Finite Group Databasebeta

← C11×#19062 #14596255

Subgroups — C11×#19062 #14596255

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic, complemented
2C11×#3235C211yesmaximal, characteristic, complemented
3C11×#3214C211yesmaximal, characteristic
4C11×#3135C211yesmaximal, characteristic, complemented
5C11×#1664C214yesmaximal, complemented
6C11×#1657C214yesmaximal, complemented
7C11×#1537C211yesmaximal, characteristic, complemented
8C11×#1531C211yesmaximal, characteristic, complemented
9C11×#1530C211yesmaximal, characteristic, complemented
10C11×#563C2214yes—
11C11×#559—21no—
12Q82×C11—21no—
13C11×#556—21no—
14C11×#556—21no—
15D4×Q8×C11—21no—
16D4×Q8×C11—21no—
17C11×#542—22no—
18C11×#542—22no—
19C11×#536—22no—
20C11×#533C2211yescharacteristic
21C11×#533C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C11×#532C2211yescharacteristic
24C11×#501C2212yes—
25C11×#496C2212yes—
26C11×#491C2212yes—
27C11×#490C2212yes—
28C11×#490C2212yes—
29C11×#489—21no—
30C11×#489—21no—
31C11×#489C2212yes—
32C11×#482—22no—
33C11×#476—21no—
34C11×#474—21no—
35C11×#461—21no—
36C11×#459—21no—
37C11×#449—22no—
38C11×#432C2211yescharacteristic
39C11×#432C2211yescharacteristic
40C11×#416—22no—
41C2×C11×#97C2211yescharacteristic
42C11×#330C2214yes—
43C11×#330C2214yes—
44C11×#329C2214yes—
45C2×C11×#41—21no—
46C2×C11×#41D412yes—
47C22×Q8×C11—22no—
48C2×C11×SD16—22no—
49C2×C11×D8—22no—
50C22×C8×C11—21no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×#127D411yescharacteristic
61C11×#127C2311yescharacteristic
62C11×#126—24no—
63C11×#126—24no—
64C11×#125C2312yes—
65C11×#125C2312yes—
66C11×#124—24no—
67C11×#124—22no—
68C11×#124—22no—
69C11×#124—21no—
70C11×#124C2312yes—
71C11×#123—24no—
72C11×#123—24no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8—24no—
81C11×#121—21no—
82C11×#121—21no—
83C11×#121—21no—
84C11×#121—21no—
85C4×Q8×C11—22no—
86C4×Q8×C11—22no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—21no—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C11×#117—22no—
98C11×#117D412yes—
99C11×#117D412yes—
100C2×C42×C11C2311yescharacteristic
101C11×#107—22no—
102C11×#106—22no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×#103—22no—
106C11×#103—22no—
107C11×#103—22no—
108C11×#102—22no—
109C11×#102—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8—21no—
115C11×#97—21no—
116C11×#97C2312yes—
117C11×#97C2312yes—
118C11×#97C2312yes—
119#19062C1111yesmaximal, characteristic, direct product factor, Sylow
120C11×#41—44no—
121C11×#41—82no—
122C2×Q8×C11—24no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—84no—
129C2×Q8×C11C2×D412yes—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—41no—
137C2×D4×C11C2×D412yes—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—41no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C11×SD16—82no—
145C11×D8—82no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4C2×D412yes—
167C11×C4⋊C4C2×D412yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—41no—
177C42×C11—24no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2411yescharacteristic
184#3550C2×C1111yescharacteristic, complemented
185#3235C2×C1111yescharacteristic, complemented
186#3214C2×C1111yescharacteristic
187#3135C2×C1111yescharacteristic, complemented
188#1664C2×C1114yescomplemented
189#1657C2×C1114yescomplemented
190#1537C2×C1111yescharacteristic, complemented
191#1531C2×C1111yescharacteristic, complemented
192#1530C2×C1111yescharacteristic, complemented
193C23×C11—22no—
194C23×C11—41no—
195C23×C11#12011yescharacteristic
196Q8×C11—42no—
197Q8×C11—42no—
198Q8×C11—42no—
199Q8×C11—42no—
200Q8×C11—42no—
201Q8×C11—42no—
202Q8×C11—84no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—82no—
211D4×C11—82no—
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—41no—
219C2×C4×C11—41no—
220C2×C4×C11—44no—
221C2×C4×C11—41no—
222C2×C4×C11—84no—
223C2×C4×C11—82no—
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C8×C11—42no—
231C8×C11—42no—
232C8×C11—42no—
233#563C22×C1114yes—
234#559—21no—
235Q82—21no—
236#556—21no—
237#556—21no—
238D4×Q8—21no—
239D4×Q8—21no—
240#542—22no—
241#542—22no—
242#536—22no—
243#533C22×C1111yescharacteristic
244#533C22×C1111yescharacteristic
245#532C22×C1111yescharacteristic
246#532C22×C1111yescharacteristic
247#501C22×C1112yes—
