Finite Group Databasebeta

← C11×#32698 #14609891

Subgroups — C11×#32698 #14609891

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2102C211yesmaximal, characteristic, complemented
2C11×#2081C211yesmaximal, characteristic, complemented
3C11×#2081C211yesmaximal, characteristic, complemented
4C11×#2069C211yesmaximal, characteristic, complemented
5C11×#2048C211yesmaximal, characteristic, complemented
6C11×#2002C211yesmaximal, characteristic
7C11×#1965C211yesmaximal, characteristic, complemented
8C11×#1932C211yesmaximal, characteristic, complemented
9C11×#1914C211yesmaximal, characteristic, complemented
10C11×#1911C211yesmaximal, characteristic, complemented
11C11×#1903C211yesmaximal, characteristic, complemented
12C11×#1887C211yesmaximal, characteristic, complemented
13C11×#1861C211yesmaximal, characteristic, complemented
14C11×#1841C211yesmaximal, characteristic, complemented
15C11×#1829C211yesmaximal, characteristic, complemented
16C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
17C11×#568C2211yescharacteristic
18C11×#535C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C11×#518C2211yescharacteristic
21C11×#430C2211yescharacteristic
22C11×#430C2211yescharacteristic
23C11×#430C2211yescharacteristic
24C11×#423C2211yescharacteristic
25C11×#421C2211yescharacteristic
26C11×#421C2211yescharacteristic
27C2×C11×#104C2211yescharacteristic
28C11×#418C2211yescharacteristic
29C11×#418C2211yescharacteristic
30C11×#418C2211yescharacteristic
31C11×#413C2211yescharacteristic
32C2×C11×#100C2211yescharacteristic
33C2×C11×#100C2211yescharacteristic
34C2×C11×#100C2211yescharacteristic
35C2×C11×#100C2211yescharacteristic
36C2×C11×#100C2211yescharacteristic
37C2×C11×#100C2211yescharacteristic
38C4×C11×M16C2211yescharacteristic
39C11×#344C2211yescharacteristic
40C11×#344C2211yescharacteristic
41C11×#344C2211yescharacteristic
42C11×#344C2211yescharacteristic
43C11×#344C2211yescharacteristic
44C11×#344C2211yescharacteristic
45C11×#339C2211yescharacteristic
46C11×#339C2211yescharacteristic
47C11×#339C2211yescharacteristic
48C11×#338C2211yescharacteristic
49C11×H(3,ℤ/4)C2211yescharacteristic
50C11×H(3,ℤ/4)C2211yescharacteristic
51C2×C11×#41C2311yescharacteristic
52C22×D4×C11—22no—
53C22×D4×C11C2311yescharacteristic
54C22×D4×C11C2311yescharacteristic
55C11×AGL(1,ℤ/8)—41no—
56C11×AGL(1,ℤ/8)—41no—
57C2×C11×SD16—21no—
58C2×C11×D8—21no—
59C11×#131—41no—
60C11×#131—41no—
61C2×C11×M16—41no—
62C2×C11×M16C2311yescharacteristic
63C2×C11×M16C2311yescharacteristic
64C2×C11×M16C2311yescharacteristic
65C2×C11×M16C2311yescharacteristic
66C2×C11×M16C2311yescharacteristic
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C11×#127—21no—
71C11×#127—21no—
72C11×#127—21no—
73C11×#127—41no—
74C11×#124—21no—
75C11×#121—41no—
76C11×#120—22no—
77C4×D4×C11—41no—
78C4×D4×C11—41no—
79C11×#117C2311yescharacteristic
80C11×#117C2311yescharacteristic
81C11×#117C2311yescharacteristic
82C2×C11×C22⋊C4—22no—
83C2×C42×C11C2311yescharacteristic
84C11×#108—41no—
85C11×#108—41no—
86C11×#108—41no—
87C11×C4⋊C8—41no—
88C11×#104—21no—
89C11×#104—21no—
90C11×#104—41no—
91C11×#104—41no—
92C11×#102—41no—
93C11×#102—41no—
94C11×#102—41no—
95C11×#101—21no—
96C11×#100—21no—
97C11×#100—41no—
98C11×#100—41no—
99C11×#100—41no—
100C11×#100—41no—
101C11×#100—41no—
102C11×#100—41no—
103C11×#97—21no—
104C4×C8×C11—21no—
105#32698C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—21no—
107C24×C11#4112yes—
108C11×#41—21no—
109C11×#41—21no—
110C11×#41—21no—
111C11×#41—21no—
112C2×Q8×C11#4111yescharacteristic
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—84no—
130C2×D4×C11#4111yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—42no—
134C22×C4×C11C2411yescharacteristic
135C11×SD16—42no—
136C11×D8—42no—
137C11×M16—21no—
138C11×M16—21no—
139C11×M16—21no—
140C11×M16—21no—
141C11×M16—21no—
142C11×M16—21no—
143C11×M16—21no—
144C11×M16—21no—
145C11×M16—21no—
146C11×M16—21no—
147C11×M16—21no—
148C11×M16—21no—
149C11×M16—21no—
150C11×M16—21no—
151C11×M16—21no—
152C11×M16—21no—
