Finite Group Databasebeta

← C11×#16298 #14593491

Subgroups — C11×#16298 #14593491

Order 2816.

2830 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#399C211yesmaximal, characteristic, complemented
2C2×C11×#396C212yesmaximal, complemented
3C2×C11×#379C211yesmaximal, characteristic
4C2×C11×#379C212yesmaximal
5C11×#1439C212yesmaximal, complemented
6C11×#1439C212yesmaximal, complemented
7C11×#1439C212yesmaximal, complemented
8C11×#1439C212yesmaximal, complemented
9C11×#1439C211yesmaximal, characteristic, complemented
10C26×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic, complemented
12C22×C11×C4⋊C4C2212yescomplemented
13C22×C11×C4⋊C4C2212yescomplemented
14C22×C11×C4⋊C4C2211yescharacteristic, complemented
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⋊C4C2212yes—
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2212yes—
24C22×C11×C22⋊C4C2211yescharacteristic
25C11×#399—24no—
26C11×#396—28no—
27C11×#379—28no—
28C11×#379—24no—
29C2×C11×#95C2212yescomplemented
30C2×C11×#95C2211yescharacteristic, complemented
31C2×C11×#95C2211yescharacteristic, complemented
32C2×C11×#95C2212yescomplemented
33C2×C11×#95C2212yescomplemented
34C2×C11×#95C2212yescomplemented
35C25×C11—24no—
36C25×C11—22no—
37C25×C11—22no—
38C25×C11—24no—
39C25×C11—41no—
40C25×C11—42no—
41C25×C11—42no—
42C25×C11—41no—
43C25×C11—41no—
44C25×C11—41no—
45C25×C11Q814yes—
46C25×C11C2312yes—
47C25×C11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—41no—
61C2×C11×C4⋊C4—42no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C4⋊C4—42no—
64C2×C11×C4⋊C4—41no—
65C2×C11×C4⋊C4—41no—
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—24no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—42no—
81C2×C11×C22⋊C4—41no—
82C2×C11×C22⋊C4—42no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—42no—
85C2×C11×C22⋊C4—42no—
86C2×C11×C22⋊C4—42no—
87C2×C11×C22⋊C4—42no—
88C2×C11×C22⋊C4—42no—
89C2×C11×C22⋊C4—42no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4—42no—
92C2×C11×C22⋊C4—42no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4D418yes—
95C2×C11×C22⋊C4D414yes—
96C11×#95—24no—
97C11×#95—22no—
98C11×#95—42no—
99C11×#95—41no—
100C11×#95—42no—
101C11×#95—42no—
102#16298C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—21no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—216no—
124C24×C11—28no—
125C24×C11—44no—
126C24×C11—48no—
127C24×C11—44no—
128C24×C11—44no—
129C24×C11—48no—
130C24×C11—48no—
131C24×C11—48no—
132C24×C11—48no—
133C24×C11—48no—
134C24×C11—44no—
135C24×C11—48no—
136C24×C11—44no—
137C24×C11—48no—
138C24×C11—44no—
139C24×C11—44no—
140C24×C11—48no—
141C24×C11—44no—
142C24×C11—48no—
143C24×C11—44no—
144C24×C11—44no—
145C24×C11—48no—
146C24×C11C2×D414yes—
147C24×C11C2×D412yes—
148C24×C11C2×Q814yes—
149C24×C11C2×Q812yes—
150C24×C11#4112yes—
151C24×C11#4114yes—
152C24×C11C2411yescharacteristic
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—21no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
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—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D414yes—
196C22×C4×C11C2×D414yes—
197C22×C4×C11C2×D412yes—
