Finite Group Databasebeta

← C11×#32938 #14610131

Subgroups — C11×#32938 #14610131

Order 2816.

1436 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#131C211yesmaximal, characteristic, complemented
2C2×C11×#468C212yesmaximal, complemented
3C2×C11×#465C211yesmaximal, characteristic, complemented
4C11×#2616C211yesmaximal, characteristic, complemented
5C11×#2615C211yesmaximal, characteristic
6C11×#1895C211yesmaximal, characteristic, complemented
7C11×#1894C211yesmaximal, characteristic, complemented
8C11×#1893C212yesmaximal, complemented
9C11×#1892C212yesmaximal, complemented
10C11×#1809C212yesmaximal, complemented
11C11×#1808C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×SD16C2211yescharacteristic
14C2×C11×#131—28no—
15C2×C11×#131—24no—
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2212yes—
18C23×C8×C11C2212yes—
19C23×C8×C11C2211yescharacteristic
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2212yes—
23C2×C11×#121C2211yescharacteristic
24C11×#468—28no—
25C11×#465—24no—
26C2×C11×#107C2212yes—
27C2×C11×#106C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2212yes—
32C11×#395—21no—
33C11×#394—22no—
34C11×#394—21no—
35C11×#393—21no—
36C11×#392—22no—
37C11×#392—21no—
38C11×#380C2212yes—
39C11×#380C2212yes—
40C11×#380C2211yescharacteristic
41C11×#380C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C2×C11×#41—24no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—24no—
49C22×Q8×C11D411yescharacteristic
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11D412yes—
54C22×D4×C11D411yescharacteristic
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C2×C11×SD16—22no—
59C2×C11×SD16—24no—
60C11×#131—232no—
61C2×C11×M16—22no—
62C2×C11×M16—24no—
63C2×C11×M16—24no—
64C2×C11×M16—24no—
65C2×C11×M16D418yescomplemented
66C22×C8×C11—24no—
67C22×C8×C11—24no—
68C22×C8×C11—24no—
69C22×C8×C11—24no—
70C22×C8×C11D414yescomplemented
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2312yes—
73C22×C8×C11C2311yescharacteristic
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—24no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—22no—
78C11×#121—22no—
79C11×#121—24no—
80C11×#121—24no—
81C11×#121—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—21no—
96C11×#107—24no—
97C11×#106—22no—
98C11×#103—22no—
99C11×#103—24no—
100C11×#102—22no—
101C11×#102—24no—
102C11×#95—22no—
103C11×#95—21no—
104C11×#95—22no—
105C11×#95—21no—
106#32938C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—21no—
108C24×C11C2×D411yescharacteristic
109C24×C11C2×D412yes—
110C11×#41—28no—
111C11×#41—216no—
112C11×#41—28no—
113C2×Q8×C11—22no—
114C2×Q8×C11—24no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×D4×C11—24no—
120C2×D4×C11—24no—
121C2×D4×C11—24no—
122C2×D4×C11—22no—
123C2×D4×C11—24no—
124C2×D4×C11—21no—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—42no—
129C2×D4×C11—44no—
130C2×D4×C11—82no—
131C2×D4×C11—82no—
132C2×D4×C11—82no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4112yes—
149C22×C4×C11#4114yes—
150C22×C4×C11C2411yescharacteristic
151C11×SD16—44no—
152C11×M16—28no—
153C11×M16—216no—
154C2×C8×C11—216no—
155C2×C8×C11—28no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11C2×D412yes—
160C2×C8×C11C2×D414yes—
161C2×C8×C11C2×D412yes—
162C2×C8×C11C2×D414yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—44no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—44no—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—44no—
177C11×C22⋊C4—81no—
178C11×C22⋊C4—82no—
179C11×C22⋊C4—81no—
180C11×C22⋊C4—82no—
181C22×#131C2×C1111yescharacteristic, complemented
