Finite Group Databasebeta

← C11×#24468 #14601661

Subgroups — C11×#24468 #14601661

Order 2816.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3488C211yesmaximal, characteristic, complemented
2C11×#3055C211yesmaximal, characteristic, complemented
3C2×C11×#453C211yesmaximal, characteristic, complemented
4C11×#3006C211yesmaximal, characteristic, complemented
5C2×C11×#421C211yesmaximal, characteristic, complemented
6C11×#2619C211yesmaximal, characteristic, complemented
7C11×#2040C211yesmaximal, characteristic, complemented
8C11×#2037C211yesmaximal, characteristic, complemented
9C11×#2006C211yesmaximal, characteristic, complemented
10C11×#2002C211yesmaximal, characteristic, complemented
11C11×#1900C211yesmaximal, characteristic, complemented
12C11×#1897C211yesmaximal, characteristic, complemented
13C11×#1883C211yesmaximal, characteristic, complemented
14C11×#1860C211yesmaximal, characteristic, complemented
15C11×#1792C211yesmaximal, characteristic, complemented
16C2×C11×H(5,𝔽2)C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
20C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×C11×M16C2211yescharacteristic, complemented
22C11×#550—21no—
23C11×#548—21no—
24C11×#546—21no—
25C11×#546—22no—
26D42×C11—22no—
27D42×C11—21no—
28C11×#537—21no—
29C11×#537C2211yescharacteristic
30C11×#535—21no—
31C11×#535C2211yescharacteristic
32C2×C11×#127C2211yescharacteristic, complemented
33C11×#525—21no—
34C11×#525C2211yescharacteristic
35C2×C11×#121—21no—
36C2×C11×#121C2211yescharacteristic
37C2×C11×#121C2211yescharacteristic, complemented
38C11×#520C2211yescharacteristic
39C2×C11×#117C2211yescharacteristic, complemented
40C11×#469—21no—
41C11×#468—21no—
42C11×#466—21no—
43C11×#465—21no—
44C11×#453—24no—
45C11×#449—21no—
46C11×#449—21no—
47C11×#448—21no—
48C11×#447—21no—
49C11×#428C2211yescharacteristic, complemented
50C11×#421—24no—
51C2×C11×#104C2211yescharacteristic
52C2×C11×#104C2211yescharacteristic
53C2×C11×#104C2211yescharacteristic, complemented
54C2×C11×#104C2211yescharacteristic, complemented
55C2×C11×#104C2211yescharacteristic, complemented
56C2×C11×#104C2211yescharacteristic, complemented
57C11×#418C2211yescharacteristic, complemented
58C11×#417C2211yescharacteristic
59C11×#417C2211yescharacteristic, complemented
60C11×#417C2211yescharacteristic, complemented
61C2×C11×#100C2211yescharacteristic, complemented
62C2×C11×#100C2211yescharacteristic, complemented
63C11×#407C2211yescharacteristic, complemented
64C11×#394—22no—
65C11×#392—22no—
66C11×#390C2211yescharacteristic, complemented
67C11×#390C2211yescharacteristic, complemented
68C11×#382C2211yescharacteristic, complemented
69C11×#343C2211yescharacteristic, complemented
70C11×#343C2211yescharacteristic, complemented
71C11×#339C2211yescharacteristic, complemented
72C11×#339C2211yescharacteristic, complemented
73C11×H(5,𝔽2)—22no—
74C11×H(5,𝔽2)—22no—
75C11×H(5,𝔽2)—41no—
76C11×H(5,𝔽2)—41no—
77C2×C11×#41—21no—
78C2×C11×#41—21no—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—22no—
82C2×C11×#41—22no—
83C2×C11×#41—41no—
84C2×C11×#41—41no—
85C2×C11×#41D411yescharacteristic, complemented
86C2×C11×#41D411yescharacteristic, complemented
87C2×C11×#41C2311yescharacteristic
88C2×C11×#41C2311yescharacteristic
89C2×C11×#41C2311yescharacteristic
90C22×Q8×C11D411yescharacteristic, complemented
91C22×D4×C11—21no—
92C22×D4×C11—22no—
