Finite Group Databasebeta

← C11×#23510 #14600703

Subgroups — C11×#23510 #14600703

Order 2816.

1414 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic
3C2×C11×#419C211yesmaximal, characteristic, complemented
4C2×C11×#416C211yesmaximal, characteristic
5C22×C11×#103C211yesmaximal, characteristic, complemented
6C11×#2317C211yesmaximal, characteristic, complemented
7C11×#2043C214yesmaximal, complemented
8C11×#2042C214yesmaximal, complemented
9C11×#1729C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#536—24no—
15C11×#536—24no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×#124C2212yes—
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#419—24no—
25C11×#417—24no—
26C11×#416—24no—
27C2×C11×#103—24no—
28C2×C11×#103C2214yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2214yes—
31C2×C11×#103C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C11×#389C2214yes—
35C11×#385—22no—
36C11×#384—21no—
37C11×#382—21no—
38C11×#336C2214yes—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41D414yes—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11D414yes—
52C22×Q8×C11C2312yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C2×C11×M16—22no—
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11C2312yes—
67C22×C8×C11C2312yes—
68C11×C4⋊Q8—24no—
69C11×C4⋊Q8—24no—
70C11×#124—24no—
71C11×#124—24no—
72C11×#123—216no—
73C11×C22⋊Q8—28no—
74C11×C22⋊Q8—28no—
75C11×#117—22no—
76C11×#117—22no—
77C11×#117—22no—
78C11×#117D414yes—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4D412yes—
93C2×C42×C11—21no—
94C2×C42×C11C2312yes—
95C11×#103—28no—
96C11×#103—24no—
97C11×#103—24no—
98C11×#103—28no—
99C11×#102—24no—
100C11×#102—24no—
101C11×#95—24no—
102#23510C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C24×C11C2×D411yescharacteristic
105C11×#41—28no—
106C11×#41—28no—
107C11×#41—44no—
108C11×#41—44no—
109C2×Q8×C11—24no—
110C2×Q8×C11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—28no—
113C2×Q8×C11—28no—
114C2×Q8×C11—22no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—42no—
123C2×Q8×C11—44no—
124C2×Q8×C11—44no—
125C2×Q8×C11—42no—
126C2×Q8×C11C2×D414yes—
127C2×Q8×C11C2×D412yes—
128C2×D4×C11—24no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11C2×D412yes—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—82no—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4112yes—
156C22×C4×C11#4112yes—
157C22×C4×C11#4112yes—
158C22×C4×C11C2411yescharacteristic
159C11×M16—44no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—44no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—84no—
176C11×C4⋊C4C2×D414yes—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C42×C11—24no—
182C42×C11—22no—
183C42×C11—22no—
184C2×#536C2×C1111yescharacteristic
185C2×#417C2×C1111yescharacteristic
186C2×#419C2×C1111yescharacteristic, complemented
187C2×#416C2×C1111yescharacteristic
188C22×#103C2×C1111yescharacteristic, complemented
189#2317C2×C1111yescharacteristic, complemented
190#2043C2×C1114yescomplemented
191#2042C2×C1114yescomplemented
192#1729C2×C1111yescharacteristic, complemented
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11#12012yes—
201C23×C11#12112yes—
202C23×C11#12412yes—
203C23×C11C22×D411yescharacteristic
204Q8×C11—24no—
205Q8×C11—22no—
206Q8×C11—24no—
207Q8×C11—22no—
208Q8×C11—42no—
209Q8×C11—41no—
210Q8×C11—42no—
211Q8×C11—41no—
212Q8×C11—48no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—48no—
216D4×C11—41no—
217D4×C11—41no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—48no—
232C2×C4×C11—48no—
233C2×C4×C11—42no—
234C2×C4×C11—44no—
235C2×C4×C11—84no—
236C2×C4×C11#12012yes—
237C2×C4×C11#12114yes—
238C2×C4×C11#12114yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12314yes—
241C2×C4×C11#12314yes—
242C2×C4×C11#12412yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C8×C11—42no—
250C8×C11—42no—
251C22×#41C22×C1111yescharacteristic
252C23×Q8C22×C1111yescharacteristic
253C22×M16C22×C1111yescharacteristic
254C23×C8C22×C1111yescharacteristic
255#536—24no—
256#536—24no—
257C2×C4⋊Q8C22×C1112yes—
258C2×#124C22×C1112yes—
259C2×#123—22no—
260C2×C22⋊Q8—21no—
261C2×C22⋊Q8—21no—
262C2×#117C22×C1111yescharacteristic
263C2×#117C22×C1111yescharacteristic
264C22×C4⋊C4C22×C1111yescharacteristic
265#419—24no—
266#417—24no—
267#416—24no—
268C2×#103—24no—
269C2×#103C22×C1114yes—
270C2×#103C22×C1112yes—
271C2×#103C22×C1114yes—
272C2×#103C22×C1112yes—
273C2×#102C22×C1112yes—
274C2×#102C22×C1112yes—
275#389C22×C1114yes—
276#385—22no—
277#384—21no—
278#382—21no—
279#336C22×C1114yes—
280C22×C11—24no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—24no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11#39414yes—
290C22×C11C2×#12011yescharacteristic
291C22×C11C2×#12111yescharacteristic
292C22×C11C2×#12411yescharacteristic
293C22×C11#57712yes—
