Finite Group Databasebeta

← C11×#61081 #14638274

Subgroups — C11×#61081 #14638274

Order 2816.

2658 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#578C212yesmaximal, complemented
2C11×#3497C212yesmaximal, complemented
3C11×#3271C218yesmaximal, complemented
4C11×#3270C218yesmaximal, complemented
5C11×#3150C211yesmaximal, characteristic, complemented
6C11×#3060C212yesmaximal, complemented
7C11×#3037C212yesmaximal, complemented
8C11×#3013C214yesmaximal, complemented
9C2×C11×#441C211yesmaximal, characteristic, complemented
10C11×#2932C211yesmaximal, characteristic, complemented
11C2×C11×2−1+4C2214yes—
12C11×#578—216no—
13C2×C11×#137C2214yes—
14C2×C11×#137C2218yes—
15C2×C11×#135C2212yes—
16C2×C11×#135C2214yes—
17C2×C11×#135C2212yes—
18C22×C11×Q16C2214yes—
19C22×C11×Q16C2211yescharacteristic
20C2×C11×#131C2212yes—
21C11×#550—22no—
22C11×#550C2214yes—
23D4×Q8×C11—22no—
24D4×Q8×C11C2214yes—
25C11×#548—24no—
26C11×#548C2218yes—
27C11×#537—24no—
28C11×#537C2214yes—
29C11×#532—24no—
30C11×#532C2212yes—
31C11×#532C2211yescharacteristic
32C2×C4×Q8×C11C2212yes—
33C11×#497C2214yes—
34C11×#496C2214yes—
35C11×#470C2214yes—
36C11×#469C2214yes—
37C11×#465C2218yes—
38C11×#464C2218yes—
39C11×#462C2214yes—
40C11×#460C2214yes—
41C11×#452C2218yes—
42C11×#451C2218yes—
43C11×#449C2218yes—
44C11×#448C2218yes—
45C11×#441C2218yes—
46C11×#435C2218yes—
47C2×C11×#106C2211yescharacteristic
48C11×#423C2211yescharacteristic
49C11×#417C2214yes—
50C2×C11×#103C2212yes—
51C11×#408C2212yes—
52C2×C11×#97C2211yescharacteristic
53C11×2−1+4—216no—
54C11×2−1+4—48no—
55C2×C11×#41—28no—
56C2×C11×#41—24no—
57C2×C11×#41C2314yes—
58C2×C11×#41C2318yes—
59C2×C11×#41C2312yes—
60C22×Q8×C11—24no—
61C22×Q8×C11C2318yes—
62C22×Q8×C11C2312yes—
63C11×#137—216no—
64C11×#137—232no—
65C11×#135—216no—
66C11×#135—28no—
67C11×#135—44no—
68C2×C11×Q16—216no—
69C2×C11×Q16D418yescomplemented
70C2×C11×Q16C2312yes—
71C2×C11×Q16C2318yes—
72C2×C11×Q16C2312yes—
73C2×C11×Q16C2314yes—
74C2×C11×SD16C2314yes—
75C2×C11×SD16C2318yes—
76C2×C11×SD16C2314yes—
77C2×C11×D8C2312yes—
78C2×C11×D8C2312yes—
79C11×#131—28no—
80C2×C11×M16C2312yes—
81C2×C11×M16C2314yes—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2314yes—
84C22×C8×C11C2311yescharacteristic
85C11×C4⋊Q8—24no—
86C11×C4⋊Q8D411yescharacteristic
87C11×C4⋊Q8C2312yes—
88C11×#127—24no—
89C11×#127D411yescharacteristic
90C11×#127C2312yes—
91C11×#124—28no—
92C11×#124D412yes—
93C11×#124C2314yes—
94C11×C22⋊Q8—24no—
95C11×C22⋊Q8—28no—
96C11×C22⋊Q8—28no—
97C11×C22⋊Q8C2318yes—
98C11×#121—28no—
99C11×#121—28no—
100C11×#121—24no—
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—28no—
104C11×#121D414yes—
105C11×#121C2318yes—
106C4×Q8×C11—22no—
107C4×Q8×C11—22no—
108C4×Q8×C11C2314yes—
109C4×Q8×C11C2314yes—
110C4×D4×C11—24no—
111C4×D4×C11—24no—
112C4×D4×C11—28no—
113C4×D4×C11—22no—
114C4×D4×C11—22no—
115C4×D4×C11C2314yes—
116C2×C11×C4⋊C4—22no—
117C2×C11×C4⋊C4C2312yes—
118C2×C42×C11—22no—
119C2×C42×C11C2311yescharacteristic
