Finite Group Databasebeta

← C11×#18406 #14595599

Subgroups — C11×#18406 #14595599

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic
2C11×#3209C211yesmaximal, characteristic, complemented
3C11×#3206C211yesmaximal, characteristic, complemented
4C11×#2563C211yesmaximal, characteristic, complemented
5C11×#1606C218yesmaximal, complemented
6C11×#1503C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic, complemented
8C11×#1460C211yesmaximal, characteristic, complemented
9C11×#559—22no—
10C11×#556—21no—
11C11×#555—21no—
12C11×#553—22no—
13C11×#550—21no—
14C11×#547—21no—
15C11×#538C2214yes—
16C11×#535—21no—
17C11×#533C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C11×#525—22no—
21C11×#520—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C11×#494—21no—
24C11×#492—21no—
25C11×#487—21no—
26C11×#487—21no—
27C11×#462—22no—
28C11×#461—22no—
29C11×#451C2214yes—
30C11×#448C2214yes—
31C11×#431C2211yescharacteristic
32C11×#431C2211yescharacteristic
33C11×#393C2214yes—
34C11×#390—21no—
35C11×#382—21no—
36C11×#380—22no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#328C2214yes—
39C11×#327C2214yes—
40C11×#323C2214yes—
41C2×C11×#41—22no—
42C2×C11×#41—21no—
43C22×Q8×C11C2312yes—
44C22×D4×C11D411yescharacteristic
45C23×C4×C11D412yes—
46C2×C11×Q16—24no—
47C2×C11×SD16—24no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
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×C11D412yes—
77C4×D4×C11—22no—
78C4×D4×C11—24no—
79C4×D4×C11—24no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11D412yes—
86C11×#117—22no—
87C11×#117—22no—
88C11×#117—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4C2312yes—
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8—21no—
100C11×#103—24no—
101C11×#103—24no—
102C11×C22⋊C8C2312yes—
103C11×C22⋊C8C2312yes—
104C4×C8×C11—21no—
105C4×C8×C11—21no—
106C11×#95—24no—
107C11×#95C2312yes—
108#18406C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11C2×D412yes—
110C11×#41—42no—
111C11×#41—42no—
112C11×#41—84no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—82no—
118C2×Q8×C11C2×D412yes—
119C2×D4×C11—22no—
120C2×D4×C11—24no—
121C2×D4×C11—24no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—44no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C11×Q16—84no—
141C11×SD16—84no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4C2×D412yes—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—84no—
169C42×C11—24no—
170C42×C11—22no—
171C42×C11—42no—
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176#3506C2×C1111yescharacteristic
177#3209C2×C1111yescharacteristic, complemented
178#3206C2×C1111yescharacteristic, complemented
179#2563C2×C1111yescharacteristic, complemented
180#1606C2×C1118yescomplemented
181#1503C2×C1111yescharacteristic, complemented
182#1502C2×C1111yescharacteristic, complemented
183#1460C2×C1111yescharacteristic, complemented
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11C22×D411yescharacteristic
191Q8×C11—42no—
192Q8×C11—44no—
193Q8×C11—44no—
194Q8×C11—42no—
195Q8×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—84no—
204D4×C11—84no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—44no—
212C2×C4×C11—44no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—82no—
220C2×C4×C11—84no—
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#13512yes—
226C2×C4×C11#13712yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C8×C11—42no—
230C8×C11—42no—
231#559—22no—
232#556—21no—
233#555—21no—
234#553—22no—
235#550—21no—
236#547—21no—
237#538C22×C1114yes—
238#535—21no—
239#533C22×C1111yescharacteristic
240#532C22×C1111yescharacteristic
241C2×C4⋊Q8C22×C1111yescharacteristic
242#525—22no—
243#520—21no—
244C2×C4×D4C22×C1111yescharacteristic
245#494—21no—
246#492—21no—
247#487—21no—
248#487—21no—
249#462—22no—
250#461—22no—
251#451C22×C1114yes—
252#448C22×C1114yes—
253#431C22×C1111yescharacteristic
254#431C22×C1111yescharacteristic
255#393C22×C1114yes—
256#390—21no—
257#382—21no—
258#380—22no—
259C4×C4⋊C4C22×C1111yescharacteristic
260#328C22×C1114yes—
261#327C22×C1114yes—
262#323C22×C1114yes—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—44no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—82no—
