Finite Group Databasebeta

← C2×C11×#2821 #14613879

Subgroups — C2×C11×#2821 #14613879

Order 2816.

2370 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C22×C11×#126C211yesmaximal, characteristic
3C11×#2821C2116yesmaximal, direct product factor
4C2×C11×#400C212yesmaximal, complemented
5C2×C11×#399C212yesmaximal
6C2×C11×#398C212yesmaximal, complemented
7C2×C11×#397C212yesmaximal
8C2×C11×#395C212yesmaximal, complemented
9C2×C11×#393C212yesmaximal
10C2×C11×#383C211yesmaximal, characteristic, complemented
11C23×Q8×C11C2212yes—
12C2×C11×C4⋊Q8—28no—
13C2×C11×C4⋊Q8C2218yescomplemented
14C2×C11×#126—28no—
15C2×C11×#126C2218yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2214yes—
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2214yes—
26C22×C42×C11C2211yescharacteristic
27C11×#400C22116yescomplemented
28C11×#399C22116yes—
29C11×#398C22116yescomplemented
30C11×#397C22116yes—
31C11×#395C22116yescomplemented
32C11×#393C22116yes—
33C11×#383C2218yescomplemented
34C2×C11×#95C2212yes—
35C2×C11×#95C2214yes—
36C2×C11×#95C2214yes—
37C2×C11×#95C2212yes—
38C2×C11×#95C2212yes—
39C25×C11C2311yescharacteristic
40C22×Q8×C11—28no—
41C22×Q8×C11—48no—
42C22×Q8×C11C2318yes—
43C23×C4×C11C2314yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2314yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C11×C4⋊Q8—232no—
52C11×#126—232no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—28no—
57C2×C11×C4⋊C4—28no—
58C2×C11×C4⋊C4—48no—
59C2×C11×C4⋊C4C2314yes—
60C2×C11×C4⋊C4C2314yes—
61C2×C11×C4⋊C4C2314yes—
62C2×C11×C4⋊C4C2318yes—
63C2×C11×C4⋊C4C2318yes—
64C2×C11×C4⋊C4C23116yes—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—48no—
69C2×C11×C22⋊C4C2314yes—
70C2×C11×C22⋊C4C2314yes—
71C2×C11×C22⋊C4C2314yes—
72C2×C11×C22⋊C4C23116yes—
73C2×C42×C11D418yes—
74C2×C42×C11C2314yes—
75C11×#95C2318yes—
76C11×#95C2318yes—
77C11×#95C2318yes—
78C11×#95C23116yes—
79C11×#95C23116yes—
80C2×#2821C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11—22no—
82C24×C11—24no—
83C24×C11—24no—
84C24×C11—24no—
85C24×C11C2412yes—
86C24×C11C2411yescharacteristic
87C2×Q8×C11—216no—
88C2×Q8×C11—416no—
89C2×Q8×C11—432no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—28no—
97C22×C4×C11—28no—
98C22×C4×C11—28no—
99C22×C4×C11—24no—
100C22×C4×C11—28no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—28no—
104C22×C4×C11—28no—
105C22×C4×C11C2×D414yes—
106C22×C4×C11C2×D414yes—
107C22×C4×C11C2×D414yes—
108C22×C4×C11C2418yes—
109C22×C4×C11C2412yes—
110C22×C4×C11C2412yes—
111C22×C4×C11C2418yes—
112C22×C4×C11C2412yes—
113C22×C4×C11C2412yes—
114C22×C4×C11C2412yes—
115C22×C4×C11C2412yes—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—28no—
118C11×C4⋊C4—28no—
119C11×C4⋊C4—216no—
120C11×C4⋊C4—216no—
121C11×C4⋊C4—416no—
122C11×C22⋊C4—28no—
123C11×C22⋊C4—28no—
124C11×C22⋊C4—28no—
125C11×C22⋊C4—416no—
126C42×C11C2×D4116yes—
127C22×C4⋊Q8C2×C1111yescharacteristic, complemented
128C22×#126C2×C1111yescharacteristic
129#2821C2×C11116yesdirect product factor
130C2×#400C2×C1112yescomplemented
131C2×#399C2×C1112yes—
132C2×#398C2×C1112yescomplemented
133C2×#397C2×C1112yes—