93C22×D4×C11—22no—
94C22×D4×C11—21no—
95C22×D4×C11—21no—
96C22×D4×C11—21no—
97C22×D4×C11—22no—
98C22×D4×C11D412yes—
99C22×D4×C11D411yescharacteristic, complemented
100C22×D4×C11C2311yescharacteristic
101C22×D4×C11C2311yescharacteristic
102C23×C4×C11—21no—
103C23×C4×C11C2311yescharacteristic
104C11×AGL(1,ℤ/8)—22no—
105C11×AGL(1,ℤ/8)—22no—
106C11×AGL(1,ℤ/8)—22no—
107C11×AGL(1,ℤ/8)—41no—
108C11×AGL(1,ℤ/8)—41no—
109C11×AGL(1,ℤ/8)—41no—
110C2×C11×SD16—21no—
111C2×C11×SD16—21no—
112C2×C11×SD16—21no—
113C2×C11×D8—21no—
114C2×C11×D8—21no—
115C2×C11×D8—21no—
116C2×C11×M16—21no—
117C2×C11×M16—22no—
118C2×C11×M16—41no—
119C2×C11×M16C2311yescharacteristic
120C2×C11×M16C2311yescharacteristic
121C2×C11×M16C2311yescharacteristic
122C2×C11×M16C2311yescharacteristic
123C22×C8×C11—21no—
124C11×#127—22no—
125C11×#127—21no—
126C11×#127—22no—
127C11×#127—41no—
128C11×#124—22no—
129C11×#124—21no—
130C11×#123—22no—
131C11×#123—21no—
132C11×C22⋊Q8—22no—
133C11×C22⋊Q8—21no—
134C11×C22⋊Q8—21no—
135C11×C22⋊Q8D411yescharacteristic, complemented
136C11×C22⋊Q8D411yescharacteristic, complemented
137C11×#121—22no—
138C11×#121—22no—
139C11×#121—22no—
140C11×#121—22no—
141C11×#121—22no—
142C11×#121—21no—
143C11×#121—21no—
144C11×#121—21no—
145C11×#121—21no—
146C11×#121—21no—
147C11×#121—21no—
148C11×#121—22no—
149C11×#121—21no—
150C11×#121—21no—
151C11×#121—21no—
152C11×#121—21no—
153C11×#121—21no—
154C11×#121—21no—
155C11×#121D411yescharacteristic, complemented
156C11×#121D411yescharacteristic, complemented
157C11×#120—22no—
158C11×#120—22no—
159C11×#120—22no—
160C11×#120—21no—
161C11×#120—22no—
162C4×Q8×C11—21no—
163C4×D4×C11—22no—
164C4×D4×C11—22no—
165C4×D4×C11—21no—
166C4×D4×C11—22no—
167C4×D4×C11—21no—
168C4×D4×C11—21no—
169C11×#117—21no—
170C11×#117—22no—
171C11×#117—41no—
172C11×#117C2311yescharacteristic
173C2×C11×C4⋊C4—21no—
174C2×C11×C4⋊C4—21no—
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4—22no—
178C2×C11×C22⋊C4—21no—
179C2×C11×C22⋊C4—21no—
180C2×C11×C22⋊C4—22no—
181C2×C11×C22⋊C4—22no—
182C2×C11×C22⋊C4D412yes—
183C2×C42×C11C2311yescharacteristic
184C2×C42×C11C2311yescharacteristic
185C11×#107—21no—
186C11×#106—21no—
187C11×#104—22no—
188C11×#104—22no—
189C11×#104—22no—
190C11×#104—22no—
191C11×#104—41no—
192C11×#104D414yescomplemented
193C11×#103—21no—
194C11×#103—21no—
195C11×#103—21no—
196C11×#102—21no—
197C11×#102—21no—
198C11×#102—21no—
199C11×#102—21no—
200C11×#102—21no—
201C11×#100—22no—
202C11×#100—41no—
203C11×C22⋊C8—21no—
204C11×C22⋊C8—21no—
205C11×#95—22no—
206#24468C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—22no—
208C24×C11—21no—
209C24×C11—21no—
210C24×C11C2×D412yes—
211C24×C11C2×D411yescharacteristic
212C11×#41—21no—
213C11×#41—21no—
214C11×#41—22no—
215C11×#41—22no—
216C11×#41—21no—
217C11×#41—21no—
218C11×#41—21no—
219C11×#41—21no—
220C11×#41—21no—
221C11×#41—21no—
222C11×#41—21no—
223C11×#41—21no—
224C11×#41—42no—
225C11×#41—42no—
226C11×#41—41no—
227C11×#41—41no—
228C11×#41—42no—
229C11×#41—42no—
230C11×#41—42no—
231C11×#41—42no—
232C11×#41—42no—
233C11×#41—42no—
234C11×#41C2×D412yes—
235C11×#41#4112yes—
236C2×Q8×C11—21no—
237C2×Q8×C11—22no—
238C2×Q8×C11—41no—
239C2×Q8×C11C2×D411yescharacteristic
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2×D411yescharacteristic
242C2×D4×C11—21no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—21no—
248C2×D4×C11—21no—
