Finite Group Databasebeta

← C11×#24462 #14601655

Subgroups — C11×#24462 #14601655

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#578C211yesmaximal, characteristic
2C2×C11×#473C211yesmaximal, characteristic, complemented
3C11×#3046C211yesmaximal, characteristic, complemented
4C2×C11×#456C211yesmaximal, characteristic, complemented
5C11×#3011C211yesmaximal, characteristic, complemented
6C11×#2898C211yesmaximal, characteristic, complemented
7C11×#2052C211yesmaximal, characteristic, complemented
8C11×#2047C211yesmaximal, characteristic, complemented
9C11×#2016C211yesmaximal, characteristic, complemented
10C11×#2005C211yesmaximal, characteristic, complemented
11C11×#1908C211yesmaximal, 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×#137C2211yescharacteristic
25C2×C11×#137C2211yescharacteristic
26C2×C11×#135—21no—
27C2×C11×#135C2211yescharacteristic
28C22×C11×Q16—21no—
29C22×C11×Q16C2211yescharacteristic
30C22×C11×Q16C2211yescharacteristic
31C2×C11×#131C2211yescharacteristic
32C2×C11×#131C2211yescharacteristic
33C11×#536C2211yescharacteristic
34C2×C11×C4⋊Q8C2211yescharacteristic
35C11×#520C2211yescharacteristic
36C11×#473—24no—
37C11×#464—21no—
38C11×#463—21no—
39C11×#462—21no—
40C11×#461—21no—
41C11×#456—24no—
42C11×#452—21no—
43C11×#452—21no—
44C11×#451—21no—
45C11×#451—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×#103C2211yescharacteristic
62C2×C11×#101C2211yescharacteristic
63C2×C11×#101C2211yescharacteristic
64C2×C11×#101C2211yescharacteristic
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+4D414yes—
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×Q8×C11C2311yescharacteristic
95C11×#137—28no—
96C11×#137—28no—
97C11×#137—22no—
98C11×#137—22no—
99C11×#137—22no—
100C11×#137—22no—
101C11×#137—22no—
102C11×#137—22no—
103C11×#137—22no—
104C11×#137D414yes—
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—22no—
114C2×C11×Q16—21no—
115C2×C11×Q16—21no—
116C2×C11×Q16—21no—
117C2×C11×Q16—21no—
118C2×C11×Q16—21no—
119C2×C11×Q16—21no—
120C2×C11×Q16—41no—
121C2×C11×Q16D411yescharacteristic
122C2×C11×SD16—21no—
123C2×C11×SD16—21no—
124C2×C11×SD16—21no—
125C2×C11×SD16—21no—
126C2×C11×SD16D411yescharacteristic
127C2×C11×SD16D411yescharacteristic
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×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×#103—21no—
174C11×#103—21no—
175C11×#103D411yescharacteristic
176C11×#103D411yescharacteristic
177C11×#102—21no—
178C11×#102—21no—
179C11×#102D411yescharacteristic
180C11×#102D411yescharacteristic
181C11×#101—22no—
182C11×#101—22no—
183C11×#101—22no—
184C11×C22⋊C8—21no—
185C11×C22⋊C8—21no—
186C11×#95—41no—
187#24462C1111yesmaximal, characteristic, direct product factor, Sylow
188C11×#41—21no—
189C11×#41—21no—
190C11×#41—21no—
191C11×#41—21no—
192C11×#41—24no—
193C11×#41—24no—
194C11×#41—24no—
195C11×#41—21no—
196C11×#41—21no—
197C11×#41—21no—
198C11×#41—21no—
199C11×#41—44no—
200C11×#41—42no—
201C11×#41—42no—
202C11×#41—42no—
203C11×#41—44no—
204C11×#41—44no—
205C11×#41—42no—
206C11×#41—44no—
207C11×#41—42no—
