Finite Group Databasebeta

← C11×#13912 #14591105

Subgroups — C11×#13912 #14591105

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C11C211yesmaximal, characteristic
2C2×C11×#388C212yesmaximal, complemented
3C2×C11×#381C211yesmaximal, characteristic, complemented
4C2×C11×#380C211yesmaximal, characteristic, complemented
5C11×#1441C212yesmaximal, complemented
6C11×#1438C212yesmaximal
7C11×#1437C212yesmaximal, complemented
8C11×#1434C211yesmaximal, characteristic, complemented
9C11×C22⋊#95C211yesmaximal, characteristic, complemented
10C11×C22⋊#95C211yesmaximal, characteristic, complemented
11C4×C11×#95C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C2×C4×D4×C11—28no—
16C2×C4×D4×C11C418yescomplemented
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2212yes—
22C22×C11×C22⋊C4C2212yes—
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2212yes—
26C22×C42×C11C2211yescharacteristic
27C11×#388—28no—
28C11×#381—24no—
29C11×#380—24no—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36C2×C11×#95C2212yes—
37C2×C11×#95C2212yes—
38C2×C11×#95C2212yes—
39C2×C11×#95C2211yescharacteristic
40C25×C11C2311yescharacteristic
41C25×C11C2311yescharacteristic
42C22×D4×C11—24no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—24no—
46C22×D4×C11C2×C414yes—
47C23×C4×C11—24no—
48C23×C4×C11—24no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—42no—
54C23×C4×C11—42no—
55C23×C4×C11C2×C414yes—
56C23×C4×C11C2×C414yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C4×D4×C11—232no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—42no—
71C2×C11×C4⋊C4C2×C414yes—
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—24no—
81C2×C11×C22⋊C4—42no—
82C2×C11×C22⋊C4—42no—
83C2×C11×C22⋊C4—42no—
84C2×C11×C22⋊C4—42no—
85C2×C11×C22⋊C4C2×C414yes—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C11×C22⋊C4D418yes—
88C2×C42×C11—24no—
89C2×C42×C11—24no—
90C2×C42×C11—24no—
91C2×C42×C11—42no—
92C2×C42×C11C2×C414yes—
93C11×#95—22no—
94C11×#95—24no—
95C11×#95—22no—
96C11×#95—24no—
97C11×#95—24no—
98C11×#95—24no—
99C11×#95—22no—
100C11×#95—24no—
101C11×#95—42no—
102C11×#95D414yescomplemented
103#13912C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—21no—
120C24×C11—21no—
121C24×C11C22×C412yes—
122C24×C11C22×C412yes—
123C24×C11C2×D414yes—
124C24×C11#4112yes—
125C24×C11#4112yes—
126C24×C11C2411yescharacteristic
127C2×D4×C11—216no—
128C2×D4×C11—216no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—28no—
144C22×C4×C11—21no—
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—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—28no—
161C22×C4×C11—28no—
162C22×C4×C11—28no—
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—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—44no—
179C22×C4×C11—48no—
180C22×C4×C11—48no—
181C22×C4×C11—48no—
182C22×C4×C11—48no—
183C22×C4×C11C22×C412yes—
184C22×C4×C11C22×C412yes—
185C22×C4×C11C22×C412yes—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C2×D414yes—
189C22×C4×C11C2×D414yes—
190C22×C4×C11C2×D414yes—
191C22×C4×C11C2×D412yes—
192C22×C4×C11#4114yes—
193C22×C4×C11#4114yes—
194C22×C4×C11#4112yes—
195C11×C4⋊C4—28no—
196C11×C4⋊C4—48no—
197C11×C22⋊C4—28no—
198C11×C22⋊C4—48no—
199C11×C22⋊C4—48no—
200C11×C22⋊C4—48no—
201C11×C22⋊C4—48no—
202C11×C22⋊C4C22⋊C4116yescomplemented
203C42×C11—28no—
204C42×C11—48no—
205C22×C4×D4C2×C1111yescharacteristic
206C2×#388C2×C1112yescomplemented
207C2×#381C2×C1111yescharacteristic, complemented
208C2×#380C2×C1111yescharacteristic, complemented
209#1441C2×C1112yescomplemented
210#1438C2×C1112yes—
211#1437C2×C1112yescomplemented
212#1434C2×C1111yescharacteristic, complemented
213C22⋊#95C2×C1111yescharacteristic, complemented
214C22⋊#95C2×C1111yescharacteristic, complemented
215C4×#95C2×C1111yescharacteristic, complemented
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—22no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—24no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—24no—
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—41no—
254C23×C11—42no—
255C23×C11—41no—
256C23×C11—42no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—42no—
