Finite Group Databasebeta

← C11×#21205 #14598398

Subgroups — C11×#21205 #14598398

Order 2816.

1526 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic
3C2×C11×#419C211yesmaximal, characteristic, complemented
4C2×C11×#416C211yesmaximal, characteristic
5C22×C11×#103C211yesmaximal, characteristic, complemented
6C2×C11×#405C211yesmaximal, characteristic, complemented
7C11×#2317C211yesmaximal, characteristic, complemented
8C11×#1960C212yesmaximal, complemented
9C11×#1959C212yesmaximal, complemented
10C11×#1958C212yesmaximal, complemented
11C11×#1956C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C11×#536—24no—
17C11×#536C418yescomplemented
18C2×C11×C4⋊Q8C2212yes—
19C2×C11×#124C2212yes—
20C2×C11×#123—22no—
21C2×C11×C22⋊Q8—22no—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C11×#419—24no—
26C11×#417—24no—
27C11×#416—24no—
28C2×C11×#103—24no—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#103C2212yes—
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2212yes—
39C11×#405—24no—
40C2×C11×#97C2212yes—
41C2×C4×C8×C11C2212yes—
42C11×#389—22no—
43C11×#385—22no—
44C11×#384C2212yes—
45C11×#382C2212yes—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41C2×C414yes—
52C22×Q8×C11—21no—
53C22×Q8×C11—22no—
54C22×Q8×C11—22no—
55C22×Q8×C11—22no—
56C22×Q8×C11—22no—
57C22×Q8×C11—22no—
58C22×Q8×C11C2×C414yes—
59C22×Q8×C11C2312yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16D414yes—
70C22×C8×C11—22no—
71C22×C8×C11—22no—
72C22×C8×C11D414yes—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2312yes—
75C22×C8×C11C2311yescharacteristic
76C11×C4⋊Q8—24no—
77C11×C4⋊Q8C2×C418yescomplemented
78C11×#124—24no—
79C11×#124C2×C418yescomplemented
80C11×#123—216no—
81C11×C22⋊Q8—216no—
82C11×#117—22no—
83C11×#117—22no—
84C11×#117C2×C414yes—
85C11×#117D414yes—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4D412yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4D412yes—
98C2×C42×C11—21no—
99C2×C42×C11C2312yes—
100C11×#103—24no—
101C11×#103—24no—
102C11×#103—22no—
103C11×#103—22no—
104C11×#103—24no—
105C11×#103—24no—
106C11×#103—24no—
107C11×#102—22no—
108C11×#102—22no—
109C11×#102—24no—
110C11×#97—24no—
111C4×C8×C11—24no—
112C11×#95—24no—
113#21205C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11—21no—
115C24×C11C2×D411yescharacteristic
116C11×#41—28no—
117C11×#41—28no—
118C11×#41—44no—
119C11×#41—44no—
120C2×Q8×C11—24no—
121C2×Q8×C11—22no—
122C2×Q8×C11—21no—
123C2×Q8×C11—28no—
124C2×Q8×C11—28no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—44no—
134C2×Q8×C11—44no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11C22×C414yes—
138C2×Q8×C11C22×C412yes—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11C22×C412yes—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—24no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—82no—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C22×C4×C11C2411yescharacteristic
170C11×M16—28no—
171C2×C8×C11—28no—
172C2×C8×C11—21no—
173C2×C8×C11—22no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—22no—
178C2×C8×C11C2×D412yes—
179C2×C8×C11C2×D412yes—
180C2×C8×C11C2×D414yes—
181C11×C4⋊C4—216no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—84no—
190C11×C4⋊C4C22⋊C418yes—
191C11×C22⋊C4—216no—
192C11×C22⋊C4—42no—
193C11×C22⋊C4C22⋊C418yes—
194C42×C11—42no—
195C42×C11C22×C414yes—
196C42×C11C2×D414yes—
197C2×#536C2×C1111yescharacteristic
198C2×#417C2×C1111yescharacteristic
199C2×#419C2×C1111yescharacteristic, complemented
200C2×#416C2×C1111yescharacteristic
201C22×#103C2×C1111yescharacteristic, complemented
202C2×#405C2×C1111yescharacteristic, complemented
203#2317C2×C1111yescharacteristic, complemented
204#1960C2×C1112yescomplemented
205#1959C2×C1112yescomplemented
206#1958C2×C1112yescomplemented
207#1956C2×C1112yescomplemented
