Finite Group Databasebeta

← C11×#24466 #14601659

Subgroups — C11×#24466 #14601659

Order 2816.

1418 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3489C211yesmaximal, characteristic
2C11×#3056C211yesmaximal, characteristic, complemented
3C2×C11×#456C211yesmaximal, characteristic, complemented
4C11×#3007C211yesmaximal, characteristic, complemented
5C22×C11×#104C211yesmaximal, characteristic, complemented
6C11×#2857C211yesmaximal, characteristic, complemented
7C11×#2039C211yesmaximal, characteristic, complemented
8C11×#2038C211yesmaximal, characteristic, complemented
9C11×#2007C211yesmaximal, characteristic, complemented
10C11×#2005C211yesmaximal, characteristic, complemented
11C11×#1901C211yesmaximal, characteristic, complemented
12C11×#1896C211yesmaximal, characteristic, complemented
13C11×#1882C211yesmaximal, characteristic, complemented
14C11×#1859C211yesmaximal, characteristic, complemented
15C11×#1793C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C2×C11×#137C2211yescharacteristic
19C2×C11×#137C2211yescharacteristic
20C2×C11×#137C2211yescharacteristic, 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×C4⋊Q8C2211yescharacteristic, complemented
33C11×#525—21no—
34C11×#525C2211yescharacteristic
35C2×C11×C22⋊Q8—21no—
36C2×C11×C22⋊Q8C2211yescharacteristic
37C2×C11×C22⋊Q8C2211yescharacteristic
38C11×#520C2211yescharacteristic
39C22×C42×C11C2211yescharacteristic
40C11×#470—21no—
41C11×#468—21no—
42C11×#467—21no—
43C11×#465—21no—
44C11×#456—24no—
45C11×#452—21no—
46C11×#452—21no—
47C11×#451—21no—
48C11×#450—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×#419C2211yescharacteristic, complemented
58C11×#417C2211yescharacteristic
59C11×#417C2211yescharacteristic
60C11×#417C2211yescharacteristic, complemented
61C2×C11×#101C2211yescharacteristic, complemented
62C2×C11×#101C2211yescharacteristic, complemented
63C11×#407C2211yescharacteristic
64C11×#391C2211yescharacteristic, complemented
65C11×#391C2211yescharacteristic, complemented
66C11×#389—22no—
67C11×#384C2211yescharacteristic, complemented
68C11×#380—22no—
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×Q8×C11C2311yescharacteristic
96C22×D4×C11—21no—
97C22×D4×C11D411yescharacteristic
98C23×C4×C11—21no—
99C23×C4×C11—21no—
100C23×C4×C11C2311yescharacteristic
101C11×#137—22no—
102C11×#137—22no—
103C11×#137—22no—
104C11×#137—41no—
105C11×#137—41no—
106C11×#137—41no—
107C2×C11×Q16—21no—
108C2×C11×Q16—21no—
109C2×C11×Q16—21no—
110C2×C11×SD16—21no—
111C2×C11×SD16—21no—
112C2×C11×SD16—21no—
113C2×C11×M16—21no—
114C2×C11×M16—22no—
115C2×C11×M16—41no—
116C2×C11×M16C2311yescharacteristic
117C2×C11×M16C2311yescharacteristic
118C2×C11×M16C2311yescharacteristic
119C2×C11×M16C2311yescharacteristic
120C22×C8×C11—21no—
121C11×C4⋊Q8—22no—
122C11×C4⋊Q8—21no—
123C11×C4⋊Q8—22no—
124C11×C4⋊Q8—41no—
125C11×#124—22no—
126C11×#124—21no—
127C11×#123—22no—
128C11×#123—22no—
129C11×#123—22no—
130C11×#123—21no—
131C11×#123—22no—
132C11×C22⋊Q8—22no—
133C11×C22⋊Q8—22no—