208C11×#41C2×D412yes—
209C11×#41C2×D412yes—
210C11×#41C2×D412yes—
211C11×#41#4112yes—
212C2×Q8×C11—21no—
213C2×Q8×C11—21no—
214C2×Q8×C11—24no—
215C2×Q8×C11—24no—
216C2×Q8×C11—24no—
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—21no—
226C2×Q8×C11—21no—
227C2×Q8×C11—21no—
228C2×Q8×C11—21no—
229C2×Q8×C11—21no—
230C2×Q8×C11—21no—
231C2×Q8×C11—41no—
232C2×Q8×C11—41no—
233C2×Q8×C11—42no—
234C2×Q8×C11—42no—
235C2×Q8×C11—42no—
236C2×Q8×C11—42no—
237C2×Q8×C11—42no—
238C2×Q8×C11C2×D412yes—
239C2×Q8×C11C2×D412yes—
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2×D411yescharacteristic
242C2×Q8×C11C2×D411yescharacteristic
243C2×D4×C11—21no—
244C2×D4×C11—21no—
245C2×D4×C11—21no—
246C2×D4×C11—41no—
247C2×D4×C11—41no—
248C2×D4×C11C2×D411yescharacteristic
249C2×D4×C11C2×D411yescharacteristic
250C2×D4×C11C2×D411yescharacteristic
251C22×C4×C11—21no—
252C22×C4×C11—21no—
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—41no—
260C22×C4×C11—41no—
261C22×C4×C11—41no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11C2411yescharacteristic
265C11×Q16—24no—
266C11×Q16—24no—
267C11×Q16—24no—
268C11×Q16—22no—
269C11×Q16—24no—
270C11×Q16—42no—
271C11×Q16—42no—
272C11×Q16—42no—
273C11×Q16—42no—
274C11×SD16—24no—
275C11×SD16—22no—
276C11×SD16—24no—
277C11×SD16—22no—
278C11×SD16—42no—
279C11×SD16—42no—
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—
317C42×C11—21no—
318C42×C11—21no—
319C42×C11—21no—
320C42×C11—41no—
321C2×#578C2×C1111yescharacteristic
322C2×#473C2×C1111yescharacteristic, complemented
323#3046C2×C1111yescharacteristic, complemented
324C2×#456C2×C1111yescharacteristic, complemented
325#3011C2×C1111yescharacteristic, complemented
326#2898C2×C1111yescharacteristic, complemented
327#2052C2×C1111yescharacteristic, complemented
328#2047C2×C1111yescharacteristic, complemented
329#2016C2×C1111yescharacteristic, complemented
330#2005C2×C1111yescharacteristic, complemented
331#1908C2×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×C11H(5,𝔽2)11yescharacteristic
340Q8×C11—21no—
341Q8×C11—21no—
342Q8×C11—22no—
343Q8×C11—22no—
344Q8×C11—21no—
345Q8×C11—22no—
346Q8×C11—22no—
347Q8×C11—21no—
348Q8×C11—44no—
349Q8×C11—44no—
350Q8×C11—41no—
351Q8×C11—41no—
352Q8×C11—41no—
353Q8×C11—41no—
354Q8×C11—41no—
355Q8×C11—41no—
356Q8×C11—41no—
357Q8×C11—41no—
358Q8×C11#12012yes—
359Q8×C11#12112yes—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—21no—
365D4×C11—21no—
366D4×C11—21no—
367D4×C11—21no—
368D4×C11—44no—
369D4×C11—44no—
370D4×C11—41no—
371D4×C11—41no—
372D4×C11#12012yes—
373D4×C11#12112yes—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—22no—
386C2×C4×C11—44no—
387C2×C4×C11—44no—
388C2×C4×C11—44no—
389C2×C4×C11—41no—
390C2×C4×C11—44no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
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—81no—
403C2×C4×C11—161no—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C2×#4111yescharacteristic
409C2×C4×C11H(5,𝔽2)11yescharacteristic
410C8×C11—21no—
411C8×C11—22no—
412C8×C11—21no—
413C8×C11—21no—
414C8×C11—21no—
415C8×C11—41no—
