Finite Group Databasebeta

← C11×#19057 #14596250

Subgroups — C11×#19057 #14596250

Order 2816.

908 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×#3548C211yesmaximal, characteristic
2C11×#3237C211yesmaximal, characteristic, complemented
3C11×#3216C211yesmaximal, characteristic, complemented
4C11×#3135C211yesmaximal, characteristic, complemented
5C11×#1662C214yesmaximal, complemented
6C11×#1661C214yesmaximal, complemented
7C11×#1536C211yesmaximal, characteristic, complemented
8C11×#1531C211yesmaximal, characteristic, complemented
9C11×#1530C211yesmaximal, characteristic, complemented
10C11×#562C2214yes—
11C11×#554—21no—
12C11×#554—21no—
13C11×#550—21no—
14C11×#550—21no—
15C11×#547—21no—
16C11×#547—21no—
17C11×#540—22no—
18C11×#537—22no—
19C11×#537—22no—
20C11×#533C2211yescharacteristic
21C11×#533C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C11×#532C2211yescharacteristic
24C11×#501C2212yes—
25C11×#497C2212yes—
26C11×#491—21no—
27C11×#491C2212yes—
28C11×#490—21no—
29C11×#489C2212yes—
30C11×#489C2212yes—
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×#416—22no—
41C2×C11×#97C2211yescharacteristic
42C11×#330C2214yes—
43C11×#329C2214yes—
44C11×#329C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D412yes—
48C2×C11×#41D412yes—
49C2×C11×Q16—22no—
50C2×C11×SD16—22no—
51C22×C8×C11—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×#127—22no—
59C11×#127D411yescharacteristic
60C11×#127D411yescharacteristic
61C11×#125—22no—
62C11×#125—21no—
63C11×#125C2312yes—
64C11×#124C2312yes—
65C11×#124C2312yes—
66C11×#123—24no—
67C11×#123—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×#121—24no—
77C11×#121—24no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#121—24no—
81C11×#121—24no—
82C11×#121—21no—
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—21no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C11×#117—21no—
97C11×#117D412yes—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4—22no—
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×#103—22no—
109C11×#103—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#19057C1111yesmaximal, characteristic, direct product factor, Sylow
120C11×#41—44no—
121C11×#41—82no—
122C11×#41—84no—
123C11×#41—84no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11C2×D412yes—
129C2×Q8×C11C2×D412yes—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11C2×D412yes—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C11×Q16—82no—
148C11×SD16—82no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—42no—
153C11×C4⋊C4—24no—
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—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—41no—
179C42×C11—22no—
180C42×C11—41no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2411yescharacteristic
185#3548C2×C1111yescharacteristic
186#3237C2×C1111yescharacteristic, complemented
187#3216C2×C1111yescharacteristic, complemented
188#3135C2×C1111yescharacteristic, complemented
189#1662C2×C1114yescomplemented
190#1661C2×C1114yescomplemented
191#1536C2×C1111yescharacteristic, complemented
192#1531C2×C1111yescharacteristic, complemented
193#1530C2×C1111yescharacteristic, complemented
194C23×C11—22no—
195C23×C11—22no—
196C23×C11#12011yescharacteristic
197Q8×C11—42no—
198Q8×C11—42no—
199Q8×C11—42no—
200Q8×C11—41no—
201Q8×C11—41no—
202Q8×C11—42no—
203Q8×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—82no—
211D4×C11—82no—
212D4×C11—84no—
213D4×C11—84no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—84no—
226C2×C4×C11—84no—
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C8×C11—42no—
234C8×C11—42no—
235C8×C11—42no—
236#562C22×C1114yes—
237#554—21no—
238#554—21no—
239#550—21no—
240#550—21no—
241#547—21no—
242#547—21no—
243#540—22no—
244#537—22no—
245#537—22no—
246#533C22×C1111yescharacteristic
247#533C22×C1111yescharacteristic
248#532C22×C1111yescharacteristic
249#532C22×C1111yescharacteristic
250#501C22×C1112yes—
251#497C22×C1112yes—
252#491—21no—
253#491C22×C1112yes—
254#490—21no—
255#489C22×C1112yes—
256#489C22×C1112yes—
257#489C22×C1112yes—
