Finite Group Databasebeta

← C11×#60726 #14637919

Subgroups — C11×#60726 #14637919

Order 2816.

1842 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3512C211yesmaximal, characteristic
2C11×#3509C211yesmaximal, characteristic, complemented
3C11×#3181C214yesmaximal, complemented
4C11×#3177C214yesmaximal, complemented
5C11×#3174C214yesmaximal, complemented
6C11×#3172C214yesmaximal, complemented
7C11×#3166C211yesmaximal, characteristic, complemented
8C11×#3152C211yesmaximal, characteristic, complemented
9C11×#3135C211yesmaximal, characteristic, complemented
10C2×C11×#491C211yesmaximal, characteristic, complemented
11C11×#3063C214yesmaximal, complemented
12C11×#2947C214yesmaximal, complemented
13C11×#2875C211yesmaximal, characteristic, complemented
14C2×C11×#137C2214yes—
15C2×C11×#131C2212yes—
16C11×#557—22no—
17C11×#556—22no—
18C11×#553—24no—
19C11×#553—22no—
20C11×#552—22no—
21C11×#552—24no—
22C11×#541C2214yes—
23C11×#541C2212yes—
24C11×#540C2212yes—
25C11×#537C2212yes—
26C11×#536C2212yes—
27C11×#533C2214yes—
28C11×#533C2211yescharacteristic
29C11×#532C2211yescharacteristic
30C2×C11×C4⋊Q8C2211yescharacteristic
31C11×#529C2214yes—
32C2×C11×#125C2211yescharacteristic
33C11×#520C2212yes—
34C11×#519C2212yes—
35C4×C11×#41C2211yescharacteristic
36C11×#501C2214yes—
37C11×#499C2214yes—
38C11×#497C2214yes—
39C11×#494C2212yes—
40C11×#492C2212yes—
41C11×#491C2212yes—
42C11×#491C2214yes—
43C11×#491C2212yes—
44C11×#491C2212yes—
45C11×#490C2212yes—
46C11×#489C2212yes—
47C11×#489C2212yes—
48C11×#470C2218yes—
49C11×#468C2218yes—
50C11×#467C2218yes—
51C11×#465C2218yes—
52C11×#441C2218yes—
53C11×#440C2218yes—
54C4×C11×Q16C2218yes—
55C4×C11×SD16C2218yes—
56C11×#428C2214yes—
57C11×#416C2214yes—
58C2×C11×#103C2214yes—
59C11×#405C2214yes—
60C11×#405C2212yes—
61C4×C11×M16C2211yescharacteristic
62C4×C11×M16C2212yes—
63C2×C11×#97C2212yes—
64C2×C11×#97C2211yescharacteristic
65C2×C11×#41C2312yes—
66C2×C11×#41C2311yescharacteristic
67C22×Q8×C11C2312yes—
68C11×#137—216no—
69C2×C11×Q16C2318yes—
70C2×C11×SD16C2318yes—
71C11×#131—28no—
72C2×C11×M16C2314yes—
73C2×C11×M16C2312yes—
74C22×C8×C11C2312yes—
75C22×C8×C11C2314yes—
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8C2312yes—
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2312yes—
81C11×C4⋊Q8C2312yes—
82C11×#127C2311yescharacteristic
83C11×#126—28no—
84C11×#126—24no—
85C11×#126—24no—
86C11×#125—24no—
87C11×#125—28no—
88C11×#125—22no—
89C11×#125—24no—
90C11×#125C2312yes—
91C11×#125C2312yes—
92C11×#125C2312yes—
93C11×#124—22no—
94C11×#124C2312yes—
95C11×#123—24no—
96C11×#123—24no—
97C11×#123—24no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8—24no—
101C11×C22⋊Q8C2314yes—
102C11×C22⋊Q8C2318yes—
103C11×#121—22no—
104C11×#121—24no—
105C11×#121—22no—
106C11×#121—24no—
107C11×#121C2314yes—
108C4×Q8×C11—24no—
109C4×Q8×C11—24no—
110C4×Q8×C11—22no—
111C4×Q8×C11D412yes—
112C4×Q8×C11C2318yes—
113C4×Q8×C11C2314yes—
114C4×D4×C11—24no—
115C4×D4×C11—24no—
116C4×D4×C11—22no—
117C4×D4×C11D414yes—
118C4×D4×C11D412yes—
119C4×D4×C11C2314yes—
120C11×#117—24no—
121C11×#117—22no—
122C11×#117—24no—
