Finite Group Databasebeta

← C11×#32964 #14610157

Subgroups — C11×#32964 #14610157

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#519C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic, complemented
3C2×C11×#475C211yesmaximal, characteristic, complemented
4C11×#2628C211yesmaximal, characteristic
5C11×#1865C212yesmaximal, complemented
6C11×#1863C212yesmaximal, complemented
7C11×#1854C212yesmaximal
8C11×#1805C211yesmaximal, characteristic, complemented
9C11×#1805C211yesmaximal, characteristic, complemented
10C11×#1798C211yesmaximal, characteristic
11C11×#1787C212yesmaximal
12C23×Q8×C11C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C11×#519—24no—
15C11×#519—24no—
16C2×C4×Q8×C11—21no—
17C2×C4×Q8×C11—21no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×C11×#117—21no—
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C11×#477—24no—
27C11×#475—24no—
28C2×C11×#107C2212yes—
29C2×C11×#106C2212yes—
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#103C2212yes—
36C2×C11×C22⋊C8C2212yes—
37C11×#400—21no—
38C11×#399—21no—
39C11×#395—21no—
40C11×#393—21no—
41C11×#389C2212yes—
42C11×#382C2211yescharacteristic
43C11×#380C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—21no—
52C22×Q8×C11—21no—
53C22×Q8×C11—22no—
54C22×Q8×C11Q814yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2312yes—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C4×Q8×C11—28no—
64C4×Q8×C11—28no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11D414yes—
72C4×Q8×C11D414yes—
73C11×#117—28no—
74C11×#117—28no—
75C11×#117—22no—
76C11×#117—22no—
77C11×#117—22no—
78C11×#117—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11—21no—
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C11×#107—24no—
103C11×#106—24no—
104C11×C4⋊C8—22no—
105C11×C4⋊C8—22no—
106C11×#103—24no—
107C11×#103—24no—
108C11×#103—24no—
109C11×#103—24no—
110C11×C22⋊C8—24no—
111C11×#95—22no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—22no—
115#32964C1111yesmaximal, characteristic, direct product factor, Sylow
116C24×C11C2×D411yescharacteristic
117C2×Q8×C11—24no—
118C2×Q8×C11—28no—
119C2×Q8×C11—28no—
120C2×Q8×C11—24no—
121C2×Q8×C11—28no—
122C2×Q8×C11—28no—
123C2×Q8×C11—24no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—42no—
131C2×Q8×C11—82no—
132C2×Q8×C11C2×D412yes—
133C2×Q8×C11C2×D412yes—
134C2×Q8×C11C2×Q812yes—
135C2×Q8×C11C2×Q812yes—
136C2×Q8×C11#4112yes—
137C2×Q8×C11#4112yes—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×Q812yes—
157C22×C4×C11#4112yes—
158C22×C4×C11C2411yescharacteristic
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—82no—
179C11×C4⋊C4C2×D412yes—
180C11×C4⋊C4C2×D412yes—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—82no—
185C42×C11—24no—
186C42×C11—24no—
187C42×C11—24no—
188C42×C11—24no—
189C42×C11—24no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11C2×D412yes—
193C42×C11C2×D412yes—
194C2×#519C2×C1111yescharacteristic
195C2×#477C2×C1111yescharacteristic, complemented
196C2×#475C2×C1111yescharacteristic, complemented
197#2628C2×C1111yescharacteristic
198#1865C2×C1112yescomplemented
199#1863C2×C1112yescomplemented
