Finite Group Databasebeta

← C11×#24289 #14601482

Subgroups — C11×#24289 #14601482

Order 2816.

1328 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#577C211yesmaximal, characteristic, complemented
2C2×C11×#471C211yesmaximal, characteristic, complemented
3C11×#3060C211yesmaximal, characteristic, complemented
4C11×#3013C211yesmaximal, characteristic, complemented
5C11×#3012C211yesmaximal, characteristic, complemented
6C2×C11×#443C211yesmaximal, characteristic, complemented
7C11×#2052C211yesmaximal, characteristic, complemented
8C11×#2051C211yesmaximal, characteristic, complemented
9C11×#2007C211yesmaximal, characteristic, complemented
10C11×#2006C211yesmaximal, characteristic, complemented
11C11×#1974C211yesmaximal, characteristic, complemented
12C11×#1968C211yesmaximal, characteristic, complemented
13C11×#1815C211yesmaximal, characteristic, complemented
14C11×#1793C211yesmaximal, characteristic, complemented
15C11×#1792C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C2×C11×H(5,𝔽2)C2211yescharacteristic
18C11×#577—24no—
19C11×#577—24no—
20C2×C11×#137—21no—
21C2×C11×#137C2211yescharacteristic
22C2×C11×#137C2211yescharacteristic, complemented
23C2×C11×AGL(1,ℤ/8)—21no—
24C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C11×#135—21no—
27C2×C11×#135C2211yescharacteristic
28C2×C11×#135C2211yescharacteristic
29C22×C11×SD16—21no—
30C22×C11×SD16C2211yescharacteristic
31C2×C11×#131C2211yescharacteristic
32C2×C11×#131C2211yescharacteristic, complemented
33C11×#537C2211yescharacteristic
34C11×#537C2211yescharacteristic, complemented
35C11×#471—24no—
36C11×#470—21no—
37C11×#469—21no—
38C11×#465—21no—
39C11×#465—21no—
40C11×#452—21no—
41C11×#452—21no—
42C11×#451—21no—
43C11×#450—21no—
44C11×#449—21no—
45C11×#449—21no—
46C11×#448—21no—
47C11×#447—21no—
48C11×#443—24no—
49C2×C11×#108C2211yescharacteristic, complemented
50C2×C11×#108C2211yescharacteristic, complemented
51C2×C11×#106C2211yescharacteristic, complemented
52C2×C11×#104C2211yescharacteristic
53C2×C11×#104C2211yescharacteristic
54C2×C11×#104C2211yescharacteristic, complemented
55C2×C11×#104C2211yescharacteristic, complemented
56C11×#417C2211yescharacteristic
57C11×#417C2211yescharacteristic
58C11×#417C2211yescharacteristic
59C11×#417C2211yescharacteristic, complemented
60C2×C11×#103C2211yescharacteristic, complemented
61C2×C11×#102C2211yescharacteristic
62C2×C11×#101C2211yescharacteristic, complemented
63C2×C11×#100C2211yescharacteristic
64C11×#408C2211yescharacteristic
65C11×#408C2211yescharacteristic, complemented
66C2×C4×C8×C11C2211yescharacteristic, complemented
67C11×#391C2211yescharacteristic, complemented
68C11×#390C2211yescharacteristic
69C11×#343C2211yescharacteristic, complemented
70C11×#343C2211yescharacteristic, complemented
71C11×2−1+4—22no—
72C11×2−1+4—22no—
73C11×2−1+4—22no—
74C11×2−1+4—41no—
75C11×H(5,𝔽2)—22no—
76C11×H(5,𝔽2)—22no—
77C11×H(5,𝔽2)—22no—
78C11×H(5,𝔽2)—41no—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41—21no—
83C2×C11×#41—41no—
