Finite Group Databasebeta

← C11×#24234 #14601427

Subgroups — C11×#24234 #14601427

Order 2816.

1440 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3500C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic, complemented
3C2×C11×#454C211yesmaximal, characteristic, complemented
4C2×C11×#453C211yesmaximal, characteristic, complemented
5C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
6C11×#2544C211yesmaximal, characteristic, complemented
7C11×#2038C211yesmaximal, characteristic, complemented
8C11×#2037C211yesmaximal, characteristic, complemented
9C11×#2003C211yesmaximal, characteristic, complemented
10C11×#2002C211yesmaximal, characteristic, complemented
11C11×#1980C211yesmaximal, characteristic, complemented
12C11×#1967C211yesmaximal, characteristic, complemented
13C11×#1806C211yesmaximal, characteristic, complemented
14C11×#1793C211yesmaximal, characteristic, complemented
15C11×#1792C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C2×C11×H(5,𝔽2)C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C11×#548—21no—
22C11×#548—21no—
23C11×#546—21no—
24C11×#546—21no—
25C11×#546—22no—
26C11×#546—22no—
27C11×#536—21no—
28C11×#536C2211yescharacteristic
29C11×#535—21no—
30C11×#535C2211yescharacteristic
31C11×#532—21no—
32C11×#532C2211yescharacteristic
33C2×C11×#127C2211yescharacteristic
34C2×C11×#124—21no—
35C2×C11×#124C2211yescharacteristic
36C2×C11×#124C2211yescharacteristic, complemented
37C4×C11×#41C2211yescharacteristic
38C2×C4×D4×C11C2211yescharacteristic, complemented
39C11×#463—21no—
40C11×#463—21no—
41C11×#461—21no—
42C11×#459—21no—
43C11×#454—24no—
44C11×#453—24no—
45C11×#442—21no—
46C11×#440—21no—
47C4×C11×SD16—21no—
48C4×C11×D8—21no—
49C11×#428C2211yescharacteristic, complemented
50C11×#423C2211yescharacteristic, complemented
51C2×C11×#104C2211yescharacteristic
52C2×C11×#104C2211yescharacteristic
53C2×C11×#104C2211yescharacteristic
54C2×C11×#104C2211yescharacteristic
55C2×C11×#104C2211yescharacteristic, complemented
56C2×C11×#104C2211yescharacteristic, complemented
57C11×#418C2211yescharacteristic, complemented
58C11×#417C2211yescharacteristic
59C11×#417C2211yescharacteristic
60C11×#417C2211yescharacteristic, complemented
61C2×C11×#101C2211yescharacteristic, complemented
62C2×C11×#101C2211yescharacteristic, complemented
63C2×C11×#100C2211yescharacteristic
64C2×C11×#100C2211yescharacteristic
65C4×C11×M16C2211yescharacteristic, complemented
66C11×#394—22no—
67C11×#391C2211yescharacteristic, complemented
68C11×#390C2211yescharacteristic
69C11×#386—22no—
70C4×C11×C4⋊C4C2211yescharacteristic, complemented
71C11×#339C2211yescharacteristic, complemented
72C11×#339C2211yescharacteristic, complemented
73C11×2−1+4—22no—
74C11×2−1+4—22no—
75C11×2−1+4—41no—
76C11×2−1+4—41no—
77C11×H(5,𝔽2)—22no—
78C11×H(5,𝔽2)—22no—
79C11×H(5,𝔽2)—41no—
80C11×H(5,𝔽2)—41no—
81C2×C11×#41—21no—
82C2×C11×#41—21no—
83C2×C11×#41—21no—
84C2×C11×#41—21no—