200#1854C2×C1112yes—
201#1805C2×C1111yescharacteristic, complemented
202#1805C2×C1111yescharacteristic, complemented
203#1798C2×C1111yescharacteristic
204#1787C2×C1112yes—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11C22⋊Q812yes—
210C23×C11C22×D411yescharacteristic
211Q8×C11—216no—
212Q8×C11—22no—
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—84no—
219Q8×C11C22⋊Q814yes—
220Q8×C11C22⋊Q814yes—
221C2×C4×C11—216no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11#12012yes—
251C2×C4×C11#12012yes—
252C2×C4×C11C22⋊Q812yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×Q811yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C8×C11—42no—
260C8×C11—42no—
261C23×Q8C22×C1111yescharacteristic
262C2×C4⋊Q8C22×C1111yescharacteristic
263#519—24no—
264#519—24no—
265C2×C4×Q8—21no—
266C2×C4×Q8—21no—
267C2×C4×Q8C22×C1111yescharacteristic
268C2×C4×Q8C22×C1111yescharacteristic
269C2×C4×Q8C22×C1111yescharacteristic
270C2×C4×Q8C22×C1111yescharacteristic
271C2×#117—21no—
272C2×#117—21no—
273C2×#117C22×C1111yescharacteristic
274C2×#117C22×C1111yescharacteristic
275#477—24no—
276#475—24no—
277C2×#107C22×C1112yes—
278C2×#106C22×C1112yes—
279C2×C4⋊C8C22×C1111yescharacteristic
280C2×C4⋊C8C22×C1111yescharacteristic
281C2×#103C22×C1112yes—
282C2×#103C22×C1112yes—
283C2×#103C22×C1112yes—
284C2×#103C22×C1112yes—
285C2×C22⋊C8C22×C1112yes—
286#400—21no—
287#399—21no—
288#395—21no—
289#393—21no—
290#389C22×C1112yes—
291#382C22×C1111yescharacteristic
292#380C22×C1112yes—
293#340C22×C1112yes—
294#340C22×C1112yes—
295#336C22×C1112yes—
296C22×C11—24no—
297C22×C11—22no—
298C22×C11—42no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11C2×#12011yescharacteristic
302C22×C11C2×C22⋊Q811yescharacteristic
303C22×C11#52511yescharacteristic
304C22×C11#57712yes—
305C22×C11#57812yes—
306C4×C11—24no—
307C4×C11—24no—
308C4×C11—22no—
309C4×C11—22no—
310C4×C11—22no—
311C4×C11—41no—
312C4×C11—42no—
313C4×C11—41no—
314C4×C11—42no—
315C4×C11—82no—
316C4×C11—82no—
317C4×C11C2×C22⋊Q811yescharacteristic
318C4×C11C2×C22⋊Q811yescharacteristic
319C4×C11#52511yescharacteristic
320C4×C11#52511yescharacteristic
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—21no—
326C22×Q8—21no—
327C22×Q8—22no—
328C22×Q8Q8×C1114yescomplemented
329C22×Q8C23×C1111yescharacteristic
330C22×Q8C23×C1111yescharacteristic
331C23×C4—21no—
332C23×C4C23×C1111yescharacteristic
333C22×C8C23×C1112yes—
334C22×C8C23×C1112yes—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4×Q8—28no—
338C4×Q8—28no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8D4×C1114yes—
346C4×Q8D4×C1114yes—
347#117—28no—
348#117—28no—
349#117—22no—
350#117—22no—
351#117—22no—
352#117—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4D4×C1111yescharacteristic
360C2×C4⋊C4D4×C1111yescharacteristic
361C2×C4⋊C4C23×C1112yes—
362C2×C4⋊C4C23×C1112yes—
363C2×C4⋊C4C23×C1111yescharacteristic
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4D4×C1111yescharacteristic
368C2×C22⋊C4D4×C1111yescharacteristic
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42C23×C1111yescharacteristic
375C2×C42C23×C1111yescharacteristic
376#107—24no—
