Finite Group Databasebeta

← C11×#24050 #14601243

Subgroups — C11×#24050 #14601243

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic
2C2×C11×#485C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C11×#2485C211yesmaximal, characteristic, complemented
5C11×#2042C211yesmaximal, characteristic, complemented
6C11×#2042C211yesmaximal, characteristic, complemented
7C11×#2034C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1894C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1864C211yesmaximal, characteristic, complemented
12C11×#1862C211yesmaximal, characteristic, complemented
13C11×#1788C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C11×#546—24no—
20C11×#546—24no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#120—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×C11×C22⋊C4—21no—
31C11×#485—24no—
32C2×C11×#107C2211yescharacteristic, complemented
33C2×C11×#106C2211yescharacteristic, complemented
34C11×#418—24no—
35C2×C11×#103C2211yescharacteristic, complemented
36C2×C11×#103C2211yescharacteristic, complemented
37C2×C11×#103C2211yescharacteristic, complemented
38C2×C11×#103C2211yescharacteristic, complemented
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic, complemented
49C2×C11×C22⋊C8C2211yescharacteristic, complemented
50C11×#397—21no—
51C11×#394—21no—
52C11×#389C2211yescharacteristic, complemented
53C11×#389C2211yescharacteristic, complemented
54C11×#388—21no—
55C11×#387—21no—
56C11×#380C2211yescharacteristic
57C11×#380C2211yescharacteristic, complemented
58C11×#380C2211yescharacteristic, complemented
59C11×#340C2211yescharacteristic, complemented
60C11×#340C2211yescharacteristic, complemented
61C11×#336C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63C25×C11—21no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—22no—
72C22×D4×C11—22no—
73C22×D4×C11—21no—
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11—22no—
77C22×D4×C11—41no—
78C22×D4×C11—41no—
79C22×D4×C11D414yes—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C2×C11×M16—22no—
88C2×C11×M16—41no—
89C2×C11×M16—41no—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×#124—22no—
95C11×#124—22no—
96C11×#123—28no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8D414yes—
99C11×#121—28no—
100C11×#121—22no—
101C11×#121—22no—
102C11×#120—28no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C11×#117—22no—
108C11×#117—22no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—28no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4D411yescharacteristic
129C2×C11×C22⋊C4D411yescharacteristic
130C2×C42×C11—21no—
131C2×C42×C11C2311yescharacteristic
132C11×#107—22no—
133C11×#106—22no—
134C11×#103—22no—
135C11×#103—22no—
136C11×#103—41no—
137C11×#103—41no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—22no—
141C11×#102—22no—
142C11×#102—22no—
143C11×#102—22no—
144C11×#102—41no—
145C11×#102—41no—
146C11×C22⋊C8—22no—
147C11×C22⋊C8—41no—
148C11×C22⋊C8—41no—
149C11×#95—21no—
150C11×#95—21no—
151C11×#95—21no—
152C11×#95—21no—
153C11×#95—21no—
154#24050C1111yesmaximal, characteristic, direct product factor, Sylow
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—24no—
158C24×C11—42no—
159C24×C11—42no—
160C24×C11—42no—
161C24×C11—42no—
162C24×C11—81no—
163C24×C11—81no—
164C24×C11C2×D411yescharacteristic
165C24×C11C2×D411yescharacteristic
166C11×#41—44no—
167C11×#41—44no—
168C11×#41—44no—
169C11×#41—44no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11C2×D412yes—
176C2×D4×C11—28no—
177C2×D4×C11—24no—
178C2×D4×C11—22no—
179C2×D4×C11—24no—
180C2×D4×C11—24no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
191C2×D4×C11—44no—
192C2×D4×C11—41no—
193C2×D4×C11—41no—
194C2×D4×C11—42no—
195C2×D4×C11—42no—
196C2×D4×C11—42no—
197C2×D4×C11—42no—
198C2×D4×C11—81no—
199C2×D4×C11—81no—