249C2×D4×C11—21no—
250C2×D4×C11—21no—
251C2×D4×C11—21no—
252C2×D4×C11—22no—
253C2×D4×C11—22no—
254C2×D4×C11—22no—
255C2×D4×C11—21no—
256C2×D4×C11—22no—
257C2×D4×C11—21no—
258C2×D4×C11—21no—
259C2×D4×C11—21no—
260C2×D4×C11—21no—
261C2×D4×C11—21no—
262C2×D4×C11—21no—
263C2×D4×C11—21no—
264C2×D4×C11—21no—
265C2×D4×C11—21no—
266C2×D4×C11—21no—
267C2×D4×C11—21no—
268C2×D4×C11—21no—
269C2×D4×C11—21no—
270C2×D4×C11—41no—
271C2×D4×C11—42no—
272C2×D4×C11—42no—
273C2×D4×C11—44no—
274C2×D4×C11—42no—
275C2×D4×C11—42no—
276C2×D4×C11—44no—
277C2×D4×C11—44no—
278C2×D4×C11—42no—
279C2×D4×C11—42no—
280C2×D4×C11—41no—
281C2×D4×C11—41no—
282C2×D4×C11—82no—
283C2×D4×C11—82no—
284C2×D4×C11—82no—
285C2×D4×C11—82no—
286C2×D4×C11—84no—
287C2×D4×C11C2×D411yescharacteristic
288C2×D4×C11C2×D411yescharacteristic
289C2×D4×C11C2×D411yescharacteristic
290C22×C4×C11—21no—
291C22×C4×C11—21no—
292C22×C4×C11—21no—
293C22×C4×C11—21no—
294C22×C4×C11—21no—
295C22×C4×C11—22no—
296C22×C4×C11—21no—
297C22×C4×C11—21no—
298C22×C4×C11—22no—
299C22×C4×C11—21no—
300C22×C4×C11—21no—
301C22×C4×C11—21no—
302C22×C4×C11—21no—
303C22×C4×C11—21no—
304C22×C4×C11—21no—
305C22×C4×C11—42no—
306C22×C4×C11—42no—
307C22×C4×C11C2×D411yescharacteristic
308C22×C4×C11C2×D411yescharacteristic
309C22×C4×C11C2×D411yescharacteristic
310C22×C4×C11C2×D411yescharacteristic
311C22×C4×C11C2×D411yescharacteristic
312C22×C4×C11C2×D412yes—
313C22×C4×C11C2411yescharacteristic
314C11×SD16—42no—
315C11×SD16—42no—
316C11×SD16—42no—
317C11×D8—42no—
318C11×D8—42no—
319C11×D8—42no—
320C11×M16—21no—
321C11×M16—21no—
322C11×M16—21no—
323C11×M16—21no—
324C11×M16—21no—
325C11×M16—21no—
326C11×M16—21no—
327C11×M16—42no—
328C11×M16C2×D412yescomplemented
329C2×C8×C11—21no—
330C2×C8×C11—21no—
331C2×C8×C11—21no—
332C2×C8×C11—21no—
333C2×C8×C11—42no—
334C11×C4⋊C4—22no—
335C11×C4⋊C4—22no—
336C11×C4⋊C4—21no—
337C11×C4⋊C4—21no—
338C11×C4⋊C4—21no—
339C11×C4⋊C4—21no—
340C11×C4⋊C4—21no—
341C11×C4⋊C4—21no—
342C11×C4⋊C4—42no—
343C11×C4⋊C4C2×D411yescharacteristic
344C11×C4⋊C4C2×D411yescharacteristic
345C11×C22⋊C4—22no—
346C11×C22⋊C4—22no—
347C11×C22⋊C4—22no—
348C11×C22⋊C4—22no—
349C11×C22⋊C4—22no—
350C11×C22⋊C4—21no—
351C11×C22⋊C4—21no—
352C11×C22⋊C4—21no—
353C11×C22⋊C4—21no—
354C11×C22⋊C4—22no—
355C11×C22⋊C4—22no—
356C11×C22⋊C4—21no—
357C11×C22⋊C4—42no—
358C11×C22⋊C4—41no—
359C11×C22⋊C4—41no—
360C11×C22⋊C4—82no—
361C11×C22⋊C4—82no—
362C42×C11—22no—
363C42×C11—21no—
364C42×C11—21no—
365C42×C11—21no—
366C42×C11—21no—
367C42×C11C2×D412yescomplemented
368#3488C2×C1111yescharacteristic, complemented
369#3055C2×C1111yescharacteristic, complemented
370C2×#453C2×C1111yescharacteristic, complemented
371#3006C2×C1111yescharacteristic, complemented
372C2×#421C2×C1111yescharacteristic, complemented
373#2619C2×C1111yescharacteristic, complemented
374#2040C2×C1111yescharacteristic, complemented
375#2037C2×C1111yescharacteristic, complemented
376#2006C2×C1111yescharacteristic, complemented
377#2002C2×C1111yescharacteristic, complemented
378#1900C2×C1111yescharacteristic, complemented
379#1897C2×C1111yescharacteristic, complemented
380#1883C2×C1111yescharacteristic, complemented
381#1860C2×C1111yescharacteristic, complemented
382#1792C2×C1111yescharacteristic, complemented
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—22no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—42no—
394C23×C11—42no—
