Finite Group Databasebeta

← C11×#21990 #14599183

Subgroups — C11×#21990 #14599183

Order 2816.

762 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
1C2×C11×#433C211yesmaximal, characteristic
2C11×#2317C211yesmaximal, characteristic
3C11×#2314C211yesmaximal, characteristic
4C11×#1949C212yesmaximal, complemented
5C11×#1948C212yesmaximal, complemented
6C11×#1854C212yesmaximal
7C11×#1853C212yesmaximal
8C11×#1847C211yesmaximal, characteristic, complemented
9C11×#1844C211yesmaximal, characteristic, complemented
10C11×#1836C211yesmaximal, characteristic, complemented
11C11×#1835C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C11×#433C418yescomplemented
16C2×C11×#107C2212yes—
17C2×C11×#106C2212yes—
18C2×C11×#106C2212yes—
19C2×C11×#106C2212yes—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C22⋊C8C2212yes—
22C2×C11×#97C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#389—22no—
25C11×#388—22no—
26C11×#387—22no—
27C11×#385—22no—
28C11×#384C2211yescharacteristic
29C11×#384C2211yescharacteristic
30C11×#384C2211yescharacteristic
31C11×#382C2211yescharacteristic
32C11×#382C2211yescharacteristic
33C11×#382C2211yescharacteristic
34C11×#380C2212yes—
35C4×C11×C4⋊C4C2212yes—
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C22×C8×C11C2312yes—
43C22×C8×C11C2312yes—
44C11×#117—42no—
45C11×#117C2×C414yes—
46C11×#117Q814yes—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—42no—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4D412yes—
62C2×C42×C11—21no—
63C2×C42×C11—22no—
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C11×#107—42no—
67C11×#106—42no—
68C11×#106—42no—
69C11×#106—42no—
70C11×C4⋊C8C2×C418yescomplemented
71C11×C22⋊C8C2×C418yes—
72C11×#97C2×C414yescomplemented
73C4×C8×C11C2×C414yescomplemented
74C11×#95—22no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79#21990C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11C2×D411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—42no—
90C22×C4×C11—82no—
91C22×C4×C11C22×C412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×Q812yes—
96C22×C4×C11C2411yescharacteristic
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11C22×C414yes—
102C2×C8×C11C22×C414yes—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—82no—
112C11×C4⋊C4—82no—
113C11×C4⋊C4—82no—
114C11×C4⋊C4C4⋊C418yes—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—82no—
117C11×C22⋊C4C4⋊C418yes—
118C42×C11—42no—
119C42×C11—82no—
120C42×C11C22×C412yes—
121C42×C11C22×C412yes—
122C42×C11C2×Q812yes—
123C42×C11C2×Q812yes—
124C2×#433C2×C1111yescharacteristic
125#2317C2×C1111yescharacteristic
126#2314C2×C1111yescharacteristic
127#1949C2×C1112yescomplemented
128#1948C2×C1112yescomplemented
129#1854C2×C1112yes—
130#1853C2×C1112yes—
131#1847C2×C1111yescharacteristic, complemented
132#1844C2×C1111yescharacteristic, complemented
133#1836C2×C1111yescharacteristic, complemented
134#1835C2×C1111yescharacteristic, complemented
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—22no—
138C23×C11—22no—
139C23×C11C2×C4⋊C412yes—
140C23×C11C22×D411yescharacteristic
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—84no—
164C2×C4×C11C2×C4⋊C414yes—
165C2×C4×C11C2×C4⋊C414yes—
166C2×C4×C11C2×C4⋊C412yes—
167C2×C4×C11C23×C411yescharacteristic
168C2×C4×C11C22×Q811yescharacteristic
169C2×C4×C11H(5,𝔽2)12yes—
170C2×C4×C112−1+412yes—
171C8×C11—24no—
172C8×C11—24no—
173C2×#117C22×C1111yescharacteristic
174C2×#117C22×C1111yescharacteristic
175C22×C4⋊C4C22×C1111yescharacteristic
176#433C4×C1118yescomplemented
177C2×#107C22×C1112yes—
178C2×#106C22×C1112yes—
179C2×#106C22×C1112yes—
180C2×#106C22×C1112yes—
181C2×C4⋊C8C22×C1112yes—
182C2×C22⋊C8C22×C1112yes—
183C2×#97C22×C1111yescharacteristic
184C2×C4×C8C22×C1111yescharacteristic
185#389—22no—
186#388—22no—
187#387—22no—
188#385—22no—
189#384C22×C1111yescharacteristic
190#384C22×C1111yescharacteristic
191#384C22×C1111yescharacteristic
192#382C22×C1111yescharacteristic
193#382C22×C1111yescharacteristic
194#382C22×C1111yescharacteristic
195#380C22×C1112yes—
196C4×C4⋊C4C22×C1112yes—
