Finite Group Databasebeta

← C11×#24464 #14601657

Subgroups — C11×#24464 #14601657

Order 2816.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 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
5C22×C11×#104C211yesmaximal, characteristic, complemented
6C11×#2856C211yesmaximal, characteristic, complemented
7C11×#2039C211yesmaximal, characteristic, complemented
8C11×#2037C211yesmaximal, characteristic, complemented
9C11×#2006C211yesmaximal, characteristic, complemented
10C11×#2002C211yesmaximal, characteristic, complemented
11C11×#1900C211yesmaximal, characteristic, complemented
12C11×#1896C211yesmaximal, characteristic, complemented
13C11×#1883C211yesmaximal, characteristic, complemented
14C11×#1859C211yesmaximal, 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×#121—22no—
37C2×C11×#121C2211yescharacteristic
38C2×C11×#121C2211yescharacteristic, complemented
39C11×#520C2211yescharacteristic
40C22×C42×C11C2211yescharacteristic, complemented
41C11×#469—21no—
42C11×#468—21no—
43C11×#466—21no—
44C11×#465—21no—
45C11×#453—24no—
46C11×#449—21no—
47C11×#449—21no—
48C11×#448—21no—
49C11×#447—21no—
50C11×#428C2211yescharacteristic, complemented
51C2×C11×#104—24no—
52C2×C11×#104C2211yescharacteristic
53C2×C11×#104C2211yescharacteristic
54C2×C11×#104C2211yescharacteristic, complemented
55C2×C11×#104C2211yescharacteristic, complemented
56C2×C11×#104C2211yescharacteristic, complemented
57C2×C11×#104C2211yescharacteristic, complemented
58C11×#418C2211yescharacteristic, complemented
59C11×#417C2211yescharacteristic
60C11×#417C2211yescharacteristic, complemented
61C11×#417C2211yescharacteristic, complemented
62C2×C11×#100C2211yescharacteristic, complemented
63C2×C11×#100C2211yescharacteristic, complemented
64C11×#407C2211yescharacteristic, complemented
65C11×#390—22no—
66C11×#390C2211yescharacteristic, complemented
67C11×#390C2211yescharacteristic, complemented
68C11×#384C2211yescharacteristic, 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×C11—21no—
104C23×C4×C11C2311yescharacteristic
105C11×AGL(1,ℤ/8)—22no—
106C11×AGL(1,ℤ/8)—22no—
107C11×AGL(1,ℤ/8)—22no—
108C11×AGL(1,ℤ/8)—41no—
109C11×AGL(1,ℤ/8)—41no—
110C11×AGL(1,ℤ/8)—41no—
111C2×C11×SD16—21no—
112C2×C11×SD16—21no—
113C2×C11×SD16—21no—
114C2×C11×D8—21no—
115C2×C11×D8—21no—
116C2×C11×D8—21no—
117C2×C11×M16—21no—
118C2×C11×M16—22no—
119C2×C11×M16—41no—
120C2×C11×M16C2311yescharacteristic
121C2×C11×M16C2311yescharacteristic
122C2×C11×M16C2311yescharacteristic
123C2×C11×M16C2311yescharacteristic
124C22×C8×C11—21no—
125C11×#127—22no—
126C11×#127—21no—
127C11×#127—22no—
128C11×#127—41no—
129C11×#124—22no—
130C11×#124—21no—
131C11×#123—22no—
132C11×#123—21no—
133C11×C22⋊Q8—22no—
134C11×C22⋊Q8—21no—
135C11×C22⋊Q8—21no—
136C11×C22⋊Q8D411yescharacteristic, complemented
137C11×C22⋊Q8D411yescharacteristic, complemented
138C11×#121—22no—
139C11×#121—22no—
140C11×#121—22no—
141C11×#121—22no—
142C11×#121—22no—
143C11×#121—21no—
144C11×#121—21no—
145C11×#121—21no—
146C11×#121—21no—
147C11×#121—21no—
148C11×#121—21no—
149C11×#121—22no—
150C11×#121—21no—
151C11×#121—21no—
152C11×#121—21no—
153C11×#121—21no—
154C11×#121—21no—
155C11×#121—21no—
