C8—222no—
244C4×C8C2×Dic1114yescomplemented
245#95—114no—
246#95—222no—
247#95—222no—
248#95—222no—
249C2×C11—21no—
250C2×C11—22no—
251C2×C11—22no—
252C2×C11—21no—
253C2×C11C2×H(3,ℤ/4)11yescharacteristic
254C2×C11#173611yescharacteristic
255C2×C11C2×#34411yescharacteristic
256C24(C2×D11)⋊C411yescharacteristic
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—224no—
262C22×C4—444no—
263C22×C4—444no—
264C22×C4—444no—
265C22×C4C4×Dic1111yescharacteristic
266C22×C4C4×Dic1111yescharacteristic
267C22×C4Dic11⋊C411yescharacteristic
268C22×C4Dic11⋊C411yescharacteristic
269C22×C4Dic11⋊C411yescharacteristic
270C22×C4Dic11⋊C411yescharacteristic
271C22×C4C4⋊Dic1111yescharacteristic
272C22×C4C4⋊Dic1111yescharacteristic
273C22×C4(C2×D11)⋊C411yescharacteristic
274C22×C4(C2×D11)⋊C411yescharacteristic
275C22×C4(C2×D11)⋊C411yescharacteristic
276C22×C4(C2×D11)⋊C411yescharacteristic
277C22×C4(C2×D11)⋊C411yescharacteristic
278C22×C4C22⋊Dic1111yescharacteristic
279C22×C4C22⋊Dic1111yescharacteristic
280C22×C4C2×C4×D1111yescharacteristic
281C22×C4C2×D4411yescharacteristic
282C22×C4C2×C22⋊D1111yescharacteristic
283M16—44no—
284M16—442no—
285M16—442no—
286C2×C8—24no—
287C2×C8—224no—
288C4⋊C4—444no—
289C4⋊C4—444no—
290C42C4×Dic1111yescharacteristic
291C42C4×Dic1111yescharacteristic
292C42Dic11⋊C411yescharacteristic
293C42Dic11⋊C411yescharacteristic
294C42Dic11⋊C411yescharacteristic
295C42Dic11⋊C411yescharacteristic
296C42C4⋊Dic1111yescharacteristic
297C42C4⋊Dic1111yescharacteristic
298C42(C2×D11)⋊C411yescharacteristic
299C42(C2×D11)⋊C411yescharacteristic
300C42C22⋊Dic1111yescharacteristic
301C42C22⋊Dic1111yescharacteristic
302C42C2×Dic2211yescharacteristic
303C42C2×C4×D1111yescharacteristic
304C42C22×Dic1111yescharacteristic
305C42C2×C22⋊D1111yescharacteristic
306C11#795911yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—22no—
310C23—22no—
311C23C11⋊#9511yescharacteristic
312C23C11⋊#9511yescharacteristic
313C23C2×(C2×D11)⋊C411yescharacteristic
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—444no—
333C2×C4—444no—
334C2×C4—444no—
335C2×C4—888no—
336C2×C4C11⋊#9511yescharacteristic
337C2×C4C11⋊#9511yescharacteristic
338C2×C4C11⋊#9511yescharacteristic
339C2×C4C11⋊#9511yescharacteristic
340C2×C4C11⋊#9511yescharacteristic
341C2×C4C11⋊#9511yescharacteristic
342C2×C4#6696112yes—
343C2×C4#6696212yes—
344C2×C4C2×C4×Dic1111yescharacteristic
345C2×C4C2×Dic11⋊C411yescharacteristic
346C2×C4C2×Dic11⋊C411yescharacteristic
347C2×C4C2×C4⋊Dic1111yescharacteristic
348C2×C4C2×(C2×D11)⋊C411yescharacteristic
349C2×C4C2×C22⋊Dic1111yescharacteristic
350C8—44no—
351C8—444no—
352C22—24no—
353C22—24no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22#1062216912yes—
361C22#1062219412yes—
362C22#1062273311yescharacteristic
363C22#1062274411yescharacteristic
364C22C2×C11⋊#9511yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—884no—
376C4#1062273412yes—
377C4#1062274612yes—
378C2—21no—
379C2—21no—
380C2—22no—
381C2—22no—
382C2C2×#1062216911yescharacteristic
383C2#1306833611yescharacteristic
384C2C2×#1062219411yescharacteristic
subgroupG/H
centerC22C2×C11⋊#95
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#2920C2
socleC22×C11C2×#95
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2920D11
hypocenterC11#7959
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
3. #13066475C2semidirect
9. C11×#431C4semidirect
13. C4×C11×M16C4semidirect
22. #10622539C4semidirect
24. #10622538C4semidirect
53. C4×C8×C11C2×C4semidirect
61. C4⋊(C11⋊C8)C2×C4semidirect
172. #431Dic11semidirect
179. C4×M16Dic11semidirect
244. C4×C8C2×Dic11semidirect
306. C11#7959semidirect

Maximal subgroups

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

subgroupindex
#130772492
C2×#106225492
#130664752
C11×#29202
#795911