Finite Group Databasebeta

← C11×#32902 #14610095

Subgroups — C11×#32902 #14610095

Order 2816.

2008 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C11C211yesmaximal, characteristic, complemented
2C2×C11×#459C212yesmaximal, complemented
3C2×C11×#447C212yesmaximal, complemented
4C11×#2856C211yesmaximal, characteristic, complemented
5C11×#1879C214yesmaximal, complemented
6C11×#1874C212yesmaximal, complemented
7C11×#1802C212yesmaximal, complemented
8C11×#1797C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11—21no—
11C22×C11×D8C2214yes—
12C2×C11×#127C2211yescharacteristic, complemented
13C2×C11×#121—21no—
14C2×C11×#121—21no—
15C2×C11×#121C2212yes—
16C2×C4×D4×C11—28no—
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2212yes—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4—21no—
23C22×C42×C11C2211yescharacteristic
24C11×#459—28no—
25C11×#447—28no—
26C2×C11×C4⋊C8C2212yescomplemented
27C2×C11×#102C2214yes—
28C2×C11×#102C2214yescomplemented
29C2×C11×C22⋊C8C2212yes—
30C11×#390—21no—
31C11×#390—21no—
32C11×#390C2212yescomplemented
33C11×#384C2211yescharacteristic, complemented
34C11×#340C2214yescomplemented
35C11×#336C2212yescomplemented
36C25×C11—21no—
37C22×D4×C11—24no—
38C22×D4×C11—24no—
39C22×D4×C11—22no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—22no—
44C22×D4×C11D414yescomplemented
45C22×D4×C11C2312yes—
46C22×D4×C11C2312yes—
47C23×C4×C11—28no—
48C23×C4×C11—21no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—44no—
52C23×C4×C11—44no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C2×C11×D8—28no—
57C2×C11×D8—28no—
58C2×C11×D8—28no—
59C22×C8×C11C2314yes—
60C11×#127—24no—
61C11×#121—24no—
62C11×#121—24no—
63C11×#121—44no—
64C11×#121—44no—
65C4×D4×C11—28no—
66C4×D4×C11—28no—
67C4×D4×C11—24no—
68C4×D4×C11—24no—
69C4×D4×C11—24no—
70C4×D4×C11D418yescomplemented
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C22⋊C4—28no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C42×C11—24no—
84C2×C42×C11D411yescharacteristic
85C2×C42×C11D411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C11×C4⋊C8—24no—
89C11×#102—28no—
90C11×#102—28no—
91C11×C22⋊C8—24no—
92#32902C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—24no—
94C24×C11—24no—
95C24×C11—24no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11—42no—
102C24×C11C2×D411yescharacteristic
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—216no—
106C2×D4×C11—216no—
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—24no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—24no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11C2×D414yes—
125C2×D4×C11C2×D414yes—
126C2×D4×C11#4114yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—28no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—28no—
137C22×C4×C11—22no—
138C22×C4×C11—41no—
139C22×C4×C11—44no—
140C22×C4×C11—432no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11D814yescomplemented
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C11×D8—416no—
156C2×C8×C11—24no—
157C2×C8×C11—24no—
158C2×C8×C11—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C2×D414yes—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—44no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11C2×D414yes—
175C22×C4×D4C2×C1111yescharacteristic, complemented
176C2×#459C2×C1112yescomplemented
177C2×#447C2×C1112yescomplemented
178#2856C2×C1111yescharacteristic, complemented
179#1879C2×C1114yescomplemented
180#1874C2×C1112yescomplemented
181#1802C2×C1112yescomplemented
182#1797C2×C1111yescharacteristic, complemented
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—216no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—48no—
192C23×C11—48no—
193C23×C11—48no—
194C23×C11—48no—
195C23×C11—48no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—48no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11#12112yes—
209C23×C11C2×D812yes—
210C23×C11AGL(1,ℤ/8)12yes—
211C23×C11C22×D411yescharacteristic
212D4×C11—216no—
213D4×C11—24no—
214D4×C11—24no—
