Finite Group Databasebeta

← C11×#61675 #14638868

Subgroups — C11×#61675 #14638868

Order 2816.

2160 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3551C211yesmaximal, characteristic, complemented
2C11×#3498C211yesmaximal, characteristic, complemented
3C11×#3318C212yesmaximal, complemented
4C11×#3317C212yesmaximal, complemented
5C11×#3310C212yesmaximal, complemented
6C11×#3309C212yesmaximal, complemented
7C11×#3271C212yesmaximal, complemented
8C11×#3268C212yesmaximal, complemented
9C11×#3265C212yesmaximal, complemented
10C11×#3264C212yesmaximal, complemented
11C11×#3217C212yesmaximal, complemented
12C11×#3200C211yesmaximal, characteristic, complemented
13C11×#3199C211yesmaximal, characteristic, complemented
14C11×#3198C212yesmaximal, complemented
15C11×#3111C212yesmaximal, complemented
16C11×#3012C212yesmaximal, complemented
17C11×#3009C211yesmaximal, characteristic, complemented
18C11×#3008C211yesmaximal, characteristic, complemented
19C11×#2980C211yesmaximal, characteristic, complemented
20C2×C11×H(5,𝔽2)C2211yescharacteristic
21C2×C11×H(5,𝔽2)C2211yescharacteristic, complemented
22C2×C11×#137C2211yescharacteristic, complemented
23C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
24C2×C11×AGL(1,ℤ/8)C2212yescomplemented
25C2×C11×#135C2212yescomplemented
26C22×C11×SD16C2211yescharacteristic, complemented
27C22×C11×D8C2211yescharacteristic, complemented
28C11×#563—21no—
29C11×#560—21no—
30C11×#555—21no—
31C11×#553C2212yescomplemented
32C11×#552C2212yescomplemented
33C11×#551—21no—
34C11×#550C2212yes—
35C11×#550C2212yescomplemented
36C11×#548C2212yescomplemented
37C11×#546C2212yescomplemented
38D42×C11—22no—
39D42×C11—22no—
40D42×C11C2212yes—
41D42×C11C2212yescomplemented
42C11×#540—22no—
43C11×#538—22no—
44C11×#537C2212yescomplemented
45C11×#536C2211yescharacteristic, complemented
46C11×#535—21no—
47C11×#535—21no—
48C11×#535C2211yescharacteristic
49C11×#535C2211yescharacteristic, complemented
50C11×#535C2211yescharacteristic, complemented
51C11×#532—21no—
52C11×#532C2211yescharacteristic
53C2×C11×#127—21no—
54C2×C11×#127C2211yescharacteristic, complemented
55C11×#529C2212yescomplemented
56C4×C11×#41C2211yescharacteristic, complemented
57C11×#496C2212yescomplemented
58C11×#496C2212yescomplemented
59C11×#490C2212yescomplemented
60C11×#490C2212yescomplemented
61C11×#485C2212yescomplemented
62C11×#482C2212yescomplemented
63C11×#482C2212yescomplemented
64C11×#482C2212yescomplemented
65C11×#481C2212yescomplemented
66C11×#480C2212yescomplemented
67C11×#479C2212yescomplemented
68C11×#478C2212yescomplemented
69C11×#469C2212yescomplemented
70C11×#469C2212yescomplemented
71C11×#468C2212yescomplemented
72C11×#468C2212yescomplemented
73C11×#466C2212yescomplemented
74C11×#466C2212yescomplemented
75C11×#465C2212yescomplemented
76C11×#465C2212yescomplemented
77C11×#464C2212yescomplemented
78C11×#463C2212yescomplemented
79C11×#460C2212yescomplemented
80C11×#460C2212yescomplemented
81C11×#459C2212yescomplemented
82C11×#459C2212yescomplemented
83C11×#452C2212yescomplemented
84C11×#452C2212yescomplemented
85C11×#452C2212yescomplemented
86C11×#450C2212yescomplemented
87C11×#450C2212yescomplemented
88C11×#450C2212yescomplemented
89C11×#450C2212yescomplemented
90C11×#449C2212yes—
91C11×#449C2212yescomplemented
92C11×#449C2212yescomplemented
93C11×#449C2212yescomplemented
94C11×#449C2212yescomplemented
95C11×#448C2212yescomplemented
96C11×#447C2212yescomplemented
97C11×#447C2212yescomplemented
98C11×#447C2212yescomplemented
99C11×#447C2212yescomplemented
100C11×#447C2212yescomplemented
101C11×#442C2212yescomplemented
102C11×#441C2212yescomplemented
103C11×#440C2212yescomplemented
104C11×#440C2212yescomplemented
105C11×#435C2212yescomplemented
106C11×#435C2212yescomplemented
107C11×#435C2212yescomplemented
108C11×#435C2212yescomplemented
109C11×#432C2212yescomplemented
110C11×#418C2211yescharacteristic, complemented
111C11×#418C2211yescharacteristic, complemented
112C11×#417C2212yescomplemented
113C11×#416C2211yescharacteristic, complemented
114C11×#416C2211yescharacteristic, complemented
