Finite Group Databasebeta

← C11×#23956 #14601149

Subgroups — C11×#23956 #14601149

Order 2816.

1284 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3494C211yesmaximal, characteristic, complemented
2C11×#3005C211yesmaximal, characteristic, complemented
3C11×#2896C211yesmaximal, characteristic, complemented
4C11×#2431C211yesmaximal, characteristic, complemented
5C11×#2028C211yesmaximal, characteristic, complemented
6C11×#2027C211yesmaximal, characteristic, complemented
7C11×#2004C211yesmaximal, characteristic, complemented
8C11×#2002C211yesmaximal, characteristic, complemented
9C11×#1900C211yesmaximal, characteristic, complemented
10C11×#1887C211yesmaximal, characteristic, complemented
11C11×#1885C211yesmaximal, characteristic, complemented
12C11×#1883C211yesmaximal, characteristic, complemented
13C11×#1882C211yesmaximal, characteristic, complemented
14C11×#1871C211yesmaximal, characteristic, complemented
15C11×#1826C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C11×#137C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C11×#555—21no—
21C11×#553—21no—
22C11×#553—21no—
23C11×#551—22no—
24C11×#547—21no—
25C11×#546—22no—
26C11×#544C2211yescharacteristic
27C11×#542—21no—
28C11×#540—21no—
29C11×#535C2211yescharacteristic
30C11×#532—21no—
31C2×C11×#127C2211yescharacteristic
32C11×#529—21no—
33C2×C11×#124C2211yescharacteristic
34C11×#525C2211yescharacteristic
35C2×C11×#121C2211yescharacteristic
36C11×#520C2211yescharacteristic
37C11×#518C2211yescharacteristic
38C2×C11×#117C2211yescharacteristic
39C11×#452—21no—
40C11×#452—21no—
41C11×#449—21no—
42C11×#449—21no—
43C2×C11×#104C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C11×#419C2211yescharacteristic
46C11×#419C2211yescharacteristic
47C11×#419C2211yescharacteristic
48C11×#418C2211yescharacteristic
49C11×#418C2211yescharacteristic
50C11×#418C2211yescharacteristic
51C11×#417—21no—
52C11×#417—21no—
53C11×#416—21no—
54C11×#416—21no—
55C2×C11×#100C2211yescharacteristic
56C2×C11×#100C2211yescharacteristic
57C11×#407C2211yescharacteristic
58C11×#392—22no—
59C11×#391C2211yescharacteristic
60C11×#390C2211yescharacteristic
61C11×#386—22no—
62C4×C11×C22⋊C4C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#339C2211yescharacteristic
66C11×#339C2211yescharacteristic
67C11×#339C2211yescharacteristic
68C11×#339C2211yescharacteristic
69C11×#339C2211yescharacteristic
70C11×#339C2211yescharacteristic
71C2×C11×#41—22no—
72C2×C11×#41—22no—
73C2×C11×#41—22no—
74C2×C11×#41—21no—
75C2×C11×#41—21no—
76C2×C11×#41—21no—
77C2×C11×#41—21no—
78C2×C11×#41—41no—
79C2×C11×#41—41no—
80C2×C11×#41C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11—22no—
84C22×D4×C11D412yes—
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C11×#137—22no—
90C11×#137—41no—
91C11×AGL(1,ℤ/8)—22no—
92C11×AGL(1,ℤ/8)—41no—
93C2×C11×Q16—21no—
94C2×C11×SD16—21no—
95C2×C11×SD16—21no—
96C2×C11×D8—21no—
97C2×C11×M16—21no—
98C2×C11×M16—41no—
99C2×C11×M16—41no—
100C2×C11×M16C2311yescharacteristic
101C2×C11×M16C2311yescharacteristic
102C2×C11×M16C2311yescharacteristic
103C2×C11×M16C2311yescharacteristic
104C22×C8×C11—21no—
105C11×C4⋊Q8—21no—
106C11×C4⋊Q8—21no—
107C11×#127—21no—
108C11×#127—22no—
109C11×#127—41no—
110C11×#126—22no—
111C11×#126—22no—
112C11×#125—21no—
113C11×#125—21no—
114C11×#124—22no—
115C11×#124—22no—
116C11×#124—21no—
117C11×#124—22no—