134C11×C22⋊Q8—22no—
135C11×C22⋊Q8—21no—
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⋊Q8—21no—
145C11×C22⋊Q8—21no—
146C11×C22⋊Q8—21no—
147C11×C22⋊Q8D411yescharacteristic
148C11×C22⋊Q8D411yescharacteristic
149C11×#121—22no—
150C11×#121—22no—
151C11×#121—22no—
152C11×#121—21no—
153C11×#121—21no—
154C11×#121—22no—
155C11×#121D411yescharacteristic
156C11×#121D411yescharacteristic
157C11×#120—22no—
158C11×#120—21no—
159C4×Q8×C11—21no—
160C4×D4×C11—22no—
161C4×D4×C11—22no—
162C4×D4×C11—21no—
163C4×D4×C11—22no—
164C4×D4×C11—21no—
165C4×D4×C11—21no—
166C11×#117—21no—
167C11×#117C2311yescharacteristic
168C2×C11×C4⋊C4—22no—
169C2×C11×C4⋊C4—21no—
170C2×C11×C4⋊C4—22no—
171C2×C11×C4⋊C4—22no—
172C2×C11×C4⋊C4—21no—
173C2×C11×C4⋊C4D412yes—
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C22⋊C4—22no—
177C2×C11×C22⋊C4—21no—
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×#103—21no—
196C11×#103—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#24466C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—21no—
208C24×C11C2×D411yescharacteristic
209C11×#41—21no—
210C11×#41—21no—
211C11×#41—22no—
212C11×#41—22no—
213C11×#41—21no—
214C11×#41—21no—
215C11×#41—21no—
216C11×#41—21no—
217C11×#41—21no—
218C11×#41—21no—
219C11×#41—21no—
220C11×#41—21no—
221C11×#41—42no—
222C11×#41—42no—
223C11×#41—41no—
224C11×#41—41no—
225C11×#41—42no—
226C11×#41—42no—
227C11×#41—42no—
228C11×#41—42no—
229C11×#41—44no—
230C11×#41—44no—
231C11×#41—42no—
232C11×#41—42no—
233C11×#41C2×D412yes—
234C11×#41#4112yes—
235C2×Q8×C11—22no—
236C2×Q8×C11—21no—
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—22no—
244C2×Q8×C11—21no—
245C2×Q8×C11—21no—
246C2×Q8×C11—21no—
247C2×Q8×C11—21no—
248C2×Q8×C11—21no—
249C2×Q8×C11—21no—
250C2×Q8×C11—41no—
251C2×Q8×C11—42no—
252C2×Q8×C11—42no—
253C2×Q8×C11—42no—
254C2×Q8×C11—42no—
255C2×Q8×C11C2×D411yescharacteristic
256C2×Q8×C11C2×D411yescharacteristic
257C2×Q8×C11C2×D411yescharacteristic
258C2×D4×C11—21no—
259C2×D4×C11—22no—
260C2×D4×C11—22no—
261C2×D4×C11—21no—
262C2×D4×C11—21no—
263C2×D4×C11—21no—
264C2×D4×C11—21no—
265C2×D4×C11—21no—
266C2×D4×C11—22no—
267C2×D4×C11—21no—
268C2×D4×C11—21no—
269C2×D4×C11—41no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11C2×D411yescharacteristic
273C2×D4×C11C2×D411yescharacteristic
274C2×D4×C11C2×D411yescharacteristic
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—24no—
284C22×C4×C11—21no—
285C22×C4×C11—21no—
286C22×C4×C11—22no—
287C22×C4×C11—21no—
288C22×C4×C11—21no—
289C22×C4×C11—21no—
290C22×C4×C11—21no—
291C22×C4×C11—21no—
292C22×C4×C11—21no—
293C22×C4×C11—42no—
294C22×C4×C11—42no—
295C22×C4×C11—42no—
296C22×C4×C11—42no—
297C22×C4×C11C2×D412yes—
298C22×C4×C11C2×D411yescharacteristic
299C22×C4×C11C2×D411yescharacteristic
300C22×C4×C11C2×D411yescharacteristic
301C22×C4×C11C2×D411yescharacteristic
302C22×C4×C11C2×D411yescharacteristic
303C22×C4×C11C2×D412yes—
304C22×C4×C11C2411yescharacteristic
305C11×Q16—42no—
306C11×Q16—42no—
307C11×Q16—42no—