156C11×#121—48no—
157C11×#121D411yescharacteristic, complemented
158C11×#121D411yescharacteristic, complemented
159C11×#120—22no—
160C11×#120—22no—
161C11×#120—22no—
162C11×#120—21no—
163C11×#120—22no—
164C4×Q8×C11—21no—
165C4×D4×C11—22no—
166C4×D4×C11—22no—
167C4×D4×C11—21no—
168C4×D4×C11—22no—
169C4×D4×C11—21no—
170C4×D4×C11—21no—
171C11×#117—21no—
172C11×#117C2311yescharacteristic
173C2×C11×C4⋊C4—21no—
174C2×C11×C4⋊C4—22no—
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4—22no—
178C2×C11×C22⋊C4—22no—
179C2×C11×C22⋊C4—22no—
180C2×C11×C22⋊C4—21no—
181C2×C11×C22⋊C4D412yes—
182C2×C42×C11—22no—
183C2×C42×C11—21no—
184C2×C42×C11—41no—
185C2×C42×C11C2311yescharacteristic
186C2×C42×C11C2311yescharacteristic
187C11×#107—21no—
188C11×#106—21no—
189C11×#104—22no—
190C11×#104—22no—
191C11×#104—22no—
192C11×#104—22no—
193C11×#104—41no—
194C11×#104D414yescomplemented
195C11×#103—21no—
196C11×#103—21no—
197C11×#103—21no—
198C11×#102—21no—
199C11×#102—21no—
200C11×#102—21no—
201C11×#102—21no—
202C11×#102—21no—
203C11×#100—22no—
204C11×#100—41no—
205C11×C22⋊C8—21no—
206C11×C22⋊C8—21no—
207#24464C1111yesmaximal, characteristic, direct product factor, Sylow
208C24×C11—22no—
209C24×C11—21no—
210C24×C11—21no—
211C24×C11C2×D411yescharacteristic
212C24×C11C2×D412yes—
213C11×#41—21no—
214C11×#41—21no—
215C11×#41—22no—
216C11×#41—22no—
217C11×#41—21no—
218C11×#41—21no—
219C11×#41—21no—
220C11×#41—21no—
221C11×#41—21no—
222C11×#41—21no—
223C11×#41—21no—
224C11×#41—21no—
225C11×#41—42no—
226C11×#41—42no—
227C11×#41—41no—
228C11×#41—41no—
229C11×#41—42no—
230C11×#41—42no—
231C11×#41—42no—
232C11×#41—42no—
233C11×#41—42no—
234C11×#41—42no—
235C11×#41C2×D412yes—
236C11×#41#4112yes—
237C2×Q8×C11—21no—
238C2×Q8×C11—22no—
239C2×Q8×C11—41no—
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2×D411yescharacteristic
242C2×Q8×C11C2×D411yescharacteristic
243C2×D4×C11—21no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—22no—
248C2×D4×C11—21no—
249C2×D4×C11—21no—
250C2×D4×C11—21no—
251C2×D4×C11—21no—
252C2×D4×C11—21no—
253C2×D4×C11—22no—
254C2×D4×C11—22no—
255C2×D4×C11—22no—
256C2×D4×C11—21no—
257C2×D4×C11—22no—
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—21no—
271C2×D4×C11—41no—
272C2×D4×C11—42no—
273C2×D4×C11—42no—
274C2×D4×C11—44no—
275C2×D4×C11—44no—
276C2×D4×C11—44no—
277C2×D4×C11—42no—
278C2×D4×C11—42no—
279C2×D4×C11—44no—
280C2×D4×C11—44no—
281C2×D4×C11—42no—
282C2×D4×C11—42no—
283C2×D4×C11—44no—
284C2×D4×C11—44no—
285C2×D4×C11—41no—
286C2×D4×C11—41no—
287C2×D4×C11—84no—
288C2×D4×C11C2×D411yescharacteristic
289C2×D4×C11C2×D411yescharacteristic
290C2×D4×C11C2×D411yescharacteristic
291C22×C4×C11—21no—
292C22×C4×C11—21no—
293C22×C4×C11—21no—
294C22×C4×C11—21no—
295C22×C4×C11—21no—
296C22×C4×C11—21no—
297C22×C4×C11—22no—
298C22×C4×C11—24no—
299C22×C4×C11—21no—
300C22×C4×C11—21no—
301C22×C4×C11—22no—
302C22×C4×C11—21no—
303C22×C4×C11—21no—
304C22×C4×C11—21no—
305C22×C4×C11—21no—
306C22×C4×C11—21no—
307C22×C4×C11—42no—
308C22×C4×C11—42no—
309C22×C4×C11—42no—
310C22×C4×C11—42no—
311C22×C4×C11C2×D411yescharacteristic
312C22×C4×C11C2×D411yescharacteristic
313C22×C4×C11C2×D411yescharacteristic
