Finite Group Databasebeta

← C11×#23924 #14601117

Subgroups — C11×#23924 #14601117

Order 2816.

1952 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic, complemented
2C2×C11×#535C211yesmaximal, characteristic, complemented
3C2×C11×#449C212yesmaximal, complemented
4C2×C11×#450C211yesmaximal, characteristic, complemented
5C2×C11×#447C211yesmaximal, characteristic, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1999C212yesmaximal, complemented
8C11×#1875C211yesmaximal, characteristic, complemented
9C11×#1874C212yesmaximal, complemented
10C11×#1873C211yesmaximal, characteristic, complemented
11C11×#1780C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic, complemented
14C23×D4×C11C2211yescharacteristic
15C22×C11×SD16C2212yes—
16C22×C11×D8C2212yes—
17C11×#537—24no—
18C11×#537—24no—
19C11×#535—28no—
20C2×C11×#127—21no—
21C2×C11×#124—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic, complemented
25C2×C11×#121—21no—
26C2×C11×#121—21no—
27C2×C11×#121—21no—
28C2×C11×#121C2212yes—
29C2×C11×#121C2212yes—
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic, complemented
32C2×C11×#120—21no—
33C2×C11×#120—21no—
34C2×C11×#117C2211yescharacteristic
35C22×C11×C4⋊C4C2211yescharacteristic, complemented
36C11×#450—24no—
37C11×#449—28no—
38C11×#447—24no—
39C2×C11×#103C2212yescomplemented
40C2×C11×#102C2212yes—
41C2×C11×#102C2212yes—
42C2×C11×#102C2212yescomplemented
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×C22⋊C8C2212yescomplemented
46C2×C11×C22⋊C8C2212yescomplemented
47C11×#340C2212yescomplemented
48C11×#340C2212yescomplemented
49C25×C11—21no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—24no—
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41—24no—
56C2×C11×#41—42no—
57C2×C11×#41—42no—
58C22×Q8×C11D411yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—24no—
66C22×D4×C11—21no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—42no—
70C22×D4×C11D411yescharacteristic
71C22×D4×C11D411yescharacteristic
72C22×D4×C11D411yescharacteristic
73C22×D4×C11C2312yes—
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11—21no—
76C23×C4×C11—21no—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C2×C11×SD16—24no—
81C2×C11×SD16—24no—
82C2×C11×SD16—42no—
83C2×C11×D8—24no—
84C2×C11×D8—24no—
85C2×C11×D8—42no—
86C22×C8×C11C2312yes—
87C22×C8×C11C2312yes—
88C11×#127—28no—
89C11×#124—28no—
90C11×C22⋊Q8—28no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8D414yescomplemented
95C11×#121—28no—
96C11×#121—28no—
97C11×#121—28no—
98C11×#121—24no—
99C11×#121—22no—
100C11×#121—24no—
101C11×#121—22no—
102C11×#121—24no—
103C11×#121—22no—
104C11×#121D418yescomplemented
105C11×#121D414yescomplemented
106C11×#120—28no—
107C11×#120—28no—
108C11×#117—24no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C42×C11—21no—
125C11×#103—24no—
126C11×#102—24no—
127C11×#102—24no—
128C11×#102—24no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—22no—
131C11×C22⋊C8—24no—
132C11×C22⋊C8—42no—
133#23924C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11—24no—
135C24×C11—21no—
136C24×C11—22no—
137C24×C11—42no—
138C24×C11—42no—
139C24×C11—82no—
140C24×C11—82no—
141C24×C11C2×D411yescharacteristic
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C11×#41—48no—
145C11×#41—48no—
146C11×#41—48no—
147C11×#41—48no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11—41no—
154C2×Q8×C11C2×D412yes—
155C2×D4×C11—24no—
156C2×D4×C11—24no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—28no—
162C2×D4×C11—24no—
163C2×D4×C11—28no—
164C2×D4×C11—24no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—21no—
