Finite Group Databasebeta

← C11×#11802 #14588995

Subgroups — C11×#11802 #14588995

Order 2816.

758 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#394C211yesmaximal, characteristic
2C11×#1821C211yesmaximal, characteristic, complemented
3C11×#1463C211yesmaximal, characteristic, complemented
4C11×#1345C214yesmaximal, complemented
5C23×D4×C11C411yescharacteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C22×C11×C22⋊C4—21no—
8C22×C11×C22⋊C4—21no—
9C11×#407—21no—
10C11×#407—21no—
11C11×#394—21no—
12C11×#394—21no—
13C11×#394C412yes—
14C11×#394C2212yes—
15C2×C11×#95C411yescharacteristic
16C11×#343—21no—
17C11×#343C2212yescomplemented
18C11×#324—21no—
19C11×#324C2212yescomplemented
20C25×C11—21no—
21C22×D4×C11—21no—
22C22×D4×C11—41no—
23C22×D4×C11—41no—
24C22×D4×C11—44no—
25C22×D4×C11C2×C412yes—
26C23×C4×C11—21no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C2×C11×M16—22no—
31C2×C11×M16—41no—
32C2×C11×C4⋊C4—41no—
33C2×C11×C4⋊C4—41no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—44no—
43C2×C11×C22⋊C4—44no—
44C11×C22⋊C8—22no—
45C11×C22⋊C8—41no—
46C11×C22⋊C8—41no—
47C11×C22⋊C8—41no—
48C11×#95—21no—
49C11×#95C2×C412yes—
50#11802C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11—24no—
52C24×C11—22no—
53C24×C11—42no—
54C24×C11—42no—
55C24×C11—42no—
56C24×C11—42no—
57C24×C11—42no—
58C24×C11—41no—
59C24×C11—41no—
60C24×C11C22⋊C411yescharacteristic
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C2×D4×C11—44no—
64C2×D4×C11—48no—
65C2×D4×C11—44no—
66C2×D4×C11—44no—
67C2×D4×C11—44no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—41no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C11×M16—42no—
89C11×M16—42no—
90C11×M16—82no—
91C2×C8×C11—42no—
92C2×C8×C11—42no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—44no—
98C11×C22⋊C4—44no—
99C11×C22⋊C4—44no—
100C11×C22⋊C4—44no—
101C2×#394C2×C1111yescharacteristic
102#1821C2×C1111yescharacteristic, complemented
103#1463C2×C1111yescharacteristic, complemented
104#1345C2×C1114yescomplemented
105C23×C11—22no—
106C23×C11—22no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—24no—
110C23×C11—42no—
111C23×C11—44no—
112C23×C11—48no—
113C23×C11—48no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—44no—
117C23×C11—42no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—84no—
121C23×C11—84no—
122C23×C11—82no—
123C23×C11—82no—
124C23×C11—82no—
125C23×C11—82no—
126C23×C11#9911yescharacteristic
127C23×C11#9911yescharacteristic
128C23×C11C2×C22⋊C411yescharacteristic
129D4×C11—44no—
130D4×C11—48no—
131D4×C11—44no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—81no—
154C2×C4×C11—84no—
155C2×C4×C11AGL(1,ℤ/8)12yes—
156C8×C11—82no—
157C8×C11—82no—
158C23×D4C4×C1111yescharacteristic
159C22×C4⋊C4C22×C1111yescharacteristic
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162#407—21no—
163#407—21no—
164#394—21no—
165#394—21no—
166#394C4×C1112yes—
167#394C22×C1112yes—
168C2×#95C4×C1111yescharacteristic
169#343—21no—
170#343C22×C1112yescomplemented
171#324—21no—
172#324C22×C1112yescomplemented
173C22×C11—24no—
174C22×C11—24no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—44no—
182C22×C11—44no—
183C22×C11—44no—
184C22×C11—82no—
185C22×C11—82no—
186C22×C11—88no—
187C22×C11—88no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11AΣL(1,𝔽16)12yes—
191C22×C11#35512yes—
192C22×C11C2×#9911yescharacteristic
193C22×C11#41811yescharacteristic