85C2×C11×#41—22no—
86C2×C11×#41C2311yescharacteristic
87C2×C11×#41C2311yescharacteristic
88C2×C11×#41C2311yescharacteristic
89C22×Q8×C11—21no—
90C22×Q8×C11—21no—
91C22×Q8×C11C2311yescharacteristic
92C22×D4×C11—22no—
93C22×D4×C11—21no—
94C22×D4×C11—21no—
95C22×D4×C11—22no—
96C22×D4×C11C2311yescharacteristic
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11—21no—
99C11×AGL(1,ℤ/8)—22no—
100C11×AGL(1,ℤ/8)—22no—
101C11×AGL(1,ℤ/8)—22no—
102C11×AGL(1,ℤ/8)—41no—
103C11×AGL(1,ℤ/8)—41no—
104C11×AGL(1,ℤ/8)D414yescomplemented
105C2×C11×SD16—21no—
106C2×C11×SD16—21no—
107C2×C11×SD16—21no—
108C2×C11×D8—21no—
109C2×C11×D8—21no—
110C2×C11×D8—21no—
111C2×C11×M16C2311yescharacteristic
112C2×C11×M16C2311yescharacteristic
113C2×C11×M16C2311yescharacteristic
114C2×C11×M16C2311yescharacteristic
115C11×C4⋊Q8—21no—
116C11×C4⋊Q8D411yescharacteristic, complemented
117C11×#127—21no—
118C11×#127—22no—
119C11×#127—41no—
120C11×#127D411yescharacteristic, complemented
121C11×#124—22no—
122C11×#124—22no—
123C11×#124—21no—
124C11×#124—21no—
125C11×#124—22no—
126C11×#124—21no—
127C11×#124—21no—
128C11×#124—21no—
129C11×#124—21no—
130C11×#124—41no—
131C11×#124D411yescharacteristic, complemented
132C11×#124D411yescharacteristic, complemented
133C11×#123—22no—
134C11×#123—22no—
135C11×#123—22no—
136C11×C22⋊Q8—22no—
137C11×C22⋊Q8—22no—
138C11×C22⋊Q8—21no—
139C11×C22⋊Q8—21no—
140C11×#121—22no—
141C11×#121—22no—
142C11×#121—22no—
143C11×#121—22no—
144C11×#121—21no—
145C11×#121—21no—
146C11×#121—21no—
147C11×#121—21no—
148C11×#120—22no—
149C11×#120—22no—
150C11×#120—22no—
151C4×Q8×C11D411yescharacteristic, complemented
152C4×Q8×C11D411yescharacteristic, complemented
153C4×D4×C11—22no—
154C4×D4×C11—22no—
155C4×D4×C11—21no—
156C4×D4×C11—21no—
157C4×D4×C11—21no—
158C4×D4×C11—21no—
159C4×D4×C11—21no—
160C4×D4×C11—21no—
161C4×D4×C11—21no—
162C4×D4×C11—21no—
163C4×D4×C11D411yescharacteristic, complemented
164C4×D4×C11D411yescharacteristic, complemented
165C11×#117—21no—
166C11×#117C2311yescharacteristic
167C2×C11×C4⋊C4—21no—
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4—22no—
170C2×C11×C22⋊C4—22no—
171C2×C11×C22⋊C4—21no—
172C2×C11×C22⋊C4—22no—
173C2×C11×C22⋊C4—22no—
174C2×C11×C22⋊C4D412yes—
175C2×C11×C22⋊C4D412yes—
176C2×C42×C11—21no—
177C2×C42×C11C2311yescharacteristic
178C2×C42×C11C2311yescharacteristic
179C2×C42×C11C2311yescharacteristic
180C11×#107—21no—
181C11×#106—21no—
182C11×C4⋊C8—21no—
183C11×C4⋊C8—21no—
184C11×#104—22no—
185C11×#104—22no—
186C11×#104—22no—
187C11×#104—22no—
188C11×#104—41no—
189C11×#104—41no—
190C11×#103—21no—
191C11×#103—21no—
192C11×#103—21no—
193C11×#102—21no—
194C11×#102—21no—
195C11×#102—21no—
196C11×#102—21no—
197C11×#102—21no—
198C11×#101—22no—
199C11×#101—41no—
200C11×#100—22no—
201C11×#100—41no—
202C11×#97—21no—
203C4×C8×C11—21no—
204C11×#95—21no—
205C11×#95—22no—
206#24234C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—22no—
208C24×C11—21no—
