Finite Group Databasebeta

← C11×#23826 #14601019

Subgroups — C11×#23826 #14601019

Order 2816.

746 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#125C211yesmaximal, characteristic, complemented
2C4×C11×#124C211yesmaximal, characteristic
3C11×#2101C212yesmaximal, complemented
4C11×#2074C211yesmaximal, characteristic, complemented
5C11×#2073C211yesmaximal, characteristic
6C11×#2042C212yesmaximal
7C11×#2026C211yesmaximal, characteristic, complemented
8C11×#2025C211yesmaximal, characteristic
9C11×#1763C212yesmaximal, complemented
10C11×#1762C212yesmaximal
11C11×#1745C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C2×C11×#124C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×C11×#103C2212yes—
17C2×C11×#103C2212yes—
18C2×C11×#102C2212yes—
19C2×C11×#102C2212yes—
20C2×C11×#97C2212yes—
21C11×#391C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#389C2212yes—
24C11×#388—22no—
25C11×#387—22no—
26C11×#382C2211yescharacteristic
27C11×#382C2211yescharacteristic
28C4×C11×C4⋊C4—22no—
29C4×C11×C4⋊C4C2212yes—
30C4×C11×C22⋊C4—22no—
31C43×C11C2211yescharacteristic
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#340C2212yes—
35C11×#340C2212yes—
36C11×#336C2211yescharacteristic
37C11×#336C2211yescharacteristic
38C11×#336C2212yes—
39C22×Q8×C11C2311yescharacteristic
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C22×C8×C11C2312yes—
43C22×C8×C11C2312yes—
44C11×#125—24no—
45C11×#124—22no—
46C11×#124—22no—
47C4×Q8×C11—24no—
48C4×D4×C11—24no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C42×C11—22no—
61C2×C42×C11D412yes—
62C2×C42×C11D412yes—
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C11×#103—24no—
67C11×#103—24no—
68C11×#102—24no—
69C11×#102—24no—
70C11×#97—24no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95—22no—
74C11×#95—22no—
75C11×#95—22no—
76#23826C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—22no—
81C2×Q8×C11#4112yes—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—21no—
85C2×D4×C11#4112yes—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—44no—
92C22×C4×C11—42no—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—44no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4#4114yes—
113C11×C22⋊C4—28no—
114C11×C22⋊C4—44no—
115C11×C22⋊C4—42no—
116C42×C11—21no—
117C42×C11—21no—
118C42×C11—22no—
119C42×C11—42no—
120C42×C11—42no—
121C42×C11—44no—
122C42×C11—42no—
123C42×C11#4114yes—
124C4×#125C2×C1111yescharacteristic, complemented
125C4×#124C2×C1111yescharacteristic
126#2101C2×C1112yescomplemented
127#2074C2×C1111yescharacteristic, complemented
128#2073C2×C1111yescharacteristic
129#2042C2×C1112yes—
130#2026C2×C1111yescharacteristic, complemented
131#2025C2×C1111yescharacteristic
132#1763C2×C1112yescomplemented
133#1762C2×C1112yes—
134#1745C2×C1111yescharacteristic, complemented
135C23×C11—22no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—42no—
139C23×C11—42no—
140C23×C11C22×D411yescharacteristic
141Q8×C11—24no—
142Q8×C11—42no—
143D4×C11—24no—
144D4×C11—42no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—24no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—84no—
167C2×C4×C11#12412yes—
168C2×C4×C11#12412yes—
169C2×C4×C11C2×#4111yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C2×C4×C11C2×#4112yes—
172C2×C4×C11C2×#4112yes—
173C8×C11—42no—
174C8×C11—42no—
175C2×#125C22×C1111yescharacteristic
176C2×#124C22×C1111yescharacteristic
177C2×C4×Q8C22×C1111yescharacteristic
178C2×C4×D4C22×C1111yescharacteristic
179C2×#103C22×C1112yes—
180C2×#103C22×C1112yes—
181C2×#102C22×C1112yes—
182C2×#102C22×C1112yes—
183C2×#97C22×C1112yes—
184#391C22×C1111yescharacteristic
185#390C22×C1111yescharacteristic
186#389C22×C1112yes—
187#388—22no—
188#387—22no—
189#382C22×C1111yescharacteristic
190#382C22×C1111yescharacteristic
191C4×C4⋊C4—22no—
192C4×C4⋊C4C22×C1112yes—
193C4×C22⋊C4—22no—
