Finite Group Databasebeta

← C11×#20974 #14598167

Subgroups — C11×#20974 #14598167

Order 2816.

1754 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#131C211yesmaximal, characteristic
2C2×C11×#536C211yesmaximal, characteristic
3C2×C11×#419C211yesmaximal, characteristic, complemented
4C22×C11×#103C211yesmaximal, characteristic, complemented
5C11×#2311C211yesmaximal, characteristic
6C11×#1894C214yesmaximal, complemented
7C11×#1892C214yesmaximal, complemented
8C11×#1736C211yesmaximal, characteristic, complemented
9C11×#1735C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C2×C11×#131—24no—
13C2×C11×#131—24no—
14C2×C11×#131—24no—
15C22×C11×M16C2212yes—
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2212yes—
18C23×C8×C11C2211yescharacteristic
19C11×#536—24no—
20C11×#536C418yescomplemented
21C2×C11×C4⋊Q8—21no—
22C2×C11×#124—21no—
23C2×C11×#123—22no—
24C2×C11×C22⋊Q8C2214yes—
25C2×C11×#117C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C11×#419—24no—
29C2×C11×#103—24no—
30C2×C11×#103C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#103C2214yes—
33C11×#391—21no—
34C11×#390—21no—
35C11×#386—22no—
36C11×#380C2214yes—
37C11×#340C2212yes—
38C11×#340C2214yes—
39C11×#340C2212yes—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yes—
45C2×C11×#41D414yes—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11C2×C414yes—
53C22×Q8×C11D411yescharacteristic
54C22×Q8×C11C2312yes—
55C22×D4×C11D412yes—
56C22×D4×C11D411yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C11×#131—232no—
62C2×C11×M16—24no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—24no—
66C2×C11×M16—24no—
67C2×C11×M16D414yes—
68C22×C8×C11—24no—
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11—24no—
72C22×C8×C11—24no—
73C22×C8×C11D414yes—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2312yes—
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—28no—
78C11×#124—28no—
79C11×#123—216no—
80C11×C22⋊Q8—28no—
81C11×C22⋊Q8C2×C4116yescomplemented
82C11×#117—22no—
83C11×#117—22no—
84C11×#117—22no—
85C11×#117C2×C414yes—
86C2×C11×C4⋊C4—24no—
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×#103—24no—
100C11×#103—24no—
101C11×#103—28no—
102C11×#95—24no—
103#20974C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11C2×D412yes—
105C24×C11C2×D411yescharacteristic
106C11×#41—28no—
107C11×#41—28no—
108C11×#41—28no—
109C11×#41—28no—
110C2×Q8×C11—24no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—28no—
115C2×Q8×C11—28no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—44no—
121C2×Q8×C11—42no—
122C2×Q8×C11—42no—
123C2×Q8×C11—44no—
124C2×Q8×C11C22⋊C414yes—
125C2×Q8×C11C22×C414yes—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11C22⋊C418yes—
131C2×D4×C11C22⋊C414yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—82no—
145C22×C4×C11C22×C414yes—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C11×M16—216no—
157C11×M16—28no—
158C2×C8×C11—216no—
159C2×C8×C11—28no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—21no—
166C2×C8×C11C2×D412yes—
167C2×C8×C11C2×D414yes—
168C2×C8×C11C2×D412yes—
169C11×C4⋊C4—216no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4C22×C414yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—216no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—84no—
181C42×C11—24no—
182C42×C11—42no—
183C22×#131C2×C1111yescharacteristic
184C2×#536C2×C1111yescharacteristic
185C2×#419C2×C1111yescharacteristic, complemented
186C22×#103C2×C1111yescharacteristic, complemented
187#2311C2×C1111yescharacteristic
188#1894C2×C1114yescomplemented
