Finite Group Databasebeta

← C11×#24245 #14601438

Subgroups — C11×#24245 #14601438

Order 2816.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic, complemented
2C2×C11×#463C211yesmaximal, characteristic, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C2×C11×#447C211yesmaximal, characteristic, complemented
5C2×C4×C11×D8C211yesmaximal, characteristic, complemented
6C11×#2535C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#2000C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1958C211yesmaximal, characteristic, complemented
12C11×#1954C211yesmaximal, characteristic, complemented
13C11×#1804C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic, complemented
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C11×#546—24no—
22C11×#546—24no—
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121—21no—
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic, complemented
30C2×C11×#120—21no—
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic, complemented
34C22×C11×C22⋊C4—21no—
35C11×#463—24no—
36C11×#449—24no—
37C11×#447—24no—
38C4×C11×D8—24no—
39C2×C11×#107C2211yescharacteristic, complemented
40C2×C11×C4⋊C8C2211yescharacteristic, complemented
41C2×C11×#103C2211yescharacteristic, complemented
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#103C2211yescharacteristic, complemented
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C2×C11×C22⋊C8C2211yescharacteristic, complemented
55C2×C4×C8×C11C2211yescharacteristic, complemented
56C11×#397—21no—
57C11×#392—21no—
58C11×#386—21no—
59C11×#386—21no—
60C11×#382C2211yescharacteristic, complemented
61C11×#380C2211yescharacteristic
62C11×#380C2211yescharacteristic, complemented
63C11×#340C2211yescharacteristic, complemented
64C11×#340C2211yescharacteristic, complemented
65C25×C11—21no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—21no—
74C22×D4×C11—21no—
75C22×D4×C11—22no—
76C22×D4×C11—22no—
77C22×D4×C11—22no—
78C22×D4×C11—22no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—41no—
83C22×D4×C11—41no—
84C22×D4×C11D411yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C23×C4×C11—21no—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—41no—
96C2×C11×D8—22no—
97C2×C11×D8—22no—
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—41no—
101C2×C11×D8D414yescomplemented
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#124—22no—
107C11×#124D414yescomplemented
108C11×#123—28no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×#121—28no—
112C11×#121—22no—
113C11×#121—22no—
114C11×#121—22no—
115C11×#121—22no—
116C11×#121—41no—
117C11×#121—41no—
118C11×#120—28no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11D414yescomplemented
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4D411yescharacteristic
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—28no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4D411yescharacteristic
143C2×C11×C22⋊C4D411yescharacteristic
144C2×C42×C11C2311yescharacteristic
145C11×#107—22no—
146C11×C4⋊C8—22no—
147C11×#103—22no—
148C11×#103—22no—
149C11×#103—41no—
150C11×#102—22no—
151C11×#102—22no—
152C11×#102—22no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—41no—
157C11×C22⋊C8—22no—
158C11×C22⋊C8—22no—
159C11×C22⋊C8—41no—
160C11×C22⋊C8—41no—
161C4×C8×C11—22no—
162C11×#95—21no—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24245C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11—24no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—42no—
175C24×C11—81no—
176C24×C11—81no—
177C24×C11C2×D411yescharacteristic
178C24×C11C2×D411yescharacteristic
179C11×#41—44no—
180C11×#41—44no—
181C11×#41—44no—
182C11×#41—44no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11C2×D412yes—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—22no—
192C2×D4×C11—24no—
193C2×D4×C11—22no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—41no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—44no—
211C2×D4×C11—44no—
212C2×D4×C11—44no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—44no—
216C2×D4×C11—42no—
217C2×D4×C11—42no—
218C2×D4×C11—42no—
219C2×D4×C11—42no—
220C2×D4×C11—81no—
221C2×D4×C11—81no—
222C2×D4×C11—81no—
223C2×D4×C11—81no—
224C2×D4×C11C2×D412yes—
225C2×D4×C11C2×D412yes—
226C2×D4×C11C2×D412yes—
227C2×D4×C11C2×D412yes—
228C2×D4×C11#4112yes—