308C11×SD16—42no—
309C11×SD16—42no—
310C11×SD16—42no—
311C11×M16—21no—
312C11×M16—21no—
313C11×M16—21no—
314C11×M16—21no—
315C11×M16—21no—
316C11×M16—21no—
317C11×M16—21no—
318C11×M16—42no—
319C11×M16C2×D412yes—
320C2×C8×C11—21no—
321C2×C8×C11—21no—
322C2×C8×C11—21no—
323C2×C8×C11—21no—
324C2×C8×C11—42no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—22no—
327C11×C4⋊C4—22no—
328C11×C4⋊C4—22no—
329C11×C4⋊C4—21no—
330C11×C4⋊C4—22no—
331C11×C4⋊C4—22no—
332C11×C4⋊C4—21no—
333C11×C4⋊C4—21no—
334C11×C4⋊C4—21no—
335C11×C4⋊C4—21no—
336C11×C4⋊C4—21no—
337C11×C4⋊C4—44no—
338C11×C4⋊C4—44no—
339C11×C4⋊C4—41no—
340C11×C4⋊C4—41no—
341C11×C4⋊C4C2×D411yescharacteristic
342C11×C4⋊C4C2×D411yescharacteristic
343C11×C22⋊C4—22no—
344C11×C22⋊C4—22no—
345C11×C22⋊C4—22no—
346C11×C22⋊C4—22no—
347C11×C22⋊C4—22no—
348C11×C22⋊C4—21no—
349C11×C22⋊C4—22no—
350C11×C22⋊C4—22no—
351C11×C22⋊C4—21no—
352C11×C22⋊C4—21no—
353C11×C22⋊C4—21no—
354C11×C22⋊C4—21no—
355C11×C22⋊C4—41no—
356C11×C22⋊C4—41no—
357C42×C11—22no—
358C42×C11—21no—
359C42×C11—21no—
360C42×C11—21no—
361C42×C11—21no—
362C42×C11—42no—
363C42×C11C2×D412yes—
364#3489C2×C1111yescharacteristic
365#3056C2×C1111yescharacteristic, complemented
366C2×#456C2×C1111yescharacteristic, complemented
367#3007C2×C1111yescharacteristic, complemented
368C22×#104C2×C1111yescharacteristic, complemented
369#2857C2×C1111yescharacteristic, complemented
370#2039C2×C1111yescharacteristic, complemented
371#2038C2×C1111yescharacteristic, complemented
372#2007C2×C1111yescharacteristic, complemented
373#2005C2×C1111yescharacteristic, complemented
374#1901C2×C1111yescharacteristic, complemented
375#1896C2×C1111yescharacteristic, complemented
376#1882C2×C1111yescharacteristic, complemented
377#1859C2×C1111yescharacteristic, complemented
378#1793C2×C1111yescharacteristic, complemented
379C23×C11—21no—
380C23×C11—21no—
381C23×C11—21no—
382C23×C11—22no—
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—41no—
386C23×C11—42no—
387C23×C11—42no—
388C23×C11—81no—
389C23×C11#12011yescharacteristic
390C23×C11#12011yescharacteristic
391C23×C11C22×D411yescharacteristic
392Q8×C11—21no—
393Q8×C11—21no—
394Q8×C11—21no—
395Q8×C11—21no—
396Q8×C11—21no—
397Q8×C11—42no—
398Q8×C11—44no—
399Q8×C11—41no—
400Q8×C11—41no—
401Q8×C11—41no—
402Q8×C11—41no—
403Q8×C11—41no—
404Q8×C11—41no—
405Q8×C11—41no—
406Q8×C11—41no—
407Q8×C11#12112yes—
408D4×C11—22no—
409D4×C11—22no—
410D4×C11—21no—
411D4×C11—21no—
412D4×C11—21no—
413D4×C11—21no—
414D4×C11—21no—
415D4×C11—42no—
416D4×C11—42no—
417D4×C11—42no—
418D4×C11—44no—
419D4×C11—41no—
420D4×C11—41no—
421D4×C11—41no—
422D4×C11—41no—
423D4×C11—42no—
424D4×C11—81no—
425D4×C11—82no—
426D4×C11#12112yes—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—21no—
430C2×C4×C11—22no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—22no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—21no—
445C2×C4×C11—22no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—22no—
