Finite Group Databasebeta

← C11×#24577 #14601770

Subgroups — C11×#24577 #14601770

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#483C211yesmaximal, characteristic
2C22×C11×#107C211yesmaximal, characteristic
3C11×#2503C211yesmaximal, characteristic
4C11×#2344C211yesmaximal, characteristic
5C11×#2085C212yesmaximal, complemented
6C11×#2068C212yesmaximal, complemented
7C11×#1949C212yesmaximal, complemented
8C11×#1928C212yesmaximal, complemented
9C11×#1892C211yesmaximal, characteristic
10C11×#1850C211yesmaximal, characteristic
11C11×#1823C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C11×#117—21no—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#483—24no—
18C2×C11×#107—24no—
19C2×C11×#107C2212yes—
20C2×C11×#107C2212yes—
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#400—22no—
29C11×#391C2212yes—
30C11×#389C2212yes—
31C11×#387—22no—
32C11×#382C2212yes—
33C11×#381—21no—
34C11×#381—21no—
35C11×#381—21no—
36C11×#380C2211yescharacteristic
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×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C22×C8×C11—22no—
48C22×C8×C11—24no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C11×#117—44no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D414yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C42×C11—22no—
73C2×C42×C11C2312yes—
74C11×#107—24no—
75C11×#107—24no—
76C11×#106—22no—
77C11×#106—22no—
78C11×C4⋊C8—24no—
79C11×#103—24no—
80C11×#103—22no—
81C11×#103—22no—
82C11×C22⋊C8—22no—
83C11×#95—22no—
84C11×#95—21no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95D412yes—
91#24577C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—21no—
94C2×Q8×C11—22no—
95C2×Q8×C11—21no—
96C2×Q8×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—24no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C2×C8×C11—28no—
118C2×C8×C11—22no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11#4114yes—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—44no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4C2×D412yes—
138C11×C4⋊C4C2×D412yes—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—42no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—44no—
146C2×#483C2×C1111yescharacteristic
147C22×#107C2×C1111yescharacteristic
148#2503C2×C1111yescharacteristic
149#2344C2×C1111yescharacteristic
150#2085C2×C1112yescomplemented
151#2068C2×C1112yescomplemented
152#1949C2×C1112yescomplemented
153#1928C2×C1112yescomplemented
154#1892C2×C1111yescharacteristic
155#1850C2×C1111yescharacteristic
156#1823C2×C1111yescharacteristic
157C23×C11—22no—
158C23×C11—22no—
159C23×C11#12112yes—
160C23×C11#13512yes—
161C23×C11AGL(1,ℤ/8)12yes—
162C23×C11C22×D411yescharacteristic
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—42no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—48no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—84no—
194C2×C4×C11#12112yes—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4112yes—
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C112−1+412yes—
199C8×C11—24no—
200C8×C11—41no—
201C8×C11—41no—
202C23×C8C22×C1111yescharacteristic
203C2×C22⋊Q8C22×C1111yescharacteristic
204C2×#117—21no—
205C22×C4⋊C4C22×C1111yescharacteristic
206C22×C4⋊C4C22×C1111yescharacteristic
207#483—24no—
208C2×#107—24no—
209C2×#107C22×C1112yes—
210C2×#107C22×C1112yes—
211C2×#106C22×C1111yescharacteristic
212C2×#106C22×C1111yescharacteristic
213C2×C4⋊C8C22×C1112yes—
214C2×#103C22×C1111yescharacteristic
215C2×#103C22×C1111yescharacteristic
216C2×#103C22×C1112yes—
217C2×C22⋊C8C22×C1111yescharacteristic
218#400—22no—
219#391C22×C1112yes—
220#389C22×C1112yes—
221#387—22no—
222#382C22×C1112yes—
223#381—21no—
224#381—21no—
225#381—21no—
226#380C22×C1111yescharacteristic
227C4×C4⋊C4C22×C1112yes—
228C4×C22⋊C4C22×C1111yescharacteristic
229#340C22×C1112yes—
230#340C22×C1112yes—
231#340C22×C1112yes—
232#336C22×C1112yes—