134C2×#395C2×C1112yescomplemented
135C2×#393C2×C1112yes—
136C2×#383C2×C1111yescharacteristic, complemented
137C23×C11—22no—
138C23×C11—24no—
139C23×C11—24no—
140C23×C11—24no—
141C23×C11—44no—
142C23×C11—44no—
143C23×C11—44no—
144C23×C11—416no—
145C23×C11C22×D412yes—
146C23×C11H(5,𝔽2)14yes—
147C23×C112−1+414yes—
148C23×C112−1+414yes—
149C23×C11C2511yescharacteristic
150Q8×C11—432no—
151C2×C4×C11—28no—
152C2×C4×C11—28no—
153C2×C4×C11—28no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—28no—
161C2×C4×C11—28no—
162C2×C4×C11—28no—
163C2×C4×C11—24no—
164C2×C4×C11—28no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—28no—
168C2×C4×C11—28no—
169C2×C4×C11—44no—
170C2×C4×C11—416no—
171C2×C4×C11—44no—
172C2×C4×C11—44no—
173C2×C4×C11—416no—
174C2×C4×C11C22×D414yes—
175C2×C4×C11C22×D414yes—
176C2×C4×C11C22×D414yes—
177C23×Q8C22×C1112yes—
178C2×C4⋊Q8—28no—
179C2×C4⋊Q8C22×C1118yescomplemented
180C2×#126—28no—
181C2×#126C22×C1118yes—
182C22×C4⋊C4C22×C1111yescharacteristic
183C22×C4⋊C4C22×C1112yes—
184C22×C4⋊C4C22×C1111yescharacteristic
185C22×C4⋊C4C22×C1112yes—
186C22×C4⋊C4C22×C1111yescharacteristic
187C22×C4⋊C4C22×C1114yes—
188C22×C22⋊C4C22×C1111yescharacteristic
189C22×C22⋊C4C22×C1111yescharacteristic
190C22×C22⋊C4C22×C1111yescharacteristic
191C22×C22⋊C4C22×C1114yes—
192C22×C42C22×C1111yescharacteristic
193#400C22×C11116yescomplemented
194#399C22×C11116yes—
195#398C22×C11116yescomplemented
196#397C22×C11116yes—
197#395C22×C11116yescomplemented
198#393C22×C11116yes—
199#383C22×C1118yescomplemented
200C2×#95C22×C1112yes—
201C2×#95C22×C1114yes—
202C2×#95C22×C1114yes—
203C2×#95C22×C1112yes—
204C2×#95C22×C1112yes—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—48no—
209C22×C11—88no—
210C22×C11#53514yes—
211C22×C11#53614yes—
212C22×C11#53614yes—
213C22×C11#563116yes—
214C22×C11C23×D411yescharacteristic
215C22×C11C2×H(5,𝔽2)12yes—
216C22×C11C2×2−1+412yes—
217C22×C11C2×2−1+412yes—
218C4×C11—24no—
219C4×C11—24no—
220C4×C11—24no—
221C4×C11—42no—
222C4×C11—48no—
223C4×C11—42no—
224C4×C11—42no—
225C4×C11—48no—
226C25C23×C1111yescharacteristic
227C22×Q8—28no—
228C22×Q8—48no—
229C22×Q8C23×C1118yes—
230C23×C4C23×C1111yescharacteristic
231C23×C4C23×C1114yes—
232C23×C4C23×C1111yescharacteristic
233C23×C4C23×C1111yescharacteristic
234C23×C4C23×C1114yes—
235C23×C4C23×C1111yescharacteristic
236C23×C4C23×C1111yescharacteristic
237C23×C4C23×C1111yescharacteristic
238C4⋊Q8—232no—
239#126—232no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—28no—
244C2×C4⋊C4—28no—
245C2×C4⋊C4—48no—
246C2×C4⋊C4C23×C1114yes—
247C2×C4⋊C4C23×C1114yes—
248C2×C4⋊C4C23×C1114yes—
249C2×C4⋊C4C23×C1118yes—
250C2×C4⋊C4C23×C1118yes—
251C2×C4⋊C4C23×C11116yes—
252C2×C22⋊C4—24no—
253C2×C22⋊C4—24no—
254C2×C22⋊C4—24no—
255C2×C22⋊C4—48no—
256C2×C22⋊C4C23×C1114yes—
257C2×C22⋊C4C23×C1114yes—
258C2×C22⋊C4C23×C1114yes—
259C2×C22⋊C4C23×C11116yes—
260C2×C42D4×C1118yes—
261C2×C42C23×C1114yes—
262#95C23×C1118yes—
263#95C23×C1118yes—
264#95C23×C1118yes—
265#95C23×C11116yes—
266#95C23×C11116yes—
267C2×C11—82no—
268C2×C11#282118yesdirect product factor
269C2×C11C2×#53511yescharacteristic