449C2×C4×C11—21no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—42no—
453C2×C4×C11—42no—
454C2×C4×C11—42no—
455C2×C4×C11—48no—
456C2×C4×C11—44no—
457C2×C4×C11—41no—
458C2×C4×C11—44no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—42no—
465C2×C4×C11—42no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—82no—
471C2×C4×C11#12011yescharacteristic
472C2×C4×C11#12011yescharacteristic
473C2×C4×C11C22×D411yescharacteristic
474C2×C4×C11C22×D411yescharacteristic
475C2×C4×C11C22×D411yescharacteristic
476C2×C4×C11C2×#4111yescharacteristic
477C2×C4×C11H(5,𝔽2)11yescharacteristic
478C2×C4×C11H(5,𝔽2)11yescharacteristic
479C8×C11—22no—
480C8×C11—41no—
481C8×C11—41no—
482C8×C11—41no—
483C2×2−1+4C22×C1111yescharacteristic
484C22×#41C22×C1111yescharacteristic
485C2×#137C22×C1111yescharacteristic
486C2×#137C22×C1111yescharacteristic
487C2×#137C22×C1111yescharacteristic, complemented
488C22×M16C22×C1111yescharacteristic
489D4×Q8—21no—
490#548—21no—
491#547—21no—
492#547—22no—
493#546—21no—
494#546—22no—
495#537—21no—
496#537C22×C1111yescharacteristic
497#536—21no—
498#536C22×C1111yescharacteristic
499C2×C4⋊Q8C22×C1111yescharacteristic, complemented
500#525—21no—
501#525C22×C1111yescharacteristic
502C2×C22⋊Q8—21no—
503C2×C22⋊Q8C22×C1111yescharacteristic
504C2×C22⋊Q8C22×C1111yescharacteristic
505#520C22×C1111yescharacteristic
506C22×C42C22×C1111yescharacteristic
507#470—21no—
508#468—21no—
509#467—21no—
510#465—21no—
511#456—24no—
512#452—21no—
513#452—21no—
514#451—21no—
515#450—21no—
516#428C22×C1111yescharacteristic, complemented
517C2×#104—24no—
518C2×#104C22×C1111yescharacteristic
519C2×#104C22×C1111yescharacteristic
520C2×#104C22×C1111yescharacteristic
521C2×#104C22×C1111yescharacteristic
522C2×#104C22×C1111yescharacteristic, complemented
523C2×#104C22×C1111yescharacteristic, complemented
524#419C22×C1111yescharacteristic, complemented
525#417C22×C1111yescharacteristic
526#417C22×C1111yescharacteristic
527#417C22×C1111yescharacteristic, complemented
528C2×#101C22×C1111yescharacteristic, complemented
529C2×#101C22×C1111yescharacteristic, complemented
530#407C22×C1111yescharacteristic
531#391C22×C1111yescharacteristic, complemented
532#391C22×C1111yescharacteristic, complemented
533#389—22no—
534#384C22×C1111yescharacteristic, complemented
535#380—22no—
536#343C22×C1111yescharacteristic, complemented
537#343C22×C1111yescharacteristic, complemented
538#339C22×C1111yescharacteristic, complemented
539#339C22×C1111yescharacteristic, complemented
540C22×C11—21no—
541C22×C11—21no—
542C22×C11—21no—
543C22×C11—21no—
544C22×C11—21no—
545C22×C11—22no—
546C22×C11—21no—
547C22×C11—21no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—41no—
551C22×C11—41no—
552C22×C11—41no—
553C22×C11—41no—
554C22×C11—41no—
555C22×C11—41no—
556C22×C11—41no—
557C22×C11—41no—
558C22×C11—84no—
559C22×C11#45612yescomplemented
560C22×C11C2×#12011yescharacteristic
561C22×C11D4211yescharacteristic
562C22×C11#54611yescharacteristic
563C4×C11—24no—
564C4×C11—21no—
565C4×C11—21no—
