Finite Group Databasebeta

← C11×#9123 #14586316

Subgroups — C11×#9123 #14586316

Order 2816.

600 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×#432C211yesmaximal, characteristic, complemented
2C11×#2850C211yesmaximal, characteristic
3C11×#1749C211yesmaximal, characteristic, complemented
4C2×C11×#329C212yesmaximal, complemented
5C11×#1295C212yesmaximal, complemented
6C2×C11×#124C2211yescharacteristic
7C2×C11×C22⋊Q8C411yescharacteristic
8C2×C11×#121C411yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C11×#432—24no—
11C2×C11×C4⋊C8—21no—
12C2×C11×C22⋊C8—21no—
13C2×C11×C22⋊C8—21no—
14C2×C11×#97C2212yes—
15C2×C11×#97C2212yes—
16C11×#391C411yescharacteristic
17C11×#390C411yescharacteristic
18C11×#388—21no—
19C11×#388—21no—
20C11×#386—21no—
21C11×#386—21no—
22C11×#382C2211yescharacteristic
23C11×#336—21no—
24C11×#329—24no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×D4×C11—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C22×C8×C11—22no—
32C22×C8×C11—22no—
33C11×#124—22no—
34C11×#124—22no—
35C11×C22⋊Q8—42no—
36C11×#121—42no—
37C2×C11×C4⋊C4—21no—
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×C11D411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C11×C4⋊C8—24no—
53C11×C22⋊C8—24no—
54C11×C22⋊C8—24no—
55C11×#97—22no—
56C11×#97—22no—
57C11×#97—22no—
58C11×#97D414yescomplemented
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63#9123C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—21no—
65C24×C11C22⋊C411yescharacteristic
66C2×Q8×C11—22no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×D4×C11—22no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C8×C11—24no—
95C2×C8×C11—24no—
96C2×C8×C11—42no—
97C2×C8×C11—42no—
98C2×C8×C11—42no—
99C2×C8×C11—42no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—42no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—41no—
110C42×C11—22no—
111C42×C11—21no—
112C42×C11—22no—
113C42×C11—21no—
114C42×C11C2×D412yes—
115C42×C11#4112yes—
116C2×#432C2×C1111yescharacteristic, complemented
117#2850C2×C1111yescharacteristic
118#1749C2×C1111yescharacteristic, complemented
119C2×#329C2×C1112yescomplemented
120#1295C2×C1112yescomplemented
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11#10412yes—
135C23×C11C2×C22⋊C411yescharacteristic
136Q8×C11—82no—
137D4×C11—82no—
138D4×C11—84no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
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—44no—
154C2×C4×C11—44no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11#10012yes—
167C2×C4×C11C4×D412yes—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12112yes—
170C2×C4×C11#12311yescharacteristic
171C8×C11—44no—
172C8×C11—44no—
173C2×#124C22×C1111yescharacteristic
174C2×C22⋊Q8C4×C1111yescharacteristic
175C2×#121C4×C1111yescharacteristic
176C22×C42C22×C1111yescharacteristic
177#432—24no—
178C2×C4⋊C8—21no—
179C2×C22⋊C8—21no—
180C2×C22⋊C8—21no—
181C2×#97C22×C1112yes—
182C2×#97C22×C1112yes—
183#391C4×C1111yescharacteristic
184#390C4×C1111yescharacteristic
185#388—21no—
186#388—21no—
187#386—21no—
188#386—21no—
189#382C22×C1111yescharacteristic
190#336—21no—
191#329—24no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11#38611yescharacteristic
207C22×C11C2×#10011yescharacteristic
208C22×C11#41311yescharacteristic
209C22×C11C2×#10411yescharacteristic
210C22×C11#42111yescharacteristic
211C22×C11#42111yescharacteristic
212C22×C11#42111yescharacteristic
213C4×C11—22no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—22no—
217C4×C11—22no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11—81no—
221C4×C11—81no—
222C4×C11—81no—
223C22×Q8C2×C4×C1111yescharacteristic
224C22×D4—21no—
225C22×D4C2×C4×C1111yescharacteristic
226C23×C4C2×C4×C1111yescharacteristic
227C23×C4D4×C1111yescharacteristic
228C23×C4D4×C1111yescharacteristic
229C22×C8—22no—
230C22×C8—22no—
231#124—22no—
232#124—22no—
233C22⋊Q8—42no—
234#121—42no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C2×C4×C1111yescharacteristic
237C2×C4⋊C4C2×C4×C1111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C42—22no—
245C2×C42—22no—
246C2×C42C2×C4×C1111yescharacteristic
247C2×C42D4×C1111yescharacteristic
248C2×C42D4×C1111yescharacteristic
249C2×C42C23×C1111yescharacteristic
250C4⋊C8—24no—
251C22⋊C8—24no—
252C22⋊C8—24no—
253#97—22no—
254#97—22no—
255#97—22no—
256#97D4×C1114yescomplemented
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261C2×C11—42no—
262C2×C11—161no—
263C2×C11#152711yescharacteristic
264C2×C11#153211yescharacteristic
265C2×C11#153511yescharacteristic
266C2×C11#153611yescharacteristic
267C2×C11#187111yescharacteristic
268C2×C11#189711yescharacteristic
269C2×C11#190011yescharacteristic
270C24—21no—
271C24C11×C22⋊C411yescharacteristic
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C11×C22⋊C411yescharacteristic
295C22×C4C11×C22⋊C411yescharacteristic
296C22×C4C11×C22⋊C411yescharacteristic
297C22×C4C22×C4×C1111yescharacteristic
298C22×C4C2×D4×C1111yescharacteristic
299C22×C4C2×D4×C1111yescharacteristic
300C2×C8—24no—
301C2×C8—24no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—42no—
315C22⋊C4—41no—
316C42—22no—
317C42—21no—
318C42—22no—
319C42—21no—
320C42C2×D4×C1112yes—
321C42C11×#4112yes—
322C11#912311yescharacteristic, direct product factor, Sylow
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23C11×#10412yes—
337C23C2×C11×C22⋊C411yescharacteristic
338Q8—82no—
339D4—82no—
340D4—84no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4C11×#10012yes—
369C2×C4C4×D4×C1112yes—
370C2×C4C11×#12011yescharacteristic
371C2×C4C11×#12112yes—
372C2×C4C11×#12311yescharacteristic
373C8—44no—
374C8—44no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22C11×#38611yescharacteristic
390C22C2×C11×#10011yescharacteristic
391C22C11×#41311yescharacteristic
392C22C2×C11×#10411yescharacteristic
393C22C11×#42111yescharacteristic
394C22C11×#42111yescharacteristic
395C22C11×#42111yescharacteristic
396C4—22no—
397C4—21no—
398C4—21no—
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—81no—
404C4—81no—
405C4—81no—
406C2—42no—
407C2—161no—
408C2C11×#152711yescharacteristic
409C2C11×#153211yescharacteristic
410C2C11×#153511yescharacteristic
411C2C11×#153611yescharacteristic
412C2C11×#187111yescharacteristic
413C2C11×#189711yescharacteristic
414C2C11×#190011yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#121C4
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
3. C11×#1749C2semidirect
4. C2×C11×#329C2semidirect
5. C11×#1295C2semidirect
58. C11×#97D4semidirect
63. #9123C11direct (N × H)
116. C2×#432C2×C11semidirect
118. #1749C2×C11semidirect
119. C2×#329C2×C11semidirect
120. #1295C2×C11semidirect
256. #97D4×C11semidirect
322. C11#9123direct (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×#28502
C11×#17492
C2×C11×#3292
C11×#12952
#912311