209C24×C11C2×D412yes—
210C11×#41—21no—
211C11×#41—21no—
212C11×#41—21no—
213C11×#41—21no—
214C11×#41—21no—
215C11×#41—21no—
216C11×#41—21no—
217C11×#41—21no—
218C11×#41—21no—
219C11×#41—21no—
220C11×#41—42no—
221C11×#41—42no—
222C11×#41—44no—
223C11×#41—44no—
224C11×#41—42no—
225C11×#41—42no—
226C11×#41—42no—
227C11×#41—42no—
228C11×#41—42no—
229C11×#41—42no—
230C11×#41C2×D412yes—
231C11×#41#4112yes—
232C2×Q8×C11—22no—
233C2×Q8×C11—21no—
234C2×Q8×C11—21no—
235C2×Q8×C11—21no—
236C2×Q8×C11—21no—
237C2×Q8×C11—21no—
238C2×Q8×C11—21no—
239C2×Q8×C11—42no—
240C2×Q8×C11—42no—
241C2×Q8×C11—42no—
242C2×Q8×C11—42no—
243C2×Q8×C11C2×D411yescharacteristic
244C2×Q8×C11C2×D411yescharacteristic
245C2×Q8×C11C2×D411yescharacteristic
246C2×D4×C11—21no—
247C2×D4×C11—22no—
248C2×D4×C11—22no—
249C2×D4×C11—22no—
250C2×D4×C11—21no—
251C2×D4×C11—21no—
252C2×D4×C11—22no—
253C2×D4×C11—22no—
254C2×D4×C11—21no—
255C2×D4×C11—21no—
256C2×D4×C11—21no—
257C2×D4×C11—21no—
258C2×D4×C11—21no—
259C2×D4×C11—21no—
260C2×D4×C11—21no—
261C2×D4×C11—21no—
262C2×D4×C11—21no—
263C2×D4×C11—21no—
264C2×D4×C11—21no—
265C2×D4×C11—21no—
266C2×D4×C11—21no—
267C2×D4×C11—42no—
268C2×D4×C11—42no—
269C2×D4×C11—44no—
270C2×D4×C11—44no—
271C2×D4×C11—44no—
272C2×D4×C11—42no—
273C2×D4×C11—42no—
274C2×D4×C11—44no—
275C2×D4×C11—82no—
276C2×D4×C11C2×D411yescharacteristic
277C2×D4×C11C2×D411yescharacteristic
278C2×D4×C11C2×D412yes—
279C2×D4×C11C2×D411yescharacteristic
280C22×C4×C11—21no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—21no—
285C22×C4×C11—21no—
286C22×C4×C11—21no—
287C22×C4×C11—21no—
288C22×C4×C11—21no—
289C22×C4×C11—21no—
290C22×C4×C11—21no—
291C22×C4×C11—41no—
292C22×C4×C11—41no—
293C22×C4×C11—82no—
294C22×C4×C11C2×D412yes—
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C11×SD16—24no—
299C11×SD16—42no—
300C11×SD16—42no—
301C11×D8—24no—
302C11×D8—42no—
303C11×D8—42no—
304C11×M16—21no—
305C11×M16—21no—
306C11×M16—21no—
307C11×M16—21no—
308C11×M16—21no—
309C11×M16—21no—
310C11×M16—21no—
311C11×M16C2×D412yes—
312C2×C8×C11—21no—
313C2×C8×C11—21no—
314C2×C8×C11—21no—
315C2×C8×C11—21no—
316C11×C4⋊C4—22no—
317C11×C4⋊C4—22no—
318C11×C4⋊C4—21no—
319C11×C4⋊C4—21no—
320C11×C4⋊C4—21no—
321C11×C4⋊C4—21no—
322C11×C4⋊C4—21no—
323C11×C4⋊C4—21no—
324C11×C4⋊C4—42no—
325C11×C4⋊C4C2×D411yescharacteristic
326C11×C4⋊C4C2×D411yescharacteristic
327C11×C22⋊C4—22no—
328C11×C22⋊C4—22no—
329C11×C22⋊C4—22no—
330C11×C22⋊C4—22no—
331C11×C22⋊C4—21no—
332C11×C22⋊C4—21no—
333C11×C22⋊C4—21no—
334C11×C22⋊C4—22no—
335C11×C22⋊C4—22no—
336C11×C22⋊C4—22no—
337C11×C22⋊C4—22no—
338C11×C22⋊C4—21no—
339C11×C22⋊C4—21no—
340C11×C22⋊C4—21no—
341C11×C22⋊C4—21no—
342C11×C22⋊C4—44no—
343C11×C22⋊C4—41no—
344C11×C22⋊C4—41no—
345C11×C22⋊C4—82no—
346C42×C11—21no—
347C42×C11—21no—
348C42×C11—21no—
349C42×C11—21no—
350C42×C11—21no—
351C42×C11—21no—
352C42×C11—21no—
353C42×C11C2×D411yescharacteristic
354C42×C11C2×D411yescharacteristic
