Finite Group Databasebeta

← C11×#10375 #14587568

Subgroups — C11×#10375 #14587568

Order 2816.

466 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2549C211yesmaximal, characteristic
2C11×#1996C211yesmaximal, characteristic
3C11×#1520C211yesmaximal, characteristic
4C2×C11×#328C211yesmaximal, characteristic
5C11×#1294C211yesmaximal, characteristic
6C11×#1289C211yesmaximal, characteristic
7C11×#1282C211yesmaximal, characteristic
8C2×C11×C22⋊Q8—21no—
9C2×C11×C22⋊Q8C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#398—21no—
13C11×#395—21no—
14C11×#391—21no—
15C11×#389—21no—
16C11×#385—21no—
17C11×#380C2211yescharacteristic
18C11×#380C2211yescharacteristic
19C4×C11×C22⋊C4C2211yescharacteristic
20C2×C11×#95C2211yescharacteristic
21C11×#342—21no—
22C11×#342—21no—
23C11×#328—21no—
24C11×#328—21no—
25C11×#328—21no—
26C11×#328—21no—
27C22×Q8×C11—21no—
28C22×Q8×C11Q811yescharacteristic, complemented
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—42no—
38C11×C22⋊Q8—42no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4Q811yescharacteristic, complemented
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4D411yescharacteristic
52C2×C11×C22⋊C4D411yescharacteristic
53C2×C42×C11—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65C11×#95D411yescharacteristic
66C11×#95D411yescharacteristic
67#10375C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11C2×D411yescharacteristic
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—42no—
72C2×Q8×C11—42no—
73C2×Q8×C11—81no—
74C2×Q8×C11—81no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—42no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—81no—
88C22×C4×C11—81no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×Q811yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—81no—
98C2×C8×C11—81no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—81no—
108C11×C4⋊C4—81no—
109C11×C4⋊C4—81no—
110C11×C22⋊C4—21no—
111C11×C22⋊C4—21no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4SD1612yes—
119C11×C22⋊C4Q1612yes—
120C42×C11—81no—
121#2549C2×C1111yescharacteristic
122#1996C2×C1111yescharacteristic
123#1520C2×C1111yescharacteristic
124C2×#328C2×C1111yescharacteristic
125#1294C2×C1111yescharacteristic
126#1289C2×C1111yescharacteristic
127#1282C2×C1111yescharacteristic
128C23×C11—41no—
129C23×C11—41no—
130C23×C11#12011yescharacteristic
131C23×C11C22⋊Q811yescharacteristic
132C23×C11#12411yescharacteristic
133C23×C11C2×SD1611yescharacteristic
134C23×C11C2×Q1611yescharacteristic
135C23×C11AGL(1,ℤ/8)11yescharacteristic
136C23×C11#13711yescharacteristic
137Q8×C11—81no—
138Q8×C11—81no—
139Q8×C11—84no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
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—82no—
167C2×C4×C11—82no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11C22⋊Q811yescharacteristic
174C2×C4×C11C22⋊Q811yescharacteristic
175C2×C4×C11#12411yescharacteristic
176C2×C4×C11#12411yescharacteristic
177C8×C11—81no—
178C8×C11—81no—
179C2×C22⋊Q8—21no—
180C2×C22⋊Q8C22×C1111yescharacteristic
181C2×C22⋊C8C22×C1111yescharacteristic
182C2×C22⋊C8C22×C1111yescharacteristic
183#398—21no—
184#395—21no—
185#391—21no—
186#389—21no—
187#385—21no—
188#380C22×C1111yescharacteristic
189#380C22×C1111yescharacteristic
190C4×C22⋊C4C22×C1111yescharacteristic
191C2×#95C22×C1111yescharacteristic
192#342—21no—
193#342—21no—
194#328—21no—
195#328—21no—
196#328—21no—
197#328—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11#39311yescharacteristic
209C22×C11#45011yescharacteristic
210C22×C11#45111yescharacteristic
211C22×C11#47511yescharacteristic
212C22×C11#47711yescharacteristic
213C22×C11#48711yescharacteristic
214C22×C11#48911yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—42no—
220C4×C11—42no—
221C4×C11—42no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11—161no—
228C22×Q8—21no—
229C22×Q8Q8×C1111yescharacteristic, complemented
230C23×C4—21no—
231C23×C4C23×C1111yescharacteristic
232C22×C8—21no—
233C22×C8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—42no—
239C22⋊Q8—42no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4Q8×C1111yescharacteristic, complemented
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4D4×C1111yescharacteristic
253C2×C22⋊C4D4×C1111yescharacteristic
254C2×C42—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95D4×C1111yescharacteristic
265#95D4×C1111yescharacteristic
266#95D4×C1111yescharacteristic
267#95D4×C1111yescharacteristic
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—21no—
274C2×C11#202411yescharacteristic
275C2×C11#203111yescharacteristic
276C2×C11#203211yescharacteristic
277C24C2×D4×C1111yescharacteristic
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8—81no—
283C2×Q8—81no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—81no—
297C22×C4—81no—
298C22×C4C2×D4×C1111yescharacteristic
299C22×C4C2×D4×C1111yescharacteristic
300C22×C4C2×Q8×C1111yescharacteristic
301C22×C4C11×#4111yescharacteristic
302C22×C4C11×#4111yescharacteristic
303C22×C4C11×#4111yescharacteristic
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—81no—
307C2×C8—81no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—81no—
317C4⋊C4—81no—
318C4⋊C4—81no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4C11×SD1612yes—
328C22⋊C4C11×Q1612yes—
329C42—81no—
330C11#1037511yescharacteristic, direct product factor, Sylow
331C23—41no—
332C23—41no—
333C23C11×#12011yescharacteristic
334C23C11×C22⋊Q811yescharacteristic
335C23C11×#12411yescharacteristic
336C23C2×C11×SD1611yescharacteristic
337C23C2×C11×Q1611yescharacteristic
338C23C11×AGL(1,ℤ/8)11yescharacteristic
339C23C11×#13711yescharacteristic
340Q8—81no—
341Q8—81no—
342Q8—84no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
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×C4—41no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4C11×C22⋊Q811yescharacteristic
377C2×C4C11×C22⋊Q811yescharacteristic
378C2×C4C11×#12411yescharacteristic
379C2×C4C11×#12411yescharacteristic
380C8—81no—
381C8—81no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22C11×#39311yescharacteristic
393C22C11×#45011yescharacteristic
394C22C11×#45111yescharacteristic
395C22C11×#47511yescharacteristic
396C22C11×#47711yescharacteristic
397C22C11×#48711yescharacteristic
398C22C11×#48911yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—42no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—161no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2—21no—
417C2—21no—
418C2C11×#202411yescharacteristic
419C2C11×#203111yescharacteristic
420C2C11×#203211yescharacteristic
subgroupG/H
center, socleC22×C11#393
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
28. C22×Q8×C11Q8semidirect
47. C2×C11×C4⋊C4Q8semidirect
67. #10375C11direct (N × H)
229. C22×Q8Q8×C11semidirect
248. C2×C4⋊C4Q8×C11semidirect
330. C11#10375direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25492
C11×#19962
C11×#15202
C2×C11×#3282
C11×#12942
C11×#12892
C11×#12822
#1037511