Finite Group Databasebeta

← #14645481

Subgroups — #14645481

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068612C211yesmaximal, characteristic, complemented
2#13067284C212yesmaximal, complemented
3#13067041C212yesmaximal, complemented
4#13066940C211yesmaximal, characteristic, complemented
5C2×C11×#550C211yesmaximal, characteristic
6C22×C11×#41—21no—
7C11×#550—24no—
8C11×#550—24no—
9C2×C11×#127C412yes—
10C2×C11×#127C2211yescharacteristic
11C2×C11×#121—21no—
12C2×C11×#121—22no—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C412yes—
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66900—21no—
17#10622538C2212yes—
18#10622537C2212yes—
19#10622182—24no—
20D4⋊(C11⋊C8)—24no—
21#10622168—21no—
22#10622166—22no—
23C2×C11×#41—28no—
24C2×C11×#41—44no—
25C2×C11×#41—42no—
26C2×C11×#41—42no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11—22no—
29C22×D4×C11—22no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C412yes—
33C22×D4×C11C2×C411yescharacteristic
34C23×C4×C11—22no—
35C23×C4×C11—21no—
36C11×#127—24no—
37C11×#127—24no—
38C11×#127—22no—
39C11×#127D414yes—
40C11×#121—28no—
41C11×#121—216no—
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C4×D4×C11—24no—
45C4×D4×C11—24no—
46C4×D4×C11—22no—
47C4×D4×C11D414yes—
48C2×C11×C4⋊C4C2×C411yescharacteristic
49C2×C11×C4⋊C4D412yes—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2×C412yes—
54C2×C42×C11C2311yescharacteristic
55C2×#4318—22no—
56#66900—42no—
57C22⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)—22no—
60C4⋊(C11⋊C8)—22no—
61C4×C11⋊C8—22no—
62#8384—111nomaximal, Sylow
63C24×C11—22no—
64C24×C11—21no—
65C11×#41—416no—
66C11×#41—416no—
67C2×Q8×C11—22no—
68C2×Q8×C11—22no—
69C2×Q8×C11D812yes—
70C2×Q8×C11SD1612yes—
71C2×D4×C11—28no—
72C2×D4×C11—28no—
73C2×D4×C11—21no—
74C2×D4×C11—22no—
75C2×D4×C11—24no—
76C2×D4×C11—24no—
77C2×D4×C11—42no—
78C2×D4×C11—44no—
79C2×D4×C11—44no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C2×D4×C11—82no—
85C2×D4×C11—84no—
86C2×D4×C11C22⋊C412yes—
87C2×D4×C11C22⋊C414yes—
88C22×C4×C11—28no—
89C22×C4×C11—21no—
90C22×C4×C11—24no—
91C22×C4×C11—44no—
92C22×C4×C11—44no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—42no—
96C22×C4×C11C22⋊C412yes—
97C22×C4×C11C22⋊C412yes—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C11×C4⋊C4—21no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4C22⋊C412yes—
105C11×C22⋊C4—28no—
106C11×C22⋊C4—24no—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11C2×D412yes—
110C42×C11C2×D412yes—
111#4318—42no—
112#4318—42no—
113C2×C11⋊C8—42no—
114C2×C11⋊C8—42no—
115C2×#550D1111yescharacteristic
116#1801—111no—
117#1545—112no—
118#1486—112no—
119#1461—111no—
120C23×C11—22no—
121C23×C11—24no—
122C23×C11—42no—
123C23×C11—44no—
124C23×C11—44no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11—41no—
128C23×C11—42no—
129C23×C11—41no—
130C23×C11C2×C22⋊C411yescharacteristic
131Q8×C11—24no—
132Q8×C11—24no—
133D4×C11—24no—
134D4×C11—44no—
135D4×C11—42no—
136D4×C11—416no—
137D4×C11—44no—
138D4×C11—44no—
139D4×C11—44no—
140D4×C11—84no—
141D4×C11—88no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—416no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—44no—
152C2×C4×C11—44no—
153C2×C4×C11—42no—
154C2×C4×C11#10214yes—
155C2×C4×C11C2×C22⋊C411yescharacteristic
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×C4×C11#12012yes—
158C2×C4×C11#12012yes—
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C2×SD1611yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)12yes—
162C11⋊C8—82no—
163C11⋊C8—82no—
164C22×#41—21no—
165#550—24no—
166#550—24no—
167C2×#127Dic1112yes—
168C2×#127C2×D1111yescharacteristic
169C2×#121—21no—
170C2×#121—22no—
171C2×C4×Q8C2×D1111yescharacteristic
172C2×C4×D4Dic1112yes—
173C2×C4×D4C2×D1111yescharacteristic
174#431—112no—
175#423—112no—
176C2×#101—221no—
177#343—221no—
178#331—224no—
179D4⋊C8—224no—
180#324—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—44no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—44no—