258#485—22no—
259#477—21no—
260#475—21no—
261#462—21no—
262#460—21no—
263#452—22no—
264#432C22×C1111yescharacteristic
265#432C22×C1111yescharacteristic
266#416—22no—
267C2×#97C22×C1111yescharacteristic
268#330C22×C1114yes—
269#329C22×C1114yes—
270#329C22×C1114yes—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11C2×#12011yescharacteristic
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11#45512yes—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41D4×C1112yes—
296C2×#41D4×C1112yes—
297C2×Q16—22no—
298C2×SD16—22no—
299C22×C8—21no—
300C4⋊Q8D4×C1111yescharacteristic
301C4⋊Q8D4×C1111yescharacteristic
302C4⋊Q8D4×C1111yescharacteristic
303C4⋊Q8D4×C1111yescharacteristic
304C4⋊Q8C23×C1111yescharacteristic
305C4⋊Q8C23×C1111yescharacteristic
306#127—22no—
307#127D4×C1111yescharacteristic
308#127D4×C1111yescharacteristic
309#125—22no—
310#125—21no—
311#125C23×C1112yes—
312#124C23×C1112yes—
313#124C23×C1112yes—
314#123—24no—
315#123—24no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324#121—24no—
325#121—24no—
326#121—22no—
327#121—22no—
328#121—24no—
329#121—24no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344#117—21no—
345#117D4×C1112yes—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C42C23×C1111yescharacteristic
349#107—22no—
350#106—22no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353#103—22no—
354#103—22no—
355#103—22no—
356#103—22no—
357#103—22no—
358#102—22no—
359#102—22no—
360#102—22no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363#97—21no—
364#97C23×C1112yes—
365#97C23×C1112yes—
366#97C23×C1112yes—
367C2×C11—41no—
368C2×C11—82no—
369C2×C11—82no—
370C2×C11C2×#45511yescharacteristic
371C2×C11#301911yescharacteristic
372C2×C11#302011yescharacteristic
373#41—44no—
374#41—82no—
375#41—84no—
376#41—84no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8C2×D4×C1112yes—
382C2×Q8C2×D4×C1112yes—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4C2×D4×C1112yes—
392C2×D4C2×D4×C1112yes—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1111yescharacteristic
400Q16—82no—
401SD16—82no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—42no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4C2×D4×C1112yes—
423C4⋊C4C2×D4×C1112yes—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—41no—
432C42—22no—
433C42—41no—
434C42C2×D4×C1111yescharacteristic
435C42C2×D4×C1111yescharacteristic
436C42C2×D4×C1111yescharacteristic
437C42C24×C1111yescharacteristic
438C11#1905711yescharacteristic, direct product factor, Sylow
439C23—22no—
440C23—22no—
441C23C11×#12011yescharacteristic
442Q8—42no—
443Q8—42no—
444Q8—42no—
445Q8—41no—
446Q8—41no—
447Q8—42no—
448Q8—42no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—82no—
456D4—82no—
457D4—84no—
458D4—84no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—84no—
471C2×C4—84no—
472C2×C4C11×#12011yescharacteristic
473C2×C4C11×#12011yescharacteristic
474C2×C4C11×#12011yescharacteristic
475C2×C4C22×D4×C1111yescharacteristic
476C2×C4C22×D4×C1111yescharacteristic
477C2×C4C22×D4×C1111yescharacteristic
478C8—42no—
479C8—42no—
480C8—42no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22C2×C11×#12011yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—81no—
501C4—81no—
502C4C11×#45512yes—
503C2—41no—
504C2—82no—
505C2—82no—
506C2C2×C11×#45511yescharacteristic
507C2C11×#301911yescharacteristic
508C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3548C2
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
3. C11×#3216C2semidirect
4. C11×#3135C2semidirect
5. C11×#1662C2semidirect
6. C11×#1661C2semidirect
7. C11×#1536C2semidirect
8. C11×#1531C2semidirect
9. C11×#1530C2semidirect
119. #19057C11direct (N × H)
186. #3237C2×C11semidirect
187. #3216C2×C11semidirect
188. #3135C2×C11semidirect
189. #1662C2×C11semidirect
190. #1661C2×C11semidirect
191. #1536C2×C11semidirect
192. #1531C2×C11semidirect
193. #1530C2×C11semidirect
438. C11#19057direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#32372
C11×#32162
C11×#31352
C11×#16622
C11×#16612
C11×#15362
C11×#15312
C11×#15302
#1905711