Finite Group Databasebeta

← C11×#24465 #14601658

Subgroups — C11×#24465 #14601658

Order 2816.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3489C211yesmaximal, characteristic, complemented
2C11×#3055C211yesmaximal, characteristic, complemented
3C2×C11×#454C211yesmaximal, characteristic, complemented
4C11×#3006C211yesmaximal, characteristic, complemented
5C22×C11×#104C211yesmaximal, characteristic, complemented
6C11×#2850C211yesmaximal, characteristic, complemented
7C11×#2040C211yesmaximal, characteristic, complemented
8C11×#2038C211yesmaximal, characteristic, complemented
9C11×#2006C211yesmaximal, characteristic, complemented
10C11×#2003C211yesmaximal, characteristic, complemented
11C11×#1901C211yesmaximal, characteristic, complemented
12C11×#1896C211yesmaximal, characteristic, complemented
13C11×#1883C211yesmaximal, characteristic, complemented
14C11×#1860C211yesmaximal, characteristic, complemented
15C11×#1793C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×C11×M16C2211yescharacteristic
22D4×Q8×C11—21no—
23C11×#548—21no—
24C11×#547—21no—
25C11×#547—22no—
26C11×#546—21no—
27C11×#546—22no—
28C11×#537—21no—
29C11×#537C2211yescharacteristic
30C11×#536—21no—
31C11×#536C2211yescharacteristic
32C2×C11×#124C2211yescharacteristic, complemented
33C11×#525—21no—
34C11×#525C2211yescharacteristic
35C2×C11×C22⋊Q8—21no—
36C2×C11×C22⋊Q8C2211yescharacteristic
37C2×C11×#121C2211yescharacteristic
38C11×#520C2211yescharacteristic
39C22×C42×C11C2211yescharacteristic
40C11×#469—21no—
41C11×#468—21no—
42C11×#466—21no—
43C11×#465—21no—
44C11×#454—24no—
45C11×#449—21no—
46C11×#449—21no—
47C11×#448—21no—
48C11×#447—21no—
49C11×#428C2211yescharacteristic, complemented
50C2×C11×#104—24no—
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
63C11×#407C2211yescharacteristic
64C11×#391C2211yescharacteristic, complemented
65C11×#390C2211yescharacteristic, complemented
66C11×#388—22no—
67C11×#386—22no—
68C11×#382C2211yescharacteristic, complemented
69C11×#343C2211yescharacteristic, complemented
70C11×#343C2211yescharacteristic, 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—
77C2×C11×#41—21no—
78C2×C11×#41—21no—
79C2×C11×#41—21no—
80C2×C11×#41—22no—
81C2×C11×#41—21no—
82C2×C11×#41—22no—
83C2×C11×#41—22no—
84C2×C11×#41—41no—
85C2×C11×#41—41no—
86C2×C11×#41D411yescharacteristic
87C2×C11×#41D411yescharacteristic
88C2×C11×#41C2311yescharacteristic
89C2×C11×#41C2311yescharacteristic
90C2×C11×#41C2311yescharacteristic
91C22×Q8×C11—21no—
92C22×Q8×C11—21no—
93C22×Q8×C11D411yescharacteristic
94C22×Q8×C11C2311yescharacteristic
95C22×D4×C11—21no—
96C22×D4×C11—21no—
97C22×D4×C11D411yescharacteristic
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11—21no—
100C23×C4×C11—21no—
101C23×C4×C11C2311yescharacteristic
102C11×AGL(1,ℤ/8)—22no—
103C11×AGL(1,ℤ/8)—22no—
104C11×AGL(1,ℤ/8)—22no—
105C11×AGL(1,ℤ/8)—41no—
106C11×AGL(1,ℤ/8)—41no—
107C11×AGL(1,ℤ/8)—41no—
108C2×C11×SD16—21no—
109C2×C11×SD16—21no—
110C2×C11×SD16—21no—
111C2×C11×D8—21no—
112C2×C11×D8—21no—
113C2×C11×D8—21no—
114C2×C11×M16—21no—
115C2×C11×M16—22no—
116C2×C11×M16—41no—
117C2×C11×M16C2311yescharacteristic
118C2×C11×M16C2311yescharacteristic
119C2×C11×M16C2311yescharacteristic