123C11×#117—24no—
124C11×#117C2312yes—
125C11×#117C2311yescharacteristic
126C11×#117C2312yes—
127C2×C11×C4⋊C4—22no—
128C2×C11×C4⋊C4—22no—
129C2×C11×C4⋊C4—22no—
130C2×C11×C4⋊C4C2312yes—
131C2×C42×C11C2311yescharacteristic
132C2×C42×C11C2312yes—
133C11×#107C2318yes—
134C11×#106C2318yes—
135C11×#103C2314yes—
136C11×#103C2314yes—
137C11×#103C2318yes—
138C11×#103C2318yes—
139C11×#102C2314yes—
140C11×#102C2314yes—
141C11×#97C2311yescharacteristic
142C11×#97C2311yescharacteristic
143C11×#97C2312yes—
144C11×#97C2312yes—
145C11×#97C2314yes—
146C4×C8×C11C2312yes—
147C4×C8×C11C2314yes—
148#60726C1111yesmaximal, characteristic, direct product factor, Sylow
149C11×#41—24no—
150C11×#41—28no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11—28no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×Q8×C11C2412yes—
156C2×Q8×C11C2414yes—
157C2×D4×C11—22no—
158C2×D4×C11—24no—
159C2×D4×C11—22no—
160C2×D4×C11C2×D412yes—
161C2×D4×C11C2×D411yescharacteristic
162C2×D4×C11C2412yes—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—24no—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C11×Q16—216no—
172C11×SD16—216no—
173C11×M16—28no—
174C11×M16#4118yes—
175C2×C8×C11—28no—
176C2×C8×C11—24no—
177C2×C8×C11C2412yes—
178C2×C8×C11C2412yes—
179C2×C8×C11C2414yes—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—28no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—28no—
192C11×C4⋊C4C2×D412yes—
193C11×C4⋊C4C2×D414yes—
194C11×C4⋊C4C2414yes—
195C11×C4⋊C4C2414yes—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—28no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4C2×D412yes—
204C11×C22⋊C4C2×D414yes—
205C42×C11—24no—
206C42×C11—28no—
207C42×C11—22no—
208C42×C11C2×D414yes—
209C42×C11C2×D412yes—
210C42×C11C2412yes—
211C42×C11C2411yescharacteristic
212C42×C11C2411yescharacteristic
213#3512C2×C1111yescharacteristic
214#3509C2×C1111yescharacteristic, complemented
215#3181C2×C1114yescomplemented
216#3177C2×C1114yescomplemented
217#3174C2×C1114yescomplemented
218#3172C2×C1114yescomplemented
219#3166C2×C1111yescharacteristic, complemented
220#3152C2×C1111yescharacteristic, complemented
221#3135C2×C1111yescharacteristic, complemented
222C2×#491C2×C1111yescharacteristic, complemented
223#3063C2×C1114yescomplemented
224#2947C2×C1114yescomplemented
225#2875C2×C1111yescharacteristic, complemented
226C23×C11—22no—
227C23×C11C22×D412yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—28no—
231Q8×C11—24no—
232Q8×C11—44no—
233Q8×C11—44no—
234D4×C11—24no—
235D4×C11—22no—
236D4×C11—24no—
237D4×C11—44no—
238D4×C11—82no—
239D4×C11—84no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—44no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11—84no—
250C2×C4×C11—82no—
251C2×C4×C11C22×D414yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4114yes—
257C2×C4×C11C2511yescharacteristic
258C8×C11—22no—
259C8×C11—22no—
260C8×C11C2×#4118yes—
261C2×#137C22×C1114yes—
262C2×#131C22×C1112yes—
263#557—22no—
264#556—22no—
265#553—24no—
266#553—22no—
267#552—22no—
268#552—24no—
269#541C22×C1114yes—
270#541C22×C1112yes—
271#540C22×C1112yes—
272#537C22×C1112yes—
