Finite Group Databasebeta

← C11×#19066 #14596259

Subgroups — C11×#19066 #14596259

Order 2816.

852 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic
2C11×#3237C211yesmaximal, characteristic, complemented
3C11×#3216C211yesmaximal, characteristic
4C11×#3162C211yesmaximal, characteristic, complemented
5C11×#1664C214yesmaximal, complemented
6C11×#1660C214yesmaximal, complemented
7C11×#1537C211yesmaximal, characteristic, complemented
8C11×#1531C211yesmaximal, characteristic, complemented
9C11×#1530C211yesmaximal, characteristic
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×#533C2211yescharacteristic
23C11×#532C2211yescharacteristic
24C11×#501—21no—
25C11×#501—21no—
26C11×#501C2212yes—
27C11×#501C2212yes—
28C11×#501C2212yes—
29C11×#497C2212yes—
30C11×#491C2212yes—
31C11×#489C2212yes—
32C11×#485—22no—
33C11×#477—21no—
34C11×#475—21no—
35C11×#462—21no—
36C11×#460—21no—
37C11×#452—22no—
38C11×#432C2211yescharacteristic
39C11×#432C2211yescharacteristic
40C11×#427—22no—
41C2×C11×#97C2211yescharacteristic
42C11×#330C2214yes—
43C11×#330C2214yes—
44C11×#329C2214yes—
45C2×C11×#41D412yes—
46C22×Q8×C11—22no—
47C2×C11×Q16—22no—
48C2×C11×SD16—22no—
49C22×C8×C11—21no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—24no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×#127D411yescharacteristic
61C11×#126—24no—
62C11×#126—24no—
63C11×#125—21no—
64C11×#125C2312yes—
65C11×#125C2312yes—
66C11×#124—24no—
67C11×#124—22no—
68C11×#124—22no—
69C11×#124C2312yes—
70C11×#123—24no—
71C11×#123—24no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×#121—21no—
83C11×#121—21no—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C11×#117—22no—
97C11×#117—21no—
98C11×#117D412yes—
99C11×#117D412yes—
100C2×C42×C11C2311yescharacteristic
101C11×#107—22no—
102C11×#107—22no—
103C11×#107—22no—
104C11×#106—22no—
105C11×#106—22no—
106C11×#106—22no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#103—22no—
112C11×#102—22no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8—21no—
115C11×#97—21no—
116C11×#97C2312yes—
117C11×#97C2312yes—
118C11×#97C2312yes—
119#19066C1111yesmaximal, characteristic, direct product factor, Sylow
120C11×#41—82no—
121C2×Q8×C11—24no—
122C2×Q8×C11—21no—
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×C11C2×D412yes—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C11×Q16—82no—
140C11×SD16—82no—
141C2×C8×C11—24no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—41no—
162C11×C4⋊C4—41no—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—41no—
175C42×C11—24no—
176C42×C11—22no—
177C42×C11—22no—
178C42×C11—41no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2411yescharacteristic
183#3550C2×C1111yescharacteristic
184#3237C2×C1111yescharacteristic, complemented
185#3216C2×C1111yescharacteristic
186#3162C2×C1111yescharacteristic, complemented
187#1664C2×C1114yescomplemented
188#1660C2×C1114yescomplemented
189#1537C2×C1111yescharacteristic, complemented
190#1531C2×C1111yescharacteristic, complemented
191#1530C2×C1111yescharacteristic
192C23×C11—22no—
193C23×C11#12011yescharacteristic
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—42no—
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11—42no—
201Q8×C11—42no—
202Q8×C11—84no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—82no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—44no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—84no—
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C8×C11—24no—
226C8×C11—42no—
227C8×C11—42no—
228#563C22×C1114yes—
229#559—21no—
230Q82—21no—
231#556—21no—
232#556—21no—
233D4×Q8—21no—
234D4×Q8—21no—
235#542—22no—
236#542—22no—
237#536—22no—
238#533C22×C1111yescharacteristic
239#533C22×C1111yescharacteristic
240#533C22×C1111yescharacteristic
241#532C22×C1111yescharacteristic
242#501—21no—
243#501—21no—
244#501C22×C1112yes—
245#501C22×C1112yes—
246#501C22×C1112yes—
247#497C22×C1112yes—
248#491C22×C1112yes—