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11C2×C22⋊C412yes—
216C23×C11#12412yes—
217C23×C11#12712yes—
218C23×C11C22×D411yescharacteristic
219Q8×C11—24no—
220Q8×C11—24no—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—42no—
224Q8×C11—42no—
225Q8×C11—41no—
226Q8×C11—41no—
227Q8×C11—48no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—48no—
231D4×C11—41no—
232D4×C11—41no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—48no—
242C2×C4×C11—48no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—42no—
249C2×C4×C11—84no—
250C2×C4×C11C2×C22⋊C418yes—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C4×D414yes—
253C2×C4×C11C4×D414yes—
254C2×C4×C11#12114yes—
255C2×C4×C11#12114yes—
256C2×C4×C11#12412yes—
257C2×C4×C11#12712yes—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C8×C11—22no—
265C8×C11—22no—
266C8×C11—24no—
267C22×#41C22×C1111yescharacteristic
268C23×Q8C22×C1111yescharacteristic
269C22×M16C22×C1111yescharacteristic
270C23×C8C22×C1111yescharacteristic
271#536—24no—
272#536C4×C1118yescomplemented
273C2×C4⋊Q8C22×C1112yes—
274C2×#124C22×C1112yes—
275C2×#123—22no—
276C2×C22⋊Q8—22no—
277C2×#117C22×C1111yescharacteristic
278C2×#117C22×C1111yescharacteristic
279C22×C4⋊C4C22×C1111yescharacteristic
280#419—24no—
281#417—24no—
282#416—24no—
283C2×#103—24no—
284C2×#103C22×C1112yes—
285C2×#103C22×C1112yes—
286C2×#103C22×C1111yescharacteristic
287C2×#103C22×C1111yescharacteristic
288C2×#103C22×C1112yes—
289C2×#103C22×C1112yes—
290C2×#103C22×C1112yes—
291C2×#102C22×C1111yescharacteristic
292C2×#102C22×C1111yescharacteristic
293C2×#102C22×C1112yes—
294#405—24no—
295C2×#97C22×C1112yes—
296C2×C4×C8C22×C1112yes—
297#389—22no—
298#385—22no—
299#384C22×C1112yes—
300#382C22×C1112yes—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—44no—
306C22×C11—42no—
307C22×C11—82no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11#39014yes—
311C22×C11C22×C22⋊C411yescharacteristic
312C22×C11C2×#12411yescharacteristic
313C22×C11C2×#12711yescharacteristic
314C22×C11#57712yes—
315C22×C11#57812yes—
316C4×C11—28no—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11—81no—
320C4×C11—82no—
321C4×C11—81no—
322C4×C11#39014yes—
323C4×C11C2×C4×D411yescharacteristic
324C4×C11C2×C4×D411yescharacteristic
325C4×C11C2×#12111yescharacteristic
326C4×C11C2×#12111yescharacteristic
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41C2×C4×C1114yes—
333C22×Q8—21no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8C2×C4×C1114yes—
340C22×Q8C23×C1112yes—
341C22×Q8C23×C1111yescharacteristic
342C22×D4—21no—
343C22×D4C23×C1111yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4C23×C1111yescharacteristic
348C2×M16—22no—
349C2×M16—22no—
350C2×M16D4×C1114yes—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8D4×C1114yes—
354C22×C8C23×C1111yescharacteristic
355C22×C8C23×C1111yescharacteristic
356C22×C8C23×C1112yes—
357C4⋊Q8—24no—
358C4⋊Q8C2×C4×C1118yescomplemented
359#124—24no—
360#124C2×C4×C1118yescomplemented
361#123—216no—
362C22⋊Q8—216no—
363#117—22no—
364#117—22no—
365#117C2×C4×C1114yes—
366#117D4×C1114yes—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4D4×C1112yes—
373C2×C4⋊C4C23×C1112yes—
374C2×C4⋊C4C23×C1111yescharacteristic
375C2×C4⋊C4C23×C1111yescharacteristic
376C2×C22⋊C4—24no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4D4×C1112yes—
379C2×C42—21no—
380C2×C42C23×C1112yes—
381#103—24no—
382#103—24no—
383#103—22no—
384#103—22no—
385#103—24no—
386#103—24no—
387#103—24no—
388#102—22no—
389#102—22no—
390#102—24no—
391#97—24no—
392C4×C8—24no—
393#95—24no—
394C2×C11—24no—
395C2×C11—82no—
396C2×C11C2×#39011yescharacteristic
397C2×C11#289812yes—
398C2×C11#313712yes—
399C2×C11#315411yescharacteristic
400C2×C11#315611yescharacteristic
401C24—21no—
402C24C2×D4×C1111yescharacteristic
403#41—28no—
