Finite Group Databasebeta

← C11×#14521 #14591714

Subgroups — C11×#14521 #14591714

Order 2816.

2282 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#392C211yesmaximal, characteristic
2C2×C11×#390C212yesmaximal, complemented
3C2×C11×#388C212yesmaximal, complemented
4C2×C11×#386C212yesmaximal, complemented
5C11×#1439C211yesmaximal, characteristic, complemented
6C11×#1439C212yesmaximal, complemented
7C11×#1438C212yesmaximal, complemented
8C11×#1436C212yesmaximal, complemented
9C11×C22⋊#95C211yesmaximal, characteristic, complemented
10C23×D4×C11C2212yes—
11C23×D4×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⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2212yes—
24C11×#392C418yescomplemented
25C11×#390—28no—
26C11×#388—28no—
27C11×#386—28no—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2212yes—
35C25×C11C2312yes—
36C25×C11C2311yescharacteristic
37C22×D4×C11—24no—
38C22×D4×C11—24no—
39C22×D4×C11—24no—
40C22×D4×C11—24no—
41C22×D4×C11—42no—
42C22×D4×C11—42no—
43C22×D4×C11—42no—
44C22×D4×C11—42no—
45C22×D4×C11—41no—
46C22×D4×C11—41no—
47C22×D4×C11C2×C418yes—
48C22×D4×C11C2×C414yescomplemented
49C23×C4×C11—22no—
50C23×C4×C11—24no—
51C23×C4×C11—42no—
52C23×C4×C11—41no—
53C23×C4×C11—41no—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2312yes—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4—41no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—24no—
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—24no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—41no—
77C2×C11×C22⋊C4—41no—
78C2×C11×C22⋊C4—41no—
79C2×C11×C22⋊C4—41no—
80C2×C11×C22⋊C4—42no—
81C2×C11×C22⋊C4—42no—
82C2×C11×C22⋊C4—42no—
83C2×C11×C22⋊C4—42no—
84C2×C11×C22⋊C4—42no—
85C2×C11×C22⋊C4—42no—
86C2×C11×C22⋊C4—42no—
87C2×C11×C22⋊C4C2×C414yes—
88C2×C11×C22⋊C4C2×C418yescomplemented
89C2×C11×C22⋊C4D414yescomplemented
90C2×C42×C11—24no—
91C2×C42×C11—24no—
92C2×C42×C11—42no—
93C11×#95—24no—
94C11×#95—24no—
95C11×#95—42no—
96C11×#95—41no—
97C11×#95—42no—
98C11×#95C2×C414yescomplemented
99C11×#95D418yescomplemented
100#14521C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—21no—
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—21no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11C22×C414yes—
124C24×C11C22×C412yes—
125C24×C11C2×D412yes—
126C24×C11#4112yes—
127C24×C11C2411yescharacteristic
128C2×D4×C11—216no—
129C2×D4×C11—216no—
130C2×D4×C11—48no—
131C2×D4×C11—44no—
132C2×D4×C11—48no—
133C2×D4×C11—48no—
134C2×D4×C11—48no—
135C2×D4×C11—48no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
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—21no—
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—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—44no—
178C22×C4×C11—48no—
179C22×C4×C11—48no—
180C22×C4×C11—44no—
181C22×C4×C11—44no—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C22×C412yes—
184C22×C4×C11C22×C414yes—
185C22×C4×C11C2×D414yes—
186C22×C4×C11C2×D414yes—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2×D414yes—
189C22×C4×C11#4114yes—
190C11×C4⋊C4—48no—
191C11×C4⋊C4—44no—
192C11×C22⋊C4—216no—
193C11×C22⋊C4—44no—
194C11×C22⋊C4—44no—
195C11×C22⋊C4—48no—
196C11×C22⋊C4—48no—
197C11×C22⋊C4—48no—
198C11×C22⋊C4—48no—
199C11×C22⋊C4—48no—
200C42×C11—48no—
201C2×#392C2×C1111yescharacteristic
202C2×#390C2×C1112yescomplemented
203C2×#388C2×C1112yescomplemented
204C2×#386C2×C1112yescomplemented
205#1439C2×C1111yescharacteristic, complemented
206#1439C2×C1112yescomplemented
207#1438C2×C1112yescomplemented
208#1436C2×C1112yescomplemented
209C22⋊#95C2×C1111yescharacteristic, complemented
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—24no—
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—24no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—41no—
234C23×C11—42no—
235C23×C11—41no—
236C23×C11—42no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11C4×D414yes—
268C23×C11C23×C411yescharacteristic
