Finite Group Databasebeta

← C11×#23030 #14600223

Subgroups — C11×#23030 #14600223

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C2×C11×#441C211yesmaximal, characteristic, complemented
3C2×C11×#427C211yesmaximal, characteristic
4C11×#2362C212yesmaximal
5C11×#1971C211yesmaximal, characteristic, complemented
6C11×#1943C211yesmaximal, characteristic, complemented
7C11×#1928C212yesmaximal, complemented
8C11×#1873C212yesmaximal
9C11×#1863C212yesmaximal, complemented
10C11×#1776C211yesmaximal, characteristic, complemented
11C11×#1752C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×Q8×C11C2212yes—
16C2×C11×#117C2212yes—
17C11×#467C418yescomplemented
18C11×#441—24no—
19C11×#427—24no—
20C2×C11×#107C2212yes—
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C11×#391C2212yes—
31C11×#389C2212yes—
32C11×#388—22no—
33C11×#388—22no—
34C11×#387—22no—
35C4×C11×C4⋊C4—22no—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C22⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41C11×#336C2211yescharacteristic
42C22×Q8×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2×C414yes—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11C2×C414yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8C2×C418yes—
56C4×Q8×C11—24no—
57C4×Q8×C11—42no—
58C11×#117—24no—
59C11×#117—42no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4D412yes—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C11×#107—24no—
75C11×#107C2×C414yes—
76C11×#106—22no—
77C11×#106D414yes—
78C11×#103—24no—
79C11×#103—42no—
80C11×#103C2×C418yes—
81C11×C22⋊C8—22no—
82C11×#97—22no—
83C11×#97—22no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95D412yes—
89#23030C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11C2×D411yescharacteristic
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11C22×C414yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4112yes—
110C22×C4×C11C2411yescharacteristic
111C11×Q16—28no—
112C2×C8×C11—28no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11C22×C412yes—
122C2×C8×C11C22×C412yes—
123C2×C8×C11C2×D412yes—
124C2×C8×C11#4112yes—
125C11×C4⋊C4—28no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—44no—
131C11×C4⋊C4—44no—
132C11×C4⋊C4C22×C414yes—
133C11×C4⋊C4C2×D414yes—
134C11×C22⋊C4—28no—
135C11×C22⋊C4—42no—
136C11×C22⋊C4—44no—
137C42×C11—21no—
138C42×C11—21no—
139C42×C11—21no—
140C42×C11—21no—
141C42×C11—44no—
142C42×C11—44no—
143C42×C11—44no—
144C2×#467C2×C1111yescharacteristic
145C2×#441C2×C1111yescharacteristic, complemented
146C2×#427C2×C1111yescharacteristic
147#2362C2×C1112yes—
148#1971C2×C1111yescharacteristic, complemented
149#1943C2×C1111yescharacteristic, complemented
150#1928C2×C1112yescomplemented
151#1873C2×C1112yes—
152#1863C2×C1112yescomplemented
153#1776C2×C1111yescharacteristic, complemented
154#1752C2×C1111yescharacteristic
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11C4×D412yes—
160C23×C11C22×D411yescharacteristic
161Q8×C11—24no—
162Q8×C11—24no—
163Q8×C11—42no—
164Q8×C11—42no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11C4×D412yes—
190C2×C4×C11C23×C411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11H(5,𝔽2)11yescharacteristic
195C2×C4×C112−1+411yescharacteristic
196C8×C11—22no—
197C8×C11—41no—
198C8×C11—41no—
199C8×C11C4×D414yes—
200C22×Q16C22×C1111yescharacteristic
201C23×C8C22×C1111yescharacteristic
202C2×C22⋊Q8C22×C1112yes—
203C2×C4×Q8C22×C1112yes—
204C2×#117C22×C1112yes—
205#467C4×C1118yescomplemented
206#441—24no—
207#427—24no—
208C2×#107C22×C1112yes—
209C2×#107C22×C1111yescharacteristic
210C2×#106C22×C1111yescharacteristic
211C2×#106C22×C1111yescharacteristic
212C2×#103C22×C1112yes—
213C2×#103C22×C1112yes—
214C2×#103C22×C1112yes—
215C2×C22⋊C8C22×C1111yescharacteristic
216C2×#97C22×C1111yescharacteristic
217C2×#97C22×C1111yescharacteristic
218#391C22×C1112yes—
219#389C22×C1112yes—
220#388—22no—
221#388—22no—
222#387—22no—
223C4×C4⋊C4—22no—
224C4×C4⋊C4C22×C1112yes—
225C4×C22⋊C4C22×C1111yescharacteristic
226#340C22×C1112yes—
227#340C22×C1112yes—
228#336C22×C1111yescharacteristic
229#336C22×C1111yescharacteristic
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11C2×C4×D411yescharacteristic