120C2×C11×M16C2311yescharacteristic
121C22×C8×C11—21no—
122C11×C4⋊Q8—22no—
123C11×C4⋊Q8—21no—
124C11×#124—22no—
125C11×#124—21no—
126C11×#124—22no—
127C11×#124—41no—
128C11×#123—22no—
129C11×#123—22no—
130C11×#123—22no—
131C11×#123—21no—
132C11×#123—22no—
133C11×C22⋊Q8—22no—
134C11×C22⋊Q8—22no—
135C11×C22⋊Q8—22no—
136C11×C22⋊Q8—21no—
137C11×C22⋊Q8—21no—
138C11×C22⋊Q8—21no—
139C11×C22⋊Q8—21no—
140C11×C22⋊Q8—21no—
141C11×C22⋊Q8—21no—
142C11×C22⋊Q8—21no—
143C11×C22⋊Q8—21no—
144C11×C22⋊Q8D411yescharacteristic
145C11×C22⋊Q8D411yescharacteristic
146C11×#121—22no—
147C11×#121—22no—
148C11×#121—22no—
149C11×#121—21no—
150C11×#121—21no—
151C11×#121—22no—
152C11×#121—21no—
153C11×#121—21no—
154C11×#121—21no—
155C11×#121—21no—
156C11×#121D411yescharacteristic
157C11×#121D411yescharacteristic
158C11×#120—22no—
159C11×#120—21no—
160C4×Q8×C11—21no—
161C4×D4×C11—22no—
162C4×D4×C11—22no—
163C4×D4×C11—21no—
164C4×D4×C11—22no—
165C4×D4×C11—21no—
166C4×D4×C11—21no—
167C11×#117—21no—
168C11×#117C2311yescharacteristic
169C2×C11×C4⋊C4—22no—
170C2×C11×C4⋊C4—21no—
171C2×C11×C4⋊C4D412yes—
172C2×C11×C4⋊C4C2311yescharacteristic
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4—22no—
175C2×C11×C22⋊C4—21no—
176C2×C11×C22⋊C4—22no—
177C2×C11×C22⋊C4—22no—
178C2×C11×C22⋊C4D412yes—
179C2×C42×C11—22no—
180C2×C42×C11—21no—
181C2×C42×C11—41no—
182C2×C42×C11C2311yescharacteristic
183C2×C42×C11C2311yescharacteristic
184C11×#107—21no—
185C11×#106—21no—
186C11×#104—22no—
187C11×#104—22no—
188C11×#104—22no—
189C11×#104—22no—
190C11×#104—41no—
191C11×#104D414yescomplemented
192C11×#103—21no—
193C11×#103—21no—
194C11×#103—21no—
195C11×#102—21no—
196C11×#102—21no—
197C11×#102—21no—
198C11×#102—21no—
199C11×#102—21no—
200C11×#101—22no—
201C11×#101—41no—
202C11×C22⋊C8—21no—
203C11×C22⋊C8—21no—
204C11×#95—22no—
205C11×#95—22no—
206#24465C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—21no—
208C24×C11—21no—
209C24×C11C2×D411yescharacteristic
210C11×#41—21no—
211C11×#41—21no—
212C11×#41—22no—
213C11×#41—22no—
214C11×#41—21no—
215C11×#41—21no—
216C11×#41—21no—
217C11×#41—21no—
218C11×#41—21no—
219C11×#41—21no—
220C11×#41—21no—
221C11×#41—21no—
222C11×#41—42no—
223C11×#41—42no—
224C11×#41—41no—
225C11×#41—41no—
226C11×#41—42no—
227C11×#41—42no—
228C11×#41—42no—
229C11×#41—42no—
230C11×#41—44no—
231C11×#41—44no—
232C11×#41—42no—
233C11×#41—42no—
234C11×#41C2×D412yes—
235C11×#41#4112yes—
236C2×Q8×C11—22no—
237C2×Q8×C11—21no—
238C2×Q8×C11—21no—
239C2×Q8×C11—21no—
240C2×Q8×C11—21no—
241C2×Q8×C11—21no—
242C2×Q8×C11—21no—
243C2×Q8×C11—21no—
244C2×Q8×C11—22no—
245C2×Q8×C11—41no—
246C2×Q8×C11—42no—
247C2×Q8×C11—42no—
248C2×Q8×C11—42no—
249C2×Q8×C11—42no—
250C2×Q8×C11C2×D411yescharacteristic
251C2×Q8×C11C2×D411yescharacteristic
252C2×Q8×C11C2×D411yescharacteristic
253C2×D4×C11—21no—
254C2×D4×C11—22no—
255C2×D4×C11—22no—
256C2×D4×C11—21no—
257C2×D4×C11—21no—
258C2×D4×C11—21no—
259C2×D4×C11—21no—
260C2×D4×C11—21no—
261C2×D4×C11—22no—
262C2×D4×C11—21no—
263C2×D4×C11—21no—
264C2×D4×C11—21no—
265C2×D4×C11—21no—
266C2×D4×C11—21no—
267C2×D4×C11—21no—
268C2×D4×C11—21no—
269C2×D4×C11—21no—
270C2×D4×C11—41no—
271C2×D4×C11—42no—
272C2×D4×C11—42no—
273C2×D4×C11—44no—
274C2×D4×C11—41no—
