Finite Group Databasebeta

← C11×#33764 #14610957

Subgroups — C11×#33764 #14610957

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3061C211yesmaximal, characteristic, complemented
2C11×#3058C211yesmaximal, characteristic, complemented
3C11×#2237C211yesmaximal, characteristic, complemented
4C11×#2234C211yesmaximal, characteristic, complemented
5C11×#2233C211yesmaximal, characteristic, complemented
6C11×#2232C211yesmaximal, characteristic, complemented
7C11×#2220C211yesmaximal, characteristic, complemented
8C11×#2218C211yesmaximal, characteristic, complemented
9C11×#2217C211yesmaximal, characteristic, complemented
10C11×#2215C211yesmaximal, characteristic, complemented
11C11×#2187C211yesmaximal, characteristic, complemented
12C11×#2186C211yesmaximal, characteristic, complemented
13C11×#2186C211yesmaximal, characteristic, complemented
14C11×#2184C211yesmaximal, characteristic, complemented
15C11×#2113C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic, complemented
17C22×C11×D8C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C11×#537—21no—
20C11×#535—21no—
21C2×C11×SD32C2211yescharacteristic
22C2×C11×SD32C2211yescharacteristic
23C2×C11×D16C2211yescharacteristic
24C2×C11×D16C2211yescharacteristic
25C2×C11×M32C2211yescharacteristic, complemented
26C22×C11×C16C2211yescharacteristic, complemented
27C11×#469—21no—
28C11×#469—21no—
29C11×#468—21no—
30C11×#468—21no—
31C11×#467C2211yescharacteristic
32C11×#467C2211yescharacteristic, complemented
33C11×#466C2211yescharacteristic
34C11×#466C2211yescharacteristic
35C11×#466C2211yescharacteristic
36C11×#466C2211yescharacteristic
37C11×#466C2211yescharacteristic
38C11×#466C2211yescharacteristic, complemented
39C11×#427C2211yescharacteristic
40C2×C11×#107C2211yescharacteristic, complemented
41C11×#418—21no—
42C11×#417—21no—
43C11×#367C2211yescharacteristic, complemented
44C11×#367C2211yescharacteristic, complemented
45C11×#366C2211yescharacteristic, complemented
46C11×#366C2211yescharacteristic, complemented
47C11×#358C2211yescharacteristic, complemented
48C11×#358C2211yescharacteristic, complemented
49C11×#357C2211yescharacteristic
50C11×#357C2211yescharacteristic
51C11×#357C2211yescharacteristic
52C11×#357C2211yescharacteristic
53C11×#357C2211yescharacteristic, complemented
54C11×#357C2211yescharacteristic, complemented
55C11×C22⋊C16C2211yescharacteristic
56C11×C22⋊C16C2211yescharacteristic
57C11×C22⋊C16C2211yescharacteristic, complemented
58C11×C22⋊C16C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C2×C11×#41D411yescharacteristic
61C22×D4×C11—21no—
62C11×#135—41no—
63C11×#135—41no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×SD16—21no—
66C2×C11×D8—21no—
67C2×C11×D8—41no—
68C2×C11×D8—41no—
69C2×C11×D8C2311yescharacteristic
70C2×C11×D8C2311yescharacteristic
71C2×C11×D8C2311yescharacteristic
72C11×#131—41no—
73C11×#131—41no—
74C2×C11×M16D411yescharacteristic
75C2×C11×M16D411yescharacteristic
76C2×C11×M16D411yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×#127—41no—
81C11×#124—41no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—41no—
85C11×#121—21no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—41no—
92C11×#121—41no—
93C11×#121—41no—
94C11×#120—41no—
95C11×#120—41no—
96C11×#117—21no—
97C2×C11×C4⋊C4—21no—
98C11×SD32—41no—
99C11×SD32—41no—
