Finite Group Databasebeta

← C11×#18914 #14596107

Subgroups — C11×#18914 #14596107

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic
3C11×#3208C211yesmaximal, characteristic
4C2×C11×#460C211yesmaximal, characteristic
5C11×#1626C214yesmaximal, complemented
6C11×#1623C214yesmaximal, complemented
7C11×#1542C211yesmaximal, characteristic, complemented
8C11×#1481C211yesmaximal, characteristic, complemented
9C11×#1479C211yesmaximal, characteristic, complemented
10C22×C11×SD16—21no—
11Q82×C11—21no—
12Q82×C11C2212yescomplemented
13C11×#557—21no—
14C11×#557—22no—
15C11×#557—22no—
16C11×#557C2212yescomplemented
17C11×#544—22no—
18C11×#544—21no—
19C11×#533—22no—
20C11×#533C2211yescharacteristic
21C11×#533C2211yescharacteristic
22C2×C11×#127C2211yescharacteristic
23C11×#519—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#492—21no—
26C11×#492C2212yes—
27C11×#486—21no—
28C11×#486C2212yes—
29C11×#460—22no—
30C11×#460—22no—
31C11×#460C2214yes—
32C11×#460C2214yes—
33C11×#450—22no—
34C11×#450—22no—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#102—21no—
39C11×#333C2212yescomplemented
40C11×#332C2212yescomplemented
41C11×Q8⋊C8C2214yescomplemented
42C11×Q8⋊C8C2214yescomplemented
43C22×Q8×C11D411yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C2×C11×SD16—24no—
48C2×C11×SD16—24no—
49C2×C11×SD16—24no—
50C2×C11×SD16—44no—
51C22×C8×C11—21no—
52C11×C4⋊Q8—24no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—24no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8D411yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×#127—21no—
63C11×#127—21no—
64C11×#127—21no—
65C11×#127C2312yes—
66C11×#125—24no—
67C11×#125—24no—
68C11×#125—22no—
69C11×#125—24no—
70C11×#125—22no—
71C11×#125—21no—
72C11×#125—21no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8D412yes—
77C11×C22⋊Q8D412yes—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—24no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—21no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11D412yes—
90C4×Q8×C11D412yes—
91C4×Q8×C11C2312yes—
92C4×Q8×C11C2312yes—
93C11×#117—24no—
94C11×#117—21no—
95C11×#117—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2312yes—
104C11×#102—24no—
105C11×#102—24no—
106C11×#102—24no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#18914C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—41no—
113C2×Q8×C11—24no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—21no—
118C2×Q8×C11SD1614yescomplemented
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11C2×D412yes—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—82no—
131C2×D4×C11—82no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C11×SD16—48no—
138C11×SD16—84no—
139C11×SD16—84no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—42no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C42×C11—24no—
168C42×C11—24no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2411yescharacteristic
177#3502C2×C1111yescharacteristic, complemented
178#3208C2×C1111yescharacteristic
179#3208C2×C1111yescharacteristic
180C2×#460C2×C1111yescharacteristic
181#1626C2×C1114yescomplemented
182#1623C2×C1114yescomplemented
183#1542C2×C1111yescharacteristic, complemented
184#1481C2×C1111yescharacteristic, complemented
185#1479C2×C1111yescharacteristic, complemented
186C23×C11—42no—
187C23×C11—82no—
188C23×C11—82no—
189C23×C11—82no—
190C23×C11#12011yescharacteristic
191Q8×C11—22no—
192Q8×C11—24no—
193Q8×C11—24no—
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—81no—
197Q8×C11—84no—
198Q8×C11C2×SD1614yes—
199D4×C11—44no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—82no—
204D4×C11—82no—
205D4×C11—82no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—41no—
215C2×C4×C11—81no—
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11C2×SD1612yes—
220C2×C4×C11#13712yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C8×C11—42no—
225C8×C11—42no—
226C8×C11—42no—
227C22×SD16—21no—
228Q82—21no—
229Q82C22×C1112yescomplemented
230#557—21no—
231#557—22no—
232#557—22no—
233#557C22×C1112yescomplemented
234#544—22no—
235#544—21no—
236#533—22no—
237#533C22×C1111yescharacteristic
238#533C22×C1111yescharacteristic
239C2×#127C22×C1111yescharacteristic
240#519—21no—
241C2×C4×Q8C22×C1111yescharacteristic
242#492—21no—
243#492C22×C1112yes—
244#486—21no—
245#486C22×C1112yes—
246#460—22no—
247#460—22no—
248#460C22×C1114yes—
249#460C22×C1114yes—
250#450—22no—
251#450—22no—
252#431C22×C1111yescharacteristic
253#431C22×C1111yescharacteristic
254C2×C4⋊C8C22×C1111yescharacteristic
255C2×#102—21no—
256#333C22×C1112yescomplemented
257#332C22×C1112yescomplemented
258Q8⋊C8C22×C1114yescomplemented
259Q8⋊C8C22×C1114yescomplemented
