Finite Group Databasebeta

← C11×#19411 #14596604

Subgroups — C11×#19411 #14596604

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic, complemented
2C11×#3079C211yesmaximal, characteristic
3C11×#3076C211yesmaximal, characteristic
4C11×#2988C211yesmaximal, characteristic
5C11×#1684C212yesmaximal, complemented
6C11×#1683C212yesmaximal, complemented
7C11×#1670C212yesmaximal, complemented
8C11×#1669C212yesmaximal, complemented
9C11×#1571C211yesmaximal, characteristic, complemented
10C11×#1550C211yesmaximal, characteristic, complemented
11C2×C11×#332C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15C11×#494C2212yes—
16C11×#487C2212yes—
17C11×#479—21no—
18C11×#478—21no—
19C11×#477—21no—
20C11×#477C2211yescharacteristic
21C11×#476—21no—
22C11×#476C2211yescharacteristic
23C11×#475C2211yescharacteristic
24C11×#475C2212yes—
25C11×#474C2211yescharacteristic
26C11×#474C2212yes—
27C11×#462—21no—
28C11×#462—21no—
29C11×#451—22no—
30C8×Q8×C11C2212yes—
31C8×D4×C11—22no—
32C8×D4×C11C2212yes—
33C11×#431—21no—
34C11×#431C2211yescharacteristic
35C11×#428—21no—
36C11×#427—21no—
37C11×#423C2211yescharacteristic
38C2×C11×C4⋊C8—21no—
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C11×#417—21no—
42C11×#416—21no—
43C11×#335C2212yes—
44C11×#335C2212yes—
45C11×#333C2212yes—
46C11×#332C2212yes—
47C11×#332C2212yes—
48C11×#332C2212yes—
49C2×C11×#41D411yescharacteristic
50C22×Q8×C11—21no—
51C2×C11×Q16—22no—
52C2×C11×Q16—22no—
53C2×C11×M16—21no—
54C22×C8×C11—21no—
55C22×C8×C11—21no—
56C22×C8×C11—22no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8C2311yescharacteristic
61C11×C4⋊Q8C2312yes—
62C11×C4⋊Q8C2311yescharacteristic
63C11×#125—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C4×Q8×C11—21no—
67C4×Q8×C11—21no—
68C4×Q8×C11D411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11D411yescharacteristic
73C4×D4×C11C2311yescharacteristic
74C11×#117—21no—
75C11×#117—21no—
76C11×#117D411yescharacteristic
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C11×#107—21no—
82C11×#107—21no—
83C11×#107—22no—
84C11×#106—21no—
85C11×#106—21no—
86C11×#106—22no—
87C11×C4⋊C8—22no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8D411yescharacteristic
92C11×C4⋊C8D411yescharacteristic
93C11×C4⋊C8C2312yes—
94C11×C4⋊C8C2311yescharacteristic
95C11×C4⋊C8C2311yescharacteristic
96C11×C4⋊C8C2312yes—
97C11×#103—21no—
98C11×#103—21no—
99C11×#103—22no—
100C11×#103—22no—
101C11×#103—22no—
102C11×#102—21no—
103C11×#102—21no—
104C11×#102—22no—
105C11×C22⋊C8—22no—
106C11×C22⋊C8D412yes—
107C4×C8×C11—22no—
108C4×C8×C11C2312yes—
109#19411C1111yesmaximal, characteristic, direct product factor, Sylow
110C11×#41—22no—
111C11×#41Q1614yescomplemented
112C2×Q8×C11—22no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—41no—
116C2×Q8×C11—81no—
117C2×Q8×C11—81no—
118C2×Q8×C11C2×D411yescharacteristic
119C2×D4×C11—21no—
120C2×D4×C11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C11×Q16—82no—
129C11×Q16—82no—
130C11×M16—42no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11—21no—
135C2×C8×C11—42no—
136C2×C8×C11—81no—
137C2×C8×C11—82no—
138C2×C8×C11C2×D412yes—
139C2×C8×C11C2×D412yes—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4C2×D411yescharacteristic
153C11×C4⋊C4C2×D411yescharacteristic
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C11×C22⋊C4—41no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—41no—