233C22×C11—24no—
234C22×C11—24no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11#46314yes—
238C22×C11C2×#12111yescharacteristic
239C22×C11#54712yes—
240C22×C11C2×#13511yescharacteristic
241C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
242C22×C11#57812yes—
243C4×C11—22no—
244C4×C11—42no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—82no—
249C4×C11—81no—
250C4×C11—82no—
251C4×C11—81no—
252C4×C11#52511yescharacteristic
253C4×C11#53611yescharacteristic
254C4×C11#55212yes—
255C22×Q8C23×C1111yescharacteristic
256C23×C4—21no—
257C23×C4—21no—
258C23×C4C23×C1111yescharacteristic
259C22×C8—22no—
260C22×C8—24no—
261C22×C8C23×C1111yescharacteristic
262C22×C8C23×C1111yescharacteristic
263C22×C8C23×C1112yes—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266#117—44no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4D4×C1114yes—
275C2×C4⋊C4C23×C1112yes—
276C2×C4⋊C4C23×C1111yescharacteristic
277C2×C4⋊C4C23×C1112yes—
278C2×C4⋊C4C23×C1111yescharacteristic
279C2×C4⋊C4C23×C1111yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4D4×C1111yescharacteristic
283C2×C22⋊C4D4×C1111yescharacteristic
284C2×C42—22no—
285C2×C42C23×C1112yes—
286#107—24no—
287#107—24no—
288#106—22no—
289#106—22no—
290C4⋊C8—24no—
291#103—24no—
292#103—22no—
293#103—22no—
294C22⋊C8—22no—
295#95—22no—
296#95—21no—
297#95—22no—
298#95—22no—
299#95—22no—
300#95—22no—
301#95—22no—
302#95D4×C1112yes—
303C2×C11—24no—
304C2×C11#241311yescharacteristic
305C2×C11C2×#46311yescharacteristic
306C2×C11#304411yescharacteristic
307C2×C11#333612yes—
308C2×C11#334312yes—
309C24C2×D4×C1111yescharacteristic
310C2×Q8—21no—
311C2×Q8—22no—
312C2×Q8—21no—
313C2×Q8—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—24no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4C2×D4×C1112yes—
329C22×C4C2×D4×C1112yes—
330C22×C4C2×D4×C1111yescharacteristic
331C22×C4C2×D4×C1112yes—
332C22×C4C11×#4112yes—
333C22×C4C24×C1111yescharacteristic
334C2×C8—28no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8C11×#4114yes—
342C4⋊C4—24no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—22no—
351C4⋊C4—44no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4C2×D4×C1112yes—
355C4⋊C4C2×D4×C1112yes—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—42no—
359C22⋊C4—42no—
360C42—22no—
361C42—22no—
362C42—44no—
363C11#2457711yescharacteristic, direct product factor, Sylow
364C23—22no—
365C23—22no—
366C23C11×#12112yes—
367C23C11×#13512yes—
368C23C11×AGL(1,ℤ/8)12yes—
369C23C22×D4×C1111yescharacteristic
370Q8—41no—
371Q8—41no—
372Q8—42no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—48no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—84no—
401C2×C4C11×#12112yes—
402C2×C4C22×D4×C1111yescharacteristic
403C2×C4C2×C11×#4112yes—
404C2×C4C2×C11×#4111yescharacteristic
405C2×C4C11×2−1+412yes—
406C8—24no—
407C8—41no—
408C8—41no—
409C22—22no—
410C22—22no—
411C22—24no—
412C22—24no—
413C22C11×#46314yes—
414C22C2×C11×#12111yescharacteristic
415C22C11×#54712yes—
416C22C2×C11×#13511yescharacteristic
417C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
418C22C11×#57812yes—
419C4—22no—
420C4—42no—
421C4—42no—
422C4—42no—
423C4—42no—
424C4—81no—
425C4—82no—
426C4—81no—
427C4—82no—
428C4C11×#52511yescharacteristic
429C4C11×#53611yescharacteristic
430C4C11×#55212yes—
431C2—24no—
432C2C11×#241311yescharacteristic
433C2C2×C11×#46311yescharacteristic
434C2C11×#304411yescharacteristic
435C2C11×#333612yes—
436C2C11×#334312yes—
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×#1928C2semidirect
91. #24577C11direct (N × H)
150. #2085C2×C11semidirect
151. #2068C2×C11semidirect
152. #1949C2×C11semidirect
153. #1928C2×C11semidirect
363. C11#24577direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4832
C22×C11×#1072
C11×#25032
C11×#23442
C11×#20852
C11×#20682
C11×#19492
C11×#19282
C11×#18922
C11×#18502
C11×#18232
#2457711