Finite Group Databasebeta

← C11×#24463 #14601656

Subgroups — C11×#24463 #14601656

Order 2816.

1336 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#577C211yesmaximal, characteristic
2C2×C11×#471C211yesmaximal, characteristic, complemented
3C11×#3046C211yesmaximal, characteristic, complemented
4C2×C11×#456C211yesmaximal, characteristic, complemented
5C11×#3009C211yesmaximal, characteristic, complemented
6C11×#2898C211yesmaximal, characteristic, complemented
7C11×#2052C211yesmaximal, characteristic, complemented
8C11×#2046C211yesmaximal, characteristic, complemented
9C11×#2013C211yesmaximal, characteristic, complemented
10C11×#2005C211yesmaximal, characteristic, complemented
11C11×#1908C211yesmaximal, characteristic, complemented
12C11×#1883C211yesmaximal, characteristic, complemented
13C11×#1876C211yesmaximal, characteristic, complemented
14C11×#1866C211yesmaximal, 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
23C2×C11×#137C2211yescharacteristic, complemented
24C2×C11×AGL(1,ℤ/8)—21no—
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C11×#135—21no—
27C2×C11×#135C2211yescharacteristic
28C22×C11×SD16—21no—
29C22×C11×SD16C2211yescharacteristic
30C22×C11×SD16C2211yescharacteristic
31C2×C11×#131C2211yescharacteristic
32C2×C11×#131C2211yescharacteristic, complemented
33C11×#536C2211yescharacteristic
34C2×C11×C4⋊Q8C2211yescharacteristic, complemented
35C11×#520C2211yescharacteristic, complemented
36C11×#471—24no—
37C11×#464—21no—
38C11×#463—21no—
39C11×#462—21no—
40C11×#461—21no—
41C11×#456—24no—
42C11×#452—21no—
43C11×#452—21no—
44C11×#450—21no—
45C11×#450—21no—
46C2×C11×#108C2211yescharacteristic, complemented
47C11×#424C2211yescharacteristic, complemented
48C2×C11×#104C2211yescharacteristic
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic, complemented
51C11×#419—21no—
52C11×#419C2211yescharacteristic, complemented
53C11×#418C2211yescharacteristic
54C11×#417—21no—
55C11×#417C2211yescharacteristic
56C11×#417C2211yescharacteristic
57C11×#416—21no—
58C11×#416C2211yescharacteristic
59C2×C11×#103—21no—
60C2×C11×#103C2211yescharacteristic, complemented
61C2×C11×#103C2211yescharacteristic, complemented
62C2×C11×#101C2211yescharacteristic, complemented
63C2×C11×#101C2211yescharacteristic, complemented
64C2×C11×#100C2211yescharacteristic
65C11×#408C2211yescharacteristic
66C11×#390C2211yescharacteristic
67C11×#343C2211yescharacteristic, complemented
68C11×#341C2211yescharacteristic, complemented
69C11×#339C2211yescharacteristic, complemented
70C11×#336C2211yescharacteristic, complemented
71C11×2−1+4—22no—
72C11×2−1+4—22no—
73C11×2−1+4—41no—
74C11×2−1+4D414yes—
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
87C22×Q8×C11—21no—
88C22×Q8×C11—21no—
89C22×Q8×C11C2311yescharacteristic
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—22no—
100C11×#137—22no—
101C11×#137—22no—
102C11×AGL(1,ℤ/8)—28no—
103C11×AGL(1,ℤ/8)—22no—
104C11×AGL(1,ℤ/8)D414yes—
105C11×#135—28no—
106C11×#135—22no—
107C11×#135—22no—
108C2×C11×Q16—21no—
109C2×C11×Q16—21no—
110C2×C11×Q16—21no—
111C2×C11×Q16D411yescharacteristic
112C2×C11×SD16—28no—
113C2×C11×SD16—21no—
114C2×C11×SD16—22no—
115C2×C11×SD16—21no—
116C2×C11×SD16—22no—