84C2×C11×#41C2311yescharacteristic
85C2×C11×#41C2311yescharacteristic
86C2×C11×#41C2311yescharacteristic
87C2×C11×#41C2311yescharacteristic
88C22×Q8×C11—21no—
89C22×Q8×C11—21no—
90C22×Q8×C11C2311yescharacteristic
91C22×D4×C11—21no—
92C22×D4×C11—21no—
93C22×D4×C11—41no—
94C22×D4×C11C2311yescharacteristic
95C11×#137—28no—
96C11×#137—22no—
97C11×#137—22no—
98C11×#137—22no—
99C11×#137—41no—
100C11×AGL(1,ℤ/8)—28no—
101C11×AGL(1,ℤ/8)—22no—
102C11×AGL(1,ℤ/8)—22no—
103C11×AGL(1,ℤ/8)—22no—
104C11×AGL(1,ℤ/8)—41no—
105C11×#135—28no—
106C11×#135—22no—
107C11×#135—22no—
108C11×#135—22no—
109C11×#135—22no—
110C2×C11×Q16—21no—
111C2×C11×Q16—21no—
112C2×C11×Q16D411yescharacteristic
113C2×C11×Q16D411yescharacteristic
114C2×C11×SD16—28no—
115C2×C11×SD16—21no—
116C2×C11×SD16—21no—
117C2×C11×SD16—21no—
118C2×C11×SD16—21no—
119C2×C11×SD16—21no—
120C2×C11×SD16—21no—
121C2×C11×SD16—22no—
122C2×C11×SD16D411yescharacteristic
123C2×C11×SD16D411yescharacteristic
124C2×C11×SD16D411yescharacteristic
125C2×C11×SD16D411yescharacteristic
126C2×C11×SD16D414yescomplemented
127C2×C11×D8—21no—
128C2×C11×D8—21no—
129C2×C11×D8D411yescharacteristic
130C2×C11×D8D411yescharacteristic
131C11×#131—22no—
132C11×#131—22no—
133C11×#131—22no—
134C11×#131D414yescomplemented
135C2×C11×M16—21no—
136C2×C11×M16—21no—
137C2×C11×M16C2311yescharacteristic
138C2×C11×M16C2311yescharacteristic
139C2×C11×M16C2311yescharacteristic
140C2×C11×M16C2311yescharacteristic
141C22×C8×C11—21no—
142C22×C8×C11—21no—
143C22×C8×C11C2311yescharacteristic
144C22×C8×C11C2311yescharacteristic
145C11×C22⋊Q8—21no—
146C11×C22⋊Q8—21no—
147C11×C22⋊Q8—21no—
148C11×C22⋊Q8—21no—
149C11×#121—21no—
150C11×#121—21no—
151C11×#121—21no—
152C11×#121—21no—
153C11×#121—41no—
154C11×#121—41no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—41no—
158C2×C42×C11C2311yescharacteristic
159C11×#108—22no—
160C11×#108—22no—
161C11×#106—21no—
162C11×#106—21no—
163C11×#104—22no—
164C11×#104—22no—
165C11×#104—41no—
166C11×#104—41no—
167C11×#103—21no—
168C11×#103—21no—
169C11×#103—21no—
170C11×#103—21no—
171C11×#103—21no—
172C11×#103—21no—
173C11×#102—21no—
174C11×#102—21no—
175C11×#102—21no—
176C11×#102—21no—
177C11×#102—21no—
178C11×#102—21no—
179C11×#101—22no—
180C11×#100—22no—
181C11×C22⋊C8—21no—
182C11×C22⋊C8—21no—
183C11×C22⋊C8—21no—
184C11×C22⋊C8—21no—
185C4×C8×C11—22no—
186C11×#95—41no—
187#24289C1111yesmaximal, characteristic, direct product factor, Sylow
188C24×C11—21no—
189C24×C11—41no—
190C11×#41—21no—
191C11×#41—21no—
192C11×#41—24no—
193C11×#41—24no—
194C11×#41—21no—
195C11×#41—21no—
196C11×#41—21no—
197C11×#41—21no—
198C11×#41—21no—
199C11×#41—21no—
200C11×#41—21no—
201C11×#41—21no—
202C11×#41—21no—
203C11×#41—21no—
204C11×#41—21no—
205C11×#41—21no—
206C11×#41—42no—
207C11×#41—44no—
208C11×#41—42no—
209C11×#41—42no—
210C11×#41—42no—
211C11×#41—44no—
212C11×#41—42no—
213C11×#41—42no—
214C11×#41C2×D412yes—
215C11×#41#4112yes—
216C2×Q8×C11—21no—
217C2×Q8×C11—24no—
218C2×Q8×C11—21no—
219C2×Q8×C11—21no—
