Finite Group Databasebeta

← C11×#11089 #14588282

Subgroups — C11×#11089 #14588282

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#99C211yesmaximal, characteristic
2C22×C11×#99C211yesmaximal, characteristic
3C22×C11×#99C211yesmaximal, characteristic
4C11×#2315C211yesmaximal, characteristic, complemented
5C2×C11×#342C211yesmaximal, characteristic, complemented
6C2×C11×#342C211yesmaximal, characteristic, complemented
7C2×C11×#342C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C2×C11×#99—22no—
16C2×C11×#99—22no—
17C2×C11×#99—22no—
18C2×C11×#99—22no—
19C2×C11×#99—22no—
20C2×C11×#99—22no—
21C2×C11×#99—22no—
22C2×C11×#99—22no—
23C2×C11×#99C414yescomplemented
24C11×#385—22no—
25C11×#385—22no—
26C11×#380—22no—
27C11×#342—22no—
28C11×#342—22no—
29C11×#342—22no—
30C25×C11Q811yescharacteristic
31C25×C11C2311yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11C2×C412yes—
45C22×D4×C11D412yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11Q811yescharacteristic
53C2×C11×C4⋊C4—24no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4C2×C412yes—
83C2×C11×C22⋊C4C2×C412yes—
84C2×C11×C22⋊C4D412yes—
85C2×C11×C22⋊C4D412yes—
86C2×C11×C22⋊C4D412yes—
87C2×C11×C22⋊C4D412yes—
88C2×C11×C22⋊C4D412yes—
89C2×C11×C22⋊C4D412yes—
90C11×#99—28no—
91C11×#99—28no—
92C11×#99—28no—
93C11×#95—24no—
94#11089C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C24×C11—21no—
97C24×C11—21no—
98C24×C11—21no—
99C24×C11—21no—
100C24×C11—21no—
101C24×C11—82no—
102C24×C11—82no—
103C24×C11C4⋊C412yescomplemented
104C24×C11C22×C411yescharacteristic
105C24×C11C2×D411yescharacteristic
106C24×C11C2×D411yescharacteristic
107C24×C11C2×D411yescharacteristic
108C24×C11C2×D411yescharacteristic
109C24×C11C2×D411yescharacteristic
110C24×C11C2×D411yescharacteristic
111C24×C11C2×D411yescharacteristic
112C24×C11C2×Q811yescharacteristic
113C24×C11#4111yescharacteristic
114C24×C11#4111yescharacteristic
115C24×C11#4111yescharacteristic
116C24×C11#4111yescharacteristic
117C24×C11#4111yescharacteristic
118C24×C11#4111yescharacteristic
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
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—41no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11—41no—
170C22×C4×C11—41no—
171C22×C4×C11—82no—
172C22×C4×C11—82no—
173C22×C4×C11—82no—
174C22×C4×C11—82no—
175C22×C4×C11—82no—
176C22×C4×C11—82no—
177C22×C4×C11C4⋊C412yescomplemented
178C11×C4⋊C4—84no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—41no—
193C11×C22⋊C4—41no—
194C11×C22⋊C4—41no—
195C11×C22⋊C4—41no—
196C11×C22⋊C4—41no—
197C11×C22⋊C4—41no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4C22⋊C414yes—
203C22×#99C2×C1111yescharacteristic
204C22×#99C2×C1111yescharacteristic
205C22×#99C2×C1111yescharacteristic
206#2315C2×C1111yescharacteristic, complemented
207C2×#342C2×C1111yescharacteristic, complemented
208C2×#342C2×C1111yescharacteristic, complemented
209C2×#342C2×C1111yescharacteristic, complemented
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—82no—
225C23×C11—82no—
226C23×C11—82no—
227C23×C11—81no—
228C23×C11—81no—
229C23×C11—81no—
230C23×C11—81no—
231C23×C11—81no—
232C23×C11—81no—
233C23×C11—81no—
234C23×C11—81no—
235C23×C11—82no—
236C23×C11—82no—
237C23×C11—82no—
238C23×C11—82no—
239C23×C11C2×C22⋊C411yescharacteristic
240C23×C11C2×C4⋊C411yescharacteristic
241C23×C11#11711yescharacteristic
242C23×C11C4×D411yescharacteristic
243C23×C11C4×D411yescharacteristic
244C23×C11C4×D411yescharacteristic
245C23×C11C4×D411yescharacteristic
246C23×C11#12011yescharacteristic
247C23×C11#12011yescharacteristic
248C23×C11#12011yescharacteristic
249C23×C11#12111yescharacteristic
250C23×C11#12111yescharacteristic
251C23×C11#12111yescharacteristic
252C23×C11#12111yescharacteristic
