Finite Group Databasebeta

← C2×C11×#2621 #14611819

Subgroups — C2×C11×#2621 #14611819

Order 2816.

3046 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊Q8C212yesmaximal
3C22×C11×#117C211yesmaximal, characteristic
4C11×#2621C2116yesmaximal, direct product factor
5C2×C11×#398C214yesmaximal, complemented
6C2×C11×#397C214yesmaximal
7C2×C11×#391C212yesmaximal, complemented
8C2×C11×#382C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2212yes—
10C24×C4×C11C2211yescharacteristic
11C2×C11×C4⋊Q8—28no—
12C2×C11×C4⋊Q8C2218yescomplemented
13C2×C11×C22⋊Q8—216no—
14C2×C11×C22⋊Q8C22116yes—
15C2×C11×#117—28no—
16C2×C11×#117C2218yes—
17C22×C11×C4⋊C4C2214yes—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2214yes—
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C22⋊C4C2212yes—
22C22×C11×C22⋊C4C2214yes—
23C22×C42×C11C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C11×#398C22132yescomplemented
26C11×#397C22132yes—
27C11×#391C22116yescomplemented
28C11×#382C2218yescomplemented
29C2×C11×#95C2214yes—
30C2×C11×#95C2218yes—
31C25×C11C2311yescharacteristic
32C22×Q8×C11—28no—
33C22×Q8×C11—28no—
34C22×Q8×C11—28no—
35C22×Q8×C11C2318yes—
36C23×C4×C11—24no—
37C23×C4×C11—24no—
38C23×C4×C11D418yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2314yes—
41C23×C4×C11C2314yes—
42C23×C4×C11C2314yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C11×C4⋊Q8—232no—
47C11×C22⋊Q8—264no—
48C11×#117—232no—
49C2×C11×C4⋊C4—28no—
50C2×C11×C4⋊C4—28no—
51C2×C11×C4⋊C4—216no—
52C2×C11×C4⋊C4—216no—
53C2×C11×C4⋊C4C2318yes—
54C2×C11×C4⋊C4C2318yes—
55C2×C11×C4⋊C4C23116yes—
56C2×C11×C4⋊C4C23116yes—
57C2×C11×C22⋊C4—216no—
58C2×C11×C22⋊C4—28no—
59C2×C11×C22⋊C4C2318yes—
60C2×C11×C22⋊C4C23116yes—
61C2×C42×C11—24no—
62C2×C42×C11D418yes—
63C2×C42×C11C2314yes—
64C2×C42×C11C2314yes—
65C11×#95C23116yes—
66C11×#95C23132yes—
67C2×#2621C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11—22no—
69C24×C11—22no—
70C24×C11—28no—
71C24×C11C2×D414yes—
72C24×C11C2412yes—
73C24×C11C2411yescharacteristic
74C2×Q8×C11—216no—
75C2×Q8×C11—216no—
76C2×Q8×C11—216no—
77C2×Q8×C11—432no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—28no—
81C22×C4×C11—232no—
82C22×C4×C11—28no—
83C22×C4×C11—28no—
84C22×C4×C11—24no—
85C22×C4×C11—28no—
86C22×C4×C11—28no—
87C22×C4×C11—28no—
88C22×C4×C11—28no—
89C22×C4×C11—28no—
90C22×C4×C11—216no—
91C22×C4×C11C2×D418yes—
92C22×C4×C11C2×D414yes—
93C22×C4×C11C2×D4116yes—
94C22×C4×C11C2×D414yes—
95C22×C4×C11C2×D414yes—
96C22×C4×C11#4114yes—
97C22×C4×C11C2414yes—
98C22×C4×C11C2418yes—
99C22×C4×C11C2418yes—
100C22×C4×C11C2414yes—
101C22×C4×C11C2412yes—
102C22×C4×C11C2412yes—
103C11×C4⋊C4—216no—
104C11×C4⋊C4—216no—
105C11×C4⋊C4—232no—
106C11×C4⋊C4—232no—
107C11×C22⋊C4—232no—
108C11×C22⋊C4—216no—
109C42×C11—28no—
110C42×C11C2×D4116yes—
111C22×C4⋊Q8C2×C1111yescharacteristic, complemented
112C22×C22⋊Q8C2×C1112yes—
113C22×#117C2×C1111yescharacteristic