118C11×#124—41no—
119C11×#123—22no—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—22no—
123C11×#123—21no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8—22no—
126C11×C22⋊Q8D411yescharacteristic, complemented
127C11×C22⋊Q8D411yescharacteristic, complemented
128C11×#121—22no—
129C11×#121—22no—
130C11×#121—22no—
131C11×#121—21no—
132C11×#121—21no—
133C11×#121—21no—
134C11×#121—21no—
135C11×#121—21no—
136C11×#121—21no—
137C11×#121D411yescharacteristic, complemented
138C11×#121D411yescharacteristic, complemented
139C11×#120—21no—
140C11×#120—22no—
141C4×Q8×C11—21no—
142C4×D4×C11—22no—
143C4×D4×C11—22no—
144C4×D4×C11—21no—
145C4×D4×C11—22no—
146C4×D4×C11—21no—
147C4×D4×C11—21no—
148C4×D4×C11—21no—
149C4×D4×C11—21no—
150C4×D4×C11—21no—
151C4×D4×C11—21no—
152C11×#117—22no—
153C11×#117—21no—
154C11×#117—21no—
155C11×#117—21no—
156C11×#117D411yescharacteristic, complemented
157C11×#117D411yescharacteristic, complemented
158C11×#117C2311yescharacteristic
159C11×#117C2311yescharacteristic
160C11×#117C2311yescharacteristic
161C2×C11×C4⋊C4—21no—
162C2×C11×C4⋊C4D411yescharacteristic, complemented
163C2×C11×C4⋊C4D411yescharacteristic, complemented
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4—21no—
166C2×C11×C22⋊C4—22no—
167C2×C11×C22⋊C4—21no—
168C2×C11×C22⋊C4—22no—
169C2×C11×C22⋊C4—22no—
170C2×C11×C22⋊C4D412yes—
171C2×C42×C11—21no—
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2311yescharacteristic
174C11×#104—41no—
175C11×#104—41no—
176C11×#103—21no—
177C11×#103—21no—
178C11×#103—21no—
179C11×#103—21no—
180C11×#103—21no—
181C11×#103—21no—
182C11×#102—21no—
183C11×#102—21no—
184C11×#102—21no—
185C11×#102—21no—
186C11×#102—21no—
187C11×#102—21no—
188C11×#100—41no—
189C11×#100—41no—
190C11×C22⋊C8—21no—
191C11×C22⋊C8—21no—
192C11×#95—21no—
193C11×#95—22no—
194#23956C1111yesmaximal, characteristic, direct product factor, Sylow
195C24×C11—21no—
196C24×C11C2×D412yes—
197C24×C11C2×D411yescharacteristic
198C11×#41—24no—
199C11×#41—24no—
200C11×#41—21no—
201C11×#41—21no—
202C11×#41—21no—
203C11×#41—21no—
204C11×#41—42no—
205C11×#41—42no—
206C11×#41—42no—
207C11×#41—42no—
208C11×#41—42no—
209C11×#41—42no—
210C11×#41—84no—
211C2×Q8×C11—22no—
212C2×Q8×C11—21no—
213C2×Q8×C11—21no—
214C2×Q8×C11—21no—
215C2×Q8×C11—21no—
216C2×Q8×C11—21no—
217C2×Q8×C11C2×D411yescharacteristic
218C2×Q8×C11#4112yescomplemented
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11—21no—
222C2×D4×C11—22no—
223C2×D4×C11—22no—
224C2×D4×C11—21no—
225C2×D4×C11—22no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—21no—
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—21no—
235C2×D4×C11—21no—
236C2×D4×C11—21no—
237C2×D4×C11—42no—
238C2×D4×C11—44no—
239C2×D4×C11—42no—
240C2×D4×C11—41no—
241C2×D4×C11—41no—
242C2×D4×C11—44no—
243C2×D4×C11—82no—
244C2×D4×C11—82no—
245C2×D4×C11C2×D411yescharacteristic
246C2×D4×C11#4112yescomplemented
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—42no—
261C22×C4×C11—42no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D412yes—
270C22×C4×C11C2411yescharacteristic
271C11×Q16—42no—
272C11×SD16—42no—
273C11×SD16—42no—
274C11×D8—42no—
275C11×M16—21no—
276C11×M16—21no—
277C11×M16—21no—
278C11×M16—21no—
279C11×M16—21no—
280C11×M16—21no—
281C11×M16—21no—
282C11×M16—21no—
283C11×M16—42no—
284C2×C8×C11—21no—
285C2×C8×C11—21no—
286C2×C8×C11—21no—
287C2×C8×C11—21no—