198C11×C4⋊C4—44no—
199C11×C4⋊C4—48no—
200C11×C4⋊C4—48no—
201C11×C4⋊C4—44no—
202C11×C22⋊C4—48no—
203C11×C22⋊C4—44no—
204C11×C22⋊C4—48no—
205C11×C22⋊C4—48no—
206C11×C22⋊C4—48no—
207C11×C22⋊C4—48no—
208C11×C22⋊C4—48no—
209C11×C22⋊C4—48no—
210C11×C22⋊C4—48no—
211C11×C22⋊C4—44no—
212C2×#399C2×C1111yescharacteristic, complemented
213C2×#396C2×C1112yescomplemented
214C2×#379C2×C1111yescharacteristic
215C2×#379C2×C1112yes—
216#1439C2×C1112yescomplemented
217#1439C2×C1112yescomplemented
218#1439C2×C1112yescomplemented
219#1439C2×C1112yescomplemented
220#1439C2×C1111yescharacteristic, complemented
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—22no—
231C23×C11—24no—
232C23×C11—22no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—22no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—416no—
252C23×C11—432no—
253C23×C11—432no—
254C23×C11—416no—
255C23×C11—416no—
256C23×C11—416no—
257C23×C11—416no—
258C23×C11—432no—
259C23×C11—432no—
260C23×C11—416no—
261C23×C11—416no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—41no—
275C23×C11—42no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—41no—
281C23×C11—42no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—42no—
285C23×C11—42no—
286C23×C11—42no—
287C23×C11—42no—
288C23×C11C22⋊Q818yes—
289C23×C11C22⋊Q814yes—
290C23×C11C22×D412yes—
291C23×C11C22×D411yescharacteristic
292C23×C11C22×Q811yescharacteristic
293C23×C11C2×#4111yescharacteristic
294C23×C11C2×#4112yes—
295C23×C11H(5,𝔽2)11yescharacteristic
296C23×C11H(5,𝔽2)11yescharacteristic
297C23×C11H(5,𝔽2)11yescharacteristic
298C23×C11H(5,𝔽2)12yes—
299C23×C11H(5,𝔽2)12yes—
300C23×C11H(5,𝔽2)11yescharacteristic
301C2×C4×C11—24no—
302C2×C4×C11—22no—
303C2×C4×C11—24no—
304C2×C4×C11—22no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—24no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—41no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—41no—
321C2×C4×C11—42no—
322C2×C4×C11—41no—
323C2×C4×C11—42no—
324C2×C4×C11—41no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C26C22×C1111yescharacteristic
347C22×C4⋊C4C22×C1111yescharacteristic, complemented
348C22×C4⋊C4C22×C1112yescomplemented
349C22×C4⋊C4C22×C1112yescomplemented
350C22×C4⋊C4C22×C1111yescharacteristic, complemented
351C22×C22⋊C4C22×C1112yes—
352C22×C22⋊C4C22×C1112yes—
353C22×C22⋊C4C22×C1112yes—
354C22×C22⋊C4C22×C1112yes—
355C22×C22⋊C4C22×C1112yes—
356C22×C22⋊C4C22×C1112yes—
357C22×C22⋊C4C22×C1112yes—
358C22×C22⋊C4C22×C1111yescharacteristic
359C22×C22⋊C4C22×C1112yes—
360C22×C22⋊C4C22×C1111yescharacteristic
361#399—24no—
362#396—28no—
363#379—28no—
364#379—24no—
365C2×#95C22×C1112yescomplemented
366C2×#95C22×C1111yescharacteristic, complemented
367C2×#95C22×C1112yescomplemented
368C2×#95C22×C1112yescomplemented
369C2×#95C22×C1111yescharacteristic, complemented
370C2×#95C22×C1112yescomplemented
371C22×C11—28no—
372C22×C11—24no—
373C22×C11—28no—
374C22×C11—28no—
375C22×C11—28no—
376C22×C11—464no—
377C22×C11—44no—
378C22×C11—42no—
379C22×C11—44no—
380C22×C11—44no—
381C22×C11—44no—
382C22×C11—44no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—44no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—44no—