253C23×C11#12111yescharacteristic
254C23×C11#12111yescharacteristic
255C23×C11#12111yescharacteristic
256C23×C11#12111yescharacteristic
257C23×C11C22⋊Q811yescharacteristic
258C23×C11C22⋊Q811yescharacteristic
259C23×C11C22⋊Q811yescharacteristic
260C23×C11C22⋊Q811yescharacteristic
261C23×C11C22⋊Q811yescharacteristic
262C23×C11C22⋊Q811yescharacteristic
263C23×C11#12311yescharacteristic
264C23×C11#12311yescharacteristic
265C23×C11#12311yescharacteristic
266C23×C11#12311yescharacteristic
267C23×C11#12311yescharacteristic
268C23×C11#12411yescharacteristic
269C23×C11#12411yescharacteristic
270C23×C11#12411yescharacteristic
271C23×C11#12611yescharacteristic
272C23×C11#12611yescharacteristic
273C23×C11#12711yescharacteristic
274D4×C11—42no—
275D4×C11—42no—
276D4×C11—42no—
277D4×C11—42no—
278D4×C11—42no—
279D4×C11—42no—
280D4×C11—42no—
281D4×C11—42no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—44no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—44no—
292C2×C4×C11—44no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—82no—
299C2×C4×C11—82no—
300C2×C4×C11—82no—
301C2×C4×C11—82no—
302C2×C4×C11—82no—
303C2×C4×C11—82no—
304C2×C4×C11—82no—
305C2×C4×C11—82no—
306C2×C4×C11—82no—
307C2×C4×C11—82no—
308C2×C4×C11—82no—
309C2×C4×C11—82no—
310C2×C4×C11—82no—
311C2×C4×C11—82no—
312C2×C4×C11—82no—
313C23×D4C22×C1111yescharacteristic
314C22×C22⋊C4C22×C1111yescharacteristic
315C22×C22⋊C4C22×C1111yescharacteristic
316C22×C22⋊C4C22×C1111yescharacteristic
317C22×C22⋊C4C22×C1111yescharacteristic
318C22×C22⋊C4C22×C1111yescharacteristic
319C22×C22⋊C4C22×C1111yescharacteristic
320C2×#99—22no—
321C2×#99—22no—
322C2×#99—22no—
323C2×#99—22no—
324C2×#99—22no—
325C2×#99—22no—
326C2×#99—22no—
327C2×#99—22no—
328C2×#99C4×C1114yescomplemented
329#385—22no—
330#385—22no—
331#380—22no—
332#342—22no—
333#342—22no—
334#342—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—42no—
371C22×C11—82no—
372C22×C11—82no—
373C22×C11—82no—
374C22×C11—82no—
375C22×C11—82no—
376C22×C11—82no—
377C22×C11—82no—
378C22×C11#38011yescharacteristic
379C22×C11#38511yescharacteristic
380C22×C11#38511yescharacteristic
381C22×C11#38611yescharacteristic
382C22×C11#38811yescharacteristic
383C22×C11#38811yescharacteristic
384C22×C11#39011yescharacteristic
385C22×C11#39211yescharacteristic
386C22×C11#39311yescharacteristic
387C22×C11#39411yescharacteristic
388C22×C11#39411yescharacteristic
389C22×C11#39611yescharacteristic
390C22×C11#39611yescharacteristic
391C22×C11#39711yescharacteristic
392C22×C11#39911yescharacteristic
393C4×C11—44no—
394C4×C11—42no—
395C4×C11—82no—
396C4×C11—82no—
397C4×C11—82no—
398C4×C11—82no—
399C4×C11—82no—
400C25Q8×C1111yescharacteristic
401C25C23×C1111yescharacteristic
402C22×D4—21no—
403C22×D4—21no—
404C22×D4—21no—
405C22×D4—21no—
406C22×D4—21no—
407C22×D4—21no—
408C22×D4—21no—
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4C2×C4×C1112yes—
415C22×D4D4×C1112yes—
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4Q8×C1111yescharacteristic
423C2×C4⋊C4—24no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4C2×C4×C1112yes—
453C2×C22⋊C4C2×C4×C1112yes—
454C2×C22⋊C4D4×C1112yes—
455C2×C22⋊C4D4×C1112yes—
456C2×C22⋊C4D4×C1112yes—
457C2×C22⋊C4D4×C1112yes—
458C2×C22⋊C4D4×C1112yes—
459C2×C22⋊C4D4×C1112yes—
460#99—28no—
461#99—28no—
462#99—28no—
463#95—24no—
464C2×C11—21no—
465C2×C11—21no—
466C2×C11—21no—
467C2×C11—21no—
468C2×C11—21no—
469C2×C11—21no—
470C2×C11—21no—
471C2×C11—21no—
472C2×C11—21no—
473C2×C11—21no—
474C2×C11—21no—
475C2×C11—21no—
476C2×C11—21no—
477C2×C11—21no—
478C2×C11—82no—
479C2×C11#143911yescharacteristic
480C2×C11#203212yes—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—82no—
488C24—82no—
489C24C11×C4⋊C412yescomplemented
490C24C22×C4×C1111yescharacteristic