172C2×D4×C11—22no—
173C2×D4×C11—22no—
174C2×D4×C11—22no—
175C2×D4×C11—48no—
176C2×D4×C11—48no—
177C2×D4×C11—41no—
178C2×D4×C11—41no—
179C2×D4×C11—41no—
180C2×D4×C11—42no—
181C2×D4×C11—42no—
182C2×D4×C11—42no—
183C2×D4×C11—42no—
184C2×D4×C11—82no—
185C2×D4×C11—82no—
186C2×D4×C11—82no—
187C2×D4×C11—82no—
188C2×D4×C11—82no—
189C2×D4×C11—82no—
190C2×D4×C11C2×D412yes—
191C2×D4×C11C2×D414yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—24no—
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—24no—
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—22no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11—82no—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D414yes—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2411yescharacteristic
217C11×SD16—48no—
218C11×D8—48no—
219C2×C8×C11—22no—
220C2×C8×C11—22no—
221C2×C8×C11—22no—
222C2×C8×C11—22no—
223C2×C8×C11—22no—
224C2×C8×C11—22no—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4C2×D412yes—
232C11×C4⋊C4C2×D412yes—
233C11×C4⋊C4C2×D414yes—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—28no—
240C11×C22⋊C4—24no—
241C42×C11—24no—
242C2×#537C2×C1111yescharacteristic, complemented
243C2×#535C2×C1111yescharacteristic, complemented
244C2×#449C2×C1112yescomplemented
245C2×#450C2×C1111yescharacteristic, complemented
246C2×#447C2×C1111yescharacteristic, complemented
247#2000C2×C1112yescomplemented
248#1999C2×C1112yescomplemented
249#1875C2×C1111yescharacteristic, complemented
250#1874C2×C1112yescomplemented
251#1873C2×C1111yescharacteristic, complemented
252#1780C2×C1111yescharacteristic, complemented
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—21no—
262C23×C11—22no—
263C23×C11—24no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—48no—
269C23×C11—41no—
270C23×C11—42no—
271C23×C11—41no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—42no—
275C23×C11—42no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—84no—
280C23×C11—84no—
281C23×C11—88no—
282C23×C11—88no—
283C23×C11#12012yes—
284C23×C11#12012yes—
285C23×C11C22×D411yescharacteristic
286Q8×C11—24no—
287Q8×C11—44no—
288Q8×C11—42no—
289D4×C11—24no—
290D4×C11—24no—
291D4×C11—24no—
292D4×C11—44no—
293D4×C11—44no—
294D4×C11—48no—
295D4×C11—44no—
296D4×C11—48no—
297D4×C11—42no—
298D4×C11—42no—
299D4×C11—42no—
300D4×C11—84no—
301D4×C11—88no—
302D4×C11—84no—
303D4×C11—88no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—24no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—48no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—84no—
329C2×C4×C11#12012yes—
330C2×C4×C11#12012yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C22×D412yes—
334C2×C4×C11H(5,𝔽2)12yes—
335C8×C11—42no—
336C8×C11—42no—
337C22×#41C22×C1111yescharacteristic
338C22×#41C22×C1111yescharacteristic, complemented
339C23×D4C22×C1111yescharacteristic
340C22×SD16C22×C1112yes—
341C22×D8C22×C1112yes—
342#537—24no—
343#537—24no—
344#535—28no—
345C2×#127—21no—
346C2×#124—21no—
347C2×C22⋊Q8—21no—
348C2×C22⋊Q8C22×C1111yescharacteristic
349C2×C22⋊Q8C22×C1111yescharacteristic, complemented
350C2×#121—21no—
351C2×#121—21no—
352C2×#121—21no—
353C2×#121C22×C1112yes—
354C2×#121C22×C1112yes—
355C2×#121C22×C1111yescharacteristic
356C2×#121C22×C1111yescharacteristic, complemented
357C2×#120—21no—
358C2×#120—21no—
359C2×#117C22×C1111yescharacteristic
360C22×C4⋊C4C22×C1111yescharacteristic, complemented
361#450—24no—
362#449—28no—
363#447—24no—
364C2×#103C22×C1112yescomplemented
365C2×#102C22×C1112yes—
366C2×#102C22×C1112yes—
367C2×#102C22×C1112yescomplemented
368C2×C22⋊C8C22×C1111yescharacteristic
