Finite Group Databasebeta

← C11×#20975 #14598168

Subgroups — C11×#20975 #14598168

Order 2816.

1946 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#131C211yesmaximal, characteristic, complemented
2C2×C11×#535C211yesmaximal, characteristic
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C22×C11×#102C211yesmaximal, characteristic, complemented
5C11×#2311C211yesmaximal, characteristic, complemented
6C11×#1895C214yesmaximal, complemented
7C11×#1893C214yesmaximal, complemented
8C11×#1736C211yesmaximal, characteristic, complemented
9C11×#1735C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C2×C11×#131—24no—
13C2×C11×#131—24no—
14C2×C11×#131—24no—
15C22×C11×M16C2211yescharacteristic
16C22×C11×M16C2212yescomplemented
17C23×C8×C11C2211yescharacteristic
18C23×C8×C11C2212yescomplemented
19C11×#535—24no—
20C11×#535C418yescomplemented
21C2×C11×#127—21no—
22C2×C11×#124—21no—
23C2×C11×#121C2214yes—
24C2×C11×#120—22no—
25C2×C11×#117C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C11×#418—24no—
29C2×C11×#102—24no—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×#102C2214yes—
33C11×#391—21no—
34C11×#390—21no—
35C11×#386—22no—
36C11×#380C2214yescomplemented
37C11×#340C2212yescomplemented
38C11×#340C2214yescomplemented
39C11×#340C2212yescomplemented
40C25×C11—21no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41C2×C414yes—
46C2×C11×#41D414yes—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11—24no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11C2×C414yes—
56C22×D4×C11D412yes—
57C22×D4×C11D411yescharacteristic
58C22×D4×C11C2312yes—
59C23×C4×C11—21no—
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C11×#131—232no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—24no—
66C2×C11×M16—24no—
67C2×C11×M16—24no—
68C2×C11×M16D414yescomplemented
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11—24no—
72C22×C8×C11—24no—
73C22×C8×C11—24no—
74C22×C8×C11D414yescomplemented
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2312yes—
78C11×#127—28no—
79C11×#124—28no—
80C11×#121—28no—
81C11×#121C2×C4116yescomplemented
82C11×#120—216no—
83C11×#117—22no—
84C11×#117—22no—
85C11×#117—22no—
86C11×#117C2×C414yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—24no—
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C11×#102—24no—
100C11×#102—24no—
101C11×#102—28no—
102C11×#95—24no—
103#20975C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—22no—
105C24×C11—24no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—82no—
109C24×C11—82no—
110C24×C11C2×D412yes—
111C24×C11C2×D411yescharacteristic
112C11×#41—28no—
113C11×#41—28no—
114C11×#41—28no—
115C11×#41—28no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11C22⋊C414yes—
119C2×D4×C11—24no—
120C2×D4×C11—24no—
121C2×D4×C11—216no—
122C2×D4×C11—24no—
123C2×D4×C11—28no—
124C2×D4×C11—28no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—44no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11—44no—
136C2×D4×C11—84no—
137C2×D4×C11—84no—
138C2×D4×C11C22⋊C418yes—
139C2×D4×C11C22⋊C414yes—
140C2×D4×C11C22×C414yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—42no—
149C22×C4×C11—82no—
150C22×C4×C11C22×C414yes—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C11×M16—216no—
162C11×M16—28no—
163C2×C8×C11—216no—
164C2×C8×C11—28no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—22no—
169C2×C8×C11—21no—
170C2×C8×C11—22no—
171C2×C8×C11C2×D412yes—
172C2×C8×C11C2×D414yes—
173C2×C8×C11C2×D412yes—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4C22×C414yes—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—216no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—84no—
185C42×C11—24no—
186C42×C11—42no—
187C22×#131C2×C1111yescharacteristic, complemented
188C2×#535C2×C1111yescharacteristic
189C2×#418C2×C1111yescharacteristic, complemented
190C22×#102C2×C1111yescharacteristic, complemented
191#2311C2×C1111yescharacteristic, complemented
192#1895C2×C1114yescomplemented
193#1893C2×C1114yescomplemented
194#1736C2×C1111yescharacteristic, complemented