355C42×C11C2×D411yescharacteristic
356C42×C11C2×D411yescharacteristic
357#3500C2×C1111yescharacteristic, complemented
358#3036C2×C1111yescharacteristic, complemented
359C2×#454C2×C1111yescharacteristic, complemented
360C2×#453C2×C1111yescharacteristic, complemented
361C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
362#2544C2×C1111yescharacteristic, complemented
363#2038C2×C1111yescharacteristic, complemented
364#2037C2×C1111yescharacteristic, complemented
365#2003C2×C1111yescharacteristic, complemented
366#2002C2×C1111yescharacteristic, complemented
367#1980C2×C1111yescharacteristic, complemented
368#1967C2×C1111yescharacteristic, complemented
369#1806C2×C1111yescharacteristic, complemented
370#1793C2×C1111yescharacteristic, complemented
371#1792C2×C1111yescharacteristic, complemented
372C23×C11—21no—
373C23×C11—22no—
374C23×C11—21no—
375C23×C11—21no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—42no—
380C23×C11—42no—
381C23×C11—44no—
382C23×C11—42no—
383C23×C11—42no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—82no—
387C23×C11—82no—
388C23×C11C22×D411yescharacteristic
389Q8×C11—21no—
390Q8×C11—21no—
391Q8×C11—21no—
392Q8×C11—21no—
393Q8×C11—21no—
394Q8×C11—44no—
395Q8×C11—41no—
396Q8×C11—41no—
397Q8×C11—41no—
398Q8×C11—41no—
399Q8×C11#12112yes—
400D4×C11—22no—
401D4×C11—22no—
402D4×C11—22no—
403D4×C11—21no—
404D4×C11—22no—
405D4×C11—21no—
406D4×C11—21no—
407D4×C11—21no—
408D4×C11—21no—
409D4×C11—44no—
410D4×C11—44no—
411D4×C11—44no—
412D4×C11—41no—
413D4×C11—41no—
414D4×C11—41no—
415D4×C11—41no—
416D4×C11—41no—
417D4×C11—41no—
418D4×C11—41no—
419D4×C11—41no—
420D4×C11—41no—
421D4×C11—41no—
422D4×C11—81no—
423D4×C11—81no—
424D4×C11—82no—
425D4×C11—82no—
426D4×C11—88no—
427D4×C11#12112yes—
428C2×C4×C11—21no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—22no—
436C2×C4×C11—21no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—44no—
442C2×C4×C11—44no—
443C2×C4×C11—41no—
444C2×C4×C11—44no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—42no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—81no—
456C2×C4×C11—81no—
457C2×C4×C11—82no—
458C2×C4×C11—82no—
459C2×C4×C11#12011yescharacteristic
460C2×C4×C11#12011yescharacteristic
461C2×C4×C11#12011yescharacteristic
462C2×C4×C11#12011yescharacteristic
463C2×C4×C11C22×D411yescharacteristic
464C2×C4×C11C22×D411yescharacteristic
465C2×C4×C11C22×D411yescharacteristic
466C2×C4×C11C2×#4111yescharacteristic
467C2×C4×C11H(5,𝔽2)11yescharacteristic
468C2×C4×C11H(5,𝔽2)11yescharacteristic
469C8×C11—22no—
470C8×C11—41no—
471C8×C11—41no—
472C8×C11—41no—
473C2×2−1+4C22×C1111yescharacteristic
474C2×H(5,𝔽2)C22×C1111yescharacteristic
475C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
476C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
477C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
478#548—21no—
479#548—21no—
480#546—21no—
481#546—21no—
482#546—22no—
483#546—22no—