369C2×C22⋊C8C22×C1111yescharacteristic
370C2×C22⋊C8C22×C1112yescomplemented
371C2×C22⋊C8C22×C1112yescomplemented
372#340C22×C1112yescomplemented
373#340C22×C1112yescomplemented
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—24no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—41no—
386C22×C11—44no—
387C22×C11—42no—
388C22×C11—41no—
389C22×C11—42no—
390C22×C11—41no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—44no—
394C22×C11—44no—
395C22×C11—816no—
396C22×C11—82no—
397C22×C11—82no—
398C22×C11—82no—
399C22×C11—82no—
400C22×C11—82no—
401C22×C11—82no—
402C22×C11C2×#12011yescharacteristic
403C22×C11C2×#12011yescharacteristic
404C22×C11#53411yescharacteristic
405C22×C11#57612yes—
406C22×C11#57712yes—
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—41no—
410C4×C11—42no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11—44no—
414C4×C11D4212yes—
415C4×C11D4212yes—
416C25—21no—
417C2×#41—22no—
418C2×#41—22no—
419C2×#41—24no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—24no—
423C2×#41—42no—
424C2×#41—42no—
425C22×Q8D4×C1111yescharacteristic
426C22×Q8C23×C1111yescharacteristic
427C22×D4—21no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4—24no—
433C22×D4—21no—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—42no—
437C22×D4D4×C1111yescharacteristic
438C22×D4D4×C1111yescharacteristic
439C22×D4D4×C1111yescharacteristic
440C22×D4C23×C1112yes—
441C22×D4C23×C1111yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C23×C1111yescharacteristic
445C23×C4C23×C1111yescharacteristic
446C23×C4C23×C1111yescharacteristic
447C2×SD16—24no—
448C2×SD16—24no—
449C2×SD16—42no—
450C2×D8—24no—
451C2×D8—24no—
452C2×D8—42no—
453C22×C8C23×C1112yes—
454C22×C8C23×C1112yes—
455#127—28no—
456#124—28no—
457C22⋊Q8—28no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8D4×C1114yescomplemented
462#121—28no—
463#121—28no—
464#121—28no—
465#121—24no—
466#121—22no—
467#121—24no—
468#121—22no—
469#121—24no—
470#121—22no—
471#121D4×C1118yescomplemented
472#121D4×C1114yescomplemented
473#120—28no—
474#120—28no—
475#117—24no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4C23×C1111yescharacteristic
482C2×C4⋊C4C23×C1111yescharacteristic
483C2×C4⋊C4C23×C1112yes—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C42—21no—
492#103—24no—
493#102—24no—
494#102—24no—
495#102—24no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—24no—
499C22⋊C8—42no—
500C2×C11—42no—
501C2×C11—42no—
502C2×C11—81no—
503C2×C11—82no—
504C2×C11—84no—
505C2×C11#240311yescharacteristic
506C2×C11#300811yescharacteristic
507C2×C11#301011yescharacteristic
508C2×C11#301212yes—
509C2×C11#319812yes—
510C24—24no—
511C24—21no—
512C24—22no—
513C24—42no—
514C24—42no—
515C24—82no—
516C24—82no—
517C24C2×D4×C1111yescharacteristic
518C24C2×D4×C1111yescharacteristic
519C24C2×D4×C1111yescharacteristic
520#41—48no—
521#41—48no—
522#41—48no—
523#41—48no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—41no—
530C2×Q8C2×D4×C1112yes—
531C2×D4—24no—
532C2×D4—24no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—28no—
538C2×D4—24no—
539C2×D4—28no—
540C2×D4—24no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—82no—
561C2×D4—82no—
562C2×D4—82no—
563C2×D4—82no—
564C2×D4—82no—
565C2×D4—82no—
566C2×D4C2×D4×C1112yes—
567C2×D4C2×D4×C1114yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—82no—
586C22×C4C2×D4×C1111yescharacteristic
587C22×C4C2×D4×C1111yescharacteristic
588C22×C4C2×D4×C1111yescharacteristic
589C22×C4C2×D4×C1114yes—
590C22×C4C2×D4×C1112yes—
591C22×C4C2×D4×C1112yes—
592C22×C4C24×C1111yescharacteristic
593SD16—48no—
