Finite Group Databasebeta

← C11×#18191 #14595384

Subgroups — C11×#18191 #14595384

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic
2C11×#3113C211yesmaximal, characteristic, complemented
3C11×#3112C211yesmaximal, characteristic, complemented
4C11×#2398C211yesmaximal, characteristic, complemented
5C11×#1612C214yesmaximal, complemented
6C11×#1606C214yesmaximal, complemented
7C11×#1506C211yesmaximal, characteristic, complemented
8C11×#1505C211yesmaximal, characteristic, complemented
9C11×#1466C211yesmaximal, characteristic, complemented
10C11×#559—22no—
11C11×#556—21no—
12C11×#555—21no—
13C11×#553—22no—
14C11×#550—21no—
15C11×#547—21no—
16C11×#538C2214yes—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#525—22no—
21C11×#520—21no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#483C2212yes—
25C11×#480C2212yes—
26C11×#477—21no—
27C11×#475—21no—
28C11×#462—21no—
29C11×#460—21no—
30C11×#451C2212yes—
31C11×#448C2212yes—
32C11×#441—22no—
33C11×#440—22no—
34C11×#432C2211yescharacteristic
35C11×#432C2211yescharacteristic
36C11×#400—21no—
37C11×#397C2212yes—
38C11×#394—21no—
39C11×#393C2212yes—
40C4×C11×C22⋊C4—22no—
41C11×#376C2211yescharacteristic
42C11×#328C2214yes—
43C11×#327C2214yes—
44C11×#323C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11D411yescharacteristic
49C23×C4×C11D412yes—
50C2×C11×Q16—22no—
51C2×C11×SD16—22no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×#127—22no—
56C11×#127D411yescharacteristic
57C11×#126—24no—
58C11×#125—21no—
59C11×#124—22no—
60C11×#124—24no—
61C11×#124—21no—
62C11×#123—24no—
63C11×#123—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8C2312yes—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—24no—
71C11×#121—21no—
72C11×#121C2312yes—
73C11×#120—24no—
74C4×Q8×C11—22no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11D412yes—
81C4×D4×C11—22no—
82C4×D4×C11—24no—
83C4×D4×C11—24no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11D412yes—
90C11×#117—22no—
91C11×#117—22no—
92C11×#117—21no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4C2312yes—
100C2×C42×C11—21no—
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C11×#107—22no—
104C11×#106—22no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#102—22no—
111C11×C22⋊C8C2312yes—
112C11×C22⋊C8C2312yes—
113C11×#97—21no—
114C11×#97—21no—
115C11×#95—21no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95C2312yes—
119#18191C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11C2×D412yes—
121C11×#41—44no—
122C11×#41—84no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—42no—
128C2×Q8×C11C2×D412yes—
129C2×D4×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11C2×D412yes—
138C22×C4×C11—21no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2411yescharacteristic
150C11×Q16—44no—
151C11×SD16—44no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—44no—
178C11×C22⋊C4—44no—
179C42×C11—24no—
180C42×C11—22no—
181C42×C11—42no—
182C42×C11—41no—
183C42×C11—41no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188#3506C2×C1111yescharacteristic
189#3113C2×C1111yescharacteristic, complemented
190#3112C2×C1111yescharacteristic, complemented
191#2398C2×C1111yescharacteristic, complemented
192#1612C2×C1114yescomplemented
193#1606C2×C1114yescomplemented
194#1506C2×C1111yescharacteristic, complemented
195#1505C2×C1111yescharacteristic, complemented
196#1466C2×C1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11C22×D411yescharacteristic
204Q8×C11—22no—
205Q8×C11—22no—
206Q8×C11—42no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—42no—
210Q8×C11—42no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—44no—
216D4×C11—42no—
217D4×C11—84no—
218D4×C11—84no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—41no—
227C2×C4×C11—44no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—44no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—82no—
238C2×C4×C11—84no—
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C8×C11—42no—
246C8×C11—42no—
247#559—22no—
248#556—21no—
249#555—21no—
250#553—22no—
251#550—21no—
252#547—21no—
253#538C22×C1114yes—
254#535—21no—
255#533C22×C1111yescharacteristic
256#532C22×C1111yescharacteristic
257#525—22no—
258#520—21no—
259C2×C4×Q8C22×C1111yescharacteristic
260C2×C4×D4C22×C1111yescharacteristic
261#483C22×C1112yes—
262#480C22×C1112yes—
263#477—21no—
264#475—21no—
265#462—21no—
266#460—21no—
267#451C22×C1112yes—
268#448C22×C1112yes—
269#441—22no—
270#440—22no—
271#432C22×C1111yescharacteristic
272#432C22×C1111yescharacteristic
273#400—21no—
274#397C22×C1112yes—
275#394—21no—
276#393C22×C1112yes—
