Finite Group Databasebeta

← C11×#9118 #14586311

Subgroups — C11×#9118 #14586311

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#432C211yesmaximal, characteristic, complemented
2C11×#2854C211yesmaximal, characteristic
3C2×C11×#327C212yesmaximal
4C11×#1434C211yesmaximal, characteristic, complemented
5C11×#1294C212yesmaximal, complemented
6C2×C11×#123—21no—
7C2×C11×#121C2211yescharacteristic
8C22×C42×C11C2211yescharacteristic
9C11×#432—24no—
10C2×C11×C4⋊C8—21no—
11C2×C11×C22⋊C8C2212yes—
12C2×C11×#97—21no—
13C11×#390C411yescharacteristic, complemented
14C11×#390C411yescharacteristic, complemented
15C11×#389C411yescharacteristic, complemented
16C11×#389C411yescharacteristic, complemented
17C11×#388—21no—
18C11×#388—21no—
19C11×#386—21no—
20C11×#380C2211yescharacteristic
21C2×C11×#95—21no—
22C2×C11×#95—21no—
23C2×C11×#95C2212yes—
24C11×#327—24no—
25C22×D4×C11—21no—
26C22×D4×C11C2×C411yescharacteristic
27C23×C4×C11—22no—
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C22×C8×C11—22no—
32C11×#123—44no—
33C11×#121—22no—
34C11×#121—22no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C42×C11—22no—
47C2×C42×C11—22no—
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C11×C4⋊C8—24no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8D414yes—
55C11×#97—24no—
56C11×#95—24no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—22no—
61C11×#95—22no—
62C11×#95—42no—
63#9118C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—21no—
65C24×C11C2×D411yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—21no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C22⋊C411yescharacteristic
94C22×C4×C11C22⋊C411yescharacteristic
95C22×C4×C11C22⋊C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11#4112yes—
100C2×C8×C11—24no—
101C2×C8×C11—42no—
102C2×C8×C11—42no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—21no—
118C42×C11—21no—
119C42×C11—21no—
120C42×C11—21no—
121C2×#432C2×C1111yescharacteristic, complemented
122#2854C2×C1111yescharacteristic
123C2×#327C2×C1112yes—
124#1434C2×C1111yescharacteristic, complemented
125#1294C2×C1112yescomplemented
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11C2×C22⋊C411yescharacteristic
138C23×C11#12112yes—
139C23×C11AGL(1,ℤ/8)11yescharacteristic
140C23×C11AGL(1,ℤ/8)12yes—
141C23×C11#13711yescharacteristic
142D4×C11—82no—
143D4×C11—82no—
144D4×C11—82no—
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—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—44no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—44no—
166C2×C4×C11—44no—
167C2×C4×C11—44no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—82no—
178C2×C4×C11—82no—
179C2×C4×C11—82no—
180C2×C4×C11—82no—
181C2×C4×C11#10412yes—
182C2×C4×C11C4×D412yes—
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12311yescharacteristic
185C8×C11—44no—
186C2×#123—21no—
187C2×#121C22×C1111yescharacteristic
188C22×C42C22×C1111yescharacteristic
189#432—24no—
190C2×C4⋊C8—21no—
191C2×C22⋊C8C22×C1112yes—
192C2×#97—21no—
193#390C4×C1111yescharacteristic, complemented
194#390C4×C1111yescharacteristic, complemented
195#389C4×C1111yescharacteristic, complemented
196#389C4×C1111yescharacteristic, complemented
197#388—21no—
198#388—21no—
199#386—21no—
200#380C22×C1111yescharacteristic
201C2×#95—21no—
202C2×#95—21no—
203C2×#95C22×C1112yes—
204#327—24no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—22no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11#38611yescharacteristic
221C22×C11#41011yescharacteristic
222C22×C11#41011yescharacteristic
223C22×C11#41711yescharacteristic
224C22×C11#41811yescharacteristic
225C22×C11C2×#10411yescharacteristic