220C2×Q8×C11—21no—
221C2×Q8×C11—21no—
222C2×Q8×C11—41no—
223C2×Q8×C11—42no—
224C2×Q8×C11—42no—
225C2×Q8×C11—42no—
226C2×Q8×C11C2×D412yes—
227C2×Q8×C11C2×D411yescharacteristic
228C2×Q8×C11C2×D411yescharacteristic
229C2×Q8×C11C2×D411yescharacteristic
230C2×Q8×C11C2×D411yescharacteristic
231C2×D4×C11—21no—
232C2×D4×C11—24no—
233C2×D4×C11—21no—
234C2×D4×C11—21no—
235C2×D4×C11—21no—
236C2×D4×C11—21no—
237C2×D4×C11—21no—
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11—21no—
241C2×D4×C11—42no—
242C2×D4×C11—41no—
243C2×D4×C11—41no—
244C2×D4×C11—42no—
245C2×D4×C11—44no—
246C2×D4×C11—44no—
247C2×D4×C11—41no—
248C2×D4×C11—42no—
249C2×D4×C11—41no—
250C2×D4×C11—41no—
251C2×D4×C11C2×D412yes—
252C2×D4×C11C2×D411yescharacteristic
253C2×D4×C11C2×D411yescharacteristic
254C2×D4×C11C2×D411yescharacteristic
255C2×D4×C11C2×D411yescharacteristic
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—41no—
265C22×C4×C11—41no—
266C22×C4×C11—41no—
267C22×C4×C11C2411yescharacteristic
268C11×Q16—24no—
269C11×Q16—22no—
270C11×Q16—22no—
271C11×Q16—42no—
272C11×SD16—24no—
273C11×SD16—24no—
274C11×SD16—22no—
275C11×SD16—24no—
276C11×SD16—24no—
277C11×SD16—22no—
278C11×SD16—22no—
279C11×SD16—22no—
280C11×SD16—42no—
281C11×SD16—42no—
282C11×D8—24no—
283C11×D8—22no—
284C11×D8—22no—
285C11×D8—42no—
286C11×M16—24no—
287C11×M16—21no—
288C11×M16—21no—
289C11×M16—21no—
290C11×M16—21no—
291C11×M16—21no—
292C11×M16—21no—
293C11×M16—21no—
294C11×M16—42no—
295C11×M16C2×D412yes—
296C2×C8×C11—24no—
297C2×C8×C11—21no—
298C2×C8×C11—21no—
299C2×C8×C11—21no—
300C2×C8×C11—21no—
301C2×C8×C11—21no—
302C2×C8×C11—21no—
303C2×C8×C11—42no—
304C2×C8×C11C2×D411yescharacteristic
305C2×C8×C11C2×D411yescharacteristic
306C2×C8×C11C2×D412yes—
307C2×C8×C11C2×D411yescharacteristic
308C2×C8×C11C2×D411yescharacteristic
309C2×C8×C11C2×D412yes—
310C11×C4⋊C4—21no—
311C11×C4⋊C4—21no—
312C11×C4⋊C4—21no—
313C11×C4⋊C4—21no—
314C11×C4⋊C4—41no—
315C11×C4⋊C4—41no—
316C11×C22⋊C4—41no—
317C11×C22⋊C4—41no—
318C11×C22⋊C4—41no—
319C11×C22⋊C4—41no—
320C11×C22⋊C4—82no—
321C42×C11—21no—
322C42×C11—21no—
323C2×#577C2×C1111yescharacteristic, complemented
324C2×#471C2×C1111yescharacteristic, complemented
325#3060C2×C1111yescharacteristic, complemented
326#3013C2×C1111yescharacteristic, complemented
327#3012C2×C1111yescharacteristic, complemented
328C2×#443C2×C1111yescharacteristic, complemented
329#2052C2×C1111yescharacteristic, complemented
330#2051C2×C1111yescharacteristic, complemented
331#2007C2×C1111yescharacteristic, complemented
332#2006C2×C1111yescharacteristic, complemented
333#1974C2×C1111yescharacteristic, complemented
334#1968C2×C1111yescharacteristic, complemented
335#1815C2×C1111yescharacteristic, complemented
336#1793C2×C1111yescharacteristic, complemented
337#1792C2×C1111yescharacteristic, complemented
338C23×C11—21no—
339C23×C11—21no—
340C23×C11—21no—
341C23×C11—21no—
342C23×C11—22no—
343C23×C11—44no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—81no—
347C23×C11—81no—
