Finite Group Databasebeta

← C11×#32918 #14610111

Subgroups — C11×#32918 #14610111

Order 2816.

1372 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#519C211yesmaximal, characteristic, complemented
2C2×C11×#464C212yesmaximal, complemented
3C2×C11×#451C211yesmaximal, characteristic, complemented
4C2×C11×#448C211yesmaximal, characteristic
5C11×#2620C211yesmaximal, characteristic
6C11×#1880C212yesmaximal, complemented
7C11×#1878C212yesmaximal, complemented
8C11×#1875C211yesmaximal, characteristic
9C11×#1873C211yesmaximal, characteristic, complemented
10C11×#1803C212yesmaximal, complemented
11C11×#1798C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2212yes—
15C2×C11×#124C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C11×#519—28no—
19C2×C4×Q8×C11—22no—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2212yes—
22C2×C11×#117—22no—
23C2×C11×#117C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C11×#464—28no—
26C11×#451—24no—
27C11×#448—24no—
28C2×C11×C4⋊C8C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C11×#396—22no—
36C11×#394—22no—
37C11×#391C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#384C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—24no—
44C22×Q8×C11—24no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11D414yes—
48C22×Q8×C11C2311yescharacteristic
49C22×Q8×C11C2312yes—
50C22×D4×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C2×C11×Q16—24no—
55C2×C11×Q16—24no—
56C2×C11×Q16—24no—
57C2×C11×SD16—24no—
58C2×C11×SD16—24no—
59C2×C11×SD16—24no—
60C22×C8×C11C2312yes—
61C22×C8×C11C2312yes—
62C11×#124—24no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×#121—22no—
66C11×#121—22no—
67C4×Q8×C11—216no—
68C4×Q8×C11—24no—
69C4×Q8×C11—24no—
70C4×Q8×C11—24no—
71C4×Q8×C11D418yescomplemented
72C11×#117—216no—
73C11×#117—24no—
74C11×#117—24no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D412yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11—22no—
90C2×C42×C11—22no—
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C11×C4⋊C8—24no—
95C11×#103—24no—
96C11×#103—24no—
97C11×#103—24no—
98C11×#102—24no—
99C11×C22⋊C8—22no—
100C11×C22⋊C8—22no—
101C11×#95—22no—
102#32918C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C24×C11C2×D411yescharacteristic
105C2×Q8×C11—24no—
106C2×Q8×C11—216no—
107C2×Q8×C11—24no—
108C2×Q8×C11—216no—
109C2×Q8×C11—24no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11C2×D414yes—
118C2×Q8×C11C2×D414yes—
119C2×Q8×C11#4114yes—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—42no—
125C2×D4×C11—82no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C11×Q16—48no—
143C11×SD16—48no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—82no—
160C11×C4⋊C4C2×D414yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—44no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—82no—
167C42×C11—28no—
168C42×C11—24no—
169C42×C11—28no—
170C42×C11—22no—
171C42×C11C2×D414yes—
172C2×#519C2×C1111yescharacteristic, complemented
173C2×#464C2×C1112yescomplemented
174C2×#451C2×C1111yescharacteristic, complemented
175C2×#448C2×C1111yescharacteristic
176#2620C2×C1111yescharacteristic
177#1880C2×C1112yescomplemented
178#1878C2×C1112yescomplemented
179#1875C2×C1111yescharacteristic
180#1873C2×C1111yescharacteristic, complemented
181#1803C2×C1112yescomplemented
182#1798C2×C1111yescharacteristic, complemented
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11#12112yes—
193C23×C11C22×D411yescharacteristic
194Q8×C11—216no—
195Q8×C11—24no—
196Q8×C11—24no—
197Q8×C11—24no—
198Q8×C11—42no—
199Q8×C11—42no—
200Q8×C11#12118yes—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—84no—
204C2×C4×C11—216no—
205C2×C4×C11—24no—
206C2×C4×C11—21no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11#12014yes—
228C2×C4×C11#12112yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D412yes—
231C2×C4×C11C2×#4112yes—
232C2×C4×C11C2×#4111yescharacteristic
233C8×C11—42no—
234C8×C11—42no—
235C23×Q8C22×C1111yescharacteristic
236C22×Q16C22×C1112yes—
237C22×SD16C22×C1112yes—
238C2×#124C22×C1111yescharacteristic
239C2×C22⋊Q8C22×C1111yescharacteristic
240C2×#121C22×C1111yescharacteristic
241#519—28no—
242C2×C4×Q8—22no—
243C2×C4×Q8C22×C1112yes—
244C2×C4×Q8C22×C1112yes—
245C2×#117—22no—
246C2×#117C22×C1111yescharacteristic
247C2×#117C22×C1111yescharacteristic
248#464—28no—
249#451—24no—
250#448—24no—
251C2×C4⋊C8C22×C1112yes—
252C2×#103C22×C1112yes—
253C2×#103C22×C1112yes—
254C2×#103C22×C1112yes—
255C2×#102C22×C1112yes—
256C2×C22⋊C8C22×C1111yescharacteristic
257C2×C22⋊C8C22×C1111yescharacteristic
258#396—22no—
259#394—22no—
260#391C22×C1111yescharacteristic
261#390C22×C1111yescharacteristic
262#384C22×C1111yescharacteristic
263#340C22×C1112yes—
264#340C22×C1112yes—