416C8×C11—41no—
417C8×C11—41no—
418C2×2−1+4C22×C1111yescharacteristic
419C2×2−1+4C22×C1111yescharacteristic
420#578—24no—
421#578—24no—
422C2×#137—21no—
423C2×#137—21no—
424C2×#137C22×C1111yescharacteristic
425C2×#137C22×C1111yescharacteristic
426C2×#137C22×C1111yescharacteristic
427C2×#137C22×C1111yescharacteristic
428C2×#135—21no—
429C2×#135C22×C1111yescharacteristic
430C22×Q16—21no—
431C22×Q16C22×C1111yescharacteristic
432C22×Q16C22×C1111yescharacteristic
433C2×#131C22×C1111yescharacteristic
434C2×#131C22×C1111yescharacteristic
435#536C22×C1111yescharacteristic
436C2×C4⋊Q8C22×C1111yescharacteristic
437#520C22×C1111yescharacteristic
438#473—24no—
439#464—21no—
440#463—21no—
441#462—21no—
442#461—21no—
443#456—24no—
444#452—21no—
445#452—21no—
446#451—21no—
447#451—21no—
448C2×#108C22×C1111yescharacteristic
449#424C22×C1111yescharacteristic
450C2×#104C22×C1111yescharacteristic
451C2×#104C22×C1111yescharacteristic
452C2×#104C22×C1111yescharacteristic
453#419—21no—
454#419C22×C1111yescharacteristic
455#419C22×C1111yescharacteristic
456#417—21no—
457#417C22×C1111yescharacteristic
458#417C22×C1111yescharacteristic
459#416—21no—
460#416C22×C1111yescharacteristic
461C2×#103—21no—
462C2×#103C22×C1111yescharacteristic
463C2×#103C22×C1111yescharacteristic
464C2×#101C22×C1111yescharacteristic
465C2×#101C22×C1111yescharacteristic
466C2×#101C22×C1111yescharacteristic
467#408C22×C1111yescharacteristic
468#391C22×C1111yescharacteristic
469#343C22×C1111yescharacteristic
470#341C22×C1111yescharacteristic
471#339C22×C1111yescharacteristic
472#336C22×C1111yescharacteristic
473C22×C11—21no—
474C22×C11—21no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—41no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11#53411yescharacteristic
485C22×C11D4211yescharacteristic
486C22×C11#54611yescharacteristic
487C4×C11—22no—
488C4×C11—22no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11—41no—
492C4×C11—42no—
493C4×C11—41no—
494C4×C11—41no—
495C4×C11—81no—
496C4×C11—81no—
497C4×C11C2×#12011yescharacteristic
498C4×C11C2×#12111yescharacteristic
499C4×C11D4211yescharacteristic
500C4×C11#54611yescharacteristic
5012−1+4—22no—
5022−1+4—22no—
5032−1+4—22no—
5042−1+4—22no—
5052−1+4—22no—
5062−1+4—41no—
5072−1+4—41no—
5082−1+4D4×C1114yes—
509C2×#41—21no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41—21no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C23×C1111yescharacteristic
516C2×#41C23×C1111yescharacteristic
517C2×#41C23×C1111yescharacteristic
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8C23×C1111yescharacteristic
523C22×Q8C23×C1111yescharacteristic
524C22×Q8C23×C1111yescharacteristic
525#137—28no—
526#137—28no—
527#137—22no—
528#137—22no—
529#137—22no—
530#137—22no—
531#137—22no—
532#137—22no—
533#137—22no—
534#137D4×C1114yes—
535#135—28no—
536#135—22no—
537#135—22no—
538C2×Q16—28no—
539C2×Q16—21no—
540C2×Q16—21no—
541C2×Q16—22no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—21no—
545C2×Q16—21no—
546C2×Q16—21no—
547C2×Q16—21no—
548C2×Q16—21no—
549C2×Q16—21no—
550C2×Q16—41no—