153C11×M16—42no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—42no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C22⋊C4—21no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11#4111yescharacteristic
176C42×C11#4111yescharacteristic
177#2102C2×C1111yescharacteristic, complemented
178#2081C2×C1111yescharacteristic, complemented
179#2081C2×C1111yescharacteristic, complemented
180#2069C2×C1111yescharacteristic, complemented
181#2048C2×C1111yescharacteristic, complemented
182#2002C2×C1111yescharacteristic
183#1965C2×C1111yescharacteristic, complemented
184#1932C2×C1111yescharacteristic, complemented
185#1914C2×C1111yescharacteristic, complemented
186#1911C2×C1111yescharacteristic, complemented
187#1903C2×C1111yescharacteristic, complemented
188#1887C2×C1111yescharacteristic, complemented
189#1861C2×C1111yescharacteristic, complemented
190#1841C2×C1111yescharacteristic, complemented
191#1829C2×C1111yescharacteristic, complemented
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—21no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—82no—
200C23×C11—82no—
201C23×C11C2×#4111yescharacteristic
202Q8×C11—21no—
203Q8×C11—21no—
204D4×C11—21no—
205D4×C11—21no—
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—41no—
215D4×C11—41no—
216D4×C11—84no—
217D4×C11—84no—
218D4×C11—162no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—162no—
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11H(5,𝔽2)11yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C8×C11—41no—
236C8×C11—41no—
237C8×C11—41no—
238C8×C11—41no—
239C8×C11—41no—
240C8×C11—41no—
241C8×C11—41no—
242C8×C11—41no—
243C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
244#568C22×C1111yescharacteristic
245#535C22×C1111yescharacteristic
246C2×#127C22×C1111yescharacteristic
247#518C22×C1111yescharacteristic
248#430C22×C1111yescharacteristic
249#430C22×C1111yescharacteristic
250#430C22×C1111yescharacteristic
251#423C22×C1111yescharacteristic
252#421C22×C1111yescharacteristic
253#421C22×C1111yescharacteristic
254C2×#104C22×C1111yescharacteristic
255#418C22×C1111yescharacteristic
256#418C22×C1111yescharacteristic
257#418C22×C1111yescharacteristic
258#413C22×C1111yescharacteristic
259C2×#100C22×C1111yescharacteristic
260C2×#100C22×C1111yescharacteristic
261C2×#100C22×C1111yescharacteristic
262C2×#100C22×C1111yescharacteristic
263C2×#100C22×C1111yescharacteristic
264C2×#100C22×C1111yescharacteristic
265C4×M16C22×C1111yescharacteristic
266#344C22×C1111yescharacteristic
267#344C22×C1111yescharacteristic
268#344C22×C1111yescharacteristic
269#344C22×C1111yescharacteristic
270#344C22×C1111yescharacteristic
271#344C22×C1111yescharacteristic
272#339C22×C1111yescharacteristic
273#339C22×C1111yescharacteristic
274#339C22×C1111yescharacteristic
275#338C22×C1111yescharacteristic
276H(3,ℤ/4)C22×C1111yescharacteristic
277H(3,ℤ/4)C22×C1111yescharacteristic
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—42no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11—81no—
284C22×C11—82no—
285C22×C11—82no—
286C22×C11—81no—
287C22×C11—161no—
288C22×C11—161no—
289C22×C11#53811yescharacteristic
290C22×C11#55111yescharacteristic
291C22×C11#55111yescharacteristic
292C4×C11—22no—
293C4×C11—41no—
294C4×C11—41no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11—81no—
298C4×C11#53811yescharacteristic
299C4×C11#54011yescharacteristic
300C4×C11#55311yescharacteristic
301C4×C11#56011yescharacteristic
302C2×#41C23×C1111yescharacteristic
303C22×D4—22no—
304C22×D4C23×C1111yescharacteristic
305C22×D4C23×C1111yescharacteristic
306AGL(1,ℤ/8)—41no—
307AGL(1,ℤ/8)—41no—
308C2×SD16—21no—
309C2×D8—21no—
310#131—41no—
311#131—41no—
312C2×M16—41no—
313C2×M16C23×C1111yescharacteristic
314C2×M16C23×C1111yescharacteristic
315C2×M16C23×C1111yescharacteristic
316C2×M16C23×C1111yescharacteristic
317C2×M16C23×C1111yescharacteristic
318C2×M16C23×C1111yescharacteristic
319C2×M16C23×C1111yescharacteristic
320C2×M16C23×C1111yescharacteristic
321#127—21no—
322#127—21no—
323#127—21no—
324#127—41no—
