Finite Group Databasebeta

← C11×#24461 #14601654

Subgroups — C11×#24461 #14601654

Order 2816.

1318 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#578C211yesmaximal, characteristic, complemented
2C2×C11×#471C211yesmaximal, characteristic, complemented
3C11×#3045C211yesmaximal, characteristic, complemented
4C2×C11×#454C211yesmaximal, characteristic, complemented
5C11×#3010C211yesmaximal, characteristic, complemented
6C11×#2898C211yesmaximal, characteristic, complemented
7C11×#2052C211yesmaximal, characteristic, complemented
8C11×#2047C211yesmaximal, characteristic, complemented
9C11×#2015C211yesmaximal, characteristic, complemented
10C11×#2004C211yesmaximal, characteristic, complemented
11C11×#1907C211yesmaximal, characteristic, complemented
12C11×#1882C211yesmaximal, characteristic, complemented
13C11×#1876C211yesmaximal, characteristic, complemented
14C11×#1866C211yesmaximal, characteristic, complemented
15C11×#1793C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C2×C11×2−1+4C2211yescharacteristic
18C11×#578—24no—
19C11×#578—24no—
20C2×C11×#137—21no—
21C2×C11×#137—21no—
22C2×C11×#137C2211yescharacteristic
23C2×C11×#137C2211yescharacteristic
24C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C11×#135—21no—
27C2×C11×#135C2211yescharacteristic
28C22×C11×Q16—21no—
29C22×C11×Q16C2211yescharacteristic
30C22×C11×SD16C2211yescharacteristic
31C2×C11×#131C2211yescharacteristic
32C2×C11×#131C2211yescharacteristic
33C11×#535C2211yescharacteristic
34C2×C11×#124C2211yescharacteristic
35C11×#520C2211yescharacteristic
36C11×#471—24no—
37C11×#464—21no—
38C11×#463—21no—
39C11×#460—21no—
40C11×#459—21no—
41C11×#454—24no—
42C11×#449—21no—
43C11×#449—21no—
44C11×#448—21no—
45C11×#448—21no—
46C2×C11×#108C2211yescharacteristic
47C11×#424C2211yescharacteristic
48C2×C11×#104C2211yescharacteristic
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic
51C11×#419—21no—
52C11×#419C2211yescharacteristic
53C11×#419C2211yescharacteristic
54C11×#417—21no—
55C11×#417C2211yescharacteristic
56C11×#417C2211yescharacteristic
57C11×#416—21no—
58C11×#416C2211yescharacteristic
59C2×C11×#103—21no—
60C2×C11×#103C2211yescharacteristic
61C2×C11×#102C2211yescharacteristic
62C2×C11×#101C2211yescharacteristic
63C2×C11×#101C2211yescharacteristic
64C2×C11×#100C2211yescharacteristic
65C11×#408C2211yescharacteristic
66C11×#391C2211yescharacteristic
67C11×#343C2211yescharacteristic
68C11×#341C2211yescharacteristic
69C11×#339C2211yescharacteristic
70C11×#336C2211yescharacteristic
71C11×2−1+4—22no—
72C11×2−1+4—22no—
73C11×2−1+4—22no—
74C11×2−1+4—22no—
75C11×2−1+4—22no—
76C11×2−1+4—41no—
77C11×2−1+4—41no—
78C11×2−1+4D414yescomplemented
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41—21no—
83C2×C11×#41—41no—
84C2×C11×#41—41no—
85C2×C11×#41C2311yescharacteristic
86C2×C11×#41C2311yescharacteristic
87C2×C11×#41C2311yescharacteristic
88C22×Q8×C11—21no—
89C22×Q8×C11—21no—
90C22×Q8×C11—21no—
91C22×Q8×C11—21no—
92C22×Q8×C11C2311yescharacteristic
93C22×Q8×C11C2311yescharacteristic
94C22×D4×C11C2311yescharacteristic
95C11×#137—28no—
96C11×#137—28no—
97C11×#137—22no—
98C11×#137—22no—
99C11×#137—22no—
100C11×#137D414yescomplemented