182C2×#468C2×C1112yescomplemented
183C2×#465C2×C1111yescharacteristic, complemented
184#2616C2×C1111yescharacteristic, complemented
185#2615C2×C1111yescharacteristic
186#1895C2×C1111yescharacteristic, complemented
187#1894C2×C1111yescharacteristic, complemented
188#1893C2×C1112yescomplemented
189#1892C2×C1112yescomplemented
190#1809C2×C1112yescomplemented
191#1808C2×C1111yescharacteristic, complemented
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—21no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—21no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—41no—
205C23×C11—42no—
206C23×C11—41no—
207C23×C11#12112yes—
208C23×C11#12114yes—
209C23×C11C22×D411yescharacteristic
210Q8×C11—28no—
211Q8×C11—41no—
212Q8×C11—41no—
213Q8×C11—42no—
214D4×C11—216no—
215D4×C11—28no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—42no—
219D4×C11—84no—
220D4×C11—88no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11#12112yes—
245C2×C4×C11#12114yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D412yes—
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4112yes—
250C8×C11—22no—
251C8×C11—24no—
252C8×C11#12014yes—
253C22×#41C22×C1111yescharacteristic
254C22×SD16C22×C1111yescharacteristic
255C2×#131—28no—
256C2×#131—24no—
257C22×M16C22×C1111yescharacteristic
258C22×M16C22×C1112yes—
259C23×C8C22×C1112yes—
260C23×C8C22×C1111yescharacteristic
261C2×C22⋊Q8C22×C1112yes—
262C2×C22⋊Q8C22×C1111yescharacteristic
263C2×#121C22×C1112yes—
264C2×#121C22×C1111yescharacteristic
265#468—28no—
266#465—24no—
267C2×#107C22×C1112yes—
268C2×#106C22×C1111yescharacteristic
269C2×#103C22×C1111yescharacteristic
270C2×#103C22×C1112yes—
271C2×#102C22×C1111yescharacteristic
272C2×#102C22×C1112yes—
273#395—21no—
274#394—21no—
275#394—22no—
276#393—21no—
277#392—21no—
278#392—22no—
279#380C22×C1111yescharacteristic
280#380C22×C1111yescharacteristic
281#380C22×C1112yes—
282#380C22×C1112yes—
283#340C22×C1112yes—
284#340C22×C1112yes—
285#340C22×C1112yes—
286C22×C11—22no—
287C22×C11—24no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11C2×#12111yescharacteristic
304C22×C11C2×#12112yes—
305C22×C11#57611yescharacteristic
306C22×C11#57712yes—
307C22×C11#57811yescharacteristic
308C4×C11—24no—
309C4×C11—22no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11—81no—
313C4×C11—82no—
314C4×C11—82no—
315C4×C11C2×#12011yescharacteristic
316C4×C11#52512yes—
317C4×C11#52511yescharacteristic
318C2×#41—24no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—24no—
322C22×Q8D4×C1111yescharacteristic
323C22×Q8C23×C1111yescharacteristic
324C22×D4—22no—
325C22×D4—21no—
326C22×D4D4×C1112yes—
327C22×D4D4×C1111yescharacteristic
328C22×D4C23×C1111yescharacteristic
329C23×C4C23×C1112yes—
330C23×C4C23×C1111yescharacteristic
331C2×SD16—22no—
332C2×SD16—24no—
333#131—232no—
334C2×M16—22no—
335C2×M16—24no—
336C2×M16—24no—
337C2×M16—24no—
338C2×M16D4×C1118yescomplemented
339C22×C8—24no—
340C22×C8—24no—
341C22×C8—24no—
342C22×C8—24no—
343C22×C8D4×C1114yescomplemented
344C22×C8C23×C1111yescharacteristic
345C22×C8C23×C1112yes—
346C22×C8C23×C1111yescharacteristic
347C22⋊Q8—22no—
348C22⋊Q8—24no—
349C22⋊Q8—24no—
350C22⋊Q8—22no—
351#121—22no—
352#121—24no—
353#121—24no—
354#121—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4C23×C1111yescharacteristic
358C2×C4⋊C4C23×C1112yes—
359C2×C4⋊C4C23×C1111yescharacteristic
360C2×C4⋊C4C23×C1112yes—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369#107—24no—
370#106—22no—
371#103—22no—
372#103—24no—
373#102—22no—
374#102—24no—
375#95—21no—