100C11×D16—41no—
101C11×D16—41no—
102C11×M32—41no—
103C2×C11×C16—41no—
104C2×C11×C16C2311yescharacteristic
105C2×C11×C16C2311yescharacteristic
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107—21no—
109C11×#107C2311yescharacteristic
110C11×#107C2311yescharacteristic
111C11×#107C2311yescharacteristic
112C11×#107C2311yescharacteristic
113C11×#106—21no—
114C11×#103—21no—
115C11×#103—21no—
116C11×#102—21no—
117C11×#102—21no—
118C11×#102—21no—
119C11×#102—21no—
120C11×#102—21no—
121C11×#102—21no—
122#33764C1111yesmaximal, characteristic, direct product factor, Sylow
123C24×C11—41no—
124C11×#41—41no—
125C11×#41—41no—
126C11×#41—42no—
127C11×#41—42no—
128C2×Q8×C11—21no—
129C2×Q8×C11D811yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11D811yescharacteristic
144C2×D4×C11D811yescharacteristic
145C2×D4×C11D811yescharacteristic
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C11×Q16—21no—
152C11×Q16—21no—
153C11×SD16—42no—
154C11×D8—21no—
155C11×D8—21no—
156C11×D8—21no—
157C11×D8—21no—
158C11×D8—21no—
159C11×D8—21no—
160C11×D8—42no—
161C11×M16—41no—
162C11×M16—41no—
163C11×M16—41no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C42×C11—41no—
191C11×C16—21no—
192C11×C16—21no—
193C11×C16—21no—
194C11×C16—21no—
195#3061C2×C1111yescharacteristic, complemented
196#3058C2×C1111yescharacteristic, complemented
197#2237C2×C1111yescharacteristic, complemented
198#2234C2×C1111yescharacteristic, complemented
199#2233C2×C1111yescharacteristic, complemented
200#2232C2×C1111yescharacteristic, complemented
201#2220C2×C1111yescharacteristic, complemented
202#2218C2×C1111yescharacteristic, complemented
203#2217C2×C1111yescharacteristic, complemented
204#2215C2×C1111yescharacteristic, complemented
205#2187C2×C1111yescharacteristic, complemented
206#2186C2×C1111yescharacteristic, complemented
207#2186C2×C1111yescharacteristic, complemented
208#2184C2×C1111yescharacteristic, complemented
209#2113C2×C1111yescharacteristic, complemented
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—82no—
214C23×C11—161no—
215C23×C11—161no—
216C23×C11C2×D811yescharacteristic
217C23×C11C2×D811yescharacteristic
218C23×C11C2×D811yescharacteristic
219Q8×C11—41no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—41no—
229D4×C11—41no—
230D4×C11—41no—
231D4×C11—82no—
232D4×C11—82no—
233D4×C11—161no—
234D4×C11—161no—
235D4×C11—161no—
236D4×C11—161no—
237D4×C11—161no—
238D4×C11—161no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—82no—
251C2×C4×C11—161no—
252C2×C4×C11C2×D811yescharacteristic
253C2×C4×C11C2×D811yescharacteristic
254C2×C4×C11C2×D811yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11H(5,𝔽2)11yescharacteristic
260C8×C11H(5,𝔽2)11yescharacteristic
261C2×#135C22×C1111yescharacteristic, complemented
262C22×D8C22×C1111yescharacteristic
263C2×#131C22×C1111yescharacteristic
264#537—21no—
265#535—21no—
266C2×SD32C22×C1111yescharacteristic
267C2×SD32C22×C1111yescharacteristic
268C2×D16C22×C1111yescharacteristic
269C2×D16C22×C1111yescharacteristic
270C2×M32C22×C1111yescharacteristic, complemented
271C22×C16C22×C1111yescharacteristic, complemented
272#469—21no—
273#469—21no—
274#468—21no—
275#468—21no—
276#467C22×C1111yescharacteristic
277#467C22×C1111yescharacteristic, complemented
278#466C22×C1111yescharacteristic