566C4×C11—22no—
567C4×C11—42no—
568C4×C11—42no—
569C4×C11—41no—
570C4×C11—41no—
571C4×C11—41no—
572C4×C11—42no—
573C4×C11—41no—
574C4×C11—81no—
575C4×C11—81no—
576C4×C11C2×#12111yescharacteristic
577C4×C11#53411yescharacteristic
578C4×C11D4211yescharacteristic
579C4×C11#54611yescharacteristic
5802−1+4—22no—
5812−1+4—22no—
5822−1+4—41no—
5832−1+4—41no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—22no—
588C2×#41—21no—
589C2×#41—22no—
590C2×#41—22no—
591C2×#41—41no—
592C2×#41—41no—
593C2×#41D4×C1111yescharacteristic
594C2×#41D4×C1111yescharacteristic
595C2×#41C23×C1111yescharacteristic
596C2×#41C23×C1111yescharacteristic
597C2×#41C23×C1111yescharacteristic
598C22×Q8—21no—
599C22×Q8—21no—
600C22×Q8D4×C1111yescharacteristic
601C22×Q8C23×C1111yescharacteristic
602C22×Q8C23×C1111yescharacteristic
603C22×D4—21no—
604C22×D4D4×C1111yescharacteristic
605C23×C4—21no—
606C23×C4—21no—
607C23×C4C23×C1111yescharacteristic
608#137—22no—
609#137—22no—
610#137—22no—
611#137—41no—
612#137—41no—
613#137—41no—
614C2×Q16—21no—
615C2×Q16—21no—
616C2×Q16—21no—
617C2×SD16—21no—
618C2×SD16—21no—
619C2×SD16—21no—
620C2×M16—21no—
621C2×M16—22no—
622C2×M16—41no—
623C2×M16C23×C1111yescharacteristic
624C2×M16C23×C1111yescharacteristic
625C2×M16C23×C1111yescharacteristic
626C2×M16C23×C1111yescharacteristic
627C22×C8—21no—
628C4⋊Q8—22no—
629C4⋊Q8—21no—
630C4⋊Q8—22no—
631C4⋊Q8—41no—
632#124—22no—
633#124—21no—
634#123—22no—
635#123—22no—
636#123—22no—
637#123—21no—
638#123—22no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8—21no—
647C22⋊Q8—21no—
648C22⋊Q8—21no—
649C22⋊Q8—21no—
650C22⋊Q8—21no—
651C22⋊Q8—21no—
652C22⋊Q8—21no—
653C22⋊Q8—21no—
654C22⋊Q8D4×C1111yescharacteristic
655C22⋊Q8D4×C1111yescharacteristic
656#121—22no—
657#121—22no—
658#121—22no—
659#121—21no—
660#121—21no—
661#121—22no—
662#121D4×C1111yescharacteristic
663#121D4×C1111yescharacteristic
664#120—22no—
665#120—21no—
666C4×Q8—21no—
667C4×D4—22no—
668C4×D4—22no—
669C4×D4—21no—
670C4×D4—22no—
671C4×D4—21no—
672C4×D4—21no—
673#117—21no—
674#117C23×C1111yescharacteristic
675C2×C4⋊C4—22no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4D4×C1112yes—
681C2×C4⋊C4C23×C1111yescharacteristic
682C2×C4⋊C4C23×C1111yescharacteristic
683C2×C22⋊C4—22no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C1112yes—
686C2×C42—22no—
687C2×C42—21no—
688C2×C42—41no—
689C2×C42C23×C1111yescharacteristic
690C2×C42C23×C1111yescharacteristic
691#107—21no—
692#106—21no—
693#104—22no—
694#104—22no—
695#104—22no—
696#104—22no—
697#104—41no—
698#104D4×C1114yescomplemented
699#103—21no—
700#103—21no—
701#103—21no—
702#103—21no—
703#103—21no—
704#102—21no—
705#102—21no—
706#102—21no—
707#101—22no—
708#101—41no—
709C22⋊C8—21no—
710C22⋊C8—21no—
711#95—22no—
712#95—22no—
713C2×C11—21no—
714C2×C11—22no—
715C2×C11—21no—
716C2×C11—41no—
717C2×C11—42no—
718C2×C11—81no—
719C2×C11—81no—
720C2×C11#241011yescharacteristic
721C2×C11C2×#45611yescharacteristic
722C2×C11#301811yescharacteristic
723C24—21no—