594D8—48no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—22no—
607C4⋊C4C2×D4×C1112yes—
608C4⋊C4C2×D4×C1112yes—
609C4⋊C4C2×D4×C1114yes—
610C22⋊C4—24no—
611C22⋊C4—28no—
612C22⋊C4—24no—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—28no—
616C22⋊C4—24no—
617C42—24no—
618C11#2392411yescharacteristic, direct product factor, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—21no—
628C23—22no—
629C23—24no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—48no—
635C23—41no—
636C23—42no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—84no—
646C23—84no—
647C23—88no—
648C23—88no—
649C23C11×#12012yes—
650C23C11×#12012yes—
651C23C22×D4×C1111yescharacteristic
652Q8—24no—
653Q8—44no—
654Q8—42no—
655D4—24no—
656D4—24no—
657D4—24no—
658D4—44no—
659D4—44no—
660D4—48no—
661D4—44no—
662D4—48no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—84no—
667D4—88no—
668D4—84no—
669D4—88no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—48no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—84no—
695C2×C4C11×#12012yes—
696C2×C4C11×#12012yes—
697C2×C4C22×D4×C1111yescharacteristic
698C2×C4C22×D4×C1111yescharacteristic
699C2×C4C22×D4×C1112yes—
700C2×C4C11×H(5,𝔽2)12yes—
701C8—42no—
702C8—42no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—41no—
715C22—44no—
716C22—42no—
717C22—41no—
718C22—42no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—44no—
723C22—44no—
724C22—816no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22—82no—
731C22C2×C11×#12011yescharacteristic
732C22C2×C11×#12011yescharacteristic
733C22C11×#53411yescharacteristic
734C22C11×#57612yes—
735C22C11×#57712yes—
736C4—22no—
737C4—22no—
738C4—41no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—44no—
743C4D42×C1112yes—
744C4D42×C1112yes—
745C2—42no—
746C2—42no—
747C2—81no—
748C2—84no—
749C2—82no—
750C2C11×#240311yescharacteristic
751C2C11×#300811yescharacteristic
752C2C11×#301011yescharacteristic
753C2C11×#301212yes—
754C2C11×#319812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#537C2semidirect
2. C2×C11×#535C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#450C2semidirect
5. C2×C11×#447C2semidirect
6. C11×#2000C2semidirect
7. C11×#1999C2semidirect
8. C11×#1875C2semidirect
9. C11×#1874C2semidirect
10. C11×#1873C2semidirect
11. C11×#1780C2semidirect
13. C22×C11×#41C22semidirect
24. C2×C11×C22⋊Q8C22semidirect
31. C2×C11×#121C22semidirect
35. C22×C11×C4⋊C4C22semidirect
39. C2×C11×#103C22semidirect
42. C2×C11×#102C22semidirect
45. C2×C11×C22⋊C8C22semidirect
46. C2×C11×C22⋊C8C22semidirect
47. C11×#340C22semidirect
48. C11×#340C22semidirect
94. C11×C22⋊Q8D4semidirect
104. C11×#121D4semidirect
105. C11×#121D4semidirect
133. #23924C11direct (N × H)
242. C2×#537C2×C11semidirect
243. C2×#535C2×C11semidirect
244. C2×#449C2×C11semidirect
245. C2×#450C2×C11semidirect
246. C2×#447C2×C11semidirect
247. #2000C2×C11semidirect
248. #1999C2×C11semidirect
249. #1875C2×C11semidirect
250. #1874C2×C11semidirect
251. #1873C2×C11semidirect
252. #1780C2×C11semidirect
338. C22×#41C22×C11semidirect
349. C2×C22⋊Q8C22×C11semidirect
356. C2×#121C22×C11semidirect
360. C22×C4⋊C4C22×C11semidirect
364. C2×#103C22×C11semidirect
367. C2×#102C22×C11semidirect
370. C2×C22⋊C8C22×C11semidirect
371. C2×C22⋊C8C22×C11semidirect
372. #340C22×C11semidirect
373. #340C22×C11semidirect
461. C22⋊Q8D4×C11semidirect
471. #121D4×C11semidirect
472. #121D4×C11semidirect
618. C11#23924direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C2×C11×#5352
C2×C11×#4492
C2×C11×#4502
C2×C11×#4472
C11×#20002
C11×#19992
C11×#18752
C11×#18742
C11×#18732
C11×#17802
#2392411