115C2×C11×#102C2212yescomplemented
116C11×#408C2212yescomplemented
117C11×#408C2211yescharacteristic, complemented
118C11×#408C2211yescharacteristic, complemented
119C11×H(5,𝔽2)—42no—
120C11×H(5,𝔽2)—42no—
121C11×H(5,𝔽2)—42no—
122C11×H(5,𝔽2)—42no—
123C2×C11×#41—21no—
124C2×C11×#41—21no—
125C2×C11×#41C2311yescharacteristic
126C2×C11×#41C2311yescharacteristic
127C2×C11×#41C2312yes—
128C2×C11×#41C2311yescharacteristic
129C2×C11×#41C2312yes—
130C2×C11×#41C2311yescharacteristic
131C2×C11×#41C2311yescharacteristic
132C22×Q8×C11C2311yescharacteristic
133C22×D4×C11—21no—
134C22×D4×C11—21no—
135C22×D4×C11—21no—
136C22×D4×C11—21no—
137C22×D4×C11—22no—
138C22×D4×C11—22no—
139C22×D4×C11—22no—
140C22×D4×C11—22no—
141C22×D4×C11C2311yescharacteristic
142C22×D4×C11C2312yes—
143C22×D4×C11C2311yescharacteristic
144C22×D4×C11C2311yescharacteristic
145C22×D4×C11C2311yescharacteristic
146C22×D4×C11C2311yescharacteristic
147C11×#137—42no—
148C11×AGL(1,ℤ/8)—44no—
149C11×AGL(1,ℤ/8)—42no—
150C11×#135—44no—
151C2×C11×Q16C2312yes—
152C2×C11×SD16—42no—
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2312yes—
155C2×C11×SD16C2312yes—
156C2×C11×SD16C2312yes—
157C2×C11×SD16C2312yes—
158C2×C11×SD16C2312yes—
159C2×C11×D8—42no—
160C2×C11×D8C2312yes—
161C2×C11×D8C2312yes—
162C2×C11×D8C2312yes—
163C2×C11×D8C2312yes—
164C2×C11×D8C2312yes—
165C2×C11×M16C2312yes—
166C2×C11×M16C2311yescharacteristic
167C2×C11×M16C2311yescharacteristic
168C22×C8×C11C2312yes—
169C22×C8×C11C2311yescharacteristic
170C22×C8×C11C2311yescharacteristic
171C11×C4⋊Q8—21no—
172C11×C4⋊Q8D411yescharacteristic
173C11×#127—21no—
174C11×#127—21no—
175C11×#127—22no—
176C11×#127—22no—
177C11×#127—21no—
178C11×#127—21no—
179C11×#127—21no—
180C11×#127D411yescharacteristic
181C11×#127C2312yes—
182C11×#127C2312yes—
183C11×#126—22no—
184C11×#126—22no—
185C11×#126—22no—
186C11×#125—22no—
187C11×#125C2312yes—
188C11×#124—21no—
189C11×#124—21no—
190C11×#124—21no—
191C11×#124—21no—
192C11×#124—22no—
193C11×#124D411yescharacteristic
194C11×#124D411yescharacteristic
195C11×#124C2312yes—
196C11×#123—21no—
197C11×#123—21no—
198C11×#123—22no—
199C11×#123—22no—
200C11×#123—22no—
201C11×#123—22no—
202C11×C22⋊Q8—22no—
203C11×C22⋊Q8—22no—
204C11×C22⋊Q8C2312yes—
205C11×C22⋊Q8C2312yes—
206C11×C22⋊Q8C2312yes—
207C11×#121—22no—
208C11×#121—22no—
209C11×#121—22no—
210C11×#121—22no—
211C11×#121—22no—
212C11×#121—22no—
213C11×#121—22no—
214C11×#121—22no—
215C11×#121—22no—
216C11×#121—22no—
217C11×#121—22no—
218C11×#121—22no—
219C11×#121D412yes—
220C11×#121D412yes—
221C11×#121C2312yes—
222C11×#121C2312yes—
223C11×#121C2312yes—
224C11×#121C2312yes—
225C11×#121C2312yes—
226C11×#121C2312yes—
227C11×#121C2312yes—
228C11×#120—21no—
229C11×#120—21no—
230C11×#120—21no—
231C11×#120—22no—
232C11×#120—21no—
233C11×#120—22no—
234C11×#120—22no—
235C11×#120—22no—
236C11×#120—22no—
237C11×#120—22no—
238C4×Q8×C11C2312yes—
239C4×Q8×C11C2312yes—
240C4×D4×C11—22no—
241C4×D4×C11—22no—
242C4×D4×C11—22no—
243C4×D4×C11—22no—
244C4×D4×C11—22no—
245C4×D4×C11—22no—
246C4×D4×C11C2312yes—
247C4×D4×C11C2312yes—
248C4×D4×C11C2312yes—
249C4×D4×C11C2312yes—
250C11×#117—22no—
251C11×#117—21no—
252C11×#117—22no—
253C11×#117C2311yescharacteristic
254C11×#117C2311yescharacteristic
255C11×#117C2311yescharacteristic
256C2×C11×C4⋊C4C2312yes—
257C2×C11×C22⋊C4—22no—
258C2×C42×C11—21no—
259C2×C42×C11C2311yescharacteristic
260C11×#107C2312yes—
261C11×#107C2312yes—
262C11×#106C2312yes—
263C11×#106C2312yes—
264C11×C4⋊C8C2312yes—
265C11×C4⋊C8C2312yes—
266C11×#103C2312yes—
267C11×#103C2312yes—
268C11×#103C2312yes—
269C11×#103C2312yes—
270C11×#102C2312yes—
271C11×#102C2312yes—
272C11×#102C2312yes—
273C11×#102C2312yes—
274C11×#102C2312yes—
275C11×#102C2312yes—
276C11×#102C2312yes—
277C11×#102C2312yes—
278C11×#102C2312yes—
279C11×#102C2312yes—
280C11×#102C2312yes—
281C11×#102C2312yes—
282C11×C22⋊C8C2312yes—
283C11×C22⋊C8C2312yes—
284C11×C22⋊C8C2312yes—
285C11×C22⋊C8C2312yes—
286C11×C22⋊C8C2312yes—
287C11×C22⋊C8C2312yes—
288C11×#97C2312yes—
289C11×#97C2312yes—
290#61675C1111yesmaximal, characteristic, direct product factor, Sylow