277C4×C22⋊C4—22no—
278#376C22×C1111yescharacteristic
279#328C22×C1114yes—
280#327C22×C1114yes—
281#323C22×C1114yes—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—44no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—82no—
292C22×C11C2×#12011yescharacteristic
293C22×C11#57512yes—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—82no—
305C4×C11—81no—
306C4×C11#45512yes—
307C2×#41—22no—
308C2×#41—21no—
309C22×Q8C23×C1111yescharacteristic
310C22×D4D4×C1111yescharacteristic
311C23×C4D4×C1112yes—
312C2×Q16—22no—
313C2×SD16—22no—
314C4⋊Q8D4×C1111yescharacteristic
315C4⋊Q8D4×C1111yescharacteristic
316C4⋊Q8D4×C1111yescharacteristic
317#127—22no—
318#127D4×C1111yescharacteristic
319#126—24no—
320#125—21no—
321#124—22no—
322#124—24no—
323#124—21no—
324#123—24no—
325#123—24no—
326C22⋊Q8—22no—
327C22⋊Q8—21no—
328C22⋊Q8C23×C1112yes—
329#121—22no—
330#121—22no—
331#121—22no—
332#121—24no—
333#121—21no—
334#121C23×C1112yes—
335#120—24no—
336C4×Q8—22no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8D4×C1112yes—
343C4×D4—22no—
344C4×D4—24no—
345C4×D4—24no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4D4×C1112yes—
352#117—22no—
353#117—22no—
354#117—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4D4×C1111yescharacteristic
358C2×C4⋊C4C23×C1111yescharacteristic
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4C23×C1112yes—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42C23×C1111yescharacteristic
365#107—22no—
366#106—22no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369#103—22no—
370#103—22no—
371#103—22no—
372#102—22no—
373C22⋊C8C23×C1112yes—
374C22⋊C8C23×C1112yes—
375#97—21no—
376#97—21no—
377#95—21no—
378#95—22no—
379#95—22no—
380#95C23×C1112yes—
381C2×C11—22no—
382C2×C11—82no—
383C2×C11—82no—
384C2×C11#300511yescharacteristic
385C2×C11C2×#45511yescharacteristic
386C2×C11#302511yescharacteristic
387C24C2×D4×C1112yes—
388#41—44no—
389#41—84no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—42no—
395C2×Q8C2×D4×C1112yes—
396C2×D4—22no—
397C2×D4—24no—
398C2×D4—24no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—42no—
404C2×D4C2×D4×C1112yes—
405C22×C4—21no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—44no—
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C2×D4×C1112yes—
416C22×C4C24×C1111yescharacteristic
417Q16—44no—
418SD16—44no—
419C2×C8—22no—
420C2×C8—22no—
421C4⋊C4—24no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4C2×D4×C1112yes—
435C4⋊C4C2×D4×C1112yes—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—44no—
445C22⋊C4—44no—
446C42—24no—
447C42—22no—
448C42—42no—
449C42—41no—
450C42—41no—
451C42C2×D4×C1111yescharacteristic
452C42C2×D4×C1111yescharacteristic
453C42C2×D4×C1111yescharacteristic
454C42C2×D4×C1111yescharacteristic
455C11#1819111yescharacteristic, direct product factor, Sylow
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—42no—
461C23—42no—
462C23C22×D4×C1111yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—42no—
466Q8—41no—
467Q8—41no—
468Q8—42no—
469Q8—42no—
470D4—42no—
471D4—42no—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—42no—
476D4—84no—
477D4—84no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—44no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—82no—
497C2×C4—84no—
498C2×C4C11×#12011yescharacteristic
499C2×C4C11×#12011yescharacteristic
500C2×C4C11×#12011yescharacteristic
501C2×C4C11×#12011yescharacteristic
502C2×C4C22×D4×C1111yescharacteristic
503C2×C4C22×D4×C1111yescharacteristic
504C8—42no—
505C8—42no—
506C22—21no—
507C22—21no—
508C22—44no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—82no—
516C22C2×C11×#12011yescharacteristic
517C22C11×#57512yes—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—82no—
529C4—81no—
530C4C11×#45512yes—
531C2—22no—
532C2—82no—
533C2—82no—
534C2C11×#300511yescharacteristic
535C2C2×C11×#45511yescharacteristic
536C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3506C2
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
2. C11×#3113C2semidirect
3. C11×#3112C2semidirect
4. C11×#2398C2semidirect
5. C11×#1612C2semidirect
6. C11×#1606C2semidirect
7. C11×#1506C2semidirect
8. C11×#1505C2semidirect
9. C11×#1466C2semidirect
119. #18191C11direct (N × H)
189. #3113C2×C11semidirect
190. #3112C2×C11semidirect
191. #2398C2×C11semidirect
192. #1612C2×C11semidirect
193. #1606C2×C11semidirect
194. #1506C2×C11semidirect
195. #1505C2×C11semidirect
196. #1466C2×C11semidirect
455. C11#18191direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#31132
C11×#31122
C11×#23982
C11×#16122
C11×#16062
C11×#15062
C11×#15052
C11×#14662
#1819111