194C22×C11#42111yescharacteristic
195C4×C11—22no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—82no—
202C25—21no—
203C22×D4—21no—
204C22×D4—41no—
205C22×D4—41no—
206C22×D4—44no—
207C22×D4C2×C4×C1112yes—
208C23×C4—21no—
209C23×C4C2×C4×C1111yescharacteristic
210C23×C4D4×C1111yescharacteristic
211C23×C4D4×C1111yescharacteristic
212C2×M16—22no—
213C2×M16—41no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4C2×C4×C1111yescharacteristic
217C2×C4⋊C4D4×C1111yescharacteristic
218C2×C4⋊C4D4×C1111yescharacteristic
219C2×C4⋊C4C23×C1111yescharacteristic
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—44no—
225C2×C22⋊C4—44no—
226C22⋊C8—22no—
227C22⋊C8—41no—
228C22⋊C8—41no—
229C22⋊C8—41no—
230#95—21no—
231#95C2×C4×C1112yes—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—22no—
235C2×C11—22no—
236C2×C11—84no—
237C2×C11#151011yescharacteristic
238C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
239C2×C11C2×#35511yescharacteristic
240C24—24no—
241C24—22no—
242C24—42no—
243C24—42no—
244C24—42no—
245C24—42no—
246C24—42no—
247C24—41no—
248C24—41no—
249C24C11×C22⋊C411yescharacteristic
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—44no—
253C2×D4—44no—
254C2×D4—48no—
255C2×D4—44no—
256C2×D4—44no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4C11×C22⋊C411yescharacteristic
272C22×C4C11×C22⋊C411yescharacteristic
273C22×C4C11×C22⋊C411yescharacteristic
274C22×C4C22×C4×C1111yescharacteristic
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C2×D4×C1111yescharacteristic
277M16—42no—
278M16—42no—
279M16—82no—
280C2×C8—42no—
281C2×C8—42no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—44no—
287C22⋊C4—44no—
288C22⋊C4—44no—
289C22⋊C4—44no—
290C11#1180211yescharacteristic, direct product factor, Sylow
291C23—22no—
292C23—22no—
293C23—21no—
294C23—21no—
295C23—24no—
296C23—42no—
297C23—44no—
298C23—48no—
299C23—48no—
300C23—42no—
301C23—42no—
302C23—44no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—84no—
307C23—84no—
308C23—82no—
309C23—82no—
310C23—82no—
311C23—82no—
312C23C11×#9911yescharacteristic
313C23C11×#9911yescharacteristic
314C23C2×C11×C22⋊C411yescharacteristic
315D4—44no—
316D4—44no—
317D4—48no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—84no—
341C2×C4C11×AGL(1,ℤ/8)12yes—
342C8—82no—
343C8—82no—
344C22—24no—
345C22—24no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—44no—
353C22—44no—
354C22—44no—
355C22—82no—
356C22—82no—
357C22—88no—
358C22—88no—
359C22—82no—
360C22—82no—
361C22C11×AΣL(1,𝔽16)12yes—
362C22C11×#35512yes—
363C22C2×C11×#9911yescharacteristic
364C22C11×#41811yescharacteristic
365C22C11×#42111yescharacteristic
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—82no—
373C2—21no—
374C2—21no—
375C2—22no—
376C2—22no—
377C2—84no—
378C2C11×#151011yescharacteristic
379C2C2×C11×AΣL(1,𝔽16)11yescharacteristic
380C2C2×C11×#35511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC23×D4×C11C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1821C2semidirect
3. C11×#1463C2semidirect
4. C11×#1345C2semidirect
17. C11×#343C22semidirect
19. C11×#324C22semidirect
50. #11802C11direct (N × H)
102. #1821C2×C11semidirect
103. #1463C2×C11semidirect
104. #1345C2×C11semidirect
170. #343C22×C11semidirect
172. #324C22×C11semidirect
290. C11#11802direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3942
C11×#18212
C11×#14632
C11×#13452
#1180211