Finite Group Databasebeta

← C11×#24390 #14601583

Subgroups — C11×#24390 #14601583

Order 2816.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic, complemented
2C2×C11×#469C211yesmaximal, characteristic, complemented
3C2×C11×#466C211yesmaximal, characteristic, complemented
4C2×C11×#447C211yesmaximal, characteristic, complemented
5C2×C11×#408C211yesmaximal, characteristic, complemented
6C11×#2615C211yesmaximal, characteristic, complemented
7C11×#2034C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1999C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1895C211yesmaximal, characteristic, complemented
12C11×#1893C211yesmaximal, characteristic, complemented
13C11×#1875C211yesmaximal, characteristic, complemented
14C11×#1854C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic, complemented
21C23×C8×C11C2211yescharacteristic, complemented
22C11×#535—24no—
23C11×#535—24no—
24C2×C11×#127—21no—
25C2×C11×#124—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic, complemented
32C2×C11×#121C2211yescharacteristic, complemented
33C2×C11×#120—21no—
34C2×C11×#120—21no—
35C2×C11×#117C2211yescharacteristic
36C11×#469—24no—
37C11×#466—24no—
38C11×#447—24no—
39C2×C11×#107C2211yescharacteristic, complemented
40C2×C11×#106C2211yescharacteristic, complemented
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic, complemented
48C2×C11×#102C2211yescharacteristic, complemented
49C11×#408—24no—
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C11×#393—21no—
55C11×#392—21no—
56C11×#392—21no—
57C11×#392—21no—
58C11×#380C2211yescharacteristic
59C11×#380C2211yescharacteristic, complemented
60C11×#380C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, 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×C11D411yescharacteristic
73C22×D4×C11—21no—
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11—22no—
78C22×D4×C11—22no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—22no—
84C22×D4×C11—22no—
85C22×D4×C11—41no—
86C22×D4×C11—41no—
87C22×D4×C11D411yescharacteristic
88C22×D4×C11D411yescharacteristic
89C22×D4×C11D411yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2311yescharacteristic
92C22×D4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C2×C11×D8—22no—
97C2×C11×D8—22no—
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—41no—
101C2×C11×D8—41no—
102C2×C11×M16—22no—
103C2×C11×M16—22no—
104C2×C11×M16—41no—
105C22×C8×C11—22no—
106C22×C8×C11—22no—
107C22×C8×C11—41no—
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×#127—28no—
113C11×#124—28no—
114C11×#121—22no—
115C11×#121—22no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—22no—
123C11×#121—22no—
124C11×#121—41no—
125C11×#121—41no—
126C11×#121D414yescomplemented
127C11×#121D414yescomplemented
128C11×#120—28no—
129C11×#120—28no—
130C11×#117—22no—
131C11×#117—22no—
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
143C2×C11×C22⋊C4—21no—
144C2×C11×C22⋊C4—21no—
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4—21no—
147C2×C11×C22⋊C4—21no—
148C2×C42×C11—21no—
149C11×#107—22no—
150C11×#106—22no—
151C11×#102—22no—
152C11×#102—22no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—41no—
158C11×#102—41no—
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—22no—
162C11×C22⋊C8D414yescomplemented
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24390C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—24no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—81no—
174C24×C11—81no—
175C24×C11—81no—
176C24×C11—81no—
177C24×C11C2×D411yescharacteristic
