Finite Group Databasebeta

← C11×#22145 #14599338

Subgroups — C11×#22145 #14599338

Order 2816.

1064 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C4×C11×#127C211yesmaximal, characteristic, complemented
3C11×#2293C211yesmaximal, characteristic, complemented
4C11×#1982C211yesmaximal, characteristic, complemented
5C11×#1970C212yesmaximal, complemented
6C11×#1947C211yesmaximal, characteristic, complemented
7C11×#1934C212yesmaximal, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1862C212yesmaximal, complemented
10C11×#1802C211yesmaximal, characteristic, complemented
11C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×C11×#117—21no—
19C11×#459C418yescomplemented
20C2×C11×#107C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C4×C8×C11C2212yes—
28C11×#390—21no—
29C11×#390—21no—
30C11×#390C2211yescharacteristic
31C11×#390C2212yes—
32C11×#390C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#388—21no—
36C11×#388—21no—
37C11×#384C2211yescharacteristic
38C4×C11×C4⋊C4C2211yescharacteristic
39C4×C11×C22⋊C4—21no—
40C43×C11C2211yescharacteristic
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C22×D4×C11C2312yes—
48C23×C4×C11—21no—
49C23×C4×C11—22no—
50C2×C11×D8—42no—
51C2×C11×D8—42no—
52C2×C11×D8C2×C418yescomplemented
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×#127—22no—
56C11×#127C2×C414yes—
57C4×D4×C11—22no—
58C4×D4×C11—42no—
59C4×D4×C11—42no—
60C4×D4×C11—44no—
61C4×D4×C11—44no—
62C4×D4×C11C2×C414yescomplemented
63C11×#117—44no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—21no—
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D411yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C11×#107—42no—
89C11×C4⋊C8—22no—
90C11×C4⋊C8C2×C414yescomplemented
91C11×#102—42no—
92C11×#102—42no—
93C11×#102—42no—
94C11×#102C2×C418yescomplemented
95C4×C8×C11—42no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99#22145C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—21no—
101C24×C11—22no—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11C22×C414yes—
119C2×D4×C11C22×C412yes—
120C22×C4×C11—21no—
121C22×C4×C11—24no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—44no—
126C22×C4×C11—44no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—44no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C11×D8—48no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11C22×C414yes—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4C22×C412yes—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—42no—
158C11×C22⋊C4—44no—
159C11×C22⋊C4—42no—
160C11×C22⋊C4—42no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—44no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—41no—
171C42×C11—42no—
172C42×C11D814yescomplemented
173C42×C11C22×C412yes—
174C42×C11#4112yes—
175C2×#459C2×C1111yescharacteristic
176C4×#127C2×C1111yescharacteristic, complemented
177#2293C2×C1111yescharacteristic, complemented
178#1982C2×C1111yescharacteristic, complemented
179#1970C2×C1112yescomplemented
180#1947C2×C1111yescharacteristic, complemented
181#1934C2×C1112yescomplemented
182#1879C2×C1112yescomplemented
183#1862C2×C1112yescomplemented
184#1802C2×C1111yescharacteristic, complemented
185C4×C4⋊C8C2×C1111yescharacteristic, complemented
186C23×C11—22no—
187C23×C11—24no—
188C23×C11—42no—
189C23×C11—41no—
190C23×C11—42no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—42no—
194C23×C11—41no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—42no—
200C23×C11C22×D411yescharacteristic
201D4×C11—22no—
202D4×C11—24no—
203D4×C11—22no—
204D4×C11—24no—
205D4×C11—48no—
206D4×C11—41no—
207D4×C11—42no—
208D4×C11—41no—
209D4×C11—42no—