291C24×C11—21no—
292C24×C11—22no—
293C24×C11—21no—
294C24×C11—21no—
295C24×C11—21no—
296C24×C11—21no—
297C11×#41—22no—
298C11×#41—22no—
299C11×#41—24no—
300C11×#41—22no—
301C11×#41—22no—
302C11×#41—41no—
303C11×#41—41no—
304C11×#41—41no—
305C11×#41—41no—
306C11×#41—41no—
307C11×#41—41no—
308C11×#41—42no—
309C11×#41—44no—
310C11×#41—44no—
311C11×#41—42no—
312C11×#41—42no—
313C2×Q8×C11—21no—
314C2×Q8×C11—41no—
315C2×Q8×C11—41no—
316C2×Q8×C11C2×D411yescharacteristic
317C2×Q8×C11C2×D411yescharacteristic
318C2×Q8×C11C2412yes—
319C2×Q8×C11C2411yescharacteristic
320C2×D4×C11—21no—
321C2×D4×C11—22no—
322C2×D4×C11—22no—
323C2×D4×C11—24no—
324C2×D4×C11—21no—
325C2×D4×C11—22no—
326C2×D4×C11—21no—
327C2×D4×C11—22no—
328C2×D4×C11—22no—
329C2×D4×C11—22no—
330C2×D4×C11—22no—
331C2×D4×C11—22no—
332C2×D4×C11—22no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11—22no—
336C2×D4×C11—22no—
337C2×D4×C11—21no—
338C2×D4×C11—21no—
339C2×D4×C11—22no—
340C2×D4×C11—21no—
341C2×D4×C11—21no—
342C2×D4×C11—22no—
343C2×D4×C11—22no—
344C2×D4×C11—21no—
345C2×D4×C11—42no—
346C2×D4×C11—41no—
347C2×D4×C11—41no—
348C2×D4×C11—41no—
349C2×D4×C11—41no—
350C2×D4×C11—41no—
351C2×D4×C11—41no—
352C2×D4×C11—41no—
353C2×D4×C11—41no—
354C2×D4×C11—44no—
355C2×D4×C11—44no—
356C2×D4×C11—44no—
357C2×D4×C11—44no—
358C2×D4×C11—48no—
359C2×D4×C11—84no—
360C2×D4×C11—84no—
361C2×D4×C11—84no—
362C2×D4×C11C2×D412yes—
363C2×D4×C11C2×D412yes—
364C2×D4×C11C2×D411yescharacteristic
365C2×D4×C11C2×D412yes—
366C2×D4×C11C2×D411yescharacteristic
367C2×D4×C11C2×D411yescharacteristic
368C2×D4×C11C2×D411yescharacteristic
369C2×D4×C11C2411yescharacteristic
370C2×D4×C11C2411yescharacteristic
371C2×D4×C11C2412yes—
372C2×D4×C11C2412yes—
373C2×D4×C11C2411yescharacteristic
374C22×C4×C11—21no—
375C22×C4×C11—22no—
376C22×C4×C11—21no—
377C22×C4×C11—22no—
378C22×C4×C11—21no—
379C22×C4×C11—21no—
380C22×C4×C11—22no—
381C22×C4×C11—22no—
382C22×C4×C11—22no—
383C22×C4×C11C2×D412yes—
384C22×C4×C11C2411yescharacteristic
385C22×C4×C11C2412yes—
386C22×C4×C11C2411yescharacteristic
387C22×C4×C11C2411yescharacteristic
388C11×Q16—24no—
389C11×SD16—24no—
390C11×SD16—24no—
391C11×SD16—42no—
392C11×SD16—42no—
393C11×SD16—42no—
394C11×SD16—42no—
395C11×D8—24no—
396C11×D8—42no—
397C11×D8—42no—
398C11×D8—42no—
399C11×D8—42no—
400C11×M16—42no—
401C11×M16—41no—
402C11×M16—41no—
403C2×C8×C11—41no—
404C2×C8×C11—41no—
405C2×C8×C11—42no—
406C2×C8×C11C2412yes—
407C2×C8×C11C2412yes—
408C2×C8×C11C2412yes—
409C2×C8×C11C2412yes—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4—22no—
414C11×C4⋊C4—22no—
415C11×C4⋊C4—22no—
416C11×C4⋊C4—22no—
417C11×C4⋊C4—22no—
418C11×C4⋊C4C2×D412yes—
419C11×C4⋊C4C2×D412yes—
420C11×C4⋊C4C2412yes—
421C11×C4⋊C4C2412yes—
422C11×C4⋊C4C2412yes—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—21no—
427C11×C22⋊C4—21no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—22no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—22no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—22no—
440C11×C22⋊C4C2×D412yes—
441C11×C22⋊C4C2×D412yes—
442C11×C22⋊C4C2×D412yes—
443C11×C22⋊C4C2×D412yes—
444C42×C11—21no—
445C42×C11—22no—
446C42×C11—21no—
447C42×C11—22no—
448C42×C11—21no—
449C42×C11C2×D411yescharacteristic
450C42×C11C2×D411yescharacteristic
451C42×C11C2412yes—
452#3551C2×C1111yescharacteristic, complemented
453#3498C2×C1111yescharacteristic, complemented
454#3318C2×C1112yescomplemented
455#3317C2×C1112yescomplemented
456#3310C2×C1112yescomplemented
457#3309C2×C1112yescomplemented
458#3271C2×C1112yescomplemented
459#3268C2×C1112yescomplemented
460#3265C2×C1112yescomplemented
461#3264C2×C1112yescomplemented
462#3217C2×C1112yescomplemented
463#3200C2×C1111yescharacteristic, complemented
464#3199C2×C1111yescharacteristic, complemented
465#3198C2×C1112yescomplemented
466#3111C2×C1112yescomplemented
467#3012C2×C1112yescomplemented
468#3009C2×C1111yescharacteristic, complemented
469#3008C2×C1111yescharacteristic, complemented
470#2980C2×C1111yescharacteristic, complemented
471C23×C11—21no—
472C23×C11—22no—
473C23×C11—21no—
474C23×C11—21no—
475C23×C11—22no—
476C23×C11—42no—
