Finite Group Databasebeta

← C11×#23822 #14601015

Subgroups — C11×#23822 #14601015

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C4×C11×#127C211yesmaximal, characteristic
3C11×#2100C212yesmaximal, complemented
4C11×#2071C212yesmaximal, complemented
5C11×#2041C212yesmaximal
6C11×#2023C212yesmaximal, complemented
7C11×#1762C214yesmaximal, complemented
8C11×#1745C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C4×Q8×C11—21no—
12C2×C4×D4×C11—21no—
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2212yes—
15C2×C11×#102C2214yes—
16C2×C11×#102C2214yes—
17C2×C11×#97C2212yes—
18C11×#391—21no—
19C11×#390—21no—
20C11×#390—21no—
21C11×#390C2212yes—
22C11×#389—21no—
23C11×#389C2212yes—
24C11×#384C2211yescharacteristic
25C11×#384C2211yescharacteristic
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2212yes—
28C43×C11C2211yescharacteristic
29C11×#340C2214yes—
30C11×#340C2214yes—
31C11×#336C2212yes—
32C11×#336C2212yes—
33C22×Q8×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11C2312yes—
37C23×C4×C11—22no—
38C22×C8×C11C2314yes—
39C11×C4⋊Q8—24no—
40C11×#127—24no—
41C4×Q8×C11—44no—
42C4×D4×C11—28no—
43C4×D4×C11—44no—
44C4×D4×C11—44no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—22no—
57C2×C42×C11—22no—
58C2×C42×C11D411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D411yescharacteristic
61C2×C42×C11D411yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C11×#102—28no—
66C11×#102—28no—
67C11×#97—24no—
68C11×#95—22no—
69C11×#95—22no—
70#23822C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—22no—
72C2×Q8×C11—24no—
73C2×Q8×C11—42no—
74C2×Q8×C11—42no—
75C2×D4×C11—24no—
76C2×D4×C11—24no—
77C2×D4×C11—24no—
78C2×D4×C11—24no—
79C2×D4×C11—22no—
80C2×D4×C11—42no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11#4114yes—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—44no—
89C22×C4×C11—44no—
90C22×C4×C11—44no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C2×C8×C11—24no—
99C2×C8×C11—24no—
100C2×C8×C11—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4—44no—
110C11×C4⋊C4#4114yes—
111C11×C22⋊C4—44no—
112C11×C22⋊C4—44no—
113C11×C22⋊C4—44no—
114C42×C11—22no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11—22no—
119C42×C11—22no—
120C42×C11—44no—
121C42×C11#4114yes—
122C4×C4⋊Q8C2×C1111yescharacteristic, complemented
123C4×#127C2×C1111yescharacteristic
124#2100C2×C1112yescomplemented
125#2071C2×C1112yescomplemented
126#2041C2×C1112yes—
127#2023C2×C1112yescomplemented
128#1762C2×C1114yescomplemented
129#1745C2×C1111yescharacteristic, complemented
130C23×C11—24no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11C22×D411yescharacteristic
138Q8×C11—48no—
139D4×C11—28no—
140D4×C11—48no—
141D4×C11—48no—
142D4×C11—44no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—24no—
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—42no—
164C2×C4×C11—88no—
165C2×C4×C11#12412yes—
166C2×C4×C11#12412yes—
167C2×C4×C11AGL(1,ℤ/8)12yes—
168C2×C4×C11AGL(1,ℤ/8)12yes—
169C2×C4×C11AGL(1,ℤ/8)12yes—
170C2×C4×C11#13712yes—
171C2×C4×C11C2×#4112yes—
172C2×C4×C11C2×#4112yes—
173C2×C4×C11C2×#4112yes—
174C8×C11—44no—
175C2×C4⋊Q8C22×C1111yescharacteristic
176C2×#127C22×C1111yescharacteristic
177C2×C4×Q8—21no—
178C2×C4×D4—21no—
179C2×C4×D4—21no—
180C2×C4×D4C22×C1112yes—
181C2×#102C22×C1114yes—
182C2×#102C22×C1114yes—
183C2×#97C22×C1112yes—
184#391—21no—
185#390—21no—
186#390—21no—
187#390C22×C1112yes—
188#389—21no—
189#389C22×C1112yes—
190#384C22×C1111yescharacteristic
191#384C22×C1111yescharacteristic
192C4×C4⋊C4—21no—
193C4×C4⋊C4C22×C1112yes—
194C43C22×C1111yescharacteristic
195#340C22×C1114yes—
196#340C22×C1114yes—
197#336C22×C1112yes—
198#336C22×C1112yes—
199C22×C11—44no—
200C22×C11—44no—
201C22×C11—44no—
202C22×C11—82no—
203C22×C11—82no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11#52511yescharacteristic
207C22×C11#52511yescharacteristic
208C22×C11C2×#12411yescharacteristic
209C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
210C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