120C11×#106C2314yes—
121C11×C4⋊C8C2314yes—
122C11×#103C2318yes—
123C11×#103C2318yes—
124C11×#102C2318yes—
125C11×C22⋊C8C2318yes—
126C11×#97C2314yes—
127#61081C1111yesmaximal, characteristic, direct product factor, Sylow
128C11×#41—24no—
129C11×#41—24no—
130C11×#41—216no—
131C11×#41—28no—
132C11×#41—28no—
133C11×#41—48no—
134C11×#41—432no—
135C11×#41—416no—
136C2×Q8×C11—22no—
137C2×Q8×C11—28no—
138C2×Q8×C11—24no—
139C2×Q8×C11—216no—
140C2×Q8×C11—48no—
141C2×Q8×C11—416no—
142C2×Q8×C11C2×D418yes—
143C2×Q8×C11C2×D412yes—
144C2×Q8×C11C2414yes—
145C2×Q8×C11C2414yes—
146C2×D4×C11—24no—
147C2×D4×C11—28no—
148C2×D4×C11—28no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11C2×D414yes—
152C2×D4×C11C2×D412yes—
153C2×D4×C11C2×D414yes—
154C2×D4×C11C2414yes—
155C22×C4×C11—22no—
156C22×C4×C11—28no—
157C22×C4×C11—22no—
158C22×C4×C11—28no—
159C22×C4×C11—24no—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2414yes—
162C22×C4×C11C2411yescharacteristic
163C11×Q16—24no—
164C11×Q16—216no—
165C11×Q16—42no—
166C11×Q16C2×D4116yes—
167C11×SD16—28no—
168C11×SD16—216no—
169C11×SD16—44no—
170C11×D8—24no—
171C11×D8—42no—
172C11×M16—28no—
173C11×M16—24no—
174C2×C8×C11—28no—
175C2×C8×C11—22no—
176C2×C8×C11C2×D414yes—
177C2×C8×C11C2412yes—
178C2×C8×C11C2414yes—
179C2×C8×C11C2412yes—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—28no—
186C11×C4⋊C4C2×D414yes—
187C11×C4⋊C4C2414yes—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—28no—
192C11×C22⋊C4C2×D418yes—
193C42×C11—24no—
194C42×C11—24no—
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11C2412yes—
198C2×#578C2×C1112yescomplemented
199#3497C2×C1112yescomplemented
200#3271C2×C1118yescomplemented
201#3270C2×C1118yescomplemented
202#3150C2×C1111yescharacteristic, complemented
203#3060C2×C1112yescomplemented
204#3037C2×C1112yescomplemented
205#3013C2×C1114yescomplemented
206C2×#441C2×C1111yescharacteristic, complemented
207#2932C2×C1111yescharacteristic, complemented
208C23×C11—24no—
209C23×C11C22×D414yes—
210C23×C11C22×D411yescharacteristic
211Q8×C11—28no—
212Q8×C11—24no—
213Q8×C11—24no—
214Q8×C11—24no—
215Q8×C11—24no—
216Q8×C11—416no—
217Q8×C11C22×D418yes—
218D4×C11—28no—
219D4×C11—24no—
220D4×C11—24no—
221D4×C11—24no—
222D4×C11—44no—
223D4×C11—416no—
224D4×C11—44no—
225D4×C11—48no—
226D4×C11—82no—
227D4×C11—88no—
228C2×C4×C11—28no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—42no—
235C2×C4×C11—416no—
236C2×C4×C11—416no—
237C2×C4×C11—48no—
238C2×C4×C11—82no—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D414yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D412yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C2×C4×C11C2511yescharacteristic
246C8×C11—24no—
247C8×C11—22no—
248C8×C11C22×D414yes—
249C2×2−1+4C22×C1114yes—
250#578—216no—
251C2×#137C22×C1114yes—
252C2×#137C22×C1118yes—
253C2×#135C22×C1112yes—
254C2×#135C22×C1114yes—
255C2×#135C22×C1112yes—
256C22×Q16C22×C1114yes—
257C22×Q16C22×C1111yescharacteristic
258C2×#131C22×C1112yes—
259#550—22no—