724C24C2×D4×C1111yescharacteristic
725#41—21no—
726#41—21no—
727#41—22no—
728#41—22no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—41no—
740#41—41no—
741#41—42no—
742#41—42no—
743#41—42no—
744#41—42no—
745#41—44no—
746#41—44no—
747#41—42no—
748#41—42no—
749#41C2×D4×C1112yes—
750#41C11×#4112yes—
751C2×Q8—22no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—22no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—42no—
771C2×Q8C2×D4×C1111yescharacteristic
772C2×Q8C2×D4×C1111yescharacteristic
773C2×Q8C2×D4×C1111yescharacteristic
774C2×D4—21no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—41no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4C2×D4×C1111yescharacteristic
789C2×D4C2×D4×C1111yescharacteristic
790C2×D4C2×D4×C1111yescharacteristic
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—24no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4C2×D4×C1112yes—
814C22×C4C2×D4×C1111yescharacteristic
815C22×C4C2×D4×C1111yescharacteristic
816C22×C4C2×D4×C1111yescharacteristic
817C22×C4C2×D4×C1111yescharacteristic
818C22×C4C2×D4×C1111yescharacteristic
819C22×C4C2×D4×C1112yes—
820C22×C4C24×C1111yescharacteristic
821Q16—42no—
822Q16—42no—
823Q16—42no—
824SD16—42no—
825SD16—42no—
826SD16—42no—
827M16—21no—
828M16—21no—
829M16—21no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—42no—
835M16C2×D4×C1112yes—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—21no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—41no—
856C4⋊C4—41no—
857C4⋊C4C2×D4×C1111yescharacteristic
858C4⋊C4C2×D4×C1111yescharacteristic
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—21no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—41no—
872C22⋊C4—41no—
873C42—22no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—42no—
879C42C2×D4×C1112yes—
880C11#2446611yescharacteristic, direct product factor, Sylow
881C23—21no—
882C23—21no—
883C23—21no—
884C23—22no—
885C23—21no—
886C23—21no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—81no—
891C23C11×#12011yescharacteristic
892C23C11×#12011yescharacteristic
893C23C22×D4×C1111yescharacteristic
894Q8—21no—
895Q8—21no—
896Q8—21no—
897Q8—21no—
898Q8—21no—
899Q8—42no—
900Q8—44no—
901Q8—41no—
902Q8—41no—
903Q8—41no—
904Q8—41no—
905Q8—41no—
906Q8—41no—
907Q8—41no—
908Q8—41no—
909Q8C11×#12112yes—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—42no—
918D4—42no—
919D4—42no—
920D4—44no—
921D4—41no—
922D4—41no—
923D4—41no—
924D4—41no—
925D4—42no—
926D4—81no—
927D4—82no—
928D4C11×#12112yes—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—48no—
958C2×C4—44no—
959C2×C4—41no—
960C2×C4—44no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—82no—
973C2×C4C11×#12011yescharacteristic
974C2×C4C11×#12011yescharacteristic
975C2×C4C22×D4×C1111yescharacteristic
976C2×C4C22×D4×C1111yescharacteristic
977C2×C4C22×D4×C1111yescharacteristic
978C2×C4C2×C11×#4111yescharacteristic
979C2×C4C11×H(5,𝔽2)11yescharacteristic
980C2×C4C11×H(5,𝔽2)11yescharacteristic
981C8—22no—
982C8—41no—