265#336C22×C1112yes—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—81no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11C2×#12011yescharacteristic
277C22×C11C2×#12111yescharacteristic
278C22×C11#52511yescharacteristic
279C22×C11#57712yes—
280C22×C11#57812yes—
281C4×C11—28no—
282C4×C11—22no—
283C4×C11—24no—
284C4×C11—42no—
285C4×C11—44no—
286C4×C11—81no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11C2×#12112yes—
290C4×C11#52512yes—
291C22×Q8—24no—
292C22×Q8—24no—
293C22×Q8—21no—
294C22×Q8—22no—
295C22×Q8D4×C1114yes—
296C22×Q8C23×C1111yescharacteristic
297C22×Q8C23×C1112yes—
298C22×D4—21no—
299C22×D4C23×C1111yescharacteristic
300C23×C4—21no—
301C23×C4C23×C1111yescharacteristic
302C2×Q16—24no—
303C2×Q16—24no—
304C2×Q16—24no—
305C2×SD16—24no—
306C2×SD16—24no—
307C2×SD16—24no—
308C22×C8C23×C1112yes—
309C22×C8C23×C1112yes—
310#124—24no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313#121—22no—
314#121—22no—
315C4×Q8—216no—
316C4×Q8—24no—
317C4×Q8—24no—
318C4×Q8—24no—
319C4×Q8D4×C1118yescomplemented
320#117—216no—
321#117—24no—
322#117—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4D4×C1112yes—
328C2×C4⋊C4C23×C1111yescharacteristic
329C2×C4⋊C4C23×C1111yescharacteristic
330C2×C4⋊C4C23×C1112yes—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4D4×C1112yes—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—21no—
340C2×C42C23×C1111yescharacteristic
341C2×C42C23×C1111yescharacteristic
342C4⋊C8—24no—
343#103—24no—
344#103—24no—
345#103—24no—
346#102—24no—
347C22⋊C8—22no—
348C22⋊C8—22no—
349#95—22no—
350C2×C11—42no—
351C2×C11—161no—
352C2×C11#284711yescharacteristic
353C2×C11#301312yes—
354C2×C11#304311yescharacteristic
355C2×C11#304411yescharacteristic
356C2×C11#312112yes—
357C24—21no—
358C24C2×D4×C1111yescharacteristic
359C2×Q8—24no—
360C2×Q8—216no—
361C2×Q8—24no—
362C2×Q8—216no—
363C2×Q8—24no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—22no—
371C2×Q8C2×D4×C1114yes—
372C2×Q8C2×D4×C1114yes—
373C2×Q8C11×#4114yes—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—22no—
378C2×D4—42no—
379C2×D4—82no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4C2×D4×C1112yes—
391C22×C4C2×D4×C1112yes—
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1112yes—
394C22×C4C11×#4112yes—
395C22×C4C24×C1111yescharacteristic
396Q16—48no—
397SD16—48no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C4⋊C4—28no—
405C4⋊C4—28no—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—42no—
413C4⋊C4—82no—
414C4⋊C4C2×D4×C1114yes—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—42no—
418C22⋊C4—44no—
419C22⋊C4—42no—
420C22⋊C4—82no—
421C42—28no—
422C42—24no—
423C42—28no—
424C42—22no—
425C42C2×D4×C1114yes—
426C11#3291811yescharacteristic, direct product factor, Sylow
427C23—21no—
428C23—21no—
429C23—22no—
430C23—22no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—42no—
435C23—42no—
436C23C11×#12112yes—
437C23C22×D4×C1111yescharacteristic
438Q8—216no—
439Q8—24no—
440Q8—24no—
441Q8—24no—
442Q8—42no—
443Q8—42no—
444Q8C11×#12118yes—
445D4—42no—
446D4—42no—
447D4—84no—
448C2×C4—216no—
449C2×C4—24no—
450C2×C4—21no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4C11×#12014yes—
472C2×C4C11×#12112yes—
473C2×C4C22×D4×C1111yescharacteristic
474C2×C4C22×D4×C1112yes—
475C2×C4C2×C11×#4112yes—
476C2×C4C2×C11×#4111yescharacteristic
477C8—42no—
478C8—42no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—42no—
483C22—42no—
484C22—82no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—82no—
489C22C2×C11×#12011yescharacteristic
490C22C2×C11×#12111yescharacteristic
491C22C11×#52511yescharacteristic
492C22C11×#57712yes—
493C22C11×#57812yes—
494C4—24no—
495C4—28no—
496C4—22no—
497C4—42no—
498C4—44no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4C2×C11×#12112yes—
503C4C11×#52512yes—
504C2—42no—
505C2—161no—
506C2C11×#284711yescharacteristic
507C2C11×#301312yes—
508C2C11×#304311yescharacteristic
509C2C11×#304411yescharacteristic
510C2C11×#312112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#519C2semidirect
2. C2×C11×#464C2semidirect
3. C2×C11×#451C2semidirect
6. C11×#1880C2semidirect
7. C11×#1878C2semidirect
9. C11×#1873C2semidirect
10. C11×#1803C2semidirect
11. C11×#1798C2semidirect
71. C4×Q8×C11D4semidirect
102. #32918C11direct (N × H)
172. C2×#519C2×C11semidirect
173. C2×#464C2×C11semidirect
174. C2×#451C2×C11semidirect
177. #1880C2×C11semidirect
178. #1878C2×C11semidirect
180. #1873C2×C11semidirect
181. #1803C2×C11semidirect
182. #1798C2×C11semidirect
319. C4×Q8D4×C11semidirect
426. C11#32918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5192
C2×C11×#4642
C2×C11×#4512
C2×C11×#4482
C11×#26202
C11×#18802
C11×#18782
C11×#18752
C11×#18732
C11×#18032
C11×#17982
#3291811