Finite Group Databasebeta

← C2×C11×#2121 #14610537

Subgroups — C2×C11×#2121 #14610537

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#534C211yesmaximal, characteristic
2C22×C11×#100C211yesmaximal, characteristic, complemented
3C22×C11×#99C211yesmaximal, characteristic, complemented
4C11×#2121C218yesmaximal, direct product factor
5C2×C11×#352C212yesmaximal, complemented
6C2×C11×AΣL(1,𝔽16)C212yesmaximal, complemented
7C23×D4×C11C411yescharacteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C22×C11×M16—21no—
10C11×#534—22no—
11C11×#534—22no—
12C11×#534C414yescomplemented
13C11×#534C2214yes—
14C2×C11×#123—21no—
15C2×C11×#123C411yescharacteristic, complemented
16C2×C11×#123C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C11×#120—21no—
20C2×C11×#120C411yescharacteristic, complemented
21C2×C11×#120C2211yescharacteristic
22C22×C11×C22⋊C4—21no—
23C22×C11×C22⋊C4C411yescharacteristic, complemented
24C2×C11×#100—22no—
25C2×C11×#100—21no—
26C2×C11×#100C2212yes—
27C2×C11×#100C2214yescomplemented
28C2×C11×#99—22no—
29C2×C11×#99—21no—
30C2×C11×#99C2212yes—
31C2×C11×#99C2214yescomplemented
32C11×#352C2218yescomplemented
33C11×AΣL(1,𝔽16)C2218yescomplemented
34C25×C11C2×C411yescharacteristic
35C25×C11C2×C411yescharacteristic, complemented
36C25×C11D411yescharacteristic
37C22×D4×C11—21no—
38C22×D4×C11—22no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—41no—
43C22×D4×C11—41no—
44C22×D4×C11—42no—
45C22×D4×C11—42no—
46C22×D4×C11—41no—
47C22×D4×C11—41no—
48C22×D4×C11C2×C411yescharacteristic
49C22×D4×C11C2×C412yes—
50C22×D4×C11C2×C414yescomplemented
51C22×D4×C11D411yescharacteristic
52C22×D4×C11D412yes—
53C22×D4×C11D411yescharacteristic
54C22×D4×C11D412yes—
55C22×D4×C11C2311yescharacteristic
56C22×D4×C11C2312yes—
57C23×C4×C11—21no—
58C23×C4×C11—41no—
59C23×C4×C11C2×C411yescharacteristic, complemented
60C23×C4×C11D411yescharacteristic
61C2×C11×M16—22no—
62C2×C11×M16—24no—
63C2×C11×M16—42no—
64C2×C11×M16—41no—
65C22×C8×C11—41no—
66C11×#123—22no—
67C11×#123—21no—
68C11×#123—21no—
69C11×#123—24no—
70C11×#123—24no—
71C11×#123C2×C414yescomplemented
72C11×#123C2×C412yescomplemented
73C11×#123C2312yes—
74C11×#121—24no—
75C11×#121—24no—
76C11×#121—24no—
77C11×#121—24no—
78C11×#120—24no—
79C11×#120—24no—
80C11×#120—22no—
81C11×#120—21no—
82C11×#120—21no—
83C11×#120C2×C414yescomplemented
84C11×#120C2×C412yescomplemented
85C11×#120C2312yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—42no—
97C2×C11×C22⋊C4—41no—
98C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
99C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
100C2×C11×C22⋊C4C2×C414yescomplemented
101C11×#100—22no—
102C11×#100—24no—
103C11×#100C2314yes—
104C11×#99—22no—
105C11×#99—24no—
106C11×#99C2314yes—
107C2×#2121C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—21no—
109C24×C11—22no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—21no—
116C24×C11—41no—
117C24×C11—41no—
118C24×C11—82no—
119C24×C11—82no—
120C24×C11—82no—
121C24×C11C22⋊C411yescharacteristic
122C24×C11C22⋊C411yescharacteristic