484#536—21no—
485#536C22×C1111yescharacteristic
486#535—21no—
487#535C22×C1111yescharacteristic
488#532—21no—
489#532C22×C1111yescharacteristic
490C2×#127C22×C1111yescharacteristic
491C2×#124—21no—
492C2×#124C22×C1111yescharacteristic
493C2×#124C22×C1111yescharacteristic, complemented
494C4×#41C22×C1111yescharacteristic
495C2×C4×D4C22×C1111yescharacteristic, complemented
496#463—21no—
497#463—21no—
498#461—21no—
499#459—21no—
500#454—24no—
501#453—24no—
502#442—21no—
503#440—21no—
504C4×SD16—21no—
505C4×D8—21no—
506#428C22×C1111yescharacteristic, complemented
507#423C22×C1111yescharacteristic, complemented
508C2×#104C22×C1111yescharacteristic
509C2×#104C22×C1111yescharacteristic
510C2×#104C22×C1111yescharacteristic
511C2×#104C22×C1111yescharacteristic
512C2×#104C22×C1111yescharacteristic, complemented
513C2×#104C22×C1111yescharacteristic, complemented
514#418C22×C1111yescharacteristic, complemented
515#417C22×C1111yescharacteristic
516#417C22×C1111yescharacteristic
517#417C22×C1111yescharacteristic, complemented
518C2×#101C22×C1111yescharacteristic, complemented
519C2×#101C22×C1111yescharacteristic, complemented
520C2×#100C22×C1111yescharacteristic
521C2×#100C22×C1111yescharacteristic
522C4×M16C22×C1111yescharacteristic, complemented
523#394—22no—
524#391C22×C1111yescharacteristic, complemented
525#390C22×C1111yescharacteristic
526#386—22no—
527C4×C4⋊C4C22×C1111yescharacteristic, complemented
528#339C22×C1111yescharacteristic, complemented
529#339C22×C1111yescharacteristic, complemented
530C22×C11—21no—
531C22×C11—21no—
532C22×C11—22no—
533C22×C11—44no—
534C22×C11—41no—
535C22×C11—41no—
536C22×C11—41no—
537C22×C11—41no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—41no—
541C22×C11—42no—
542C22×C11—41no—
543C22×C11—41no—
544C22×C11—42no—
545C22×C11—41no—
546C22×C11—82no—
547C22×C11—82no—
548C22×C11—82no—
549C22×C11—81no—
550C22×C11—81no—
551C22×C11—164no—
552C22×C11C2×#12011yescharacteristic
553C22×C11D4211yescharacteristic
554C22×C11#54611yescharacteristic
555C4×C11—22no—
556C4×C11—21no—
557C4×C11—21no—
558C4×C11—21no—
559C4×C11—21no—
560C4×C11—42no—
561C4×C11—42no—
562C4×C11—41no—
563C4×C11—41no—
564C4×C11—41no—
565C4×C11—41no—
566C4×C11—81no—
567C4×C11—81no—
568C4×C11C2×#12111yescharacteristic
569C4×C11#53511yescharacteristic
570C4×C11D4211yescharacteristic
571C4×C11#54611yescharacteristic
5722−1+4—22no—
5732−1+4—22no—
5742−1+4—41no—
5752−1+4—41no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—22no—
578H(5,𝔽2)—41no—
579H(5,𝔽2)—41no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—22no—
585C2×#41C23×C1111yescharacteristic
586C2×#41C23×C1111yescharacteristic
587C2×#41C23×C1111yescharacteristic
588C22×Q8—21no—
589C22×Q8—21no—
590C22×Q8C23×C1111yescharacteristic
591C22×D4—22no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4C23×C1111yescharacteristic
596C22×D4C23×C1111yescharacteristic
597C23×C4—21no—
598AGL(1,ℤ/8)—22no—