215D4×C11—24no—
216D4×C11—44no—
217D4×C11—44no—
218D4×C11—84no—
219D4×C11—88no—
220D4×C11—84no—
221D4×C11#12118yescomplemented
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—28no—
231C2×C4×C11—21no—
232C2×C4×C11—24no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—44no—
236C2×C4×C11—416no—
237C2×C4×C11—48no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—416no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11#12012yes—
245C2×C4×C11#12012yes—
246C2×C4×C11#12112yes—
247C2×C4×C11C2×D812yes—
248C2×C4×C11C2×D812yes—
249C2×C4×C11AGL(1,ℤ/8)12yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D412yes—
252C2×C4×C11C2×#4112yes—
253C2×C4×C11C2×#4111yescharacteristic
254C8×C11—44no—
255C23×D4C22×C1111yescharacteristic
256C24×C4—21no—
257C22×D8C22×C1114yes—
258C2×#127C22×C1111yescharacteristic, complemented
259C2×#121—21no—
260C2×#121—21no—
261C2×#121C22×C1112yes—
262C2×C4×D4—28no—
263C2×C4×D4—21no—
264C2×C4×D4—21no—
265C2×C4×D4C22×C1112yes—
266C2×C4×D4C22×C1112yes—
267C22×C4⋊C4C22×C1111yescharacteristic
268C22×C22⋊C4—21no—
269C22×C42C22×C1111yescharacteristic
270#459—28no—
271#447—28no—
272C2×C4⋊C8C22×C1112yescomplemented
273C2×#102C22×C1114yes—
274C2×#102C22×C1114yescomplemented
275C2×C22⋊C8C22×C1112yes—
276#390—21no—
277#390—21no—
278#390C22×C1112yescomplemented
279#384C22×C1111yescharacteristic, complemented
280#340C22×C1114yescomplemented
281#336C22×C1112yescomplemented
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—28no—
289C22×C11—432no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11#45914yescomplemented
304C22×C11C2×#12011yescharacteristic
305C22×C11C2×#12111yescharacteristic
306C22×C11#52511yescharacteristic
307C22×C11C22×D811yescharacteristic
308C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
310C22×C11#57511yescharacteristic
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—44no—
315C4×C11—41no—
316C4×C11—82no—
317C4×C11#44714yescomplemented
318C4×C11C2×#12112yes—
319C4×C11#52512yes—
320C25—21no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—22no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—22no—
328C22×D4D4×C1114yescomplemented
329C22×D4C23×C1112yes—
330C22×D4C23×C1112yes—
331C23×C4—28no—
332C23×C4—21no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—44no—
336C23×C4—44no—
337C23×C4D4×C1111yescharacteristic
338C23×C4D4×C1111yescharacteristic
339C23×C4C23×C1111yescharacteristic
340C2×D8—28no—
341C2×D8—28no—
342C2×D8—28no—
343C22×C8C23×C1114yes—
344#127—24no—
345#121—24no—
346#121—24no—
347#121—44no—
348#121—44no—
349C4×D4—28no—
350C4×D4—28no—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4—24no—
354C4×D4D4×C1118yescomplemented
355C2×C4⋊C4—21no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4C23×C1112yes—
360C2×C4⋊C4C23×C1112yes—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C42—24no—
368C2×C42D4×C1111yescharacteristic
369C2×C42D4×C1111yescharacteristic
370C2×C42C23×C1111yescharacteristic
371C2×C42C23×C1111yescharacteristic
372C4⋊C8—24no—
373#102—28no—
374#102—28no—
375C22⋊C8—24no—
376C2×C11—24no—
377C2×C11—48no—
378C2×C11—162no—
379C2×C11#284711yescharacteristic
380C2×C11C2×#44711yescharacteristic
381C2×C11#300611yescharacteristic
382C2×C11C2×#45911yescharacteristic
383C2×C11#303611yescharacteristic
384C2×C11#310011yescharacteristic
385C2×C11#310911yescharacteristic
386C24—24no—
387C24—24no—
388C24—24no—
389C24—22no—
390C24—22no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24C2×D4×C1111yescharacteristic
396C2×D4—24no—
397C2×D4—24no—
398C2×D4—216no—
399C2×D4—216no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—24no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—44no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4C2×D4×C1114yes—
418C2×D4C2×D4×C1114yes—
419C2×D4C11×#4114yes—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—28no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—28no—
430C22×C4—22no—
431C22×C4—41no—
432C22×C4—44no—