114#2621C2×C11116yesdirect product factor
115C2×#398C2×C1114yescomplemented
116C2×#397C2×C1114yes—
117C2×#391C2×C1112yescomplemented
118C2×#382C2×C1111yescharacteristic, complemented
119C23×C11—28no—
120C23×C11—216no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—28no—
124C23×C11—48no—
125C23×C11—48no—
126C23×C11C22×D414yes—
127C23×C11C22×D412yes—
128C23×C11C22×D412yes—
129C23×C11C2×#4112yes—
130C23×C112−1+418yes—
131C23×C11C2511yescharacteristic
132Q8×C11—432no—
133C2×C4×C11—28no—
134C2×C4×C11—216no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—28no—
138C2×C4×C11—232no—
139C2×C4×C11—24no—
140C2×C4×C11—28no—
141C2×C4×C11—28no—
142C2×C4×C11—28no—
143C2×C4×C11—28no—
144C2×C4×C11—28no—
145C2×C4×C11—216no—
146C2×C4×C11—416no—
147C2×C4×C11—48no—
148C2×C4×C11—416no—
149C2×C4×C11#121116yes—
150C2×C4×C11C22×D418yes—
151C2×C4×C11C22×D414yes—
152C2×C4×C11C22×D414yes—
153C2×C4×C11C22×D414yes—
154C2×C4×C11C2×#4114yes—
155C23×Q8C22×C1112yes—
156C24×C4C22×C1111yescharacteristic
157C2×C4⋊Q8—28no—
158C2×C4⋊Q8C22×C1118yescomplemented
159C2×C22⋊Q8—216no—
160C2×C22⋊Q8C22×C11116yes—
161C2×#117—28no—
162C2×#117C22×C1118yes—
163C22×C4⋊C4C22×C1114yes—
164C22×C4⋊C4C22×C1112yes—
165C22×C4⋊C4C22×C1114yes—
166C22×C4⋊C4C22×C1112yes—
167C22×C22⋊C4C22×C1112yes—
168C22×C22⋊C4C22×C1114yes—
169C22×C42C22×C1111yescharacteristic
170C22×C42C22×C1111yescharacteristic
171#398C22×C11132yescomplemented
172#397C22×C11132yes—
173#391C22×C11116yescomplemented
174#382C22×C1118yescomplemented
175C2×#95C22×C1114yes—
176C2×#95C22×C1118yes—
177C22×C11—24no—
178C22×C11—28no—
179C22×C11—416no—
180C22×C11—44no—
181C22×C11—44no—
182C22×C11C2×#12114yes—
183C22×C11#53618yes—
184C22×C11#53618yes—
185C22×C11#54118yes—
186C22×C11C23×D411yescharacteristic
187C22×C11C23×D411yescharacteristic
188C22×C11C22×#4111yescharacteristic
189C22×C11C2×2−1+414yes—
190C4×C11—24no—
191C4×C11—28no—
192C4×C11—48no—
193C4×C11—44no—
194C4×C11—48no—
195C4×C11C2×#12118yes—
196C25C23×C1111yescharacteristic
197C22×Q8—28no—
198C22×Q8—28no—
199C22×Q8—28no—
200C22×Q8C23×C1118yes—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4D4×C1118yes—
204C23×C4C23×C1114yes—
205C23×C4C23×C1114yes—
206C23×C4C23×C1112yes—
207C23×C4C23×C1112yes—
208C23×C4C23×C1111yescharacteristic
209C23×C4C23×C1114yes—
210C23×C4C23×C1111yescharacteristic
211C4⋊Q8—232no—
212C22⋊Q8—264no—
213#117—232no—
214C2×C4⋊C4—28no—
215C2×C4⋊C4—28no—
216C2×C4⋊C4—216no—
217C2×C4⋊C4—216no—
218C2×C4⋊C4C23×C1118yes—
219C2×C4⋊C4C23×C1118yes—
220C2×C4⋊C4C23×C11116yes—
221C2×C4⋊C4C23×C11116yes—
222C2×C22⋊C4—216no—
223C2×C22⋊C4—28no—
224C2×C22⋊C4C23×C1118yes—
225C2×C22⋊C4C23×C11116yes—
226C2×C42—24no—
227C2×C42D4×C1118yes—
228C2×C42C23×C1114yes—
229C2×C42C23×C1114yes—
230#95C23×C11116yes—
231#95C23×C11132yes—
232C2×C11—44no—
233C2×C11#262118yesdirect product factor
234C2×C11C22×#12111yescharacteristic
235C2×C11C2×#53612yes—
236C2×C11C2×#53612yes—