288C2×C8×C11—42no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4—21no—
298C11×C4⋊C4—21no—
299C11×C4⋊C4C2×D411yescharacteristic
300C11×C4⋊C4C2×D411yescharacteristic
301C11×C4⋊C4C2×D411yescharacteristic
302C11×C4⋊C4C2×D411yescharacteristic
303C11×C4⋊C4C2×D411yescharacteristic
304C11×C4⋊C4C2×D411yescharacteristic
305C11×C22⋊C4—22no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—21no—
312C11×C22⋊C4—21no—
313C11×C22⋊C4—21no—
314C11×C22⋊C4—21no—
315C11×C22⋊C4—21no—
316C11×C22⋊C4—21no—
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4—21no—
320C11×C22⋊C4—21no—
321C11×C22⋊C4—44no—
322C11×C22⋊C4—42no—
323C11×C22⋊C4—82no—
324C42×C11—22no—
325C42×C11—21no—
326C42×C11—21no—
327C42×C11—21no—
328C42×C11—21no—
329C42×C11—21no—
330C42×C11—21no—
331C42×C11—21no—
332C42×C11—21no—
333C42×C11—21no—
334#3494C2×C1111yescharacteristic, complemented
335#3005C2×C1111yescharacteristic, complemented
336#2896C2×C1111yescharacteristic, complemented
337#2431C2×C1111yescharacteristic, complemented
338#2028C2×C1111yescharacteristic, complemented
339#2027C2×C1111yescharacteristic, complemented
340#2004C2×C1111yescharacteristic, complemented
341#2002C2×C1111yescharacteristic, complemented
342#1900C2×C1111yescharacteristic, complemented
343#1887C2×C1111yescharacteristic, complemented
344#1885C2×C1111yescharacteristic, complemented
345#1883C2×C1111yescharacteristic, complemented
346#1882C2×C1111yescharacteristic, complemented
347#1871C2×C1111yescharacteristic, complemented
348#1826C2×C1111yescharacteristic, complemented
349C23×C11—21no—
350C23×C11—21no—
351C23×C11—22no—
352C23×C11—21no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—42no—
359C23×C11—42no—
360C23×C11—42no—
361C23×C11—42no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11#12011yescharacteristic
365C23×C11#12011yescharacteristic
366C23×C11C22×D411yescharacteristic
367Q8×C11—22no—
368Q8×C11—21no—
369Q8×C11—22no—
370Q8×C11—21no—
371Q8×C11—41no—
372Q8×C11—41no—
373Q8×C11—82no—
374D4×C11—22no—
375D4×C11—21no—
376D4×C11—22no—
377D4×C11—21no—
378D4×C11—44no—
379D4×C11—42no—
380D4×C11—44no—
381D4×C11—44no—
382D4×C11—41no—
383D4×C11—41no—
384D4×C11—41no—
385D4×C11—41no—
386D4×C11—41no—
387D4×C11—41no—
388D4×C11—41no—
389D4×C11—41no—
390D4×C11—81no—
391D4×C11—82no—
392D4×C11—82no—
393D4×C11—82no—
394D4×C11—88no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—22no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—44no—
416C2×C4×C11—44no—
417C2×C4×C11—41no—
418C2×C4×C11—42no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—42no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—81no—
429C2×C4×C11—82no—
430C2×C4×C11—82no—
431C2×C4×C11—82no—
432C2×C4×C11#12011yescharacteristic
433C2×C4×C11#12011yescharacteristic
434C2×C4×C11C22×D411yescharacteristic
435C2×C4×C11C22×D411yescharacteristic
436C2×C4×C11C2×#4111yescharacteristic
437C2×C4×C11C2×#4111yescharacteristic
438C2×C4×C11H(5,𝔽2)11yescharacteristic
439C2×C4×C11H(5,𝔽2)11yescharacteristic
440C8×C11—41no—
441C8×C11—41no—
442C8×C11—41no—
443C8×C11—41no—
444C22×#41C22×C1111yescharacteristic
445C2×#137C22×C1111yescharacteristic
446C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
447C22×M16C22×C1111yescharacteristic
448#555—21no—
449#553—21no—
450#553—21no—
451#551—22no—
452#547—21no—
453#546—22no—
454#544C22×C1111yescharacteristic
455#542—21no—