275C2×D4×C11—41no—
276C2×D4×C11C2×D411yescharacteristic
277C2×D4×C11C2×D411yescharacteristic
278C2×D4×C11C2×D411yescharacteristic
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—21no—
287C22×C4×C11—21no—
288C22×C4×C11—21no—
289C22×C4×C11—22no—
290C22×C4×C11—21no—
291C22×C4×C11—21no—
292C22×C4×C11—21no—
293C22×C4×C11—21no—
294C22×C4×C11—21no—
295C22×C4×C11—42no—
296C22×C4×C11—42no—
297C22×C4×C11—42no—
298C22×C4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11C2×D412yes—
301C22×C4×C11C2×D411yescharacteristic
302C22×C4×C11C2×D411yescharacteristic
303C22×C4×C11C2×D411yescharacteristic
304C22×C4×C11C2×D411yescharacteristic
305C22×C4×C11C2×D411yescharacteristic
306C22×C4×C11C2×D412yes—
307C22×C4×C11C2411yescharacteristic
308C11×SD16—42no—
309C11×SD16—42no—
310C11×SD16—42no—
311C11×D8—42no—
312C11×D8—42no—
313C11×D8—42no—
314C11×M16—21no—
315C11×M16—21no—
316C11×M16—21no—
317C11×M16—21no—
318C11×M16—21no—
319C11×M16—21no—
320C11×M16—21no—
321C11×M16—42no—
322C11×M16C2×D412yes—
323C2×C8×C11—21no—
324C2×C8×C11—21no—
325C2×C8×C11—21no—
326C2×C8×C11—21no—
327C2×C8×C11—42no—
328C11×C4⋊C4—22no—
329C11×C4⋊C4—22no—
330C11×C4⋊C4—22no—
331C11×C4⋊C4—22no—
332C11×C4⋊C4—21no—
333C11×C4⋊C4—22no—
334C11×C4⋊C4—22no—
335C11×C4⋊C4—21no—
336C11×C4⋊C4—21no—
337C11×C4⋊C4—21no—
338C11×C4⋊C4—21no—
339C11×C4⋊C4—21no—
340C11×C4⋊C4C2×D411yescharacteristic
341C11×C4⋊C4C2×D411yescharacteristic
342C11×C22⋊C4—22no—
343C11×C22⋊C4—22no—
344C11×C22⋊C4—22no—
345C11×C22⋊C4—22no—
346C11×C22⋊C4—22no—
347C11×C22⋊C4—21no—
348C11×C22⋊C4—22no—
349C11×C22⋊C4—22no—
350C11×C22⋊C4—21no—
351C11×C22⋊C4—21no—
352C11×C22⋊C4—21no—
353C11×C22⋊C4—21no—
354C11×C22⋊C4—44no—
355C11×C22⋊C4—44no—
356C11×C22⋊C4—41no—
357C11×C22⋊C4—41no—
358C42×C11—22no—
359C42×C11—21no—
360C42×C11—21no—
361C42×C11—21no—
362C42×C11—21no—
363C42×C11—42no—
364C42×C11C2×D412yes—
365#3489C2×C1111yescharacteristic, complemented
366#3055C2×C1111yescharacteristic, complemented
367C2×#454C2×C1111yescharacteristic, complemented
368#3006C2×C1111yescharacteristic, complemented
369C22×#104C2×C1111yescharacteristic, complemented
370#2850C2×C1111yescharacteristic, complemented
371#2040C2×C1111yescharacteristic, complemented
372#2038C2×C1111yescharacteristic, complemented
373#2006C2×C1111yescharacteristic, complemented
374#2003C2×C1111yescharacteristic, complemented
375#1901C2×C1111yescharacteristic, complemented
376#1896C2×C1111yescharacteristic, complemented
377#1883C2×C1111yescharacteristic, complemented
378#1860C2×C1111yescharacteristic, complemented
379#1793C2×C1111yescharacteristic, complemented
380C23×C11—21no—
381C23×C11—21no—
382C23×C11—21no—
383C23×C11—22no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—41no—
387C23×C11—42no—
388C23×C11—42no—
389C23×C11—42no—
390C23×C11—42no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—81no—
395C23×C11#12011yescharacteristic
396C23×C11#12011yescharacteristic
397C23×C11C22×D411yescharacteristic
398Q8×C11—21no—
399Q8×C11—21no—
400Q8×C11—21no—
401Q8×C11—21no—
402Q8×C11—21no—
403Q8×C11—42no—
404Q8×C11—44no—
405Q8×C11—41no—
406Q8×C11—41no—
407Q8×C11—41no—
408Q8×C11—41no—
409Q8×C11#12112yes—
410D4×C11—22no—
411D4×C11—22no—
412D4×C11—21no—
413D4×C11—21no—