314C22×C4×C11C2×D411yescharacteristic
315C22×C4×C11C2×D411yescharacteristic
316C22×C4×C11C2×D412yes—
317C22×C4×C11C2411yescharacteristic
318C11×SD16—42no—
319C11×SD16—42no—
320C11×SD16—42no—
321C11×D8—42no—
322C11×D8—42no—
323C11×D8—42no—
324C11×M16—21no—
325C11×M16—21no—
326C11×M16—21no—
327C11×M16—21no—
328C11×M16—21no—
329C11×M16—21no—
330C11×M16—21no—
331C11×M16—42no—
332C11×M16C2×D412yescomplemented
333C2×C8×C11—21no—
334C2×C8×C11—21no—
335C2×C8×C11—21no—
336C2×C8×C11—21no—
337C2×C8×C11—42no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—21no—
341C11×C4⋊C4—21no—
342C11×C4⋊C4—21no—
343C11×C4⋊C4—21no—
344C11×C4⋊C4—21no—
345C11×C4⋊C4—21no—
346C11×C4⋊C4—44no—
347C11×C4⋊C4C2×D411yescharacteristic
348C11×C4⋊C4C2×D411yescharacteristic
349C11×C22⋊C4—22no—
350C11×C22⋊C4—22no—
351C11×C22⋊C4—22no—
352C11×C22⋊C4—22no—
353C11×C22⋊C4—22no—
354C11×C22⋊C4—21no—
355C11×C22⋊C4—21no—
356C11×C22⋊C4—21no—
357C11×C22⋊C4—21no—
358C11×C22⋊C4—22no—
359C11×C22⋊C4—22no—
360C11×C22⋊C4—21no—
361C11×C22⋊C4—44no—
362C11×C22⋊C4—44no—
363C11×C22⋊C4—41no—
364C11×C22⋊C4—41no—
365C42×C11—22no—
366C42×C11—21no—
367C42×C11—21no—
368C42×C11—21no—
369C42×C11—21no—
370C42×C11—42no—
371C42×C11C2×D412yescomplemented
372#3488C2×C1111yescharacteristic, complemented
373#3055C2×C1111yescharacteristic, complemented
374C2×#453C2×C1111yescharacteristic, complemented
375#3006C2×C1111yescharacteristic, complemented
376C22×#104C2×C1111yescharacteristic, complemented
377#2856C2×C1111yescharacteristic, complemented
378#2039C2×C1111yescharacteristic, complemented
379#2037C2×C1111yescharacteristic, complemented
380#2006C2×C1111yescharacteristic, complemented
381#2002C2×C1111yescharacteristic, complemented
382#1900C2×C1111yescharacteristic, complemented
383#1896C2×C1111yescharacteristic, complemented
384#1883C2×C1111yescharacteristic, complemented
385#1859C2×C1111yescharacteristic, complemented
386#1792C2×C1111yescharacteristic, complemented
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—21no—
393C23×C11—21no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—41no—
397C23×C11—42no—
398C23×C11—44no—
399C23×C11—42no—
400C23×C11—42no—
401C23×C11—42no—
402C23×C11—42no—
403C23×C11—42no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—81no—
408C23×C11—82no—
409C23×C11—82no—
410C23×C11#12011yescharacteristic
411C23×C11#12011yescharacteristic
412C23×C11C22×D411yescharacteristic
413Q8×C11—21no—
414Q8×C11—21no—
415Q8×C11—21no—
416Q8×C11—21no—
417Q8×C11—21no—
418Q8×C11—42no—
419Q8×C11#12112yescomplemented
420D4×C11—22no—
421D4×C11—22no—
422D4×C11—21no—
423D4×C11—21no—
424D4×C11—21no—
425D4×C11—21no—
426D4×C11—21no—
427D4×C11—42no—
428D4×C11—42no—
429D4×C11—44no—
430D4×C11—42no—
431D4×C11—44no—
432D4×C11—41no—
433D4×C11—41no—
434D4×C11—41no—
435D4×C11—41no—
436D4×C11—44no—
437D4×C11—42no—
438D4×C11—41no—
439D4×C11—41no—
440D4×C11—41no—
441D4×C11—41no—
442D4×C11—41no—
443D4×C11—41no—
444D4×C11—41no—
445D4×C11—41no—
446D4×C11—88no—
447D4×C11—81no—
448D4×C11—82no—
449D4×C11—82no—
450D4×C11—82no—
451D4×C11—82no—
452D4×C11—82no—
453D4×C11—82no—
454D4×C11#12112yescomplemented
