Finite Group Databasebeta

← C11×#14513 #14591706

Subgroups — C11×#14513 #14591706

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#390C211yesmaximal, characteristic
2C2×C11×#386C211yesmaximal, characteristic
3C2×C11×#386C211yesmaximal, characteristic
4C11×#1442C212yesmaximal, complemented
5C11×#1439C212yesmaximal, complemented
6C11×#1439C212yesmaximal, complemented
7C11×#1436C212yesmaximal, complemented
8C11×C22⋊#95C212yesmaximal, complemented
9C11×C22⋊#95C212yesmaximal, complemented
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C11×#390—24no—
23C11×#386—24no—
24C11×#386C418yescomplemented
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C22×D4×C11—41no—
37C22×D4×C11—41no—
38C22×D4×C11—41no—
39C22×D4×C11—41no—
40C22×D4×C11C2×C414yes—
41C22×D4×C11D414yes—
42C22×D4×C11Q814yes—
43C23×C4×C11—22no—
44C23×C4×C11—24no—
45C23×C4×C11—41no—
46C23×C4×C11—41no—
47C23×C4×C11—41no—
48C23×C4×C11—41no—
49C23×C4×C11—42no—
50C23×C4×C11—42no—
51C23×C4×C11—42no—
52C23×C4×C11C2×C414yescomplemented
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—41no—
63C2×C11×C4⋊C4—41no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4—42no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—42no—
74C2×C11×C22⋊C4—42no—
75C2×C11×C22⋊C4—41no—
76C2×C11×C22⋊C4—41no—
77C2×C11×C22⋊C4—42no—
78C2×C11×C22⋊C4—42no—
79C2×C11×C22⋊C4—42no—
80C2×C11×C22⋊C4—41no—
81C2×C11×C22⋊C4—41no—
82C2×C11×C22⋊C4C2×C418yes—
83C2×C11×C22⋊C4C2×C414yescomplemented
84C2×C42×C11—22no—
85C2×C42×C11—41no—
86C2×C42×C11—41no—
87C11×#95—24no—
88C11×#95—24no—
89C11×#95—42no—
90C11×#95—42no—
91C11×#95—42no—
92C11×#95—42no—
93C11×#95—42no—
94C11×#95—42no—
95C11×#95C2×C418yescomplemented
96#14513C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—21no—
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11C22×C412yes—
114C24×C11C22×C412yes—
115C24×C11C2×D412yes—
116C24×C11C2×D412yes—
117C24×C11C2×Q812yes—
118C24×C11C2×Q812yes—
119C24×C11C2411yescharacteristic
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11C4⋊C4116yescomplemented
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
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—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—48no—
170C22×C4×C11—44no—
171C22×C4×C11—44no—
172C22×C4×C11—48no—
173C22×C4×C11—48no—
174C22×C4×C11—44no—
175C22×C4×C11—48no—
176C22×C4×C11—44no—
177C22×C4×C11—44no—
178C22×C4×C11—44no—
179C22×C4×C11C22×C414yes—
180C22×C4×C11C22×C414yes—
181C22×C4×C11C22×C412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2×Q812yes—
184C22×C4×C11#4114yes—
185C22×C4×C11#4114yes—
186C11×C4⋊C4—44no—
187C11×C4⋊C4—48no—
188C11×C22⋊C4—48no—
189C11×C22⋊C4—44no—
190C11×C22⋊C4—48no—
191C11×C22⋊C4—48no—
192C11×C22⋊C4—48no—
193C11×C22⋊C4—44no—
194C42×C11—44no—
195C2×#390C2×C1111yescharacteristic
196C2×#386C2×C1111yescharacteristic
197C2×#386C2×C1111yescharacteristic
198#1442C2×C1112yescomplemented
199#1439C2×C1112yescomplemented
200#1439C2×C1112yescomplemented
201#1436C2×C1112yescomplemented
202C22⋊#95C2×C1112yescomplemented
203C22⋊#95C2×C1112yescomplemented
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—42no—
243C23×C11—41no—
244C23×C11—42no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C2×C4⋊C414yes—
249C23×C11C2×C4⋊C414yes—
250C23×C11C23×C411yescharacteristic
251C23×C11C22×D411yescharacteristic
252C23×C11C22×Q811yescharacteristic
253C23×C11C2×#4112yes—
254C23×C11C2×#4112yes—
255C23×C11H(5,𝔽2)11yescharacteristic
256C23×C11H(5,𝔽2)11yescharacteristic
257C23×C11H(5,𝔽2)11yescharacteristic
258C23×C11H(5,𝔽2)11yescharacteristic