551C2×Q16D4×C1111yescharacteristic
552C2×SD16—21no—
553C2×SD16—21no—
554C2×SD16—21no—
555C2×SD16—21no—
556C2×SD16D4×C1111yescharacteristic
557C2×SD16D4×C1111yescharacteristic
558C2×D8D4×C1111yescharacteristic
559#131—22no—
560#131—22no—
561#131—22no—
562#131—41no—
563C2×M16—21no—
564C2×M16—21no—
565C2×M16C23×C1111yescharacteristic
566C2×M16C23×C1111yescharacteristic
567C2×M16C23×C1111yescharacteristic
568C2×M16C23×C1111yescharacteristic
569C22×C8—21no—
570C22×C8—21no—
571C22×C8C23×C1111yescharacteristic
572C22×C8C23×C1111yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—21no—
575C4⋊Q8—41no—
576#124—21no—
577#123—41no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C4×Q8—21no—
581C4×D4—21no—
582C4×D4—41no—
583#117—21no—
584#117C23×C1111yescharacteristic
585C2×C4⋊C4—21no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4C23×C1111yescharacteristic
588C2×C42C23×C1111yescharacteristic
589#108—22no—
590C4⋊C8—21no—
591C4⋊C8—21no—
592#104—22no—
593#104—22no—
594#104—41no—
595#103—21no—
596#103—21no—
597#103—21no—
598#103—21no—
599#103—21no—
600#103—21no—
601#103—21no—
602#103—21no—
603#103—21no—
604#103—21no—
605#103D4×C1111yescharacteristic
606#103D4×C1111yescharacteristic
607#102—21no—
608#102—21no—
609#102D4×C1111yescharacteristic
610#102D4×C1111yescharacteristic
611#101—22no—
612#101—22no—
613#101—22no—
614C22⋊C8—21no—
615C22⋊C8—21no—
616#95—41no—
617C2×C11—21no—
618C2×C11—21no—
619C2×C11—42no—
620C2×C11—42no—
621C2×C11—81no—
622C2×C11#241011yescharacteristic
623C2×C11#328911yescharacteristic
624C2×C11#329311yescharacteristic
625#41—21no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—24no—
630#41—24no—
631#41—24no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—44no—
637#41—42no—
638#41—42no—
639#41—42no—
640#41—44no—
641#41—44no—
642#41—42no—
643#41—44no—
644#41—42no—
645#41C2×D4×C1112yes—
646#41C2×D4×C1112yes—
647#41C2×D4×C1112yes—
648#41C11×#4112yes—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—24no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—41no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8—42no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8—42no—
675C2×Q8C2×D4×C1112yes—
676C2×Q8C2×D4×C1112yes—
677C2×Q8C2×D4×C1111yescharacteristic
678C2×Q8C2×D4×C1111yescharacteristic
679C2×Q8C2×D4×C1111yescharacteristic
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—41no—
684C2×D4—41no—
685C2×D4C2×D4×C1111yescharacteristic
686C2×D4C2×D4×C1111yescharacteristic
687C2×D4C2×D4×C1111yescharacteristic
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4C24×C1111yescharacteristic
702Q16—24no—
703Q16—24no—
704Q16—24no—
705Q16—22no—
706Q16—24no—
707Q16—42no—
708Q16—42no—
709Q16—42no—
710Q16—42no—
711SD16—24no—
712SD16—22no—
713SD16—24no—
714SD16—22no—
715SD16—42no—
716SD16—42no—
717D8—22no—
718M16—24no—
719M16—21no—
720M16—21no—
721M16—21no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—42no—
727M16C2×D4×C1112yes—
728C2×C8—24no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—42no—
738C2×C8C2×D4×C1111yescharacteristic
739C2×C8C2×D4×C1111yescharacteristic