210D4×C11—48no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—48no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—88no—
236C2×C4×C11C4×D412yes—
237C2×C4×C11C4×D412yes—
238C2×C4×C11C2×D812yes—
239C2×C4×C11C2×D812yes—
240C2×C4×C11C2×D812yes—
241C2×C4×C11#13512yes—
242C2×C4×C11AGL(1,ℤ/8)12yes—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C8×C11—24no—
250C8×C11—42no—
251C22×D8C22×C1112yes—
252C2×#127C22×C1111yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C22×C1111yescharacteristic
256C2×C4×D4C22×C1112yes—
257C2×#117—21no—
258#459C4×C1118yescomplemented
259C2×#107C22×C1112yes—
260C2×C4⋊C8C22×C1111yescharacteristic
261C2×C4⋊C8C22×C1111yescharacteristic
262C2×#102C22×C1112yes—
263C2×#102C22×C1112yes—
264C2×#102C22×C1112yes—
265C2×#102C22×C1112yes—
266C2×C4×C8C22×C1112yes—
267#390—21no—
268#390—21no—
269#390C22×C1112yes—
270#390C22×C1111yescharacteristic
271#390C22×C1111yescharacteristic
272#389C22×C1111yescharacteristic
273#389C22×C1111yescharacteristic
274#388—21no—
275#388—21no—
276#384C22×C1111yescharacteristic
277C4×C4⋊C4C22×C1111yescharacteristic
278C4×C22⋊C4—21no—
279C43C22×C1111yescharacteristic
280#340C22×C1112yes—
281#340C22×C1112yes—
282#336C22×C1112yes—
283C22×C11—42no—
284C22×C11—44no—
285C22×C11—42no—
286C22×C11—44no—
287C22×C11—44no—
288C22×C11—42no—
289C22×C11—82no—
290C22×C11—81no—
291C22×C11—82no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—82no—
295C22×C11—81no—
296C22×C11—82no—
297C22×C11C2×C4×D411yescharacteristic
298C22×C11#53511yescharacteristic
299C22×C11#53711yescharacteristic
300C22×C11C22×D811yescharacteristic
301C22×C11C2×#13511yescharacteristic
302C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C11#57511yescharacteristic
304C4×C11—22no—
305C4×C11—22no—
306C4×C11—22no—
307C4×C11—22no—
308C4×C11—42no—
309C4×C11—41no—
310C4×C11—81no—
311C4×C11—82no—
312C4×C11—81no—
313C4×C11C4×D814yes—
314C4×C11#51811yescharacteristic
315C4×C11#52011yescharacteristic
316C4×C11#54011yescharacteristic
317C4×C11#54211yescharacteristic
318C22×D4—21no—
319C22×D4—21no—
320C22×D4C23×C1112yes—
321C22×D4C23×C1111yescharacteristic
322C23×C4—21no—
323C23×C4—22no—
324C2×D8—42no—
325C2×D8—42no—
326C2×D8C2×C4×C1118yescomplemented
327C22×C8C23×C1112yes—
328C22×C8C23×C1112yes—
329#127—22no—
330#127C2×C4×C1114yes—
331C4×D4—22no—
332C4×D4—42no—
333C4×D4—42no—
334C4×D4—44no—
335C4×D4—44no—
336C4×D4C2×C4×C1114yescomplemented
337#117—44no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4C23×C1112yes—
343C2×C4⋊C4C23×C1111yescharacteristic
344C2×C4⋊C4C23×C1111yescharacteristic
345C2×C4⋊C4C23×C1111yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C42—21no—
355C2×C42D4×C1111yescharacteristic
356C2×C42D4×C1111yescharacteristic
357C2×C42D4×C1111yescharacteristic
358C2×C42D4×C1111yescharacteristic
359C2×C42C23×C1111yescharacteristic
360C2×C42C23×C1111yescharacteristic
361C2×C42C23×C1111yescharacteristic
362#107—42no—
363C4⋊C8—22no—
364C4⋊C8C2×C4×C1114yescomplemented
365#102—42no—
366#102—42no—
367#102—42no—
368#102C2×C4×C1118yescomplemented
369C4×C8—42no—
370#95—21no—
371#95—21no—
372#95—21no—
373C2×C11—82no—
374C2×C11—84no—
375C2×C11#232411yescharacteristic
376C2×C11C2×C4×D811yescharacteristic
377C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
378C2×C11#320511yescharacteristic
379C2×C11#321211yescharacteristic
380C2×C11#324511yescharacteristic
381C2×C11#324711yescharacteristic
382C24—21no—
383C24—22no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4C22×C4×C1114yes—
401C2×D4C22×C4×C1112yes—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—44no—
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C24×C1111yescharacteristic
