Finite Group Databasebeta

← C11×#21944 #14599137

Subgroups — C11×#21944 #14599137

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#407C211yesmaximal, characteristic
2C11×#2280C211yesmaximal, characteristic
3C2×C11×#380C211yesmaximal, characteristic
4C11×#1854C214yesmaximal, complemented
5C11×#1853C212yesmaximal, complemented
6C11×#1852C212yesmaximal, complemented
7C11×#1809C214yesmaximal, complemented
8C24×C4×C11C2211yescharacteristic
9C22×C11×M16C2212yes—
10C2×C11×#117C2212yes—
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C22⋊C4—21no—
13C2×C11×#107C2214yescomplemented
14C2×C11×#106C2214yescomplemented
15C11×#407C418yescomplemented
16C2×C11×C22⋊C8C2212yes—
17C2×C11×C22⋊C8C2212yes—
18C11×#381—21no—
19C11×#380—21no—
20C11×#380—21no—
21C11×#380C2212yes—
22C11×#380C2212yes—
23C11×#380C2212yes—
24C11×#380C2211yescharacteristic
25C11×#380C2211yescharacteristic
26C11×#379—21no—
27C4×C11×C22⋊C4—21no—
28C4×C11×C22⋊C4—21no—
29C2×C11×#95—21no—
30C11×#340C2214yescomplemented
31C11×#340C2214yescomplemented
32C25×C11D411yescharacteristic
33C23×C4×C11—22no—
34C23×C4×C11—44no—
35C23×C4×C11C2×C414yes—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11Q814yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C2×C11×M16—44no—
44C2×C11×M16C2×C418yescomplemented
45C22×C8×C11C2314yes—
46C11×#117—44no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—44no—
49C2×C11×C4⋊C4C2314yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—44no—
59C2×C42×C11—22no—
60C11×#107—44no—
61C11×#106—44no—
62C11×C22⋊C8C2×C418yes—
63C11×C22⋊C8C2×C418yescomplemented
64C11×#95—22no—
65C11×#95—22no—
66C11×#95—22no—
67C11×#95—21no—
68C11×#95—21no—
69#21944C1111yesmaximal, characteristic, direct product factor, Sylow
70C24×C11—22no—
71C24×C11—22no—
72C24×C11—42no—
73C24×C11—42no—
74C24×C11C4⋊C414yes—
75C24×C11C2×D411yescharacteristic
76C24×C11C2×D411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—24no—
84C22×C4×C11—48no—
85C22×C4×C11—48no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—44no—
90C22×C4×C11—44no—
91C22×C4×C11—44no—
92C22×C4×C11C4⋊C414yes—
93C22×C4×C11C4⋊C414yes—
94C22×C4×C11C4⋊C414yes—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×Q812yes—
102C22×C4×C11C2×Q812yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11C2411yescharacteristic
105C11×M16—48no—
106C2×C8×C11—24no—
107C2×C8×C11—24no—
108C2×C8×C11C22×C418yes—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—44no—
114C11×C22⋊C4—44no—
115C11×C22⋊C4—44no—
116C11×C22⋊C4—44no—
117C11×C22⋊C4—44no—
118C11×C22⋊C4—42no—
119C11×C22⋊C4—42no—
120C42×C11—44no—
121C2×#407C2×C1111yescharacteristic
122#2280C2×C1111yescharacteristic
123C2×#380C2×C1111yescharacteristic
124#1854C2×C1114yescomplemented
125#1853C2×C1112yescomplemented
126#1852C2×C1112yescomplemented
127#1809C2×C1114yescomplemented
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11—28no—
139C23×C11—44no—
140C23×C11—44no—
141C23×C11—48no—
142C23×C11—48no—
143C23×C11C2×C4⋊C412yes—
144C23×C11C2×C4⋊C412yes—
145C23×C11C2×C4⋊C412yes—
146C23×C11AGL(1,ℤ/8)12yes—
147C23×C11#13712yes—
148C23×C11C22×D411yescharacteristic
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—44no—
159C2×C4×C11—44no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—44no—
164C2×C4×C11—44no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—44no—
170C2×C4×C11—88no—
171C2×C4×C11C2×C4⋊C412yes—
172C2×C4×C11C2×C4⋊C412yes—
173C2×C4×C11C2×C4⋊C412yes—
174C2×C4×C11C23×C411yescharacteristic
175C2×C4×C11C22×Q811yescharacteristic
176C2×C4×C11H(5,𝔽2)14yes—
177C8×C11—28no—
178C24×C4C22×C1111yescharacteristic
179C22×M16C22×C1112yes—
180C2×#117C22×C1112yes—
181C22×C4⋊C4C22×C1112yes—
182C22×C22⋊C4—21no—
183C2×#107C22×C1114yescomplemented
184C2×#106C22×C1114yescomplemented
185#407C4×C1118yescomplemented
186C2×C22⋊C8C22×C1112yes—
187C2×C22⋊C8C22×C1112yes—
188#381—21no—
189#380—21no—
190#380—21no—
191#380C22×C1112yes—
192#380C22×C1112yes—
193#380C22×C1111yescharacteristic
194#380C22×C1111yescharacteristic
195#380C22×C1112yes—
196#379—21no—
197C4×C22⋊C4—21no—
198C4×C22⋊C4—21no—
199C2×#95—21no—
200#340C22×C1114yescomplemented
201#340C22×C1114yescomplemented
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—24no—
205C22×C11—24no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—416no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11#42814yes—
218C22×C11C22×C4⋊C411yescharacteristic
219C22×C11#53412yes—