456#540—21no—
457#535C22×C1111yescharacteristic
458#532—21no—
459C2×#127C22×C1111yescharacteristic
460#529—21no—
461C2×#124C22×C1111yescharacteristic
462#525C22×C1111yescharacteristic
463C2×#121C22×C1111yescharacteristic
464#520C22×C1111yescharacteristic
465#518C22×C1111yescharacteristic
466C2×#117C22×C1111yescharacteristic
467#452—21no—
468#452—21no—
469#449—21no—
470#449—21no—
471C2×#104C22×C1111yescharacteristic
472C2×#104C22×C1111yescharacteristic
473#419C22×C1111yescharacteristic
474#419C22×C1111yescharacteristic
475#419C22×C1111yescharacteristic
476#418C22×C1111yescharacteristic
477#418C22×C1111yescharacteristic
478#418C22×C1111yescharacteristic
479#417—21no—
480#417—21no—
481#416—21no—
482#416—21no—
483C2×#100C22×C1111yescharacteristic
484C2×#100C22×C1111yescharacteristic
485#407C22×C1111yescharacteristic
486#392—22no—
487#391C22×C1111yescharacteristic
488#390C22×C1111yescharacteristic
489#386—22no—
490C4×C22⋊C4C22×C1111yescharacteristic
491#343C22×C1111yescharacteristic
492#343C22×C1111yescharacteristic
493#339C22×C1111yescharacteristic
494#339C22×C1111yescharacteristic
495#339C22×C1111yescharacteristic
496#339C22×C1111yescharacteristic
497#339C22×C1111yescharacteristic
498#339C22×C1111yescharacteristic
499C22×C11—21no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—21no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—44no—
508C22×C11—42no—
509C22×C11—41no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—41no—
513C22×C11—41no—
514C22×C11—42no—
515C22×C11—81no—
516C22×C11—81no—
517C22×C11—82no—
518C22×C11—82no—
519C22×C11—82no—
520C22×C11—81no—
521C22×C11—81no—
522C22×C11C2×#12011yescharacteristic
523C22×C11#54611yescharacteristic
524C22×C11#54611yescharacteristic
525C4×C11—21no—
526C4×C11—21no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11—41no—
530C4×C11—41no—
531C4×C11—41no—
532C4×C11—41no—
533C4×C11—41no—
534C4×C11—41no—
535C4×C11—42no—
536C4×C11—41no—
537C4×C11—81no—
538C4×C11#52511yescharacteristic
539C4×C11#53511yescharacteristic
540C4×C11#54611yescharacteristic
541C4×C11#54611yescharacteristic
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41C23×C1111yescharacteristic
552C22×Q8C23×C1111yescharacteristic
553C22×D4—21no—
554C22×D4—22no—
555C22×D4D4×C1112yes—
556C22×D4C23×C1111yescharacteristic
557C22×D4C23×C1111yescharacteristic
558C23×C4—21no—
559C23×C4C23×C1111yescharacteristic
560#137—22no—
561#137—41no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—41no—
564C2×Q16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×D8—21no—
568C2×M16—21no—
569C2×M16—41no—
570C2×M16—41no—
571C2×M16C23×C1111yescharacteristic
572C2×M16C23×C1111yescharacteristic
573C2×M16C23×C1111yescharacteristic
574C2×M16C23×C1111yescharacteristic
575C22×C8—21no—
576C4⋊Q8—21no—
577C4⋊Q8—21no—
578#127—21no—
579#127—22no—
580#127—41no—
581#126—22no—
582#126—22no—
583#125—21no—
584#125—21no—
585#124—22no—
586#124—22no—
587#124—21no—
588#124—22no—
589#124—41no—
590#123—22no—
591#123—22no—
592#123—22no—
593#123—22no—
594#123—21no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8D4×C1111yescharacteristic, complemented
598C22⋊Q8D4×C1111yescharacteristic, complemented
599#121—22no—
600#121—22no—
601#121—22no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121D4×C1111yescharacteristic, complemented
609#121D4×C1111yescharacteristic, complemented
610#120—21no—