270C2×C11C2×#53611yescharacteristic
271C2×C11C2×#53611yescharacteristic
272C2×C11C2×#56314yes—
273C24—22no—
274C24—24no—
275C24—24no—
276C24—24no—
277C24C24×C1112yes—
278C24C24×C1111yescharacteristic
279C2×Q8—216no—
280C2×Q8—416no—
281C2×Q8—432no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—28no—
289C22×C4—28no—
290C22×C4—28no—
291C22×C4—24no—
292C22×C4—28no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—28no—
296C22×C4—28no—
297C22×C4C2×D4×C1114yes—
298C22×C4C2×D4×C1114yes—
299C22×C4C2×D4×C1114yes—
300C22×C4C24×C1118yes—
301C22×C4C24×C1112yes—
302C22×C4C24×C1112yes—
303C22×C4C24×C1118yes—
304C22×C4C24×C1112yes—
305C22×C4C24×C1112yes—
306C22×C4C24×C1112yes—
307C22×C4C24×C1112yes—
308C4⋊C4—28no—
309C4⋊C4—28no—
310C4⋊C4—28no—
311C4⋊C4—216no—
312C4⋊C4—216no—
313C4⋊C4—416no—
314C22⋊C4—28no—
315C22⋊C4—28no—
316C22⋊C4—28no—
317C22⋊C4—416no—
318C42C2×D4×C11116yes—
319C11C2×#282111yescharacteristic, direct product factor, Sylow
320C23—22no—
321C23—24no—
322C23—24no—
323C23—24no—
324C23—44no—
325C23—44no—
326C23—44no—
327C23—416no—
328C23C22×D4×C1112yes—
329C23C11×H(5,𝔽2)14yes—
330C23C11×2−1+414yes—
331C23C11×2−1+414yes—
332C23C25×C1111yescharacteristic
333Q8—432no—
334C2×C4—28no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—28no—
344C2×C4—28no—
345C2×C4—28no—
346C2×C4—24no—
347C2×C4—28no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—28no—
351C2×C4—28no—
352C2×C4—44no—
353C2×C4—416no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—416no—
357C2×C4C22×D4×C1114yes—
358C2×C4C22×D4×C1114yes—
359C2×C4C22×D4×C1114yes—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—48no—
364C22—88no—
365C22C11×#53514yes—
366C22C11×#53614yes—
367C22C11×#53614yes—
368C22C11×#563116yes—
369C22C23×D4×C1111yescharacteristic
370C22C2×C11×H(5,𝔽2)12yes—
371C22C2×C11×2−1+412yes—
372C22C2×C11×2−1+412yes—
373C4—24no—
374C4—24no—
375C4—24no—
376C4—48no—
377C4—42no—
378C4—42no—
379C4—42no—
380C4—48no—
381C2—82no—
382C2C11×#282118yesdirect product factor
383C2C2×C11×#53511yescharacteristic
384C2C2×C11×#53611yescharacteristic
385C2C2×C11×#53611yescharacteristic
386C2C2×C11×#56314yes—
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
1. C22×C11×C4⋊Q8C2semidirect
3. C11×#2821C2direct (N × H)
4. C2×C11×#400C2semidirect
6. C2×C11×#398C2semidirect
8. C2×C11×#395C2semidirect
10. C2×C11×#383C2semidirect
13. C2×C11×C4⋊Q8C22semidirect
27. C11×#400C22semidirect
29. C11×#398C22semidirect
31. C11×#395C22semidirect
33. C11×#383C22semidirect
80. C2×#2821C11direct (N × H)
127. C22×C4⋊Q8C2×C11semidirect
129. #2821C2×C11direct (N × H)
130. C2×#400C2×C11semidirect
132. C2×#398C2×C11semidirect
134. C2×#395C2×C11semidirect
136. C2×#383C2×C11semidirect
179. C2×C4⋊Q8C22×C11semidirect
193. #400C22×C11semidirect
195. #398C22×C11semidirect
197. #395C22×C11semidirect
199. #383C22×C11semidirect
268. C2×C11#2821direct (N × H)
319. C11C2×#2821direct (N × H)
382. C2C11×#2821direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C22×C11×#1262
C11×#28212
C2×C11×#4002
C2×C11×#3992
C2×C11×#3982
C2×C11×#3972
C2×C11×#3952
C2×C11×#3932
C2×C11×#3832
C2×#282111