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—82no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—164no—
266C22×C11#44812yes—
267C22×C11C2×#12011yescharacteristic
268C4×C11—24no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11#44812yes—
278C4×C11C22×SD1611yescharacteristic
279C4×C11C2×#13711yescharacteristic
280C4×C11#57712yes—
281C22×Q8D4×C1111yescharacteristic
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—21no—
285C2×SD16—24no—
286C2×SD16—24no—
287C2×SD16—24no—
288C2×SD16—44no—
289C22×C8—21no—
290C4⋊Q8—24no—
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293C4⋊Q8—24no—
294C4⋊Q8—22no—
295C4⋊Q8—22no—
296C4⋊Q8D4×C1111yescharacteristic
297C4⋊Q8D4×C1111yescharacteristic
298C4⋊Q8C23×C1111yescharacteristic
299C4⋊Q8C23×C1111yescharacteristic
300#127—21no—
301#127—21no—
302#127—21no—
303#127C23×C1112yes—
304#125—24no—
305#125—24no—
306#125—22no—
307#125—24no—
308#125—22no—
309#125—21no—
310#125—21no—
311C22⋊Q8—24no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8D4×C1112yes—
315C22⋊Q8D4×C1112yes—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—24no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×Q8D4×C1112yes—
328C4×Q8D4×C1112yes—
329C4×Q8C23×C1112yes—
330C4×Q8C23×C1112yes—
331#117—24no—
332#117—21no—
333#117—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4D4×C1111yescharacteristic
336C2×C42—21no—
337C2×C42C23×C1111yescharacteristic
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8C23×C1112yes—
341C4⋊C8C23×C1112yes—
342#102—24no—
343#102—24no—
344#102—24no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C4×C8—21no—
348C4×C8C23×C1112yes—
349C2×C11—22no—
350C2×C11—162no—
351C2×C11C2×#44811yescharacteristic
352C2×C11#301011yescharacteristic
353C2×C11#302111yescharacteristic
354C24—41no—
355C2×Q8—24no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—21no—
360C2×Q8C11×SD1614yescomplemented
361C2×Q8C2×D4×C1112yes—
362C2×Q8C2×D4×C1112yes—
363C2×Q8C2×D4×C1112yes—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—82no—
373C2×D4—82no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1111yescharacteristic
379SD16—48no—
380SD16—84no—
381SD16—84no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—42no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4C2×D4×C1112yes—
405C4⋊C4C2×D4×C1112yes—
406C4⋊C4C2×D4×C1112yes—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C42—24no—
410C42—24no—
411C42—22no—
412C42—22no—
413C42—22no—
414C42—22no—
415C42C2×D4×C1111yescharacteristic
416C42C2×D4×C1111yescharacteristic
417C42C2×D4×C1111yescharacteristic
418C42C24×C1111yescharacteristic
419C11#1891411yescharacteristic, direct product factor, Sylow
420C23—42no—
421C23—82no—
422C23—82no—
423C23—82no—
424C23C11×#12011yescharacteristic
425Q8—22no—
426Q8—24no—
427Q8—24no—
428Q8—42no—
429Q8—42no—
430Q8—81no—
431Q8—84no—
432Q8C2×C11×SD1614yes—
433D4—44no—
434D4—42no—
435D4—42no—
436D4—44no—
437D4—82no—
438D4—82no—
439D4—82no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—81no—
450C2×C4C11×#12011yescharacteristic
451C2×C4C11×#12011yescharacteristic
452C2×C4C11×#12011yescharacteristic
453C2×C4C2×C11×SD1612yes—
454C2×C4C11×#13712yes—
455C2×C4C22×D4×C1111yescharacteristic
456C2×C4C22×D4×C1111yescharacteristic
457C2×C4C22×D4×C1111yescharacteristic
458C8—42no—
459C8—42no—
460C8—42no—
461C22—21no—
462C22—21no—
463C22—82no—
464C22—82no—
465C22—82no—
466C22—164no—
467C22C11×#44812yes—
468C22C2×C11×#12011yescharacteristic
469C4—24no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—42no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—42no—
478C4C11×#44812yes—
479C4C22×C11×SD1611yescharacteristic
480C4C2×C11×#13711yescharacteristic
481C4C11×#57712yes—
482C2—22no—
483C2—162no—
484C2C2×C11×#44811yescharacteristic
485C2C11×#301011yescharacteristic
486C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C42 ▷ 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×#3502C2semidirect
5. C11×#1626C2semidirect
6. C11×#1623C2semidirect
7. C11×#1542C2semidirect
8. C11×#1481C2semidirect
9. C11×#1479C2semidirect
12. Q82×C11C22semidirect
16. C11×#557C22semidirect
39. C11×#333C22semidirect
40. C11×#332C22semidirect
41. C11×Q8⋊C8C22semidirect
42. C11×Q8⋊C8C22semidirect
111. #18914C11direct (N × H)
118. C2×Q8×C11SD16semidirect
177. #3502C2×C11semidirect
181. #1626C2×C11semidirect
182. #1623C2×C11semidirect
183. #1542C2×C11semidirect
184. #1481C2×C11semidirect
185. #1479C2×C11semidirect
229. Q82C22×C11semidirect
233. #557C22×C11semidirect
256. #333C22×C11semidirect
257. #332C22×C11semidirect
258. Q8⋊C8C22×C11semidirect
259. Q8⋊C8C22×C11semidirect
360. C2×Q8C11×SD16semidirect
419. C11#18914direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35022
C11×#32082
C2×C11×#4602
C11×#16262
C11×#16232
C11×#15422
C11×#14812
C11×#14792
#1891411