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—22no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—42no—
478C2×C4×C11—42no—
479C2×C4×C11—42no—
480C2×C4×C11—48no—
481C2×C4×C11—44no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—42no—
489C2×C4×C11—42no—
490C2×C4×C11—41no—
491C2×C4×C11—82no—
492C2×C4×C11#12011yescharacteristic
493C2×C4×C11#12011yescharacteristic
494C2×C4×C11C22×D411yescharacteristic
495C2×C4×C11C22×D411yescharacteristic
496C2×C4×C11C22×D411yescharacteristic
497C2×C4×C11C2×#4111yescharacteristic
498C2×C4×C11H(5,𝔽2)11yescharacteristic
499C2×C4×C11H(5,𝔽2)11yescharacteristic
500C8×C11—22no—
501C8×C11—41no—
502C8×C11—41no—
503C8×C11—41no—
504C2×H(5,𝔽2)C22×C1111yescharacteristic
505C22×#41C22×C1111yescharacteristic
506C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
507C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
508C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
509C22×M16C22×C1111yescharacteristic, complemented
510#550—21no—
511#548—21no—
512#546—21no—
513#546—22no—
514D42—22no—
515D42—21no—
516#537—21no—
517#537C22×C1111yescharacteristic
518#535—21no—
519#535C22×C1111yescharacteristic
520C2×#127C22×C1111yescharacteristic, complemented
521#525—21no—
522#525C22×C1111yescharacteristic
523C2×#121—21no—
524C2×#121—22no—
525C2×#121C22×C1111yescharacteristic
526C2×#121C22×C1111yescharacteristic, complemented
527#520C22×C1111yescharacteristic
528C22×C42C22×C1111yescharacteristic, complemented
529#469—21no—
530#468—21no—
531#466—21no—
532#465—21no—
533#453—24no—
534#449—21no—
535#449—21no—
536#448—21no—
537#447—21no—
538#428C22×C1111yescharacteristic, complemented
539C2×#104—24no—
540C2×#104C22×C1111yescharacteristic
541C2×#104C22×C1111yescharacteristic
542C2×#104C22×C1111yescharacteristic, complemented
543C2×#104C22×C1111yescharacteristic, complemented
544C2×#104C22×C1111yescharacteristic, complemented
545C2×#104C22×C1111yescharacteristic, complemented
546#418C22×C1111yescharacteristic, complemented
547#417C22×C1111yescharacteristic
548#417C22×C1111yescharacteristic, complemented
549#417C22×C1111yescharacteristic, complemented
550C2×#100C22×C1111yescharacteristic, complemented
551C2×#100C22×C1111yescharacteristic, complemented
552#407C22×C1111yescharacteristic, complemented
553#390—22no—
554#390C22×C1111yescharacteristic, complemented
555#390C22×C1111yescharacteristic, complemented
556#384C22×C1111yescharacteristic, complemented
557#343C22×C1111yescharacteristic, complemented
558#343C22×C1111yescharacteristic, complemented
559#339C22×C1111yescharacteristic, complemented
560#339C22×C1111yescharacteristic, complemented
561C22×C11—21no—
562C22×C11—21no—
563C22×C11—21no—
564C22×C11—21no—
565C22×C11—21no—
566C22×C11—22no—
567C22×C11—21no—
568C22×C11—21no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—41no—
572C22×C11—41no—
573C22×C11—41no—
574C22×C11—41no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—41no—
578C22×C11—41no—
579C22×C11—41no—
580C22×C11—42no—
581C22×C11—41no—
582C22×C11—84no—
583C22×C11—82no—
584C22×C11—82no—
585C22×C11—82no—
586C22×C11—82no—
587C22×C11—81no—
588C22×C11—81no—
589C22×C11—81no—
590C22×C11—164no—
591C22×C11#45312yescomplemented