117C2×C11×SD16—22no—
118C2×C11×SD16—21no—
119C2×C11×SD16—21no—
120C2×C11×SD16—21no—
121C2×C11×SD16—21no—
122C2×C11×SD16—21no—
123C2×C11×SD16—21no—
124C2×C11×SD16—41no—
125C2×C11×SD16D411yescharacteristic
126C2×C11×SD16D411yescharacteristic
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×C4⋊Q8—22no—
144C11×C4⋊Q8—21no—
145C11×C4⋊Q8—41no—
146C11×#124—21no—
147C11×#123—41no—
148C11×C22⋊Q8—21no—
149C11×C22⋊Q8—21no—
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⋊C4—41no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4—41no—
159C2×C42×C11C2311yescharacteristic
160C11×#108—22no—
161C11×C4⋊C8—21no—
162C11×C4⋊C8—21no—
163C11×#104—22no—
164C11×#104—22no—
165C11×#104—41no—
166C11×#103—21no—
167C11×#103—21no—
168C11×#103—21no—
169C11×#103—21no—
170C11×#103—21no—
171C11×#103—21no—
172C11×#103—21no—
173C11×#103—21no—
174C11×#103D411yescharacteristic
175C11×#103D411yescharacteristic
176C11×#102—21no—
177C11×#102—21no—
178C11×#102—21no—
179C11×#102—21no—
180C11×#102D411yescharacteristic
181C11×#102D411yescharacteristic
182C11×#101—22no—
183C11×#101—22no—
184C11×#100—22no—
185C11×C22⋊C8—21no—
186C11×C22⋊C8—21no—
187#24463C1111yesmaximal, characteristic, direct product factor, Sylow
188C24×C11—21no—
189C24×C11—41no—
190C11×#41—21no—
191C11×#41—21no—
192C11×#41—21no—
193C11×#41—21no—
194C11×#41—24no—
195C11×#41—24no—
196C11×#41—24no—
197C11×#41—21no—
198C11×#41—21no—
199C11×#41—21no—
200C11×#41—21no—
201C11×#41—44no—
202C11×#41—42no—
203C11×#41—42no—
204C11×#41—42no—
205C11×#41—44no—
206C11×#41—42no—
207C11×#41—42no—
208C11×#41C2×D412yes—
209C11×#41C2×D412yes—
210C11×#41C2×D412yes—
211C11×#41#4112yes—
212C2×Q8×C11—21no—
213C2×Q8×C11—24no—
214C2×Q8×C11—24no—
215C2×Q8×C11—21no—
216C2×Q8×C11—21no—
217C2×Q8×C11—21no—
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—41no—
226C2×Q8×C11—42no—
227C2×Q8×C11—42no—
228C2×Q8×C11C2×D412yes—
229C2×Q8×C11C2×D411yescharacteristic
230C2×Q8×C11C2×D411yescharacteristic
231C2×Q8×C11C2×D411yescharacteristic
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—24no—
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×C11C2×D412yes—
250C2×D4×C11C2×D411yescharacteristic
251C2×D4×C11C2×D411yescharacteristic
252C2×D4×C11C2×D411yescharacteristic
253C22×C4×C11—21no—
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—41no—
261C22×C4×C11—41no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11C2411yescharacteristic
265C11×Q16—24no—
266C11×Q16—22no—
267C11×Q16—42no—
268C11×Q16—42no—
269C11×SD16—24no—
270C11×SD16—24no—
271C11×SD16—24no—
272C11×SD16—22no—
273C11×SD16—24no—
274C11×SD16—22no—
275C11×SD16—42no—
276C11×SD16—42no—
277C11×SD16—42no—
278C11×SD16—42no—
279C11×D8—24no—
280C11×D8—22no—
281C11×M16—24no—
282C11×M16—21no—
283C11×M16—21no—
284C11×M16—21no—
285C11×M16—21no—
286C11×M16—21no—
287C11×M16—21no—
288C11×M16—21no—
289C11×M16—42no—
290C11×M16C2×D412yes—
291C2×C8×C11—24no—
292C2×C8×C11—21no—
293C2×C8×C11—21no—
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—42no—
301C2×C8×C11C2×D411yescharacteristic
302C2×C8×C11C2×D411yescharacteristic
303C2×C8×C11C2×D411yescharacteristic
304C2×C8×C11C2×D411yescharacteristic
305C11×C4⋊C4—21no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—41no—