273#536C22×C1112yes—
274#533C22×C1114yes—
275#533C22×C1111yescharacteristic
276#532C22×C1111yescharacteristic
277C2×C4⋊Q8C22×C1111yescharacteristic
278#529C22×C1114yes—
279C2×#125C22×C1111yescharacteristic
280#520C22×C1112yes—
281#519C22×C1112yes—
282C4×#41C22×C1111yescharacteristic
283#501C22×C1114yes—
284#499C22×C1114yes—
285#497C22×C1114yes—
286#494C22×C1112yes—
287#492C22×C1112yes—
288#491C22×C1112yes—
289#491C22×C1114yes—
290#491C22×C1112yes—
291#491C22×C1112yes—
292#490C22×C1112yes—
293#489C22×C1112yes—
294#489C22×C1112yes—
295#470C22×C1118yes—
296#468C22×C1118yes—
297#467C22×C1118yes—
298#465C22×C1118yes—
299#441C22×C1118yes—
300#440C22×C1118yes—
301C4×Q16C22×C1118yes—
302C4×SD16C22×C1118yes—
303#428C22×C1114yes—
304#416C22×C1114yes—
305C2×#103C22×C1114yes—
306#405C22×C1114yes—
307#405C22×C1112yes—
308C4×M16C22×C1111yescharacteristic
309C4×M16C22×C1112yes—
310C2×#97C22×C1111yescharacteristic
311C2×#97C22×C1112yes—
312C22×C11—22no—
313C22×C11—24no—
314C22×C11—22no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11#53212yes—
319C22×C11C23×D411yescharacteristic
320C4×C11—22no—
321C4×C11—24no—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—44no—
325C4×C11—44no—
326C4×C11—42no—
327C4×C11—44no—
328C4×C11#53212yes—
329C4×C11C22×#4112yes—
330C2×#41C23×C1112yes—
331C2×#41C23×C1111yescharacteristic
332C22×Q8C23×C1112yes—
333#137—216no—
334C2×Q16C23×C1118yes—
335C2×SD16C23×C1118yes—
336#131—28no—
337C2×M16C23×C1114yes—
338C2×M16C23×C1112yes—
339C22×C8C23×C1112yes—
340C22×C8C23×C1114yes—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C4⋊Q8C23×C1112yes—
344C4⋊Q8C23×C1112yes—
345C4⋊Q8C23×C1111yescharacteristic
346C4⋊Q8C23×C1112yes—
347#127C23×C1111yescharacteristic
348#126—28no—
349#126—24no—
350#126—24no—
351#125—24no—
352#125—28no—
353#125—22no—
354#125—24no—
355#125C23×C1112yes—
356#125C23×C1112yes—
357#125C23×C1112yes—
358#124—22no—
359#124C23×C1112yes—
360#123—24no—
361#123—24no—
362#123—24no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—24no—
366C22⋊Q8C23×C1114yes—
367C22⋊Q8C23×C1118yes—
368#121—22no—
369#121—24no—
370#121—22no—
371#121—24no—
372#121C23×C1114yes—
373C4×Q8—24no—
374C4×Q8—24no—
375C4×Q8—22no—
376C4×Q8D4×C1112yes—
377C4×Q8C23×C1118yes—
378C4×Q8C23×C1114yes—
379C4×D4—24no—
380C4×D4—24no—
381C4×D4—22no—
382C4×D4D4×C1114yes—
383C4×D4D4×C1112yes—
384C4×D4C23×C1114yes—
385#117—24no—
386#117—22no—
387#117—24no—
388#117—24no—
389#117C23×C1112yes—
390#117C23×C1111yescharacteristic
391#117C23×C1112yes—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4C23×C1112yes—
396C2×C42C23×C1111yescharacteristic
397C2×C42C23×C1112yes—
398#107C23×C1118yes—
399#106C23×C1118yes—
400#103C23×C1118yes—
401#103C23×C1118yes—
402#103C23×C1114yes—
403#103C23×C1114yes—
404#102C23×C1114yes—
405#102C23×C1114yes—
406#97C23×C1111yescharacteristic
407#97C23×C1111yescharacteristic
408#97C23×C1112yes—
409#97C23×C1114yes—
410#97C23×C1112yes—
411C4×C8C23×C1114yes—
412C4×C8C23×C1112yes—
413C2×C11—22no—
414C2×C11—42no—
415C2×C11—82no—
416C2×C11C2×#53211yescharacteristic
417C2×C11#358612yes—
418#41—24no—