599AGL(1,ℤ/8)—22no—
600AGL(1,ℤ/8)—22no—
601AGL(1,ℤ/8)—41no—
602AGL(1,ℤ/8)—41no—
603AGL(1,ℤ/8)D4×C1114yescomplemented
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—21no—
607C2×D8—21no—
608C2×D8—21no—
609C2×D8—21no—
610C2×M16C23×C1111yescharacteristic
611C2×M16C23×C1111yescharacteristic
612C2×M16C23×C1111yescharacteristic
613C2×M16C23×C1111yescharacteristic
614C4⋊Q8—21no—
615C4⋊Q8D4×C1111yescharacteristic, complemented
616#127—21no—
617#127—22no—
618#127—41no—
619#127D4×C1111yescharacteristic, complemented
620#124—22no—
621#124—22no—
622#124—21no—
623#124—21no—
624#124—22no—
625#124—21no—
626#124—21no—
627#124—21no—
628#124—21no—
629#124—41no—
630#124D4×C1111yescharacteristic, complemented
631#124D4×C1111yescharacteristic, complemented
632#123—22no—
633#123—22no—
634#123—22no—
635C22⋊Q8—22no—
636C22⋊Q8—22no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639#121—22no—
640#121—22no—
641#121—22no—
642#121—22no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#120—22no—
648#120—22no—
649#120—22no—
650C4×Q8D4×C1111yescharacteristic, complemented
651C4×Q8D4×C1111yescharacteristic, complemented
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4D4×C1111yescharacteristic, complemented
663C4×D4D4×C1111yescharacteristic, complemented
664#117—21no—
665#117C23×C1111yescharacteristic
666C2×C4⋊C4—21no—
667C2×C4⋊C4C23×C1111yescharacteristic
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4D4×C1112yes—
674C2×C22⋊C4D4×C1112yes—
675C2×C42—21no—
676C2×C42C23×C1111yescharacteristic
677C2×C42C23×C1111yescharacteristic
678C2×C42C23×C1111yescharacteristic
679#107—21no—
680#106—21no—
681C4⋊C8—21no—
682C4⋊C8—21no—
683#104—22no—
684#104—22no—
685#104—22no—
686#104—22no—
687#104—41no—
688#104—41no—
689#103—21no—
690#103—21no—
691#103—21no—
692#102—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#101—22no—
698#101—41no—
699#100—22no—
700#100—41no—
701#97—21no—
702C4×C8—21no—
703#95—21no—
704#95—22no—
705C2×C11—21no—
706C2×C11—21no—
707C2×C11—42no—
708C2×C11—81no—
709C2×C11—82no—
710C2×C11—82no—
711C2×C11—81no—
712C2×C11#240811yescharacteristic
713C2×C11#301811yescharacteristic
714C2×C11#302111yescharacteristic
715C24—22no—
716C24—21no—
717C24C2×D4×C1112yes—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—21no—
724#41—21no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—42no—
729#41—42no—
730#41—44no—
731#41—44no—
732#41—42no—
733#41—42no—
734#41—42no—
735#41—42no—
736#41—42no—
737#41—42no—
738#41C2×D4×C1112yes—
739#41C11×#4112yes—
740C2×Q8—22no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—42no—
748C2×Q8—42no—
749C2×Q8—42no—
750C2×Q8—42no—
751C2×Q8C2×D4×C1111yescharacteristic
752C2×Q8C2×D4×C1111yescharacteristic
753C2×Q8C2×D4×C1111yescharacteristic
754C2×D4—21no—
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—42no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—42no—
781C2×D4—42no—
782C2×D4—44no—
783C2×D4—82no—