236C22×C11D4211yescharacteristic
237C22×C11#54711yescharacteristic
238C22×C11#57512yes—
239C22×C11#57812yes—
240C4×C11—22no—
241C4×C11—42no—
242C4×C11—44no—
243C4×C11—44no—
244C4×C11—42no—
245C4×C11—44no—
246C4×C11—82no—
247C4×C11C2×C4×D411yescharacteristic
248C4×C11#52011yescharacteristic
249C4×C11#54811yescharacteristic
250C4×C11#55311yescharacteristic
251C22×Q8C23×C1112yes—
252C23×C4C23×C1111yescharacteristic
253C2×Q16—22no—
254C2×Q16—22no—
255C2×Q16C2×C4×C1114yes—
256C22×C8—22no—
257C22×C8—22no—
258C22×C8C2×C4×C1114yes—
259C22×C8C23×C1111yescharacteristic
260C22×C8C23×C1111yescharacteristic
261C22×C8C23×C1111yescharacteristic
262C22×C8C23×C1111yescharacteristic
263C22⋊Q8—24no—
264C22⋊Q8C2×C4×C1118yes—
265C4×Q8—24no—
266C4×Q8—42no—
267#117—24no—
268#117—42no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4C23×C1112yes—
273C2×C4⋊C4C23×C1112yes—
274C2×C4⋊C4C23×C1112yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4D4×C1112yes—
278C2×C42—22no—
279C2×C42—22no—
280C2×C42—22no—
281C2×C42C23×C1111yescharacteristic
282C2×C42C23×C1111yescharacteristic
283#107—24no—
284#107C2×C4×C1114yes—
285#106—22no—
286#106D4×C1114yes—
287#103—24no—
288#103—42no—
289#103C2×C4×C1118yes—
290C22⋊C8—22no—
291#97—22no—
292#97—22no—
293#95—22no—
294#95—22no—
295#95—22no—
296#95—22no—
297#95D4×C1112yes—
298C2×C11—42no—
299C2×C11#236111yescharacteristic
300C2×C11#294311yescharacteristic
301C2×C11#295011yescharacteristic
302C2×C11#326912yes—
303C2×C11#334912yes—
304C24C2×D4×C1111yescharacteristic
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8C22×C4×C1114yes—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4C22×C4×C1112yes—
320C22×C4C2×D4×C1112yes—
321C22×C4C2×D4×C1112yes—
322C22×C4C2×D4×C1111yescharacteristic
323C22×C4C11×#4112yes—
324C22×C4C24×C1111yescharacteristic
325Q16—28no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—28no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8C22×C4×C1112yes—
336C2×C8C22×C4×C1112yes—
337C2×C8C2×D4×C1112yes—
338C2×C8C11×#4112yes—
339C4⋊C4—28no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—44no—
345C4⋊C4—44no—
346C4⋊C4C22×C4×C1114yes—
347C4⋊C4C2×D4×C1114yes—
348C22⋊C4—28no—
349C22⋊C4—42no—
350C22⋊C4—44no—
351C42—21no—
352C42—21no—
353C42—21no—
354C42—21no—
355C42—44no—
356C42—44no—
357C42—44no—
358C11#2303011yescharacteristic, direct product factor, Sylow
359C23—21no—
360C23—21no—
361C23—22no—
362C23—22no—
363C23C4×D4×C1112yes—
364C23C22×D4×C1111yescharacteristic
365Q8—24no—
366Q8—24no—
367Q8—42no—
368Q8—42no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4C4×D4×C1112yes—
394C2×C4C23×C4×C1111yescharacteristic
395C2×C4C22×D4×C1111yescharacteristic
396C2×C4C2×C11×#4111yescharacteristic
397C2×C4C2×C11×#4111yescharacteristic
398C2×C4C11×H(5,𝔽2)11yescharacteristic
399C2×C4C11×2−1+411yescharacteristic
400C8—22no—
401C8—41no—
402C8—41no—
403C8C4×D4×C1114yes—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—42no—
408C22—42no—
409C22C2×C4×D4×C1111yescharacteristic
410C22D42×C1111yescharacteristic
411C22C11×#54711yescharacteristic
412C22C11×#57512yes—
413C22C11×#57812yes—
414C4—22no—
415C4—44no—
416C4—42no—
417C4—44no—
418C4—42no—
419C4—44no—
420C4—82no—
421C4C2×C4×D4×C1111yescharacteristic
422C4C11×#52011yescharacteristic
423C4C11×#54811yescharacteristic
424C4C11×#55311yescharacteristic
425C2—42no—
426C2C11×#236111yescharacteristic
427C2C11×#294311yescharacteristic
428C2C11×#295011yescharacteristic
429C2C11×#326912yes—
430C2C11×#334912yes—
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 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#441C2semidirect
5. C11×#1971C2semidirect
6. C11×#1943C2semidirect
7. C11×#1928C2semidirect
9. C11×#1863C2semidirect
10. C11×#1776C2semidirect
17. C11×#467C4semidirect
89. #23030C11direct (N × H)
145. C2×#441C2×C11semidirect
148. #1971C2×C11semidirect
149. #1943C2×C11semidirect
150. #1928C2×C11semidirect
152. #1863C2×C11semidirect
153. #1776C2×C11semidirect
205. #467C4×C11semidirect
358. C11#23030direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C11×#4412
C2×C11×#4272
C11×#23622
C11×#19712
C11×#19432
C11×#19282
C11×#18732
C11×#18632
C11×#17762
C11×#17522
#2303011