Finite Group Databasebeta

← C11×#24723 #14601916

Subgroups — C11×#24723 #14601916

Order 2816.

674 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×#3079C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C4×C11×#137C211yesmaximal, characteristic
4C11×#2925C211yesmaximal, characteristic
5C11×#2079C212yesmaximal
6C11×#2052C212yesmaximal
7C11×#1997C211yesmaximal, characteristic, complemented
8C11×#1951C212yesmaximal, complemented
9C11×#1950C211yesmaximal, characteristic, complemented
10C11×#1930C212yesmaximal, complemented
11C11×#1801C211yesmaximal, characteristic, complemented
12C2×C11×#137C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C11×#477—21no—
17C11×#476—21no—
18C11×#475—21no—
19C11×#475—21no—
20C11×#475—21no—
21C11×#475—22no—
22C11×#474—21no—
23C11×#441—21no—
24C11×#440—21no—
25C4×C11×Q16—21no—
26C4×C11×SD16—21no—
27C11×#433—22no—
28C11×#432—21no—
29C11×#431—21no—
30C2×C11×#108C2212yes—
31C11×#428C2211yescharacteristic
32C11×#428C2212yes—
33C2×C11×#106C2212yes—
34C11×#423C2211yescharacteristic
35C11×#423C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C11×#419C2211yescharacteristic
38C11×#417C2211yescharacteristic
39C11×#417C2212yes—
40C2×C11×#103C2212yes—
41C2×C11×#101C2212yes—
42C11×#408C2212yes—
43C11×#405C2212yes—
44C4×C11×M16C2211yescharacteristic
45C11×#343C2212yes—
46C11×#343C2212yes—
47C11×#343C2212yes—
48C11×#341C2212yes—
49C2×C11×#41C2311yescharacteristic
50C22×Q8×C11—21no—
51C22×Q8×C11C2311yescharacteristic
52C11×#137—22no—
53C11×#137—22no—
54C2×C11×Q16—21no—
55C2×C11×SD16—21no—
56C2×C11×M16C2311yescharacteristic
57C2×C11×M16C2312yes—
58C2×C11×M16C2312yes—
59C2×C11×M16C2311yescharacteristic
60C22×C8×C11C2312yes—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C4×Q8×C11—21no—
66C4×Q8×C11—21no—
67C4×Q8×C11—21no—
68C4×Q8×C11—21no—
69C4×Q8×C11D411yescharacteristic
70C4×Q8×C11D411yescharacteristic
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11D411yescharacteristic
74C4×D4×C11D411yescharacteristic
75C11×#117—21no—
76C11×#117C2311yescharacteristic
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C11×#108—24no—
85C11×#107—21no—
86C11×#107—22no—
87C11×#106—22no—
88C11×#106—22no—
89C11×#106—21no—
90C11×#106—22no—
91C11×C4⋊C8—21no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8—21no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8D411yescharacteristic
96C11×C4⋊C8D411yescharacteristic
97C11×C4⋊C8D412yes—
98C11×#103—21no—
99C11×#103—22no—
100C11×#103—22no—
101C11×#103—22no—
102C11×#103—21no—
103C11×#103—21no—
104C11×#102—21no—
105C11×#102—22no—
106C11×#101—24no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—22no—
109C11×#97—22no—
110C11×#97—21no—
111C4×C8×C11—22no—
112C4×C8×C11—21no—
113#24723C1111yesmaximal, characteristic, direct product factor, Sylow
114C11×#41—21no—
115C11×#41—21no—
116C11×#41—21no—
117C11×#41—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—41no—
124C2×Q8×C11—41no—
125C2×Q8×C11—82no—
126C2×Q8×C11C2×D411yescharacteristic
127C2×Q8×C11#4112yes—
128C2×D4×C11—21no—
129C2×D4×C11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11#4111yescharacteristic
137C22×C4×C11#4111yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C11×Q16—24no—
140C11×SD16—24no—
141C11×M16—21no—
142C11×M16—22no—
143C11×M16—22no—
144C11×M16—22no—
145C11×M16—21no—
146C11×M16—21no—
147C11×M16—22no—
148C11×M16#4112yes—
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11C2×D412yes—