784C2×D4C2×D4×C1111yescharacteristic
785C2×D4C2×D4×C1111yescharacteristic
786C2×D4C2×D4×C1112yes—
787C2×D4C2×D4×C1111yescharacteristic
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—82no—
802C22×C4C2×D4×C1112yes—
803C22×C4C2×D4×C1111yescharacteristic
804C22×C4C2×D4×C1111yescharacteristic
805C22×C4C24×C1111yescharacteristic
806SD16—24no—
807SD16—42no—
808SD16—42no—
809D8—24no—
810D8—42no—
811D8—42no—
812M16—21no—
813M16—21no—
814M16—21no—
815M16—21no—
816M16—21no—
817M16—21no—
818M16—21no—
819M16C2×D4×C1112yes—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—42no—
833C4⋊C4C2×D4×C1111yescharacteristic
834C4⋊C4C2×D4×C1111yescharacteristic
835C22⋊C4—22no—
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—22no—
845C22⋊C4—22no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—44no—
851C22⋊C4—41no—
852C22⋊C4—41no—
853C22⋊C4—82no—
854C42—21no—
855C42—21no—
856C42—21no—
857C42—21no—
858C42—21no—
859C42—21no—
860C42—21no—
861C42C2×D4×C1111yescharacteristic
862C42C2×D4×C1111yescharacteristic
863C42C2×D4×C1111yescharacteristic
864C42C2×D4×C1111yescharacteristic
865C11#2423411yescharacteristic, direct product factor, Sylow
866C23—21no—
867C23—22no—
868C23—21no—
869C23—21no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—42no—
874C23—42no—
875C23—44no—
876C23—42no—
877C23—42no—
878C23—41no—
879C23—41no—
880C23—82no—
881C23—82no—
882C23C22×D4×C1111yescharacteristic
883Q8—21no—
884Q8—21no—
885Q8—21no—
886Q8—21no—
887Q8—21no—
888Q8—44no—
889Q8—41no—
890Q8—41no—
891Q8—41no—
892Q8—41no—
893Q8C11×#12112yes—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—21no—
898D4—22no—
899D4—21no—
900D4—21no—
901D4—21no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—41no—
914D4—41no—
915D4—41no—
916D4—81no—
917D4—81no—
918D4—82no—
919D4—82no—
920D4—88no—
921D4C11×#12112yes—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—41no—
938C2×C4—44no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—81no—
950C2×C4—81no—
951C2×C4—82no—
952C2×C4—82no—
953C2×C4C11×#12011yescharacteristic
954C2×C4C11×#12011yescharacteristic
955C2×C4C11×#12011yescharacteristic
956C2×C4C11×#12011yescharacteristic
957C2×C4C22×D4×C1111yescharacteristic
958C2×C4C22×D4×C1111yescharacteristic
959C2×C4C22×D4×C1111yescharacteristic
960C2×C4C2×C11×#4111yescharacteristic
961C2×C4C11×H(5,𝔽2)11yescharacteristic
962C2×C4C11×H(5,𝔽2)11yescharacteristic
963C8—22no—
964C8—41no—
965C8—41no—
966C8—41no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—44no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—42no—
976C22—42no—
977C22—41no—
978C22—42no—
979C22—41no—
980C22—41no—
981C22—42no—
982C22—41no—
983C22—82no—
984C22—82no—
985C22—82no—
986C22—81no—
987C22—81no—
988C22—164no—
989C22C2×C11×#12011yescharacteristic
990C22D42×C1111yescharacteristic
991C22C11×#54611yescharacteristic
992C4—22no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—21no—
997C4—42no—
998C4—42no—
999C4—41no—
1000C4—41no—