195#1735C2×C1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11—48no—
208C23×C11—88no—
209C23×C11—84no—
210C23×C11—84no—
211C23×C11—88no—
212C23×C11C2×C22⋊C414yes—
213C23×C11C2×C22⋊C412yes—
214C23×C11#12112yes—
215C23×C11#12112yes—
216C23×C11C22×D411yescharacteristic
217Q8×C11—28no—
218D4×C11—216no—
219D4×C11—24no—
220D4×C11—24no—
221D4×C11—28no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—48no—
225D4×C11—816no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—44no—
239C2×C4×C11—42no—
240C2×C4×C11—84no—
241C2×C4×C11C2×C22⋊C414yes—
242C2×C4×C11C2×C22⋊C412yes—
243C2×C4×C11C4×D414yes—
244C2×C4×C11C4×D414yes—
245C2×C4×C11#12014yes—
246C2×C4×C11#12112yes—
247C2×C4×C11#12112yes—
248C2×C4×C11#12314yes—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C8×C11—22no—
256C8×C11—24no—
257C8×C11—22no—
258C22×#41C22×C1111yescharacteristic
259C23×D4C22×C1111yescharacteristic
260C2×#131—24no—
261C2×#131—24no—
262C2×#131—24no—
263C22×M16C22×C1111yescharacteristic
264C22×M16C22×C1112yescomplemented
265C23×C8C22×C1111yescharacteristic
266C23×C8C22×C1112yescomplemented
267#535—24no—
268#535C4×C1118yescomplemented
269C2×#127—21no—
270C2×#124—21no—
271C2×#121C22×C1114yes—
272C2×#120—22no—
273C2×#117C22×C1111yescharacteristic
274C2×#117C22×C1111yescharacteristic
275C22×C4⋊C4C22×C1111yescharacteristic
276#418—24no—
277C2×#102—24no—
278C2×#102C22×C1112yes—
279C2×#102C22×C1112yes—
280C2×#102C22×C1114yes—
281#391—21no—
282#390—21no—
283#386—22no—
284#380C22×C1114yescomplemented
285#340C22×C1112yescomplemented
286#340C22×C1114yescomplemented
287#340C22×C1112yescomplemented
288C22×C11—24no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—24no—
292C22×C11—28no—
293C22×C11—24no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11—48no—
298C22×C11—44no—
299C22×C11—816no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—84no—
303C22×C11#38614yes—
304C22×C11C22×C22⋊C411yescharacteristic
305C22×C11C2×#12111yescharacteristic
306C22×C11C2×#12111yescharacteristic
307C22×C11#57612yes—
308C22×C11#57712yes—
309C4×C11—24no—
310C4×C11—44no—
311C4×C11—82no—
312C4×C11—82no—
313C4×C11#38614yes—
314C4×C11C2×C4×D411yescharacteristic
315C4×C11C2×C4×D411yescharacteristic
316C4×C11C2×#12011yescharacteristic
317C4×C11C2×#12311yescharacteristic
318C25—21no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41C2×C4×C1114yes—
324C2×#41D4×C1114yes—
325C22×Q8D4×C1111yescharacteristic
326C22×D4—24no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—21no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4C2×C4×C1114yes—
334C22×D4D4×C1112yes—
335C22×D4D4×C1111yescharacteristic
336C22×D4C23×C1112yes—
337C23×C4—21no—
338C23×C4C23×C1112yes—
339C23×C4C23×C1111yescharacteristic
340#131—232no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—24no—
344C2×M16—24no—
345C2×M16—24no—
346C2×M16D4×C1114yescomplemented
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—24no—
350C22×C8—24no—
351C22×C8—24no—
352C22×C8D4×C1114yescomplemented
353C22×C8C23×C1111yescharacteristic
354C22×C8C23×C1111yescharacteristic
355C22×C8C23×C1112yes—
356#127—28no—
357#124—28no—
358#121—28no—
359#121C2×C4×C11116yescomplemented
360#120—216no—
361#117—22no—
362#117—22no—
363#117—22no—
364#117C2×C4×C1114yes—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4C23×C1112yes—
369C2×C4⋊C4C23×C1112yes—
370C2×C4⋊C4C23×C1112yes—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—24no—
375C2×C42—21no—
376C2×C42—21no—
377#102—24no—
378#102—24no—
379#102—28no—
380#95—24no—
381C2×C11—24no—
382C2×C11—44no—
383C2×C11—84no—
384C2×C11C2×#38611yescharacteristic
385C2×C11#289712yes—
386C2×C11#305711yescharacteristic
387C2×C11#305811yescharacteristic
388C2×C11#306212yes—
389C24—22no—
390C24—24no—
391C24—42no—
392C24—42no—
393C24—82no—
394C24—82no—
395C24C2×D4×C1112yes—
396C24C2×D4×C1111yescharacteristic
397#41—28no—
398#41—28no—
399#41—28no—
400#41—28no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8C11×C22⋊C414yes—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—216no—