101C11×AGL(1,ℤ/8)—22no—
102C11×AGL(1,ℤ/8)—22no—
103C11×AGL(1,ℤ/8)—22no—
104C11×AGL(1,ℤ/8)—22no—
105C11×#135—28no—
106C11×#135—22no—
107C11×#135—22no—
108C2×C11×Q16—28no—
109C2×C11×Q16—21no—
110C2×C11×Q16—21no—
111C2×C11×Q16—22no—
112C2×C11×Q16—22no—
113C2×C11×Q16—21no—
114C2×C11×Q16—21no—
115C2×C11×Q16D411yescharacteristic
116C2×C11×SD16—21no—
117C2×C11×SD16—21no—
118C2×C11×SD16—22no—
119C2×C11×SD16—21no—
120C2×C11×SD16—21no—
121C2×C11×SD16—21no—
122C2×C11×SD16—21no—
123C2×C11×SD16—41no—
124C2×C11×SD16D411yescharacteristic
125C2×C11×SD16D411yescharacteristic
126C2×C11×D8—21no—
127C2×C11×D8—21no—
128C2×C11×D8D411yescharacteristic
129C11×#131—22no—
130C11×#131—22no—
131C11×#131—22no—
132C11×#131—41no—
133C2×C11×M16—21no—
134C2×C11×M16—21no—
135C2×C11×M16C2311yescharacteristic
136C2×C11×M16C2311yescharacteristic
137C2×C11×M16C2311yescharacteristic
138C2×C11×M16C2311yescharacteristic
139C22×C8×C11—21no—
140C22×C8×C11—21no—
141C22×C8×C11C2311yescharacteristic
142C22×C8×C11C2311yescharacteristic
143C11×#127—21no—
144C11×#124—22no—
145C11×#124—21no—
146C11×#124—41no—
147C11×#121—21no—
148C11×#121—21no—
149C11×#120—41no—
150C4×Q8×C11—21no—
151C4×D4×C11—21no—
152C4×D4×C11—41no—
153C11×#117—21no—
154C11×#117C2311yescharacteristic
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—41no—
158C2×C42×C11C2311yescharacteristic
159C11×#108—22no—
160C11×C4⋊C8—21no—
161C11×C4⋊C8—21no—
162C11×#104—22no—
163C11×#104—22no—
164C11×#104—41no—
165C11×#103—21no—
166C11×#103—21no—
167C11×#103—21no—
168C11×#103—21no—
169C11×#103—21no—
170C11×#103—21no—
171C11×#103—21no—
172C11×#103—21no—
173C11×#103D411yescharacteristic
174C11×#103D411yescharacteristic
175C11×#102—21no—
176C11×#102—21no—
177C11×#102—21no—
178C11×#102—21no—
179C11×#102D411yescharacteristic
180C11×#102D411yescharacteristic
181C11×#101—22no—
182C11×#101—22no—
183C11×#100—22no—
184C11×C22⋊C8—21no—
185C11×C22⋊C8—21no—
186C11×#95—41no—
187#24461C1111yesmaximal, characteristic, direct product factor, Sylow
188C24×C11—21no—
189C11×#41—21no—
190C11×#41—21no—
191C11×#41—21no—
192C11×#41—21no—
193C11×#41—24no—
194C11×#41—24no—
195C11×#41—24no—
196C11×#41—21no—
197C11×#41—21no—
198C11×#41—21no—
199C11×#41—21no—
200C11×#41—44no—
201C11×#41—42no—
202C11×#41—42no—
203C11×#41—42no—
204C11×#41—44no—
205C11×#41—44no—
206C11×#41—42no—
207C11×#41—44no—
208C11×#41—42no—
209C11×#41C2×D412yes—
210C11×#41C2×D412yes—
211C11×#41C2×D412yes—
212C11×#41#4112yes—
213C2×Q8×C11—21no—
214C2×Q8×C11—21no—
215C2×Q8×C11—24no—
216C2×Q8×C11—24no—
217C2×Q8×C11—24no—
218C2×Q8×C11—21no—
219C2×Q8×C11—21no—
220C2×Q8×C11—21no—
221C2×Q8×C11—21no—
222C2×Q8×C11—21no—
223C2×Q8×C11—21no—
224C2×Q8×C11—21no—
225C2×Q8×C11—21no—
226C2×Q8×C11—41no—
227C2×Q8×C11—41no—
228C2×Q8×C11—42no—
229C2×Q8×C11—42no—
230C2×Q8×C11—42no—
231C2×Q8×C11—42no—
232C2×Q8×C11—42no—
233C2×Q8×C11C2×D412yes—
234C2×Q8×C11C2×D412yes—
235C2×Q8×C11C2×D411yescharacteristic
236C2×Q8×C11C2×D411yescharacteristic
237C2×Q8×C11C2×D411yescharacteristic
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11—21no—
241C2×D4×C11—21no—
242C2×D4×C11—21no—
243C2×D4×C11—21no—
244C2×D4×C11—21no—
245C2×D4×C11—21no—
246C2×D4×C11—21no—
247C2×D4×C11—41no—