123C24×C11C22⋊C412yes—
124C24×C11C22⋊C412yes—
125C24×C11C22⋊C411yescharacteristic
126C24×C11C22×C411yescharacteristic
127C24×C11C22×C412yes—
128C24×C11C22×C412yescomplemented
129C24×C11C2×D411yescharacteristic
130C24×C11C2×D412yes—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—24no—
135C2×D4×C11—22no—
136C2×D4×C11—41no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—41no—
140C2×D4×C11—42no—
141C2×D4×C11—41no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11—41no—
145C2×D4×C11—42no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—41no—
151C2×D4×C11—41no—
152C2×D4×C11—44no—
153C2×D4×C11—44no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11—44no—
160C2×D4×C11—44no—
161C2×D4×C11—82no—
162C2×D4×C11—82no—
163C2×D4×C11C22⋊C412yes—
164C2×D4×C11C22⋊C412yes—
165C2×D4×C11C22⋊C412yes—
166C2×D4×C11C22×C412yes—
167C2×D4×C11C22×C411yescharacteristic
168C2×D4×C11C2×D411yescharacteristic
169C2×D4×C11C2×D412yes—
170C2×D4×C11C2×D411yescharacteristic
171C2×D4×C11C2×D412yes—
172C2×D4×C11C2411yescharacteristic
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—24no—
181C22×C4×C11—41no—
182C22×C4×C11—41no—
183C22×C4×C11—44no—
184C22×C4×C11—42no—
185C22×C4×C11—82no—
186C22×C4×C11—84no—
187C22×C4×C11C22⋊C411yescharacteristic
188C22×C4×C11C22⋊C412yes—
189C22×C4×C11C22×C412yescomplemented
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D412yes—
192C11×M16—24no—
193C11×M16—42no—
194C11×M16—44no—
195C2×C8×C11—44no—
196C2×C8×C11—42no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—24no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—44no—
212C11×C22⋊C4C22×C412yescomplemented
213C11×C22⋊C4C22×C412yescomplemented
214C2×#534C2×C1111yescharacteristic
215C22×#100C2×C1111yescharacteristic, complemented
216C22×#99C2×C1111yescharacteristic, complemented
217#2121C2×C1118yesdirect product factor
218C2×#352C2×C1112yescomplemented
219C2×AΣL(1,𝔽16)C2×C1112yescomplemented
220C23×C11—22no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—22no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—21no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—44no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—82no—
250C23×C11—82no—
251C23×C11—82no—
252C23×C11—82no—
253C23×C11—82no—
254C23×C11—82no—
255C23×C11—82no—
256C23×C11—82no—
257C23×C11—84no—
258C23×C11—84no—
259C23×C11—82no—
260C23×C11—84no—
261C23×C11—84no—
262C23×C11#9911yescharacteristic
263C23×C11#9911yescharacteristic
264C23×C11#9912yes—
265C23×C11C2×C22⋊C411yescharacteristic
266C23×C11C2×C22⋊C411yescharacteristic
267C23×C11C2×C22⋊C412yes—
268C23×C11C2×C22⋊C411yescharacteristic
269C23×C11C2×C22⋊C412yes—
270C23×C11C2×C22⋊C412yes—
271C23×C11C23×C411yescharacteristic
272C23×C11C22×D411yescharacteristic
273D4×C11—42no—
274D4×C11—42no—
275D4×C11—42no—
276D4×C11—42no—
277D4×C11—41no—
278D4×C11—41no—
279D4×C11—42no—
280D4×C11—41no—
281D4×C11—42no—
282D4×C11—41no—
283D4×C11—48no—
284D4×C11—44no—
285D4×C11—44no—
286D4×C11—84no—
287D4×C11—82no—
288D4×C11—82no—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—42no—