592C22×C11C2×#12011yescharacteristic
593C22×C11D4211yescharacteristic
594C22×C11#54611yescharacteristic
595C4×C11—24no—
596C4×C11—21no—
597C4×C11—21no—
598C4×C11—22no—
599C4×C11—42no—
600C4×C11—41no—
601C4×C11—41no—
602C4×C11—42no—
603C4×C11—41no—
604C4×C11—41no—
605C4×C11—81no—
606C4×C11C2×#12111yescharacteristic
607C4×C11#53411yescharacteristic
608C4×C11D4211yescharacteristic
609C4×C11#54611yescharacteristic
610H(5,𝔽2)—22no—
611H(5,𝔽2)—22no—
612H(5,𝔽2)—41no—
613H(5,𝔽2)—41no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41—21no—
617C2×#41—21no—
618C2×#41—22no—
619C2×#41—22no—
620C2×#41—41no—
621C2×#41—41no—
622C2×#41D4×C1111yescharacteristic, complemented
623C2×#41D4×C1111yescharacteristic, complemented
624C2×#41C23×C1111yescharacteristic
625C2×#41C23×C1111yescharacteristic
626C2×#41C23×C1111yescharacteristic
627C22×Q8D4×C1111yescharacteristic, complemented
628C22×D4—21no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—21no—
634C22×D4—22no—
635C22×D4D4×C1112yes—
636C22×D4D4×C1111yescharacteristic, complemented
637C22×D4C23×C1111yescharacteristic
638C22×D4C23×C1111yescharacteristic
639C23×C4—21no—
640C23×C4—21no—
641C23×C4C23×C1111yescharacteristic
642AGL(1,ℤ/8)—22no—
643AGL(1,ℤ/8)—22no—
644AGL(1,ℤ/8)—22no—
645AGL(1,ℤ/8)—41no—
646AGL(1,ℤ/8)—41no—
647AGL(1,ℤ/8)—41no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×D8—21no—
652C2×D8—21no—
653C2×D8—21no—
654C2×M16—21no—
655C2×M16—22no—
656C2×M16—41no—
657C2×M16C23×C1111yescharacteristic
658C2×M16C23×C1111yescharacteristic
659C2×M16C23×C1111yescharacteristic
660C2×M16C23×C1111yescharacteristic
661C22×C8—21no—
662#127—22no—
663#127—21no—
664#127—22no—
665#127—41no—
666#124—22no—
667#124—21no—
668#123—22no—
669#123—21no—
670C22⋊Q8—22no—
671C22⋊Q8—21no—
672C22⋊Q8—21no—
673C22⋊Q8D4×C1111yescharacteristic, complemented
674C22⋊Q8D4×C1111yescharacteristic, complemented
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—21no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—48no—
694#121D4×C1111yescharacteristic, complemented
695#121D4×C1111yescharacteristic, complemented
696#120—22no—
697#120—22no—
698#120—22no—
699#120—21no—
700#120—22no—
701C4×Q8—21no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—21no—
705C4×D4—22no—
706C4×D4—21no—
707C4×D4—21no—
708#117—21no—
709#117C23×C1111yescharacteristic
710C2×C4⋊C4—21no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4C23×C1111yescharacteristic
713C2×C4⋊C4C23×C1111yescharacteristic
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4D4×C1112yes—
719C2×C42—22no—
720C2×C42—21no—
721C2×C42—41no—
722C2×C42C23×C1111yescharacteristic
723C2×C42C23×C1111yescharacteristic
724#107—21no—
725#106—21no—
726#104—22no—
727#104—22no—
728#104—22no—
729#104—22no—
730#104—41no—
731#104D4×C1114yescomplemented
732#103—21no—
733#103—21no—
734#103—21no—
735#102—21no—
736#102—21no—
737#102—21no—
738#102—21no—
739#102—21no—
740#100—22no—
741#100—41no—
742C22⋊C8—21no—
743C22⋊C8—21no—
744C2×C11—21no—
745C2×C11—21no—
746C2×C11—22no—
747C2×C11—41no—
748C2×C11—42no—
749C2×C11—81no—
750C2×C11—82no—
751C2×C11—81no—
752C2×C11—161no—
753C2×C11#241011yescharacteristic
754C2×C11C2×#45311yescharacteristic