477C23×C11—44no—
478C23×C11—42no—
479C23×C11—42no—
480C23×C11—42no—
481C23×C11—81no—
482C23×C11—82no—
483C23×C11—82no—
484C23×C11—82no—
485C23×C11—82no—
486C23×C11—82no—
487C23×C11—82no—
488C23×C11—82no—
489C23×C11C22×D411yescharacteristic
490C23×C11C22×D411yescharacteristic
491C23×C11C22×D412yes—
492C23×C11C22×D411yescharacteristic
493Q8×C11—21no—
494Q8×C11—22no—
495Q8×C11—22no—
496Q8×C11—41no—
497Q8×C11—41no—
498Q8×C11—81no—
499Q8×C11H(5,𝔽2)12yes—
500D4×C11—24no—
501D4×C11—21no—
502D4×C11—22no—
503D4×C11—22no—
504D4×C11—21no—
505D4×C11—21no—
506D4×C11—22no—
507D4×C11—22no—
508D4×C11—21no—
509D4×C11—21no—
510D4×C11—41no—
511D4×C11—41no—
512D4×C11—42no—
513D4×C11—41no—
514D4×C11—41no—
515D4×C11—42no—
516D4×C11—42no—
517D4×C11—44no—
518D4×C11—42no—
519D4×C11—42no—
520D4×C11—42no—
521D4×C11—44no—
522D4×C11—42no—
523D4×C11—42no—
524D4×C11—42no—
525D4×C11—44no—
526D4×C11—44no—
527D4×C11—81no—
528D4×C11—82no—
529D4×C11—82no—
530D4×C11—82no—
531D4×C11—82no—
532D4×C11—82no—
533D4×C11—82no—
534D4×C11—82no—
535D4×C11—82no—
536D4×C11—82no—
537D4×C11—82no—
538D4×C11H(5,𝔽2)12yes—
539C2×C4×C11—24no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—21no—
543C2×C4×C11—22no—
544C2×C4×C11—22no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—21no—
548C2×C4×C11—21no—
549C2×C4×C11—22no—
550C2×C4×C11—22no—
551C2×C4×C11—22no—
552C2×C4×C11—22no—
553C2×C4×C11—42no—
554C2×C4×C11—44no—
555C2×C4×C11—42no—
556C2×C4×C11—42no—
557C2×C4×C11—44no—
558C2×C4×C11—82no—
559C2×C4×C11—82no—
560C2×C4×C11—82no—
561C2×C4×C11—81no—
562C2×C4×C11C22×D411yescharacteristic
563C2×C4×C11C22×D412yes—
564C2×C4×C11C22×D412yes—
565C2×C4×C11C22×D411yescharacteristic
566C2×C4×C11C22×D411yescharacteristic
567C2×C4×C11C22×D412yes—
568C2×C4×C11C2511yescharacteristic
569C8×C11—22no—
570C8×C11—22no—
571C8×C11—22no—
572C8×C11—22no—
573C2×H(5,𝔽2)C22×C1111yescharacteristic
574C2×H(5,𝔽2)C22×C1111yescharacteristic, complemented
575C2×#137C22×C1111yescharacteristic, complemented
576C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
577C2×AGL(1,ℤ/8)C22×C1112yescomplemented
578C2×#135C22×C1112yescomplemented
579C22×SD16C22×C1111yescharacteristic, complemented
580C22×D8C22×C1111yescharacteristic, complemented
581#563—21no—
582#560—21no—
583#555—21no—
584#553C22×C1112yescomplemented
585#552C22×C1112yescomplemented
586#551—21no—
587#550C22×C1112yes—
588#550C22×C1112yescomplemented
589#548C22×C1112yescomplemented
590#546C22×C1112yescomplemented
591D42—22no—
592D42—22no—
593D42C22×C1112yes—
594D42C22×C1112yescomplemented
595#540—22no—
596#538—22no—
597#537C22×C1112yescomplemented
598#536C22×C1111yescharacteristic, complemented
599#535—21no—
600#535—21no—
601#535C22×C1111yescharacteristic
602#535C22×C1111yescharacteristic, complemented
603#535C22×C1111yescharacteristic, complemented
604#532—21no—
605#532C22×C1111yescharacteristic
606C2×#127—21no—
607C2×#127C22×C1111yescharacteristic, complemented
608#529C22×C1112yescomplemented
609C4×#41C22×C1111yescharacteristic, complemented
610#496C22×C1112yescomplemented
611#496C22×C1112yescomplemented
612#490C22×C1112yescomplemented
613#490C22×C1112yescomplemented
614#485C22×C1112yescomplemented
615#482C22×C1112yescomplemented
616#482C22×C1112yescomplemented
617#482C22×C1112yescomplemented
618#481C22×C1112yescomplemented
619#480C22×C1112yescomplemented
620#479C22×C1112yescomplemented
621#478C22×C1112yescomplemented
622#469C22×C1112yescomplemented
623#469C22×C1112yescomplemented
624#468C22×C1112yescomplemented
625#468C22×C1112yescomplemented
626#466C22×C1112yescomplemented
627#466C22×C1112yescomplemented
628#465C22×C1112yescomplemented
629#465C22×C1112yescomplemented
630#464C22×C1112yescomplemented
631#463C22×C1112yescomplemented
632#460C22×C1112yescomplemented
633#460C22×C1112yescomplemented
634#459C22×C1112yescomplemented
635#459C22×C1112yescomplemented
636#452C22×C1112yescomplemented
637#452C22×C1112yescomplemented
638#452C22×C1112yescomplemented
639#450C22×C1112yescomplemented
640#450C22×C1112yescomplemented
641#450C22×C1112yescomplemented
642#450C22×C1112yescomplemented
643#449C22×C1112yes—