414D4×C11—21no—
415D4×C11—21no—
416D4×C11—21no—
417D4×C11—42no—
418D4×C11—42no—
419D4×C11—42no—
420D4×C11—44no—
421D4×C11—41no—
422D4×C11—41no—
423D4×C11—41no—
424D4×C11—41no—
425D4×C11—42no—
426D4×C11—41no—
427D4×C11—41no—
428D4×C11—41no—
429D4×C11—41no—
430D4×C11—81no—
431D4×C11—82no—
432D4×C11—82no—
433D4×C11—82no—
434D4×C11#12112yes—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—22no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—21no—
450C2×C4×C11—22no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—21no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—42no—
459C2×C4×C11—42no—
460C2×C4×C11—42no—
461C2×C4×C11—44no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—44no—
466C2×C4×C11—48no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—42no—
473C2×C4×C11—42no—
474C2×C4×C11—41no—
475C2×C4×C11—82no—
476C2×C4×C11#12011yescharacteristic
477C2×C4×C11#12011yescharacteristic
478C2×C4×C11C22×D411yescharacteristic
479C2×C4×C11C22×D411yescharacteristic
480C2×C4×C11C22×D411yescharacteristic
481C2×C4×C11C2×#4111yescharacteristic
482C2×C4×C11H(5,𝔽2)11yescharacteristic
483C2×C4×C11H(5,𝔽2)11yescharacteristic
484C8×C11—22no—
485C8×C11—41no—
486C8×C11—41no—
487C8×C11—41no—
488C2×2−1+4C22×C1111yescharacteristic
489C22×#41C22×C1111yescharacteristic
490C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
491C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
492C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
493C22×M16C22×C1111yescharacteristic
494D4×Q8—21no—
495#548—21no—
496#547—21no—
497#547—22no—
498#546—21no—
499#546—22no—
500#537—21no—
501#537C22×C1111yescharacteristic
502#536—21no—
503#536C22×C1111yescharacteristic
504C2×#124C22×C1111yescharacteristic, complemented
505#525—21no—
506#525C22×C1111yescharacteristic
507C2×C22⋊Q8—21no—
508C2×C22⋊Q8C22×C1111yescharacteristic
509C2×#121C22×C1111yescharacteristic
510#520C22×C1111yescharacteristic
511C22×C42C22×C1111yescharacteristic
512#469—21no—
513#468—21no—
514#466—21no—
515#465—21no—
516#454—24no—
517#449—21no—
518#449—21no—
519#448—21no—
520#447—21no—
521#428C22×C1111yescharacteristic, complemented
522C2×#104—24no—
523C2×#104C22×C1111yescharacteristic
524C2×#104C22×C1111yescharacteristic
525C2×#104C22×C1111yescharacteristic
526C2×#104C22×C1111yescharacteristic
527C2×#104C22×C1111yescharacteristic, complemented
528C2×#104C22×C1111yescharacteristic, complemented
529#418C22×C1111yescharacteristic, complemented
530#417C22×C1111yescharacteristic
531#417C22×C1111yescharacteristic
532#417C22×C1111yescharacteristic, complemented
533C2×#101C22×C1111yescharacteristic, complemented
534C2×#101C22×C1111yescharacteristic, complemented
535#407C22×C1111yescharacteristic
536#391C22×C1111yescharacteristic, complemented
537#390C22×C1111yescharacteristic, complemented
538#388—22no—
539#386—22no—
540#382C22×C1111yescharacteristic, complemented
541#343C22×C1111yescharacteristic, complemented
542#343C22×C1111yescharacteristic, complemented
543#339C22×C1111yescharacteristic, complemented
544#339C22×C1111yescharacteristic, complemented
545C22×C11—21no—
546C22×C11—21no—
547C22×C11—21no—
548C22×C11—21no—
549C22×C11—21no—
550C22×C11—22no—
551C22×C11—21no—