306C2×C4×C11—44no—
307C2×C4×C11—84no—
308C2×C4×C11—88no—
309C2×C4×C11—84no—
310C2×C4×C11C2×C22⋊C412yes—
311C2×C4×C11C2×C22⋊C411yescharacteristic
312C2×C4×C11C22×D411yescharacteristic
313C8×C11—44no—
314C23×D4C4×C1111yescharacteristic, complemented
315C23×D4C22×C1111yescharacteristic
316C22×M16—21no—
317#534—22no—
318#534—22no—
319#534C4×C1114yescomplemented
320#534C22×C1114yes—
321C2×#123—21no—
322C2×#123C4×C1111yescharacteristic, complemented
323C2×#123C22×C1111yescharacteristic
324C2×#121—21no—
325C2×#121—21no—
326C2×#120—21no—
327C2×#120C4×C1111yescharacteristic, complemented
328C2×#120C22×C1111yescharacteristic
329C22×C22⋊C4—21no—
330C22×C22⋊C4C4×C1111yescharacteristic, complemented
331C2×#100—22no—
332C2×#100—21no—
333C2×#100C22×C1112yes—
334C2×#100C22×C1114yescomplemented
335C2×#99—22no—
336C2×#99—21no—
337C2×#99C22×C1112yes—
338C2×#99C22×C1114yescomplemented
339#352C22×C1118yescomplemented
340AΣL(1,𝔽16)C22×C1118yescomplemented
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—21no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—44no—
359C22×C11—42no—
360C22×C11—44no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—82no—
372C22×C11—82no—
373C22×C11—82no—
374C22×C11—82no—
375C22×C11—82no—
376C22×C11—82no—
377C22×C11—82no—
378C22×C11—84no—
379C22×C11—84no—
380C22×C11—82no—
381C22×C11C2×#9911yescharacteristic
382C22×C11C2×#9912yes—
383C22×C11C2×#9912yes—
384C22×C11C2×#9911yescharacteristic
385C22×C11C22×C22⋊C411yescharacteristic
386C4×C11—22no—
387C4×C11—21no—
388C4×C11—21no—
389C4×C11—42no—
390C4×C11—42no—
391C4×C11—42no—
392C4×C11—84no—
393C25C2×C4×C1111yescharacteristic
394C25C2×C4×C1111yescharacteristic, complemented
395C25D4×C1111yescharacteristic
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—22no—
399C22×D4—21no—
400C22×D4—21no—
401C22×D4—41no—
402C22×D4—41no—
403C22×D4—42no—
404C22×D4—41no—
405C22×D4—41no—
406C22×D4—42no—
407C22×D4C2×C4×C1111yescharacteristic
408C22×D4C2×C4×C1112yes—
409C22×D4C2×C4×C1114yescomplemented
410C22×D4D4×C1111yescharacteristic
411C22×D4D4×C1112yes—
412C22×D4D4×C1111yescharacteristic
413C22×D4D4×C1112yes—
414C22×D4C23×C1111yescharacteristic
415C22×D4C23×C1112yes—
416C23×C4—21no—
417C23×C4—41no—
418C23×C4C2×C4×C1111yescharacteristic, complemented
419C23×C4D4×C1111yescharacteristic
420C2×M16—22no—
421C2×M16—24no—
422C2×M16—41no—
423C2×M16—42no—
424C22×C8—41no—
425#123—22no—
426#123—21no—
427#123—21no—
428#123—24no—
429#123—24no—
430#123C2×C4×C1114yescomplemented
431#123C2×C4×C1112yescomplemented
432#123C23×C1112yes—
433#121—24no—
434#121—24no—
435#121—24no—
436#121—24no—
437#120—24no—
438#120—24no—
439#120—22no—
440#120—21no—
441#120—21no—
442#120C2×C4×C1114yescomplemented
443#120C2×C4×C1112yescomplemented
444#120C23×C1112yes—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—41no—
457C2×C22⋊C4C2×C4×C1111yescharacteristic, complemented
458C2×C22⋊C4C2×C4×C1111yescharacteristic, complemented
459C2×C22⋊C4C2×C4×C1114yescomplemented
460#100—22no—
461#100—24no—
462#100C23×C1114yes—
463#99—22no—
464#99—24no—