433C22×C4—432no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4C11×D814yescomplemented
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×D4×C1112yes—
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C11×#4112yes—
447C22×C4C24×C1111yescharacteristic
448D8—416no—
449C2×C8—24no—
450C2×C8—24no—
451C2×C8—24no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4C2×D4×C1114yes—
459C22⋊C4—28no—
460C22⋊C4—28no—
461C22⋊C4—44no—
462C22⋊C4—44no—
463C22⋊C4—44no—
464C42—22no—
465C42—22no—
466C42—22no—
467C42C2×D4×C1114yes—
468C11#3290211yescharacteristic, direct product factor, Sylow
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—216no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—48no—
478C23—48no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—48no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23C11×#12112yes—
495C23C2×C11×D812yes—
496C23C11×AGL(1,ℤ/8)12yes—
497C23C22×D4×C1111yescharacteristic
498D4—216no—
499D4—24no—
500D4—24no—
501D4—24no—
502D4—44no—
503D4—44no—
504D4—84no—
505D4—88no—
506D4—84no—
507D4C11×#12118yescomplemented
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—28no—
517C2×C4—21no—
518C2×C4—24no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—44no—
522C2×C4—416no—
523C2×C4—48no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—416no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4C11×#12012yes—
531C2×C4C11×#12012yes—
532C2×C4C11×#12112yes—
533C2×C4C2×C11×D812yes—
534C2×C4C2×C11×D812yes—
535C2×C4C11×AGL(1,ℤ/8)12yes—
536C2×C4C22×D4×C1111yescharacteristic
537C2×C4C22×D4×C1112yes—
538C2×C4C2×C11×#4112yes—
539C2×C4C2×C11×#4111yescharacteristic
540C8—44no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—28no—
548C22—432no—
549C22—44no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—44no—
554C22—44no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—82no—
560C22—82no—
561C22—82no—
562C22C11×#45914yescomplemented
563C22C2×C11×#12011yescharacteristic
564C22C2×C11×#12111yescharacteristic
565C22C11×#52511yescharacteristic
566C22C22×C11×D811yescharacteristic
567C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
568C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
569C22C11×#57511yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—44no—
574C4—41no—
575C4—82no—
576C4C11×#44714yescomplemented
577C4C2×C11×#12112yes—
578C4C11×#52512yes—
579C2—24no—
580C2—48no—
581C2—162no—
582C2C11×#284711yescharacteristic
583C2C2×C11×#44711yescharacteristic
584C2C11×#300611yescharacteristic
585C2C2×C11×#45911yescharacteristic
586C2C11×#303611yescharacteristic
587C2C11×#310011yescharacteristic
588C2C11×#310911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×D4×C11C2semidirect
2. C2×C11×#459C2semidirect
3. C2×C11×#447C2semidirect
4. C11×#2856C2semidirect
5. C11×#1879C2semidirect
6. C11×#1874C2semidirect
7. C11×#1802C2semidirect
8. C11×#1797C2semidirect
12. C2×C11×#127C22semidirect
26. C2×C11×C4⋊C8C22semidirect
28. C2×C11×#102C22semidirect
32. C11×#390C22semidirect
33. C11×#384C22semidirect
34. C11×#340C22semidirect
35. C11×#336C22semidirect
44. C22×D4×C11D4semidirect
70. C4×D4×C11D4semidirect
92. #32902C11direct (N × H)
146. C22×C4×C11D8semidirect
175. C22×C4×D4C2×C11semidirect
176. C2×#459C2×C11semidirect
177. C2×#447C2×C11semidirect
178. #2856C2×C11semidirect
179. #1879C2×C11semidirect
180. #1874C2×C11semidirect
181. #1802C2×C11semidirect
182. #1797C2×C11semidirect
221. D4×C11#121semidirect
258. C2×#127C22×C11semidirect
272. C2×C4⋊C8C22×C11semidirect
274. C2×#102C22×C11semidirect
278. #390C22×C11semidirect
279. #384C22×C11semidirect
280. #340C22×C11semidirect
281. #336C22×C11semidirect
303. C22×C11#459semidirect
317. C4×C11#447semidirect
328. C22×D4D4×C11semidirect
354. C4×D4D4×C11semidirect
439. C22×C4C11×D8semidirect
468. C11#32902direct (N × H)
507. D4C11×#121semidirect
562. C22C11×#459semidirect
576. C4C11×#447semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C112
C2×C11×#4592
C2×C11×#4472
C11×#28562
C11×#18792
C11×#18742
C11×#18022
C11×#17972
#3290211