376#95—22no—
377#95—21no—
378#95—22no—
379C2×C11—42no—
380C2×C11—44no—
381C2×C11—161no—
382C2×C11#284711yescharacteristic
383C2×C11#305711yescharacteristic
384C2×C11#306111yescharacteristic
385C2×C11#306212yes—
386C2×C11#306312yes—
387C24—21no—
388C24C2×D4×C1111yescharacteristic
389C24C2×D4×C1112yes—
390#41—28no—
391#41—216no—
392#41—28no—
393C2×Q8—22no—
394C2×Q8—24no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—24no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—22no—
408C2×D4—42no—
409C2×D4—44no—
410C2×D4—82no—
411C2×D4—82no—
412C2×D4—82no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4C2×D4×C1112yes—
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1114yes—
427C22×C4C2×D4×C1112yes—
428C22×C4C11×#4112yes—
429C22×C4C11×#4114yes—
430C22×C4C24×C1111yescharacteristic
431SD16—44no—
432M16—28no—
433M16—216no—
434C2×C8—216no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—28no—
439C2×C8C2×D4×C1112yes—
440C2×C8C2×D4×C1114yes—
441C2×C8C2×D4×C1112yes—
442C2×C8C2×D4×C1114yes—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—42no—
452C4⋊C4—44no—
453C22⋊C4—42no—
454C22⋊C4—44no—
455C22⋊C4—42no—
456C22⋊C4—44no—
457C22⋊C4—81no—
458C22⋊C4—82no—
459C22⋊C4—81no—
460C22⋊C4—82no—
461C11#3293811yescharacteristic, direct product factor, Sylow
462C23—22no—
463C23—22no—
464C23—22no—
465C23—21no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—21no—
471C23—22no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—42no—
476C23—41no—
477C23C11×#12112yes—
478C23C11×#12114yes—
479C23C22×D4×C1111yescharacteristic
480Q8—28no—
481Q8—41no—
482Q8—41no—
483Q8—42no—
484D4—216no—
485D4—28no—
486D4—41no—
487D4—41no—
488D4—42no—
489D4—84no—
490D4—88no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4C11×#12112yes—
515C2×C4C11×#12114yes—
516C2×C4C22×D4×C1111yescharacteristic
517C2×C4C22×D4×C1112yes—
518C2×C4C2×C11×#4111yescharacteristic
519C2×C4C2×C11×#4112yes—
520C8—22no—
521C8—24no—
522C8C11×#12014yes—
523C22—22no—
524C22—22no—
525C22—24no—
526C22—24no—
527C22—22no—
528C22—24no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—81no—
536C22—81no—
537C22—82no—
538C22—82no—
539C22—81no—
540C22C2×C11×#12111yescharacteristic
541C22C2×C11×#12112yes—
542C22C11×#57611yescharacteristic
543C22C11×#57712yes—
544C22C11×#57811yescharacteristic
545C4—24no—
546C4—22no—
547C4—81no—
548C4—81no—
549C4—82no—
550C4—82no—
551C4—81no—
552C4C2×C11×#12011yescharacteristic
553C4C11×#52512yes—
554C4C11×#52511yescharacteristic
555C2—42no—
556C2—44no—
557C2—161no—
558C2C11×#284711yescharacteristic
559C2C11×#305711yescharacteristic
560C2C11×#306111yescharacteristic
561C2C11×#306212yes—
562C2C11×#306312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#131C2semidirect
2. C2×C11×#468C2semidirect
3. C2×C11×#465C2semidirect
4. C11×#2616C2semidirect
6. C11×#1895C2semidirect
7. C11×#1894C2semidirect
8. C11×#1893C2semidirect
9. C11×#1892C2semidirect
10. C11×#1809C2semidirect
11. C11×#1808C2semidirect
65. C2×C11×M16D4semidirect
70. C22×C8×C11D4semidirect
106. #32938C11direct (N × H)
181. C22×#131C2×C11semidirect
182. C2×#468C2×C11semidirect
183. C2×#465C2×C11semidirect
184. #2616C2×C11semidirect
186. #1895C2×C11semidirect
187. #1894C2×C11semidirect
188. #1893C2×C11semidirect
189. #1892C2×C11semidirect
190. #1809C2×C11semidirect
191. #1808C2×C11semidirect
338. C2×M16D4×C11semidirect
343. C22×C8D4×C11semidirect
461. C11#32938direct (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×#4682
C2×C11×#4652
C11×#26162
C11×#26152
C11×#18952
C11×#18942
C11×#18932
C11×#18922
C11×#18092
C11×#18082
#3293811