229C22×C4×C11—24no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—24no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—42no—
249C22×C4×C11—42no—
250C22×C4×C11—42no—
251C22×C4×C11—81no—
252C22×C4×C11—81no—
253C22×C4×C11—81no—
254C22×C4×C11—81no—
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C11×SD16—44no—
261C11×D8—28no—
262C11×D8—44no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C2×C8×C11C2×D412yes—
275C11×C4⋊C4—24no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4C2×D412yes—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—24no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—42no—
293C11×C22⋊C4—42no—
294C11×C22⋊C4—42no—
295C11×C22⋊C4—81no—
296C11×C22⋊C4—81no—
297C42×C11C2×D412yes—
298C42×C11C2×D412yes—
299C2×#546C2×C1111yescharacteristic, complemented
300C2×#463C2×C1111yescharacteristic, complemented
301C2×#449C2×C1111yescharacteristic, complemented
302C2×#447C2×C1111yescharacteristic, complemented
303C2×C4×D8C2×C1111yescharacteristic, complemented
304#2535C2×C1111yescharacteristic, complemented
305#2036C2×C1111yescharacteristic, complemented
306#2033C2×C1111yescharacteristic, complemented
307#2000C2×C1111yescharacteristic, complemented
308#1999C2×C1111yescharacteristic, complemented
309#1958C2×C1111yescharacteristic, complemented
310#1954C2×C1111yescharacteristic, complemented
311#1804C2×C1111yescharacteristic, complemented
312#1788C2×C1111yescharacteristic, complemented
313#1786C2×C1111yescharacteristic, complemented
314C23×C11—21no—
315C23×C11—22no—
316C23×C11—21no—
317C23×C11—22no—
318C23×C11—21no—
319C23×C11—22no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—22no—
324C23×C11—21no—
325C23×C11—22no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—48no—
333C23×C11—48no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—84no—
351C23×C11—84no—
352C23×C11—84no—
353C23×C11—84no—
354C23×C11—84no—
355C23×C11#13512yes—
356C23×C11C22×D411yescharacteristic
357Q8×C11—22no—
358Q8×C11—22no—
359Q8×C11—41no—
360Q8×C11—41no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—44no—
369D4×C11—48no—
370D4×C11—48no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—84no—
376D4×C11—84no—
377D4×C11—84no—
378D4×C11#12114yes—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—22no—
384C2×C4×C11—21no—
385C2×C4×C11—22no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—48no—
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—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—41no—
413C2×C4×C11—84no—
414C2×C4×C11—84no—
415C2×C4×C11#12012yes—
416C2×C4×C11#12012yes—
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C2×#4111yescharacteristic
421C2×C4×C11H(5,𝔽2)11yescharacteristic
422C2×C4×C11H(5,𝔽2)11yescharacteristic
423C8×C11—22no—
424C8×C11—41no—
425C8×C11—41no—
426C8×C11—41no—
427C22×#41C22×C1111yescharacteristic
428C23×D4C22×C1111yescharacteristic
429C22×SD16C22×C1111yescharacteristic, complemented
430C22×D8C22×C1111yescharacteristic
431C22×D8C22×C1111yescharacteristic
432#546—24no—
433#546—24no—
434C2×#124C22×C1111yescharacteristic
435C2×#123—21no—
436C2×C22⋊Q8C22×C1111yescharacteristic
437C2×#121—21no—
438C2×#121C22×C1111yescharacteristic
439C2×#121C22×C1111yescharacteristic
440C2×#121C22×C1111yescharacteristic, complemented
441C2×#120—21no—
442C2×C4×D4C22×C1111yescharacteristic
443C2×C4×D4C22×C1111yescharacteristic
444C2×C4×D4C22×C1111yescharacteristic, complemented
445C22×C22⋊C4—21no—
446#463—24no—
447#449—24no—
448#447—24no—
449C4×D8—24no—
450C2×#107C22×C1111yescharacteristic, complemented
451C2×C4⋊C8C22×C1111yescharacteristic, complemented
452C2×#103C22×C1111yescharacteristic, complemented
453C2×#103C22×C1111yescharacteristic, complemented
454C2×#103C22×C1111yescharacteristic, complemented
455C2×#102C22×C1111yescharacteristic
456C2×#102C22×C1111yescharacteristic
457C2×#102C22×C1111yescharacteristic
458C2×#102C22×C1111yescharacteristic
459C2×#102C22×C1111yescharacteristic
460C2×#102C22×C1111yescharacteristic
461C2×#102C22×C1111yescharacteristic, complemented
462C2×C22⋊C8C22×C1111yescharacteristic
463C2×C22⋊C8C22×C1111yescharacteristic
464C2×C22⋊C8C22×C1111yescharacteristic, complemented
465C2×C22⋊C8C22×C1111yescharacteristic, complemented
466C2×C4×C8C22×C1111yescharacteristic, complemented
467#397—21no—
468#392—21no—
469#386—21no—