465#99C23×C1114yes—
466C2×C11—21no—
467C2×C11—21no—
468C2×C11—22no—
469C2×C11—22no—
470C2×C11—41no—
471C2×C11—42no—
472C2×C11—41no—
473C2×C11—42no—
474C2×C11—41no—
475C2×C11—41no—
476C2×C11—82no—
477C2×C11#212112yesdirect product factor
478C2×C11C22×#9911yescharacteristic
479C24—21no—
480C24—21no—
481C24—22no—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—41no—
488C24—41no—
489C24—82no—
490C24—82no—
491C24—82no—
492C24C11×C22⋊C411yescharacteristic
493C24C11×C22⋊C411yescharacteristic
494C24C11×C22⋊C412yes—
495C24C11×C22⋊C412yes—
496C24C11×C22⋊C411yescharacteristic
497C24C22×C4×C1111yescharacteristic
498C24C22×C4×C1112yes—
499C24C22×C4×C1112yescomplemented
500C24C2×D4×C1111yescharacteristic
501C24C2×D4×C1112yes—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—22no—
505C2×D4—24no—
506C2×D4—22no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—41no—
512C2×D4—42no—
513C2×D4—41no—
514C2×D4—42no—
515C2×D4—41no—
516C2×D4—42no—
517C2×D4—41no—
518C2×D4—42no—
519C2×D4—41no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—41no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—82no—
533C2×D4—82no—
534C2×D4C11×C22⋊C412yes—
535C2×D4C11×C22⋊C412yes—
536C2×D4C11×C22⋊C412yes—
537C2×D4C22×C4×C1112yes—
538C2×D4C22×C4×C1111yescharacteristic
539C2×D4C2×D4×C1111yescharacteristic
540C2×D4C2×D4×C1112yes—
541C2×D4C2×D4×C1111yescharacteristic
542C2×D4C2×D4×C1112yes—
543C2×D4C24×C1111yescharacteristic
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—42no—
555C22×C4—44no—
556C22×C4—82no—
557C22×C4—84no—
558C22×C4C11×C22⋊C411yescharacteristic
559C22×C4C11×C22⋊C412yes—
560C22×C4C22×C4×C1112yescomplemented
561C22×C4C2×D4×C1111yescharacteristic
562C22×C4C2×D4×C1112yes—
563M16—24no—
564M16—42no—
565M16—44no—
566C2×C8—42no—
567C2×C8—44no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—24no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—24no—
581C22⋊C4—42no—
582C22⋊C4—44no—
583C22⋊C4C22×C4×C1112yescomplemented
584C22⋊C4C22×C4×C1112yescomplemented
585C11C2×#212111yescharacteristic, direct product factor, Sylow
586C23—22no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—22no—
593C23—21no—
594C23—21no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—21no—
601C23—22no—
602C23—22no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—44no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23—82no—
620C23—82no—
621C23—82no—
622C23—82no—
623C23—84no—
624C23—84no—
625C23—82no—
626C23—84no—
627C23—84no—
628C23C11×#9911yescharacteristic
629C23C11×#9911yescharacteristic
630C23C11×#9912yes—
631C23C2×C11×C22⋊C411yescharacteristic
632C23C2×C11×C22⋊C411yescharacteristic
633C23C2×C11×C22⋊C412yes—
634C23C2×C11×C22⋊C411yescharacteristic
635C23C2×C11×C22⋊C412yes—
636C23C2×C11×C22⋊C412yes—
637C23C23×C4×C1111yescharacteristic
638C23C22×D4×C1111yescharacteristic
639D4—42no—
640D4—42no—
641D4—42no—
642D4—42no—
643D4—41no—
644D4—41no—
645D4—42no—
646D4—41no—
647D4—42no—
648D4—41no—
649D4—48no—
650D4—44no—
651D4—44no—
652D4—84no—
653D4—82no—
654D4—82no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—84no—
