Finite Group Databasebeta

← C11×#11113 #14588306

Subgroups — C11×#11113 #14588306

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic, complemented
2C22×C11×#104C211yesmaximal, characteristic
3C2×C11×#417C211yesmaximal, characteristic
4C11×#2311C211yesmaximal, characteristic
5C2×C11×#343C211yesmaximal, characteristic, complemented
6C2×C11×#339C211yesmaximal, characteristic, complemented
7C11×C4⋊#95C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C11×#428—22no—
16C11×#428—22no—
17C2×C11×#107—21no—
18C2×C11×#106—21no—
19C2×C11×#104—22no—
20C2×C11×#104—22no—
21C2×C11×#104C414yescomplemented
22C11×#417—22no—
23C11×#417—22no—
24C2×C11×#103—21no—
25C2×C11×#102—21no—
26C11×#391—21no—
27C11×#390—21no—
28C11×#386—22no—
29C11×#380—21no—
30C11×#380—21no—
31C2×C11×#95—22no—
32C11×#343—22no—
33C11×#339—22no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41C2×C412yes—
45C2×C11×#41Q812yes—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11D412yes—
53C23×C4×C11C2311yescharacteristic
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16C2×C412yes—
63C2×C11×M16D412yes—
64C2×C11×M16D412yes—
65C2×C11×M16D412yes—
66C22×C8×C11—21no—
67C22×C8×C11—21no—
68C11×#117—21no—
69C11×#117—21no—
70C11×#117—21no—
71C11×#117—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D412yes—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C2×C42×C11C2×C412yes—
96C11×#107—24no—
97C11×#106—24no—
98C11×#104—28no—
99C11×#103—24no—
100C11×#102—24no—
101C11×#95—22no—
102C11×#95—22no—
103C11×#95—44no—
104#11113C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11—21no—
106C24×C11C2×D411yescharacteristic
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—22no—
110C11×#41—22no—
111C11×#41—22no—
112C11×#41—22no—
113C11×#41—22no—
114C11×#41—22no—
115C11×#41—41no—
116C11×#41—41no—
117C11×#41—41no—
118C11×#41—41no—
119C11×#41—41no—
120C11×#41—41no—
121C11×#41—41no—
122C11×#41—41no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11C4⋊C412yes—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C2×D4×C11C4⋊C412yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11—41no—
160C22×C4×C11—41no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×Q811yescharacteristic
175C22×C4×C11#4111yescharacteristic
176C22×C4×C11#4111yescharacteristic
177C22×C4×C11#4111yescharacteristic
178C22×C4×C11#4111yescharacteristic
179C22×C4×C11#4111yescharacteristic
180C22×C4×C11#4111yescharacteristic
181C11×M16—22no—
182C11×M16—22no—
183C11×M16—22no—
184C11×M16—22no—
185C11×M16—22no—
186C11×M16—41no—
187C11×M16—41no—
188C11×M16C22⋊C414yescomplemented
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C2×C8×C11—22no—
192C2×C8×C11—22no—
193C2×C8×C11—41no—
194C2×C8×C11—41no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—41no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4—41no—
204C11×C4⋊C4—41no—
205C11×C4⋊C4—41no—
206C11×C4⋊C4—41no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—41no—
209C11×C22⋊C4—82no—
210C11×C22⋊C4—82no—
211C42×C11—22no—
212C42×C11—22no—
213C42×C11—41no—
214C42×C11—41no—
215C42×C11—41no—
216C42×C11—41no—
217C2×#428C2×C1111yescharacteristic, complemented
218C22×#104C2×C1111yescharacteristic
219C2×#417C2×C1111yescharacteristic
220#2311C2×C1111yescharacteristic
221C2×#343C2×C1111yescharacteristic, complemented
222C2×#339C2×C1111yescharacteristic, complemented
223C4⋊#95C2×C1111yescharacteristic, complemented
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C4×D411yescharacteristic
236C23×C11#12011yescharacteristic
237C23×C11#12111yescharacteristic
238C23×C11#12111yescharacteristic
239C23×C11C22⋊Q811yescharacteristic
240C23×C11#12311yescharacteristic
241C23×C11#12711yescharacteristic
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11—41no—
245Q8×C11—41no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—41no—
253D4×C11—41no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—44no—
269C2×C4×C11—44no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—41no—
275C2×C4×C11—42no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—42no—
279C2×C4×C11—41no—
280C2×C4×C11—82no—