269C23×C11C22×D411yescharacteristic
270C23×C11C22×D412yes—
271C23×C11C2×#4111yescharacteristic
272C23×C11C2×#4112yes—
273C23×C11H(5,𝔽2)11yescharacteristic
274C23×C11H(5,𝔽2)12yes—
275C23×C11H(5,𝔽2)11yescharacteristic
276C23×C11H(5,𝔽2)12yes—
277C23×C11H(5,𝔽2)11yescharacteristic
278C23×C112−1+411yescharacteristic
279D4×C11—432no—
280D4×C11—416no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—416no—
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—41no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—41no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—41no—
317C2×C4×C11—42no—
318C2×C4×C11—41no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11C4×D418yes—
327C23×D4C22×C1112yes—
328C23×D4C22×C1111yescharacteristic
329C24×C4C22×C1111yescharacteristic
330C22×C4⋊C4C22×C1112yes—
331C22×C4⋊C4C22×C1111yescharacteristic
332C22×C22⋊C4C22×C1112yes—
333C22×C22⋊C4C22×C1112yes—
334C22×C22⋊C4C22×C1112yes—
335C22×C22⋊C4C22×C1112yes—
336C22×C22⋊C4C22×C1112yes—
337C22×C22⋊C4C22×C1112yes—
338C22×C22⋊C4C22×C1111yescharacteristic
339C22×C22⋊C4C22×C1111yescharacteristic
340C22×C42C22×C1112yes—
341#392C4×C1118yescomplemented
342#390—28no—
343#388—28no—
344#386—28no—
345C2×#95C22×C1112yes—
346C2×#95C22×C1112yes—
347C2×#95C22×C1112yes—
348C2×#95C22×C1112yes—
349C2×#95C22×C1111yescharacteristic
350C2×#95C22×C1111yescharacteristic
351C2×#95C22×C1112yes—
352C22×C11—24no—
353C22×C11—28no—
354C22×C11—44no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—44no—
359C22×C11—42no—
360C22×C11—44no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—44no—
364C22×C11—44no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11—44no—
369C22×C11—44no—
370C22×C11—82no—
371C22×C11—82no—
372C22×C11—82no—
373C22×C11—82no—
374C22×C11—82no—
375C22×C11—82no—
376C22×C11—82no—
377C22×C11—82no—
378C22×C11C2×C4×D412yes—
379C22×C11C2×C4×D411yescharacteristic
380C22×C11#51812yes—
381C22×C11#51811yescharacteristic
382C22×C11#52011yescharacteristic
383C22×C11#53411yescharacteristic
384C22×C11#53512yes—
385C22×C11#53712yes—
386C22×C11#53711yescharacteristic
387C22×C11#53811yescharacteristic
388C22×C11#53911yescharacteristic
389C22×C11#54012yes—
390C22×C11#54212yes—
391C22×C11D4212yes—
392C22×C11D4211yescharacteristic
393C22×C11#54612yes—
394C22×C11#54612yes—
395C22×C11#55012yes—
396C22×C11#55112yes—
397C22×C11#55911yescharacteristic
398C22×C11#56012yes—
399C22×C11#56011yescharacteristic
400C22×C11H(3,𝔽4)11yescharacteristic
401C4×C11—28no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—44no—
405C4×C11—44no—
406C4×C11—44no—
407C4×C11—82no—
408C25C23×C1112yes—
409C25C23×C1111yescharacteristic
410C22×D4—24no—
411C22×D4—24no—
412C22×D4—24no—
413C22×D4—24no—
414C22×D4—42no—
415C22×D4—42no—
416C22×D4—42no—
417C22×D4—42no—
418C22×D4—41no—
419C22×D4—41no—
420C22×D4C2×C4×C1118yes—
421C22×D4C2×C4×C1114yescomplemented
422C23×C4—22no—
423C23×C4—24no—
424C23×C4—42no—
425C23×C4—41no—
426C23×C4—41no—
427C23×C4C23×C1112yes—
428C23×C4C23×C1111yescharacteristic
429C23×C4C23×C1111yescharacteristic
430C23×C4C23×C1112yes—
431C23×C4C23×C1112yes—
432C23×C4C23×C1112yes—
433C23×C4C23×C1112yes—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—41no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—41no—
450C2×C22⋊C4—41no—
451C2×C22⋊C4—41no—
452C2×C22⋊C4—41no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4C2×C4×C1114yes—
461C2×C22⋊C4C2×C4×C1118yescomplemented
462C2×C22⋊C4D4×C1114yescomplemented
463C2×C42—24no—
464C2×C42—24no—
465C2×C42—42no—
466#95—24no—
467#95—24no—
468#95—42no—
469#95—41no—
470#95—42no—
471#95C2×C4×C1114yescomplemented
472#95D4×C1118yescomplemented
473C2×C11—44no—
474C2×C11—84no—
475C2×C11#232412yes—
476C2×C11#232511yescharacteristic
477C2×C11#235812yes—
478C2×C11#236611yescharacteristic
479C2×C11#237511yescharacteristic
480C2×C11#267011yescharacteristic
481C2×C11#267312yes—
482C2×C11#267511yescharacteristic
483C2×C11#270512yes—