226C22×C11#42111yescharacteristic
227C22×C11#46812yes—
228C22×C11#46912yes—
229C4×C11—22no—
230C4×C11—22no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—84no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11—81no—
240C22×D4—21no—
241C22×D4C2×C4×C1111yescharacteristic
242C23×C4—22no—
243C23×C4D4×C1111yescharacteristic
244C23×C4D4×C1111yescharacteristic
245C23×C4C23×C1111yescharacteristic
246C22×C8—22no—
247#123—44no—
248#121—22no—
249#121—22no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C2×C4×C1111yescharacteristic
253C2×C4⋊C4C2×C4×C1111yescharacteristic
254C2×C4⋊C4C2×C4×C1111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C42—22no—
262C2×C42—22no—
263C2×C42C2×C4×C1111yescharacteristic
264C2×C42C2×C4×C1111yescharacteristic
265C2×C42D4×C1111yescharacteristic
266C2×C42D4×C1111yescharacteristic
267C4⋊C8—24no—
268C22⋊C8—22no—
269C22⋊C8D4×C1114yes—
270#97—24no—
271#95—24no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—22no—
276#95—22no—
277#95—42no—
278C2×C11—22no—
279C2×C11—22no—
280C2×C11—161no—
281C2×C11#150511yescharacteristic
282C2×C11#150911yescharacteristic
283C2×C11#151211yescharacteristic
284C2×C11#151411yescharacteristic
285C2×C11#187111yescharacteristic
286C2×C11#189511yescharacteristic
287C2×C11#189911yescharacteristic
288C24—21no—
289C24C2×D4×C1111yescharacteristic
290C2×D4—22no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4C11×C22⋊C411yescharacteristic
317C22×C4C11×C22⋊C411yescharacteristic
318C22×C4C11×C22⋊C411yescharacteristic
319C22×C4C11×C22⋊C411yescharacteristic
320C22×C4C22×C4×C1111yescharacteristic
321C22×C4C2×D4×C1111yescharacteristic
322C22×C4C2×D4×C1112yes—
323C22×C4C11×#4112yes—
324C2×C8—24no—
325C2×C8—42no—
326C2×C8—42no—
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C42—22no—
340C42—22no—
341C42—21no—
342C42—21no—
343C42—21no—
344C42—21no—
345C11#911811yescharacteristic, direct product factor, Sylow
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23C2×C11×C22⋊C411yescharacteristic
358C23C11×#12112yes—
359C23C11×AGL(1,ℤ/8)11yescharacteristic
360C23C11×AGL(1,ℤ/8)12yes—
361C23C11×#13711yescharacteristic
362D4—82no—
363D4—82no—
364D4—82no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4C11×#10412yes—
402C2×C4C4×D4×C1112yes—
403C2×C4C11×#12011yescharacteristic
404C2×C4C11×#12311yescharacteristic
405C8—44no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22C11×#38611yescharacteristic
422C22C11×#41011yescharacteristic
423C22C11×#41011yescharacteristic
424C22C11×#41711yescharacteristic
425C22C11×#41811yescharacteristic
426C22C2×C11×#10411yescharacteristic
427C22C11×#42111yescharacteristic
428C22C11×#46812yes—
429C22C11×#46912yes—
430C4—22no—
431C4—21no—
432C4—22no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—84no—
438C4—81no—
439C4—81no—
440C4—81no—
441C2—22no—
442C2—22no—
443C2—161no—
444C2C11×#150511yescharacteristic
445C2C11×#150911yescharacteristic
446C2C11×#151211yescharacteristic
447C2C11×#151411yescharacteristic
448C2C11×#187111yescharacteristic
449C2C11×#189511yescharacteristic
450C2C11×#189911yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#432C2semidirect
4. C11×#1434C2semidirect
5. C11×#1294C2semidirect
13. C11×#390C4semidirect
14. C11×#390C4semidirect
15. C11×#389C4semidirect
16. C11×#389C4semidirect
63. #9118C11direct (N × H)
121. C2×#432C2×C11semidirect
124. #1434C2×C11semidirect
125. #1294C2×C11semidirect
193. #390C4×C11semidirect
194. #390C4×C11semidirect
195. #389C4×C11semidirect
196. #389C4×C11semidirect
345. C11#9118direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4322
C11×#28542
C2×C11×#3272
C11×#14342
C11×#12942
#911811