281C2×C4×C11—81no—
282C2×C4×C11—81no—
283C2×C4×C11—82no—
284C2×C4×C11C2×C22⋊C411yescharacteristic
285C2×C4×C11C2×C4⋊C411yescharacteristic
286C2×C4×C11#11711yescharacteristic
287C2×C4×C11C4×D411yescharacteristic
288C2×C4×C11C4×D411yescharacteristic
289C2×C4×C11C4×D411yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11#12111yescharacteristic
293C2×C4×C11#12111yescharacteristic
294C2×C4×C11#12111yescharacteristic
295C2×C4×C11#12111yescharacteristic
296C2×C4×C11#12111yescharacteristic
297C2×C4×C11#12111yescharacteristic
298C2×C4×C11C22⋊Q811yescharacteristic
299C2×C4×C11C22⋊Q811yescharacteristic
300C2×C4×C11C22⋊Q811yescharacteristic
301C2×C4×C11C22⋊Q811yescharacteristic
302C2×C4×C11C22⋊Q811yescharacteristic
303C2×C4×C11#12311yescharacteristic
304C2×C4×C11#12311yescharacteristic
305C2×C4×C11#12311yescharacteristic
306C2×C4×C11#12311yescharacteristic
307C2×C4×C11#12411yescharacteristic
308C2×C4×C11#12411yescharacteristic
309C2×C4×C11#12411yescharacteristic
310C2×C4×C11#12611yescharacteristic
311C2×C4×C11#12611yescharacteristic
312C8×C11—24no—
313C8×C11—42no—
314C22×#41C22×C1111yescharacteristic
315C22×M16C22×C1111yescharacteristic
316C22×M16C22×C1111yescharacteristic
317C2×#117C22×C1111yescharacteristic
318C22×C4⋊C4C22×C1111yescharacteristic
319C22×C4⋊C4C22×C1111yescharacteristic
320C22×C42C22×C1111yescharacteristic
321#428—22no—
322#428—22no—
323C2×#107—21no—
324C2×#106—21no—
325C2×#104—22no—
326C2×#104—22no—
327C2×#104C4×C1114yescomplemented
328#417—22no—
329#417—22no—
330C2×#103—21no—
331C2×#102—21no—
332#391—21no—
333#390—21no—
334#386—22no—
335#380—21no—
336#380—21no—
337C2×#95—22no—
338#343—22no—
339#339—22no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—21no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11#38511yescharacteristic
360C22×C11#38811yescharacteristic
361C22×C11#39011yescharacteristic
362C22×C11#39211yescharacteristic
363C22×C11#39411yescharacteristic
364C22×C11#39611yescharacteristic
365C22×C11#39911yescharacteristic
366C22×C11#45311yescharacteristic
367C22×C11#45411yescharacteristic
368C22×C11#45511yescharacteristic
369C22×C11#45611yescharacteristic
370C4×C11—44no—
371C4×C11—42no—
372C4×C11—81no—
373C4×C11—82no—
374C4×C11—81no—
375C4×C11—82no—
376C4×C11#38011yescharacteristic
377C4×C11#38511yescharacteristic
378C4×C11#38611yescharacteristic
379C4×C11#38811yescharacteristic
380C4×C11#39311yescharacteristic
381C4×C11#39411yescharacteristic
382C4×C11#39611yescharacteristic
383C4×C11#39711yescharacteristic
384C2×#41—21no—
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—21no—
388C2×#41—21no—
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—21no—
392C2×#41—21no—
393C2×#41—21no—
394C2×#41C2×C4×C1112yes—
395C2×#41Q8×C1112yes—
396C22×Q8D4×C1111yescharacteristic
397C22×D4—21no—
398C22×D4D4×C1111yescharacteristic
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—21no—
402C23×C4D4×C1112yes—
403C23×C4C23×C1111yescharacteristic
404C2×M16—21no—
405C2×M16—21no—
406C2×M16—21no—
407C2×M16—21no—
408C2×M16—21no—
409C2×M16—21no—
410C2×M16—21no—
411C2×M16—21no—
412C2×M16C2×C4×C1112yes—
413C2×M16D4×C1112yes—
414C2×M16D4×C1112yes—
415C2×M16D4×C1112yes—
416C22×C8—21no—
417C22×C8—21no—
418#117—21no—
419#117—21no—
420#117—21no—
421#117—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C1112yes—
434C2×C4⋊C4D4×C1111yescharacteristic
435C2×C4⋊C4D4×C1111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42C2×C4×C1112yes—
446#107—24no—
447#106—24no—
448#104—28no—
449#103—24no—
450#102—24no—
451#95—22no—
452#95—22no—
453#95—44no—
454C2×C11—21no—
455C2×C11—21no—
456C2×C11—21no—
457C2×C11—21no—
458C2×C11—82no—
459C2×C11#143911yescharacteristic
460C2×C11#185911yescharacteristic
461C2×C11#186011yescharacteristic
462C2×C11#200611yescharacteristic
463C2×C11#200711yescharacteristic
464C2×C11#203711yescharacteristic
465C2×C11#203811yescharacteristic
466C24—21no—
467C24C2×D4×C1111yescharacteristic
468#41—22no—
469#41—22no—
470#41—22no—
471#41—22no—
472#41—22no—
473#41—22no—
474#41—22no—
475#41—22no—
476#41—41no—
477#41—41no—