308C11×C4⋊C4—41no—
309C11×C4⋊C4—41no—
310C11×C4⋊C4—44no—
311C11×C4⋊C4C2×D411yescharacteristic
312C11×C4⋊C4C2×D411yescharacteristic
313C11×C22⋊C4—21no—
314C11×C22⋊C4—41no—
315C11×C22⋊C4—41no—
316C11×C22⋊C4—41no—
317C11×C22⋊C4—82no—
318C42×C11—21no—
319C42×C11—21no—
320C42×C11—21no—
321C42×C11—41no—
322C2×#577C2×C1111yescharacteristic
323C2×#471C2×C1111yescharacteristic, complemented
324#3046C2×C1111yescharacteristic, complemented
325C2×#456C2×C1111yescharacteristic, complemented
326#3009C2×C1111yescharacteristic, complemented
327#2898C2×C1111yescharacteristic, complemented
328#2052C2×C1111yescharacteristic, complemented
329#2046C2×C1111yescharacteristic, complemented
330#2013C2×C1111yescharacteristic, complemented
331#2005C2×C1111yescharacteristic, complemented
332#1908C2×C1111yescharacteristic, complemented
333#1883C2×C1111yescharacteristic, complemented
334#1876C2×C1111yescharacteristic, complemented
335#1866C2×C1111yescharacteristic, complemented
336#1792C2×C1111yescharacteristic, complemented
337C23×C11—21no—
338C23×C11—21no—
339C23×C11—21no—
340C23×C11—22no—
341C23×C11—44no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—81no—
345C23×C11—81no—
346C23×C11—161no—
347C23×C11—161no—
348C23×C11H(5,𝔽2)11yescharacteristic
349Q8×C11—21no—
350Q8×C11—21no—
351Q8×C11—22no—
352Q8×C11—21no—
353Q8×C11—22no—
354Q8×C11—21no—
355Q8×C11—44no—
356Q8×C11—41no—
357Q8×C11—41no—
358Q8×C11—41no—
359Q8×C11—41no—
360Q8×C11—41no—
361Q8×C11—41no—
362Q8×C11#12012yes—
363Q8×C11#12112yes—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—22no—
369D4×C11—21no—
370D4×C11—21no—
371D4×C11—22no—
372D4×C11—21no—
373D4×C11—21no—
374D4×C11—44no—
375D4×C11—44no—
376D4×C11—44no—
377D4×C11—41no—
378D4×C11—41no—
379D4×C11—41no—
380D4×C11—41no—
381D4×C11#12012yes—
382D4×C11#12112yes—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—21no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—44no—
395C2×C4×C11—44no—
396C2×C4×C11—44no—
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—41no—
407C2×C4×C11—81no—
408C2×C4×C11—161no—
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C2×#4111yescharacteristic
414C2×C4×C11H(5,𝔽2)11yescharacteristic
415C8×C11—21no—
416C8×C11—22no—
417C8×C11—21no—
418C8×C11—21no—
419C8×C11—21no—
420C8×C11—41no—
421C8×C11—41no—
422C8×C11—41no—
423C2×2−1+4C22×C1111yescharacteristic
424C2×H(5,𝔽2)C22×C1111yescharacteristic
425#577—24no—
426#577—24no—
427C2×#137—21no—
428C2×#137C22×C1111yescharacteristic
429C2×#137C22×C1111yescharacteristic
430C2×#137C22×C1111yescharacteristic, complemented
431C2×AGL(1,ℤ/8)—21no—
432C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
433C2×#135—21no—
434C2×#135C22×C1111yescharacteristic
435C22×SD16—21no—
436C22×SD16C22×C1111yescharacteristic
437C22×SD16C22×C1111yescharacteristic
438C2×#131C22×C1111yescharacteristic
439C2×#131C22×C1111yescharacteristic, complemented
440#536C22×C1111yescharacteristic
441C2×C4⋊Q8C22×C1111yescharacteristic, complemented
442#520C22×C1111yescharacteristic, complemented
443#471—24no—
444#464—21no—
445#463—21no—
446#462—21no—
447#461—21no—
448#456—24no—
449#452—21no—
450#452—21no—
451#450—21no—
452#450—21no—
