Finite Group Databasebeta

← C11×#24593 #14601786

Subgroups — C11×#24593 #14601786

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#485C211yesmaximal, characteristic
2C2×C11×#428C211yesmaximal, characteristic
3C11×#2503C211yesmaximal, characteristic
4C11×#2347C211yesmaximal, characteristic
5C11×#2085C212yesmaximal, complemented
6C11×#2068C212yesmaximal, complemented
7C11×#1949C212yesmaximal, complemented
8C11×#1927C212yesmaximal, complemented
9C11×#1894C211yesmaximal, characteristic
10C11×#1851C211yesmaximal, characteristic
11C11×#1824C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C11×#485—24no—
17C11×#428—24no—
18C2×C11×#107C2212yes—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2212yes—
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#400—21no—
28C11×#400—21no—
29C11×#391C2212yes—
30C11×#389C2212yes—
31C11×#388—22no—
32C11×#383—21no—
33C11×#382C2212yes—
34C11×#381—22no—
35C11×#380C2211yescharacteristic
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C2×C11×M16—22no—
47C2×C11×M16—24no—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—22no—
53C11×#117—22no—
54C11×#117D414yes—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4D412yes—
69C2×C42×C11—21no—
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C11×#107—24no—
73C11×#107—22no—
74C11×#106—24no—
75C11×#106—22no—
76C11×C4⋊C8—24no—
77C11×#103—24no—
78C11×#103—22no—
79C11×#103—22no—
80C11×C22⋊C8—22no—
81C11×#95—21no—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95D411yescharacteristic
89C11×#95D411yescharacteristic
90#24593C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11C2×D411yescharacteristic
92C2×Q8×C11—21no—
93C2×Q8×C11—22no—
94C2×Q8×C11—21no—
95C2×Q8×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—44no—
105C22×C4×C11—42no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11#4112yes—
111C22×C4×C11C2411yescharacteristic
112C11×M16—28no—
113C2×C8×C11—22no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11#4114yes—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—44no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4C2×D412yes—
132C11×C4⋊C4C2×D412yes—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C11×C22⋊C4—81no—
137C42×C11—24no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11—82no—
141C2×#485C2×C1111yescharacteristic
142C2×#428C2×C1111yescharacteristic
143#2503C2×C1111yescharacteristic
144#2347C2×C1111yescharacteristic
145#2085C2×C1112yescomplemented
146#2068C2×C1112yescomplemented
147#1949C2×C1112yescomplemented
148#1927C2×C1112yescomplemented
149#1894C2×C1111yescharacteristic
150#1851C2×C1111yescharacteristic
151#1824C2×C1111yescharacteristic
152C23×C11—22no—
153C23×C11—22no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11#12112yes—
157C23×C11C22×D411yescharacteristic
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—42no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—44no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—84no—
187C2×C4×C11#12112yes—
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4112yes—
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C112−1+412yes—
192C8×C11—24no—
193C8×C11—41no—
194C8×C11—41no—
195C22×M16C22×C1111yescharacteristic
196C2×C22⋊Q8C22×C1111yescharacteristic
197C2×#117C22×C1111yescharacteristic
198C22×C4⋊C4C22×C1111yescharacteristic
199#485—24no—
200#428—24no—
201C2×#107C22×C1111yescharacteristic
202C2×#107C22×C1112yes—
203C2×#106C22×C1111yescharacteristic
204C2×#106C22×C1112yes—
205C2×C4⋊C8C22×C1112yes—
206C2×#103C22×C1111yescharacteristic
207C2×#103C22×C1111yescharacteristic
208C2×#103C22×C1112yes—
209C2×C22⋊C8C22×C1111yescharacteristic
210#400—21no—
211#400—21no—
212#391C22×C1112yes—
213#389C22×C1112yes—
214#388—22no—
215#383—21no—
216#382C22×C1112yes—
217#381—22no—
218#380C22×C1111yescharacteristic
219C4×C4⋊C4—21no—
220C4×C4⋊C4C22×C1112yes—