156C2×C8×C11C2×D412yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4—41no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4C2×D411yescharacteristic
168C11×C4⋊C4C2×D411yescharacteristic
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—41no—
176C42×C11—41no—
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181#3079C2×C1111yescharacteristic
182C2×#475C2×C1111yescharacteristic, complemented
183C4×#137C2×C1111yescharacteristic
184#2925C2×C1111yescharacteristic
185#2079C2×C1112yes—
186#2052C2×C1112yes—
187#1997C2×C1111yescharacteristic, complemented
188#1951C2×C1112yescomplemented
189#1950C2×C1111yescharacteristic, complemented
190#1930C2×C1112yescomplemented
191#1801C2×C1111yescharacteristic, complemented
192C23×C11—21no—
193C23×C11C2×#4111yescharacteristic
194Q8×C11—22no—
195Q8×C11—21no—
196Q8×C11—21no—
197Q8×C11—22no—
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11—82no—
201Q8×C11—82no—
202D4×C11—21no—
203D4×C11—21no—
204D4×C11—41no—
205D4×C11—41no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—81no—
220C2×C4×C11—81no—
221C2×C4×C11—82no—
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C2×C4×C112−1+411yescharacteristic
232C8×C11—22no—
233C8×C11—22no—
234C8×C11—22no—
235C8×C11—42no—
236C8×C11—41no—
237C8×C11—42no—
238C2×#137C22×C1111yescharacteristic
239C2×C4⋊Q8C22×C1111yescharacteristic
240C4×#41C22×C1111yescharacteristic
241C2×C4×Q8C22×C1111yescharacteristic
242#477—21no—
243#476—21no—
244#475—21no—
245#475—21no—
246#475—21no—
247#475—22no—
248#474—21no—
249#441—21no—
250#440—21no—
251C4×Q16—21no—
252C4×SD16—21no—
253#433—22no—
254#432—21no—
255#431—21no—
256C2×#108C22×C1112yes—
257#428C22×C1112yes—
258#428C22×C1111yescharacteristic
259C2×#106C22×C1112yes—
260#423C22×C1111yescharacteristic
261#423C22×C1111yescharacteristic
262C2×C4⋊C8C22×C1111yescharacteristic
263#419C22×C1111yescharacteristic
264#417C22×C1112yes—
265#417C22×C1111yescharacteristic
266C2×#103C22×C1112yes—
267C2×#101C22×C1112yes—
268#408C22×C1112yes—
269#405C22×C1112yes—
270C4×M16C22×C1111yescharacteristic
271#343C22×C1112yes—
272#343C22×C1112yes—
273#343C22×C1112yes—
274#341C22×C1112yes—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11C2×#12111yescharacteristic
281C22×C11#55211yescharacteristic
282C22×C11#55611yescharacteristic
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—41no—
287C4×C11—42no—
288C4×C11—41no—
289C4×C11—41no—
290C4×C11—82no—
291C4×C11—81no—
292C4×C11#47112yes—
293C4×C11#52511yescharacteristic
294C4×C11#53611yescharacteristic
295C4×C11#54711yescharacteristic
296C4×C11#54811yescharacteristic
297C2×#41C23×C1111yescharacteristic
298C22×Q8—21no—
299C22×Q8C23×C1111yescharacteristic
300#137—22no—
301#137—22no—
302C2×Q16—21no—
303C2×SD16—21no—
304C2×M16C23×C1111yescharacteristic
305C2×M16C23×C1112yes—
306C2×M16C23×C1112yes—
307C2×M16C23×C1111yescharacteristic
308C22×C8C23×C1112yes—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8D4×C1111yescharacteristic
318C4×Q8D4×C1111yescharacteristic
319C4×D4—21no—
320C4×D4—21no—
321C4×D4D4×C1111yescharacteristic
322C4×D4D4×C1111yescharacteristic
323#117—21no—
324#117C23×C1111yescharacteristic
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4C23×C1111yescharacteristic
328C2×C4⋊C4C23×C1112yes—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42C23×C1111yescharacteristic
332#108—24no—
333#107—21no—
334#107—22no—
335#106—22no—
336#106—22no—
337#106—21no—
338#106—22no—
339C4⋊C8—21no—