377#106—24no—
378C4⋊C8—22no—
379C4⋊C8—22no—
380#103—24no—
381#103—24no—
382#103—24no—
383#103—24no—
384C22⋊C8—24no—
385#95—22no—
386#95—21no—
387#95—21no—
388#95—22no—
389C2×C11—42no—
390C2×C11#284811yescharacteristic
391C2×C11#301011yescharacteristic
392C2×C11#301111yescharacteristic
393C2×C11#308212yes—
394C2×C11#312112yes—
395C24C2×D4×C1111yescharacteristic
396C2×Q8—24no—
397C2×Q8—28no—
398C2×Q8—28no—
399C2×Q8—24no—
400C2×Q8—28no—
401C2×Q8—28no—
402C2×Q8—24no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—42no—
410C2×Q8—82no—
411C2×Q8C2×D4×C1112yes—
412C2×Q8C2×D4×C1112yes—
413C2×Q8C2×Q8×C1112yes—
414C2×Q8C2×Q8×C1112yes—
415C2×Q8C11×#4112yes—
416C2×Q8C11×#4112yes—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×Q8×C1112yes—
436C22×C4C11×#4112yes—
437C22×C4C24×C1111yescharacteristic
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—42no—
457C4⋊C4—82no—
458C4⋊C4C2×D4×C1112yes—
459C4⋊C4C2×D4×C1112yes—
460C22⋊C4—24no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—82no—
464C42—24no—
465C42—24no—
466C42—24no—
467C42—24no—
468C42—24no—
469C42—21no—
470C42—21no—
471C42C2×D4×C1112yes—
472C42C2×D4×C1112yes—
473C11#3296411yescharacteristic, direct product factor, Sylow
474C23—21no—
475C23—21no—
476C23—22no—
477C23—22no—
478C23C11×C22⋊Q812yes—
479C23C22×D4×C1111yescharacteristic
480Q8—216no—
481Q8—22no—
482Q8—22no—
483Q8—22no—
484Q8—22no—
485Q8—22no—
486Q8—22no—
487Q8—84no—
488Q8C11×C22⋊Q814yes—
489Q8C11×C22⋊Q814yes—
490C2×C4—216no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4C11×#12012yes—
520C2×C4C11×#12012yes—
521C2×C4C11×C22⋊Q812yes—
522C2×C4C22×D4×C1111yescharacteristic
523C2×C4C22×D4×C1111yescharacteristic
524C2×C4C22×Q8×C1111yescharacteristic
525C2×C4C2×C11×#4111yescharacteristic
526C2×C4C2×C11×#4111yescharacteristic
527C2×C4C2×C11×#4111yescharacteristic
528C8—42no—
529C8—42no—
530C22—24no—
531C22—22no—
532C22—41no—
533C22—41no—
534C22—42no—
535C22C2×C11×#12011yescharacteristic
536C22C2×C11×C22⋊Q811yescharacteristic
537C22C11×#52511yescharacteristic
538C22C11×#57712yes—
539C22C11×#57812yes—
540C4—22no—
541C4—22no—
542C4—24no—
543C4—24no—
544C4—22no—
545C4—41no—
546C4—42no—
547C4—41no—
548C4—42no—
549C4—82no—
550C4—82no—
551C4C2×C11×C22⋊Q811yescharacteristic
552C4C2×C11×C22⋊Q811yescharacteristic
553C4C11×#52511yescharacteristic
554C4C11×#52511yescharacteristic
555C2—42no—
556C2C11×#284811yescharacteristic
557C2C11×#301011yescharacteristic
558C2C11×#301111yescharacteristic
559C2C11×#308212yes—
560C2C11×#312112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#477C2semidirect
3. C2×C11×#475C2semidirect
5. C11×#1865C2semidirect
6. C11×#1863C2semidirect
8. C11×#1805C2semidirect
9. C11×#1805C2semidirect
54. C22×Q8×C11Q8semidirect
115. #32964C11direct (N × H)
195. C2×#477C2×C11semidirect
196. C2×#475C2×C11semidirect
198. #1865C2×C11semidirect
199. #1863C2×C11semidirect
201. #1805C2×C11semidirect
202. #1805C2×C11semidirect
328. C22×Q8Q8×C11semidirect
473. C11#32964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5192
C2×C11×#4772
C2×C11×#4752
C11×#26282
C11×#18652
C11×#18632
C11×#18542
C11×#18052
C11×#17982
C11×#17872
#3296411