178C24×C11C2×D411yescharacteristic
179C24×C11C2×D411yescharacteristic
180C11×#41—44no—
181C11×#41—44no—
182C11×#41—44no—
183C11×#41—44no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11—41no—
187C2×D4×C11—24no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—24no—
193C2×D4×C11—24no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
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—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—44no—
215C2×D4×C11—44no—
216C2×D4×C11—44no—
217C2×D4×C11—44no—
218C2×D4×C11—41no—
219C2×D4×C11—41no—
220C2×D4×C11—41no—
221C2×D4×C11—42no—
222C2×D4×C11—42no—
223C2×D4×C11—42no—
224C2×D4×C11—42no—
225C2×D4×C11—42no—
226C2×D4×C11—81no—
227C2×D4×C11—81no—
228C2×D4×C11—81no—
229C2×D4×C11—81no—
230C2×D4×C11—81no—
231C2×D4×C11—81no—
232C2×D4×C11—81no—
233C2×D4×C11—81no—
234C2×D4×C11—81no—
235C2×D4×C11—81no—
236C2×D4×C11—81no—
237C2×D4×C11—81no—
238C2×D4×C11—81no—
239C2×D4×C11—81no—
240C2×D4×C11C2×D412yes—
241C2×D4×C11C2×D412yes—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
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—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×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D412yes—
267C22×C4×C11#4112yes—
268C22×C4×C11C2411yescharacteristic
269C11×D8—44no—
270C11×D8—44no—
271C11×M16—44no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C2×C8×C11—21no—
275C2×C8×C11—21no—
276C2×C8×C11—21no—
277C2×C8×C11—21no—
278C2×C8×C11—21no—
279C2×C8×C11—21no—
280C2×C8×C11—21no—
281C2×C8×C11—21no—
282C2×C8×C11—44no—
283C2×C8×C11C2×D412yes—
284C2×C8×C11C2×D412yes—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2×D412yes—
295C11×C22⋊C4—24no—
296C11×C22⋊C4—24no—
297C11×C22⋊C4—24no—
298C11×C22⋊C4—24no—
299C11×C22⋊C4—24no—
300C11×C22⋊C4—42no—
301C11×C22⋊C4—42no—
302C11×C22⋊C4—42no—
303C11×C22⋊C4—81no—
304C11×C22⋊C4—81no—
305C11×C22⋊C4—81no—
306C42×C11—24no—
307C2×#535C2×C1111yescharacteristic, complemented
308C2×#469C2×C1111yescharacteristic, complemented
309C2×#466C2×C1111yescharacteristic, complemented
310C2×#447C2×C1111yescharacteristic, complemented
311C2×#408C2×C1111yescharacteristic, complemented
312#2615C2×C1111yescharacteristic, complemented
313#2034C2×C1111yescharacteristic, complemented
314#2033C2×C1111yescharacteristic, complemented
315#1999C2×C1111yescharacteristic, complemented
316#1999C2×C1111yescharacteristic, complemented
317#1895C2×C1111yescharacteristic, complemented
318#1893C2×C1111yescharacteristic, complemented
319#1875C2×C1111yescharacteristic, complemented
320#1854C2×C1111yescharacteristic, complemented
321#1786C2×C1111yescharacteristic, complemented
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—21no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—21no—
337C23×C11—21no—
338C23×C11—21no—
339C23×C11—21no—
340C23×C11—21no—
341C23×C11—21no—
342C23×C11—21no—
343C23×C11—48no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—84no—
364C23×C11—84no—
365C23×C11—84no—
366C23×C11—84no—
367C23×C11—84no—
368C23×C11—84no—
369C23×C11#12012yes—
370C23×C11#12112yes—
371C23×C11C22×D411yescharacteristic
372Q8×C11—44no—
373D4×C11—22no—
374D4×C11—22no—
375D4×C11—22no—
376D4×C11—22no—
377D4×C11—44no—
378D4×C11—44no—
379D4×C11—48no—
380D4×C11—44no—
381D4×C11—41no—
382D4×C11—41no—
383D4×C11—41no—
384D4×C11—41no—
385D4×C11—41no—
386D4×C11—41no—
387D4×C11—41no—
388D4×C11—41no—
389D4×C11—84no—
390D4×C11—84no—
391D4×C11—84no—
392D4×C11—84no—
393D4×C11—84no—
394D4×C11—84no—
395D4×C11—84no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11#12012yes—