470#386—21no—
471#382C22×C1111yescharacteristic, complemented
472#380C22×C1111yescharacteristic
473#380C22×C1111yescharacteristic, complemented
474#340C22×C1111yescharacteristic, complemented
475#340C22×C1111yescharacteristic, complemented
476C22×C11—24no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—41no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—41no—
489C22×C11—42no—
490C22×C11—41no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—41no—
494C22×C11—42no—
495C22×C11—41no—
496C22×C11—42no—
497C22×C11—41no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—41no—
501C22×C11—41no—
502C22×C11—41no—
503C22×C11—816no—
504C22×C11—81no—
505C22×C11—81no—
506C22×C11—81no—
507C22×C11—81no—
508C22×C11—81no—
509C22×C11—81no—
510C22×C11—81no—
511C22×C11—81no—
512C22×C11C2×#12011yescharacteristic
513C22×C11D4211yescharacteristic
514C22×C11#54611yescharacteristic
515C22×C11C2×#13511yescharacteristic
516C22×C11#57511yescharacteristic
517C22×C11#57611yescharacteristic
518C22×C11#57611yescharacteristic
519C4×C11—22no—
520C4×C11—22no—
521C4×C11—41no—
522C4×C11—41no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—81no—
526C4×C11—81no—
527C4×C11—81no—
528C4×C11C2×#12111yescharacteristic
529C4×C11#53511yescharacteristic
530C4×C11D4211yescharacteristic
531C4×C11#54611yescharacteristic
532C25—21no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—41no—
538C2×#41—41no—
539C22×Q8C23×C1111yescharacteristic
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—22no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—41no—
550C22×D4—41no—
551C22×D4D4×C1111yescharacteristic
552C22×D4C23×C1111yescharacteristic
553C22×D4C23×C1111yescharacteristic
554C22×D4C23×C1111yescharacteristic
555C23×C4—21no—
556C23×C4—21no—
557C23×C4—21no—
558C23×C4C23×C1111yescharacteristic
559C23×C4C23×C1111yescharacteristic
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—41no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—41no—
568C2×D8D4×C1114yescomplemented
569C22×C8C23×C1111yescharacteristic
570C22×C8C23×C1111yescharacteristic
571C22×C8C23×C1111yescharacteristic
572C22×C8C23×C1111yescharacteristic
573#124—22no—
574#124D4×C1114yescomplemented
575#123—28no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578#121—28no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—41no—
584#121—41no—
585#120—28no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4D4×C1114yescomplemented
592C2×C4⋊C4—21no—
593C2×C4⋊C4D4×C1111yescharacteristic
594C2×C4⋊C4C23×C1111yescharacteristic
595C2×C4⋊C4C23×C1111yescharacteristic
596C2×C4⋊C4C23×C1111yescharacteristic
597C2×C4⋊C4C23×C1111yescharacteristic
598C2×C22⋊C4—28no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4D4×C1111yescharacteristic
610C2×C22⋊C4D4×C1111yescharacteristic
611C2×C42C23×C1111yescharacteristic
612#107—22no—
613C4⋊C8—22no—
614#103—22no—
615#103—22no—
616#103—41no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—22no—
622#102—22no—
623#102—41no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8—41no—
627C22⋊C8—41no—
628C4×C8—22no—
629#95—21no—
630#95—21no—
631#95—21no—
632#95—21no—
633C2×C11—42no—
634C2×C11—44no—
635C2×C11—81no—
636C2×C11—82no—
637C2×C11—82no—
638C2×C11#240811yescharacteristic
639C2×C11#300211yescharacteristic
640C2×C11#300811yescharacteristic
641C2×C11#327311yescharacteristic
642C2×C11#328011yescharacteristic
643C2×C11#329711yescharacteristic
644C2×C11#332211yescharacteristic
645C24—21no—
646C24—24no—
647C24—21no—
648C24—21no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24C2×D4×C1111yescharacteristic
656C24C2×D4×C1111yescharacteristic
657#41—44no—
658#41—44no—
659#41—44no—
660#41—44no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8C2×D4×C1112yes—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—41no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C2×D4×C1112yes—
703C2×D4C2×D4×C1112yes—
704C2×D4C2×D4×C1112yes—
705C2×D4C2×D4×C1112yes—
706C2×D4C11×#4112yes—
707C22×C4—24no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
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—21no—
721C22×C4—21no—
722C22×C4—24no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—81no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4C2×D4×C1111yescharacteristic
734C22×C4C2×D4×C1111yescharacteristic