260#550C22×C1114yes—
261D4×Q8—22no—
262D4×Q8C22×C1114yes—
263#548—24no—
264#548C22×C1118yes—
265#537—24no—
266#537C22×C1114yes—
267#532—24no—
268#532C22×C1112yes—
269#532C22×C1111yescharacteristic
270C2×C4×Q8C22×C1112yes—
271#497C22×C1114yes—
272#496C22×C1114yes—
273#470C22×C1114yes—
274#469C22×C1114yes—
275#465C22×C1118yes—
276#464C22×C1118yes—
277#462C22×C1114yes—
278#460C22×C1114yes—
279#452C22×C1118yes—
280#451C22×C1118yes—
281#449C22×C1118yes—
282#448C22×C1118yes—
283#441C22×C1118yes—
284#435C22×C1118yes—
285C2×#106C22×C1111yescharacteristic
286#423C22×C1111yescharacteristic
287#417C22×C1114yes—
288C2×#103C22×C1112yes—
289#408C22×C1112yes—
290C2×#97C22×C1111yescharacteristic
291C22×C11—22no—
292C22×C11—28no—
293C22×C11—24no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11D4212yes—
298C22×C11C23×D411yescharacteristic
299C4×C11—22no—
300C4×C11—22no—
301C4×C11—28no—
302C4×C11—24no—
303C4×C11—44no—
304C4×C11—44no—
305C4×C11D4212yes—
306C4×C11C23×D411yescharacteristic
307C4×C11C2×H(5,𝔽2)11yescharacteristic
3082−1+4—216no—
3092−1+4—48no—
310C2×#41—28no—
311C2×#41—24no—
312C2×#41C23×C1114yes—
313C2×#41C23×C1118yes—
314C2×#41C23×C1112yes—
315C22×Q8—24no—
316C22×Q8C23×C1118yes—
317C22×Q8C23×C1112yes—
318#137—216no—
319#137—232no—
320#135—216no—
321#135—28no—
322#135—44no—
323C2×Q16—216no—
324C2×Q16D4×C1118yescomplemented
325C2×Q16C23×C1112yes—
326C2×Q16C23×C1118yes—
327C2×Q16C23×C1112yes—
328C2×Q16C23×C1114yes—
329C2×SD16C23×C1118yes—
330C2×SD16C23×C1114yes—
331C2×SD16C23×C1114yes—
332C2×D8C23×C1112yes—
333C2×D8C23×C1112yes—
334#131—28no—
335C2×M16C23×C1112yes—
336C2×M16C23×C1114yes—
337C22×C8C23×C1114yes—
338C22×C8C23×C1111yescharacteristic
339C22×C8C23×C1111yescharacteristic
340C4⋊Q8—24no—
341C4⋊Q8D4×C1111yescharacteristic
342C4⋊Q8C23×C1112yes—
343#127—24no—
344#127D4×C1111yescharacteristic
345#127C23×C1112yes—
346#124—28no—
347#124D4×C1112yes—
348#124C23×C1114yes—
349C22⋊Q8—24no—
350C22⋊Q8—28no—
351C22⋊Q8—28no—
352C22⋊Q8C23×C1118yes—
353#121—28no—
354#121—28no—
355#121—24no—
356#121—22no—
357#121—22no—
358#121—28no—
359#121D4×C1114yes—
360#121C23×C1118yes—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8C23×C1114yes—
364C4×Q8C23×C1114yes—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—28no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4C23×C1114yes—
371C2×C4⋊C4—22no—
372C2×C4⋊C4C23×C1112yes—
373C2×C42—22no—
374C2×C42C23×C1111yescharacteristic
375#106C23×C1114yes—
376C4⋊C8C23×C1114yes—
377#103C23×C1118yes—
378#103C23×C1118yes—
379#102C23×C1118yes—
380C22⋊C8C23×C1118yes—
381#97C23×C1114yes—
382C2×C11—22no—
383C2×C11—44no—
384C2×C11—84no—
385C2×C11C2×D4211yescharacteristic
386C2×C11#358612yes—
387#41—24no—
388#41—24no—
389#41—216no—
390#41—28no—
391#41—28no—
392#41—48no—
393#41—432no—
394#41—416no—
395C2×Q8—22no—
396C2×Q8—28no—
397C2×Q8—24no—
398C2×Q8—216no—
399C2×Q8—48no—
400C2×Q8—416no—
401C2×Q8C2×D4×C1118yes—
402C2×Q8C2×D4×C1112yes—
403C2×Q8C24×C1114yes—
404C2×Q8C24×C1114yes—