431C2×C4×C11#12112yes—
432C2×C4×C11C22×D411yescharacteristic
433C2×C4×C11C22×D411yescharacteristic
434C2×C4×C11C22×D411yescharacteristic
435C2×C4×C11C2×#4111yescharacteristic
436C2×C4×C11H(5,𝔽2)11yescharacteristic
437C2×C4×C11H(5,𝔽2)11yescharacteristic
438C8×C11—22no—
439C8×C11—22no—
440C8×C11—41no—
441C8×C11—41no—
442C22×#41C22×C1111yescharacteristic
443C23×D4C22×C1111yescharacteristic
444C22×D8C22×C1111yescharacteristic
445C22×D8C22×C1111yescharacteristic
446C22×M16C22×C1111yescharacteristic, complemented
447C23×C8C22×C1111yescharacteristic, complemented
448#535—24no—
449#535—24no—
450C2×#127—21no—
451C2×#124—21no—
452C2×#121C22×C1111yescharacteristic
453C2×#121C22×C1111yescharacteristic
454C2×#121C22×C1111yescharacteristic
455C2×#121C22×C1111yescharacteristic
456C2×#121C22×C1111yescharacteristic
457C2×#121C22×C1111yescharacteristic, complemented
458C2×#121C22×C1111yescharacteristic, complemented
459C2×#120—21no—
460C2×#120—21no—
461C2×#117C22×C1111yescharacteristic
462#469—24no—
463#466—24no—
464#447—24no—
465C2×#107C22×C1111yescharacteristic, complemented
466C2×#106C22×C1111yescharacteristic, complemented
467C2×#102C22×C1111yescharacteristic
468C2×#102C22×C1111yescharacteristic
469C2×#102C22×C1111yescharacteristic
470C2×#102C22×C1111yescharacteristic
471C2×#102C22×C1111yescharacteristic
472C2×#102C22×C1111yescharacteristic
473C2×#102C22×C1111yescharacteristic, complemented
474C2×#102C22×C1111yescharacteristic, complemented
475#408—24no—
476C2×C22⋊C8C22×C1111yescharacteristic
477C2×C22⋊C8C22×C1111yescharacteristic
478C2×C22⋊C8C22×C1111yescharacteristic, complemented
479C2×C22⋊C8C22×C1111yescharacteristic, complemented
480#393—21no—
481#392—21no—
482#392—21no—
483#392—21no—
484#380C22×C1111yescharacteristic
485#380C22×C1111yescharacteristic, complemented
486#380C22×C1111yescharacteristic, complemented
487#340C22×C1111yescharacteristic, complemented
488#340C22×C1111yescharacteristic, complemented
489#340C22×C1111yescharacteristic, complemented
490#340C22×C1111yescharacteristic, complemented
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—22no—
495C22×C11—22no—
496C22×C11—22no—
497C22×C11—41no—
498C22×C11—41no—
499C22×C11—41no—
500C22×C11—41no—
501C22×C11—41no—
502C22×C11—41no—
503C22×C11—41no—
504C22×C11—41no—
505C22×C11—41no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—41no—
509C22×C11—41no—
510C22×C11—41no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—41no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—41no—
517C22×C11—41no—
518C22×C11—816no—
519C22×C11—81no—
520C22×C11—81no—
521C22×C11—81no—
522C22×C11—81no—
523C22×C11—81no—
524C22×C11—81no—
525C22×C11—81no—
526C22×C11—81no—
527C22×C11—81no—
528C22×C11—81no—
529C22×C11—81no—
530C22×C11—81no—
531C22×C11—81no—
532C22×C11—81no—
533C22×C11—81no—
534C22×C11C2×#12011yescharacteristic
535C22×C11C2×#12111yescharacteristic
536C22×C11#53411yescharacteristic
537C22×C11#57611yescharacteristic
538C22×C11#57611yescharacteristic
539C22×C11#57611yescharacteristic
540C22×C11#57711yescharacteristic
541C4×C11—22no—
542C4×C11—22no—
543C4×C11—41no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11—81no—
547C4×C11—81no—
548C4×C11—81no—
549C4×C11D4211yescharacteristic
550C4×C11D4211yescharacteristic
551C4×C11#54611yescharacteristic
552C4×C11#54611yescharacteristic
553C25—21no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—41no—
559C2×#41—41no—
560C22×Q8D4×C1111yescharacteristic
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—22no—
566C22×D4—22no—
567C22×D4—21no—