248C2×D4×C11—41no—
249C2×D4×C11—41no—
250C2×D4×C11—41no—
251C2×D4×C11C2×D411yescharacteristic
252C2×D4×C11C2×D411yescharacteristic
253C2×D4×C11C2×D411yescharacteristic
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—41no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11—41no—
265C22×C4×C11—41no—
266C22×C4×C11C2411yescharacteristic
267C11×Q16—24no—
268C11×Q16—24no—
269C11×Q16—24no—
270C11×Q16—22no—
271C11×Q16—24no—
272C11×SD16—24no—
273C11×SD16—22no—
274C11×SD16—24no—
275C11×SD16—22no—
276C11×SD16—42no—
277C11×SD16—42no—
278C11×SD16—42no—
279C11×SD16—42no—
280C11×D8—22no—
281C11×D8—42no—
282C11×D8—42no—
283C11×M16—24no—
284C11×M16—21no—
285C11×M16—21no—
286C11×M16—21no—
287C11×M16—21no—
288C11×M16—21no—
289C11×M16—21no—
290C11×M16—21no—
291C11×M16—42no—
292C11×M16C2×D412yes—
293C2×C8×C11—24no—
294C2×C8×C11—21no—
295C2×C8×C11—21no—
296C2×C8×C11—21no—
297C2×C8×C11—21no—
298C2×C8×C11—21no—
299C2×C8×C11—21no—
300C2×C8×C11—21no—
301C2×C8×C11—21no—
302C2×C8×C11—42no—
303C2×C8×C11C2×D411yescharacteristic
304C2×C8×C11C2×D411yescharacteristic
305C2×C8×C11C2×D411yescharacteristic
306C2×C8×C11C2×D411yescharacteristic
307C11×C4⋊C4—21no—
308C11×C4⋊C4—21no—
309C11×C4⋊C4—41no—
310C11×C4⋊C4C2×D411yescharacteristic
311C11×C4⋊C4C2×D411yescharacteristic
312C11×C22⋊C4—21no—
313C11×C22⋊C4—41no—
314C11×C22⋊C4—41no—
315C11×C22⋊C4—41no—
316C11×C22⋊C4—44no—
317C42×C11—21no—
318C42×C11—21no—
319C42×C11—21no—
320C42×C11—41no—
321C2×#578C2×C1111yescharacteristic, complemented
322C2×#471C2×C1111yescharacteristic, complemented
323#3045C2×C1111yescharacteristic, complemented
324C2×#454C2×C1111yescharacteristic, complemented
325#3010C2×C1111yescharacteristic, complemented
326#2898C2×C1111yescharacteristic, complemented
327#2052C2×C1111yescharacteristic, complemented
328#2047C2×C1111yescharacteristic, complemented
329#2015C2×C1111yescharacteristic, complemented
330#2004C2×C1111yescharacteristic, complemented
331#1907C2×C1111yescharacteristic, complemented
332#1882C2×C1111yescharacteristic, complemented
333#1876C2×C1111yescharacteristic, complemented
334#1866C2×C1111yescharacteristic, complemented
335#1793C2×C1111yescharacteristic, complemented
336C23×C11—21no—
337C23×C11—21no—
338C23×C11—21no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—81no—
343C23×C11—81no—
344C23×C11H(5,𝔽2)11yescharacteristic
345Q8×C11—21no—
346Q8×C11—21no—
347Q8×C11—22no—
348Q8×C11—22no—
349Q8×C11—21no—
350Q8×C11—22no—
351Q8×C11—22no—
352Q8×C11—21no—
353Q8×C11—44no—
354Q8×C11—44no—
355Q8×C11—41no—
356Q8×C11—41no—
357Q8×C11—41no—
358Q8×C11—41no—
359Q8×C11#12012yes—
360Q8×C11#12112yes—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—21no—
366D4×C11—21no—
367D4×C11—21no—
368D4×C11—21no—
369D4×C11—44no—
370D4×C11—44no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—41no—
377D4×C11—161no—
378D4×C11—161no—
379D4×C11#12012yes—
380D4×C11#12112yes—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—22no—
392C2×C4×C11—44no—
393C2×C4×C11—44no—
394C2×C4×C11—44no—
395C2×C4×C11—44no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—81no—
407C2×C4×C11—161no—
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C2×#4111yescharacteristic