279#466C22×C1111yescharacteristic
280#466C22×C1111yescharacteristic
281#466C22×C1111yescharacteristic
282#466C22×C1111yescharacteristic
283#466C22×C1111yescharacteristic, complemented
284#427C22×C1111yescharacteristic
285C2×#107C22×C1111yescharacteristic, complemented
286#418—21no—
287#417—21no—
288#367C22×C1111yescharacteristic, complemented
289#367C22×C1111yescharacteristic, complemented
290#366C22×C1111yescharacteristic, complemented
291#366C22×C1111yescharacteristic, complemented
292#358C22×C1111yescharacteristic, complemented
293#358C22×C1111yescharacteristic, complemented
294#357C22×C1111yescharacteristic
295#357C22×C1111yescharacteristic
296#357C22×C1111yescharacteristic
297#357C22×C1111yescharacteristic
298#357C22×C1111yescharacteristic, complemented
299#357C22×C1111yescharacteristic, complemented
300C22⋊C16C22×C1111yescharacteristic
301C22⋊C16C22×C1111yescharacteristic
302C22⋊C16C22×C1111yescharacteristic, complemented
303C22⋊C16C22×C1111yescharacteristic, complemented
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—164no—
323C22×C11C22×D811yescharacteristic
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—81no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11#53411yescharacteristic
333C4×C11#57511yescharacteristic
334C2×#41—21no—
335C2×#41D4×C1111yescharacteristic
336C22×D4—21no—
337#135—41no—
338#135—41no—
339C2×Q16C23×C1111yescharacteristic
340C2×SD16—21no—
341C2×D8—21no—
342C2×D8—41no—
343C2×D8—41no—
344C2×D8C23×C1111yescharacteristic
345C2×D8C23×C1111yescharacteristic
346C2×D8C23×C1111yescharacteristic
347#131—41no—
348#131—41no—
349C2×M16D4×C1111yescharacteristic
350C2×M16D4×C1111yescharacteristic
351C2×M16D4×C1111yescharacteristic
352C22×C8C23×C1111yescharacteristic
353C22×C8C23×C1111yescharacteristic
354C22×C8C23×C1111yescharacteristic
355#127—41no—
356#124—41no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—41no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—41no—
367#121—41no—
368#121—41no—
369#120—41no—
370#120—41no—
371#117—21no—
372C2×C4⋊C4—21no—
373SD32—41no—
374SD32—41no—
375D16—41no—
376D16—41no—
377M32—41no—
378C2×C16—41no—
379C2×C16C23×C1111yescharacteristic
380C2×C16C23×C1111yescharacteristic
381C2×C16C23×C1111yescharacteristic
382C2×C16C23×C1111yescharacteristic
383#107—21no—
384#107C23×C1111yescharacteristic
385#107C23×C1111yescharacteristic
386#107C23×C1111yescharacteristic
387#107C23×C1111yescharacteristic
388#106—21no—
389#103—21no—
390#103—21no—
391#102—21no—
392#102—21no—
393#102—21no—
394#102—21no—
395#102—21no—
396#102—21no—
397C2×C11—41no—
398C2×C11—41no—
399C2×C11—41no—
400C2×C11—161no—
401C2×C11—161no—
402C2×C11—161no—
403C2×C11#318611yescharacteristic
404C2×C11#341511yescharacteristic
405C2×C11#341611yescharacteristic
406C24—41no—
407#41—41no—
408#41—41no—
409#41—42no—
410#41—42no—
411C2×Q8—21no—
412C2×Q8C11×D811yescharacteristic
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4C11×D811yescharacteristic
427C2×D4C11×D811yescharacteristic
428C2×D4C11×D811yescharacteristic
429C22×C4—41no—
430C22×C4—41no—
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434Q16—21no—
435Q16—21no—
436SD16—42no—
437D8—21no—
438D8—21no—
439D8—21no—
440D8—21no—
441D8—21no—
442D8—21no—
443D8—42no—
444M16—41no—
445M16—41no—
446M16—41no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8C2×D4×C1111yescharacteristic