259C23×C11H(5,𝔽2)12yes—
260C23×C11H(5,𝔽2)12yes—
261D4×C11—416no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—416no—
281C2×C4×C11—416no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11C2×C4⋊C414yes—
313C23×D4C22×C1111yescharacteristic
314C24×C4C22×C1111yescharacteristic
315C24×C4C22×C1111yescharacteristic
316C22×C4⋊C4C22×C1112yes—
317C22×C4⋊C4C22×C1111yescharacteristic
318C22×C22⋊C4C22×C1112yes—
319C22×C22⋊C4C22×C1112yes—
320C22×C22⋊C4C22×C1112yes—
321C22×C22⋊C4C22×C1111yescharacteristic
322C22×C22⋊C4C22×C1112yes—
323C22×C22⋊C4C22×C1111yescharacteristic
324C22×C42C22×C1111yescharacteristic
325#390—24no—
326#386—24no—
327#386C4×C1118yescomplemented
328C2×#95C22×C1112yes—
329C2×#95C22×C1112yes—
330C2×#95C22×C1112yes—
331C2×#95C22×C1112yes—
332C2×#95C22×C1112yes—
333C2×#95C22×C1112yes—
334C2×#95C22×C1112yes—
335C2×#95C22×C1112yes—
336C2×#95C22×C1112yes—
337C22×C11—24no—
338C22×C11—24no—
339C22×C11—28no—
340C22×C11—28no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—44no—
350C22×C11—44no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—44no—
356C22×C11—44no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11C22×C4⋊C411yescharacteristic
360C22×C11C4×#4112yes—
361C22×C11#51811yescharacteristic
362C22×C11#51811yescharacteristic
363C22×C11#51812yes—
364C22×C11#53411yescharacteristic
365C22×C11#53411yescharacteristic
366C22×C11#53812yes—
367C22×C11#53812yes—
368C22×C11#54012yes—
369C22×C11#54012yes—
370C22×C11#54311yescharacteristic
371C22×C11#54311yescharacteristic
372C22×C11#54612yes—
373C22×C11#54612yes—
374C22×C11#55111yescharacteristic
375C22×C11#55312yes—
376C22×C11#55412yes—
377C22×C11#55412yes—
378C22×C11#55911yescharacteristic
379C22×C11#56012yes—
380C22×C11#56011yescharacteristic
381C22×C11H(3,𝔽4)11yescharacteristic
382C4×C11—24no—
383C4×C11—44no—
384C4×C11—44no—
385C4×C11—44no—
386C4×C11—44no—
387C4×C11—82no—
388C4×C11—82no—
389C25C23×C1111yescharacteristic
390C25C23×C1111yescharacteristic
391C22×D4—41no—
392C22×D4—41no—
393C22×D4—41no—
394C22×D4—41no—
395C22×D4C2×C4×C1114yes—
396C22×D4D4×C1114yes—
397C22×D4Q8×C1114yes—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—41no—
401C23×C4—41no—
402C23×C4—41no—
403C23×C4—41no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4C2×C4×C1114yescomplemented
408C23×C4C23×C1112yes—
409C23×C4C23×C1112yes—
410C23×C4C23×C1112yes—
411C23×C4C23×C1112yes—
412C23×C4C23×C1112yes—
413C23×C4C23×C1112yes—
414C23×C4C23×C1111yescharacteristic
415C2×C4⋊C4—22no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—41no—
431C2×C22⋊C4—41no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—41no—
436C2×C22⋊C4—41no—
437C2×C22⋊C4C2×C4×C1118yes—
438C2×C22⋊C4C2×C4×C1114yescomplemented
439C2×C42—22no—
440C2×C42—41no—
441C2×C42—41no—
442#95—24no—
443#95—24no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95C2×C4×C1118yescomplemented
451C2×C11—44no—
452C2×C11—44no—
453C2×C11#231511yescharacteristic
454C2×C11#233312yes—
455C2×C11#234912yes—
456C2×C11#237411yescharacteristic
457C2×C11#237511yescharacteristic
458C2×C11#268411yescharacteristic
459C2×C11#268812yes—
460C2×C11#270911yescharacteristic
461C2×C11#274811yescharacteristic
462C2×C11#278012yes—
463C2×C11#280411yescharacteristic
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24C22×C4×C1112yes—
481C24C22×C4×C1112yes—
482C24C2×D4×C1112yes—
483C24C2×D4×C1112yes—
484C24C2×Q8×C1112yes—
485C24C2×Q8×C1112yes—
486C24C24×C1111yescharacteristic
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4C11×C4⋊C4116yescomplemented