200C2×D4×C11C2×D412yes—
201C2×D4×C11C2×D412yes—
202C2×D4×C11#4112yes—
203C2×D4×C11#4112yes—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—24no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—24no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11—81no—
225C22×C4×C11—81no—
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2411yescharacteristic
233C11×M16—44no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—22no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—42no—
258C11×C4⋊C4—81no—
259C11×C4⋊C4C2×D412yes—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—22no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—22no—
267C11×C22⋊C4—42no—
268C11×C22⋊C4—42no—
269C11×C22⋊C4—81no—
270C11×C22⋊C4—81no—
271C42×C11—21no—
272C42×C11—21no—
273C42×C11—42no—
274C2×#546C2×C1111yescharacteristic
275C2×#485C2×C1111yescharacteristic, complemented
276C2×#418C2×C1111yescharacteristic, complemented
277#2485C2×C1111yescharacteristic, complemented
278#2042C2×C1111yescharacteristic, complemented
279#2042C2×C1111yescharacteristic, complemented
280#2034C2×C1111yescharacteristic, complemented
281#2033C2×C1111yescharacteristic, complemented
282#1894C2×C1111yescharacteristic, complemented
283#1870C2×C1111yescharacteristic, complemented
284#1864C2×C1111yescharacteristic, complemented
285#1862C2×C1111yescharacteristic, complemented
286#1788C2×C1111yescharacteristic, complemented
287#1788C2×C1111yescharacteristic, complemented
288#1786C2×C1111yescharacteristic, complemented
289C23×C11—22no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—22no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—48no—
307C23×C11—48no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—84no—
319C23×C11—84no—
320C23×C11—84no—
321C23×C11—84no—
322C23×C11—84no—
323C23×C11#12012yes—
324C23×C11C22×D411yescharacteristic
325Q8×C11—22no—
326Q8×C11—22no—
327Q8×C11—41no—
328Q8×C11—41no—
329D4×C11—22no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—48no—
335D4×C11—44no—
336D4×C11—48no—
337D4×C11—41no—
338D4×C11—41no—
339D4×C11—84no—
340D4×C11#12314yes—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—22no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—48no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—84no—
380C2×C4×C11#12012yes—
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C2×#4111yescharacteristic
384C2×C4×C11C2×#4111yescharacteristic
385C2×C4×C11H(5,𝔽2)11yescharacteristic
386C2×C4×C11H(5,𝔽2)11yescharacteristic
387C8×C11—41no—
388C8×C11—41no—
389C8×C11—41no—
390C8×C11—41no—
391C22×#41C22×C1111yescharacteristic
392C23×D4C22×C1111yescharacteristic
393C22×M16C22×C1111yescharacteristic
394#546—24no—
395#546—24no—
396C2×#124C22×C1111yescharacteristic
397C2×#123—21no—
398C2×C22⋊Q8C22×C1111yescharacteristic
399C2×#121—21no—
400C2×#121C22×C1111yescharacteristic
401C2×#120—21no—
402C2×C4×D4C22×C1111yescharacteristic
403C2×C4×D4C22×C1111yescharacteristic
404C2×#117C22×C1111yescharacteristic
405C22×C22⋊C4—21no—
406#485—24no—
407C2×#107C22×C1111yescharacteristic, complemented
408C2×#106C22×C1111yescharacteristic, complemented
409#418—24no—
410C2×#103C22×C1111yescharacteristic, complemented
411C2×#103C22×C1111yescharacteristic, complemented
412C2×#103C22×C1111yescharacteristic, complemented
413C2×#103C22×C1111yescharacteristic, complemented
414C2×#102C22×C1111yescharacteristic
415C2×#102C22×C1111yescharacteristic
416C2×#102C22×C1111yescharacteristic
417C2×#102C22×C1111yescharacteristic
418C2×#102C22×C1111yescharacteristic
419C2×#102C22×C1111yescharacteristic
420C2×#102C22×C1111yescharacteristic
421C2×#102C22×C1111yescharacteristic
422C2×C22⋊C8C22×C1111yescharacteristic
423C2×C22⋊C8C22×C1111yescharacteristic, complemented
424C2×C22⋊C8C22×C1111yescharacteristic, complemented