407C2×D4—24no—
408C2×D4—28no—
409C2×D4—28no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—44no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—44no—
421C2×D4—84no—
422C2×D4—84no—
423C2×D4C11×C22⋊C418yes—
424C2×D4C11×C22⋊C414yes—
425C2×D4C22×C4×C1114yes—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—42no—
434C22×C4—82no—
435C22×C4C22×C4×C1114yes—
436C22×C4C22×C4×C1112yes—
437C22×C4C2×D4×C1112yes—
438C22×C4C2×D4×C1114yes—
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1112yes—
441C22×C4C2×D4×C1112yes—
442C22×C4C2×D4×C1112yes—
443C22×C4C11×#4112yes—
444C22×C4C11×#4112yes—
445C22×C4C24×C1111yescharacteristic
446M16—216no—
447M16—28no—
448C2×C8—216no—
449C2×C8—28no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—22no—
456C2×C8C2×D4×C1112yes—
457C2×C8C2×D4×C1114yes—
458C2×C8C2×D4×C1112yes—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—42no—
465C4⋊C4C22×C4×C1114yes—
466C22⋊C4—24no—
467C22⋊C4—216no—
468C22⋊C4—42no—
469C22⋊C4—84no—
470C42—24no—
471C42—42no—
472C11#2097511yescharacteristic, direct product factor, Sylow
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—42no—
481C23—42no—
482C23—48no—
483C23—44no—
484C23—44no—
485C23—88no—
486C23—84no—
487C23—84no—
488C23—88no—
489C23C2×C11×C22⋊C414yes—
490C23C2×C11×C22⋊C412yes—
491C23C11×#12112yes—
492C23C11×#12112yes—
493C23C22×D4×C1111yescharacteristic
494Q8—28no—
495D4—216no—
496D4—24no—
497D4—24no—
498D4—28no—
499D4—42no—
500D4—48no—
501D4—42no—
502D4—816no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—42no—
517C2×C4—84no—
518C2×C4C2×C11×C22⋊C414yes—
519C2×C4C2×C11×C22⋊C412yes—
520C2×C4C4×D4×C1114yes—
521C2×C4C4×D4×C1114yes—
522C2×C4C11×#12014yes—
523C2×C4C11×#12112yes—
524C2×C4C11×#12112yes—
525C2×C4C11×#12314yes—
526C2×C4C23×C4×C1111yescharacteristic
527C2×C4C22×D4×C1111yescharacteristic
528C2×C4C22×D4×C1111yescharacteristic
529C2×C4C22×D4×C1111yescharacteristic
530C2×C4C2×C11×#4111yescharacteristic
531C2×C4C2×C11×#4111yescharacteristic
532C8—22no—
533C8—24no—
534C8—22no—
535C22—24no—
536C22—22no—
537C22—22no—
538C22—24no—
539C22—28no—
540C22—24no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—48no—
545C22—44no—
546C22—816no—
547C22—82no—
548C22—82no—
549C22—84no—
550C22C11×#38614yes—
551C22C22×C11×C22⋊C411yescharacteristic
552C22C2×C11×#12111yescharacteristic
553C22C2×C11×#12111yescharacteristic
554C22C11×#57612yes—
555C22C11×#57712yes—
556C4—24no—
557C4—44no—
558C4—82no—
559C4—82no—
560C4C11×#38614yes—
561C4C2×C4×D4×C1111yescharacteristic
562C4C2×C4×D4×C1111yescharacteristic
563C4C2×C11×#12011yescharacteristic
564C4C2×C11×#12311yescharacteristic
565C2—24no—
566C2—44no—
567C2—84no—
568C2C2×C11×#38611yescharacteristic
569C2C11×#289712yes—
570C2C11×#305711yescharacteristic
571C2C11×#305811yescharacteristic
572C2C11×#306212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#131C2semidirect
3. C2×C11×#418C2semidirect
4. C22×C11×#102C2semidirect
5. C11×#2311C2semidirect
6. C11×#1895C2semidirect
7. C11×#1893C2semidirect
8. C11×#1736C2semidirect
9. C11×#1735C2semidirect
16. C22×C11×M16C22semidirect
18. C23×C8×C11C22semidirect
20. C11×#535C4semidirect
36. C11×#380C22semidirect
37. C11×#340C22semidirect
38. C11×#340C22semidirect
39. C11×#340C22semidirect
68. C2×C11×M16D4semidirect
74. C22×C8×C11D4semidirect
81. C11×#121C2×C4semidirect
103. #20975C11direct (N × H)
187. C22×#131C2×C11semidirect
189. C2×#418C2×C11semidirect
190. C22×#102C2×C11semidirect
191. #2311C2×C11semidirect
192. #1895C2×C11semidirect
193. #1893C2×C11semidirect
194. #1736C2×C11semidirect
195. #1735C2×C11semidirect
264. C22×M16C22×C11semidirect
266. C23×C8C22×C11semidirect
268. #535C4×C11semidirect
284. #380C22×C11semidirect
285. #340C22×C11semidirect
286. #340C22×C11semidirect
287. #340C22×C11semidirect
346. C2×M16D4×C11semidirect
352. C22×C8D4×C11semidirect
359. #121C2×C4×C11semidirect
472. C11#20975direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1312
C2×C11×#5352
C2×C11×#4182
C22×C11×#1022
C11×#23112
C11×#18952
C11×#18932
C11×#17362
C11×#17352
#2097511