484C2×C11#271211yescharacteristic
485C2×C11#275211yescharacteristic
486C24—22no—
487C24—22no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24C22×C4×C1114yes—
509C24C22×C4×C1112yes—
510C24C2×D4×C1112yes—
511C24C11×#4112yes—
512C24C24×C1111yescharacteristic
513C2×D4—216no—
514C2×D4—216no—
515C2×D4—48no—
516C2×D4—44no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—44no—
524C2×D4—44no—
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—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—44no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4C22×C4×C1112yes—
568C22×C4C22×C4×C1112yes—
569C22×C4C22×C4×C1114yes—
570C22×C4C2×D4×C1114yes—
571C22×C4C2×D4×C1114yes—
572C22×C4C2×D4×C1114yes—
573C22×C4C2×D4×C1114yes—
574C22×C4C11×#4114yes—
575C4⋊C4—48no—
576C4⋊C4—44no—
577C22⋊C4—216no—
578C22⋊C4—44no—
579C22⋊C4—44no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C42—48no—
586C11#1452111yescharacteristic, direct product factor, Sylow
587C23—24no—
588C23—22no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23—41no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23C4×D4×C1114yes—
645C23C23×C4×C1111yescharacteristic
646C23C22×D4×C1111yescharacteristic
647C23C22×D4×C1112yes—
648C23C2×C11×#4111yescharacteristic
649C23C2×C11×#4112yes—
650C23C11×H(5,𝔽2)11yescharacteristic
651C23C11×H(5,𝔽2)12yes—
652C23C11×H(5,𝔽2)11yescharacteristic
653C23C11×H(5,𝔽2)12yes—
654C23C11×H(5,𝔽2)11yescharacteristic
655C23C11×2−1+411yescharacteristic
656D4—432no—
657D4—416no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—416no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4C4×D4×C1118yes—
704C22—24no—
705C22—28no—
706C22—42no—
707C22—44no—
708C22—42no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—82no—
723C22—82no—
724C22—82no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22C2×C4×D4×C1112yes—
731C22C2×C4×D4×C1111yescharacteristic
732C22C11×#51812yes—
733C22C11×#51811yescharacteristic
734C22C11×#52011yescharacteristic
735C22C11×#53411yescharacteristic
736C22C11×#53512yes—
737C22C11×#53712yes—
738C22C11×#53711yescharacteristic
739C22C11×#53811yescharacteristic
740C22C11×#53911yescharacteristic
741C22C11×#54012yes—
742C22C11×#54212yes—
743C22D42×C1111yescharacteristic
744C22D42×C1112yes—
745C22C11×#54612yes—
746C22C11×#54612yes—
747C22C11×#55012yes—
748C22C11×#55112yes—
749C22C11×#55911yescharacteristic
750C22C11×#56012yes—
751C22C11×#56011yescharacteristic
752C22C11×H(3,𝔽4)11yescharacteristic
753C4—28no—
754C4—44no—
755C4—44no—
756C4—44no—
757C4—42no—
758C4—42no—
759C4—82no—
760C2—44no—
761C2—84no—
762C2C11×#232412yes—
763C2C11×#232511yescharacteristic
764C2C11×#235812yes—
765C2C11×#236611yescharacteristic
766C2C11×#237511yescharacteristic
767C2C11×#267011yescharacteristic
768C2C11×#267312yes—
769C2C11×#267511yescharacteristic
770C2C11×#270512yes—
771C2C11×#271211yescharacteristic
772C2C11×#275211yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#390C2semidirect
3. C2×C11×#388C2semidirect
4. C2×C11×#386C2semidirect
5. C11×#1439C2semidirect
6. C11×#1439C2semidirect
7. C11×#1438C2semidirect
8. C11×#1436C2semidirect
9. C11×C22⋊#95C2semidirect
24. C11×#392C4semidirect
48. C22×D4×C11C2×C4semidirect
88. C2×C11×C22⋊C4C2×C4semidirect
89. C2×C11×C22⋊C4D4semidirect
98. C11×#95C2×C4semidirect
99. C11×#95D4semidirect
100. #14521C11direct (N × H)
202. C2×#390C2×C11semidirect
203. C2×#388C2×C11semidirect
204. C2×#386C2×C11semidirect
205. #1439C2×C11semidirect
206. #1439C2×C11semidirect
207. #1438C2×C11semidirect
208. #1436C2×C11semidirect
209. C22⋊#95C2×C11semidirect
341. #392C4×C11semidirect
421. C22×D4C2×C4×C11semidirect
461. C2×C22⋊C4C2×C4×C11semidirect
462. C2×C22⋊C4D4×C11semidirect
471. #95C2×C4×C11semidirect
472. #95D4×C11semidirect
586. C11#14521direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3922
C2×C11×#3902
C2×C11×#3882
C2×C11×#3862
C11×#14392
C11×#14382
C11×#14362
C11×C22⋊#952
#1452111