248#496C22×C1112yes—
249#491C22×C1112yes—
250#490C22×C1112yes—
251#490C22×C1112yes—
252#489—21no—
253#489—21no—
254#489C22×C1112yes—
255#482—22no—
256#476—21no—
257#474—21no—
258#461—21no—
259#459—21no—
260#449—22no—
261#432C22×C1111yescharacteristic
262#432C22×C1111yescharacteristic
263#416—22no—
264C2×#97C22×C1111yescharacteristic
265#330C22×C1114yes—
266#330C22×C1114yes—
267#329C22×C1114yes—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11C2×#12011yescharacteristic
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—81no—
289C4×C11#45412yes—
290C2×#41—21no—
291C2×#41D4×C1112yes—
292C22×Q8—22no—
293C2×SD16—22no—
294C2×D8—22no—
295C22×C8—21no—
296C4⋊Q8—22no—
297C4⋊Q8—22no—
298C4⋊Q8—24no—
299C4⋊Q8D4×C1111yescharacteristic
300C4⋊Q8D4×C1111yescharacteristic
301C4⋊Q8D4×C1111yescharacteristic
302C4⋊Q8D4×C1111yescharacteristic
303C4⋊Q8D4×C1111yescharacteristic
304C4⋊Q8C23×C1111yescharacteristic
305#127D4×C1111yescharacteristic
306#127C23×C1111yescharacteristic
307#126—24no—
308#126—24no—
309#125C23×C1112yes—
310#125C23×C1112yes—
311#124—24no—
312#124—22no—
313#124—22no—
314#124—21no—
315#124C23×C1112yes—
316#123—24no—
317#123—24no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—21no—
342#117—22no—
343#117D4×C1112yes—
344#117D4×C1112yes—
345C2×C42C23×C1111yescharacteristic
346#107—22no—
347#106—22no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350#103—22no—
351#103—22no—
352#103—22no—
353#102—22no—
354#102—22no—
355#102—22no—
356#102—22no—
357#102—22no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360#97—21no—
361#97C23×C1112yes—
362#97C23×C1112yes—
363#97C23×C1112yes—
364C2×C11—41no—
365C2×C11—82no—
366C2×C11—161no—
367C2×C11C2×#45411yescharacteristic
368C2×C11#301911yescharacteristic
369C2×C11#302011yescharacteristic
370#41—44no—
371#41—82no—
372C2×Q8—24no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—84no—
379C2×Q8C2×D4×C1112yes—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4C2×D4×C1112yes—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—41no—
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394SD16—82no—
395D8—82no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—42no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4C2×D4×C1112yes—
415C4⋊C4C2×D4×C1112yes—
416C4⋊C4C2×D4×C1112yes—
417C4⋊C4C2×D4×C1112yes—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C42—24no—
428C42—22no—
429C42—22no—
430C42C2×D4×C1111yescharacteristic
431C42C2×D4×C1111yescharacteristic
432C42C2×D4×C1111yescharacteristic
433C42C24×C1111yescharacteristic
434C11#1906211yescharacteristic, direct product factor, Sylow
435C23—22no—
436C23—41no—
437C23C11×#12011yescharacteristic
438Q8—42no—
439Q8—42no—
440Q8—42no—
441Q8—42no—
442Q8—42no—
443Q8—42no—
444Q8—84no—
445D4—42no—
446D4—42no—
447D4—41no—
448D4—41no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—82no—
453D4—82no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—44no—
463C2×C4—41no—
464C2×C4—84no—
465C2×C4—82no—
466C2×C4C11×#12011yescharacteristic
467C2×C4C11×#12011yescharacteristic
468C2×C4C11×#12011yescharacteristic
469C2×C4C22×D4×C1111yescharacteristic
470C2×C4C22×D4×C1111yescharacteristic
471C2×C4C22×D4×C1111yescharacteristic
472C8—42no—
473C8—42no—
474C8—42no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22C2×C11×#12011yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—42no—
493C4—42no—
494C4—42no—
495C4—81no—
496C4C11×#45412yes—
497C2—41no—
498C2—82no—
499C2—161no—
500C2C2×C11×#45411yescharacteristic
501C2C11×#301911yescharacteristic
502C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3214C2
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×#3550C2semidirect
2. C11×#3235C2semidirect
4. C11×#3135C2semidirect
5. C11×#1664C2semidirect
6. C11×#1657C2semidirect
7. C11×#1537C2semidirect
8. C11×#1531C2semidirect
9. C11×#1530C2semidirect
119. #19062C11direct (N × H)
184. #3550C2×C11semidirect
185. #3235C2×C11semidirect
187. #3135C2×C11semidirect
188. #1664C2×C11semidirect
189. #1657C2×C11semidirect
190. #1537C2×C11semidirect
191. #1531C2×C11semidirect
192. #1530C2×C11semidirect
434. C11#19062direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35502
C11×#32352
C11×#32142
C11×#31352
C11×#16642
C11×#16572
C11×#15372
C11×#15312
C11×#15302
#1906211