983C8—41no—
984C8—41no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—22no—
991C22—21no—
992C22—21no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—84no—
1004C22C11×#45612yescomplemented
1005C22C2×C11×#12011yescharacteristic
1006C22D42×C1111yescharacteristic
1007C22C11×#54611yescharacteristic
1008C4—24no—
1009C4—21no—
1010C4—21no—
1011C4—22no—
1012C4—42no—
1013C4—42no—
1014C4—41no—
1015C4—41no—
1016C4—41no—
1017C4—42no—
1018C4—41no—
1019C4—81no—
1020C4—81no—
1021C4C2×C11×#12111yescharacteristic
1022C4C11×#53411yescharacteristic
1023C4D42×C1111yescharacteristic
1024C4C11×#54611yescharacteristic
1025C2—21no—
1026C2—22no—
1027C2—21no—
1028C2—41no—
1029C2—42no—
1030C2—81no—
1031C2—81no—
1032C2C11×#241011yescharacteristic
1033C2C2×C11×#45611yescharacteristic
1034C2C11×#301811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3489C2
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
2. C11×#3056C2semidirect
3. C2×C11×#456C2semidirect
4. C11×#3007C2semidirect
5. C22×C11×#104C2semidirect
6. C11×#2857C2semidirect
7. C11×#2039C2semidirect
8. C11×#2038C2semidirect
9. C11×#2007C2semidirect
10. C11×#2005C2semidirect
11. C11×#1901C2semidirect
12. C11×#1896C2semidirect
13. C11×#1882C2semidirect
14. C11×#1859C2semidirect
15. C11×#1793C2semidirect
20. C2×C11×#137C22semidirect
32. C2×C11×C4⋊Q8C22semidirect
49. C11×#428C22semidirect
55. C2×C11×#104C22semidirect
56. C2×C11×#104C22semidirect
57. C11×#419C22semidirect
60. C11×#417C22semidirect
61. C2×C11×#101C22semidirect
62. C2×C11×#101C22semidirect
64. C11×#391C22semidirect
65. C11×#391C22semidirect
67. C11×#384C22semidirect
69. C11×#343C22semidirect
70. C11×#343C22semidirect
71. C11×#339C22semidirect
72. C11×#339C22semidirect
191. C11×#104D4semidirect
206. #24466C11direct (N × H)
365. #3056C2×C11semidirect
366. C2×#456C2×C11semidirect
367. #3007C2×C11semidirect
368. C22×#104C2×C11semidirect
369. #2857C2×C11semidirect
370. #2039C2×C11semidirect
371. #2038C2×C11semidirect
372. #2007C2×C11semidirect
373. #2005C2×C11semidirect
374. #1901C2×C11semidirect
375. #1896C2×C11semidirect
376. #1882C2×C11semidirect
377. #1859C2×C11semidirect
378. #1793C2×C11semidirect
487. C2×#137C22×C11semidirect
499. C2×C4⋊Q8C22×C11semidirect
516. #428C22×C11semidirect
522. C2×#104C22×C11semidirect
523. C2×#104C22×C11semidirect
524. #419C22×C11semidirect
527. #417C22×C11semidirect
528. C2×#101C22×C11semidirect
529. C2×#101C22×C11semidirect
531. #391C22×C11semidirect
532. #391C22×C11semidirect
534. #384C22×C11semidirect
536. #343C22×C11semidirect
537. #343C22×C11semidirect
538. #339C22×C11semidirect
539. #339C22×C11semidirect
559. C22×C11#456semidirect
698. #104D4×C11semidirect
880. C11#24466direct (N × H)
1004. C22C11×#456semidirect

Maximal subgroups

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

subgroupindex
C11×#34892
C11×#30562
C2×C11×#4562
C11×#30072
C22×C11×#1042
C11×#28572
C11×#20392
C11×#20382
C11×#20072
C11×#20052
C11×#19012
C11×#18962
C11×#18822
C11×#18592
C11×#17932
#2446611