419#41—28no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—28no—
423C2×Q8C2×D4×C1111yescharacteristic
424C2×Q8C24×C1112yes—
425C2×Q8C24×C1114yes—
426C2×D4—22no—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4C2×D4×C1112yes—
430C2×D4C2×D4×C1111yescharacteristic
431C2×D4C24×C1112yes—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4C2×D4×C1112yes—
437C22×C4C2×D4×C1114yes—
438C22×C4C24×C1112yes—
439C22×C4C24×C1111yescharacteristic
440Q16—216no—
441SD16—216no—
442M16—28no—
443M16C11×#4118yes—
444C2×C8—24no—
445C2×C8—28no—
446C2×C8C24×C1112yes—
447C2×C8C24×C1112yes—
448C2×C8C24×C1114yes—
449C4⋊C4—22no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—28no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—24no—
460C4⋊C4—28no—
461C4⋊C4C2×D4×C1112yes—
462C4⋊C4C2×D4×C1114yes—
463C4⋊C4C24×C1114yes—
464C4⋊C4C24×C1114yes—
465C22⋊C4—22no—
466C22⋊C4—28no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—22no—
472C22⋊C4C2×D4×C1112yes—
473C22⋊C4C2×D4×C1114yes—
474C42—24no—
475C42—28no—
476C42—22no—
477C42C2×D4×C1114yes—
478C42C2×D4×C1112yes—
479C42C24×C1112yes—
480C42C24×C1111yescharacteristic
481C42C24×C1111yescharacteristic
482C11#6072611yescharacteristic, direct product factor, Sylow
483C23—22no—
484C23C22×D4×C1112yes—
485C23C22×D4×C1111yescharacteristic
486Q8—22no—
487Q8—28no—
488Q8—24no—
489Q8—44no—
490Q8—44no—
491D4—24no—
492D4—22no—
493D4—24no—
494D4—44no—
495D4—82no—
496D4—84no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—84no—
507C2×C4—82no—
508C2×C4C22×D4×C1114yes—
509C2×C4C22×D4×C1112yes—
510C2×C4C22×D4×C1112yes—
511C2×C4C22×D4×C1112yes—
512C2×C4C22×D4×C1111yescharacteristic
513C2×C4C2×C11×#4114yes—
514C2×C4C25×C1111yescharacteristic
515C8—22no—
516C8—22no—
517C8C2×C11×#4118yes—
518C22—22no—
519C22—22no—
520C22—24no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22C11×#53212yes—
525C22C23×D4×C1111yescharacteristic
526C4—22no—
527C4—22no—
528C4—24no—
529C4—22no—
530C4—42no—
531C4—44no—
532C4—44no—
533C4—44no—
534C4C11×#53212yes—
535C4C22×C11×#4112yes—
536C2—22no—
537C2—42no—
538C2—82no—
539C2C2×C11×#53211yescharacteristic
540C2C11×#358612yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3512C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3509C2semidirect
3. C11×#3181C2semidirect
4. C11×#3177C2semidirect
5. C11×#3174C2semidirect
6. C11×#3172C2semidirect
7. C11×#3166C2semidirect
8. C11×#3152C2semidirect
9. C11×#3135C2semidirect
10. C2×C11×#491C2semidirect
11. C11×#3063C2semidirect
12. C11×#2947C2semidirect
13. C11×#2875C2semidirect
148. #60726C11direct (N × H)
214. #3509C2×C11semidirect
215. #3181C2×C11semidirect
216. #3177C2×C11semidirect
217. #3174C2×C11semidirect
218. #3172C2×C11semidirect
219. #3166C2×C11semidirect
220. #3152C2×C11semidirect
221. #3135C2×C11semidirect
222. C2×#491C2×C11semidirect
223. #3063C2×C11semidirect
224. #2947C2×C11semidirect
225. #2875C2×C11semidirect
482. C11#60726direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35122
C11×#35092
C11×#31812
C11×#31772
C11×#31742
C11×#31722
C11×#31662
C11×#31522
C11×#31352
C2×C11×#4912
C11×#30632
C11×#29472
C11×#28752
#6072611