Finite Group Databasebeta

← C2×C11×#2583 #14612025

Subgroups — C2×C11×#2583 #14612025

Order 2816.

3094 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C211yesmaximal, characteristic
2C23×C11×C4⋊C4C211yesmaximal, characteristic
3C11×#2583C2116yesmaximal, direct product factor
4C2×C11×#398C212yesmaximal, complemented
5C2×C11×#395C212yesmaximal, complemented
6C2×C11×#389C214yesmaximal, complemented
7C2×C11×#385C212yesmaximal
8C2×C11×#385C212yesmaximal
9C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C2×C11×C22⋊Q8—28no—
15C2×C11×C22⋊Q8C2218yes—
16C22×C11×C4⋊C4—28no—
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2214yes—
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C4⋊C4C2218yes—
22C22×C11×C4⋊C4C2212yes—
23C22×C11×C4⋊C4C2214yes—
24C22×C11×C22⋊C4C2212yes—
25C22×C11×C22⋊C4C2212yes—
26C22×C42×C11C2212yes—
27C11×#398C22116yescomplemented
28C11×#395C22116yescomplemented
29C11×#389C22132yescomplemented
30C11×#385C22116yes—
31C11×#385C22116yes—
32C4×C11×C22⋊C4C2218yes—
33C2×C11×#95C2212yes—
34C2×C11×#95C2214yes—
35C2×C11×#95C2214yes—
36C25×C11C2311yescharacteristic
37C22×Q8×C11—24no—
38C22×Q8×C11—44no—
39C22×Q8×C11C2314yes—
40C23×C4×C11—24no—
41C23×C4×C11—28no—
42C23×C4×C11—24no—
43C23×C4×C11—44no—
44C23×C4×C11—44no—
45C23×C4×C11D418yes—
46C23×C4×C11C2314yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2314yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2314yes—
55C23×C4×C11C2314yes—
56C11×C22⋊Q8—232no—
57C2×C11×C4⋊C4—28no—
58C2×C11×C4⋊C4—28no—
59C2×C11×C4⋊C4—232no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—28no—
62C2×C11×C4⋊C4—216no—
63C2×C11×C4⋊C4—48no—
64C2×C11×C4⋊C4C2318yes—
65C2×C11×C4⋊C4C2318yes—
66C2×C11×C4⋊C4C23116yes—
67C2×C11×C4⋊C4C2318yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C23116yes—
70C2×C11×C22⋊C4—28no—
71C2×C11×C22⋊C4Q8116yescomplemented
72C2×C11×C22⋊C4C2318yes—
73C2×C11×C22⋊C4C2318yes—
74C2×C42×C11—44no—
75C2×C42×C11C2318yes—
76C11×#95C2318yes—
77C11×#95C23116yes—
78C11×#95C23116yes—
79C2×#2583C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11—24no—
81C24×C11—24no—
82C24×C11C2×D414yes—
83C24×C11C2×Q818yes—
84C24×C11C2412yes—
85C24×C11C2411yescharacteristic
86C2×Q8×C11—28no—
87C2×Q8×C11—48no—
88C2×Q8×C11—416no—
89C22×C4×C11—232no—
90C22×C4×C11—28no—
91C22×C4×C11—24no—
92C22×C4×C11—28no—
93C22×C4×C11—24no—
94C22×C4×C11—28no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—216no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—28no—
101C22×C4×C11—24no—
102C22×C4×C11—28no—
103C22×C4×C11—28no—
104C22×C4×C11—28no—
105C22×C4×C11—416no—
106C22×C4×C11—48no—
107C22×C4×C11—48no—
108C22×C4×C11—416no—
109C22×C4×C11C2×D414yes—
110C22×C4×C11C2×D414yes—
111C22×C4×C11C2×D4116yes—
112C22×C4×C11C2×Q8116yes—
113C22×C4×C11#4118yes—
114C22×C4×C11C2414yes—
115C22×C4×C11C2414yes—
116C22×C4×C11C2414yes—
117C22×C4×C11C2412yes—
118C22×C4×C11C2412yes—
119C22×C4×C11C2418yes—
120C22×C4×C11C2414yes—
121C11×C4⋊C4—216no—
122C11×C4⋊C4—216no—
123C11×C4⋊C4—28no—
124C11×C4⋊C4—216no—
125C11×C4⋊C4—232no—
126C11×C4⋊C4—416no—
127C11×C22⋊C4—216no—
128C11×C22⋊C4C2×Q8132yescomplemented
129C42×C11—48no—
130C22×C22⋊Q8C2×C1111yescharacteristic
131C23×C4⋊C4C2×C1111yescharacteristic