755C2×C11#301811yescharacteristic
756C24—22no—
757C24—21no—
758C24—21no—
759C24C2×D4×C1111yescharacteristic
760C24C2×D4×C1112yes—
761#41—21no—
762#41—21no—
763#41—22no—
764#41—22no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—42no—
774#41—42no—
775#41—41no—
776#41—41no—
777#41—42no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41C2×D4×C1112yes—
784#41C11×#4112yes—
785C2×Q8—21no—
786C2×Q8—22no—
787C2×Q8—41no—
788C2×Q8C2×D4×C1111yescharacteristic
789C2×Q8C2×D4×C1111yescharacteristic
790C2×Q8C2×D4×C1111yescharacteristic
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—21no—
805C2×D4—22no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—41no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—41no—
834C2×D4—41no—
835C2×D4—84no—
836C2×D4C2×D4×C1111yescharacteristic
837C2×D4C2×D4×C1111yescharacteristic
838C2×D4C2×D4×C1111yescharacteristic
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—24no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4C2×D4×C1111yescharacteristic
860C22×C4C2×D4×C1111yescharacteristic
861C22×C4C2×D4×C1111yescharacteristic
862C22×C4C2×D4×C1111yescharacteristic
863C22×C4C2×D4×C1111yescharacteristic
864C22×C4C2×D4×C1112yes—
865C22×C4C24×C1111yescharacteristic
866SD16—42no—
867SD16—42no—
868SD16—42no—
869D8—42no—
870D8—42no—
871D8—42no—
872M16—21no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—42no—
880M16C2×D4×C1112yescomplemented
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—42no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—44no—
895C4⋊C4C2×D4×C1111yescharacteristic
896C4⋊C4C2×D4×C1111yescharacteristic
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—21no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—21no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—41no—
912C22⋊C4—41no—
913C42—22no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—42no—
919C42C2×D4×C1112yescomplemented
920C11#2446411yescharacteristic, direct product factor, Sylow
921C23—21no—
922C23—21no—
923C23—21no—
924C23—22no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23C11×#12011yescharacteristic
945C23C11×#12011yescharacteristic
946C23C22×D4×C1111yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8C11×#12112yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—44no—
971D4—42no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—81no—
982D4—82no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4C11×#12112yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4C11×#12011yescharacteristic
1027C2×C4C11×#12011yescharacteristic
1028C2×C4C22×D4×C1111yescharacteristic
1029C2×C4C22×D4×C1111yescharacteristic
1030C2×C4C22×D4×C1111yescharacteristic
1031C2×C4C2×C11×#4111yescharacteristic
1032C2×C4C11×H(5,𝔽2)11yescharacteristic
1033C2×C4C11×H(5,𝔽2)11yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—21no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—41no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22C11×#45312yescomplemented
1069C22C2×C11×#12011yescharacteristic
1070C22D42×C1111yescharacteristic
1071C22C11×#54611yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—42no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×C11×#12111yescharacteristic