260C23×C11C2×C22⋊C414yes—
261C23×C11#11714yes—
262C23×C11C23×C411yescharacteristic
263C23×C11C22×D412yes—
264C23×C11C22×D411yescharacteristic
265C23×C11C2×#4112yes—
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C23×C11C2×#4112yes—
270C23×C11H(5,𝔽2)12yes—
271C23×C11H(5,𝔽2)11yescharacteristic
272C23×C112−1+411yescharacteristic
273D4×C11—232no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
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—24no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
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—416no—
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—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
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—42no—
318C2×C4×C11—42no—
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×C11C2×C22⋊C414yes—
326C2×C4×C11C2×C22⋊C414yes—
327C2×C4×C11#11714yes—
328C2×C4×C11C4×D414yes—
329C23×D4C22×C1111yescharacteristic
330C24×C4C22×C1111yescharacteristic
331C24×C4C22×C1111yescharacteristic
332C2×C4×D4—28no—
333C2×C4×D4C4×C1118yescomplemented
334C22×C4⋊C4C22×C1112yes—
335C22×C4⋊C4C22×C1111yescharacteristic
336C22×C22⋊C4C22×C1112yes—
337C22×C22⋊C4C22×C1112yes—
338C22×C22⋊C4C22×C1112yes—
339C22×C22⋊C4C22×C1112yes—
340C22×C22⋊C4C22×C1111yescharacteristic
341C22×C22⋊C4C22×C1111yescharacteristic
342C22×C42C22×C1112yes—
343C22×C42C22×C1111yescharacteristic
344#388—28no—
345#381—24no—
346#380—24no—
347C2×#95C22×C1111yescharacteristic
348C2×#95C22×C1112yes—
349C2×#95C22×C1111yescharacteristic
350C2×#95C22×C1111yescharacteristic
351C2×#95C22×C1112yes—
352C2×#95C22×C1112yes—
353C2×#95C22×C1112yes—
354C2×#95C22×C1112yes—
355C2×#95C22×C1112yes—
356C2×#95C22×C1111yescharacteristic
357C22×C11—24no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—24no—
361C22×C11—24no—
362C22×C11—24no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—44no—
370C22×C11—44no—
371C22×C11—44no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—44no—
376C22×C11—44no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11C22×C22⋊C411yescharacteristic
380C22×C11C2×#11711yescharacteristic
381C22×C11C2×#11711yescharacteristic
382C22×C11C2×C4×D411yescharacteristic
383C22×C11C4×#4111yescharacteristic
384C22×C11#51811yescharacteristic
385C22×C11#52011yescharacteristic
386C22×C11#52512yes—
387C22×C11#52512yes—
388C22×C11#52912yes—
389C22×C11#53212yes—
390C22×C11#54012yes—
391C22×C11#54212yes—
392C22×C11D4212yes—
393C22×C11#54612yes—
394C22×C11#54612yes—
395C22×C11#54611yescharacteristic
396C22×C11#54712yes—
397C22×C11#54811yescharacteristic
398C22×C11#55112yes—
399C22×C11#55211yescharacteristic
400C22×C11#55311yescharacteristic
401C22×C11#55312yes—
402C4×C11—24no—
403C4×C11—24no—
404C4×C11—24no—
405C4×C11—24no—
406C4×C11—42no—
407C4×C11—44no—
408C4×C11—44no—
409C4×C11—82no—
410C4×C11—82no—
411C25C23×C1111yescharacteristic
412C25C23×C1111yescharacteristic
413C22×D4—24no—
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—24no—
417C22×D4C2×C4×C1114yes—
418C23×C4—24no—
419C23×C4—24no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4C2×C4×C1114yes—
427C23×C4C2×C4×C1114yes—
428C23×C4C23×C1112yes—
429C23×C4C23×C1112yes—
430C23×C4C23×C1111yescharacteristic
431C23×C4C23×C1112yes—
432C23×C4C23×C1112yes—
433C23×C4C23×C1111yescharacteristic
434C23×C4C23×C1111yescharacteristic
435C23×C4C23×C1111yescharacteristic
436C23×C4C23×C1111yescharacteristic
437C4×D4—232no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4C2×C4×C1114yes—
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—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4C2×C4×C1114yes—
457C2×C22⋊C4C2×C4×C1114yes—
458C2×C22⋊C4D4×C1118yes—
459C2×C42—24no—
460C2×C42—24no—
461C2×C42—24no—
462C2×C42—42no—
463C2×C42C2×C4×C1114yes—
464#95—22no—
465#95—24no—
466#95—22no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—22no—
471#95—24no—
472#95—42no—
473#95D4×C1114yescomplemented
474C2×C11—44no—
475C2×C11—44no—
476C2×C11#228011yescharacteristic
477C2×C11#229311yescharacteristic
478C2×C11#231911yescharacteristic
479C2×C11D4×C22⋊C411yescharacteristic
480C2×C11#233911yescharacteristic
481C2×C11#235211yescharacteristic