132#2583C2×C11116yesdirect product factor
133C2×#398C2×C1112yescomplemented
134C2×#395C2×C1112yescomplemented
135C2×#389C2×C1114yescomplemented
136C2×#385C2×C1112yes—
137C2×#385C2×C1112yes—
138C2×C4×C22⋊C4C2×C1111yescharacteristic
139C23×C11—28no—
140C23×C11—28no—
141C23×C11—232no—
142C23×C11—24no—
143C23×C11—24no—
144C23×C11C4⋊Q8116yes—
145C23×C11C22×D414yes—
146C23×C11C22×D412yes—
147C23×C11C22×Q818yes—
148C23×C11C22×Q814yes—
149C23×C11C2×#4114yes—
150C23×C11H(5,𝔽2)14yes—
151C23×C11C2511yescharacteristic
152Q8×C11—416no—
153C2×C4×C11—232no—
154C2×C4×C11—216no—
155C2×C4×C11—28no—
156C2×C4×C11—28no—
157C2×C4×C11—232no—
158C2×C4×C11—24no—
159C2×C4×C11—28no—
160C2×C4×C11—24no—
161C2×C4×C11—28no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—28no—
168C2×C4×C11—28no—
169C2×C4×C11—28no—
170C2×C4×C11—416no—
171C2×C4×C11—416no—
172C2×C4×C11—48no—
173C2×C4×C11—48no—
174C2×C4×C11—48no—
175C2×C4×C11C22×D414yes—
176C2×C4×C11C22×D414yes—
177C2×C4×C11C22×Q8116yes—
178C2×C4×C11C2×#4118yes—
179C23×Q8C22×C1111yescharacteristic
180C24×C4C22×C1111yescharacteristic
181C24×C4C22×C1111yescharacteristic
182C24×C4C22×C1111yescharacteristic
183C2×C22⋊Q8—28no—
184C2×C22⋊Q8C22×C1118yes—
185C22×C4⋊C4—28no—
186C22×C4⋊C4C22×C1118yes—
187C22×C4⋊C4C22×C1112yes—
188C22×C4⋊C4C22×C1111yescharacteristic
189C22×C4⋊C4C22×C1114yes—
190C22×C4⋊C4C22×C1112yes—
191C22×C4⋊C4C22×C1112yes—
192C22×C4⋊C4C22×C1114yes—
193C22×C22⋊C4C22×C1112yes—
194C22×C22⋊C4C22×C1112yes—
195C22×C42C22×C1112yes—
196#398C22×C11116yescomplemented
197#395C22×C11116yescomplemented
198#389C22×C11132yescomplemented
199#385C22×C11116yes—
200#385C22×C11116yes—
201C4×C22⋊C4C22×C1118yes—
202C2×#95C22×C1112yes—
203C2×#95C22×C1114yes—
204C2×#95C22×C1114yes—
205C22×C11—232no—
206C22×C11—24no—
207C22×C11—24no—
208C22×C11—216no—
209C22×C11#52514yes—
210C22×C11C2×C4⋊Q818yes—
211C22×C11C2×C4⋊Q814yes—
212C22×C11#53414yes—
213C22×C11#554116yes—
214C22×C11C23×D411yescharacteristic
215C22×C11C23×Q812yes—
216C22×C11C22×#4112yes—
217C22×C11C2×H(5,𝔽2)12yes—
218C4×C11—28no—
219C4×C11—24no—
220C4×C11—24no—
221C4×C11—216no—
222C4×C11—44no—
223C4×C11—44no—
224C4×C11—44no—
225C25C23×C1111yescharacteristic
226C22×Q8—24no—
227C22×Q8—44no—
228C22×Q8C23×C1114yes—
229C23×C4—24no—
230C23×C4—28no—
231C23×C4—24no—
232C23×C4—44no—
233C23×C4—44no—
234C23×C4D4×C1118yes—
235C23×C4C23×C1112yes—
236C23×C4C23×C1112yes—
237C23×C4C23×C1112yes—
238C23×C4C23×C1114yes—
239C23×C4C23×C1111yescharacteristic
240C23×C4C23×C1111yescharacteristic
241C23×C4C23×C1114yes—
242C23×C4C23×C1112yes—
243C23×C4C23×C1114yes—
244C23×C4C23×C1114yes—
245C22⋊Q8—232no—
246C2×C4⋊C4—28no—
247C2×C4⋊C4—28no—
248C2×C4⋊C4—232no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—28no—
251C2×C4⋊C4—216no—
252C2×C4⋊C4—48no—
253C2×C4⋊C4C23×C1118yes—
254C2×C4⋊C4C23×C1118yes—
255C2×C4⋊C4C23×C1118yes—
256C2×C4⋊C4C23×C1114yes—
257C2×C4⋊C4C23×C11116yes—
258C2×C4⋊C4C23×C11116yes—
259C2×C22⋊C4—28no—
260C2×C22⋊C4Q8×C11116yescomplemented
261C2×C22⋊C4C23×C1118yes—
262C2×C22⋊C4C23×C1118yes—
263C2×C42—44no—
264C2×C42C23×C1118yes—
265#95C23×C1118yes—
266#95C23×C11116yes—
267#95C23×C11116yes—
268C2×C11—28no—
269C2×C11#258318yesdirect product factor
270C2×C11C2×#52511yescharacteristic