211C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
212C22×C11C2×#13711yescharacteristic
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—22no—
217C4×C11—22no—
218C4×C11—22no—
219C4×C11—44no—
220C4×C11—82no—
221C4×C11—82no—
222C4×C11#52914yes—
223C22×Q8—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4C23×C1112yes—
227C23×C4—22no—
228C22×C8C23×C1114yes—
229C4⋊Q8—24no—
230#127—24no—
231C4×Q8—44no—
232C4×D4—28no—
233C4×D4—44no—
234C4×D4—44no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C23×C1112yes—
242C2×C4⋊C4C23×C1112yes—
243C2×C4⋊C4C23×C1112yes—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C42—22no—
248C2×C42D4×C1111yescharacteristic
249C2×C42D4×C1111yescharacteristic
250C2×C42D4×C1111yescharacteristic
251C2×C42D4×C1111yescharacteristic
252C2×C42C23×C1111yescharacteristic
253C2×C42C23×C1111yescharacteristic
254C2×C42C23×C1111yescharacteristic
255#102—28no—
256#102—28no—
257#97—24no—
258#95—22no—
259#95—22no—
260C2×C11—84no—
261C2×C11#239811yescharacteristic
262C2×C11#310911yescharacteristic
263C2×C11#310911yescharacteristic
264C2×C11#311011yescharacteristic
265C2×C11#311211yescharacteristic
266C2×C11#313811yescharacteristic
267C2×C11#314111yescharacteristic
268C24—22no—
269C2×Q8—24no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×D4—24no—
273C2×D4—24no—
274C2×D4—24no—
275C2×D4—24no—
276C2×D4—22no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4C11×#4114yes—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—44no—
286C22×C4—44no—
287C22×C4—44no—
288C22×C4C2×D4×C1111yescharacteristic
289C22×C4C2×D4×C1111yescharacteristic
290C22×C4C2×D4×C1111yescharacteristic
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C2×D4×C1111yescharacteristic
294C22×C4C24×C1111yescharacteristic
295C2×C8—24no—
296C2×C8—24no—
297C2×C8—24no—
298C4⋊C4—24no—
299C4⋊C4—22no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—44no—
306C4⋊C4—42no—
307C4⋊C4C11×#4114yes—
308C22⋊C4—44no—
309C22⋊C4—44no—
310C22⋊C4—44no—
311C42—22no—
312C42—22no—
313C42—22no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—44no—
318C42C11×#4114yes—
319C11#2382211yescharacteristic, direct product factor, Sylow
320C23—24no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23C22×D4×C1111yescharacteristic
328Q8—48no—
329D4—28no—
330D4—48no—
331D4—48no—
332D4—44no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—24no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—88no—
355C2×C4C11×#12412yes—
356C2×C4C11×#12412yes—
357C2×C4C11×AGL(1,ℤ/8)12yes—
358C2×C4C11×AGL(1,ℤ/8)12yes—
359C2×C4C11×AGL(1,ℤ/8)12yes—
360C2×C4C11×#13712yes—
361C2×C4C2×C11×#4112yes—
362C2×C4C2×C11×#4112yes—
363C2×C4C2×C11×#4112yes—
364C8—44no—
365C22—44no—
366C22—44no—
367C22—44no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22C11×#52511yescharacteristic
373C22C11×#52511yescharacteristic
374C22C2×C11×#12411yescharacteristic
375C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
376C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
377C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
378C22C2×C11×#13711yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—22no—
384C4—22no—
385C4—44no—
386C4—82no—
387C4—82no—
388C4C11×#52914yes—
389C2—84no—
390C2C11×#239811yescharacteristic
391C2C11×#310911yescharacteristic
392C2C11×#310911yescharacteristic
393C2C11×#311011yescharacteristic
394C2C11×#311211yescharacteristic
395C2C11×#313811yescharacteristic
396C2C11×#314111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
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×C4⋊Q8C2semidirect
3. C11×#2100C2semidirect
4. C11×#2071C2semidirect
6. C11×#2023C2semidirect
7. C11×#1762C2semidirect
8. C11×#1745C2semidirect
70. #23822C11direct (N × H)
122. C4×C4⋊Q8C2×C11semidirect
124. #2100C2×C11semidirect
125. #2071C2×C11semidirect
127. #2023C2×C11semidirect
128. #1762C2×C11semidirect
129. #1745C2×C11semidirect
319. C11#23822direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×C4⋊Q82
C4×C11×#1272
C11×#21002
C11×#20712
C11×#20412
C11×#20232
C11×#17622
C11×#17452
#2382211