413C2×C4×C11H(5,𝔽2)11yescharacteristic
414C8×C11—21no—
415C8×C11—22no—
416C8×C11—21no—
417C8×C11—21no—
418C8×C11—21no—
419C8×C11—41no—
420C8×C11—41no—
421C8×C11—41no—
422C2×2−1+4C22×C1111yescharacteristic
423C2×2−1+4C22×C1111yescharacteristic
424#578—24no—
425#578—24no—
426C2×#137—21no—
427C2×#137—21no—
428C2×#137C22×C1111yescharacteristic
429C2×#137C22×C1111yescharacteristic
430C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
431C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
432C2×#135—21no—
433C2×#135C22×C1111yescharacteristic
434C22×Q16—21no—
435C22×Q16C22×C1111yescharacteristic
436C22×SD16C22×C1111yescharacteristic
437C2×#131C22×C1111yescharacteristic
438C2×#131C22×C1111yescharacteristic
439#535C22×C1111yescharacteristic
440C2×#124C22×C1111yescharacteristic
441#520C22×C1111yescharacteristic
442#471—24no—
443#464—21no—
444#463—21no—
445#460—21no—
446#459—21no—
447#454—24no—
448#449—21no—
449#449—21no—
450#448—21no—
451#448—21no—
452C2×#108C22×C1111yescharacteristic
453#424C22×C1111yescharacteristic
454C2×#104C22×C1111yescharacteristic
455C2×#104C22×C1111yescharacteristic
456C2×#104C22×C1111yescharacteristic
457#419—21no—
458#419C22×C1111yescharacteristic
459#419C22×C1111yescharacteristic
460#417—21no—
461#417C22×C1111yescharacteristic
462#417C22×C1111yescharacteristic
463#416—21no—
464#416C22×C1111yescharacteristic
465C2×#103—21no—
466C2×#103C22×C1111yescharacteristic
467C2×#102C22×C1111yescharacteristic
468C2×#101C22×C1111yescharacteristic
469C2×#101C22×C1111yescharacteristic
470C2×#100C22×C1111yescharacteristic
471#408C22×C1111yescharacteristic
472#391C22×C1111yescharacteristic
473#343C22×C1111yescharacteristic
474#341C22×C1111yescharacteristic
475#339C22×C1111yescharacteristic
476#336C22×C1111yescharacteristic
477C22×C11—21no—
478C22×C11—21no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—82no—
489C22×C11—81no—
490C22×C11—81no—
491C22×C11—81no—
492C22×C11—161no—
493C22×C11#53411yescharacteristic
494C22×C11D4211yescharacteristic
495C22×C11#54611yescharacteristic
496C4×C11—22no—
497C4×C11—22no—
498C4×C11—42no—
499C4×C11—41no—
500C4×C11—42no—
501C4×C11—41no—
502C4×C11—41no—
503C4×C11—81no—
504C4×C11—81no—
505C4×C11C2×#12011yescharacteristic
506C4×C11C2×#12111yescharacteristic
507C4×C11D4211yescharacteristic
508C4×C11#54611yescharacteristic
5092−1+4—22no—
5102−1+4—22no—
5112−1+4—22no—
5122−1+4—22no—
5132−1+4—22no—
5142−1+4—41no—
5152−1+4—41no—
5162−1+4D4×C1114yescomplemented
517C2×#41—21no—
518C2×#41—21no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41C23×C1111yescharacteristic
524C2×#41C23×C1111yescharacteristic
525C2×#41C23×C1111yescharacteristic
526C22×Q8—21no—
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8C23×C1111yescharacteristic
531C22×Q8C23×C1111yescharacteristic
532C22×D4C23×C1111yescharacteristic
533#137—28no—
534#137—28no—
535#137—22no—
536#137—22no—
537#137—22no—
538#137D4×C1114yescomplemented
539AGL(1,ℤ/8)—22no—
540AGL(1,ℤ/8)—22no—
541AGL(1,ℤ/8)—22no—
542AGL(1,ℤ/8)—22no—
543#135—28no—
544#135—22no—
545#135—22no—
546C2×Q16—28no—
547C2×Q16—21no—
548C2×Q16—21no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—21no—
552C2×Q16—21no—
553C2×Q16D4×C1111yescharacteristic