568C22×D4—21no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—41no—
574C22×D4—41no—
575C22×D4D4×C1111yescharacteristic
576C22×D4D4×C1111yescharacteristic
577C22×D4D4×C1111yescharacteristic
578C22×D4C23×C1111yescharacteristic
579C22×D4C23×C1111yescharacteristic
580C22×D4C23×C1111yescharacteristic
581C23×C4C23×C1111yescharacteristic
582C23×C4C23×C1111yescharacteristic
583C23×C4C23×C1111yescharacteristic
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—22no—
587C2×D8—22no—
588C2×D8—41no—
589C2×D8—41no—
590C2×M16—22no—
591C2×M16—22no—
592C2×M16—41no—
593C22×C8—22no—
594C22×C8—22no—
595C22×C8—41no—
596C22×C8C23×C1111yescharacteristic
597C22×C8C23×C1111yescharacteristic
598C22×C8C23×C1111yescharacteristic
599C22×C8C23×C1111yescharacteristic
600#127—28no—
601#124—28no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—41no—
613#121—41no—
614#121D4×C1114yescomplemented
615#121D4×C1114yescomplemented
616#120—28no—
617#120—28no—
618#117—22no—
619#117—22no—
620C2×C4⋊C4C23×C1111yescharacteristic
621C2×C4⋊C4C23×C1111yescharacteristic
622C2×C4⋊C4C23×C1111yescharacteristic
623C2×C4⋊C4C23×C1111yescharacteristic
624C2×C4⋊C4C23×C1111yescharacteristic
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C42—21no—
637#107—22no—
638#106—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102—41no—
646#102—41no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8—22no—
650C22⋊C8D4×C1114yescomplemented
651#95—21no—
652#95—21no—
653#95—21no—
654C2×C11—42no—
655C2×C11—42no—
656C2×C11—81no—
657C2×C11—82no—
658C2×C11—82no—
659C2×C11—161no—
660C2×C11#241011yescharacteristic
661C2×C11#300811yescharacteristic
662C2×C11#301211yescharacteristic
663C2×C11#305811yescharacteristic
664C2×C11#306211yescharacteristic
665C2×C11#319811yescharacteristic
666C2×C11#319911yescharacteristic
667C24—24no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—42no—
672C24—42no—
673C24—81no—
674C24—81no—
675C24—81no—
676C24—81no—
677C24C2×D4×C1111yescharacteristic
678C24C2×D4×C1111yescharacteristic
679C24C2×D4×C1111yescharacteristic
680#41—44no—
681#41—44no—
682#41—44no—
683#41—44no—
684C2×Q8—22no—
685C2×Q8—22no—
686C2×Q8—41no—
687C2×D4—24no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
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—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—81no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4C2×D4×C1112yes—
741C2×D4C2×D4×C1112yes—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4C2×D4×C1111yescharacteristic
762C22×C4C2×D4×C1111yescharacteristic
763C22×C4C2×D4×C1112yes—
764C22×C4C2×D4×C1112yes—
765C22×C4C2×D4×C1111yescharacteristic
766C22×C4C2×D4×C1112yes—
767C22×C4C11×#4112yes—
768C22×C4C24×C1111yescharacteristic
769D8—44no—
770D8—44no—
771M16—44no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—44no—
783C2×C8C2×D4×C1112yes—
784C2×C8C2×D4×C1112yes—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4C2×D4×C1112yes—
794C4⋊C4C2×D4×C1112yes—
795C22⋊C4—24no—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—42no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C42—24no—
807C11#2439011yescharacteristic, direct product factor, Sylow
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—48no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23C11×#12012yes—
856C23C11×#12112yes—
857C23C22×D4×C1111yescharacteristic
858Q8—44no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—44no—
864D4—44no—
865D4—48no—
866D4—44no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—84no—
876D4—84no—
