Finite Group Databasebeta

← C11×#18391 #14595584

Subgroups — C11×#18391 #14595584

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic, complemented
3C11×#3205C211yesmaximal, characteristic
4C11×#2548C211yesmaximal, characteristic, complemented
5C11×#1597C218yesmaximal, complemented
6C11×#1503C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic, complemented
8C11×#1461C211yesmaximal, characteristic, complemented
9C11×#559—21no—
10C11×#557—21no—
11C11×#556—21no—
12C11×#556—22no—
13C11×#554—21no—
14C11×#552—22no—
15C11×#539C2214yes—
16C11×#536—21no—
17C11×#533C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C11×#529—22no—
21C2×C11×#124—21no—
22C11×#520—21no—
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#493—21no—
25C11×#492—21no—
26C11×#486—21no—
27C11×#486—21no—
28C11×#460—22no—
29C11×#459—22no—
30C11×#450C2214yes—
31C11×#447C2214yes—
32C11×#431C2211yescharacteristic
33C11×#431C2211yescharacteristic
34C11×#394C2214yes—
35C11×#390—21no—
36C11×#390—22no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#328C2214yes—
39C11×#327C2214yes—
40C11×#324C2214yes—
41C2×C11×#41—21no—
42C22×Q8×C11D411yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C2×C11×SD16—24no—
47C2×C11×D8—24no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8D411yescharacteristic
50C11×C4⋊Q8D411yescharacteristic
51C11×C4⋊Q8D411yescharacteristic
52C11×#127—21no—
53C11×#127—21no—
54C11×#127—21no—
55C11×#127—21no—
56C11×#127D411yescharacteristic
57C11×#126—24no—
58C11×#126—24no—
59C11×#125—22no—
60C11×#125—24no—
61C11×#125—21no—
62C11×#124—22no—
63C11×#124—22no—
64C11×#124—21no—
65C11×#124—44no—
66C11×#123—24no—
67C11×#123—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8C2312yes—
73C11×#121—21no—
74C11×#121C2312yes—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11D412yes—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—24no—
86C4×D4×C11—21no—
87C4×D4×C11D412yes—
88C11×#117—22no—
89C11×#117—24no—
90C11×#117—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—24no—
97C2×C42×C11—21no—
98C2×C42×C11D412yes—
99C2×C42×C11C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×#102—24no—
103C11×#102—24no—
104C11×C22⋊C8C2312yes—
105C11×C22⋊C8C2312yes—
106C4×C8×C11—21no—
107C4×C8×C11—21no—
108C11×#95C2312yes—
109#18391C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—22no—
111C11×#41—42no—
112C11×#41—42no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—44no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11—82no—
133C2×D4×C11C2×D412yes—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C11×SD16—84no—
143C11×D8—84no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4C2×D412yes—
161C11×C4⋊C4C2×D412yes—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—48no—
169C11×C22⋊C4—84no—
170C42×C11—24no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—42no—
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179#3507C2×C1111yescharacteristic, complemented
180#3208C2×C1111yescharacteristic, complemented
181#3205C2×C1111yescharacteristic
182#2548C2×C1111yescharacteristic, complemented
183#1597C2×C1118yescomplemented
184#1503C2×C1111yescharacteristic, complemented
185#1502C2×C1111yescharacteristic, complemented
186#1461C2×C1111yescharacteristic, complemented
187C23×C11—22no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11C22×D411yescharacteristic
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—42no—
198Q8×C11—42no—
199D4×C11—42no—
200D4×C11—44no—
201D4×C11—44no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—82no—
207D4×C11—82no—
208D4×C11—82no—
209D4×C11—82no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—44no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—84no—
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11#13512yes—
230C2×C4×C11AGL(1,ℤ/8)12yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C8×C11—42no—
234C8×C11—42no—
235#559—21no—
236#557—21no—
237#556—21no—
238#556—22no—
239#554—21no—
240#552—22no—
241#539C22×C1114yes—
242#536—21no—
243#533C22×C1111yescharacteristic
244#532C22×C1111yescharacteristic
245C2×#127C22×C1111yescharacteristic
246#529—22no—
247C2×#124—21no—
248#520—21no—
249C2×C4×Q8C22×C1111yescharacteristic
250#493—21no—
251#492—21no—
252#486—21no—
253#486—21no—
254#460—22no—
255#459—22no—
256#450C22×C1114yes—
257#447C22×C1114yes—
258#431C22×C1111yescharacteristic
259#431C22×C1111yescharacteristic
260#394C22×C1114yes—
261#390—21no—
262#390—22no—
263C4×C4⋊C4C22×C1111yescharacteristic
264#328C22×C1114yes—
265#327C22×C1114yes—