237C2×C11C2×#54112yes—
238C24—22no—
239C24—22no—
240C24—28no—
241C24C2×D4×C1114yes—
242C24C24×C1112yes—
243C24C24×C1111yescharacteristic
244C2×Q8—216no—
245C2×Q8—216no—
246C2×Q8—216no—
247C2×Q8—432no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—28no—
251C22×C4—232no—
252C22×C4—28no—
253C22×C4—28no—
254C22×C4—24no—
255C22×C4—28no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—216no—
260C22×C4—28no—
261C22×C4C2×D4×C1118yes—
262C22×C4C2×D4×C1114yes—
263C22×C4C2×D4×C11116yes—
264C22×C4C2×D4×C1114yes—
265C22×C4C2×D4×C1114yes—
266C22×C4C11×#4114yes—
267C22×C4C24×C1114yes—
268C22×C4C24×C1118yes—
269C22×C4C24×C1118yes—
270C22×C4C24×C1114yes—
271C22×C4C24×C1112yes—
272C22×C4C24×C1112yes—
273C4⋊C4—216no—
274C4⋊C4—216no—
275C4⋊C4—232no—
276C4⋊C4—232no—
277C22⋊C4—232no—
278C22⋊C4—216no—
279C42—28no—
280C42C2×D4×C11116yes—
281C11C2×#262111yescharacteristic, direct product factor, Sylow
282C23—28no—
283C23—216no—
284C23—22no—
285C23—22no—
286C23—28no—
287C23—48no—
288C23—48no—
289C23C22×D4×C1114yes—
290C23C22×D4×C1112yes—
291C23C22×D4×C1112yes—
292C23C2×C11×#4112yes—
293C23C11×2−1+418yes—
294C23C25×C1111yescharacteristic
295Q8—432no—
296C2×C4—28no—
297C2×C4—216no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—28no—
301C2×C4—232no—
302C2×C4—24no—
303C2×C4—28no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—28no—
308C2×C4—216no—
309C2×C4—416no—
310C2×C4—48no—
311C2×C4—416no—
312C2×C4C11×#121116yes—
313C2×C4C22×D4×C1118yes—
314C2×C4C22×D4×C1114yes—
315C2×C4C22×D4×C1114yes—
316C2×C4C22×D4×C1114yes—
317C2×C4C2×C11×#4114yes—
318C22—24no—
319C22—28no—
320C22—44no—
321C22—44no—
322C22—416no—
323C22C2×C11×#12114yes—
324C22C11×#53618yes—
325C22C11×#53618yes—
326C22C11×#54118yes—
327C22C23×D4×C1111yescharacteristic
328C22C23×D4×C1111yescharacteristic
329C22C22×C11×#4111yescharacteristic
330C22C2×C11×2−1+414yes—
331C4—24no—
332C4—28no—
333C4—48no—
334C4—44no—
335C4—48no—
336C4C2×C11×#12118yes—
337C2—44no—
338C2C11×#262118yesdirect product factor
339C2C22×C11×#12111yescharacteristic
340C2C2×C11×#53612yes—
341C2C2×C11×#53612yes—
342C2C2×C11×#54112yes—
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
4. C11×#2621C2direct (N × H)
5. C2×C11×#398C2semidirect
7. C2×C11×#391C2semidirect
8. C2×C11×#382C2semidirect
12. C2×C11×C4⋊Q8C22semidirect
25. C11×#398C22semidirect
27. C11×#391C22semidirect
28. C11×#382C22semidirect
67. C2×#2621C11direct (N × H)
111. C22×C4⋊Q8C2×C11semidirect
114. #2621C2×C11direct (N × H)
115. C2×#398C2×C11semidirect
117. C2×#391C2×C11semidirect
118. C2×#382C2×C11semidirect
158. C2×C4⋊Q8C22×C11semidirect
171. #398C22×C11semidirect
173. #391C22×C11semidirect
174. #382C22×C11semidirect
233. C2×C11#2621direct (N × H)
281. C11C2×#2621direct (N × H)
338. C2C11×#2621direct (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×C22⋊Q82
C22×C11×#1172
C11×#26212
C2×C11×#3982
C2×C11×#3972
C2×C11×#3912
C2×C11×#3822
C2×#262111