391C22×C11—44no—
392C22×C11—42no—
393C22×C11—44no—
394C22×C11—42no—
395C22×C11—44no—
396C22×C11—42no—
397C22×C11—44no—
398C22×C11C2×C22⋊Q812yes—
399C22×C11C2×C22⋊Q811yescharacteristic
400C22×C11#53412yes—
401C22×C11#53411yescharacteristic
402C22×C11#53512yes—
403C22×C11#53511yescharacteristic
404C22×C11#53811yescharacteristic
405C22×C11#53812yes—
406C22×C11#53811yescharacteristic
407C22×C11#53812yes—
408C22×C11#54311yescharacteristic
409C22×C11#54312yes—
410C22×C11#54311yescharacteristic
411C22×C11D4211yescharacteristic
412C22×C11D4212yes—
413C22×C11#54612yes—
414C22×C11#54612yes—
415C22×C11#54612yes—
416C22×C11#55112yes—
417C22×C11#55111yescharacteristic
418C22×C11#56011yescharacteristic
419C22×C11#56011yescharacteristic
420C22×C11#56012yes—
421C4×C11—44no—
422C4×C11—42no—
423C4×C11—44no—
424C4×C11—42no—
425C4×C11—82no—
426C4×C11—82no—
427C4×C11—82no—
428C25—24no—
429C25—22no—
430C25—22no—
431C25—24no—
432C25—41no—
433C25—42no—
434C25—42no—
435C25—41no—
436C25—41no—
437C25—41no—
438C25Q8×C1114yes—
439C25C23×C1112yes—
440C25C23×C1111yescharacteristic
441C23×C4C23×C1112yes—
442C23×C4C23×C1112yes—
443C23×C4C23×C1112yes—
444C23×C4C23×C1111yescharacteristic
445C23×C4C23×C1112yes—
446C23×C4C23×C1112yes—
447C23×C4C23×C1111yescharacteristic
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—41no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—41no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—41no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—41no—
487C2×C22⋊C4D4×C1118yes—
488C2×C22⋊C4D4×C1114yes—
489#95—24no—
490#95—22no—
491#95—42no—
492#95—41no—
493#95—42no—
494#95—42no—
495C2×C11—48no—
496C2×C11—44no—
497C2×C11#243711yescharacteristic
498C2×C11#243712yes—
499C2×C11#262612yes—
500C2×C11#262611yescharacteristic
501C2×C11#266811yescharacteristic
502C2×C11#266911yescharacteristic
503C2×C11#267812yes—
504C2×C11#268512yes—
505C2×C11#269711yescharacteristic
506C2×C11#273511yescharacteristic
507C2×C11#284211yescharacteristic
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—21no—
516C24—21no—
517C24—22no—
518C24—21no—
519C24—22no—
520C24—22no—
521C24—21no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—216no—
529C24—28no—
530C24—44no—
531C24—48no—
532C24—44no—
533C24—44no—
534C24—48no—
535C24—48no—
536C24—48no—
537C24—48no—
538C24—48no—
539C24—44no—
540C24—48no—
541C24—44no—
542C24—48no—
543C24—44no—
544C24—44no—
545C24—48no—
546C24—44no—
547C24—48no—
548C24—44no—
549C24—44no—
550C24—48no—
551C24C2×D4×C1114yes—
552C24C2×D4×C1112yes—
553C24C2×Q8×C1114yes—
554C24C2×Q8×C1112yes—
555C24C11×#4112yes—
556C24C11×#4114yes—
557C24C24×C1111yescharacteristic
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4C2×D4×C1112yes—
600C22×C4C2×D4×C1114yes—
601C22×C4C2×D4×C1114yes—
602C22×C4C2×D4×C1112yes—
603C4⋊C4—44no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—44no—
607C22⋊C4—48no—
608C22⋊C4—44no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—44no—
617C11#1629811yescharacteristic, direct product factor, Sylow
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—416no—
649C23—432no—
650C23—432no—
651C23—416no—
652C23—416no—
653C23—416no—
654C23—432no—