220C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
221C22×C11C2×#13711yescharacteristic
222C22×C11#57512yes—
223C4×C11—22no—
224C4×C11—22no—
225C4×C11—22no—
226C4×C11—82no—
227C4×C11—84no—
228C4×C11—82no—
229C4×C11#51812yes—
230C4×C11#54312yes—
231C25D4×C1111yescharacteristic
232C23×C4—22no—
233C23×C4—44no—
234C23×C4C2×C4×C1114yes—
235C23×C4D4×C1111yescharacteristic
236C23×C4D4×C1111yescharacteristic
237C23×C4D4×C1111yescharacteristic
238C23×C4Q8×C1114yes—
239C23×C4C23×C1111yescharacteristic
240C23×C4C23×C1111yescharacteristic
241C23×C4C23×C1111yescharacteristic
242C2×M16—44no—
243C2×M16C2×C4×C1118yescomplemented
244C22×C8C23×C1114yes—
245#117—44no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—44no—
248C2×C4⋊C4C23×C1114yes—
249C2×C4⋊C4C23×C1112yes—
250C2×C4⋊C4C23×C1112yes—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—44no—
258C2×C42—22no—
259#107—44no—
260#106—44no—
261C22⋊C8C2×C4×C1118yes—
262C22⋊C8C2×C4×C1118yescomplemented
263#95—22no—
264#95—22no—
265#95—22no—
266#95—21no—
267#95—21no—
268C2×C11—24no—
269C2×C11—42no—
270C2×C11—42no—
271C2×C11#231511yescharacteristic
272C2×C11C2×#42811yescharacteristic
273C2×C11#291111yescharacteristic
274C2×C11#319412yes—
275C2×C11#319612yes—
276C24—22no—
277C24—22no—
278C24—42no—
279C24—42no—
280C24C11×C4⋊C414yes—
281C24C2×D4×C1111yescharacteristic
282C24C2×D4×C1111yescharacteristic
283C24C2×D4×C1111yescharacteristic
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—48no—
291C22×C4—48no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—44no—
296C22×C4—44no—
297C22×C4—44no—
298C22×C4C11×C4⋊C414yes—
299C22×C4C11×C4⋊C414yes—
300C22×C4C11×C4⋊C414yes—
301C22×C4C22×C4×C1112yes—
302C22×C4C22×C4×C1112yes—
303C22×C4C22×C4×C1112yes—
304C22×C4C2×D4×C1111yescharacteristic
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C2×D4×C1111yescharacteristic
307C22×C4C2×Q8×C1112yes—
308C22×C4C2×Q8×C1112yes—
309C22×C4C2×Q8×C1112yes—
310C22×C4C24×C1111yescharacteristic
311M16—48no—
312C2×C8—24no—
313C2×C8—24no—
314C2×C8C22×C4×C1118yes—
315C4⋊C4—24no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—44no—
320C22⋊C4—44no—
321C22⋊C4—44no—
322C22⋊C4—44no—
323C22⋊C4—44no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C42—44no—
327C11#2194411yescharacteristic, direct product factor, Sylow
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—28no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—22no—
338C23—22no—
339C23—44no—
340C23—44no—
341C23—48no—
342C23—48no—
343C23C2×C11×C4⋊C412yes—
344C23C2×C11×C4⋊C412yes—
345C23C2×C11×C4⋊C412yes—
346C23C11×AGL(1,ℤ/8)12yes—
347C23C11×#13712yes—
348C23C22×D4×C1111yescharacteristic
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—44no—
370C2×C4—88no—
371C2×C4C2×C11×C4⋊C412yes—
372C2×C4C2×C11×C4⋊C412yes—
373C2×C4C2×C11×C4⋊C412yes—
374C2×C4C23×C4×C1111yescharacteristic
375C2×C4C22×Q8×C1111yescharacteristic
376C2×C4C11×H(5,𝔽2)14yes—
377C8—28no—
378C22—22no—
379C22—24no—
380C22—24no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—416no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22C11×#42814yes—
394C22C22×C11×C4⋊C411yescharacteristic
395C22C11×#53412yes—
396C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
397C22C2×C11×#13711yescharacteristic
398C22C11×#57512yes—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—84no—
403C4—82no—
404C4—82no—
405C4C11×#51812yes—
406C4C11×#54312yes—
407C2—24no—
408C2—42no—
409C2—42no—
410C2C11×#231511yescharacteristic
411C2C2×C11×#42811yescharacteristic
412C2C11×#291111yescharacteristic
413C2C11×#319412yes—
414C2C11×#319612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1854C2semidirect
5. C11×#1853C2semidirect
6. C11×#1852C2semidirect
7. C11×#1809C2semidirect
13. C2×C11×#107C22semidirect
14. C2×C11×#106C22semidirect
15. C11×#407C4semidirect
30. C11×#340C22semidirect
31. C11×#340C22semidirect
44. C2×C11×M16C2×C4semidirect
63. C11×C22⋊C8C2×C4semidirect
69. #21944C11direct (N × H)
124. #1854C2×C11semidirect
125. #1853C2×C11semidirect
126. #1852C2×C11semidirect
127. #1809C2×C11semidirect
183. C2×#107C22×C11semidirect
184. C2×#106C22×C11semidirect
185. #407C4×C11semidirect
200. #340C22×C11semidirect
201. #340C22×C11semidirect
243. C2×M16C2×C4×C11semidirect
262. C22⋊C8C2×C4×C11semidirect
327. C11#21944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4072
C11×#22802
C2×C11×#3802
C11×#18542
C11×#18532
C11×#18522
C11×#18092
#2194411