189#1892C2×C1114yescomplemented
190#1736C2×C1111yescharacteristic, complemented
191#1735C2×C1111yescharacteristic, complemented
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11C2×C22⋊C414yes—
199C23×C11C2×C22⋊C412yes—
200C23×C11#12112yes—
201C23×C11#12112yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—28no—
204Q8×C11—24no—
205Q8×C11—24no—
206Q8×C11—42no—
207Q8×C11—42no—
208Q8×C11—48no—
209D4×C11—216no—
210D4×C11—28no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—48no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11—42no—
229C2×C4×C11—84no—
230C2×C4×C11C2×C22⋊C414yes—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C4×D414yes—
233C2×C4×C11C4×D414yes—
234C2×C4×C11#12014yes—
235C2×C4×C11#12112yes—
236C2×C4×C11#12112yes—
237C2×C4×C11#12314yes—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C8×C11—22no—
245C8×C11—24no—
246C8×C11—22no—
247C22×#41C22×C1111yescharacteristic
248C23×Q8C22×C1111yescharacteristic
249C2×#131—24no—
250C2×#131—24no—
251C2×#131—24no—
252C22×M16C22×C1112yes—
253C22×M16C22×C1111yescharacteristic
254C23×C8C22×C1112yes—
255C23×C8C22×C1111yescharacteristic
256#536—24no—
257#536C4×C1118yescomplemented
258C2×C4⋊Q8—21no—
259C2×#124—21no—
260C2×#123—22no—
261C2×C22⋊Q8C22×C1114yes—
262C2×#117C22×C1111yescharacteristic
263C2×#117C22×C1111yescharacteristic
264C22×C4⋊C4C22×C1111yescharacteristic
265#419—24no—
266C2×#103—24no—
267C2×#103C22×C1112yes—
268C2×#103C22×C1112yes—
269C2×#103C22×C1114yes—
270#391—21no—
271#390—21no—
272#386—22no—
273#380C22×C1114yes—
274#340C22×C1112yes—
275#340C22×C1114yes—
276#340C22×C1112yes—
277C22×C11—24no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—24no—
281C22×C11—28no—
282C22×C11—24no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—44no—
286C22×C11#38614yes—
287C22×C11C22×C22⋊C411yescharacteristic
288C22×C11C2×#12111yescharacteristic
289C22×C11C2×#12111yescharacteristic
290C22×C11#57712yes—
291C22×C11#57812yes—
292C4×C11—24no—
293C4×C11—44no—
294C4×C11—44no—
295C4×C11—82no—
296C4×C11—82no—
297C4×C11#38614yes—
298C4×C11C2×C4×D411yescharacteristic
299C4×C11C2×C4×D411yescharacteristic
300C4×C11C2×#12011yescharacteristic
301C4×C11C2×#12311yescharacteristic
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—22no—
306C2×#41C2×C4×C1114yes—
307C2×#41D4×C1114yes—
308C22×Q8—21no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8C2×C4×C1114yes—
315C22×Q8D4×C1111yescharacteristic
316C22×Q8C23×C1112yes—
317C22×D4D4×C1112yes—
318C22×D4D4×C1111yescharacteristic
319C23×C4—21no—
320C23×C4—21no—
321C23×C4C23×C1112yes—
322C23×C4C23×C1111yescharacteristic
323#131—232no—
324C2×M16—24no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—24no—
328C2×M16—24no—
329C2×M16D4×C1114yes—
330C22×C8—24no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—24no—
334C22×C8—24no—
335C22×C8D4×C1114yes—
336C22×C8C23×C1111yescharacteristic
337C22×C8C23×C1112yes—
338C22×C8C23×C1111yescharacteristic
339C4⋊Q8—28no—
340#124—28no—
341#123—216no—
342C22⋊Q8—28no—
343C22⋊Q8C2×C4×C11116yescomplemented
344#117—22no—
345#117—22no—
346#117—22no—
347#117C2×C4×C1114yes—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4C23×C1112yes—
353C2×C4⋊C4C23×C1112yes—
354C2×C4⋊C4C23×C1112yes—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—24no—
359C2×C42—21no—
360C2×C42—21no—
361#103—24no—
362#103—24no—
363#103—28no—
364#95—24no—
365C2×C11—24no—
366C2×C11—44no—
367C2×C11C2×#38611yescharacteristic
368C2×C11#289812yes—
369C2×C11#305711yescharacteristic
370C2×C11#305911yescharacteristic
371C2×C11#306312yes—
372C24C2×D4×C1112yes—