735C22×C4C2×D4×C1111yescharacteristic
736C22×C4C2×D4×C1111yescharacteristic
737C22×C4C24×C1111yescharacteristic
738SD16—44no—
739D8—28no—
740D8—44no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8C2×D4×C1112yes—
753C4⋊C4—24no—
754C4⋊C4—22no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4C2×D4×C1112yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—22no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—81no—
774C22⋊C4—81no—
775C42C2×D4×C1112yes—
776C42C2×D4×C1112yes—
777C11#2424511yescharacteristic, direct product factor, Sylow
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C11×#13512yes—
820C23C22×D4×C1111yescharacteristic
821Q8—22no—
822Q8—22no—
823Q8—41no—
824Q8—41no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—44no—
833D4—48no—
834D4—48no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4C11×#12114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4C11×#12012yes—
880C2×C4C11×#12012yes—
881C2×C4C22×D4×C1111yescharacteristic
882C2×C4C22×D4×C1111yescharacteristic
883C2×C4C22×D4×C1111yescharacteristic
884C2×C4C2×C11×#4111yescharacteristic
885C2×C4C11×H(5,𝔽2)11yescharacteristic
886C2×C4C11×H(5,𝔽2)11yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—41no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—42no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×C11×#12011yescharacteristic
928C22D42×C1111yescharacteristic
929C22C11×#54611yescharacteristic
930C22C2×C11×#13511yescharacteristic
931C22C11×#57511yescharacteristic
932C22C11×#57611yescharacteristic
933C22C11×#57611yescharacteristic
934C4—22no—
935C4—22no—
936C4—41no—
937C4—41no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×C11×#12111yescharacteristic
944C4C11×#53511yescharacteristic
945C4D42×C1111yescharacteristic
946C4C11×#54611yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—82no—
952C2C11×#240811yescharacteristic
953C2C11×#300211yescharacteristic
954C2C11×#300811yescharacteristic
955C2C11×#327311yescharacteristic
956C2C11×#328011yescharacteristic
957C2C11×#329711yescharacteristic
958C2C11×#332211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#546C2semidirect
2. C2×C11×#463C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#447C2semidirect
5. C2×C4×C11×D8C2semidirect
6. C11×#2535C2semidirect
7. C11×#2036C2semidirect
8. C11×#2033C2semidirect
9. C11×#2000C2semidirect
10. C11×#1999C2semidirect
11. C11×#1958C2semidirect
12. C11×#1954C2semidirect
13. C11×#1804C2semidirect
14. C11×#1788C2semidirect
15. C11×#1786C2semidirect
18. C22×C11×SD16C22semidirect
29. C2×C11×#121C22semidirect
33. C2×C4×D4×C11C22semidirect
39. C2×C11×#107C22semidirect
40. C2×C11×C4⋊C8C22semidirect
41. C2×C11×#103C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#103C22semidirect
50. C2×C11×#102C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. C2×C11×C22⋊C8C22semidirect
55. C2×C4×C8×C11C22semidirect
60. C11×#382C22semidirect
62. C11×#380C22semidirect
63. C11×#340C22semidirect
64. C11×#340C22semidirect
101. C2×C11×D8D4semidirect
107. C11×#124D4semidirect
124. C4×D4×C11D4semidirect
166. #24245C11direct (N × H)
299. C2×#546C2×C11semidirect
300. C2×#463C2×C11semidirect
301. C2×#449C2×C11semidirect
302. C2×#447C2×C11semidirect
303. C2×C4×D8C2×C11semidirect
304. #2535C2×C11semidirect
305. #2036C2×C11semidirect
306. #2033C2×C11semidirect
307. #2000C2×C11semidirect
308. #1999C2×C11semidirect
309. #1958C2×C11semidirect
310. #1954C2×C11semidirect
311. #1804C2×C11semidirect
312. #1788C2×C11semidirect
313. #1786C2×C11semidirect
429. C22×SD16C22×C11semidirect
440. C2×#121C22×C11semidirect
444. C2×C4×D4C22×C11semidirect
450. C2×#107C22×C11semidirect
451. C2×C4⋊C8C22×C11semidirect
452. C2×#103C22×C11semidirect
453. C2×#103C22×C11semidirect
454. C2×#103C22×C11semidirect
461. C2×#102C22×C11semidirect
464. C2×C22⋊C8C22×C11semidirect
465. C2×C22⋊C8C22×C11semidirect
466. C2×C4×C8C22×C11semidirect
471. #382C22×C11semidirect
473. #380C22×C11semidirect
474. #340C22×C11semidirect
475. #340C22×C11semidirect
568. C2×D8D4×C11semidirect
574. #124D4×C11semidirect
591. C4×D4D4×C11semidirect
777. C11#24245direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5462
C2×C11×#4632
C2×C11×#4492
C2×C11×#4472
C2×C4×C11×D82
C11×#25352
C11×#20362
C11×#20332
C11×#20002
C11×#19992
C11×#19582
C11×#19542
C11×#18042
C11×#17882
C11×#17862
#2424511