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8D4×C1111yescharacteristic
344C4⋊C8D4×C1111yescharacteristic
345C4⋊C8D4×C1112yes—
346#103—21no—
347#103—22no—
348#103—22no—
349#103—22no—
350#103—21no—
351#103—21no—
352#102—21no—
353#102—22no—
354#101—24no—
355C22⋊C8—22no—
356C22⋊C8—22no—
357#97—22no—
358#97—21no—
359C4×C8—22no—
360C4×C8—21no—
361C2×C11—21no—
362C2×C11—21no—
363C2×C11—81no—
364C2×C11#241511yescharacteristic
365C2×C11C2×#47111yescharacteristic
366C2×C11#306911yescharacteristic
367#41—21no—
368#41—21no—
369#41—21no—
370#41—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—41no—
377C2×Q8—41no—
378C2×Q8—82no—
379C2×Q8C2×D4×C1111yescharacteristic
380C2×Q8C11×#4112yes—
381C2×D4—21no—
382C2×D4C2×D4×C1111yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4C11×#4111yescharacteristic
390C22×C4C11×#4111yescharacteristic
391C22×C4C24×C1111yescharacteristic
392Q16—24no—
393SD16—24no—
394M16—21no—
395M16—22no—
396M16—22no—
397M16—22no—
398M16—21no—
399M16—21no—
400M16—22no—
401M16C11×#4112yes—
402C2×C8—21no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—21no—
407C2×C8—22no—
408C2×C8C2×D4×C1112yes—
409C2×C8C2×D4×C1112yes—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4C2×D4×C1111yescharacteristic
421C4⋊C4C2×D4×C1111yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—21no—
425C42—21no—
426C42—21no—
427C42—21no—
428C42—41no—
429C42—41no—
430C42C2×D4×C1111yescharacteristic
431C42C2×D4×C1111yescharacteristic
432C42C2×D4×C1111yescharacteristic
433C42C2×D4×C1111yescharacteristic
434C11#2472311yescharacteristic, direct product factor, Sylow
435C23—21no—
436C23C2×C11×#4111yescharacteristic
437Q8—22no—
438Q8—21no—
439Q8—21no—
440Q8—22no—
441Q8—41no—
442Q8—41no—
443Q8—82no—
444Q8—82no—
445D4—21no—
446D4—21no—
447D4—41no—
448D4—41no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—82no—
465C2×C4C11×#12111yescharacteristic
466C2×C4C11×#12111yescharacteristic
467C2×C4C11×#12111yescharacteristic
468C2×C4C11×#12111yescharacteristic
469C2×C4C22×D4×C1111yescharacteristic
470C2×C4C22×D4×C1111yescharacteristic
471C2×C4C2×C11×#4111yescharacteristic
472C2×C4C2×C11×#4111yescharacteristic
473C2×C4C11×2−1+411yescharacteristic
474C2×C4C11×2−1+411yescharacteristic
475C8—22no—
476C8—22no—
477C8—22no—
478C8—42no—
479C8—41no—
480C8—42no—
481C22—21no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22C2×C11×#12111yescharacteristic
487C22C11×#55211yescharacteristic
488C22C11×#55611yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—41no—
493C4—42no—
494C4—41no—
495C4—41no—
496C4—82no—
497C4—81no—
498C4C11×#47112yes—
499C4C11×#52511yescharacteristic
500C4C11×#53611yescharacteristic
501C4C11×#54711yescharacteristic
502C4C11×#54811yescharacteristic
503C2—21no—
504C2—21no—
505C2—81no—
506C2C11×#241511yescharacteristic
507C2C2×C11×#47111yescharacteristic
508C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C11×#475C2semidirect
7. C11×#1997C2semidirect
8. C11×#1951C2semidirect
9. C11×#1950C2semidirect
10. C11×#1930C2semidirect
11. C11×#1801C2semidirect
113. #24723C11direct (N × H)
182. C2×#475C2×C11semidirect
187. #1997C2×C11semidirect
188. #1951C2×C11semidirect
189. #1950C2×C11semidirect
190. #1930C2×C11semidirect
191. #1801C2×C11semidirect
434. C11#24723direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30792
C2×C11×#4752
C4×C11×#1372
C11×#29252
C11×#20792
C11×#20522
C11×#19972
C11×#19512
C11×#19502
C11×#19302
C11×#18012
#2472311