197#340C22×C1112yes—
198#340C22×C1112yes—
199#340C22×C1112yes—
200#340C22×C1112yes—
201C22×C11—22no—
202C22×C11—24no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—42no—
206C22×C11C22×C4⋊C411yescharacteristic
207C22×C11#53511yescharacteristic
208C22×C11#53611yescharacteristic
209C22×C11#57712yes—
210C22×C11#57712yes—
211C4×C11—22no—
212C4×C11—24no—
213C4×C11—24no—
214C4×C11—81no—
215C4×C11—82no—
216C4×C11—81no—
217C4×C11—81no—
218C4×C11—81no—
219C4×C11—82no—
220C4×C11#52012yes—
221C4×C11#54412yes—
222C23×C4—21no—
223C23×C4C23×C1111yescharacteristic
224C22×C8C23×C1112yes—
225C22×C8C23×C1112yes—
226#117—42no—
227#117C2×C4×C1114yes—
228#117Q8×C1114yes—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4D4×C1112yes—
235C2×C4⋊C4C23×C1111yescharacteristic
236C2×C4⋊C4C23×C1111yescharacteristic
237C2×C4⋊C4C23×C1111yescharacteristic
238C2×C4⋊C4C23×C1111yescharacteristic
239C2×C4⋊C4C23×C1112yes—
240C2×C4⋊C4C23×C1112yes—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4D4×C1112yes—
244C2×C42—21no—
245C2×C42—22no—
246C2×C42C23×C1111yescharacteristic
247C2×C42C23×C1111yescharacteristic
248#107—42no—
249#106—42no—
250#106—42no—
251#106—42no—
252C4⋊C8C2×C4×C1118yescomplemented
253C22⋊C8C2×C4×C1118yes—
254#97C2×C4×C1114yescomplemented
255C4×C8C2×C4×C1114yescomplemented
256#95—22no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95—22no—
261C2×C11—42no—
262C2×C11#231711yescharacteristic
263C2×C11#291212yes—
264C2×C11#322111yescharacteristic
265C2×C11#322211yescharacteristic
266C2×C11#324412yes—
267C24C2×D4×C1111yescharacteristic
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—42no—
277C22×C4—82no—
278C22×C4C22×C4×C1112yes—
279C22×C4C2×D4×C1112yes—
280C22×C4C2×D4×C1111yescharacteristic
281C22×C4C2×D4×C1112yes—
282C22×C4C2×Q8×C1112yes—
283C22×C4C24×C1111yescharacteristic
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8C22×C4×C1114yes—
289C2×C8C22×C4×C1114yes—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—24no—
297C4⋊C4—42no—
298C4⋊C4—82no—
299C4⋊C4—82no—
300C4⋊C4—82no—
301C4⋊C4C11×C4⋊C418yes—
302C22⋊C4—42no—
303C22⋊C4—82no—
304C22⋊C4C11×C4⋊C418yes—
305C42—42no—
306C42—82no—
307C42C22×C4×C1112yes—
308C42C22×C4×C1112yes—
309C42C2×Q8×C1112yes—
310C42C2×Q8×C1112yes—
311C11#2199011yescharacteristic, direct product factor, Sylow
312C23—21no—
313C23—21no—
314C23—22no—
315C23—22no—
316C23C2×C11×C4⋊C412yes—
317C23C22×D4×C1111yescharacteristic
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—84no—
341C2×C4C2×C11×C4⋊C414yes—
342C2×C4C2×C11×C4⋊C414yes—
343C2×C4C2×C11×C4⋊C412yes—
344C2×C4C23×C4×C1111yescharacteristic
345C2×C4C22×Q8×C1111yescharacteristic
346C2×C4C11×H(5,𝔽2)12yes—
347C2×C4C11×2−1+412yes—
348C8—24no—
349C8—24no—
350C22—24no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—42no—
355C22C22×C11×C4⋊C411yescharacteristic
356C22C11×#53511yescharacteristic
357C22C11×#53611yescharacteristic
358C22C11×#57712yes—
359C22C11×#57712yes—
360C4—24no—
361C4—24no—
362C4—22no—
363C4—81no—
364C4—82no—
365C4—81no—
366C4—81no—
367C4—81no—
368C4—82no—
369C4C11×#52012yes—
370C4C11×#54412yes—
371C2—42no—
372C2C11×#231711yescharacteristic
373C2C11×#291212yes—
374C2C11×#322111yescharacteristic
375C2C11×#322211yescharacteristic
376C2C11×#324412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1949C2semidirect
5. C11×#1948C2semidirect
8. C11×#1847C2semidirect
9. C11×#1844C2semidirect
10. C11×#1836C2semidirect
11. C11×#1835C2semidirect
15. C11×#433C4semidirect
70. C11×C4⋊C8C2×C4semidirect
72. C11×#97C2×C4semidirect
73. C4×C8×C11C2×C4semidirect
79. #21990C11direct (N × H)
127. #1949C2×C11semidirect
128. #1948C2×C11semidirect
131. #1847C2×C11semidirect
132. #1844C2×C11semidirect
133. #1836C2×C11semidirect
134. #1835C2×C11semidirect
176. #433C4×C11semidirect
252. C4⋊C8C2×C4×C11semidirect
254. #97C2×C4×C11semidirect
255. C4×C8C2×C4×C11semidirect
311. C11#21990direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4332
C11×#23172
C11×#23142
C11×#19492
C11×#19482
C11×#18542
C11×#18532
C11×#18472
C11×#18442
C11×#18362
C11×#18352
#2199011