419D8—48no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8C22×C4×C1114yes—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—42no—
434C4⋊C4—42no—
435C4⋊C4—42no—
436C4⋊C4—42no—
437C4⋊C4C22×C4×C1112yes—
438C22⋊C4—24no—
439C22⋊C4—44no—
440C22⋊C4—42no—
441C22⋊C4—42no—
442C22⋊C4—42no—
443C22⋊C4—44no—
444C22⋊C4—44no—
445C22⋊C4—42no—
446C42—22no—
447C42—22no—
448C42—21no—
449C42—21no—
450C42—21no—
451C42—21no—
452C42—41no—
453C42—42no—
454C42C11×D814yescomplemented
455C42C22×C4×C1112yes—
456C42C11×#4112yes—
457C11#2214511yescharacteristic, direct product factor, Sylow
458C23—22no—
459C23—24no—
460C23—42no—
461C23—41no—
462C23—42no—
463C23—41no—
464C23—41no—
465C23—42no—
466C23—41no—
467C23—42no—
468C23—42no—
469C23—41no—
470C23—41no—
471C23—42no—
472C23C22×D4×C1111yescharacteristic
473D4—22no—
474D4—24no—
475D4—22no—
476D4—24no—
477D4—48no—
478D4—41no—
479D4—42no—
480D4—41no—
481D4—42no—
482D4—48no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—48no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—88no—
508C2×C4C4×D4×C1112yes—
509C2×C4C4×D4×C1112yes—
510C2×C4C2×C11×D812yes—
511C2×C4C2×C11×D812yes—
512C2×C4C2×C11×D812yes—
513C2×C4C11×#13512yes—
514C2×C4C11×AGL(1,ℤ/8)12yes—
515C2×C4C23×C4×C1111yescharacteristic
516C2×C4C2×C11×#4111yescharacteristic
517C2×C4C11×H(5,𝔽2)11yescharacteristic
518C2×C4C11×H(5,𝔽2)11yescharacteristic
519C2×C4C11×H(5,𝔽2)11yescharacteristic
520C2×C4C11×2−1+411yescharacteristic
521C8—24no—
522C8—42no—
523C22—42no—
524C22—44no—
525C22—44no—
526C22—42no—
527C22—42no—
528C22—44no—
529C22—82no—
530C22—81no—
531C22—82no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—81no—
536C22—82no—
537C22C2×C4×D4×C1111yescharacteristic
538C22C11×#53511yescharacteristic
539C22C11×#53711yescharacteristic
540C22C22×C11×D811yescharacteristic
541C22C2×C11×#13511yescharacteristic
542C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
543C22C11×#57511yescharacteristic
544C4—22no—
545C4—22no—
546C4—22no—
547C4—22no—
548C4—42no—
549C4—41no—
550C4—82no—
551C4—81no—
552C4—81no—
553C4C4×C11×D814yes—
554C4C11×#51811yescharacteristic
555C4C11×#52011yescharacteristic
556C4C11×#54011yescharacteristic
557C4C11×#54211yescharacteristic
558C2—82no—
559C2—84no—
560C2C11×#232411yescharacteristic
561C2C2×C4×C11×D811yescharacteristic
562C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
563C2C11×#320511yescharacteristic
564C2C11×#321211yescharacteristic
565C2C11×#324511yescharacteristic
566C2C11×#324711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#127C2semidirect
3. C11×#2293C2semidirect
4. C11×#1982C2semidirect
5. C11×#1970C2semidirect
6. C11×#1947C2semidirect
7. C11×#1934C2semidirect
8. C11×#1879C2semidirect
9. C11×#1862C2semidirect
10. C11×#1802C2semidirect
11. C4×C11×C4⋊C8C2semidirect
19. C11×#459C4semidirect
52. C2×C11×D8C2×C4semidirect
62. C4×D4×C11C2×C4semidirect
90. C11×C4⋊C8C2×C4semidirect
94. C11×#102C2×C4semidirect
99. #22145C11direct (N × H)
172. C42×C11D8semidirect
176. C4×#127C2×C11semidirect
177. #2293C2×C11semidirect
178. #1982C2×C11semidirect
179. #1970C2×C11semidirect
180. #1947C2×C11semidirect
181. #1934C2×C11semidirect
182. #1879C2×C11semidirect
183. #1862C2×C11semidirect
184. #1802C2×C11semidirect
185. C4×C4⋊C8C2×C11semidirect
258. #459C4×C11semidirect
326. C2×D8C2×C4×C11semidirect
336. C4×D4C2×C4×C11semidirect
364. C4⋊C8C2×C4×C11semidirect
368. #102C2×C4×C11semidirect
454. C42C11×D8semidirect
457. C11#22145direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C4×C11×#1272
C11×#22932
C11×#19822
C11×#19702
C11×#19472
C11×#19342
C11×#18792
C11×#18622
C11×#18022
C4×C11×C4⋊C82
#2214511