1084C4C11×#53411yescharacteristic
1085C4D42×C1111yescharacteristic
1086C4C11×#54611yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2C11×#241011yescharacteristic
1097C2C2×C11×#45311yescharacteristic
1098C2C11×#301811yescharacteristic
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. C22×C11×#104C2semidirect
6. C11×#2856C2semidirect
7. C11×#2039C2semidirect
8. C11×#2037C2semidirect
9. C11×#2006C2semidirect
10. C11×#2002C2semidirect
11. C11×#1900C2semidirect
12. C11×#1896C2semidirect
13. C11×#1883C2semidirect
14. C11×#1859C2semidirect
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
38. C2×C11×#121C22semidirect
40. C22×C42×C11C22semidirect
50. C11×#428C22semidirect
54. C2×C11×#104C22semidirect
55. C2×C11×#104C22semidirect
56. C2×C11×#104C22semidirect
57. C2×C11×#104C22semidirect
58. C11×#418C22semidirect
60. C11×#417C22semidirect
61. C11×#417C22semidirect
62. C2×C11×#100C22semidirect
63. C2×C11×#100C22semidirect
64. C11×#407C22semidirect
66. C11×#390C22semidirect
67. C11×#390C22semidirect
68. C11×#384C22semidirect
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
136. C11×C22⋊Q8D4semidirect
137. C11×C22⋊Q8D4semidirect
157. C11×#121D4semidirect
158. C11×#121D4semidirect
194. C11×#104D4semidirect
207. #24464C11direct (N × H)
332. C11×M16C2×D4semidirect
371. C42×C11C2×D4semidirect
372. #3488C2×C11semidirect
373. #3055C2×C11semidirect
374. C2×#453C2×C11semidirect
375. #3006C2×C11semidirect
376. C22×#104C2×C11semidirect
377. #2856C2×C11semidirect
378. #2039C2×C11semidirect
379. #2037C2×C11semidirect
380. #2006C2×C11semidirect
381. #2002C2×C11semidirect
382. #1900C2×C11semidirect
383. #1896C2×C11semidirect
384. #1883C2×C11semidirect
385. #1859C2×C11semidirect
386. #1792C2×C11semidirect
419. Q8×C11#121semidirect
454. D4×C11#121semidirect
507. C2×AGL(1,ℤ/8)C22×C11semidirect
508. C2×AGL(1,ℤ/8)C22×C11semidirect
509. C22×M16C22×C11semidirect
520. C2×#127C22×C11semidirect
526. C2×#121C22×C11semidirect
528. C22×C42C22×C11semidirect
538. #428C22×C11semidirect
542. C2×#104C22×C11semidirect
543. C2×#104C22×C11semidirect
544. C2×#104C22×C11semidirect
545. C2×#104C22×C11semidirect
546. #418C22×C11semidirect
548. #417C22×C11semidirect
549. #417C22×C11semidirect
550. C2×#100C22×C11semidirect
551. C2×#100C22×C11semidirect
552. #407C22×C11semidirect
554. #390C22×C11semidirect
555. #390C22×C11semidirect
556. #384C22×C11semidirect
557. #343C22×C11semidirect
558. #343C22×C11semidirect
559. #339C22×C11semidirect
560. #339C22×C11semidirect
591. C22×C11#453semidirect
622. C2×#41D4×C11semidirect
623. C2×#41D4×C11semidirect
627. C22×Q8D4×C11semidirect
636. C22×D4D4×C11semidirect
673. C22⋊Q8D4×C11semidirect
674. C22⋊Q8D4×C11semidirect
694. #121D4×C11semidirect
695. #121D4×C11semidirect
731. #104D4×C11semidirect
880. M16C2×D4×C11semidirect
919. C42C2×D4×C11semidirect
920. C11#24464direct (N × H)
953. Q8C11×#121semidirect
988. D4C11×#121semidirect
1068. C22C11×#453semidirect

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
C22×C11×#1042
C11×#28562
C11×#20392
C11×#20372
C11×#20062
C11×#20022
C11×#19002
C11×#18962
C11×#18832
C11×#18592
C11×#17922
#2446411