Finite Group Databasebeta

← C11×#18998 #14596191

Subgroups — C11×#18998 #14596191

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#562C211yesmaximal, characteristic
2C11×#3236C211yesmaximal, characteristic, complemented
3C11×#3215C211yesmaximal, characteristic, complemented
4C11×#3140C211yesmaximal, characteristic, complemented
5C11×#1662C214yesmaximal, complemented
6C11×#1661C214yesmaximal, complemented
7C11×#1533C211yesmaximal, characteristic, complemented
8C11×#1528C211yesmaximal, characteristic, complemented
9C11×#1527C211yesmaximal, characteristic, complemented
10C11×#562—22no—
11C11×#562—22no—
12C11×#562—22no—
13C11×#562C2214yes—
14C11×#533C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×C11×#124C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×#121—21no—
23C2×C11×#121—21no—
24C11×#501C2212yescomplemented
25C11×#497C2212yescomplemented
26C11×#491C2212yescomplemented
27C11×#489C2212yescomplemented
28C11×#489C2212yescomplemented
29C11×#489C2212yescomplemented
30C11×#488—22no—
31C11×#484—21no—
32C11×#483—21no—
33C11×#479—22no—
34C11×#464—22no—
35C11×#451—21no—
36C11×#450—21no—
37C11×#432C2211yescharacteristic
38C11×#432C2211yescharacteristic
39C11×#419—21no—
40C11×#418—21no—
41C4×C11×M16C2211yescharacteristic
42C11×#330C2214yescomplemented
43C11×#329C2214yescomplemented
44C11×#329C2214yescomplemented
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C2×C11×Q16—22no—
54C2×C11×SD16—22no—
55C2×C11×M16—21no—
56C11×C4⋊Q8C2311yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×#125—21no—
59C11×#125—21no—
60C11×#125—21no—
61C11×#125D412yes—
62C11×#125C2312yes—
63C11×#124—21no—
64C11×#124—21no—
65C11×#124—21no—
66C11×#124—21no—
67C11×#124D412yes—
68C11×#124D412yes—
69C11×#124C2312yes—
70C11×#124C2312yes—
71C11×#123—24no—
72C11×#123—24no—
73C11×#123—24no—
74C11×#123—24no—
75C11×C22⋊Q8—24no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×#121—24no—
82C11×#121—24no—
83C11×#121—24no—
84C11×#121—24no—
85C4×Q8×C11—21no—
86C4×Q8×C11—21no—
87C11×#117—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
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×#97C2312yes—
116C11×#97C2312yes—
117C11×#97C2312yes—
118C4×C8×C11—21no—
119#18998C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C24×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—42no—
127C2×Q8×C11—81no—
128C2×Q8×C11C2×D412yes—
129C2×Q8×C11C2×D412yes—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—42no—
135C2×D4×C11—81no—
136C2×D4×C11—82no—
137C2×D4×C11—82no—
138C2×D4×C11C2×D412yes—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—82no—
147C22×C4×C11—82no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C11×Q16—82no—
152C11×SD16—82no—
153C11×M16—42no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4C2×D412yes—
172C11×C4⋊C4C2×D412yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—41no—
184C42×C11—41no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2411yescharacteristic
189C2×#562C2×C1111yescharacteristic
190#3236C2×C1111yescharacteristic, complemented
191#3215C2×C1111yescharacteristic, complemented
192#3140C2×C1111yescharacteristic, complemented
193#1662C2×C1114yescomplemented
194#1661C2×C1114yescomplemented
195#1533C2×C1111yescharacteristic, complemented
196#1528C2×C1111yescharacteristic, complemented
197#1527C2×C1111yescharacteristic, complemented
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11#12011yescharacteristic
207Q8×C11—42no—
208Q8×C11—42no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—81no—
212Q8×C11—81no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—81no—
216D4×C11—81no—
217D4×C11—84no—
218D4×C11—84no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—84no—
233C2×C4×C11—84no—
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C8×C11—42no—
241C8×C11—42no—
242C8×C11—42no—
243#562—22no—
244#562—22no—
245#562—22no—
246#562C22×C1114yes—
247#533C22×C1111yescharacteristic
248C2×#125C22×C1111yescharacteristic
249C2×#124C22×C1111yescharacteristic
250C2×#124C22×C1111yescharacteristic
251C2×#123—21no—
252C2×#123—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—21no—
255C2×#121—21no—
256C2×#121—21no—
257#501C22×C1112yescomplemented
258#497C22×C1112yescomplemented
259#491C22×C1112yescomplemented
260#489C22×C1112yescomplemented
261#489C22×C1112yescomplemented
262#489C22×C1112yescomplemented
263#488—22no—
264#484—21no—
265#483—21no—
266#479—22no—
267#464—22no—
268#451—21no—
269#450—21no—
270#432C22×C1111yescharacteristic
271#432C22×C1111yescharacteristic
272#419—21no—
273#418—21no—
274C4×M16C22×C1111yescharacteristic
275#330C22×C1114yescomplemented