491C24C2×D4×C1111yescharacteristic
492C24C2×D4×C1111yescharacteristic
493C24C2×D4×C1111yescharacteristic
494C24C2×D4×C1111yescharacteristic
495C24C2×D4×C1111yescharacteristic
496C24C2×D4×C1111yescharacteristic
497C24C2×D4×C1111yescharacteristic
498C24C2×Q8×C1111yescharacteristic
499C24C11×#4111yescharacteristic
500C24C11×#4111yescharacteristic
501C24C11×#4111yescharacteristic
502C24C11×#4111yescharacteristic
503C24C11×#4111yescharacteristic
504C24C11×#4111yescharacteristic
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—82no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4C11×C4⋊C412yescomplemented
564C4⋊C4—84no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4C11×C22⋊C414yes—
589C11#1108911yescharacteristic, direct product factor, Sylow
590C23—22no—
591C23—22no—
592C23—22no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—82no—
605C23—82no—
606C23—82no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23C2×C11×C22⋊C411yescharacteristic
620C23C2×C11×C4⋊C411yescharacteristic
621C23C11×#11711yescharacteristic
622C23C4×D4×C1111yescharacteristic
623C23C4×D4×C1111yescharacteristic
624C23C4×D4×C1111yescharacteristic
625C23C4×D4×C1111yescharacteristic
626C23C11×#12011yescharacteristic
627C23C11×#12011yescharacteristic
628C23C11×#12011yescharacteristic
629C23C11×#12111yescharacteristic
630C23C11×#12111yescharacteristic
631C23C11×#12111yescharacteristic
632C23C11×#12111yescharacteristic
633C23C11×#12111yescharacteristic
634C23C11×#12111yescharacteristic
635C23C11×#12111yescharacteristic
636C23C11×#12111yescharacteristic
637C23C11×C22⋊Q811yescharacteristic
638C23C11×C22⋊Q811yescharacteristic
639C23C11×C22⋊Q811yescharacteristic
640C23C11×C22⋊Q811yescharacteristic
641C23C11×C22⋊Q811yescharacteristic
642C23C11×C22⋊Q811yescharacteristic
643C23C11×#12311yescharacteristic
644C23C11×#12311yescharacteristic
645C23C11×#12311yescharacteristic
646C23C11×#12311yescharacteristic
647C23C11×#12311yescharacteristic
648C23C11×#12411yescharacteristic
649C23C11×#12411yescharacteristic
650C23C11×#12411yescharacteristic
651C23C11×#12611yescharacteristic
652C23C11×#12611yescharacteristic
653C23C11×#12711yescharacteristic
654D4—42no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—44no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4—82no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4—82no—
691C2×C4—82no—
692C2×C4—82no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22C11×#38011yescharacteristic
737C22C11×#38511yescharacteristic
738C22C11×#38511yescharacteristic
739C22C11×#38611yescharacteristic
740C22C11×#38811yescharacteristic
741C22C11×#38811yescharacteristic
742C22C11×#39011yescharacteristic
743C22C11×#39211yescharacteristic
744C22C11×#39311yescharacteristic
745C22C11×#39411yescharacteristic
746C22C11×#39411yescharacteristic
747C22C11×#39611yescharacteristic
748C22C11×#39611yescharacteristic
749C22C11×#39711yescharacteristic
750C22C11×#39911yescharacteristic
751C4—44no—
752C4—42no—
753C4—82no—
754C4—82no—
755C4—82no—
756C4—82no—
757C4—82no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—82no—
773C2C11×#143911yescharacteristic
774C2C11×#203212yes—
subgroupG/H
center, socleC22×C11#393
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2315C2semidirect
5. C2×C11×#342C2semidirect
6. C2×C11×#342C2semidirect
7. C2×C11×#342C2semidirect
23. C2×C11×#99C4semidirect
94. #11089C11direct (N × H)
103. C24×C11C4⋊C4semidirect
177. C22×C4×C11C4⋊C4semidirect
206. #2315C2×C11semidirect
207. C2×#342C2×C11semidirect
208. C2×#342C2×C11semidirect
209. C2×#342C2×C11semidirect
328. C2×#99C4×C11semidirect
489. C24C11×C4⋊C4semidirect
563. C22×C4C11×C4⋊C4semidirect
589. C11#11089direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#992
C11×#23152
C2×C11×#3422
#1108911