740C2×C8C2×D4×C1111yescharacteristic
741C2×C8C2×D4×C1111yescharacteristic
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—41no—
745C4⋊C4—41no—
746C4⋊C4—41no—
747C4⋊C4—44no—
748C4⋊C4C2×D4×C1111yescharacteristic
749C4⋊C4C2×D4×C1111yescharacteristic
750C22⋊C4—21no—
751C22⋊C4—41no—
752C22⋊C4—41no—
753C22⋊C4—41no—
754C42—21no—
755C42—21no—
756C42—21no—
757C42—41no—
758C11#2446211yescharacteristic, direct product factor, Sylow
759C23—21no—
760C23—21no—
761C23—21no—
762C23C11×H(5,𝔽2)11yescharacteristic
763Q8—21no—
764Q8—21no—
765Q8—22no—
766Q8—22no—
767Q8—21no—
768Q8—22no—
769Q8—22no—
770Q8—21no—
771Q8—44no—
772Q8—44no—
773Q8—41no—
774Q8—41no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8C11×#12012yes—
782Q8C11×#12112yes—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—44no—
792D4—44no—
793D4—41no—
794D4—41no—
795D4C11×#12012yes—
796D4C11×#12112yes—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—41no—
813C2×C4—44no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—81no—
826C2×C4—161no—
827C2×C4C22×D4×C1111yescharacteristic
828C2×C4C22×D4×C1111yescharacteristic
829C2×C4C22×D4×C1111yescharacteristic
830C2×C4C22×D4×C1111yescharacteristic
831C2×C4C2×C11×#4111yescharacteristic
832C2×C4C11×H(5,𝔽2)11yescharacteristic
833C8—21no—
834C8—22no—
835C8—21no—
836C8—21no—
837C8—21no—
838C8—41no—
839C8—41no—
840C8—41no—
841C22—21no—
842C22—21no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22C11×#53411yescharacteristic
853C22D42×C1111yescharacteristic
854C22C11×#54611yescharacteristic
855C4—22no—
856C4—22no—
857C4—42no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—41no—
863C4—81no—
864C4—81no—
865C4C2×C11×#12011yescharacteristic
866C4C2×C11×#12111yescharacteristic
867C4D42×C1111yescharacteristic
868C4C11×#54611yescharacteristic
869C2—21no—
870C2—21no—
871C2—42no—
872C2—42no—
873C2—81no—
874C2C11×#241011yescharacteristic
875C2C11×#328911yescharacteristic
876C2C11×#329311yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#578C2
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×#473C2semidirect
3. C11×#3046C2semidirect
4. C2×C11×#456C2semidirect
5. C11×#3011C2semidirect
6. C11×#2898C2semidirect
7. C11×#2052C2semidirect
8. C11×#2047C2semidirect
9. C11×#2016C2semidirect
10. C11×#2005C2semidirect
11. C11×#1908C2semidirect
12. C11×#1882C2semidirect
13. C11×#1876C2semidirect
14. C11×#1866C2semidirect
15. C11×#1793C2semidirect
187. #24462C11direct (N × H)
322. C2×#473C2×C11semidirect
323. #3046C2×C11semidirect
324. C2×#456C2×C11semidirect
325. #3011C2×C11semidirect
326. #2898C2×C11semidirect
327. #2052C2×C11semidirect
328. #2047C2×C11semidirect
329. #2016C2×C11semidirect
330. #2005C2×C11semidirect
331. #1908C2×C11semidirect
332. #1882C2×C11semidirect
333. #1876C2×C11semidirect
334. #1866C2×C11semidirect
335. #1793C2×C11semidirect
758. C11#24462direct (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×#4732
C11×#30462
C2×C11×#4562
C11×#30112
C11×#28982
C11×#20522
C11×#20472
C11×#20162
C11×#20052
C11×#19082
C11×#18822
C11×#18762
C11×#18662
C11×#17932
#2446211