674C2×C4—88no—
675C2×C4—84no—
676C2×C4C2×C11×C22⋊C412yes—
677C2×C4C2×C11×C22⋊C411yescharacteristic
678C2×C4C22×D4×C1111yescharacteristic
679C8—44no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—22no—
687C22—22no—
688C22—21no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—44no—
698C22—42no—
699C22—42no—
700C22—44no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22—82no—
717C22—84no—
718C22—84no—
719C22—82no—
720C22C2×C11×#9911yescharacteristic
721C22C2×C11×#9912yes—
722C22C2×C11×#9912yes—
723C22C2×C11×#9911yescharacteristic
724C22C22×C11×C22⋊C411yescharacteristic
725C4—21no—
726C4—22no—
727C4—21no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—84no—
732C2—21no—
733C2—21no—
734C2—22no—
735C2—22no—
736C2—41no—
737C2—42no—
738C2—41no—
739C2—41no—
740C2—41no—
741C2—42no—
742C2—82no—
743C2C11×#212112yesdirect product factor
744C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC23C23×C4×C11
Frattini, cosocleC2×D4C24×C11
prime radicalC2×C11×#534C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C23×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#100C2semidirect
3. C22×C11×#99C2semidirect
4. C11×#2121C2direct (N × H)
5. C2×C11×#352C2semidirect
6. C2×C11×AΣL(1,𝔽16)C2semidirect
7. C23×D4×C11C4semidirect
12. C11×#534C4semidirect
15. C2×C11×#123C4semidirect
20. C2×C11×#120C4semidirect
23. C22×C11×C22⋊C4C4semidirect
27. C2×C11×#100C22semidirect
31. C2×C11×#99C22semidirect
32. C11×#352C22semidirect
33. C11×AΣL(1,𝔽16)C22semidirect
35. C25×C11C2×C4semidirect
50. C22×D4×C11C2×C4semidirect
59. C23×C4×C11C2×C4semidirect
71. C11×#123C2×C4semidirect
72. C11×#123C2×C4semidirect
83. C11×#120C2×C4semidirect
84. C11×#120C2×C4semidirect
98. C2×C11×C22⋊C4C2×C4semidirect
99. C2×C11×C22⋊C4C2×C4semidirect
100. C2×C11×C22⋊C4C2×C4semidirect
107. C2×#2121C11direct (N × H)
128. C24×C11C22×C4semidirect
189. C22×C4×C11C22×C4semidirect
212. C11×C22⋊C4C22×C4semidirect
213. C11×C22⋊C4C22×C4semidirect
215. C22×#100C2×C11semidirect
216. C22×#99C2×C11semidirect
217. #2121C2×C11direct (N × H)
218. C2×#352C2×C11semidirect
219. C2×AΣL(1,𝔽16)C2×C11semidirect
314. C23×D4C4×C11semidirect
319. #534C4×C11semidirect
322. C2×#123C4×C11semidirect
327. C2×#120C4×C11semidirect
330. C22×C22⋊C4C4×C11semidirect
334. C2×#100C22×C11semidirect
338. C2×#99C22×C11semidirect
339. #352C22×C11semidirect
340. AΣL(1,𝔽16)C22×C11semidirect
394. C25C2×C4×C11semidirect
409. C22×D4C2×C4×C11semidirect
418. C23×C4C2×C4×C11semidirect
430. #123C2×C4×C11semidirect
431. #123C2×C4×C11semidirect
442. #120C2×C4×C11semidirect
443. #120C2×C4×C11semidirect
457. C2×C22⋊C4C2×C4×C11semidirect
458. C2×C22⋊C4C2×C4×C11semidirect
459. C2×C22⋊C4C2×C4×C11semidirect
477. C2×C11#2121direct (N × H)
499. C24C22×C4×C11semidirect
560. C22×C4C22×C4×C11semidirect
583. C22⋊C4C22×C4×C11semidirect
584. C22⋊C4C22×C4×C11semidirect
585. C11C2×#2121direct (N × H)
743. C2C11×#2121direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5342
C22×C11×#1002
C22×C11×#992
C11×#21212
C2×C11×#3522
C2×C11×AΣL(1,𝔽16)2
C2×#212111