611#120—22no—
612C4×Q8—21no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—21no—
616C4×D4—22no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623#117—22no—
624#117—21no—
625#117—21no—
626#117—21no—
627#117D4×C1111yescharacteristic, complemented
628#117D4×C1111yescharacteristic, complemented
629#117C23×C1111yescharacteristic
630#117C23×C1111yescharacteristic
631#117C23×C1111yescharacteristic
632C2×C4⋊C4—21no—
633C2×C4⋊C4D4×C1111yescharacteristic, complemented
634C2×C4⋊C4D4×C1111yescharacteristic, complemented
635C2×C4⋊C4C23×C1111yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—22no—
641C2×C22⋊C4D4×C1112yes—
642C2×C42—21no—
643C2×C42C23×C1111yescharacteristic
644C2×C42C23×C1111yescharacteristic
645#104—41no—
646#104—41no—
647#103—21no—
648#103—21no—
649#103—21no—
650#103—21no—
651#103—21no—
652#103—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#102—21no—
657#102—21no—
658#102—21no—
659#100—41no—
660#100—41no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663#95—21no—
664#95—22no—
665C2×C11—21no—
666C2×C11—21no—
667C2×C11—41no—
668C2×C11—41no—
669C2×C11—81no—
670C2×C11—82no—
671C2×C11—82no—
672C2×C11#240411yescharacteristic
673C2×C11#301811yescharacteristic
674C2×C11#301911yescharacteristic
675C24—21no—
676C24C2×D4×C1112yes—
677C24C2×D4×C1111yescharacteristic
678#41—24no—
679#41—24no—
680#41—21no—
681#41—21no—
682#41—21no—
683#41—21no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41—42no—
690#41—84no—
691C2×Q8—22no—
692C2×Q8—21no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8C2×D4×C1111yescharacteristic
698C2×Q8C11×#4112yescomplemented
699C2×D4—21no—
700C2×D4—22no—
701C2×D4—21no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—21no—
705C2×D4—22no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—42no—
718C2×D4—44no—
719C2×D4—42no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—44no—
723C2×D4—82no—
724C2×D4—82no—
725C2×D4C2×D4×C1111yescharacteristic
726C2×D4C11×#4112yescomplemented
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4C2×D4×C1111yescharacteristic
745C22×C4C2×D4×C1111yescharacteristic
746C22×C4C2×D4×C1111yescharacteristic
747C22×C4C2×D4×C1111yescharacteristic
748C22×C4C2×D4×C1111yescharacteristic
749C22×C4C2×D4×C1112yes—
750C22×C4C24×C1111yescharacteristic
751Q16—42no—
752SD16—42no—
753SD16—42no—
754D8—42no—
755M16—21no—
756M16—21no—
757M16—21no—
758M16—21no—
759M16—21no—
760M16—21no—
761M16—21no—
762M16—21no—
763M16—42no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—42no—
769C4⋊C4—22no—
770C4⋊C4—22no—
771C4⋊C4—22no—
772C4⋊C4—22no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—21no—
777C4⋊C4—21no—
778C4⋊C4—21no—
779C4⋊C4C2×D4×C1111yescharacteristic
780C4⋊C4C2×D4×C1111yescharacteristic
781C4⋊C4C2×D4×C1111yescharacteristic
782C4⋊C4C2×D4×C1111yescharacteristic
783C4⋊C4C2×D4×C1111yescharacteristic
784C4⋊C4C2×D4×C1111yescharacteristic
785C22⋊C4—22no—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—44no—
802C22⋊C4—42no—
803C22⋊C4—82no—
804C42—22no—
805C42—21no—
806C42—21no—
807C42—21no—
808C42—21no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—21no—
813C42—21no—
814C11#2395611yescharacteristic, direct product factor, Sylow
815C23—21no—
816C23—21no—
817C23—22no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—41no—
823C23—41no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—41no—