395C23×C11—44no—
396C23×C11—42no—
397C23×C11—42no—
398C23×C11—42no—
399C23×C11—42no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11—81no—
404C23×C11—82no—
405C23×C11—82no—
406C23×C11#12011yescharacteristic
407C23×C11#12011yescharacteristic
408C23×C11C22×D411yescharacteristic
409Q8×C11—21no—
410Q8×C11—21no—
411Q8×C11—21no—
412Q8×C11—21no—
413Q8×C11—21no—
414Q8×C11—42no—
415Q8×C11#12112yes—
416D4×C11—22no—
417D4×C11—22no—
418D4×C11—21no—
419D4×C11—21no—
420D4×C11—21no—
421D4×C11—21no—
422D4×C11—21no—
423D4×C11—42no—
424D4×C11—42no—
425D4×C11—44no—
426D4×C11—42no—
427D4×C11—44no—
428D4×C11—44no—
429D4×C11—42no—
430D4×C11—41no—
431D4×C11—41no—
432D4×C11—41no—
433D4×C11—41no—
434D4×C11—41no—
435D4×C11—41no—
436D4×C11—41no—
437D4×C11—41no—
438D4×C11—41no—
439D4×C11—41no—
440D4×C11—41no—
441D4×C11—41no—
442D4×C11—81no—
443D4×C11—82no—
444D4×C11—82no—
445D4×C11—82no—
446D4×C11—82no—
447D4×C11—88no—
448D4×C11—82no—
449D4×C11—82no—
450D4×C11#12112yes—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—21no—
454C2×C4×C11—21no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—22no—
464C2×C4×C11—21no—
465C2×C4×C11—22no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—22no—
470C2×C4×C11—42no—
471C2×C4×C11—42no—
472C2×C4×C11—42no—
473C2×C4×C11—44no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—42no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—42no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—82no—
487C2×C4×C11#12011yescharacteristic
488C2×C4×C11#12011yescharacteristic
489C2×C4×C11C22×D411yescharacteristic
490C2×C4×C11C22×D411yescharacteristic
491C2×C4×C11C22×D411yescharacteristic
492C2×C4×C11C2×#4111yescharacteristic
493C2×C4×C11H(5,𝔽2)11yescharacteristic
494C2×C4×C11H(5,𝔽2)11yescharacteristic
495C8×C11—22no—
496C8×C11—41no—
497C8×C11—41no—
498C8×C11—41no—
499C2×H(5,𝔽2)C22×C1111yescharacteristic
500C22×#41C22×C1111yescharacteristic
501C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
502C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
503C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
504C22×M16C22×C1111yescharacteristic, complemented
505#550—21no—
506#548—21no—
507#546—21no—
508#546—22no—
509D42—22no—
510D42—21no—
511#537—21no—
512#537C22×C1111yescharacteristic
513#535—21no—
514#535C22×C1111yescharacteristic
515C2×#127C22×C1111yescharacteristic, complemented
516#525—21no—
517#525C22×C1111yescharacteristic
518C2×#121—21no—
519C2×#121C22×C1111yescharacteristic
520C2×#121C22×C1111yescharacteristic, complemented
521#520C22×C1111yescharacteristic
522C2×#117C22×C1111yescharacteristic, complemented
523#469—21no—
524#468—21no—
525#466—21no—
526#465—21no—
527#453—24no—
528#449—21no—
529#449—21no—
530#448—21no—
531#447—21no—
532#428C22×C1111yescharacteristic, complemented
533#421—24no—
534C2×#104C22×C1111yescharacteristic
535C2×#104C22×C1111yescharacteristic
536C2×#104C22×C1111yescharacteristic, complemented
537C2×#104C22×C1111yescharacteristic, complemented
538C2×#104C22×C1111yescharacteristic, complemented
539C2×#104C22×C1111yescharacteristic, complemented
540#418C22×C1111yescharacteristic, complemented
541#417C22×C1111yescharacteristic
542#417C22×C1111yescharacteristic, complemented
543#417C22×C1111yescharacteristic, complemented
544C2×#100C22×C1111yescharacteristic, complemented
545C2×#100C22×C1111yescharacteristic, complemented