644#449C22×C1112yescomplemented
645#449C22×C1112yescomplemented
646#449C22×C1112yescomplemented
647#449C22×C1112yescomplemented
648#448C22×C1112yescomplemented
649#447C22×C1112yescomplemented
650#447C22×C1112yescomplemented
651#447C22×C1112yescomplemented
652#447C22×C1112yescomplemented
653#447C22×C1112yescomplemented
654#442C22×C1112yescomplemented
655#441C22×C1112yescomplemented
656#440C22×C1112yescomplemented
657#440C22×C1112yescomplemented
658#435C22×C1112yescomplemented
659#435C22×C1112yescomplemented
660#435C22×C1112yescomplemented
661#435C22×C1112yescomplemented
662#432C22×C1112yescomplemented
663#418C22×C1111yescharacteristic, complemented
664#418C22×C1111yescharacteristic, complemented
665#417C22×C1112yescomplemented
666#416C22×C1111yescharacteristic, complemented
667#416C22×C1111yescharacteristic, complemented
668C2×#102C22×C1112yescomplemented
669#408C22×C1112yescomplemented
670#408C22×C1111yescharacteristic, complemented
671#408C22×C1111yescharacteristic, complemented
672C22×C11—22no—
673C22×C11—22no—
674C22×C11—22no—
675C22×C11—22no—
676C22×C11—22no—
677C22×C11—21no—
678C22×C11—21no—
679C22×C11—22no—
680C22×C11—22no—
681C22×C11—21no—
682C22×C11—42no—
683C22×C11—42no—
684C22×C11—42no—
685C22×C11—42no—
686C22×C11—42no—
687C22×C11—42no—
688C22×C11—42no—
689C22×C11—41no—
690C22×C11—41no—
691C22×C11—42no—
692C22×C11—42no—
693C22×C11—164no—
694C22×C11—162no—
695C22×C11—162no—
696C22×C11—162no—
697C22×C11—162no—
698C22×C11—162no—
699C22×C11C23×D411yescharacteristic
700C4×C11—22no—
701C4×C11—22no—
702C4×C11—21no—
703C4×C11—22no—
704C4×C11—22no—
705C4×C11—21no—
706C4×C11—21no—
707C4×C11—42no—
708C4×C11—42no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11C2×H(5,𝔽2)11yescharacteristic
712C4×C11C2×H(5,𝔽2)11yescharacteristic
713H(5,𝔽2)—42no—
714H(5,𝔽2)—42no—
715H(5,𝔽2)—42no—
716H(5,𝔽2)—42no—
717C2×#41—21no—
718C2×#41—21no—
719C2×#41C23×C1111yescharacteristic
720C2×#41C23×C1111yescharacteristic
721C2×#41C23×C1112yes—
722C2×#41C23×C1111yescharacteristic
723C2×#41C23×C1112yes—
724C2×#41C23×C1111yescharacteristic
725C2×#41C23×C1111yescharacteristic
726C22×Q8C23×C1111yescharacteristic
727C22×D4—21no—
728C22×D4—21no—
729C22×D4—21no—
730C22×D4—21no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4C23×C1111yescharacteristic
736C22×D4C23×C1112yes—
737C22×D4C23×C1111yescharacteristic
738C22×D4C23×C1111yescharacteristic
739C22×D4C23×C1111yescharacteristic
740C22×D4C23×C1111yescharacteristic
741#137—42no—
742AGL(1,ℤ/8)—44no—
743AGL(1,ℤ/8)—42no—
744#135—44no—
745C2×Q16C23×C1112yes—
746C2×SD16—42no—
747C2×SD16C23×C1112yes—
748C2×SD16C23×C1112yes—
749C2×SD16C23×C1112yes—
750C2×SD16C23×C1112yes—
751C2×SD16C23×C1112yes—
752C2×SD16C23×C1112yes—
753C2×D8—42no—
754C2×D8C23×C1112yes—
755C2×D8C23×C1112yes—
756C2×D8C23×C1112yes—
757C2×D8C23×C1112yes—
758C2×D8C23×C1112yes—
759C2×M16C23×C1112yes—
760C2×M16C23×C1111yescharacteristic
761C2×M16C23×C1111yescharacteristic
762C22×C8C23×C1111yescharacteristic
763C22×C8C23×C1111yescharacteristic
764C22×C8C23×C1112yes—
765C4⋊Q8—21no—
766C4⋊Q8D4×C1111yescharacteristic
767#127—21no—
768#127—21no—
769#127—22no—
770#127—22no—
771#127—21no—
772#127—21no—
773#127—21no—
774#127D4×C1111yescharacteristic
775#127C23×C1112yes—
776#127C23×C1112yes—
777#126—22no—
778#126—22no—
779#126—22no—
780#125—22no—
781#125C23×C1112yes—
782#124—21no—
783#124—21no—
784#124—21no—
785#124—21no—
786#124—22no—
787#124D4×C1111yescharacteristic
788#124D4×C1111yescharacteristic
789#124C23×C1112yes—
790#123—21no—
791#123—21no—
792#123—22no—
793#123—22no—
794#123—22no—
795#123—22no—
796C22⋊Q8—22no—
797C22⋊Q8—22no—
798C22⋊Q8C23×C1112yes—
799C22⋊Q8C23×C1112yes—
800C22⋊Q8C23×C1112yes—
801#121—22no—
802#121—22no—
803#121—22no—
804#121—22no—
805#121—22no—
806#121—22no—
807#121—22no—
808#121—22no—
809#121—22no—
810#121—22no—
811#121—22no—
812#121—22no—
813#121D4×C1112yes—
814#121D4×C1112yes—
815#121C23×C1112yes—
816#121C23×C1112yes—
817#121C23×C1112yes—
818#121C23×C1112yes—
819#121C23×C1112yes—
820#121C23×C1112yes—
821#121C23×C1112yes—
822#120—21no—
823#120—21no—
824#120—21no—
825#120—22no—
826#120—21no—