554C2×SD16—21no—
555C2×SD16—21no—
556C2×SD16—22no—
557C2×SD16—21no—
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×SD16—41no—
562C2×SD16D4×C1111yescharacteristic
563C2×SD16D4×C1111yescharacteristic
564C2×D8—21no—
565C2×D8—21no—
566C2×D8D4×C1111yescharacteristic
567#131—22no—
568#131—22no—
569#131—22no—
570#131—41no—
571C2×M16—21no—
572C2×M16—21no—
573C2×M16C23×C1111yescharacteristic
574C2×M16C23×C1111yescharacteristic
575C2×M16C23×C1111yescharacteristic
576C2×M16C23×C1111yescharacteristic
577C22×C8—21no—
578C22×C8—21no—
579C22×C8C23×C1111yescharacteristic
580C22×C8C23×C1111yescharacteristic
581#127—21no—
582#124—22no—
583#124—21no—
584#124—41no—
585#121—21no—
586#121—21no—
587#120—41no—
588C4×Q8—21no—
589C4×D4—21no—
590C4×D4—41no—
591#117—21no—
592#117C23×C1111yescharacteristic
593C2×C4⋊C4—21no—
594C2×C4⋊C4C23×C1111yescharacteristic
595C2×C22⋊C4—41no—
596C2×C42C23×C1111yescharacteristic
597#108—22no—
598C4⋊C8—21no—
599C4⋊C8—21no—
600#104—22no—
601#104—22no—
602#104—41no—
603#103—21no—
604#103—21no—
605#103—21no—
606#103—21no—
607#103—21no—
608#103—21no—
609#103—21no—
610#103—21no—
611#103D4×C1111yescharacteristic
612#103D4×C1111yescharacteristic
613#102—21no—
614#102—21no—
615#102—21no—
616#102—21no—
617#102D4×C1111yescharacteristic
618#102D4×C1111yescharacteristic
619#101—22no—
620#101—22no—
621#100—22no—
622C22⋊C8—21no—
623C22⋊C8—21no—
624#95—41no—
625C2×C11—21no—
626C2×C11—21no—
627C2×C11—42no—
628C2×C11—42no—
629C2×C11—81no—
630C2×C11—161no—
631C2×C11#241011yescharacteristic
632C2×C11#328911yescharacteristic
633C2×C11#329011yescharacteristic
634C24—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—24no—
640#41—24no—
641#41—24no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—44no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—44no—
651#41—44no—
652#41—42no—
653#41—44no—
654#41—42no—
655#41C2×D4×C1112yes—
656#41C2×D4×C1112yes—
657#41C2×D4×C1112yes—
658#41C11×#4112yes—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—24no—
662C2×Q8—24no—
663C2×Q8—24no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×Q8—41no—
674C2×Q8—42no—
675C2×Q8—42no—
676C2×Q8—42no—
677C2×Q8—42no—
678C2×Q8—42no—
679C2×Q8C2×D4×C1112yes—
680C2×Q8C2×D4×C1112yes—
681C2×Q8C2×D4×C1111yescharacteristic
682C2×Q8C2×D4×C1111yescharacteristic
683C2×Q8C2×D4×C1111yescharacteristic
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—41no—
694C2×D4—41no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4C2×D4×C1111yescharacteristic
698C2×D4C2×D4×C1111yescharacteristic
699C2×D4C2×D4×C1111yescharacteristic
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4—41no—
712C22×C4C24×C1111yescharacteristic
713Q16—24no—
714Q16—24no—
715Q16—24no—
716Q16—22no—
717Q16—24no—
718SD16—24no—
719SD16—22no—
720SD16—24no—
721SD16—22no—
722SD16—42no—
723SD16—42no—
724SD16—42no—
725SD16—42no—
726D8—22no—
727D8—42no—
728D8—42no—
729M16—24no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—42no—
738M16C2×D4×C1112yes—
739C2×C8—24no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C1111yescharacteristic
750C2×C8C2×D4×C1111yescharacteristic
751C2×C8C2×D4×C1111yescharacteristic
752C2×C8C2×D4×C1111yescharacteristic