1001C4—41no—
1002C4—41no—
1003C4—81no—
1004C4—81no—
1005C4C2×C11×#12111yescharacteristic
1006C4C11×#53511yescharacteristic
1007C4D42×C1111yescharacteristic
1008C4C11×#54611yescharacteristic
1009C2—21no—
1010C2—21no—
1011C2—42no—
1012C2—82no—
1013C2—82no—
1014C2—81no—
1015C2—81no—
1016C2C11×#240811yescharacteristic
1017C2C11×#301811yescharacteristic
1018C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3500C2semidirect
2. C11×#3036C2semidirect
3. C2×C11×#454C2semidirect
4. C2×C11×#453C2semidirect
5. C4×C11×AGL(1,ℤ/8)C2semidirect
6. C11×#2544C2semidirect
7. C11×#2038C2semidirect
8. C11×#2037C2semidirect
9. C11×#2003C2semidirect
10. C11×#2002C2semidirect
11. C11×#1980C2semidirect
12. C11×#1967C2semidirect
13. C11×#1806C2semidirect
14. C11×#1793C2semidirect
15. C11×#1792C2semidirect
20. C2×C11×AGL(1,ℤ/8)C22semidirect
36. C2×C11×#124C22semidirect
38. C2×C4×D4×C11C22semidirect
49. C11×#428C22semidirect
50. C11×#423C22semidirect
55. C2×C11×#104C22semidirect
56. C2×C11×#104C22semidirect
57. C11×#418C22semidirect
60. C11×#417C22semidirect
61. C2×C11×#101C22semidirect
62. C2×C11×#101C22semidirect
65. C4×C11×M16C22semidirect
67. C11×#391C22semidirect
70. C4×C11×C4⋊C4C22semidirect
71. C11×#339C22semidirect
72. C11×#339C22semidirect
104. C11×AGL(1,ℤ/8)D4semidirect
116. C11×C4⋊Q8D4semidirect
120. C11×#127D4semidirect
131. C11×#124D4semidirect
132. C11×#124D4semidirect
151. C4×Q8×C11D4semidirect
152. C4×Q8×C11D4semidirect
163. C4×D4×C11D4semidirect
164. C4×D4×C11D4semidirect
206. #24234C11direct (N × H)
357. #3500C2×C11semidirect
358. #3036C2×C11semidirect
359. C2×#454C2×C11semidirect
360. C2×#453C2×C11semidirect
361. C4×AGL(1,ℤ/8)C2×C11semidirect
362. #2544C2×C11semidirect
363. #2038C2×C11semidirect
364. #2037C2×C11semidirect
365. #2003C2×C11semidirect
366. #2002C2×C11semidirect
367. #1980C2×C11semidirect
368. #1967C2×C11semidirect
369. #1806C2×C11semidirect
370. #1793C2×C11semidirect
371. #1792C2×C11semidirect
477. C2×AGL(1,ℤ/8)C22×C11semidirect
493. C2×#124C22×C11semidirect
495. C2×C4×D4C22×C11semidirect
506. #428C22×C11semidirect
507. #423C22×C11semidirect
512. C2×#104C22×C11semidirect
513. C2×#104C22×C11semidirect
514. #418C22×C11semidirect
517. #417C22×C11semidirect
518. C2×#101C22×C11semidirect
519. C2×#101C22×C11semidirect
522. C4×M16C22×C11semidirect
524. #391C22×C11semidirect
527. C4×C4⋊C4C22×C11semidirect
528. #339C22×C11semidirect
529. #339C22×C11semidirect
603. AGL(1,ℤ/8)D4×C11semidirect
615. C4⋊Q8D4×C11semidirect
619. #127D4×C11semidirect
630. #124D4×C11semidirect
631. #124D4×C11semidirect
650. C4×Q8D4×C11semidirect
651. C4×Q8D4×C11semidirect
662. C4×D4D4×C11semidirect
663. C4×D4D4×C11semidirect
865. C11#24234direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35002
C11×#30362
C2×C11×#4542
C2×C11×#4532
C4×C11×AGL(1,ℤ/8)2
C11×#25442
C11×#20382
C11×#20372
C11×#20032
C11×#20022
C11×#19802
C11×#19672
C11×#18062
C11×#17932
C11×#17922
#2423411