325#124—21no—
326#121—41no—
327#120—22no—
328C4×D4—41no—
329C4×D4—41no—
330#117C23×C1111yescharacteristic
331#117C23×C1111yescharacteristic
332#117C23×C1111yescharacteristic
333C2×C22⋊C4—22no—
334C2×C42C23×C1111yescharacteristic
335#108—41no—
336#108—41no—
337#108—41no—
338C4⋊C8—41no—
339#104—21no—
340#104—21no—
341#104—41no—
342#104—41no—
343#102—41no—
344#102—41no—
345#102—41no—
346#101—21no—
347#100—21no—
348#100—41no—
349#100—41no—
350#100—41no—
351#100—41no—
352#100—41no—
353#100—41no—
354#97—21no—
355C4×C8—21no—
356C2×C11—21no—
357C2×C11—21no—
358C2×C11—21no—
359C2×C11—81no—
360C2×C11—82no—
361C2×C11—161no—
362C2×C11#274911yescharacteristic
363C24—21no—
364C24C11×#4112yes—
365#41—21no—
366#41—21no—
367#41—21no—
368#41—21no—
369C2×Q8C11×#4111yescharacteristic
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—84no—
387C2×D4C11×#4111yescharacteristic
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—42no—
391C22×C4C24×C1111yescharacteristic
392SD16—42no—
393D8—42no—
394M16—21no—
395M16—21no—
396M16—21no—
397M16—21no—
398M16—21no—
399M16—21no—
400M16—21no—
401M16—21no—
402M16—21no—
403M16—21no—
404M16—21no—
405M16—21no—
406M16—21no—
407M16—21no—
408M16—21no—
409M16—21no—
410M16—42no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—42no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—21no—
425C22⋊C4—21no—
426C22⋊C4—42no—
427C22⋊C4—42no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—21no—
432C42C11×#4111yescharacteristic
433C42C11×#4111yescharacteristic
434C11#3269811yescharacteristic, direct product factor, Sylow
435C23—22no—
436C23—22no—
437C23—21no—
438C23—22no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—82no—
443C23—82no—
444C23C2×C11×#4111yescharacteristic
445Q8—21no—
446Q8—21no—
447D4—21no—
448D4—21no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—41no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—41no—
459D4—84no—
460D4—84no—
461D4—162no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—162no—
472C2×C4C2×C11×#4111yescharacteristic
473C2×C4C2×C11×#4111yescharacteristic
474C2×C4C11×H(5,𝔽2)11yescharacteristic
475C2×C4C11×H(5,𝔽2)11yescharacteristic
476C2×C4C11×H(5,𝔽2)11yescharacteristic
477C2×C4C11×H(5,𝔽2)11yescharacteristic
478C8—41no—
479C8—41no—
480C8—41no—
481C8—41no—
482C8—41no—
483C8—41no—
484C8—41no—
485C8—41no—
486C22—41no—
487C22—41no—
488C22—42no—
489C22—82no—
490C22—82no—
491C22—81no—
492C22—82no—
493C22—82no—
494C22—81no—
495C22—161no—
496C22—161no—
497C22C11×#53811yescharacteristic
498C22C11×#55111yescharacteristic
499C22C11×#55111yescharacteristic
500C4—22no—
501C4—41no—
502C4—41no—
503C4—81no—
504C4—81no—
505C4—81no—
506C4C11×#53811yescharacteristic
507C4C11×#54011yescharacteristic
508C4C11×#55311yescharacteristic
509C4C11×#56011yescharacteristic
510C2—21no—
511C2—21no—
512C2—21no—
513C2—82no—
514C2—81no—
515C2—161no—
516C2C11×#274911yescharacteristic
subgroupG/H
center, socleC2×C11#2749
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2002C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2102C2semidirect
2. C11×#2081C2semidirect
3. C11×#2081C2semidirect
4. C11×#2069C2semidirect
5. C11×#2048C2semidirect
7. C11×#1965C2semidirect
8. C11×#1932C2semidirect
9. C11×#1914C2semidirect
10. C11×#1911C2semidirect
11. C11×#1903C2semidirect
12. C11×#1887C2semidirect
13. C11×#1861C2semidirect
14. C11×#1841C2semidirect
15. C11×#1829C2semidirect
105. #32698C11direct (N × H)
177. #2102C2×C11semidirect
178. #2081C2×C11semidirect
179. #2081C2×C11semidirect
180. #2069C2×C11semidirect
181. #2048C2×C11semidirect
183. #1965C2×C11semidirect
184. #1932C2×C11semidirect
185. #1914C2×C11semidirect
186. #1911C2×C11semidirect
187. #1903C2×C11semidirect
188. #1887C2×C11semidirect
189. #1861C2×C11semidirect
190. #1841C2×C11semidirect
191. #1829C2×C11semidirect
434. C11#32698direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#21022
C11×#20812
C11×#20692
C11×#20482
C11×#20022
C11×#19652
C11×#19322
C11×#19142
C11×#19112
C11×#19032
C11×#18872
C11×#18612
C11×#18412
C11×#18292
#3269811