552C22×C11—21no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—41no—
556C22×C11—41no—
557C22×C11—41no—
558C22×C11—41no—
559C22×C11—41no—
560C22×C11—41no—
561C22×C11—41no—
562C22×C11—41no—
563C22×C11—84no—
564C22×C11—82no—
565C22×C11—82no—
566C22×C11—81no—
567C22×C11—81no—
568C22×C11—81no—
569C22×C11#45412yescomplemented
570C22×C11C2×#12011yescharacteristic
571C22×C11D4211yescharacteristic
572C22×C11#54611yescharacteristic
573C4×C11—21no—
574C4×C11—21no—
575C4×C11—22no—
576C4×C11—42no—
577C4×C11—42no—
578C4×C11—42no—
579C4×C11—41no—
580C4×C11—41no—
581C4×C11—41no—
582C4×C11—42no—
583C4×C11—41no—
584C4×C11—81no—
585C4×C11C2×#12111yescharacteristic
586C4×C11#53411yescharacteristic
587C4×C11D4211yescharacteristic
588C4×C11#54611yescharacteristic
5892−1+4—22no—
5902−1+4—22no—
5912−1+4—41no—
5922−1+4—41no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—22no—
599C2×#41—22no—
600C2×#41—41no—
601C2×#41—41no—
602C2×#41D4×C1111yescharacteristic
603C2×#41D4×C1111yescharacteristic
604C2×#41C23×C1111yescharacteristic
605C2×#41C23×C1111yescharacteristic
606C2×#41C23×C1111yescharacteristic
607C22×Q8—21no—
608C22×Q8—21no—
609C22×Q8D4×C1111yescharacteristic
610C22×Q8C23×C1111yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4D4×C1111yescharacteristic
614C22×D4C23×C1111yescharacteristic
615C23×C4—21no—
616C23×C4—21no—
617C23×C4C23×C1111yescharacteristic
618AGL(1,ℤ/8)—22no—
619AGL(1,ℤ/8)—22no—
620AGL(1,ℤ/8)—22no—
621AGL(1,ℤ/8)—41no—
622AGL(1,ℤ/8)—41no—
623AGL(1,ℤ/8)—41no—
624C2×SD16—21no—
625C2×SD16—21no—
626C2×SD16—21no—
627C2×D8—21no—
628C2×D8—21no—
629C2×D8—21no—
630C2×M16—21no—
631C2×M16—22no—
632C2×M16—41no—
633C2×M16C23×C1111yescharacteristic
634C2×M16C23×C1111yescharacteristic
635C2×M16C23×C1111yescharacteristic
636C2×M16C23×C1111yescharacteristic
637C22×C8—21no—
638C4⋊Q8—22no—
639C4⋊Q8—21no—
640#124—22no—
641#124—21no—
642#124—22no—
643#124—41no—
644#123—22no—
645#123—22no—
646#123—22no—
647#123—21no—
648#123—22no—
649C22⋊Q8—22no—
650C22⋊Q8—22no—
651C22⋊Q8—22no—
652C22⋊Q8—21no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8—21no—
658C22⋊Q8—21no—
659C22⋊Q8—21no—
660C22⋊Q8D4×C1111yescharacteristic
661C22⋊Q8D4×C1111yescharacteristic
662#121—22no—
663#121—22no—
664#121—22no—
665#121—21no—
666#121—21no—
667#121—22no—
668#121—21no—
669#121—21no—
670#121—21no—
671#121—21no—
672#121D4×C1111yescharacteristic
673#121D4×C1111yescharacteristic
674#120—22no—
675#120—21no—
676C4×Q8—21no—
677C4×D4—22no—
678C4×D4—22no—
679C4×D4—21no—
680C4×D4—22no—
681C4×D4—21no—
682C4×D4—21no—
683#117—21no—
684#117C23×C1111yescharacteristic
685C2×C4⋊C4—22no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4D4×C1112yes—
688C2×C4⋊C4C23×C1111yescharacteristic
689C2×C4⋊C4C23×C1111yescharacteristic
690C2×C22⋊C4—22no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4D4×C1112yes—
695C2×C42—22no—
696C2×C42—21no—
697C2×C42—41no—
698C2×C42C23×C1111yescharacteristic
699C2×C42C23×C1111yescharacteristic
700#107—21no—
701#106—21no—
702#104—22no—
703#104—22no—
704#104—22no—
705#104—22no—
706#104—41no—
707#104D4×C1114yescomplemented
708#103—21no—
709#103—21no—
710#103—21no—
711#102—21no—
712#102—21no—
713#102—21no—
714#102—21no—
715#102—21no—
716#101—22no—
717#101—41no—
718C22⋊C8—21no—