194C43C22×C1111yescharacteristic
195#340C22×C1112yes—
196#340C22×C1112yes—
197#340C22×C1112yes—
198#340C22×C1112yes—
199#336C22×C1111yescharacteristic
200#336C22×C1111yescharacteristic
201#336C22×C1112yes—
202C22×C11—44no—
203C22×C11—42no—
204C22×C11—82no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11#52511yescharacteristic
208C22×C11#52511yescharacteristic
209C22×C11C2×#12411yescharacteristic
210C22×C11#57512yes—
211C22×C11#57512yes—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—42no—
215C4×C11—42no—
216C4×C11—44no—
217C4×C11—42no—
218C4×C11—82no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11#52912yes—
222C4×C11#52912yes—
223C22×Q8C23×C1111yescharacteristic
224C22×D4C23×C1111yescharacteristic
225C23×C4—21no—
226C22×C8C23×C1112yes—
227C22×C8C23×C1112yes—
228#125—24no—
229#124—22no—
230#124—22no—
231C4×Q8—24no—
232C4×D4—24no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4C23×C1111yescharacteristic
237C2×C4⋊C4C23×C1111yescharacteristic
238C2×C4⋊C4C23×C1112yes—
239C2×C4⋊C4C23×C1112yes—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C42—21no—
244C2×C42—22no—
245C2×C42D4×C1112yes—
246C2×C42D4×C1112yes—
247C2×C42C23×C1111yescharacteristic
248C2×C42C23×C1111yescharacteristic
249C2×C42C23×C1111yescharacteristic
250#103—24no—
251#103—24no—
252#102—24no—
253#102—24no—
254#97—24no—
255#95—22no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—22no—
260C2×C11—82no—
261C2×C11#239811yescharacteristic
262C2×C11#311112yes—
263C2×C11#311112yes—
264C2×C11#314011yescharacteristic
265C2×C11#314211yescharacteristic
266C24—21no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8C11×#4112yes—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—21no—
274C2×D4C11×#4112yes—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—44no—
281C22×C4—42no—
282C22×C4C2×D4×C1112yes—
283C22×C4C2×D4×C1112yes—
284C22×C4C2×D4×C1111yescharacteristic
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C24×C1111yescharacteristic
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C4⋊C4—28no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—44no—
300C4⋊C4—42no—
301C4⋊C4C11×#4114yes—
302C22⋊C4—28no—
303C22⋊C4—44no—
304C22⋊C4—42no—
305C42—21no—
306C42—21no—
307C42—22no—
308C42—42no—
309C42—42no—
310C42—44no—
311C42—42no—
312C42C11×#4114yes—
313C11#2382611yescharacteristic, direct product factor, Sylow
314C23—22no—
315C23—41no—
316C23—41no—
317C23—42no—
318C23—42no—
319C23C22×D4×C1111yescharacteristic
320Q8—24no—
321Q8—42no—
322D4—24no—
323D4—42no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—84no—
346C2×C4C11×#12412yes—
347C2×C4C11×#12412yes—
348C2×C4C2×C11×#4111yescharacteristic
349C2×C4C2×C11×#4111yescharacteristic
350C2×C4C2×C11×#4112yes—
351C2×C4C2×C11×#4112yes—
352C8—42no—
353C8—42no—
354C22—42no—
355C22—44no—
356C22—82no—
357C22—81no—
358C22—81no—
359C22C11×#52511yescharacteristic
360C22C11×#52511yescharacteristic
361C22C2×C11×#12411yescharacteristic
362C22C11×#57512yes—
363C22C11×#57512yes—
364C4—22no—
365C4—22no—
366C4—42no—
367C4—42no—
368C4—42no—
369C4—44no—
370C4—82no—
371C4—81no—
372C4—81no—
373C4C11×#52912yes—
374C4C11×#52912yes—
375C2—82no—
376C2C11×#239811yescharacteristic
377C2C11×#311112yes—
378C2C11×#311112yes—
379C2C11×#314011yescharacteristic
380C2C11×#314211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×C11×#125C2semidirect
3. C11×#2101C2semidirect
4. C11×#2074C2semidirect
7. C11×#2026C2semidirect
9. C11×#1763C2semidirect
11. C11×#1745C2semidirect
76. #23826C11direct (N × H)
124. C4×#125C2×C11semidirect
126. #2101C2×C11semidirect
127. #2074C2×C11semidirect
130. #2026C2×C11semidirect
132. #1763C2×C11semidirect
134. #1745C2×C11semidirect
313. C11#23826direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×#1252
C4×C11×#1242
C11×#21012
C11×#20742
C11×#20732
C11×#20422
C11×#20262
C11×#20252
C11×#17632
C11×#17622
C11×#17452
#2382611