273C22×C11C2×#12011yescharacteristic
274C22×C11C2×#13511yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—82no—
284C4×C11—82no—
285C4×C11#45212yes—
286C4×C11#45212yes—
287C4×C11#45512yes—
288C2×#41—22no—
289C2×#41—21no—
290C22×Q8C23×C1112yes—
291C22×D4D4×C1111yescharacteristic
292C23×C4D4×C1112yes—
293C2×Q16—24no—
294C2×SD16—24no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8D4×C1111yescharacteristic
300C4⋊Q8D4×C1111yescharacteristic
301C4⋊Q8D4×C1111yescharacteristic
302#127—22no—
303#127D4×C1111yescharacteristic
304#126—24no—
305#125—21no—
306#124—22no—
307#124—24no—
308#124—21no—
309#123—24no—
310#123—24no—
311C22⋊Q8—22no—
312C22⋊Q8—21no—
313C22⋊Q8C23×C1112yes—
314#121—22no—
315#121—22no—
316#121—22no—
317#121—24no—
318#121—21no—
319#121C23×C1112yes—
320#120—24no—
321C4×Q8—22no—
322C4×Q8—21no—
323C4×Q8D4×C1112yes—
324C4×D4—22no—
325C4×D4—24no—
326C4×D4—24no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4D4×C1112yes—
333#117—22no—
334#117—22no—
335#117—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4D4×C1111yescharacteristic
341C2×C22⋊C4—24no—
342C2×C22⋊C4C23×C1112yes—
343C2×C42—21no—
344C2×C42C23×C1111yescharacteristic
345C4⋊C8—21no—
346C4⋊C8—21no—
347#103—24no—
348#103—24no—
349C22⋊C8C23×C1112yes—
350C22⋊C8C23×C1112yes—
351C4×C8—21no—
352C4×C8—21no—
353#95—24no—
354#95C23×C1112yes—
355C2×C11—21no—
356C2×C11—21no—
357C2×C11—82no—
358C2×C11—82no—
359C2×C11C2×#45211yescharacteristic
360C2×C11C2×#45511yescharacteristic
361C2×C11#302711yescharacteristic
362C24C2×D4×C1112yes—
363#41—42no—
364#41—42no—
365#41—84no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—82no—
371C2×Q8C2×D4×C1112yes—
372C2×D4—22no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4C2×D4×C1112yes—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—44no—
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C2×D4×C1112yes—
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C24×C1111yescharacteristic
393Q16—84no—
394SD16—84no—
395C2×C8—22no—
396C2×C8—22no—
397C4⋊C4—24no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—42no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4C2×D4×C1112yes—
412C4⋊C4C2×D4×C1112yes—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—84no—
422C42—24no—
423C42—22no—
424C42—42no—
425C42C2×D4×C1111yescharacteristic
426C42C2×D4×C1111yescharacteristic
427C42C2×D4×C1111yescharacteristic
428C42C2×D4×C1111yescharacteristic
429C11#1840611yescharacteristic, direct product factor, Sylow
430C23—22no—
431C23—22no—
432C23—22no—
433C23—22no—
434C23—42no—
435C23—42no—
436C23C22×D4×C1111yescharacteristic
437Q8—42no—
438Q8—44no—
439Q8—44no—
440Q8—42no—
441Q8—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—84no—
450D4—84no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—82no—
466C2×C4—84no—
467C2×C4C11×#12011yescharacteristic
468C2×C4C11×#12011yescharacteristic
469C2×C4C11×#12011yescharacteristic
470C2×C4C11×#12011yescharacteristic
471C2×C4C11×#13512yes—
472C2×C4C11×#13712yes—
473C2×C4C22×D4×C1111yescharacteristic
474C2×C4C22×D4×C1111yescharacteristic
475C8—42no—
476C8—42no—
477C22—21no—
478C22—21no—
479C22—44no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—82no—
487C22C2×C11×#12011yescharacteristic
488C22C2×C11×#13511yescharacteristic
489C22C2×C11×#13711yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—82no—
498C4—82no—
499C4C11×#45212yes—
500C4C11×#45212yes—
501C4C11×#45512yes—
502C2—21no—
503C2—21no—
504C2—82no—
505C2—82no—
506C2C2×C11×#45211yescharacteristic
507C2C2×C11×#45511yescharacteristic
508C2C11×#302711yescharacteristic
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×#3209C2semidirect
3. C11×#3206C2semidirect
4. C11×#2563C2semidirect
5. C11×#1606C2semidirect
6. C11×#1503C2semidirect
7. C11×#1502C2semidirect
8. C11×#1460C2semidirect
108. #18406C11direct (N × H)
177. #3209C2×C11semidirect
178. #3206C2×C11semidirect
179. #2563C2×C11semidirect
180. #1606C2×C11semidirect
181. #1503C2×C11semidirect
182. #1502C2×C11semidirect
183. #1460C2×C11semidirect
429. C11#18406direct (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×#32092
C11×#32062
C11×#25632
C11×#16062
C11×#15032
C11×#15022
C11×#14602
#1840611