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—41no—
756C4⋊C4C2×D4×C1111yescharacteristic
757C4⋊C4C2×D4×C1111yescharacteristic
758C22⋊C4—21no—
759C22⋊C4—41no—
760C22⋊C4—41no—
761C22⋊C4—41no—
762C22⋊C4—44no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—41no—
767C11#2446111yescharacteristic, direct product factor, Sylow
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—81no—
775C23—81no—
776C23C11×H(5,𝔽2)11yescharacteristic
777Q8—21no—
778Q8—21no—
779Q8—22no—
780Q8—22no—
781Q8—21no—
782Q8—22no—
783Q8—22no—
784Q8—21no—
785Q8—44no—
786Q8—44no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8C11×#12012yes—
792Q8C11×#12112yes—
793D4—22no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—21no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—44no—
802D4—44no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—161no—
810D4—161no—
811D4C11×#12012yes—
812D4C11×#12112yes—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—161no—
840C2×C4C22×D4×C1111yescharacteristic
841C2×C4C22×D4×C1111yescharacteristic
842C2×C4C22×D4×C1111yescharacteristic
843C2×C4C22×D4×C1111yescharacteristic
844C2×C4C2×C11×#4111yescharacteristic
845C2×C4C11×H(5,𝔽2)11yescharacteristic
846C8—21no—
847C8—22no—
848C8—21no—
849C8—21no—
850C8—21no—
851C8—41no—
852C8—41no—
853C8—41no—
854C22—21no—
855C22—21no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—82no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—161no—
870C22C11×#53411yescharacteristic
871C22D42×C1111yescharacteristic
872C22C11×#54611yescharacteristic
873C4—22no—
874C4—22no—
875C4—42no—
876C4—41no—
877C4—42no—
878C4—41no—
879C4—41no—
880C4—81no—
881C4—81no—
882C4C2×C11×#12011yescharacteristic
883C4C2×C11×#12111yescharacteristic
884C4D42×C1111yescharacteristic
885C4C11×#54611yescharacteristic
886C2—21no—
887C2—21no—
888C2—42no—
889C2—42no—
890C2—81no—
891C2—161no—
892C2C11×#241011yescharacteristic
893C2C11×#328911yescharacteristic
894C2C11×#329011yescharacteristic
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×#578C2semidirect
2. C2×C11×#471C2semidirect
3. C11×#3045C2semidirect
4. C2×C11×#454C2semidirect
5. C11×#3010C2semidirect
6. C11×#2898C2semidirect
7. C11×#2052C2semidirect
8. C11×#2047C2semidirect
9. C11×#2015C2semidirect
10. C11×#2004C2semidirect
11. C11×#1907C2semidirect
12. C11×#1882C2semidirect
13. C11×#1876C2semidirect
14. C11×#1866C2semidirect
15. C11×#1793C2semidirect
78. C11×2−1+4D4semidirect
100. C11×#137D4semidirect
187. #24461C11direct (N × H)
321. C2×#578C2×C11semidirect
322. C2×#471C2×C11semidirect
323. #3045C2×C11semidirect
324. C2×#454C2×C11semidirect
325. #3010C2×C11semidirect
326. #2898C2×C11semidirect
327. #2052C2×C11semidirect
328. #2047C2×C11semidirect
329. #2015C2×C11semidirect
330. #2004C2×C11semidirect
331. #1907C2×C11semidirect
332. #1882C2×C11semidirect
333. #1876C2×C11semidirect
334. #1866C2×C11semidirect
335. #1793C2×C11semidirect
516. 2−1+4D4×C11semidirect
538. #137D4×C11semidirect
767. C11#24461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5782
C2×C11×#4712
C11×#30452
C2×C11×#4542
C11×#30102
C11×#28982
C11×#20522
C11×#20472
C11×#20152
C11×#20042
C11×#19072
C11×#18822
C11×#18762
C11×#18662
C11×#17932
#2446111