348C23×C11—161no—
349C23×C11—161no—
350C23×C11H(5,𝔽2)11yescharacteristic
351Q8×C11—21no—
352Q8×C11—21no—
353Q8×C11—22no—
354Q8×C11—21no—
355Q8×C11—21no—
356Q8×C11—21no—
357Q8×C11—22no—
358Q8×C11—21no—
359Q8×C11—21no—
360Q8×C11—44no—
361Q8×C11—41no—
362Q8×C11—41no—
363Q8×C11#12112yes—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—21no—
367D4×C11—22no—
368D4×C11—21no—
369D4×C11—21no—
370D4×C11—21no—
371D4×C11—21no—
372D4×C11—22no—
373D4×C11—21no—
374D4×C11—21no—
375D4×C11—44no—
376D4×C11—44no—
377D4×C11—44no—
378D4×C11—41no—
379D4×C11—41no—
380D4×C11—41no—
381D4×C11—41no—
382D4×C11—41no—
383D4×C11—41no—
384D4×C11—41no—
385D4×C11—41no—
386D4×C11—161no—
387D4×C11—161no—
388D4×C11#12112yes—
389C2×C4×C11—21no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—22no—
397C2×C4×C11—44no—
398C2×C4×C11—44no—
399C2×C4×C11—41no—
400C2×C4×C11—44no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—81no—
413C2×C4×C11—81no—
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C2×#4111yescharacteristic
419C2×C4×C11H(5,𝔽2)11yescharacteristic
420C8×C11—22no—
421C8×C11—21no—
422C8×C11—21no—
423C8×C11—41no—
424C8×C11—41no—
425C8×C11—41no—
426C8×C11#12012yes—
427C8×C11#12012yes—
428C2×2−1+4C22×C1111yescharacteristic
429C2×H(5,𝔽2)C22×C1111yescharacteristic
430#577—24no—
431#577—24no—
432C2×#137—21no—
433C2×#137C22×C1111yescharacteristic
434C2×#137C22×C1111yescharacteristic, complemented
435C2×AGL(1,ℤ/8)—21no—
436C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
437C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
438C2×#135—21no—
439C2×#135C22×C1111yescharacteristic
440C2×#135C22×C1111yescharacteristic
441C22×SD16—21no—
442C22×SD16C22×C1111yescharacteristic
443C2×#131C22×C1111yescharacteristic
444C2×#131C22×C1111yescharacteristic, complemented
445#537C22×C1111yescharacteristic
446#537C22×C1111yescharacteristic, complemented
447#471—24no—
448#470—21no—
449#469—21no—
450#465—21no—
451#465—21no—
452#452—21no—
453#452—21no—
454#451—21no—
455#450—21no—
456#449—21no—
457#449—21no—
458#448—21no—
459#447—21no—
460#443—24no—
461C2×#108C22×C1111yescharacteristic, complemented
462C2×#108C22×C1111yescharacteristic, complemented
463C2×#106C22×C1111yescharacteristic, complemented
464C2×#104C22×C1111yescharacteristic
465C2×#104C22×C1111yescharacteristic
466C2×#104C22×C1111yescharacteristic, complemented
467C2×#104C22×C1111yescharacteristic, complemented
468#417C22×C1111yescharacteristic
469#417C22×C1111yescharacteristic
470#417C22×C1111yescharacteristic
471#417C22×C1111yescharacteristic, complemented
472C2×#103C22×C1111yescharacteristic, complemented
473C2×#102C22×C1111yescharacteristic
474C2×#101C22×C1111yescharacteristic, complemented
475C2×#100C22×C1111yescharacteristic
476#408C22×C1111yescharacteristic
477#408C22×C1111yescharacteristic, complemented
478C2×C4×C8C22×C1111yescharacteristic, complemented
479#391C22×C1111yescharacteristic, complemented
480#390C22×C1111yescharacteristic
481#343C22×C1111yescharacteristic, complemented