294C22×C11#57812yes—
295C4×C11—42no—
296C4×C11—44no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—44no—
300C4×C11—82no—
301C4×C11#39414yes—
302C4×C11C2×#12111yescharacteristic
303C4×C11C2×#12111yescharacteristic
304C4×C11C2×#12311yescharacteristic
305C4×C11C2×#12311yescharacteristic
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41D4×C1114yes—
312C22×Q8—21no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8D4×C1114yes—
319C22×Q8C23×C1112yes—
320C22×Q8C23×C1111yescharacteristic
321C22×D4—21no—
322C22×D4C23×C1111yescharacteristic
323C23×C4—21no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C23×C1111yescharacteristic
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8C23×C1112yes—
334C22×C8C23×C1112yes—
335C4⋊Q8—24no—
336C4⋊Q8—24no—
337#124—24no—
338#124—24no—
339#123—216no—
340C22⋊Q8—28no—
341C22⋊Q8—28no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117D4×C1114yes—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4D4×C1111yescharacteristic
353C2×C4⋊C4D4×C1111yescharacteristic
354C2×C4⋊C4C23×C1112yes—
355C2×C4⋊C4C23×C1112yes—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4D4×C1112yes—
360C2×C42—21no—
361C2×C42C23×C1112yes—
362#103—28no—
363#103—24no—
364#103—24no—
365#103—28no—
366#102—24no—
367#102—24no—
368#95—24no—
369C2×C11—24no—
370C2×C11—82no—
371C2×C11C2×#39411yescharacteristic
372C2×C11#301011yescharacteristic
373C2×C11#301111yescharacteristic
374C2×C11#304612yes—
375C2×C11#313712yes—
376C24—21no—
377C24C2×D4×C1111yescharacteristic
378#41—28no—
379#41—28no—
380#41—44no—
381#41—44no—
382C2×Q8—24no—
383C2×Q8—22no—
384C2×Q8—21no—
385C2×Q8—28no—
386C2×Q8—28no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—42no—
396C2×Q8—44no—
397C2×Q8—44no—
398C2×Q8—42no—
399C2×Q8C2×D4×C1114yes—
400C2×Q8C2×D4×C1112yes—
401C2×D4—24no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4C2×D4×C1112yes—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—82no—
422C22×C4C2×D4×C1112yes—
423C22×C4C2×D4×C1112yes—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1112yes—
426C22×C4C2×D4×C1112yes—
427C22×C4C2×D4×C1112yes—
428C22×C4C11×#4112yes—
429C22×C4C11×#4112yes—
430C22×C4C11×#4112yes—
431C22×C4C24×C1111yescharacteristic
432M16—44no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—44no—
440C4⋊C4—28no—
441C4⋊C4—28no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—84no—
449C4⋊C4C2×D4×C1114yes—
450C22⋊C4—28no—
451C22⋊C4—28no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C42—24no—
455C42—22no—
456C42—22no—
457C11#2351011yescharacteristic, direct product factor, Sylow
458C23—22no—
459C23—22no—
460C23—22no—
461C23—41no—
462C23—41no—
463C23—42no—
464C23—42no—
465C23C11×#12012yes—
466C23C11×#12112yes—
467C23C11×#12412yes—
468C23C22×D4×C1111yescharacteristic
469Q8—24no—
470Q8—22no—
471Q8—24no—
472Q8—22no—
473Q8—42no—
474Q8—41no—
475Q8—42no—
476Q8—41no—
477Q8—48no—
478D4—22no—
479D4—22no—
480D4—48no—
481D4—41no—
482D4—41no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—48no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—48no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—84no—
501C2×C4C11×#12012yes—
502C2×C4C11×#12114yes—
503C2×C4C11×#12114yes—
504C2×C4C11×#12112yes—
505C2×C4C11×#12314yes—
506C2×C4C11×#12314yes—
507C2×C4C11×#12412yes—
508C2×C4C22×D4×C1111yescharacteristic
509C2×C4C22×D4×C1111yescharacteristic
510C2×C4C22×D4×C1111yescharacteristic
511C2×C4C2×C11×#4111yescharacteristic
512C2×C4C2×C11×#4111yescharacteristic
513C2×C4C2×C11×#4111yescharacteristic
514C8—42no—
515C8—42no—
516C22—22no—
517C22—22no—
518C22—24no—
519C22—24no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—82no—
524C22—82no—
525C22C11×#39414yes—
526C22C2×C11×#12011yescharacteristic
527C22C2×C11×#12111yescharacteristic
528C22C2×C11×#12411yescharacteristic
529C22C11×#57712yes—
530C22C11×#57812yes—
531C4—42no—
532C4—44no—
533C4—42no—
534C4—42no—
535C4—44no—
536C4—82no—
537C4C11×#39414yes—
538C4C2×C11×#12111yescharacteristic
539C4C2×C11×#12111yescharacteristic
540C4C2×C11×#12311yescharacteristic
541C4C2×C11×#12311yescharacteristic
542C2—24no—
543C2—82no—
544C2C2×C11×#39411yescharacteristic
545C2C11×#301011yescharacteristic
546C2C11×#301111yescharacteristic
547C2C11×#304612yes—
548C2C11×#313712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#419C2semidirect
5. C22×C11×#103C2semidirect
6. C11×#2317C2semidirect
7. C11×#2043C2semidirect
8. C11×#2042C2semidirect
9. C11×#1729C2semidirect
102. #23510C11direct (N × H)
186. C2×#419C2×C11semidirect
188. C22×#103C2×C11semidirect
189. #2317C2×C11semidirect
190. #2043C2×C11semidirect
191. #2042C2×C11semidirect
192. #1729C2×C11semidirect
457. C11#23510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4172
C2×C11×#4192
C2×C11×#4162
C22×C11×#1032
C11×#23172
C11×#20432
C11×#20422
C11×#17292
#2351011