454C2×C8C2×D4×C1111yescharacteristic
455C2×C8C2×D4×C1111yescharacteristic
456C2×C8C24×C1111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—41no—
474C16—21no—
475C16—21no—
476C16—21no—
477C16—21no—
478C11#3376411yescharacteristic, direct product factor, Sylow
479C23—41no—
480C23—41no—
481C23—41no—
482C23—82no—
483C23—161no—
484C23—161no—
485C23C2×C11×D811yescharacteristic
486C23C2×C11×D811yescharacteristic
487C23C2×C11×D811yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—82no—
501D4—82no—
502D4—161no—
503D4—161no—
504D4—161no—
505D4—161no—
506D4—161no—
507D4—161no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—82no—
520C2×C4—161no—
521C2×C4C2×C11×D811yescharacteristic
522C2×C4C2×C11×D811yescharacteristic
523C2×C4C2×C11×D811yescharacteristic
524C2×C4C22×D4×C1111yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8C11×H(5,𝔽2)11yescharacteristic
529C8C11×H(5,𝔽2)11yescharacteristic
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—164no—
549C22C22×C11×D811yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C11×#53411yescharacteristic
559C4C11×#57511yescharacteristic
560C2—41no—
561C2—41no—
562C2—41no—
563C2—161no—
564C2—161no—
565C2—161no—
566C2C11×#318611yescharacteristic
567C2C11×#341511yescharacteristic
568C2C11×#341611yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3061C2semidirect
2. C11×#3058C2semidirect
3. C11×#2237C2semidirect
4. C11×#2234C2semidirect
5. C11×#2233C2semidirect
6. C11×#2232C2semidirect
7. C11×#2220C2semidirect
8. C11×#2218C2semidirect
9. C11×#2217C2semidirect
10. C11×#2215C2semidirect
11. C11×#2187C2semidirect
12. C11×#2186C2semidirect
13. C11×#2186C2semidirect
14. C11×#2184C2semidirect
15. C11×#2113C2semidirect
16. C2×C11×#135C22semidirect
25. C2×C11×M32C22semidirect
26. C22×C11×C16C22semidirect
32. C11×#467C22semidirect
38. C11×#466C22semidirect
40. C2×C11×#107C22semidirect
43. C11×#367C22semidirect
44. C11×#367C22semidirect
45. C11×#366C22semidirect
46. C11×#366C22semidirect
47. C11×#358C22semidirect
48. C11×#358C22semidirect
53. C11×#357C22semidirect
54. C11×#357C22semidirect
57. C11×C22⋊C16C22semidirect
58. C11×C22⋊C16C22semidirect
122. #33764C11direct (N × H)
195. #3061C2×C11semidirect
196. #3058C2×C11semidirect
197. #2237C2×C11semidirect
198. #2234C2×C11semidirect
199. #2233C2×C11semidirect
200. #2232C2×C11semidirect
201. #2220C2×C11semidirect
202. #2218C2×C11semidirect
203. #2217C2×C11semidirect
204. #2215C2×C11semidirect
205. #2187C2×C11semidirect
206. #2186C2×C11semidirect
207. #2186C2×C11semidirect
208. #2184C2×C11semidirect
209. #2113C2×C11semidirect
261. C2×#135C22×C11semidirect
270. C2×M32C22×C11semidirect
271. C22×C16C22×C11semidirect
277. #467C22×C11semidirect
283. #466C22×C11semidirect
285. C2×#107C22×C11semidirect
288. #367C22×C11semidirect
289. #367C22×C11semidirect
290. #366C22×C11semidirect
291. #366C22×C11semidirect
292. #358C22×C11semidirect
293. #358C22×C11semidirect
298. #357C22×C11semidirect
299. #357C22×C11semidirect
302. C22⋊C16C22×C11semidirect
303. C22⋊C16C22×C11semidirect
478. C11#33764direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30612
C11×#30582
C11×#22372
C11×#22342
C11×#22332
C11×#22322
C11×#22202
C11×#22182
C11×#22172
C11×#22152
C11×#21872
C11×#21862
C11×#21842
C11×#21132
#3376411