829C23—41no—
830C23C11×#12011yescharacteristic
831C23C11×#12011yescharacteristic
832C23C22×D4×C1111yescharacteristic
833Q8—22no—
834Q8—21no—
835Q8—22no—
836Q8—21no—
837Q8—41no—
838Q8—41no—
839Q8—82no—
840D4—22no—
841D4—21no—
842D4—22no—
843D4—21no—
844D4—44no—
845D4—42no—
846D4—44no—
847D4—44no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—82no—
858D4—82no—
859D4—82no—
860D4—88no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—42no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—81no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4C11×#12011yescharacteristic
899C2×C4C11×#12011yescharacteristic
900C2×C4C22×D4×C1111yescharacteristic
901C2×C4C22×D4×C1111yescharacteristic
902C2×C4C2×C11×#4111yescharacteristic
903C2×C4C2×C11×#4111yescharacteristic
904C2×C4C11×H(5,𝔽2)11yescharacteristic
905C2×C4C11×H(5,𝔽2)11yescharacteristic
906C8—41no—
907C8—41no—
908C8—41no—
909C8—41no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—44no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—42no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—81no—
927C22—81no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—81no—
932C22—81no—
933C22C2×C11×#12011yescharacteristic
934C22C11×#54611yescharacteristic
935C22C11×#54611yescharacteristic
936C4—21no—
937C4—21no—
938C4—42no—
939C4—42no—
940C4—41no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—81no—
949C4C11×#52511yescharacteristic
950C4C11×#53511yescharacteristic
951C4C11×#54611yescharacteristic
952C4C11×#54611yescharacteristic
953C2—21no—
954C2—21no—
955C2—41no—
956C2—41no—
957C2—82no—
958C2—82no—
959C2—81no—
960C2C11×#240411yescharacteristic
961C2C11×#301811yescharacteristic
962C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3494C2semidirect
2. C11×#3005C2semidirect
3. C11×#2896C2semidirect
4. C11×#2431C2semidirect
5. C11×#2028C2semidirect
6. C11×#2027C2semidirect
7. C11×#2004C2semidirect
8. C11×#2002C2semidirect
9. C11×#1900C2semidirect
10. C11×#1887C2semidirect
11. C11×#1885C2semidirect
12. C11×#1883C2semidirect
13. C11×#1882C2semidirect
14. C11×#1871C2semidirect
15. C11×#1826C2semidirect
126. C11×C22⋊Q8D4semidirect
127. C11×C22⋊Q8D4semidirect
137. C11×#121D4semidirect
138. C11×#121D4semidirect
156. C11×#117D4semidirect
157. C11×#117D4semidirect
162. C2×C11×C4⋊C4D4semidirect
163. C2×C11×C4⋊C4D4semidirect
194. #23956C11direct (N × H)
218. C2×Q8×C11#41semidirect
246. C2×D4×C11#41semidirect
334. #3494C2×C11semidirect
335. #3005C2×C11semidirect
336. #2896C2×C11semidirect
337. #2431C2×C11semidirect
338. #2028C2×C11semidirect
339. #2027C2×C11semidirect
340. #2004C2×C11semidirect
341. #2002C2×C11semidirect
342. #1900C2×C11semidirect
343. #1887C2×C11semidirect
344. #1885C2×C11semidirect
345. #1883C2×C11semidirect
346. #1882C2×C11semidirect
347. #1871C2×C11semidirect
348. #1826C2×C11semidirect
597. C22⋊Q8D4×C11semidirect
598. C22⋊Q8D4×C11semidirect
608. #121D4×C11semidirect
609. #121D4×C11semidirect
627. #117D4×C11semidirect
628. #117D4×C11semidirect
633. C2×C4⋊C4D4×C11semidirect
634. C2×C4⋊C4D4×C11semidirect
698. C2×Q8C11×#41semidirect
726. C2×D4C11×#41semidirect
814. C11#23956direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34942
C11×#30052
C11×#28962
C11×#24312
C11×#20282
C11×#20272
C11×#20042
C11×#20022
C11×#19002
C11×#18872
C11×#18852
C11×#18832
C11×#18822
C11×#18712
C11×#18262
#2395611