478#41—41no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C11×C4⋊C412yes—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4C11×C4⋊C412yes—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4C22×C4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×Q8×C1111yescharacteristic
536C22×C4C11×#4111yescharacteristic
537C22×C4C11×#4111yescharacteristic
538C22×C4C11×#4111yescharacteristic
539C22×C4C11×#4111yescharacteristic
540C22×C4C11×#4111yescharacteristic
541C22×C4C11×#4111yescharacteristic
542M16—22no—
543M16—22no—
544M16—22no—
545M16—22no—
546M16—22no—
547M16—41no—
548M16—41no—
549M16C11×C22⋊C414yescomplemented
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—41no—
555C2×C8—41no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—82no—
571C22⋊C4—82no—
572C42—22no—
573C42—22no—
574C42—41no—
575C42—41no—
576C42—41no—
577C42—41no—
578C11#1111311yescharacteristic, direct product factor, Sylow
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23C4×D4×C1111yescharacteristic
591C23C11×#12011yescharacteristic
592C23C11×#12111yescharacteristic
593C23C11×#12111yescharacteristic
594C23C11×C22⋊Q811yescharacteristic
595C23C11×#12311yescharacteristic
596C23C11×#12711yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—22no—
602D4—22no—
603D4—42no—
604D4—42no—
605D4—42no—
606D4—42no—
607D4—41no—
608D4—41no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—82no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—82no—
639C2×C4C2×C11×C22⋊C411yescharacteristic
640C2×C4C2×C11×C4⋊C411yescharacteristic
641C2×C4C11×#11711yescharacteristic
642C2×C4C4×D4×C1111yescharacteristic
643C2×C4C4×D4×C1111yescharacteristic
644C2×C4C4×D4×C1111yescharacteristic
645C2×C4C11×#12011yescharacteristic
646C2×C4C11×#12011yescharacteristic
647C2×C4C11×#12111yescharacteristic
648C2×C4C11×#12111yescharacteristic
649C2×C4C11×#12111yescharacteristic
650C2×C4C11×#12111yescharacteristic
651C2×C4C11×#12111yescharacteristic
652C2×C4C11×#12111yescharacteristic
653C2×C4C11×C22⋊Q811yescharacteristic
654C2×C4C11×C22⋊Q811yescharacteristic
655C2×C4C11×C22⋊Q811yescharacteristic
656C2×C4C11×C22⋊Q811yescharacteristic
657C2×C4C11×C22⋊Q811yescharacteristic
658C2×C4C11×#12311yescharacteristic
659C2×C4C11×#12311yescharacteristic
660C2×C4C11×#12311yescharacteristic
661C2×C4C11×#12311yescharacteristic
662C2×C4C11×#12411yescharacteristic
663C2×C4C11×#12411yescharacteristic
664C2×C4C11×#12411yescharacteristic
665C2×C4C11×#12611yescharacteristic
666C2×C4C11×#12611yescharacteristic
667C8—24no—
668C8—42no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22C11×#38511yescharacteristic
689C22C11×#38811yescharacteristic
690C22C11×#39011yescharacteristic
691C22C11×#39211yescharacteristic
692C22C11×#39411yescharacteristic
693C22C11×#39611yescharacteristic
694C22C11×#39911yescharacteristic
695C22C11×#45311yescharacteristic
696C22C11×#45411yescharacteristic
697C22C11×#45511yescharacteristic
698C22C11×#45611yescharacteristic
699C4—44no—
700C4—42no—
701C4—82no—
702C4—81no—
703C4—81no—
704C4—82no—
705C4C11×#38011yescharacteristic
706C4C11×#38511yescharacteristic
707C4C11×#38611yescharacteristic
708C4C11×#38811yescharacteristic
709C4C11×#39311yescharacteristic
710C4C11×#39411yescharacteristic
711C4C11×#39611yescharacteristic
712C4C11×#39711yescharacteristic
713C2—21no—
714C2—21no—
715C2—21no—
716C2—21no—
717C2—82no—
718C2C11×#143911yescharacteristic
719C2C11×#185911yescharacteristic
720C2C11×#186011yescharacteristic
721C2C11×#200611yescharacteristic
722C2C11×#200711yescharacteristic
723C2C11×#203711yescharacteristic
724C2C11×#203811yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#428C2semidirect
5. C2×C11×#343C2semidirect
6. C2×C11×#339C2semidirect
7. C11×C4⋊#95C2semidirect
21. C2×C11×#104C4semidirect
104. #11113C11direct (N × H)
188. C11×M16C22⋊C4semidirect
217. C2×#428C2×C11semidirect
221. C2×#343C2×C11semidirect
222. C2×#339C2×C11semidirect
223. C4⋊#95C2×C11semidirect
327. C2×#104C4×C11semidirect
549. M16C11×C22⋊C4semidirect
578. C11#11113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C22×C11×#1042
C2×C11×#4172
C11×#23112
C2×C11×#3432
C2×C11×#3392
C11×C4⋊#952
#1111311