482C2×C11#235311yescharacteristic
483C2×C11#245712yes—
484C2×C11#246112yes—
485C2×C11#246412yes—
486C2×C11#246812yes—
487C24—21no—
488C24—21no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—21no—
493C24—21no—
494C24—22no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—21no—
499C24—21no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—21no—
504C24C22×C4×C1112yes—
505C24C22×C4×C1112yes—
506C24C2×D4×C1114yes—
507C24C11×#4112yes—
508C24C11×#4112yes—
509C24C24×C1111yescharacteristic
510C2×D4—216no—
511C2×D4—216no—
512C2×D4—28no—
513C2×D4—28no—
514C2×D4—28no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—28no—
527C22×C4—21no—
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—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4C22×C4×C1112yes—
567C22×C4C22×C4×C1112yes—
568C22×C4C22×C4×C1112yes—
569C22×C4C22×C4×C1112yes—
570C22×C4C22×C4×C1112yes—
571C22×C4C2×D4×C1114yes—
572C22×C4C2×D4×C1114yes—
573C22×C4C2×D4×C1114yes—
574C22×C4C2×D4×C1112yes—
575C22×C4C11×#4114yes—
576C22×C4C11×#4114yes—
577C22×C4C11×#4112yes—
578C4⋊C4—28no—
579C4⋊C4—48no—
580C22⋊C4—28no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4C11×C22⋊C4116yescomplemented
586C42—28no—
587C42—48no—
588C11#1391211yescharacteristic, direct product factor, Sylow
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23C2×C11×C22⋊C414yes—
634C23C11×#11714yes—
635C23C23×C4×C1111yescharacteristic
636C23C22×D4×C1112yes—
637C23C22×D4×C1111yescharacteristic
638C23C2×C11×#4112yes—
639C23C2×C11×#4111yescharacteristic
640C23C2×C11×#4111yescharacteristic
641C23C2×C11×#4111yescharacteristic
642C23C2×C11×#4112yes—
643C23C11×H(5,𝔽2)12yes—
644C23C11×H(5,𝔽2)11yescharacteristic
645C23C11×2−1+411yescharacteristic
646D4—232no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—416no—
673C2×C4—416no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4C2×C11×C22⋊C414yes—
699C2×C4C2×C11×C22⋊C414yes—
700C2×C4C11×#11714yes—
701C2×C4C4×D4×C1114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—44no—
709C22—44no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22C22×C11×C22⋊C411yescharacteristic
725C22C2×C11×#11711yescharacteristic
726C22C2×C11×#11711yescharacteristic
727C22C2×C4×D4×C1111yescharacteristic
728C22C4×C11×#4111yescharacteristic
729C22C11×#51811yescharacteristic
730C22C11×#52011yescharacteristic
731C22C11×#52512yes—
732C22C11×#52512yes—
733C22C11×#52912yes—
734C22C11×#53212yes—
735C22C11×#54012yes—
736C22C11×#54212yes—
737C22D42×C1112yes—
738C22C11×#54612yes—
739C22C11×#54612yes—
740C22C11×#54611yescharacteristic
741C22C11×#54712yes—
742C22C11×#54811yescharacteristic
743C22C11×#55112yes—
744C22C11×#55211yescharacteristic
745C22C11×#55311yescharacteristic
746C22C11×#55312yes—
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—44no—
752C4—44no—
753C4—42no—
754C4—82no—
755C4—82no—
756C2—44no—
757C2—44no—
758C2C11×#228011yescharacteristic
759C2C11×#229311yescharacteristic
760C2C11×#231911yescharacteristic
761C2D4×C11×C22⋊C411yescharacteristic
762C2C11×#233911yescharacteristic
763C2C11×#235211yescharacteristic
764C2C11×#235311yescharacteristic
765C2C11×#245712yes—
766C2C11×#246112yes—
767C2C11×#246412yes—
768C2C11×#246812yes—
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
2. C2×C11×#388C2semidirect
3. C2×C11×#381C2semidirect
4. C2×C11×#380C2semidirect
5. C11×#1441C2semidirect
7. C11×#1437C2semidirect
8. C11×#1434C2semidirect
9. C11×C22⋊#95C2semidirect
10. C11×C22⋊#95C2semidirect
11. C4×C11×#95C2semidirect
16. C2×C4×D4×C11C4semidirect
102. C11×#95D4semidirect
103. #13912C11direct (N × H)
202. C11×C22⋊C4C22⋊C4semidirect
206. C2×#388C2×C11semidirect
207. C2×#381C2×C11semidirect
208. C2×#380C2×C11semidirect
209. #1441C2×C11semidirect
211. #1437C2×C11semidirect
212. #1434C2×C11semidirect
213. C22⋊#95C2×C11semidirect
214. C22⋊#95C2×C11semidirect
215. C4×#95C2×C11semidirect
333. C2×C4×D4C4×C11semidirect
473. #95D4×C11semidirect
585. C22⋊C4C11×C22⋊C4semidirect
588. C11#13912direct (N × H)

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×#3882
C2×C11×#3812
C2×C11×#3802
C11×#14412
C11×#14382
C11×#14372
C11×#14342
C11×C22⋊#952
C4×C11×#952
#1391211