187C22×C11—44no—
188C22×C11—42no—
189C22×C11—82no—
190C22×C11—84no—
191C22×C11—82no—
192C22×C11—84no—
193C22×C11#37911yescharacteristic
194C22×C11C2×#10211yescharacteristic
195C22×C11#41811yescharacteristic
196C4×C11—22no—
197C4×C11—21no—
198C4×C11—24no—
199C4×C11—42no—
200C4×C11—42no—
201C4×C11#41312yes—
202C4×C11#44712yes—
203C4×C11#45012yes—
204C2×#41—28no—
205C2×#41—44no—
206C2×#41—42no—
207C2×#41—42no—
208C22×Q8C22⋊D1111yescharacteristic
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—21no—
212C22×D4—21no—
213C22×D4C2×Dic1112yes—
214C22×D4C2×Dic1111yescharacteristic
215C23×C4—22no—
216C23×C4—21no—
217C2×M16—222no—
218#127—24no—
219#127—24no—
220#127—22no—
221#127C22⋊D1114yes—
222#121—28no—
223#121—216no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×D4—24no—
227C4×D4—24no—
228C4×D4—22no—
229C4×D4C22⋊D1114yes—
230C2×C4⋊C4C2×Dic1111yescharacteristic
231C2×C4⋊C4C22⋊D1112yes—
232C2×C4⋊C4C22⋊D1111yescharacteristic
233C2×C22⋊C4—22no—
234C2×C22⋊C4—21no—
235C2×C42C2×Dic1112yes—
236C2×C42C22×D1111yescharacteristic
237C4⋊C8—222no—
238C4⋊C8—222no—
239C4⋊C8—222no—
240#101—442no—
241C22⋊C8—222no—
242C4×C8—222no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—82no—
246C2×C11—84no—
247C2×C11#178511yescharacteristic
248C2×C11#178611yescharacteristic
249C2×C11#179511yescharacteristic
250C24—22no—
251C24—21no—
252#41—416no—
253#41—416no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8#432312yes—
257C2×Q8#432412yes—
258C2×D4—28no—
259C2×D4—28no—
260C2×D4—21no—
261C2×D4—22no—
262C2×D4—24no—
263C2×D4—24no—
264C2×D4—42no—
265C2×D4—44no—
266C2×D4—44no—
267C2×D4—44no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—41no—
271C2×D4—82no—
272C2×D4—84no—
273C2×D4C22⋊Dic1112yes—
274C2×D4C22⋊Dic1114yes—
275C22×C4—28no—
276C22×C4—21no—
277C22×C4—24no—
278C22×C4—44no—
279C22×C4—44no—
280C22×C4—41no—
281C22×C4—42no—
282C22×C4—41no—
283C22×C4C22⋊Dic1112yes—
284C22×C4C22⋊Dic1112yes—
285C22×C4C22×Dic1111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288M16—442no—
289M16—442no—
290C2×C8—442no—
291C2×C8—442no—
292C4⋊C4—21no—
293C4⋊C4—24no—
294C4⋊C4—22no—
295C4⋊C4C22⋊Dic1112yes—
296C22⋊C4—28no—
297C22⋊C4—24no—
298C42—22no—
299C42—22no—
300C42C2×C22⋊D1112yes—
301C42C2×C22⋊D1112yes—
302C11#838411yescharacteristic, complemented, Sylow
303C23—22no—
304C23—24no—
305C23—42no—
306C23—44no—
307C23—44no—
308C23—42no—
309C23—42no—
310C23—41no—
311C23—42no—
312C23—41no—
313C23C2×C22⋊Dic1111yescharacteristic
314Q8—24no—
315Q8—24no—
316D4—24no—
317D4—44no—
318D4—42no—
319D4—416no—
320D4—44no—
321D4—44no—
322D4—44no—
323D4—84no—
324D4—88no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—416no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—42no—
337C2×C4#6689614yes—
338C2×C4C2×#432311yescharacteristic
339C2×C4#6698512yes—
340C2×C4C2×#432411yescharacteristic
341C2×C4C2×C22⋊Dic1111yescharacteristic
342C2×C4C2×C22⋊Dic1111yescharacteristic
343C2×C4#6700612yes—
344C2×C4#6700612yes—
345C8—882no—
346C8—882no—
347C22—21no—
348C22—21no—
349C22—42no—
350C22—44no—
351C22—44no—
352C22—42no—
353C22—44no—
354C22—42no—
355C22—82no—
356C22—84no—
357C22—82no—
358C22—84no—
359C22C2×#6689611yescharacteristic
360C22#1062282811yescharacteristic
361C22#1062286011yescharacteristic
362C4—21no—
363C4—24no—
364C4—22no—
365C4—42no—
366C4—42no—
367C4#1062283012yes—
368C4#1062283112yes—
369C4#1062285012yes—
370C2—21no—
371C2—21no—
372C2—82no—
373C2—84no—
374C2#1306854411yescharacteristic
375C2#1306854711yescharacteristic
376C2#1306858611yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC2×C11×#550C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenterC2×#550D11
hypocenterC11#8384
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13068612C2semidirect
2. #13067284C2semidirect
3. #13067041C2semidirect
4. #13066940C2semidirect
302. C11#8384semidirect

Maximal subgroups

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

subgroupindex
#130686122
#130672842
#130670412
#130669402
C2×C11×#5502
#838411