719C22⋊C8—21no—
720#95—22no—
721#95—22no—
722C2×C11—21no—
723C2×C11—21no—
724C2×C11—22no—
725C2×C11—41no—
726C2×C11—42no—
727C2×C11—81no—
728C2×C11—81no—
729C2×C11—161no—
730C2×C11#241011yescharacteristic
731C2×C11C2×#45411yescharacteristic
732C2×C11#301811yescharacteristic
733C24—21no—
734C24—21no—
735C24C2×D4×C1111yescharacteristic
736#41—21no—
737#41—21no—
738#41—22no—
739#41—22no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—21no—
748#41—42no—
749#41—42no—
750#41—41no—
751#41—41no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—44no—
757#41—44no—
758#41—42no—
759#41—42no—
760#41C2×D4×C1112yes—
761#41C11×#4112yes—
762C2×Q8—22no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—22no—
771C2×Q8—41no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8C2×D4×C1111yescharacteristic
777C2×Q8C2×D4×C1111yescharacteristic
778C2×Q8C2×D4×C1111yescharacteristic
779C2×D4—21no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—41no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—44no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4C2×D4×C1111yescharacteristic
803C2×D4C2×D4×C1111yescharacteristic
804C2×D4C2×D4×C1111yescharacteristic
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4C2×D4×C1112yes—
827C22×C4C2×D4×C1111yescharacteristic
828C22×C4C2×D4×C1111yescharacteristic
829C22×C4C2×D4×C1111yescharacteristic
830C22×C4C2×D4×C1111yescharacteristic
831C22×C4C2×D4×C1111yescharacteristic
832C22×C4C2×D4×C1112yes—
833C22×C4C24×C1111yescharacteristic
834SD16—42no—
835SD16—42no—
836SD16—42no—
837D8—42no—
838D8—42no—
839D8—42no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—21no—
844M16—21no—
845M16—21no—
846M16—21no—
847M16—42no—
848M16C2×D4×C1112yes—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—42no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—21no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4C2×D4×C1111yescharacteristic
867C4⋊C4C2×D4×C1111yescharacteristic
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—21no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—41no—
883C22⋊C4—41no—
884C42—22no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—42no—
890C42C2×D4×C1112yes—
891C11#2446511yescharacteristic, direct product factor, Sylow
892C23—21no—
893C23—21no—
894C23—21no—
895C23—22no—
896C23—21no—
897C23—21no—
898C23—41no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—81no—
907C23C11×#12011yescharacteristic
908C23C11×#12011yescharacteristic
909C23C22×D4×C1111yescharacteristic
910Q8—21no—
911Q8—21no—
912Q8—21no—
913Q8—21no—
914Q8—21no—
915Q8—42no—
916Q8—44no—
917Q8—41no—
918Q8—41no—
919Q8—41no—
920Q8—41no—
921Q8C11×#12112yes—
922D4—22no—
923D4—22no—
924D4—21no—
925D4—21no—
926D4—21no—
927D4—21no—
928D4—21no—
929D4—42no—
930D4—42no—
931D4—42no—
932D4—44no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—42no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—82no—
944D4—82no—
945D4—82no—
946D4C11×#12112yes—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—44no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—44no—
978C2×C4—48no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—82no—
988C2×C4C11×#12011yescharacteristic
989C2×C4C11×#12011yescharacteristic