827#120—22no—
828#120—22no—
829#120—22no—
830#120—22no—
831#120—22no—
832C4×Q8C23×C1112yes—
833C4×Q8C23×C1112yes—
834C4×D4—22no—
835C4×D4—22no—
836C4×D4—22no—
837C4×D4—22no—
838C4×D4—22no—
839C4×D4—22no—
840C4×D4C23×C1112yes—
841C4×D4C23×C1112yes—
842C4×D4C23×C1112yes—
843C4×D4C23×C1112yes—
844#117—22no—
845#117—21no—
846#117—22no—
847#117C23×C1111yescharacteristic
848#117C23×C1111yescharacteristic
849#117C23×C1111yescharacteristic
850C2×C4⋊C4C23×C1112yes—
851C2×C22⋊C4—22no—
852C2×C42—21no—
853C2×C42C23×C1111yescharacteristic
854#107C23×C1112yes—
855#107C23×C1112yes—
856#106C23×C1112yes—
857#106C23×C1112yes—
858C4⋊C8C23×C1112yes—
859C4⋊C8C23×C1112yes—
860#103C23×C1112yes—
861#103C23×C1112yes—
862#103C23×C1112yes—
863#103C23×C1112yes—
864#102C23×C1112yes—
865#102C23×C1112yes—
866#102C23×C1112yes—
867#102C23×C1112yes—
868#102C23×C1112yes—
869#102C23×C1112yes—
870#102C23×C1112yes—
871#102C23×C1112yes—
872#102C23×C1112yes—
873#102C23×C1112yes—
874#102C23×C1112yes—
875#102C23×C1112yes—
876C22⋊C8C23×C1112yes—
877C22⋊C8C23×C1112yes—
878C22⋊C8C23×C1112yes—
879C22⋊C8C23×C1112yes—
880C22⋊C8C23×C1112yes—
881C22⋊C8C23×C1112yes—
882#97C23×C1112yes—
883#97C23×C1112yes—
884C2×C11—42no—
885C2×C11—41no—
886C2×C11—41no—
887C2×C11—41no—
888C2×C11—42no—
889C2×C11—82no—
890C2×C11—81no—
891C2×C11—81no—
892C2×C11—82no—
893C2×C11#348411yescharacteristic
894C2×C11#358512yes—
895C24—21no—
896C24—22no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901#41—22no—
902#41—22no—
903#41—24no—
904#41—22no—
905#41—22no—
906#41—41no—
907#41—41no—
908#41—41no—
909#41—41no—
910#41—41no—
911#41—41no—
912#41—42no—
913#41—44no—
914#41—44no—
915#41—42no—
916#41—42no—
917C2×Q8—21no—
918C2×Q8—41no—
919C2×Q8—41no—
920C2×Q8C2×D4×C1111yescharacteristic
921C2×Q8C2×D4×C1111yescharacteristic
922C2×Q8C24×C1112yes—
923C2×Q8C24×C1111yescharacteristic
924C2×D4—21no—
925C2×D4—22no—
926C2×D4—22no—
927C2×D4—24no—
928C2×D4—21no—
929C2×D4—22no—
930C2×D4—21no—
931C2×D4—22no—
932C2×D4—22no—
933C2×D4—22no—
934C2×D4—22no—
935C2×D4—22no—
936C2×D4—22no—
937C2×D4—22no—
938C2×D4—22no—
939C2×D4—22no—
940C2×D4—22no—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—22no—
944C2×D4—21no—
945C2×D4—21no—
946C2×D4—22no—
947C2×D4—22no—
948C2×D4—21no—
949C2×D4—42no—
950C2×D4—41no—
951C2×D4—41no—
952C2×D4—41no—
953C2×D4—41no—
954C2×D4—41no—
955C2×D4—41no—
956C2×D4—41no—
957C2×D4—41no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—48no—
963C2×D4—84no—
964C2×D4—84no—
965C2×D4—84no—
966C2×D4C2×D4×C1112yes—
967C2×D4C2×D4×C1112yes—
968C2×D4C2×D4×C1111yescharacteristic
969C2×D4C2×D4×C1112yes—
970C2×D4C2×D4×C1111yescharacteristic
971C2×D4C2×D4×C1111yescharacteristic
972C2×D4C2×D4×C1111yescharacteristic
973C2×D4C24×C1111yescharacteristic
974C2×D4C24×C1111yescharacteristic
975C2×D4C24×C1112yes—
976C2×D4C24×C1112yes—
977C2×D4C24×C1111yescharacteristic
978C22×C4—21no—
979C22×C4—22no—
980C22×C4—21no—
981C22×C4—22no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4C2×D4×C1112yes—
988C22×C4C24×C1111yescharacteristic
989C22×C4C24×C1112yes—
990C22×C4C24×C1111yescharacteristic
991C22×C4C24×C1111yescharacteristic
992Q16—24no—
993SD16—24no—
994SD16—24no—
995SD16—42no—
996SD16—42no—
997SD16—42no—
998SD16—42no—
999D8—24no—
1000D8—42no—
1001D8—42no—
1002D8—42no—
1003D8—42no—
1004M16—42no—
1005M16—41no—
1006M16—41no—
1007C2×C8—41no—
1008C2×C8—41no—
1009C2×C8—42no—
1010C2×C8C24×C1112yes—
1011C2×C8C24×C1112yes—
1012C2×C8C24×C1112yes—
1013C2×C8C24×C1112yes—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4C2×D4×C1112yes—
1023C4⋊C4C2×D4×C1112yes—
1024C4⋊C4C24×C1112yes—
1025C4⋊C4C24×C1112yes—
1026C4⋊C4C24×C1112yes—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—21no—
1030C22⋊C4—21no—
1031C22⋊C4—21no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4C2×D4×C1112yes—
1045C22⋊C4C2×D4×C1112yes—
1046C22⋊C4C2×D4×C1112yes—
1047C22⋊C4C2×D4×C1112yes—
1048C42—21no—
1049C42—22no—
1050C42—21no—
1051C42—22no—
1052C42—21no—
1053C42C2×D4×C1111yescharacteristic
1054C42C2×D4×C1111yescharacteristic
1055C42C24×C1112yes—
1056C11#6167511yescharacteristic, direct product factor, Sylow