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—48no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—44no—
542C22×C4—48no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4C22×C4×C1114yes—
547C22×C4C22×C4×C1114yes—
548C22×C4C22×C4×C1112yes—
549C22×C4C2×D4×C1112yes—
550C22×C4C2×Q8×C1112yes—
551C22×C4C11×#4114yes—
552C22×C4C11×#4114yes—
553C4⋊C4—44no—
554C4⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—44no—
557C22⋊C4—48no—
558C22⋊C4—48no—
559C22⋊C4—48no—
560C22⋊C4—44no—
561C42—44no—
562C11#1451311yescharacteristic, direct product factor, Sylow
563C23—24no—
564C23—24no—
565C23—22no—
566C23—24no—
567C23—22no—
568C23—24no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—41no—
596C23—41no—
597C23—42no—
598C23—42no—
599C23—41no—
600C23—41no—
601C23—42no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23C2×C11×C4⋊C414yes—
608C23C2×C11×C4⋊C414yes—
609C23C23×C4×C1111yescharacteristic
610C23C22×D4×C1111yescharacteristic
611C23C22×Q8×C1111yescharacteristic
612C23C2×C11×#4112yes—
613C23C2×C11×#4112yes—
614C23C11×H(5,𝔽2)11yescharacteristic
615C23C11×H(5,𝔽2)11yescharacteristic
616C23C11×H(5,𝔽2)11yescharacteristic
617C23C11×H(5,𝔽2)11yescharacteristic
618C23C11×H(5,𝔽2)12yes—
619C23C11×H(5,𝔽2)12yes—
620D4—416no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—416no—
640C2×C4—416no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4C2×C11×C4⋊C414yes—
672C22—24no—
673C22—24no—
674C22—28no—
675C22—28no—
676C22—42no—
677C22—42no—
678C22—44no—
679C22—44no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—44no—
685C22—44no—
686C22—42no—
687C22—42no—
688C22—44no—
689C22—44no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22C22×C11×C4⋊C411yescharacteristic
695C22C4×C11×#4112yes—
696C22C11×#51811yescharacteristic
697C22C11×#51811yescharacteristic
698C22C11×#51812yes—
699C22C11×#53411yescharacteristic
700C22C11×#53411yescharacteristic
701C22C11×#53812yes—
702C22C11×#53812yes—
703C22C11×#54012yes—
704C22C11×#54012yes—
705C22C11×#54311yescharacteristic
706C22C11×#54311yescharacteristic
707C22C11×#54612yes—
708C22C11×#54612yes—
709C22C11×#55111yescharacteristic
710C22C11×#55312yes—
711C22C11×#55412yes—
712C22C11×#55412yes—
713C22C11×#55911yescharacteristic
714C22C11×#56012yes—
715C22C11×#56011yescharacteristic
716C22C11×H(3,𝔽4)11yescharacteristic
717C4—24no—
718C4—44no—
719C4—44no—
720C4—44no—
721C4—44no—
722C4—82no—
723C4—82no—
724C2—44no—
725C2—44no—
726C2C11×#231511yescharacteristic
727C2C11×#233312yes—
728C2C11×#234912yes—
729C2C11×#237411yescharacteristic
730C2C11×#237511yescharacteristic
731C2C11×#268411yescharacteristic
732C2C11×#268812yes—
733C2C11×#270911yescharacteristic
734C2C11×#274811yescharacteristic
735C2C11×#278012yes—
736C2C11×#280411yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1442C2semidirect
5. C11×#1439C2semidirect
6. C11×#1439C2semidirect
7. C11×#1436C2semidirect
8. C11×C22⋊#95C2semidirect
9. C11×C22⋊#95C2semidirect
24. C11×#386C4semidirect
52. C23×C4×C11C2×C4semidirect
83. C2×C11×C22⋊C4C2×C4semidirect
95. C11×#95C2×C4semidirect
96. #14513C11direct (N × H)
126. C2×D4×C11C4⋊C4semidirect
198. #1442C2×C11semidirect
199. #1439C2×C11semidirect
200. #1439C2×C11semidirect
201. #1436C2×C11semidirect
202. C22⋊#95C2×C11semidirect
203. C22⋊#95C2×C11semidirect
327. #386C4×C11semidirect
407. C23×C4C2×C4×C11semidirect
438. C2×C22⋊C4C2×C4×C11semidirect
450. #95C2×C4×C11semidirect
493. C2×D4C11×C4⋊C4semidirect
562. C11#14513direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3902
C2×C11×#3862
C11×#14422
C11×#14392
C11×#14362
C11×C22⋊#952
#1451311