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11#4111yescharacteristic
165C42×C11C2411yescharacteristic
166#3209C2×C1111yescharacteristic, complemented
167#3079C2×C1111yescharacteristic
168#3076C2×C1111yescharacteristic
169#2988C2×C1111yescharacteristic
170#1684C2×C1112yescomplemented
171#1683C2×C1112yescomplemented
172#1670C2×C1112yescomplemented
173#1669C2×C1112yescomplemented
174#1571C2×C1111yescharacteristic, complemented
175#1550C2×C1111yescharacteristic, complemented
176C2×#332C2×C1111yescharacteristic, complemented
177C23×C11—21no—
178C23×C11#12111yescharacteristic
179Q8×C11—21no—
180Q8×C11—41no—
181Q8×C11—42no—
182Q8×C11—41no—
183Q8×C11—42no—
184Q8×C11—81no—
185Q8×C11—82no—
186Q8×C11C2×Q1612yes—
187D4×C11—24no—
188D4×C11—21no—
189D4×C11C2×Q1612yes—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—24no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—81no—
203C2×C4×C11—82no—
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11C2×Q1612yes—
208C2×C4×C11#13512yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C8×C11—22no—
213C8×C11—22no—
214C8×C11—41no—
215C8×C11—41no—
216C8×C11—42no—
217C8×C11—42no—
218#533C22×C1111yescharacteristic
219C2×C4⋊Q8C22×C1111yescharacteristic
220C4×#41C22×C1111yescharacteristic
221#494C22×C1112yes—
222#487C22×C1112yes—
223#479—21no—
224#478—21no—
225#477—21no—
226#477C22×C1111yescharacteristic
227#476—21no—
228#476C22×C1111yescharacteristic
229#475C22×C1111yescharacteristic
230#475C22×C1112yes—
231#474C22×C1111yescharacteristic
232#474C22×C1112yes—
233#462—21no—
234#462—21no—
235#451—22no—
236C8×Q8C22×C1112yes—
237C8×D4—22no—
238C8×D4C22×C1112yes—
239#431—21no—
240#431C22×C1111yescharacteristic
241#428—21no—
242#427—21no—
243#423C22×C1111yescharacteristic
244C2×C4⋊C8—21no—
245C2×C4⋊C8C22×C1111yescharacteristic
246C2×C4⋊C8C22×C1111yescharacteristic
247#417—21no—
248#416—21no—
249#335C22×C1112yes—
250#335C22×C1112yes—
251#333C22×C1112yes—
252#332C22×C1112yes—
253#332C22×C1112yes—
254#332C22×C1112yes—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—22no—
258C22×C11—41no—
259C22×C11—41no—
260C22×C11#46712yes—
261C22×C11C2×#12111yescharacteristic
262C4×C11—21no—
263C4×C11—22no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—41no—
267C4×C11—41no—
268C4×C11—82no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11#46712yes—
272C4×C11C22×Q1611yescharacteristic
273C4×C11C2×#13511yescharacteristic
274C4×C11#57611yescharacteristic
275C4×C11#57711yescharacteristic
276C2×#41D4×C1111yescharacteristic
277C22×Q8—21no—
278C2×Q16—22no—
279C2×Q16—22no—
280C2×M16—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—22no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8C23×C1112yes—
288C4⋊Q8C23×C1111yescharacteristic
289C4⋊Q8C23×C1111yescharacteristic
290#125—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8D4×C1111yescharacteristic
296C4×Q8C23×C1111yescharacteristic
297C4×D4—21no—
298C4×D4—21no—
299C4×D4D4×C1111yescharacteristic
300C4×D4C23×C1111yescharacteristic
301#117—21no—
302#117—21no—
303#117D4×C1111yescharacteristic
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C42—21no—
307C2×C42C23×C1111yescharacteristic
308#107—21no—
309#107—21no—
310#107—22no—
311#106—21no—
312#106—21no—
313#106—22no—
314C4⋊C8—22no—
315C4⋊C8—21no—
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8D4×C1111yescharacteristic
319C4⋊C8D4×C1111yescharacteristic
320C4⋊C8C23×C1112yes—