1057C23—21no—
1058C23—22no—
1059C23—21no—
1060C23—21no—
1061C23—22no—
1062C23—42no—
1063C23—44no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—81no—
1068C23—82no—
1069C23—82no—
1070C23—82no—
1071C23—82no—
1072C23—82no—
1073C23—82no—
1074C23—82no—
1075C23C22×D4×C1111yescharacteristic
1076C23C22×D4×C1111yescharacteristic
1077C23C22×D4×C1111yescharacteristic
1078C23C22×D4×C1112yes—
1079Q8—21no—
1080Q8—22no—
1081Q8—22no—
1082Q8—41no—
1083Q8—41no—
1084Q8—81no—
1085Q8C11×H(5,𝔽2)12yes—
1086D4—24no—
1087D4—21no—
1088D4—22no—
1089D4—22no—
1090D4—21no—
1091D4—21no—
1092D4—22no—
1093D4—22no—
1094D4—21no—
1095D4—21no—
1096D4—41no—
1097D4—41no—
1098D4—42no—
1099D4—41no—
1100D4—41no—
1101D4—42no—
1102D4—42no—
1103D4—44no—
1104D4—42no—
1105D4—42no—
1106D4—42no—
1107D4—44no—
1108D4—42no—
1109D4—42no—
1110D4—42no—
1111D4—44no—
1112D4—44no—
1113D4—81no—
1114D4—82no—
1115D4—82no—
1116D4—82no—
1117D4—82no—
1118D4—82no—
1119D4—82no—
1120D4—82no—
1121D4—82no—
1122D4—82no—
1123D4—82no—
1124D4C11×H(5,𝔽2)12yes—
1125C2×C4—24no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—42no—
1140C2×C4—44no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—44no—
1144C2×C4—82no—
1145C2×C4—82no—
1146C2×C4—82no—
1147C2×C4—81no—
1148C2×C4C22×D4×C1111yescharacteristic
1149C2×C4C22×D4×C1112yes—
1150C2×C4C22×D4×C1112yes—
1151C2×C4C22×D4×C1111yescharacteristic
1152C2×C4C22×D4×C1111yescharacteristic
1153C2×C4C22×D4×C1112yes—
1154C2×C4C25×C1111yescharacteristic
1155C8—22no—
1156C8—22no—
1157C8—22no—
1158C8—22no—
1159C22—21no—
1160C22—21no—
1161C22—22no—
1162C22—22no—
1163C22—21no—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—22no—
1169C22—42no—
1170C22—41no—
1171C22—41no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22—42no—
1178C22—42no—
1179C22—42no—
1180C22—162no—
1181C22—162no—
1182C22—164no—
1183C22—162no—
1184C22—162no—
1185C22—162no—
1186C22C23×D4×C1111yescharacteristic
1187C4—21no—
1188C4—22no—
1189C4—22no—
1190C4—21no—
1191C4—21no—
1192C4—22no—
1193C4—22no—
1194C4—42no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4C2×C11×H(5,𝔽2)11yescharacteristic
1199C4C2×C11×H(5,𝔽2)11yescharacteristic
1200C2—41no—
1201C2—41no—
1202C2—41no—
1203C2—42no—
1204C2—42no—
1205C2—81no—
1206C2—81no—
1207C2—82no—
1208C2—82no—
1209C2C11×#348411yescharacteristic
1210C2C11×#358512yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#532 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3551C2semidirect
2. C11×#3498C2semidirect
3. C11×#3318C2semidirect
4. C11×#3317C2semidirect
5. C11×#3310C2semidirect
6. C11×#3309C2semidirect
7. C11×#3271C2semidirect
8. C11×#3268C2semidirect
9. C11×#3265C2semidirect
10. C11×#3264C2semidirect
11. C11×#3217C2semidirect
12. C11×#3200C2semidirect
13. C11×#3199C2semidirect
14. C11×#3198C2semidirect
15. C11×#3111C2semidirect
16. C11×#3012C2semidirect
17. C11×#3009C2semidirect
18. C11×#3008C2semidirect
19. C11×#2980C2semidirect
21. C2×C11×H(5,𝔽2)C22semidirect
22. C2×C11×#137C22semidirect
23. C2×C11×AGL(1,ℤ/8)C22semidirect
24. C2×C11×AGL(1,ℤ/8)C22semidirect
25. C2×C11×#135C22semidirect
26. C22×C11×SD16C22semidirect
27. C22×C11×D8C22semidirect
31. C11×#553C22semidirect
32. C11×#552C22semidirect
35. C11×#550C22semidirect
36. C11×#548C22semidirect
37. C11×#546C22semidirect
41. D42×C11C22semidirect
44. C11×#537C22semidirect
45. C11×#536C22semidirect
49. C11×#535C22semidirect
50. C11×#535C22semidirect
54. C2×C11×#127C22semidirect
55. C11×#529C22semidirect
56. C4×C11×#41C22semidirect
57. C11×#496C22semidirect
58. C11×#496C22semidirect
59. C11×#490C22semidirect
60. C11×#490C22semidirect
61. C11×#485C22semidirect
62. C11×#482C22semidirect
63. C11×#482C22semidirect
64. C11×#482C22semidirect
65. C11×#481C22semidirect
66. C11×#480C22semidirect
67. C11×#479C22semidirect
68. C11×#478C22semidirect
69. C11×#469C22semidirect
70. C11×#469C22semidirect
71. C11×#468C22semidirect
72. C11×#468C22semidirect
73. C11×#466C22semidirect
74. C11×#466C22semidirect
75. C11×#465C22semidirect
76. C11×#465C22semidirect
77. C11×#464C22semidirect
78. C11×#463C22semidirect
79. C11×#460C22semidirect