405C2×D4—24no—
406C2×D4—28no—
407C2×D4—28no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4C2×D4×C1114yes—
411C2×D4C2×D4×C1112yes—
412C2×D4C2×D4×C1114yes—
413C2×D4C24×C1114yes—
414C22×C4—22no—
415C22×C4—28no—
416C22×C4—22no—
417C22×C4—28no—
418C22×C4—24no—
419C22×C4C2×D4×C1112yes—
420C22×C4C24×C1114yes—
421C22×C4C24×C1111yescharacteristic
422Q16—216no—
423Q16—24no—
424Q16—42no—
425Q16C2×D4×C11116yes—
426SD16—216no—
427SD16—28no—
428SD16—44no—
429D8—24no—
430D8—42no—
431M16—24no—
432M16—28no—
433C2×C8—22no—
434C2×C8—28no—
435C2×C8C2×D4×C1114yes—
436C2×C8C24×C1112yes—
437C2×C8C24×C1114yes—
438C2×C8C24×C1112yes—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—28no—
445C4⋊C4C2×D4×C1114yes—
446C4⋊C4C24×C1114yes—
447C22⋊C4—28no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—28no—
451C22⋊C4C2×D4×C1118yes—
452C42—24no—
453C42—24no—
454C42C2×D4×C1111yescharacteristic
455C42C2×D4×C1111yescharacteristic
456C42C24×C1112yes—
457C11#6108111yescharacteristic, direct product factor, Sylow
458C23—24no—
459C23C22×D4×C1114yes—
460C23C22×D4×C1111yescharacteristic
461Q8—28no—
462Q8—24no—
463Q8—24no—
464Q8—24no—
465Q8—24no—
466Q8—416no—
467Q8C22×D4×C1118yes—
468D4—28no—
469D4—24no—
470D4—24no—
471D4—24no—
472D4—44no—
473D4—416no—
474D4—44no—
475D4—48no—
476D4—82no—
477D4—88no—
478C2×C4—28no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—42no—
485C2×C4—416no—
486C2×C4—416no—
487C2×C4—48no—
488C2×C4—82no—
489C2×C4C22×D4×C1112yes—
490C2×C4C22×D4×C1112yes—
491C2×C4C22×D4×C1114yes—
492C2×C4C22×D4×C1111yescharacteristic
493C2×C4C22×D4×C1112yes—
494C2×C4C11×H(5,𝔽2)12yes—
495C2×C4C25×C1111yescharacteristic
496C8—24no—
497C8—22no—
498C8C22×D4×C1114yes—
499C22—22no—
500C22—24no—
501C22—28no—
502C22—44no—
503C22—44no—
504C22—44no—
505C22D42×C1112yes—
506C22C23×D4×C1111yescharacteristic
507C4—28no—
508C4—24no—
509C4—22no—
510C4—22no—
511C4—44no—
512C4—44no—
513C4D42×C1112yes—
514C4C23×D4×C1111yescharacteristic
515C4C2×C11×H(5,𝔽2)11yescharacteristic
516C2—22no—
517C2—44no—
518C2—84no—
519C2C2×D42×C1111yescharacteristic
520C2C11×#358612yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#532 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#578C2semidirect
2. C11×#3497C2semidirect
3. C11×#3271C2semidirect
4. C11×#3270C2semidirect
5. C11×#3150C2semidirect
6. C11×#3060C2semidirect
7. C11×#3037C2semidirect
8. C11×#3013C2semidirect
9. C2×C11×#441C2semidirect
10. C11×#2932C2semidirect
69. C2×C11×Q16D4semidirect
127. #61081C11direct (N × H)
198. C2×#578C2×C11semidirect
199. #3497C2×C11semidirect
200. #3271C2×C11semidirect
201. #3270C2×C11semidirect
202. #3150C2×C11semidirect
203. #3060C2×C11semidirect
204. #3037C2×C11semidirect
205. #3013C2×C11semidirect
206. C2×#441C2×C11semidirect
207. #2932C2×C11semidirect
324. C2×Q16D4×C11semidirect
457. C11#61081direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5782
C11×#34972
C11×#32712
C11×#32702
C11×#31502
C11×#30602
C11×#30372
C11×#30132
C2×C11×#4412
C11×#29322
#6108111