321C4⋊C8C23×C1111yescharacteristic
322C4⋊C8C23×C1111yescharacteristic
323C4⋊C8C23×C1112yes—
324#103—21no—
325#103—21no—
326#103—22no—
327#103—22no—
328#103—22no—
329#102—21no—
330#102—21no—
331#102—22no—
332C22⋊C8—22no—
333C22⋊C8D4×C1112yes—
334C4×C8—22no—
335C4×C8C23×C1112yes—
336C2×C11—22no—
337C2×C11—42no—
338C2×C11#304511yescharacteristic
339C2×C11C2×#46711yescharacteristic
340C2×C11#306911yescharacteristic
341#41—22no—
342#41C11×Q1614yescomplemented
343C2×Q8—22no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—41no—
347C2×Q8—81no—
348C2×Q8—81no—
349C2×Q8C2×D4×C1111yescharacteristic
350C2×D4—21no—
351C2×D4C2×D4×C1111yescharacteristic
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C2×D4×C1111yescharacteristic
358C22×C4C11×#4111yescharacteristic
359Q16—82no—
360Q16—82no—
361M16—42no—
362C2×C8—22no—
363C2×C8—21no—
364C2×C8—22no—
365C2×C8—21no—
366C2×C8—42no—
367C2×C8—82no—
368C2×C8—81no—
369C2×C8C2×D4×C1112yes—
370C2×C8C2×D4×C1112yes—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4C2×D4×C1111yescharacteristic
384C4⋊C4C2×D4×C1111yescharacteristic
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—41no—
389C42—21no—
390C42—21no—
391C42—21no—
392C42—41no—
393C42C2×D4×C1111yescharacteristic
394C42C2×D4×C1111yescharacteristic
395C42C11×#4111yescharacteristic
396C42C24×C1111yescharacteristic
397C11#1941111yescharacteristic, direct product factor, Sylow
398C23—21no—
399C23C11×#12111yescharacteristic
400Q8—21no—
401Q8—41no—
402Q8—42no—
403Q8—41no—
404Q8—42no—
405Q8—81no—
406Q8—82no—
407Q8C2×C11×Q1612yes—
408D4—24no—
409D4—21no—
410D4C2×C11×Q1612yes—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—24no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—81no—
424C2×C4—82no—
425C2×C4C11×#12111yescharacteristic
426C2×C4C11×#12111yescharacteristic
427C2×C4C11×#12111yescharacteristic
428C2×C4C2×C11×Q1612yes—
429C2×C4C11×#13512yes—
430C2×C4C22×D4×C1111yescharacteristic
431C2×C4C22×D4×C1111yescharacteristic
432C2×C4C2×C11×#4111yescharacteristic
433C8—22no—
434C8—22no—
435C8—41no—
436C8—41no—
437C8—42no—
438C8—42no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—41no—
443C22—41no—
444C22C11×#46712yes—
445C22C2×C11×#12111yescharacteristic
446C4—21no—
447C4—22no—
448C4—21no—
449C4—21no—
450C4—41no—
451C4—41no—
452C4—82no—
453C4—81no—
454C4—81no—
455C4C11×#46712yes—
456C4C22×C11×Q1611yescharacteristic
457C4C2×C11×#13511yescharacteristic
458C4C11×#57611yescharacteristic
459C4C11×#57711yescharacteristic
460C2—22no—
461C2—42no—
462C2C11×#304511yescharacteristic
463C2C2×C11×#46711yescharacteristic
464C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#41D4
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×#3209C2semidirect
5. C11×#1684C2semidirect
6. C11×#1683C2semidirect
7. C11×#1670C2semidirect
8. C11×#1669C2semidirect
9. C11×#1571C2semidirect
10. C11×#1550C2semidirect
11. C2×C11×#332C2semidirect
109. #19411C11direct (N × H)
111. C11×#41Q16semidirect
166. #3209C2×C11semidirect
170. #1684C2×C11semidirect
171. #1683C2×C11semidirect
172. #1670C2×C11semidirect
173. #1669C2×C11semidirect
174. #1571C2×C11semidirect
175. #1550C2×C11semidirect
176. C2×#332C2×C11semidirect
342. #41C11×Q16semidirect
397. C11#19411direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32092
C11×#30792
C11×#30762
C11×#29882
C11×#16842
C11×#16832
C11×#16702
C11×#16692
C11×#15712
C11×#15502
C2×C11×#3322
#1941111