655C23—432no—
656C23—416no—
657C23—416no—
658C23—416no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C11×C22⋊Q818yes—
686C23C11×C22⋊Q814yes—
687C23C22×D4×C1112yes—
688C23C22×D4×C1111yescharacteristic
689C23C22×Q8×C1111yescharacteristic
690C23C2×C11×#4111yescharacteristic
691C23C2×C11×#4112yes—
692C23C11×H(5,𝔽2)11yescharacteristic
693C23C11×H(5,𝔽2)11yescharacteristic
694C23C11×H(5,𝔽2)11yescharacteristic
695C23C11×H(5,𝔽2)12yes—
696C23C11×H(5,𝔽2)12yes—
697C23C11×H(5,𝔽2)11yescharacteristic
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C22—28no—
744C22—28no—
745C22—28no—
746C22—28no—
747C22—24no—
748C22—464no—
749C22—44no—
750C22—42no—
751C22—42no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—42no—
760C22—44no—
761C22—42no—
762C22—44no—
763C22—42no—
764C22—44no—
765C22—44no—
766C22—42no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22C2×C11×C22⋊Q812yes—
771C22C2×C11×C22⋊Q811yescharacteristic
772C22C11×#53412yes—
773C22C11×#53411yescharacteristic
774C22C11×#53512yes—
775C22C11×#53511yescharacteristic
776C22C11×#53811yescharacteristic
777C22C11×#53812yes—
778C22C11×#53811yescharacteristic
779C22C11×#53812yes—
780C22C11×#54311yescharacteristic
781C22C11×#54312yes—
782C22C11×#54311yescharacteristic
783C22D42×C1111yescharacteristic
784C22D42×C1112yes—
785C22C11×#54612yes—
786C22C11×#54612yes—
787C22C11×#54612yes—
788C22C11×#55112yes—
789C22C11×#55111yescharacteristic
790C22C11×#56011yescharacteristic
791C22C11×#56011yescharacteristic
792C22C11×#56012yes—
793C4—44no—
794C4—42no—
795C4—44no—
796C4—42no—
797C4—82no—
798C4—82no—
799C4—82no—
800C2—48no—
801C2—44no—
802C2C11×#243711yescharacteristic
803C2C11×#243712yes—
804C2C11×#262612yes—
805C2C11×#262611yescharacteristic
806C2C11×#266811yescharacteristic
807C2C11×#266911yescharacteristic
808C2C11×#267812yes—
809C2C11×#268512yes—
810C2C11×#269711yescharacteristic
811C2C11×#273511yescharacteristic
812C2C11×#284211yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC26×C11C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#399C2semidirect
2. C2×C11×#396C2semidirect
5. C11×#1439C2semidirect
6. C11×#1439C2semidirect
7. C11×#1439C2semidirect
8. C11×#1439C2semidirect
9. C11×#1439C2semidirect
11. C22×C11×C4⋊C4C22semidirect
12. C22×C11×C4⋊C4C22semidirect
13. C22×C11×C4⋊C4C22semidirect
14. C22×C11×C4⋊C4C22semidirect
29. C2×C11×#95C22semidirect
30. C2×C11×#95C22semidirect
31. C2×C11×#95C22semidirect
32. C2×C11×#95C22semidirect
33. C2×C11×#95C22semidirect
34. C2×C11×#95C22semidirect
102. #16298C11direct (N × H)
212. C2×#399C2×C11semidirect
213. C2×#396C2×C11semidirect
216. #1439C2×C11semidirect
217. #1439C2×C11semidirect
218. #1439C2×C11semidirect
219. #1439C2×C11semidirect
220. #1439C2×C11semidirect
347. C22×C4⋊C4C22×C11semidirect
348. C22×C4⋊C4C22×C11semidirect
349. C22×C4⋊C4C22×C11semidirect
350. C22×C4⋊C4C22×C11semidirect
365. C2×#95C22×C11semidirect
366. C2×#95C22×C11semidirect
367. C2×#95C22×C11semidirect
368. C2×#95C22×C11semidirect
369. C2×#95C22×C11semidirect
370. C2×#95C22×C11semidirect
617. C11#16298direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3992
C2×C11×#3962
C2×C11×#3792
C11×#14392
#1629811