Finite Group Databasebeta

← C11×#24579 #14601772

Subgroups — C11×#24579 #14601772

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#484C211yesmaximal, characteristic
2C22×C11×#106C211yesmaximal, characteristic
3C11×#2503C211yesmaximal, characteristic
4C11×#2345C211yesmaximal, characteristic
5C11×#2085C212yesmaximal, complemented
6C11×#2066C212yesmaximal, complemented
7C11×#1949C212yesmaximal, complemented
8C11×#1927C212yesmaximal, complemented
9C11×#1892C211yesmaximal, characteristic
10C11×#1850C211yesmaximal, characteristic
11C11×#1823C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C11×#484—24no—
17C2×C11×#107C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106—24no—
20C2×C11×#106C2212yes—
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#400—22no—
28C11×#391C2212yes—
29C11×#389C2212yes—
30C11×#387—22no—
31C11×#382C2212yes—
32C11×#381—21no—
33C11×#381—21no—
34C11×#380—21no—
35C11×#380C2211yescharacteristic
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C22⋊C4—21no—
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—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4D414yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C42×C11—22no—
72C2×C42×C11C2312yes—
73C11×#107—22no—
74C11×#107—22no—
75C11×#106—24no—
76C11×#106—24no—
77C11×C4⋊C8—24no—
78C11×#103—24no—
79C11×#103—22no—
80C11×#103—22no—
81C11×C22⋊C8—22no—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—21no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D412yes—
90#24579C1111yesmaximal, 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—24no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—82no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11#4112yes—
114C22×C4×C11C2411yescharacteristic
115C2×C8×C11—28no—
116C2×C8×C11—22no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11#4114yes—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—82no—
135C11×C4⋊C4C2×D412yes—
136C11×C4⋊C4C2×D412yes—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—42no—
140C11×C22⋊C4—42no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—82no—
144C2×#484C2×C1111yescharacteristic
145C22×#106C2×C1111yescharacteristic
146#2503C2×C1111yescharacteristic
147#2345C2×C1111yescharacteristic
148#2085C2×C1112yescomplemented
149#2066C2×C1112yescomplemented
150#1949C2×C1112yescomplemented
151#1927C2×C1112yescomplemented
152#1892C2×C1111yescharacteristic
153#1850C2×C1111yescharacteristic
154#1823C2×C1111yescharacteristic
155C23×C11—22no—
156C23×C11—22no—
157C23×C11#12112yes—
158C23×C11#13512yes—
159C23×C11#13712yes—
160C23×C11C22×D411yescharacteristic
161Q8×C11—41no—
162Q8×C11—41no—
163Q8×C11—42no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
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—42no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
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—84no—
189C2×C4×C11—84no—
190C2×C4×C11#12112yes—
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4112yes—
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C112−1+412yes—
195C8×C11—24no—
196C8×C11—41no—
197C8×C11—41no—
198C23×C8C22×C1111yescharacteristic
199C2×C22⋊Q8C22×C1111yescharacteristic
200C22×C4⋊C4C22×C1111yescharacteristic
201C22×C4⋊C4C22×C1111yescharacteristic
202#484—24no—
203C2×#107C22×C1111yescharacteristic
204C2×#107C22×C1111yescharacteristic
205C2×#106—24no—
206C2×#106C22×C1112yes—
207C2×#106C22×C1112yes—
208C2×C4⋊C8C22×C1112yes—
209C2×#103C22×C1111yescharacteristic
210C2×#103C22×C1112yes—
211C2×#103C22×C1111yescharacteristic
212C2×C22⋊C8C22×C1111yescharacteristic
213#400—22no—
214#391C22×C1112yes—
215#389C22×C1112yes—
216#387—22no—
217#382C22×C1112yes—
218#381—21no—
219#381—21no—
220#380—21no—
221#380C22×C1111yescharacteristic
222C4×C4⋊C4C22×C1112yes—
223C4×C22⋊C4—21no—
224C4×C22⋊C4C22×C1111yescharacteristic
225#340C22×C1112yes—