249#489C22×C1112yes—
250#485—22no—
251#477—21no—
252#475—21no—
253#462—21no—
254#460—21no—
255#452—22no—
256#432C22×C1111yescharacteristic
257#432C22×C1111yescharacteristic
258#427—22no—
259C2×#97C22×C1111yescharacteristic
260#330C22×C1114yes—
261#330C22×C1114yes—
262#329C22×C1114yes—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11C2×#12011yescharacteristic
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11#45612yes—
283C2×#41D4×C1112yes—
284C22×Q8—22no—
285C2×Q16—22no—
286C2×SD16—22no—
287C22×C8—21no—
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C4⋊Q8—24no—
291C4⋊Q8D4×C1111yescharacteristic
292C4⋊Q8D4×C1111yescharacteristic
293C4⋊Q8D4×C1111yescharacteristic
294C4⋊Q8D4×C1111yescharacteristic
295C4⋊Q8D4×C1111yescharacteristic
296C4⋊Q8C23×C1111yescharacteristic
297C4⋊Q8C23×C1111yescharacteristic
298#127D4×C1111yescharacteristic
299#126—24no—
300#126—24no—
301#125—21no—
302#125C23×C1112yes—
303#125C23×C1112yes—
304#124—24no—
305#124—22no—
306#124—22no—
307#124C23×C1112yes—
308#123—24no—
309#123—24no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320#121—21no—
321#121—21no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—21no—
333C4×D4—21no—
334#117—22no—
335#117—21no—
336#117D4×C1112yes—
337#117D4×C1112yes—
338C2×C42C23×C1111yescharacteristic
339#107—22no—
340#107—22no—
341#107—22no—
342#106—22no—
343#106—22no—
344#106—22no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347#103—22no—
348#103—22no—
349#103—22no—
350#102—22no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353#97—21no—
354#97C23×C1112yes—
355#97C23×C1112yes—
356#97C23×C1112yes—
357C2×C11—41no—
358C2×C11—82no—
359C2×C11C2×#45611yescharacteristic
360C2×C11#301911yescharacteristic
361C2×C11#302011yescharacteristic
362#41—82no—
363C2×Q8—24no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—84no—
371C2×Q8C2×D4×C1112yes—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4C2×D4×C1112yes—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1111yescharacteristic
381Q16—82no—
382SD16—82no—
383C2×C8—24no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4C2×D4×C1112yes—
406C4⋊C4C2×D4×C1112yes—
407C4⋊C4C2×D4×C1112yes—
408C4⋊C4C2×D4×C1112yes—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—41no—
417C42—24no—
418C42—22no—
419C42—22no—
420C42—41no—
421C42C2×D4×C1111yescharacteristic
422C42C2×D4×C1111yescharacteristic
423C42C2×D4×C1111yescharacteristic
424C42C24×C1111yescharacteristic
425C11#1906611yescharacteristic, direct product factor, Sylow
426C23—22no—
427C23C11×#12011yescharacteristic
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—42no—
432Q8—41no—
433Q8—41no—
434Q8—42no—
435Q8—42no—
436Q8—84no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—82no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—84no—
453C2×C4C11×#12011yescharacteristic
454C2×C4C11×#12011yescharacteristic
455C2×C4C11×#12011yescharacteristic
456C2×C4C22×D4×C1111yescharacteristic
457C2×C4C22×D4×C1111yescharacteristic
458C2×C4C22×D4×C1111yescharacteristic
459C8—24no—
460C8—42no—
461C8—42no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22C2×C11×#12011yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—81no—
480C4—81no—
481C4C11×#45612yes—
482C2—41no—
483C2—82no—
484C2C2×C11×#45611yescharacteristic
485C2C11×#301911yescharacteristic
486C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
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
2. C11×#3237C2semidirect
4. C11×#3162C2semidirect
5. C11×#1664C2semidirect
6. C11×#1660C2semidirect
7. C11×#1537C2semidirect
8. C11×#1531C2semidirect
119. #19066C11direct (N × H)
184. #3237C2×C11semidirect
186. #3162C2×C11semidirect
187. #1664C2×C11semidirect
188. #1660C2×C11semidirect
189. #1537C2×C11semidirect
190. #1531C2×C11semidirect
425. C11#19066direct (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×#32372
C11×#32162
C11×#31622
C11×#16642
C11×#16602
C11×#15372
C11×#15312
C11×#15302
#1906611