453C2×#108C22×C1111yescharacteristic, complemented
454#424C22×C1111yescharacteristic, complemented
455C2×#104C22×C1111yescharacteristic
456C2×#104C22×C1111yescharacteristic
457C2×#104C22×C1111yescharacteristic, complemented
458#419—21no—
459#419C22×C1111yescharacteristic, complemented
460#418C22×C1111yescharacteristic
461#417—21no—
462#417C22×C1111yescharacteristic
463#417C22×C1111yescharacteristic
464#416—21no—
465#416C22×C1111yescharacteristic
466C2×#103—21no—
467C2×#103C22×C1111yescharacteristic, complemented
468C2×#103C22×C1111yescharacteristic, complemented
469C2×#101C22×C1111yescharacteristic, complemented
470C2×#101C22×C1111yescharacteristic, complemented
471C2×#100C22×C1111yescharacteristic
472#408C22×C1111yescharacteristic
473#390C22×C1111yescharacteristic
474#343C22×C1111yescharacteristic, complemented
475#341C22×C1111yescharacteristic, complemented
476#339C22×C1111yescharacteristic, complemented
477#336C22×C1111yescharacteristic, complemented
478C22×C11—21no—
479C22×C11—21no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—41no—
487C22×C11—42no—
488C22×C11—41no—
489C22×C11—41no—
490C22×C11—82no—
491C22×C11—81no—
492C22×C11—81no—
493C22×C11—161no—
494C22×C11—164no—
495C22×C11#53411yescharacteristic
496C22×C11D4211yescharacteristic
497C22×C11#54611yescharacteristic
498C4×C11—22no—
499C4×C11—22no—
500C4×C11—42no—
501C4×C11—41no—
502C4×C11—42no—
503C4×C11—41no—
504C4×C11—41no—
505C4×C11—81no—
506C4×C11—81no—
507C4×C11C2×#12011yescharacteristic
508C4×C11C2×#12111yescharacteristic
509C4×C11D4211yescharacteristic
510C4×C11#54611yescharacteristic
5112−1+4—22no—
5122−1+4—22no—
5132−1+4—41no—
5142−1+4D4×C1114yes—
515H(5,𝔽2)—22no—
516H(5,𝔽2)—22no—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—41no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—21no—
523C2×#41—41no—
524C2×#41C23×C1111yescharacteristic
525C2×#41C23×C1111yescharacteristic
526C2×#41C23×C1111yescharacteristic
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8C23×C1111yescharacteristic
530C22×Q8C23×C1111yescharacteristic
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—41no—
534C22×D4C23×C1111yescharacteristic
535#137—28no—
536#137—22no—
537#137—22no—
538#137—22no—
539#137—22no—
540#137—22no—
541#137—22no—
542AGL(1,ℤ/8)—28no—
543AGL(1,ℤ/8)—22no—
544AGL(1,ℤ/8)D4×C1114yes—
545#135—28no—
546#135—22no—
547#135—22no—
548C2×Q16—21no—
549C2×Q16—21no—
550C2×Q16—21no—
551C2×Q16D4×C1111yescharacteristic
552C2×SD16—28no—
553C2×SD16—21no—
554C2×SD16—22no—
555C2×SD16—21no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×SD16—21no—
562C2×SD16—21no—
563C2×SD16—21no—
564C2×SD16—41no—
565C2×SD16D4×C1111yescharacteristic
566C2×SD16D4×C1111yescharacteristic
567C2×D8—21no—
568C2×D8D4×C1111yescharacteristic
569#131—22no—
570#131—22no—
571#131—22no—
572#131—41no—
573C2×M16—21no—
574C2×M16—21no—
575C2×M16C23×C1111yescharacteristic
576C2×M16C23×C1111yescharacteristic
577C2×M16C23×C1111yescharacteristic
578C2×M16C23×C1111yescharacteristic
579C22×C8—21no—
580C22×C8—21no—
581C22×C8C23×C1111yescharacteristic
582C22×C8C23×C1111yescharacteristic
583C4⋊Q8—22no—
584C4⋊Q8—21no—
585C4⋊Q8—41no—
586#124—21no—
587#123—41no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C4×Q8—21no—