404#41—28no—
405#41—44no—
406#41—44no—
407C2×Q8—24no—
408C2×Q8—22no—
409C2×Q8—21no—
410C2×Q8—28no—
411C2×Q8—28no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—44no—
421C2×Q8—44no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8C22×C4×C1114yes—
425C2×Q8C22×C4×C1112yes—
426C2×D4—24no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4C22×C4×C1112yes—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—82no—
448C22×C4C22×C4×C1112yes—
449C22×C4C2×D4×C1114yes—
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1112yes—
452C22×C4C2×D4×C1112yes—
453C22×C4C2×D4×C1112yes—
454C22×C4C11×#4112yes—
455C22×C4C11×#4112yes—
456C22×C4C24×C1111yescharacteristic
457M16—28no—
458C2×C8—28no—
459C2×C8—21no—
460C2×C8—22no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—22no—
465C2×C8C2×D4×C1112yes—
466C2×C8C2×D4×C1112yes—
467C2×C8C2×D4×C1114yes—
468C4⋊C4—216no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—84no—
477C4⋊C4C11×C22⋊C418yes—
478C22⋊C4—216no—
479C22⋊C4—42no—
480C22⋊C4C11×C22⋊C418yes—
481C42—42no—
482C42C22×C4×C1114yes—
483C42C2×D4×C1114yes—
484C11#2120511yescharacteristic, direct product factor, Sylow
485C23—22no—
486C23—22no—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—42no—
491C23—42no—
492C23C2×C11×C22⋊C412yes—
493C23C11×#12412yes—
494C23C11×#12712yes—
495C23C22×D4×C1111yescharacteristic
496Q8—24no—
497Q8—24no—
498Q8—22no—
499Q8—22no—
500Q8—42no—
501Q8—42no—
502Q8—41no—
503Q8—41no—
504Q8—48no—
505D4—22no—
506D4—22no—
507D4—48no—
508D4—41no—
509D4—41no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—48no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—48no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—84no—
527C2×C4C2×C11×C22⋊C418yes—
528C2×C4C2×C11×C22⋊C412yes—
529C2×C4C4×D4×C1114yes—
530C2×C4C4×D4×C1114yes—
531C2×C4C11×#12114yes—
532C2×C4C11×#12114yes—
533C2×C4C11×#12412yes—
534C2×C4C11×#12712yes—
535C2×C4C23×C4×C1111yescharacteristic
536C2×C4C22×D4×C1111yescharacteristic
537C2×C4C22×D4×C1111yescharacteristic
538C2×C4C22×D4×C1111yescharacteristic
539C2×C4C2×C11×#4111yescharacteristic
540C2×C4C2×C11×#4111yescharacteristic
541C8—22no—
542C8—22no—
543C8—24no—
544C22—24no—
545C22—22no—
546C22—22no—
547C22—24no—
548C22—44no—
549C22—42no—
550C22—81no—
551C22—81no—
552C22—82no—
553C22C11×#39014yes—
554C22C22×C11×C22⋊C411yescharacteristic
555C22C2×C11×#12411yescharacteristic
556C22C2×C11×#12711yescharacteristic
557C22C11×#57712yes—
558C22C11×#57812yes—
559C4—28no—
560C4—42no—
561C4—44no—
562C4—82no—
563C4—81no—
564C4—81no—
565C4C11×#39014yes—
566C4C2×C4×D4×C1111yescharacteristic
567C4C2×C4×D4×C1111yescharacteristic
568C4C2×C11×#12111yescharacteristic
569C4C2×C11×#12111yescharacteristic
570C2—24no—
571C2—82no—
572C2C2×C11×#39011yescharacteristic
573C2C11×#289812yes—
574C2C11×#313712yes—
575C2C11×#315411yescharacteristic
576C2C11×#315611yescharacteristic
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 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#419C2semidirect
5. C22×C11×#103C2semidirect
6. C2×C11×#405C2semidirect
7. C11×#2317C2semidirect
8. C11×#1960C2semidirect
9. C11×#1959C2semidirect
10. C11×#1958C2semidirect
11. C11×#1956C2semidirect
17. C11×#536C4semidirect
77. C11×C4⋊Q8C2×C4semidirect
79. C11×#124C2×C4semidirect
113. #21205C11direct (N × H)
199. C2×#419C2×C11semidirect
201. C22×#103C2×C11semidirect
202. C2×#405C2×C11semidirect
203. #2317C2×C11semidirect
204. #1960C2×C11semidirect
205. #1959C2×C11semidirect
206. #1958C2×C11semidirect
207. #1956C2×C11semidirect
272. #536C4×C11semidirect
358. C4⋊Q8C2×C4×C11semidirect
360. #124C2×C4×C11semidirect
484. C11#21205direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4172
C2×C11×#4192
C2×C11×#4162
C22×C11×#1032
C2×C11×#4052
C11×#23172
C11×#19602
C11×#19592
C11×#19582
C11×#19562
#2120511