425#397—21no—
426#394—21no—
427#389C22×C1111yescharacteristic, complemented
428#389C22×C1111yescharacteristic, complemented
429#388—21no—
430#387—21no—
431#380C22×C1111yescharacteristic
432#380C22×C1111yescharacteristic, complemented
433#380C22×C1111yescharacteristic, complemented
434#340C22×C1111yescharacteristic, complemented
435#340C22×C1111yescharacteristic, complemented
436#336C22×C1111yescharacteristic, complemented
437#336C22×C1111yescharacteristic, complemented
438C22×C11—22no—
439C22×C11—24no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—41no—
445C22×C11—42no—
446C22×C11—41no—
447C22×C11—42no—
448C22×C11—41no—
449C22×C11—42no—
450C22×C11—41no—
451C22×C11—42no—
452C22×C11—41no—
453C22×C11—42no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11—816no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11C2×#12011yescharacteristic
468C22×C11#54611yescharacteristic
469C22×C11#54611yescharacteristic
470C22×C11#57511yescharacteristic
471C22×C11#57511yescharacteristic
472C22×C11#57611yescharacteristic
473C22×C11#57711yescharacteristic
474C4×C11—22no—
475C4×C11—41no—
476C4×C11—42no—
477C4×C11—41no—
478C4×C11—41no—
479C4×C11—42no—
480C4×C11—81no—
481C4×C11—81no—
482C4×C11—81no—
483C4×C11—81no—
484C4×C11C2×#12311yescharacteristic
485C4×C11#53411yescharacteristic
486C4×C11#54611yescharacteristic
487C4×C11#54611yescharacteristic
488C25—21no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C22×Q8C23×C1111yescharacteristic
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4D4×C1114yes—
505C22×D4D4×C1111yescharacteristic
506C22×D4C23×C1111yescharacteristic
507C22×D4C23×C1111yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C23×C1111yescharacteristic
511C23×C4C23×C1111yescharacteristic
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8C23×C1111yescharacteristic
516C22×C8C23×C1111yescharacteristic
517C22×C8C23×C1111yescharacteristic
518C22×C8C23×C1111yescharacteristic
519#124—22no—
520#124—22no—
521#123—28no—
522C22⋊Q8—22no—
523C22⋊Q8D4×C1114yes—
524#121—28no—
525#121—22no—
526#121—22no—
527#120—28no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532#117—22no—
533#117—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4D4×C1111yescharacteristic
538C2×C4⋊C4C23×C1111yescharacteristic
539C2×C4⋊C4C23×C1111yescharacteristic
540C2×C4⋊C4C23×C1111yescharacteristic
541C2×C4⋊C4C23×C1111yescharacteristic
542C2×C4⋊C4C23×C1111yescharacteristic
543C2×C22⋊C4—28no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4D4×C1111yescharacteristic
554C2×C22⋊C4D4×C1111yescharacteristic
555C2×C42—21no—
556C2×C42C23×C1111yescharacteristic
557#107—22no—
558#106—22no—
559#103—22no—
560#103—22no—
561#103—41no—
562#103—41no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—41no—
570#102—41no—
571C22⋊C8—22no—
572C22⋊C8—41no—
573C22⋊C8—41no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579C2×C11—42no—
580C2×C11—44no—
581C2×C11—81no—
582C2×C11—82no—
583C2×C11#240511yescharacteristic
584C2×C11#300511yescharacteristic
585C2×C11#301211yescharacteristic
586C2×C11#331111yescharacteristic
587C2×C11#331911yescharacteristic
588C2×C11#332211yescharacteristic
589C2×C11#332311yescharacteristic
590C24—21no—
591C24—21no—
592C24—24no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×D4×C1111yescharacteristic
600C24C2×D4×C1111yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C1112yes—
611C2×D4—28no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C1112yes—
636C2×D4C2×D4×C1112yes—
637C2×D4C11×#4112yes—
638C2×D4C11×#4112yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4C2×D4×C1111yescharacteristic
662C22×C4C2×D4×C1111yescharacteristic
663C22×C4C2×D4×C1111yescharacteristic
664C22×C4C2×D4×C1111yescharacteristic
665C22×C4C2×D4×C1112yes—
666C22×C4C2×D4×C1112yes—
667C22×C4C24×C1111yescharacteristic