591C4×D4—21no—
592C4×D4—41no—
593#117—21no—
594#117C23×C1111yescharacteristic
595C2×C4⋊C4—21no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4C23×C1111yescharacteristic
598C2×C22⋊C4—41no—
599C2×C42C23×C1111yescharacteristic
600#108—22no—
601C4⋊C8—21no—
602C4⋊C8—21no—
603#104—22no—
604#104—22no—
605#104—41no—
606#103—21no—
607#103—21no—
608#103—21no—
609#103—21no—
610#103—21no—
611#103—21no—
612#103—21no—
613#103—21no—
614#103D4×C1111yescharacteristic
615#103D4×C1111yescharacteristic
616#102—21no—
617#102—21no—
618#102—21no—
619#102—21no—
620#102D4×C1111yescharacteristic
621#102D4×C1111yescharacteristic
622#101—22no—
623#101—22no—
624#100—22no—
625C22⋊C8—21no—
626C22⋊C8—21no—
627C2×C11—21no—
628C2×C11—21no—
629C2×C11—42no—
630C2×C11—42no—
631C2×C11—81no—
632C2×C11—82no—
633C2×C11#241011yescharacteristic
634C2×C11#328911yescharacteristic
635C2×C11#329111yescharacteristic
636C24—21no—
637C24—41no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—24no—
643#41—24no—
644#41—24no—
645#41—21no—
646#41—21no—
647#41—21no—
648#41—21no—
649#41—44no—
650#41—42no—
651#41—42no—
652#41—42no—
653#41—44no—
654#41—42no—
655#41—42no—
656#41C2×D4×C1112yes—
657#41C2×D4×C1112yes—
658#41C2×D4×C1112yes—
659#41C11×#4112yes—
660C2×Q8—21no—
661C2×Q8—24no—
662C2×Q8—24no—
663C2×Q8—21no—
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—21no—
673C2×Q8—41no—
674C2×Q8—42no—
675C2×Q8—42no—
676C2×Q8C2×D4×C1112yes—
677C2×Q8C2×D4×C1111yescharacteristic
678C2×Q8C2×D4×C1111yescharacteristic
679C2×Q8C2×D4×C1111yescharacteristic
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—24no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—41no—
691C2×D4—41no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—41no—
696C2×D4—42no—
697C2×D4C2×D4×C1112yes—
698C2×D4C2×D4×C1111yescharacteristic
699C2×D4C2×D4×C1111yescharacteristic
700C2×D4C2×D4×C1111yescharacteristic
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4—41no—
712C22×C4C24×C1111yescharacteristic
713Q16—24no—
714Q16—22no—
715Q16—42no—
716Q16—42no—
717SD16—24no—
718SD16—24no—
719SD16—24no—
720SD16—22no—
721SD16—24no—
722SD16—22no—
723SD16—42no—
724SD16—42no—
725SD16—42no—
726SD16—42no—
727D8—24no—
728D8—22no—
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⋊C4—41no—
757C4⋊C4—41no—
758C4⋊C4—44no—
759C4⋊C4C2×D4×C1111yescharacteristic
760C4⋊C4C2×D4×C1111yescharacteristic
761C22⋊C4—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C22⋊C4—41no—
765C22⋊C4—82no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—41no—
770C11#2446311yescharacteristic, direct product factor, Sylow
771C23—21no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—44no—
776C23—41no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—161no—
781C23—161no—
782C23C11×H(5,𝔽2)11yescharacteristic
783Q8—21no—
784Q8—21no—
785Q8—22no—
786Q8—21no—
787Q8—22no—
788Q8—21no—
789Q8—44no—
790Q8—41no—
791Q8—41no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796Q8C11×#12012yes—
797Q8C11×#12112yes—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—21no—
804D4—21no—
805D4—22no—
806D4—21no—
807D4—21no—
808D4—44no—
809D4—44no—
810D4—44no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4C11×#12012yes—