373C24C2×D4×C1111yescharacteristic
374#41—28no—
375#41—28no—
376#41—28no—
377#41—28no—
378C2×Q8—24no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—28no—
383C2×Q8—28no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—44no—
389C2×Q8—42no—
390C2×Q8—42no—
391C2×Q8—44no—
392C2×Q8C11×C22⋊C414yes—
393C2×Q8C22×C4×C1114yes—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4C11×C22⋊C418yes—
399C2×D4C11×C22⋊C414yes—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—82no—
413C22×C4C22×C4×C1114yes—
414C22×C4C22×C4×C1112yes—
415C22×C4C2×D4×C1112yes—
416C22×C4C2×D4×C1114yes—
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×D4×C1112yes—
419C22×C4C2×D4×C1112yes—
420C22×C4C2×D4×C1112yes—
421C22×C4C11×#4112yes—
422C22×C4C11×#4112yes—
423C22×C4C24×C1111yescharacteristic
424M16—216no—
425M16—28no—
426C2×C8—216no—
427C2×C8—28no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—21no—
434C2×C8C2×D4×C1112yes—
435C2×C8C2×D4×C1114yes—
436C2×C8C2×D4×C1112yes—
437C4⋊C4—216no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—42no—
444C4⋊C4C22×C4×C1114yes—
445C22⋊C4—24no—
446C22⋊C4—216no—
447C22⋊C4—42no—
448C22⋊C4—84no—
449C42—24no—
450C42—42no—
451C11#2097411yescharacteristic, direct product factor, Sylow
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—24no—
457C23—24no—
458C23C2×C11×C22⋊C414yes—
459C23C2×C11×C22⋊C412yes—
460C23C11×#12112yes—
461C23C11×#12112yes—
462C23C22×D4×C1111yescharacteristic
463Q8—28no—
464Q8—24no—
465Q8—24no—
466Q8—42no—
467Q8—48no—
468Q8—42no—
469D4—216no—
470D4—28no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—48no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—84no—
490C2×C4C2×C11×C22⋊C414yes—
491C2×C4C2×C11×C22⋊C412yes—
492C2×C4C4×D4×C1114yes—
493C2×C4C4×D4×C1114yes—
494C2×C4C11×#12014yes—
495C2×C4C11×#12112yes—
496C2×C4C11×#12112yes—
497C2×C4C11×#12314yes—
498C2×C4C23×C4×C1111yescharacteristic
499C2×C4C22×D4×C1111yescharacteristic
500C2×C4C22×D4×C1111yescharacteristic
501C2×C4C22×D4×C1111yescharacteristic
502C2×C4C2×C11×#4111yescharacteristic
503C2×C4C2×C11×#4111yescharacteristic
504C8—22no—
505C8—24no—
506C8—22no—
507C22—24no—
508C22—22no—
509C22—22no—
510C22—24no—
511C22—28no—
512C22—24no—
513C22—42no—
514C22—42no—
515C22—44no—
516C22C11×#38614yes—
517C22C22×C11×C22⋊C411yescharacteristic
518C22C2×C11×#12111yescharacteristic
519C22C2×C11×#12111yescharacteristic
520C22C11×#57712yes—
521C22C11×#57812yes—
522C4—24no—
523C4—44no—
524C4—44no—
525C4—82no—
526C4—82no—
527C4C11×#38614yes—
528C4C2×C4×D4×C1111yescharacteristic
529C4C2×C4×D4×C1111yescharacteristic
530C4C2×C11×#12011yescharacteristic
531C4C2×C11×#12311yescharacteristic
532C2—24no—
533C2—44no—
534C2C2×C11×#38611yescharacteristic
535C2C11×#289812yes—
536C2C11×#305711yescharacteristic
537C2C11×#305911yescharacteristic
538C2C11×#306312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
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
3. C2×C11×#419C2semidirect
4. C22×C11×#103C2semidirect
6. C11×#1894C2semidirect
7. C11×#1892C2semidirect
8. C11×#1736C2semidirect
9. C11×#1735C2semidirect
20. C11×#536C4semidirect
81. C11×C22⋊Q8C2×C4semidirect
103. #20974C11direct (N × H)
185. C2×#419C2×C11semidirect
186. C22×#103C2×C11semidirect
188. #1894C2×C11semidirect
189. #1892C2×C11semidirect
190. #1736C2×C11semidirect
191. #1735C2×C11semidirect
257. #536C4×C11semidirect
343. C22⋊Q8C2×C4×C11semidirect
451. C11#20974direct (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×#5362
C2×C11×#4192
C22×C11×#1032
C11×#23112
C11×#18942
C11×#18922
C11×#17362
C11×#17352
#2097411