226#340C22×C1112yes—
227#340C22×C1112yes—
228#336C22×C1112yes—
229C22×C11—24no—
230C22×C11—24no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11#46414yes—
234C22×C11C2×#12111yescharacteristic
235C22×C11#54712yes—
236C22×C11C2×#13511yescharacteristic
237C22×C11C2×#13711yescharacteristic
238C22×C11#57712yes—
239C4×C11—22no—
240C4×C11—42no—
241C4×C11—42no—
242C4×C11—42no—
243C4×C11—42no—
244C4×C11—82no—
245C4×C11—81no—
246C4×C11—82no—
247C4×C11—81no—
248C4×C11#52511yescharacteristic
249C4×C11#53611yescharacteristic
250C4×C11#55212yes—
251C22×Q8C23×C1111yescharacteristic
252C23×C4—21no—
253C23×C4—21no—
254C23×C4C23×C1111yescharacteristic
255C22×C8—22no—
256C22×C8—24no—
257C22×C8C23×C1111yescharacteristic
258C22×C8C23×C1111yescharacteristic
259C22×C8C23×C1112yes—
260C22⋊Q8—22no—
261C22⋊Q8—22no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4D4×C1114yes—
270C2×C4⋊C4C23×C1112yes—
271C2×C4⋊C4C23×C1111yescharacteristic
272C2×C4⋊C4C23×C1112yes—
273C2×C4⋊C4C23×C1111yescharacteristic
274C2×C4⋊C4C23×C1111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4D4×C1111yescharacteristic
278C2×C22⋊C4D4×C1111yescharacteristic
279C2×C42—22no—
280C2×C42C23×C1112yes—
281#107—22no—
282#107—22no—
283#106—24no—
284#106—24no—
285C4⋊C8—24no—
286#103—24no—
287#103—22no—
288#103—22no—
289C22⋊C8—22no—
290#95—22no—
291#95—22no—
292#95—21no—
293#95—22no—
294#95—22no—
295#95—22no—
296#95—22no—
297#95D4×C1112yes—
298C2×C11—24no—
299C2×C11#241311yescharacteristic
300C2×C11C2×#46411yescharacteristic
301C2×C11#304211yescharacteristic
302C2×C11#333712yes—
303C2×C11#334412yes—
304C24C2×D4×C1111yescharacteristic
305C2×Q8—21no—
306C2×Q8—22no—
307C2×Q8—21no—
308C2×Q8—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—24no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—82no—
322C22×C4C2×D4×C1112yes—
323C22×C4C2×D4×C1112yes—
324C22×C4C2×D4×C1111yescharacteristic
325C22×C4C2×D4×C1112yes—
326C22×C4C11×#4112yes—
327C22×C4C24×C1111yescharacteristic
328C2×C8—28no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8C11×#4114yes—
336C4⋊C4—24no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—22no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—82no—
348C4⋊C4C2×D4×C1112yes—
349C4⋊C4C2×D4×C1112yes—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C42—22no—
355C42—22no—
356C42—82no—
357C11#2457911yescharacteristic, direct product factor, Sylow
358C23—22no—
359C23—22no—
360C23C11×#12112yes—
361C23C11×#13512yes—
362C23C11×#13712yes—
363C23C22×D4×C1111yescharacteristic
364Q8—41no—
365Q8—41no—
366Q8—42no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—84no—
392C2×C4—84no—
393C2×C4C11×#12112yes—
394C2×C4C22×D4×C1111yescharacteristic
395C2×C4C2×C11×#4112yes—
396C2×C4C2×C11×#4111yescharacteristic
397C2×C4C11×2−1+412yes—
398C8—24no—
399C8—41no—
400C8—41no—
401C22—22no—
402C22—22no—
403C22—24no—
404C22—24no—
405C22C11×#46414yes—
406C22C2×C11×#12111yescharacteristic
407C22C11×#54712yes—
408C22C2×C11×#13511yescharacteristic
409C22C2×C11×#13711yescharacteristic
410C22C11×#57712yes—
411C4—22no—
412C4—42no—
413C4—42no—
414C4—42no—
415C4—42no—
416C4—81no—
417C4—82no—
418C4—81no—
419C4—82no—
420C4C11×#52511yescharacteristic
421C4C11×#53611yescharacteristic
422C4C11×#55212yes—
423C2—24no—
424C2C11×#241311yescharacteristic
425C2C2×C11×#46411yescharacteristic
426C2C11×#304211yescharacteristic
427C2C11×#333712yes—
428C2C11×#334412yes—
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×#2066C2semidirect
7. C11×#1949C2semidirect
8. C11×#1927C2semidirect
90. #24579C11direct (N × H)
148. #2085C2×C11semidirect
149. #2066C2×C11semidirect
150. #1949C2×C11semidirect
151. #1927C2×C11semidirect
357. C11#24579direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4842
C22×C11×#1062
C11×#25032
C11×#23452
C11×#20852
C11×#20662
C11×#19492
C11×#19272
C11×#18922
C11×#18502
C11×#18232
#2457911