877D4—84no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4C11×#12012yes—
917C2×C4C11×#12112yes—
918C2×C4C22×D4×C1111yescharacteristic
919C2×C4C22×D4×C1111yescharacteristic
920C2×C4C22×D4×C1111yescharacteristic
921C2×C4C2×C11×#4111yescharacteristic
922C2×C4C11×H(5,𝔽2)11yescharacteristic
923C2×C4C11×H(5,𝔽2)11yescharacteristic
924C8—22no—
925C8—22no—
926C8—41no—
927C8—41no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—42no—
944C22—42no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—42no—
949C22—42no—
950C22—41no—
951C22—42no—
952C22—42no—
953C22—41no—
954C22—41no—
955C22—816no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×C11×#12011yescharacteristic
972C22C2×C11×#12111yescharacteristic
973C22C11×#53411yescharacteristic
974C22C11×#57611yescharacteristic
975C22C11×#57611yescharacteristic
976C22C11×#57611yescharacteristic
977C22C11×#57711yescharacteristic
978C4—22no—
979C4—22no—
980C4—41no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4D42×C1111yescharacteristic
987C4D42×C1111yescharacteristic
988C4C11×#54611yescharacteristic
989C4C11×#54611yescharacteristic
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2C11×#241011yescharacteristic
997C2C11×#300811yescharacteristic
998C2C11×#301211yescharacteristic
999C2C11×#305811yescharacteristic
1000C2C11×#306211yescharacteristic
1001C2C11×#319811yescharacteristic
1002C2C11×#319911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#535C2semidirect
2. C2×C11×#469C2semidirect
3. C2×C11×#466C2semidirect
4. C2×C11×#447C2semidirect
5. C2×C11×#408C2semidirect
6. C11×#2615C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1999C2semidirect
10. C11×#1999C2semidirect
11. C11×#1895C2semidirect
12. C11×#1893C2semidirect
13. C11×#1875C2semidirect
14. C11×#1854C2semidirect
15. C11×#1786C2semidirect
20. C22×C11×M16C22semidirect
21. C23×C8×C11C22semidirect
31. C2×C11×#121C22semidirect
32. C2×C11×#121C22semidirect
39. C2×C11×#107C22semidirect
40. C2×C11×#106C22semidirect
47. C2×C11×#102C22semidirect
48. C2×C11×#102C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. C2×C11×C22⋊C8C22semidirect
59. C11×#380C22semidirect
60. C11×#380C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#340C22semidirect
64. C11×#340C22semidirect
126. C11×#121D4semidirect
127. C11×#121D4semidirect
162. C11×C22⋊C8D4semidirect
166. #24390C11direct (N × H)
307. C2×#535C2×C11semidirect
308. C2×#469C2×C11semidirect
309. C2×#466C2×C11semidirect
310. C2×#447C2×C11semidirect
311. C2×#408C2×C11semidirect
312. #2615C2×C11semidirect
313. #2034C2×C11semidirect
314. #2033C2×C11semidirect
315. #1999C2×C11semidirect
316. #1999C2×C11semidirect
317. #1895C2×C11semidirect
318. #1893C2×C11semidirect
319. #1875C2×C11semidirect
320. #1854C2×C11semidirect
321. #1786C2×C11semidirect
446. C22×M16C22×C11semidirect
447. C23×C8C22×C11semidirect
457. C2×#121C22×C11semidirect
458. C2×#121C22×C11semidirect
465. C2×#107C22×C11semidirect
466. C2×#106C22×C11semidirect
473. C2×#102C22×C11semidirect
474. C2×#102C22×C11semidirect
478. C2×C22⋊C8C22×C11semidirect
479. C2×C22⋊C8C22×C11semidirect
485. #380C22×C11semidirect
486. #380C22×C11semidirect
487. #340C22×C11semidirect
488. #340C22×C11semidirect
489. #340C22×C11semidirect
490. #340C22×C11semidirect
614. #121D4×C11semidirect
615. #121D4×C11semidirect
650. C22⋊C8D4×C11semidirect
807. C11#24390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4692
C2×C11×#4662
C2×C11×#4472
C2×C11×#4082
C11×#26152
C11×#20342
C11×#20332
C11×#19992
C11×#18952
C11×#18932
C11×#18752
C11×#18542
C11×#17862
#2439011