221C4×C22⋊C4C22×C1111yescharacteristic
222#340C22×C1112yes—
223#340C22×C1112yes—
224#340C22×C1112yes—
225#336C22×C1112yes—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11C2×#12111yescharacteristic
232C22×C11#54712yes—
233C22×C11#57512yes—
234C22×C11#57711yescharacteristic
235C22×C11#57811yescharacteristic
236C4×C11—22no—
237C4×C11—42no—
238C4×C11—42no—
239C4×C11—42no—
240C4×C11—42no—
241C4×C11—82no—
242C4×C11—81no—
243C4×C11—82no—
244C4×C11—81no—
245C4×C11#52511yescharacteristic
246C4×C11#53611yescharacteristic
247C4×C11#55212yes—
248C22×Q8C23×C1111yescharacteristic
249C23×C4—21no—
250C23×C4C23×C1111yescharacteristic
251C2×M16—22no—
252C2×M16—24no—
253C22×C8C23×C1111yescharacteristic
254C22×C8C23×C1111yescharacteristic
255C22×C8C23×C1112yes—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258#117—22no—
259#117D4×C1114yes—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4C23×C1112yes—
266C2×C4⋊C4C23×C1111yescharacteristic
267C2×C4⋊C4C23×C1112yes—
268C2×C4⋊C4C23×C1111yescharacteristic
269C2×C4⋊C4C23×C1111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4D4×C1112yes—
274C2×C42—21no—
275C2×C42—22no—
276C2×C42C23×C1112yes—
277#107—24no—
278#107—22no—
279#106—24no—
280#106—22no—
281C4⋊C8—24no—
282#103—24no—
283#103—22no—
284#103—22no—
285C22⋊C8—22no—
286#95—21no—
287#95—22no—
288#95—22no—
289#95—22no—
290#95—22no—
291#95—22no—
292#95—22no—
293#95D4×C1111yescharacteristic
294#95D4×C1111yescharacteristic
295C2×C11—42no—
296C2×C11#241311yescharacteristic
297C2×C11#304011yescharacteristic
298C2×C11#304611yescharacteristic
299C2×C11#334912yes—
300C2×C11#335112yes—
301C24C2×D4×C1111yescharacteristic
302C2×Q8—21no—
303C2×Q8—22no—
304C2×Q8—21no—
305C2×Q8—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—44no—
315C22×C4—42no—
316C22×C4C2×D4×C1112yes—
317C22×C4C2×D4×C1112yes—
318C22×C4C2×D4×C1111yescharacteristic
319C22×C4C2×D4×C1112yes—
320C22×C4C11×#4112yes—
321C22×C4C24×C1111yescharacteristic
322M16—28no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8C11×#4114yes—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—44no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4C2×D4×C1112yes—
342C4⋊C4C2×D4×C1112yes—
343C22⋊C4—24no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—81no—
347C42—24no—
348C42—22no—
349C42—22no—
350C42—82no—
351C11#2459311yescharacteristic, direct product factor, Sylow
352C23—22no—
353C23—22no—
354C23—21no—
355C23—21no—
356C23C11×#12112yes—
357C23C22×D4×C1111yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—42no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—84no—
387C2×C4C11×#12112yes—
388C2×C4C22×D4×C1111yescharacteristic
389C2×C4C2×C11×#4112yes—
390C2×C4C2×C11×#4111yescharacteristic
391C2×C4C11×2−1+412yes—
392C8—24no—
393C8—41no—
394C8—41no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—42no—
399C22—42no—
400C22C2×C11×#12111yescharacteristic
401C22C11×#54712yes—
402C22C11×#57512yes—
403C22C11×#57711yescharacteristic
404C22C11×#57811yescharacteristic
405C4—22no—
406C4—42no—
407C4—42no—
408C4—42no—
409C4—42no—
410C4—81no—
411C4—82no—
412C4—81no—
413C4—82no—
414C4C11×#52511yescharacteristic
415C4C11×#53611yescharacteristic
416C4C11×#55212yes—
417C2—42no—
418C2C11×#241311yescharacteristic
419C2C11×#304011yescharacteristic
420C2C11×#304611yescharacteristic
421C2C11×#334912yes—
422C2C11×#335112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×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
5. C11×#2085C2semidirect
6. C11×#2068C2semidirect
7. C11×#1949C2semidirect
8. C11×#1927C2semidirect
90. #24593C11direct (N × H)
145. #2085C2×C11semidirect
146. #2068C2×C11semidirect
147. #1949C2×C11semidirect
148. #1927C2×C11semidirect
351. C11#24593direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4852
C2×C11×#4282
C11×#25032
C11×#23472
C11×#20852
C11×#20682
C11×#19492
C11×#19272
C11×#18942
C11×#18512
C11×#18242
#2459311