816D4C11×#12112yes—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—81no—
842C2×C4—161no—
843C2×C4C22×D4×C1111yescharacteristic
844C2×C4C22×D4×C1111yescharacteristic
845C2×C4C22×D4×C1111yescharacteristic
846C2×C4C22×D4×C1111yescharacteristic
847C2×C4C2×C11×#4111yescharacteristic
848C2×C4C11×H(5,𝔽2)11yescharacteristic
849C8—21no—
850C8—22no—
851C8—21no—
852C8—21no—
853C8—21no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—21no—
858C22—21no—
859C22—22no—
860C22—22no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—42no—
867C22—41no—
868C22—41no—
869C22—82no—
870C22—81no—
871C22—81no—
872C22—161no—
873C22—164no—
874C22C11×#53411yescharacteristic
875C22D42×C1111yescharacteristic
876C22C11×#54611yescharacteristic
877C4—22no—
878C4—22no—
879C4—42no—
880C4—41no—
881C4—42no—
882C4—41no—
883C4—41no—
884C4—81no—
885C4—81no—
886C4C2×C11×#12011yescharacteristic
887C4C2×C11×#12111yescharacteristic
888C4D42×C1111yescharacteristic
889C4C11×#54611yescharacteristic
890C2—21no—
891C2—21no—
892C2—42no—
893C2—42no—
894C2—81no—
895C2—82no—
896C2C11×#241011yescharacteristic
897C2C11×#328911yescharacteristic
898C2C11×#329111yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#577C2
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
2. C2×C11×#471C2semidirect
3. C11×#3046C2semidirect
4. C2×C11×#456C2semidirect
5. C11×#3009C2semidirect
6. C11×#2898C2semidirect
7. C11×#2052C2semidirect
8. C11×#2046C2semidirect
9. C11×#2013C2semidirect
10. C11×#2005C2semidirect
11. C11×#1908C2semidirect
12. C11×#1883C2semidirect
13. C11×#1876C2semidirect
14. C11×#1866C2semidirect
15. C11×#1792C2semidirect
23. C2×C11×#137C22semidirect
32. C2×C11×#131C22semidirect
34. C2×C11×C4⋊Q8C22semidirect
35. C11×#520C22semidirect
46. C2×C11×#108C22semidirect
47. C11×#424C22semidirect
50. C2×C11×#104C22semidirect
52. C11×#419C22semidirect
60. C2×C11×#103C22semidirect
61. C2×C11×#103C22semidirect
62. C2×C11×#101C22semidirect
63. C2×C11×#101C22semidirect
67. C11×#343C22semidirect
68. C11×#341C22semidirect
69. C11×#339C22semidirect
70. C11×#336C22semidirect
187. #24463C11direct (N × H)
323. C2×#471C2×C11semidirect
324. #3046C2×C11semidirect
325. C2×#456C2×C11semidirect
326. #3009C2×C11semidirect
327. #2898C2×C11semidirect
328. #2052C2×C11semidirect
329. #2046C2×C11semidirect
330. #2013C2×C11semidirect
331. #2005C2×C11semidirect
332. #1908C2×C11semidirect
333. #1883C2×C11semidirect
334. #1876C2×C11semidirect
335. #1866C2×C11semidirect
336. #1792C2×C11semidirect
430. C2×#137C22×C11semidirect
439. C2×#131C22×C11semidirect
441. C2×C4⋊Q8C22×C11semidirect
442. #520C22×C11semidirect
453. C2×#108C22×C11semidirect
454. #424C22×C11semidirect
457. C2×#104C22×C11semidirect
459. #419C22×C11semidirect
467. C2×#103C22×C11semidirect
468. C2×#103C22×C11semidirect
469. C2×#101C22×C11semidirect
470. C2×#101C22×C11semidirect
474. #343C22×C11semidirect
475. #341C22×C11semidirect
476. #339C22×C11semidirect
477. #336C22×C11semidirect
770. C11#24463direct (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×#30462
C2×C11×#4562
C11×#30092
C11×#28982
C11×#20522
C11×#20462
C11×#20132
C11×#20052
C11×#19082
C11×#18832
C11×#18762
C11×#18662
C11×#17922
#2446311