482#343C22×C1111yescharacteristic, complemented
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—22no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—41no—
489C22×C11—41no—
490C22×C11—42no—
491C22×C11—41no—
492C22×C11—41no—
493C22×C11—41no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—82no—
499C22×C11—81no—
500C22×C11—81no—
501C22×C11—161no—
502C22×C11—164no—
503C22×C11#53511yescharacteristic
504C22×C11D4211yescharacteristic
505C22×C11#54611yescharacteristic
506C4×C11—22no—
507C4×C11—42no—
508C4×C11—41no—
509C4×C11—41no—
510C4×C11—42no—
511C4×C11—41no—
512C4×C11—81no—
513C4×C11—81no—
514C4×C11C2×#12011yescharacteristic
515C4×C11C2×#12111yescharacteristic
516C4×C11D4211yescharacteristic
517C4×C11#54611yescharacteristic
5182−1+4—22no—
5192−1+4—22no—
5202−1+4—22no—
5212−1+4—41no—
522H(5,𝔽2)—22no—
523H(5,𝔽2)—22no—
524H(5,𝔽2)—22no—
525H(5,𝔽2)—41no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—21no—
530C2×#41—41no—
531C2×#41C23×C1111yescharacteristic
532C2×#41C23×C1111yescharacteristic
533C2×#41C23×C1111yescharacteristic
534C2×#41C23×C1111yescharacteristic
535C22×Q8—21no—
536C22×Q8—21no—
537C22×Q8C23×C1111yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—41no—
541C22×D4C23×C1111yescharacteristic
542#137—28no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—41no—
547AGL(1,ℤ/8)—28no—
548AGL(1,ℤ/8)—22no—
549AGL(1,ℤ/8)—22no—
550AGL(1,ℤ/8)—22no—
551AGL(1,ℤ/8)—41no—
552#135—28no—
553#135—22no—
554#135—22no—
555#135—22no—
556#135—22no—
557C2×Q16—21no—
558C2×Q16—21no—
559C2×Q16D4×C1111yescharacteristic
560C2×Q16D4×C1111yescharacteristic
561C2×SD16—28no—
562C2×SD16—21no—
563C2×SD16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—22no—
569C2×SD16D4×C1111yescharacteristic
570C2×SD16D4×C1111yescharacteristic
571C2×SD16D4×C1111yescharacteristic
572C2×SD16D4×C1111yescharacteristic
573C2×SD16D4×C1114yescomplemented
574C2×D8—21no—
575C2×D8—21no—
576C2×D8D4×C1111yescharacteristic
577C2×D8D4×C1111yescharacteristic
578#131—22no—
579#131—22no—
580#131—22no—
581#131D4×C1114yescomplemented
582C2×M16—21no—
583C2×M16—21no—
584C2×M16C23×C1111yescharacteristic
585C2×M16C23×C1111yescharacteristic
586C2×M16C23×C1111yescharacteristic
587C2×M16C23×C1111yescharacteristic
588C22×C8—21no—
589C22×C8—21no—
590C22×C8C23×C1111yescharacteristic
591C22×C8C23×C1111yescharacteristic
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—41no—
601#121—41no—
602C2×C4⋊C4C23×C1111yescharacteristic
603C2×C4⋊C4C23×C1111yescharacteristic
604C2×C22⋊C4—41no—
605C2×C42C23×C1111yescharacteristic
606#108—22no—
607#108—22no—
608#106—21no—
609#106—21no—
610#104—22no—
611#104—22no—
612#104—41no—
613#104—41no—
614#103—21no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#102—21no—
621#102—21no—
622#102—21no—
623#102—21no—
624#102—21no—
625#102—21no—
626#101—22no—
627#100—22no—
628C22⋊C8—21no—
629C22⋊C8—21no—
630C22⋊C8—21no—
631C22⋊C8—21no—
632C4×C8—22no—
633#95—41no—
634C2×C11—21no—
635C2×C11—21no—
636C2×C11—42no—
637C2×C11—81no—
638C2×C11—81no—