990C2×C4C22×D4×C1111yescharacteristic
991C2×C4C22×D4×C1111yescharacteristic
992C2×C4C22×D4×C1111yescharacteristic
993C2×C4C2×C11×#4111yescharacteristic
994C2×C4C11×H(5,𝔽2)11yescharacteristic
995C2×C4C11×H(5,𝔽2)11yescharacteristic
996C8—22no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—22no—
1006C22—21no—
1007C22—21no—
1008C22—42no—
1009C22—42no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—81no—
1022C22—81no—
1023C22—81no—
1024C22C11×#45412yescomplemented
1025C22C2×C11×#12011yescharacteristic
1026C22D42×C1111yescharacteristic
1027C22C11×#54611yescharacteristic
1028C4—21no—
1029C4—21no—
1030C4—22no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—81no—
1040C4C2×C11×#12111yescharacteristic
1041C4C11×#53411yescharacteristic
1042C4D42×C1111yescharacteristic
1043C4C11×#54611yescharacteristic
1044C2—21no—
1045C2—21no—
1046C2—22no—
1047C2—41no—
1048C2—42no—
1049C2—81no—
1050C2—81no—
1051C2—161no—
1052C2C11×#241011yescharacteristic
1053C2C2×C11×#45411yescharacteristic
1054C2C11×#301811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3489C2semidirect
2. C11×#3055C2semidirect
3. C2×C11×#454C2semidirect
4. C11×#3006C2semidirect
5. C22×C11×#104C2semidirect
6. C11×#2850C2semidirect
7. C11×#2040C2semidirect
8. C11×#2038C2semidirect
9. C11×#2006C2semidirect
10. C11×#2003C2semidirect
11. C11×#1901C2semidirect
12. C11×#1896C2semidirect
13. C11×#1883C2semidirect
14. C11×#1860C2semidirect
15. C11×#1793C2semidirect
20. C2×C11×AGL(1,ℤ/8)C22semidirect
32. C2×C11×#124C22semidirect
49. C11×#428C22semidirect
55. C2×C11×#104C22semidirect
56. C2×C11×#104C22semidirect
57. C11×#418C22semidirect
60. C11×#417C22semidirect
61. C2×C11×#101C22semidirect
62. C2×C11×#101C22semidirect
64. C11×#391C22semidirect
65. C11×#390C22semidirect
68. C11×#382C22semidirect
69. C11×#343C22semidirect
70. C11×#343C22semidirect
71. C11×#339C22semidirect
72. C11×#339C22semidirect
191. C11×#104D4semidirect
206. #24465C11direct (N × H)
365. #3489C2×C11semidirect
366. #3055C2×C11semidirect
367. C2×#454C2×C11semidirect
368. #3006C2×C11semidirect
369. C22×#104C2×C11semidirect
370. #2850C2×C11semidirect
371. #2040C2×C11semidirect
372. #2038C2×C11semidirect
373. #2006C2×C11semidirect
374. #2003C2×C11semidirect
375. #1901C2×C11semidirect
376. #1896C2×C11semidirect
377. #1883C2×C11semidirect
378. #1860C2×C11semidirect
379. #1793C2×C11semidirect
492. C2×AGL(1,ℤ/8)C22×C11semidirect
504. C2×#124C22×C11semidirect
521. #428C22×C11semidirect
527. C2×#104C22×C11semidirect
528. C2×#104C22×C11semidirect
529. #418C22×C11semidirect
532. #417C22×C11semidirect
533. C2×#101C22×C11semidirect
534. C2×#101C22×C11semidirect
536. #391C22×C11semidirect
537. #390C22×C11semidirect
540. #382C22×C11semidirect
541. #343C22×C11semidirect
542. #343C22×C11semidirect
543. #339C22×C11semidirect
544. #339C22×C11semidirect
569. C22×C11#454semidirect
707. #104D4×C11semidirect
891. C11#24465direct (N × H)
1024. C22C11×#454semidirect

Maximal subgroups

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

subgroupindex
C11×#34892
C11×#30552
C2×C11×#4542
C11×#30062
C22×C11×#1042
C11×#28502
C11×#20402
C11×#20382
C11×#20062
C11×#20032
C11×#19012
C11×#18962
C11×#18832
C11×#18602
C11×#17932
#2446511