276#329C22×C1114yescomplemented
277#329C22×C1114yescomplemented
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—84no—
287C22×C11—84no—
288C22×C11#45512yes—
289C22×C11C2×#12011yescharacteristic
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—81no—
301C4×C11—81no—
302C22×Q8D4×C1111yescharacteristic
303C22×Q8D4×C1111yescharacteristic
304C22×D4—21no—
305C22×D4—21no—
306C22×D4D4×C1111yescharacteristic
307C22×D4D4×C1111yescharacteristic
308C23×C4—21no—
309C23×C4—21no—
310C2×Q16—22no—
311C2×SD16—22no—
312C2×M16—21no—
313C4⋊Q8C23×C1111yescharacteristic
314C4⋊Q8C23×C1111yescharacteristic
315#125—21no—
316#125—21no—
317#125—21no—
318#125D4×C1112yes—
319#125C23×C1112yes—
320#124—21no—
321#124—21no—
322#124—21no—
323#124—21no—
324#124D4×C1112yes—
325#124D4×C1112yes—
326#124C23×C1112yes—
327#124C23×C1112yes—
328#123—24no—
329#123—24no—
330#123—24no—
331#123—24no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338#121—24no—
339#121—24no—
340#121—24no—
341#121—24no—
342C4×Q8—21no—
343C4×Q8—21no—
344#117—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4D4×C1111yescharacteristic
350C2×C4⋊C4D4×C1111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C42C23×C1111yescharacteristic
358#107—22no—
359#106—22no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362#103—22no—
363#103—22no—
364#103—22no—
365#103—22no—
366#103—22no—
367#102—22no—
368#102—22no—
369#102—22no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372#97C23×C1112yes—
373#97C23×C1112yes—
374#97C23×C1112yes—
375C4×C8—21no—
376C2×C11—22no—
377C2×C11—82no—
378C2×C11—82no—
379C2×C11C2×#45511yescharacteristic
380C2×C11#301911yescharacteristic
381C2×C11#302011yescharacteristic
382C24—21no—
383C24—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—42no—
389C2×Q8—81no—
390C2×Q8C2×D4×C1112yes—
391C2×Q8C2×D4×C1112yes—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—81no—
398C2×D4—82no—
399C2×D4—82no—
400C2×D4C2×D4×C1112yes—
401C2×D4C2×D4×C1112yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—82no—
409C22×C4—82no—
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413Q16—82no—
414SD16—82no—
415M16—42no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4C2×D4×C1112yes—
434C4⋊C4C2×D4×C1112yes—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—41no—
446C42—41no—
447C42C2×D4×C1111yescharacteristic
448C42C2×D4×C1111yescharacteristic
449C42C2×D4×C1111yescharacteristic
450C42C24×C1111yescharacteristic
451C11#1899811yescharacteristic, direct product factor, Sylow
452C23—22no—
453C23—22no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23C11×#12011yescharacteristic
461Q8—42no—
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—81no—
466Q8—81no—
467D4—42no—
468D4—42no—
469D4—81no—
470D4—81no—
471D4—84no—
472D4—84no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—84no—
487C2×C4—84no—
488C2×C4C11×#12011yescharacteristic
489C2×C4C11×#12011yescharacteristic
490C2×C4C11×#12011yescharacteristic
491C2×C4C22×D4×C1111yescharacteristic
492C2×C4C22×D4×C1111yescharacteristic
493C2×C4C22×D4×C1111yescharacteristic
494C8—42no—
495C8—42no—
496C8—42no—
497C22—21no—
498C22—21no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—84no—
506C22—84no—
507C22C11×#45512yes—
508C22C2×C11×#12011yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—81no—
520C4—81no—
521C2—22no—
522C2—82no—
523C2—82no—
524C2C2×C11×#45511yescharacteristic
525C2C11×#301911yescharacteristic
526C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#562C2
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×#3236C2semidirect
3. C11×#3215C2semidirect
4. C11×#3140C2semidirect
5. C11×#1662C2semidirect
6. C11×#1661C2semidirect
7. C11×#1533C2semidirect
8. C11×#1528C2semidirect
9. C11×#1527C2semidirect
24. C11×#501C22semidirect
25. C11×#497C22semidirect
26. C11×#491C22semidirect
27. C11×#489C22semidirect
28. C11×#489C22semidirect
29. C11×#489C22semidirect
42. C11×#330C22semidirect
43. C11×#329C22semidirect
44. C11×#329C22semidirect
119. #18998C11direct (N × H)
190. #3236C2×C11semidirect
191. #3215C2×C11semidirect
192. #3140C2×C11semidirect
193. #1662C2×C11semidirect
194. #1661C2×C11semidirect
195. #1533C2×C11semidirect
196. #1528C2×C11semidirect
197. #1527C2×C11semidirect
257. #501C22×C11semidirect
258. #497C22×C11semidirect
259. #491C22×C11semidirect
260. #489C22×C11semidirect
261. #489C22×C11semidirect
262. #489C22×C11semidirect
275. #330C22×C11semidirect
276. #329C22×C11semidirect
277. #329C22×C11semidirect
451. C11#18998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5622
C11×#32362
C11×#32152
C11×#31402
C11×#16622
C11×#16612
C11×#15332
C11×#15282
C11×#15272
#1899811