639C2×C11—81no—
640C2×C11—82no—
641C2×C11#240811yescharacteristic
642C2×C11#329011yescharacteristic
643C2×C11#329111yescharacteristic
644C24—21no—
645C24—41no—
646#41—21no—
647#41—21no—
648#41—24no—
649#41—24no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—42no—
663#41—44no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41—44no—
668#41—42no—
669#41—42no—
670#41C2×D4×C1112yes—
671#41C11×#4112yes—
672C2×Q8—21no—
673C2×Q8—24no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—41no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8C2×D4×C1112yes—
683C2×Q8C2×D4×C1111yescharacteristic
684C2×Q8C2×D4×C1111yescharacteristic
685C2×Q8C2×D4×C1111yescharacteristic
686C2×Q8C2×D4×C1111yescharacteristic
687C2×D4—21no—
688C2×D4—24no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—42no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—42no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—41no—
704C2×D4—42no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4C2×D4×C1112yes—
708C2×D4C2×D4×C1111yescharacteristic
709C2×D4C2×D4×C1111yescharacteristic
710C2×D4C2×D4×C1111yescharacteristic
711C2×D4C2×D4×C1111yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4C24×C1111yescharacteristic
724Q16—24no—
725Q16—22no—
726Q16—22no—
727Q16—42no—
728SD16—24no—
729SD16—24no—
730SD16—22no—
731SD16—22no—
732SD16—22no—
733SD16—24no—
734SD16—24no—
735SD16—22no—
736SD16—42no—
737SD16—42no—
738D8—24no—
739D8—22no—
740D8—22no—
741D8—42no—
742M16—21no—
743M16—24no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—42no—
751M16C2×D4×C1112yes—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—24no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—42no—
760C2×C8C2×D4×C1111yescharacteristic
761C2×C8C2×D4×C1111yescharacteristic
762C2×C8C2×D4×C1112yes—
763C2×C8C2×D4×C1111yescharacteristic
764C2×C8C2×D4×C1111yescharacteristic
765C2×C8C2×D4×C1112yes—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—41no—
771C4⋊C4—41no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—41no—
775C22⋊C4—41no—
776C22⋊C4—82no—
777C42—21no—
778C42—21no—
779C11#2428911yescharacteristic, direct product factor, Sylow
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—44no—
786C23—41no—
787C23—41no—
788C23—81no—
789C23—81no—
790C23—161no—
791C23—161no—
792C23C11×H(5,𝔽2)11yescharacteristic
793Q8—21no—
794Q8—21no—
795Q8—22no—
796Q8—21no—
797Q8—21no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—21no—
802Q8—44no—
803Q8—41no—
804Q8—41no—
805Q8C11×#12112yes—
806D4—22no—
807D4—22no—
808D4—21no—
809D4—22no—
810D4—21no—
811D4—21no—
812D4—21no—
813D4—21no—
814D4—22no—
815D4—21no—
816D4—21no—
817D4—44no—
818D4—44no—
819D4—44no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—161no—
829D4—161no—
830D4C11×#12112yes—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—41no—
842C2×C4—44no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4C22×D4×C1111yescharacteristic
857C2×C4C22×D4×C1111yescharacteristic
858C2×C4C22×D4×C1111yescharacteristic