266#324C22×C1114yes—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—84no—
273C22×C11—84no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11C2×#12011yescharacteristic
278C22×C11C2×#13511yescharacteristic
279C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—82no—
289C4×C11#44912yes—
290C4×C11#44912yes—
291C4×C11#45412yes—
292C2×#41—21no—
293C22×Q8D4×C1111yescharacteristic
294C22×D4—21no—
295C22×D4—21no—
296C22×D4C23×C1112yes—
297C2×SD16—24no—
298C2×D8—24no—
299C4⋊Q8—22no—
300C4⋊Q8D4×C1111yescharacteristic
301C4⋊Q8D4×C1111yescharacteristic
302C4⋊Q8D4×C1111yescharacteristic
303#127—21no—
304#127—21no—
305#127—21no—
306#127—21no—
307#127D4×C1111yescharacteristic
308#126—24no—
309#126—24no—
310#125—22no—
311#125—24no—
312#125—21no—
313#124—22no—
314#124—22no—
315#124—21no—
316#124—44no—
317#123—24no—
318#123—24no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—24no—
322C22⋊Q8—21no—
323C22⋊Q8C23×C1112yes—
324#121—21no—
325#121C23×C1112yes—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8D4×C1112yes—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—24no—
337C4×D4—21no—
338C4×D4D4×C1112yes—
339#117—22no—
340#117—24no—
341#117—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4D4×C1111yescharacteristic
345C2×C4⋊C4C23×C1112yes—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C42—21no—
349C2×C42D4×C1112yes—
350C2×C42C23×C1111yescharacteristic
351C4⋊C8—21no—
352C4⋊C8—21no—
353#102—24no—
354#102—24no—
355C22⋊C8C23×C1112yes—
356C22⋊C8C23×C1112yes—
357C4×C8—21no—
358C4×C8—21no—
359#95C23×C1112yes—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—82no—
363C2×C11—162no—
364C2×C11C2×#44911yescharacteristic
365C2×C11C2×#45411yescharacteristic
366C2×C11#302711yescharacteristic
367C24—22no—
368#41—42no—
369#41—42no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8C2×D4×C1112yes—
377C2×D4—22no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—44no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—82no—
390C2×D4C2×D4×C1112yes—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4C2×D4×C1112yes—
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1112yes—
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C24×C1111yescharacteristic
399SD16—84no—
400D8—84no—
401C2×C8—22no—
402C2×C8—22no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—42no—
417C4⋊C4C2×D4×C1112yes—
418C4⋊C4C2×D4×C1112yes—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—48no—
426C22⋊C4—84no—
427C42—24no—
428C42—22no—
429C42—22no—
430C42—22no—
431C42—42no—
432C42C2×D4×C1111yescharacteristic
433C42C2×D4×C1111yescharacteristic
434C42C2×D4×C1111yescharacteristic
435C42C2×D4×C1111yescharacteristic
436C11#1839111yescharacteristic, direct product factor, Sylow
437C23—22no—
438C23—44no—
439C23—44no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23C22×D4×C1111yescharacteristic
444Q8—42no—
445Q8—42no—
446Q8—42no—
447Q8—42no—
448Q8—42no—
449D4—42no—
450D4—44no—
451D4—44no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—82no—
457D4—82no—
458D4—82no—
459D4—82no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—84no—
475C2×C4C11×#12011yescharacteristic
476C2×C4C11×#12011yescharacteristic
477C2×C4C11×#12011yescharacteristic
478C2×C4C11×#12011yescharacteristic
479C2×C4C11×#13512yes—
480C2×C4C11×AGL(1,ℤ/8)12yes—
481C2×C4C22×D4×C1111yescharacteristic
482C2×C4C22×D4×C1111yescharacteristic
483C8—42no—
484C8—42no—
485C22—21no—
486C22—21no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—84no—
491C22—84no—
492C22—82no—
493C22—82no—
494C22—82no—
495C22C2×C11×#12011yescharacteristic
496C22C2×C11×#13511yescharacteristic
497C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—82no—
507C4C11×#44912yes—
508C4C11×#44912yes—
509C4C11×#45412yes—
510C2—21no—
511C2—21no—
512C2—82no—
513C2—162no—
514C2C2×C11×#44911yescharacteristic
515C2C2×C11×#45411yescharacteristic
516C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3205C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3507C2semidirect
2. C11×#3208C2semidirect
4. C11×#2548C2semidirect
5. C11×#1597C2semidirect
6. C11×#1503C2semidirect
7. C11×#1502C2semidirect
8. C11×#1461C2semidirect
109. #18391C11direct (N × H)
179. #3507C2×C11semidirect
180. #3208C2×C11semidirect
182. #2548C2×C11semidirect
183. #1597C2×C11semidirect
184. #1503C2×C11semidirect
185. #1502C2×C11semidirect
186. #1461C2×C11semidirect
436. C11#18391direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#32082
C11×#32052
C11×#25482
C11×#15972
C11×#15032
C11×#15022
C11×#14612
#1839111