546#407C22×C1111yescharacteristic, complemented
547#394—22no—
548#392—22no—
549#390C22×C1111yescharacteristic, complemented
550#390C22×C1111yescharacteristic, complemented
551#382C22×C1111yescharacteristic, complemented
552#343C22×C1111yescharacteristic, complemented
553#343C22×C1111yescharacteristic, complemented
554#339C22×C1111yescharacteristic, complemented
555#339C22×C1111yescharacteristic, complemented
556C22×C11—21no—
557C22×C11—21no—
558C22×C11—21no—
559C22×C11—21no—
560C22×C11—22no—
561C22×C11—21no—
562C22×C11—21no—
563C22×C11—21no—
564C22×C11—21no—
565C22×C11—41no—
566C22×C11—41no—
567C22×C11—41no—
568C22×C11—41no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—41no—
572C22×C11—41no—
573C22×C11—41no—
574C22×C11—42no—
575C22×C11—41no—
576C22×C11—81no—
577C22×C11—81no—
578C22×C11—82no—
579C22×C11—82no—
580C22×C11—82no—
581C22×C11—82no—
582C22×C11—84no—
583C22×C11—81no—
584C22×C11—81no—
585C22×C11—81no—
586C22×C11—164no—
587C22×C11C2×#12011yescharacteristic
588C22×C11D4211yescharacteristic
589C22×C11#54611yescharacteristic
590C4×C11—21no—
591C4×C11—21no—
592C4×C11—22no—
593C4×C11—42no—
594C4×C11—41no—
595C4×C11—41no—
596C4×C11—42no—
597C4×C11—41no—
598C4×C11—41no—
599C4×C11—81no—
600C4×C11—81no—
601C4×C11C2×#12111yescharacteristic
602C4×C11#53411yescharacteristic
603C4×C11D4211yescharacteristic
604C4×C11#54611yescharacteristic
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C1111yescharacteristic, complemented
618C2×#41D4×C1111yescharacteristic, complemented
619C2×#41C23×C1111yescharacteristic
620C2×#41C23×C1111yescharacteristic
621C2×#41C23×C1111yescharacteristic
622C22×Q8D4×C1111yescharacteristic, complemented
623C22×D4—21no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—21no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4—22no—
630C22×D4D4×C1112yes—
631C22×D4D4×C1111yescharacteristic, complemented
632C22×D4C23×C1111yescharacteristic
633C22×D4C23×C1111yescharacteristic
634C23×C4—21no—
635C23×C4C23×C1111yescharacteristic
636AGL(1,ℤ/8)—22no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—41no—
640AGL(1,ℤ/8)—41no—
641AGL(1,ℤ/8)—41no—
642C2×SD16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×D8—21no—
646C2×D8—21no—
647C2×D8—21no—
648C2×M16—21no—
649C2×M16—22no—
650C2×M16—41no—
651C2×M16C23×C1111yescharacteristic
652C2×M16C23×C1111yescharacteristic
653C2×M16C23×C1111yescharacteristic
654C2×M16C23×C1111yescharacteristic
655C22×C8—21no—
656#127—22no—
657#127—21no—
658#127—22no—
659#127—41no—
660#124—22no—
661#124—21no—
662#123—22no—
663#123—21no—
664C22⋊Q8—22no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C1111yescharacteristic, complemented
668C22⋊Q8D4×C1111yescharacteristic, complemented
669#121—22no—
670#121—22no—
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—22no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—21no—
686#121—21no—
687#121D4×C1111yescharacteristic, complemented
688#121D4×C1111yescharacteristic, complemented
689#120—22no—
690#120—22no—
691#120—22no—
692#120—21no—
693#120—22no—
694C4×Q8—21no—
695C4×D4—22no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—22no—
699C4×D4—21no—
700C4×D4—21no—
701#117—21no—
702#117—22no—
703#117—41no—
704#117C23×C1111yescharacteristic
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4C23×C1111yescharacteristic
708C2×C4⋊C4C23×C1111yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C1112yes—