668M16—44no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C4⋊C4—24no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—42no—
693C4⋊C4—81no—
694C4⋊C4C2×D4×C1112yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—22no—
700C22⋊C4—24no—
701C22⋊C4—22no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C42—21no—
707C42—21no—
708C42—42no—
709C11#2405011yescharacteristic, direct product factor, Sylow
710C23—22no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—48no—
728C23—48no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—84no—
744C23C11×#12012yes—
745C23C22×D4×C1111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—44no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4C11×#12314yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4C11×#12012yes—
802C2×C4C22×D4×C1111yescharacteristic
803C2×C4C22×D4×C1111yescharacteristic
804C2×C4C2×C11×#4111yescharacteristic
805C2×C4C2×C11×#4111yescharacteristic
806C2×C4C11×H(5,𝔽2)11yescharacteristic
807C2×C4C11×H(5,𝔽2)11yescharacteristic
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×C11×#12011yescharacteristic
842C22C11×#54611yescharacteristic
843C22C11×#54611yescharacteristic
844C22C11×#57511yescharacteristic
845C22C11×#57511yescharacteristic
846C22C11×#57611yescharacteristic
847C22C11×#57711yescharacteristic
848C4—22no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4C2×C11×#12311yescharacteristic
859C4C11×#53411yescharacteristic
860C4C11×#54611yescharacteristic
861C4C11×#54611yescharacteristic
862C2—42no—
863C2—44no—
864C2—81no—
865C2—82no—
866C2C11×#240511yescharacteristic
867C2C11×#300511yescharacteristic
868C2C11×#301211yescharacteristic
869C2C11×#331111yescharacteristic
870C2C11×#331911yescharacteristic
871C2C11×#332211yescharacteristic
872C2C11×#332311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#546C2
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
2. C2×C11×#485C2semidirect
3. C2×C11×#418C2semidirect
4. C11×#2485C2semidirect
5. C11×#2042C2semidirect
6. C11×#2042C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1894C2semidirect
10. C11×#1870C2semidirect
11. C11×#1864C2semidirect
12. C11×#1862C2semidirect
13. C11×#1788C2semidirect
14. C11×#1788C2semidirect
15. C11×#1786C2semidirect
32. C2×C11×#107C22semidirect
33. C2×C11×#106C22semidirect
35. C2×C11×#103C22semidirect
36. C2×C11×#103C22semidirect
37. C2×C11×#103C22semidirect
38. C2×C11×#103C22semidirect
48. C2×C11×C22⋊C8C22semidirect
49. C2×C11×C22⋊C8C22semidirect
52. C11×#389C22semidirect
53. C11×#389C22semidirect
57. C11×#380C22semidirect
58. C11×#380C22semidirect
59. C11×#340C22semidirect
60. C11×#340C22semidirect
61. C11×#336C22semidirect
62. C11×#336C22semidirect
154. #24050C11direct (N × H)
275. C2×#485C2×C11semidirect
276. C2×#418C2×C11semidirect
277. #2485C2×C11semidirect
278. #2042C2×C11semidirect
279. #2042C2×C11semidirect
280. #2034C2×C11semidirect
281. #2033C2×C11semidirect
282. #1894C2×C11semidirect
283. #1870C2×C11semidirect
284. #1864C2×C11semidirect
285. #1862C2×C11semidirect
286. #1788C2×C11semidirect
287. #1788C2×C11semidirect
288. #1786C2×C11semidirect
407. C2×#107C22×C11semidirect
408. C2×#106C22×C11semidirect
410. C2×#103C22×C11semidirect
411. C2×#103C22×C11semidirect
412. C2×#103C22×C11semidirect
413. C2×#103C22×C11semidirect
423. C2×C22⋊C8C22×C11semidirect
424. C2×C22⋊C8C22×C11semidirect
427. #389C22×C11semidirect
428. #389C22×C11semidirect
432. #380C22×C11semidirect
433. #380C22×C11semidirect
434. #340C22×C11semidirect
435. #340C22×C11semidirect
436. #336C22×C11semidirect
437. #336C22×C11semidirect
709. C11#24050direct (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×#4852
C2×C11×#4182
C11×#24852
C11×#20422
C11×#20342
C11×#20332
C11×#18942
C11×#18702
C11×#18642
C11×#18622
C11×#17882
C11×#17862
#2405011