Finite Group Databasebeta

← C11×#18215 #14595408

Subgroups — C11×#18215 #14595408

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic
2C11×#3104C211yesmaximal, characteristic, complemented
3C11×#3103C211yesmaximal, characteristic
4C11×#2581C211yesmaximal, characteristic, complemented
5C11×#1615C214yesmaximal, complemented
6C11×#1603C214yesmaximal, complemented
7C11×#1518C211yesmaximal, characteristic, complemented
8C11×#1517C211yesmaximal, characteristic
9C11×#1461C211yesmaximal, characteristic, complemented
10C11×#559—21no—
11C11×#557—21no—
12C11×#556—21no—
13C11×#556—22no—
14C11×#554—21no—
15C11×#552—22no—
16C11×#539C2214yes—
17C11×#536—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#529—22no—
21C11×#520—21no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#484C2212yes—
25C11×#481C2212yes—
26C11×#477—21no—
27C11×#475—21no—
28C11×#462—21no—
29C11×#460—21no—
30C11×#451C2212yes—
31C11×#448C2212yes—
32C4×C11×Q16—22no—
33C4×C11×SD16—22no—
34C11×#431C2211yescharacteristic
35C11×#431C2211yescharacteristic
36C11×#400C2212yes—
37C11×#395C2212yes—
38C11×#391—21no—
39C11×#389—21no—
40C11×#387—22no—
41C11×#382C2211yescharacteristic
42C11×#328C2214yes—
43C11×#327C2214yes—
44C11×#324C2214yes—
45C2×C11×#41—21no—
46C22×Q8×C11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C2×C11×Q16—22no—
49C2×C11×SD16—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8D411yescharacteristic
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×#127D411yescharacteristic
55C11×#126—24no—
56C11×#126—24no—
57C11×#125—22no—
58C11×#125—24no—
59C11×#125—21no—
60C11×#124—22no—
61C11×#124—22no—
62C11×#124—21no—
63C11×#123—24no—
64C11×#123—24no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8C2312yes—
70C11×#121—21no—
71C11×#121C2312yes—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11D412yes—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—24no—
87C4×D4×C11—21no—
88C4×D4×C11D412yes—
89C11×#117—22no—
90C11×#117—24no—
91C11×#117—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2312yes—
99C2×C42×C11—21no—
100C2×C42×C11D412yes—
101C2×C42×C11C2311yescharacteristic
102C11×#107—22no—
103C11×#106—22no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8—21no—
106C11×#103—22no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#102—22no—
110C11×C22⋊C8C2312yes—
111C11×C22⋊C8C2312yes—
112C4×C8×C11—21no—
113C4×C8×C11—21no—
114C11×#95—21no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95C2312yes—
119#18215C1111yesmaximal, characteristic, direct product factor, Sylow
120C11×#41—42no—
121C11×#41—42no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—42no—
131C2×Q8×C11C2×D412yes—
132C2×D4×C11—22no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11C2×D412yes—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C11×Q16—44no—
147C11×SD16—44no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—44no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C42×C11—24no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—41no—
182C42×C11—41no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187#3507C2×C1111yescharacteristic
188#3104C2×C1111yescharacteristic, complemented
189#3103C2×C1111yescharacteristic
190#2581C2×C1111yescharacteristic, complemented
191#1615C2×C1114yescomplemented
192#1603C2×C1114yescomplemented
193#1518C2×C1111yescharacteristic, complemented
194#1517C2×C1111yescharacteristic
195#1461C2×C1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11C22×D411yescharacteristic
198Q8×C11—22no—
199Q8×C11—22no—
200Q8×C11—42no—
201Q8×C11—42no—
202Q8×C11—41no—
203Q8×C11—41no—
204Q8×C11—42no—
205Q8×C11—42no—
206Q8×C11—42no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—42no—
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—22no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—44no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—84no—
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#13512yes—
237C2×C4×C11#13712yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C8×C11—42no—
241C8×C11—42no—
242#559—21no—
243#557—21no—
244#556—21no—
245#556—22no—
246#554—21no—
247#552—22no—
248#539C22×C1114yes—
249#536—21no—
250#533C22×C1111yescharacteristic
251#532C22×C1111yescharacteristic
252#529—22no—
253#520—21no—
254C2×C4×Q8C22×C1111yescharacteristic
255C2×C4×Q8C22×C1111yescharacteristic
256#484C22×C1112yes—
257#481C22×C1112yes—
258#477—21no—
259#475—21no—
260#462—21no—
261#460—21no—