715C2×C42C23×C1111yescharacteristic
716C2×C42C23×C1111yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C1114yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C2×C11—21no—
739C2×C11—21no—
740C2×C11—41no—
741C2×C11—41no—
742C2×C11—42no—
743C2×C11—81no—
744C2×C11—82no—
745C2×C11—81no—
746C2×C11—161no—
747C2×C11#241011yescharacteristic
748C2×C11#301911yescharacteristic
749C2×C11#302111yescharacteristic
750C24—22no—
751C24—21no—
752C24—21no—
753C24C2×D4×C1112yes—
754C24C2×D4×C1111yescharacteristic
755#41—21no—
756#41—21no—
757#41—22no—
758#41—22no—
759#41—21no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—42no—
768#41—42no—
769#41—41no—
770#41—41no—
771#41—42no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41C2×D4×C1112yes—
778#41C11×#4112yes—
779C2×Q8—21no—
780C2×Q8—22no—
781C2×Q8—41no—
782C2×Q8C2×D4×C1111yescharacteristic
783C2×Q8C2×D4×C1111yescharacteristic
784C2×Q8C2×D4×C1111yescharacteristic
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—21no—
799C2×D4—22no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—41no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—44no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—41no—
824C2×D4—41no—
825C2×D4—82no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—84no—
830C2×D4C2×D4×C1111yescharacteristic
831C2×D4C2×D4×C1111yescharacteristic
832C2×D4C2×D4×C1111yescharacteristic
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4C2×D4×C1111yescharacteristic
851C22×C4C2×D4×C1111yescharacteristic
852C22×C4C2×D4×C1111yescharacteristic
853C22×C4C2×D4×C1111yescharacteristic
854C22×C4C2×D4×C1111yescharacteristic
855C22×C4C2×D4×C1112yes—
856C22×C4C24×C1111yescharacteristic
857SD16—42no—
858SD16—42no—
859SD16—42no—
860D8—42no—
861D8—42no—
862D8—42no—
863M16—21no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—42no—
871M16C2×D4×C1112yescomplemented
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—42no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—42no—
886C4⋊C4C2×D4×C1111yescharacteristic
887C4⋊C4C2×D4×C1111yescharacteristic
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—21no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—21no—
900C22⋊C4—42no—
901C22⋊C4—41no—
902C22⋊C4—41no—
903C22⋊C4—82no—
904C22⋊C4—82no—
905C42—22no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42C2×D4×C1112yescomplemented
911C11#2446811yescharacteristic, direct product factor, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23C11×#12011yescharacteristic
936C23C11×#12011yescharacteristic
937C23C22×D4×C1111yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8C11×#12112yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—81no—
972D4—82no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4C11×#12112yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4C11×#12011yescharacteristic
1017C2×C4C11×#12011yescharacteristic
1018C2×C4C22×D4×C1111yescharacteristic
1019C2×C4C22×D4×C1111yescharacteristic
1020C2×C4C22×D4×C1111yescharacteristic
1021C2×C4C2×C11×#4111yescharacteristic
1022C2×C4C11×H(5,𝔽2)11yescharacteristic
1023C2×C4C11×H(5,𝔽2)11yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—41no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×C11×#12011yescharacteristic
1060C22D42×C1111yescharacteristic
1061C22C11×#54611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—42no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×C11×#12111yescharacteristic