80. C11×#460C22semidirect
81. C11×#459C22semidirect
82. C11×#459C22semidirect
83. C11×#452C22semidirect
84. C11×#452C22semidirect
85. C11×#452C22semidirect
86. C11×#450C22semidirect
87. C11×#450C22semidirect
88. C11×#450C22semidirect
89. C11×#450C22semidirect
91. C11×#449C22semidirect
92. C11×#449C22semidirect
93. C11×#449C22semidirect
94. C11×#449C22semidirect
95. C11×#448C22semidirect
96. C11×#447C22semidirect
97. C11×#447C22semidirect
98. C11×#447C22semidirect
99. C11×#447C22semidirect
100. C11×#447C22semidirect
101. C11×#442C22semidirect
102. C11×#441C22semidirect
103. C11×#440C22semidirect
104. C11×#440C22semidirect
105. C11×#435C22semidirect
106. C11×#435C22semidirect
107. C11×#435C22semidirect
108. C11×#435C22semidirect
109. C11×#432C22semidirect
110. C11×#418C22semidirect
111. C11×#418C22semidirect
112. C11×#417C22semidirect
113. C11×#416C22semidirect
114. C11×#416C22semidirect
115. C2×C11×#102C22semidirect
116. C11×#408C22semidirect
117. C11×#408C22semidirect
118. C11×#408C22semidirect
290. #61675C11direct (N × H)
452. #3551C2×C11semidirect
453. #3498C2×C11semidirect
454. #3318C2×C11semidirect
455. #3317C2×C11semidirect
456. #3310C2×C11semidirect
457. #3309C2×C11semidirect
458. #3271C2×C11semidirect
459. #3268C2×C11semidirect
460. #3265C2×C11semidirect
461. #3264C2×C11semidirect
462. #3217C2×C11semidirect
463. #3200C2×C11semidirect
464. #3199C2×C11semidirect
465. #3198C2×C11semidirect
466. #3111C2×C11semidirect
467. #3012C2×C11semidirect
468. #3009C2×C11semidirect
469. #3008C2×C11semidirect
470. #2980C2×C11semidirect
574. C2×H(5,𝔽2)C22×C11semidirect
575. C2×#137C22×C11semidirect
576. C2×AGL(1,ℤ/8)C22×C11semidirect
577. C2×AGL(1,ℤ/8)C22×C11semidirect
578. C2×#135C22×C11semidirect
579. C22×SD16C22×C11semidirect
580. C22×D8C22×C11semidirect
584. #553C22×C11semidirect
585. #552C22×C11semidirect
588. #550C22×C11semidirect
589. #548C22×C11semidirect
590. #546C22×C11semidirect
594. D42C22×C11semidirect
597. #537C22×C11semidirect
598. #536C22×C11semidirect
602. #535C22×C11semidirect
603. #535C22×C11semidirect
607. C2×#127C22×C11semidirect
608. #529C22×C11semidirect
609. C4×#41C22×C11semidirect
610. #496C22×C11semidirect
611. #496C22×C11semidirect
612. #490C22×C11semidirect
613. #490C22×C11semidirect
614. #485C22×C11semidirect
615. #482C22×C11semidirect
616. #482C22×C11semidirect
617. #482C22×C11semidirect
618. #481C22×C11semidirect
619. #480C22×C11semidirect
620. #479C22×C11semidirect
621. #478C22×C11semidirect
622. #469C22×C11semidirect
623. #469C22×C11semidirect
624. #468C22×C11semidirect
625. #468C22×C11semidirect
626. #466C22×C11semidirect
627. #466C22×C11semidirect
628. #465C22×C11semidirect
629. #465C22×C11semidirect
630. #464C22×C11semidirect
631. #463C22×C11semidirect
632. #460C22×C11semidirect
633. #460C22×C11semidirect
634. #459C22×C11semidirect
635. #459C22×C11semidirect
636. #452C22×C11semidirect
637. #452C22×C11semidirect
638. #452C22×C11semidirect
639. #450C22×C11semidirect
640. #450C22×C11semidirect
641. #450C22×C11semidirect
642. #450C22×C11semidirect
644. #449C22×C11semidirect
645. #449C22×C11semidirect
646. #449C22×C11semidirect
647. #449C22×C11semidirect
648. #448C22×C11semidirect
649. #447C22×C11semidirect
650. #447C22×C11semidirect
651. #447C22×C11semidirect
652. #447C22×C11semidirect
653. #447C22×C11semidirect
654. #442C22×C11semidirect
655. #441C22×C11semidirect
656. #440C22×C11semidirect
657. #440C22×C11semidirect
658. #435C22×C11semidirect
659. #435C22×C11semidirect
660. #435C22×C11semidirect
661. #435C22×C11semidirect
662. #432C22×C11semidirect
663. #418C22×C11semidirect
664. #418C22×C11semidirect
665. #417C22×C11semidirect
666. #416C22×C11semidirect
667. #416C22×C11semidirect
668. C2×#102C22×C11semidirect
669. #408C22×C11semidirect
670. #408C22×C11semidirect
671. #408C22×C11semidirect
1056. C11#61675direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35512
C11×#34982
C11×#33182
C11×#33172
C11×#33102
C11×#33092
C11×#32712
C11×#32682
C11×#32652
C11×#32642
C11×#32172
C11×#32002
C11×#31992
C11×#31982
C11×#31112
C11×#30122
C11×#30092
C11×#30082
C11×#29802
#6167511