271C2×C11C22×C4⋊Q811yescharacteristic
272C2×C11C2×#53411yescharacteristic
273C2×C11C2×#55414yes—
274C24—24no—
275C24—24no—
276C24C2×D4×C1114yes—
277C24C2×Q8×C1118yes—
278C24C24×C1112yes—
279C24C24×C1111yescharacteristic
280C2×Q8—28no—
281C2×Q8—48no—
282C2×Q8—416no—
283C22×C4—232no—
284C22×C4—28no—
285C22×C4—24no—
286C22×C4—28no—
287C22×C4—24no—
288C22×C4—28no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—216no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—28no—
295C22×C4—24no—
296C22×C4—28no—
297C22×C4—28no—
298C22×C4—28no—
299C22×C4—416no—
300C22×C4—48no—
301C22×C4—48no—
302C22×C4—416no—
303C22×C4C2×D4×C1114yes—
304C22×C4C2×D4×C1114yes—
305C22×C4C2×D4×C11116yes—
306C22×C4C2×Q8×C11116yes—
307C22×C4C11×#4118yes—
308C22×C4C24×C1114yes—
309C22×C4C24×C1114yes—
310C22×C4C24×C1114yes—
311C22×C4C24×C1112yes—
312C22×C4C24×C1112yes—
313C22×C4C24×C1118yes—
314C22×C4C24×C1114yes—
315C4⋊C4—216no—
316C4⋊C4—216no—
317C4⋊C4—28no—
318C4⋊C4—216no—
319C4⋊C4—232no—
320C4⋊C4—416no—
321C22⋊C4—216no—
322C22⋊C4C2×Q8×C11132yescomplemented
323C42—48no—
324C11C2×#258311yescharacteristic, direct product factor, Sylow
325C23—28no—
326C23—28no—
327C23—232no—
328C23—24no—
329C23—24no—
330C23C11×C4⋊Q8116yes—
331C23C22×D4×C1114yes—
332C23C22×D4×C1112yes—
333C23C22×Q8×C1118yes—
334C23C22×Q8×C1114yes—
335C23C2×C11×#4114yes—
336C23C11×H(5,𝔽2)14yes—
337C23C25×C1111yescharacteristic
338Q8—416no—
339C2×C4—232no—
340C2×C4—216no—
341C2×C4—28no—
342C2×C4—28no—
343C2×C4—232no—
344C2×C4—24no—
345C2×C4—28no—
346C2×C4—24no—
347C2×C4—28no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—28no—
354C2×C4—28no—
355C2×C4—28no—
356C2×C4—416no—
357C2×C4—416no—
358C2×C4—48no—
359C2×C4—48no—
360C2×C4—48no—
361C2×C4C22×D4×C1114yes—
362C2×C4C22×D4×C1114yes—
363C2×C4C22×Q8×C11116yes—
364C2×C4C2×C11×#4118yes—
365C22—24no—
366C22—24no—
367C22—216no—
368C22—232no—
369C22C11×#52514yes—
370C22C2×C11×C4⋊Q818yes—
371C22C2×C11×C4⋊Q814yes—
372C22C11×#53414yes—
373C22C11×#554116yes—
374C22C23×D4×C1111yescharacteristic
375C22C23×Q8×C1112yes—
376C22C22×C11×#4112yes—
377C22C2×C11×H(5,𝔽2)12yes—
378C4—28no—
379C4—24no—
380C4—24no—
381C4—216no—
382C4—44no—
383C4—44no—
384C4—44no—
385C2—28no—
386C2C11×#258318yesdirect product factor
387C2C2×C11×#52511yescharacteristic
388C2C22×C11×C4⋊Q811yescharacteristic
389C2C2×C11×#53411yescharacteristic
390C2C2×C11×#55414yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2583C2direct (N × H)
4. C2×C11×#398C2semidirect
5. C2×C11×#395C2semidirect
6. C2×C11×#389C2semidirect
27. C11×#398C22semidirect
28. C11×#395C22semidirect
29. C11×#389C22semidirect
71. C2×C11×C22⋊C4Q8semidirect
79. C2×#2583C11direct (N × H)
128. C11×C22⋊C4C2×Q8semidirect
132. #2583C2×C11direct (N × H)
133. C2×#398C2×C11semidirect
134. C2×#395C2×C11semidirect
135. C2×#389C2×C11semidirect
196. #398C22×C11semidirect
197. #395C22×C11semidirect
198. #389C22×C11semidirect
260. C2×C22⋊C4Q8×C11semidirect
269. C2×C11#2583direct (N × H)
322. C22⋊C4C2×Q8×C11semidirect
324. C11C2×#2583direct (N × H)
386. C2C11×#2583direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C23×C11×C4⋊C42
C11×#25832
C2×C11×#3982
C2×C11×#3952
C2×C11×#3892
C2×C11×#3852
C2×C4×C11×C22⋊C42
C2×#258311