1074C4C11×#53411yescharacteristic
1075C4D42×C1111yescharacteristic
1076C4C11×#54611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2C11×#241011yescharacteristic
1087C2C11×#301911yescharacteristic
1088C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3488C2semidirect
2. C11×#3055C2semidirect
3. C2×C11×#453C2semidirect
4. C11×#3006C2semidirect
5. C2×C11×#421C2semidirect
6. C11×#2619C2semidirect
7. C11×#2040C2semidirect
8. C11×#2037C2semidirect
9. C11×#2006C2semidirect
10. C11×#2002C2semidirect
11. C11×#1900C2semidirect
12. C11×#1897C2semidirect
13. C11×#1883C2semidirect
14. C11×#1860C2semidirect
15. C11×#1792C2semidirect
19. C2×C11×AGL(1,ℤ/8)C22semidirect
20. C2×C11×AGL(1,ℤ/8)C22semidirect
21. C22×C11×M16C22semidirect
32. C2×C11×#127C22semidirect
37. C2×C11×#121C22semidirect
39. C2×C11×#117C22semidirect
49. C11×#428C22semidirect
53. C2×C11×#104C22semidirect
54. C2×C11×#104C22semidirect
55. C2×C11×#104C22semidirect
56. C2×C11×#104C22semidirect
57. C11×#418C22semidirect
59. C11×#417C22semidirect
60. C11×#417C22semidirect
61. C2×C11×#100C22semidirect
62. C2×C11×#100C22semidirect
63. C11×#407C22semidirect
66. C11×#390C22semidirect
67. C11×#390C22semidirect
68. C11×#382C22semidirect
69. C11×#343C22semidirect
70. C11×#343C22semidirect
71. C11×#339C22semidirect
72. C11×#339C22semidirect
85. C2×C11×#41D4semidirect
86. C2×C11×#41D4semidirect
90. C22×Q8×C11D4semidirect
99. C22×D4×C11D4semidirect
135. C11×C22⋊Q8D4semidirect
136. C11×C22⋊Q8D4semidirect
155. C11×#121D4semidirect
156. C11×#121D4semidirect
192. C11×#104D4semidirect
206. #24468C11direct (N × H)
328. C11×M16C2×D4semidirect
367. C42×C11C2×D4semidirect
368. #3488C2×C11semidirect
369. #3055C2×C11semidirect
370. C2×#453C2×C11semidirect
371. #3006C2×C11semidirect
372. C2×#421C2×C11semidirect
373. #2619C2×C11semidirect
374. #2040C2×C11semidirect
375. #2037C2×C11semidirect
376. #2006C2×C11semidirect
377. #2002C2×C11semidirect
378. #1900C2×C11semidirect
379. #1897C2×C11semidirect
380. #1883C2×C11semidirect
381. #1860C2×C11semidirect
382. #1792C2×C11semidirect
502. C2×AGL(1,ℤ/8)C22×C11semidirect
503. C2×AGL(1,ℤ/8)C22×C11semidirect
504. C22×M16C22×C11semidirect
515. C2×#127C22×C11semidirect
520. C2×#121C22×C11semidirect
522. C2×#117C22×C11semidirect
532. #428C22×C11semidirect
536. C2×#104C22×C11semidirect
537. C2×#104C22×C11semidirect
538. C2×#104C22×C11semidirect
539. C2×#104C22×C11semidirect
540. #418C22×C11semidirect
542. #417C22×C11semidirect
543. #417C22×C11semidirect
544. C2×#100C22×C11semidirect
545. C2×#100C22×C11semidirect
546. #407C22×C11semidirect
549. #390C22×C11semidirect
550. #390C22×C11semidirect
551. #382C22×C11semidirect
552. #343C22×C11semidirect
553. #343C22×C11semidirect
554. #339C22×C11semidirect
555. #339C22×C11semidirect
617. C2×#41D4×C11semidirect
618. C2×#41D4×C11semidirect
622. C22×Q8D4×C11semidirect
631. C22×D4D4×C11semidirect
667. C22⋊Q8D4×C11semidirect
668. C22⋊Q8D4×C11semidirect
687. #121D4×C11semidirect
688. #121D4×C11semidirect
724. #104D4×C11semidirect
871. M16C2×D4×C11semidirect
910. C42C2×D4×C11semidirect
911. C11#24468direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34882
C11×#30552
C2×C11×#4532
C11×#30062
C2×C11×#4212
C11×#26192
C11×#20402
C11×#20372
C11×#20062
C11×#20022
C11×#19002
C11×#18972
C11×#18832
C11×#18602
C11×#17922
#2446811