262#451C22×C1112yes—
263#448C22×C1112yes—
264C4×Q16—22no—
265C4×SD16—22no—
266#431C22×C1111yescharacteristic
267#431C22×C1111yescharacteristic
268#400C22×C1112yes—
269#395C22×C1112yes—
270#391—21no—
271#389—21no—
272#387—22no—
273#382C22×C1111yescharacteristic
274#328C22×C1114yes—
275#327C22×C1114yes—
276#324C22×C1114yes—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11C2×#12011yescharacteristic
283C22×C11C2×#13511yescharacteristic
284C22×C11C2×#13711yescharacteristic
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—82no—
296C4×C11—81no—
297C4×C11#45212yes—
298C4×C11#45212yes—
299C2×#41—21no—
300C22×Q8D4×C1111yescharacteristic
301C22×Q8C23×C1111yescharacteristic
302C2×Q16—22no—
303C2×SD16—22no—
304C4⋊Q8—22no—
305C4⋊Q8D4×C1111yescharacteristic
306C4⋊Q8D4×C1111yescharacteristic
307C4⋊Q8D4×C1111yescharacteristic
308#127D4×C1111yescharacteristic
309#126—24no—
310#126—24no—
311#125—22no—
312#125—24no—
313#125—21no—
314#124—22no—
315#124—22no—
316#124—21no—
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×Q8—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8D4×C1112yes—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—24no—
341C4×D4—21no—
342C4×D4D4×C1112yes—
343#117—22no—
344#117—24no—
345#117—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4D4×C1111yescharacteristic
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1112yes—
353C2×C42—21no—
354C2×C42D4×C1112yes—
355C2×C42C23×C1111yescharacteristic
356#107—22no—
357#106—22no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360#103—22no—
361#103—22no—
362#103—22no—
363#102—22no—
364C22⋊C8C23×C1112yes—
365C22⋊C8C23×C1112yes—
366C4×C8—21no—
367C4×C8—21no—
368#95—21no—
369#95—22no—
370#95—22no—
371#95—22no—
372#95C23×C1112yes—
373C2×C11—21no—
374C2×C11—21no—
375C2×C11—82no—
376C2×C11C2×#45211yescharacteristic
377C2×C11#302011yescharacteristic
378C2×C11#302511yescharacteristic
379#41—42no—
380#41—42no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—42no—
390C2×Q8C2×D4×C1112yes—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4C2×D4×C1112yes—
395C22×C4—21no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4C2×D4×C1112yes—
401C22×C4C2×D4×C1112yes—
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C24×C1111yescharacteristic
405Q16—44no—
406SD16—44no—
407C2×C8—22no—
408C2×C8—22no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—44no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—42no—
428C4⋊C4C2×D4×C1112yes—
429C4⋊C4C2×D4×C1112yes—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C42—24no—
437C42—22no—
438C42—22no—
439C42—22no—
440C42—41no—
441C42—41no—
442C42C2×D4×C1111yescharacteristic
443C42C2×D4×C1111yescharacteristic
444C42C2×D4×C1111yescharacteristic
445C42C2×D4×C1111yescharacteristic
446C11#1821511yescharacteristic, direct product factor, Sylow
447C23—22no—
448C23C22×D4×C1111yescharacteristic
449Q8—22no—
450Q8—22no—
451Q8—42no—
452Q8—42no—
453Q8—41no—
454Q8—41no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—84no—
483C2×C4C11×#12011yescharacteristic
484C2×C4C11×#12011yescharacteristic
485C2×C4C11×#12011yescharacteristic
486C2×C4C11×#12011yescharacteristic
487C2×C4C11×#13512yes—
488C2×C4C11×#13712yes—
489C2×C4C22×D4×C1111yescharacteristic
490C2×C4C22×D4×C1111yescharacteristic
491C8—42no—
492C8—42no—
493C22—21no—
494C22—21no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22C2×C11×#12011yescharacteristic
499C22C2×C11×#13511yescharacteristic
500C22C2×C11×#13711yescharacteristic
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—42no—
506C4—42no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—42no—
511C4—82no—
512C4—81no—
513C4C11×#45212yes—
514C4C11×#45212yes—
515C2—21no—
516C2—21no—
517C2—82no—
518C2C2×C11×#45211yescharacteristic
519C2C11×#302011yescharacteristic
520C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#532C22
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×#3104C2semidirect
4. C11×#2581C2semidirect
5. C11×#1615C2semidirect
6. C11×#1603C2semidirect
7. C11×#1518C2semidirect
9. C11×#1461C2semidirect
119. #18215C11direct (N × H)
188. #3104C2×C11semidirect
190. #2581C2×C11semidirect
191. #1615C2×C11semidirect
192. #1603C2×C11semidirect
193. #1518C2×C11semidirect
195. #1461C2×C11semidirect
446. C11#18215direct (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×#31042
C11×#31032
C11×#25812
C11×#16152
C11×#16032
C11×#15182
C11×#15172
C11×#14612
#1821511