859C2×C4C22×D4×C1111yescharacteristic
860C2×C4C2×C11×#4111yescharacteristic
861C2×C4C11×H(5,𝔽2)11yescharacteristic
862C8—22no—
863C8—21no—
864C8—21no—
865C8—41no—
866C8—41no—
867C8—41no—
868C8C11×#12012yes—
869C8C11×#12012yes—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—82no—
886C22—81no—
887C22—81no—
888C22—161no—
889C22—164no—
890C22C11×#53511yescharacteristic
891C22D42×C1111yescharacteristic
892C22C11×#54611yescharacteristic
893C4—22no—
894C4—42no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—41no—
899C4—81no—
900C4—81no—
901C4C2×C11×#12011yescharacteristic
902C4C2×C11×#12111yescharacteristic
903C4D42×C1111yescharacteristic
904C4C11×#54611yescharacteristic
905C2—21no—
906C2—21no—
907C2—42no—
908C2—81no—
909C2—81no—
910C2—81no—
911C2—82no—
912C2C11×#240811yescharacteristic
913C2C11×#329011yescharacteristic
914C2C11×#329111yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#577C2semidirect
2. C2×C11×#471C2semidirect
3. C11×#3060C2semidirect
4. C11×#3013C2semidirect
5. C11×#3012C2semidirect
6. C2×C11×#443C2semidirect
7. C11×#2052C2semidirect
8. C11×#2051C2semidirect
9. C11×#2007C2semidirect
10. C11×#2006C2semidirect
11. C11×#1974C2semidirect
12. C11×#1968C2semidirect
13. C11×#1815C2semidirect
14. C11×#1793C2semidirect
15. C11×#1792C2semidirect
22. C2×C11×#137C22semidirect
32. C2×C11×#131C22semidirect
34. C11×#537C22semidirect
49. C2×C11×#108C22semidirect
50. C2×C11×#108C22semidirect
51. C2×C11×#106C22semidirect
54. C2×C11×#104C22semidirect
55. C2×C11×#104C22semidirect
59. C11×#417C22semidirect
60. C2×C11×#103C22semidirect
62. C2×C11×#101C22semidirect
65. C11×#408C22semidirect
66. C2×C4×C8×C11C22semidirect
67. C11×#391C22semidirect
69. C11×#343C22semidirect
70. C11×#343C22semidirect
126. C2×C11×SD16D4semidirect
134. C11×#131D4semidirect
187. #24289C11direct (N × H)
323. C2×#577C2×C11semidirect
324. C2×#471C2×C11semidirect
325. #3060C2×C11semidirect
326. #3013C2×C11semidirect
327. #3012C2×C11semidirect
328. C2×#443C2×C11semidirect
329. #2052C2×C11semidirect
330. #2051C2×C11semidirect
331. #2007C2×C11semidirect
332. #2006C2×C11semidirect
333. #1974C2×C11semidirect
334. #1968C2×C11semidirect
335. #1815C2×C11semidirect
336. #1793C2×C11semidirect
337. #1792C2×C11semidirect
434. C2×#137C22×C11semidirect
444. C2×#131C22×C11semidirect
446. #537C22×C11semidirect
461. C2×#108C22×C11semidirect
462. C2×#108C22×C11semidirect
463. C2×#106C22×C11semidirect
466. C2×#104C22×C11semidirect
467. C2×#104C22×C11semidirect
471. #417C22×C11semidirect
472. C2×#103C22×C11semidirect
474. C2×#101C22×C11semidirect
477. #408C22×C11semidirect
478. C2×C4×C8C22×C11semidirect
479. #391C22×C11semidirect
481. #343C22×C11semidirect
482. #343C22×C11semidirect
573. C2×SD16D4×C11semidirect
581. #131D4×C11semidirect
779. C11#24289direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5772
C2×C11×#4712
C11×#30602
C11×#30132
C11×#30122
C2×C11×#4432
C11×#20522
C11×#20512
C11×#20072
C11×#20062
C11×#19742
C11×#19682
C11×#18152
C11×#17932
C11×#17922
#2428911