Finite Group Databasebeta

← C11×#24467 #14601660

Subgroups — C11×#24467 #14601660

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3488C211yesmaximal, characteristic
2C11×#3056C211yesmaximal, characteristic, complemented
3C2×C11×#455C211yesmaximal, characteristic, complemented
4C11×#3007C211yesmaximal, characteristic, complemented
5C22×C11×#104C211yesmaximal, characteristic, complemented
6C11×#2850C211yesmaximal, characteristic, complemented
7C11×#2040C211yesmaximal, characteristic, complemented
8C11×#2037C211yesmaximal, characteristic, complemented
9C11×#2007C211yesmaximal, characteristic, complemented
10C11×#2004C211yesmaximal, characteristic, complemented
11C11×#1900C211yesmaximal, characteristic, complemented
12C11×#1896C211yesmaximal, characteristic, complemented
13C11×#1882C211yesmaximal, characteristic, complemented
14C11×#1860C211yesmaximal, characteristic, complemented
15C11×#1792C211yesmaximal, characteristic, complemented
16C2×C11×H(5,𝔽2)C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C2×C11×#137C2211yescharacteristic
19C2×C11×#137C2211yescharacteristic, complemented
20C2×C11×#137C2211yescharacteristic, complemented
21C22×C11×M16C2211yescharacteristic, complemented
22C11×#550—21no—
23C11×#548—21no—
24C11×#546—21no—
25C11×#546—22no—
26D42×C11—22no—
27D42×C11—21no—
28C11×#537—21no—
29C11×#537C2211yescharacteristic
30C11×#535—21no—
31C11×#535C2211yescharacteristic
32C2×C11×#124C2211yescharacteristic, complemented
33C11×#525—21no—
34C11×#525C2211yescharacteristic
35C2×C11×C22⋊Q8C2211yescharacteristic, complemented
36C2×C11×#121—21no—
37C2×C11×#121C2211yescharacteristic
38C11×#520C2211yescharacteristic
39C22×C42×C11C2211yescharacteristic, complemented
40C11×#470—21no—
41C11×#468—21no—
42C11×#467—21no—
43C11×#465—21no—
44C11×#455—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, complemented
54C2×C11×#104C2211yescharacteristic, complemented
55C2×C11×#104C2211yescharacteristic, complemented
56C2×C11×#104C2211yescharacteristic, complemented
57C11×#419C2211yescharacteristic, complemented
58C11×#417C2211yescharacteristic
59C11×#417C2211yescharacteristic, complemented
60C11×#417C2211yescharacteristic, complemented
61C2×C11×#100C2211yescharacteristic, complemented
62C2×C11×#100C2211yescharacteristic, complemented
63C11×#407C2211yescharacteristic, complemented
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×H(5,𝔽2)—22no—
74C11×H(5,𝔽2)—22no—
75C11×H(5,𝔽2)—41no—
76C11×H(5,𝔽2)—41no—
77C2×C11×#41—21no—
78C2×C11×#41—21no—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—22no—
82C2×C11×#41—22no—
83C2×C11×#41—41no—
84C2×C11×#41—41no—
85C2×C11×#41D411yescharacteristic
86C2×C11×#41D411yescharacteristic
87C2×C11×#41C2311yescharacteristic
88C2×C11×#41C2311yescharacteristic
89C2×C11×#41C2311yescharacteristic
90C22×Q8×C11D411yescharacteristic
91C22×Q8×C11C2311yescharacteristic
92C22×D4×C11—21no—
93C22×D4×C11—22no—
94C22×D4×C11—22no—
95C22×D4×C11—21no—
96C22×D4×C11—21no—
97C22×D4×C11D411yescharacteristic
98C22×D4×C11D412yes—
99C22×D4×C11C2311yescharacteristic
100C23×C4×C11—21no—
101C23×C4×C11—21no—
102C23×C4×C11C2311yescharacteristic
103C11×#137—22no—
104C11×#137—22no—
105C11×#137—22no—
106C11×#137—41no—
107C11×#137—41no—
108C11×#137—41no—
109C2×C11×Q16—21no—
110C2×C11×Q16—21no—
111C2×C11×Q16—21no—
112C2×C11×SD16—21no—
113C2×C11×SD16—21no—
114C2×C11×SD16—21no—
115C2×C11×M16—21no—
116C2×C11×M16—22no—
117C2×C11×M16—41no—
118C2×C11×M16C2311yescharacteristic
119C2×C11×M16C2311yescharacteristic
120C2×C11×M16C2311yescharacteristic
121C2×C11×M16C2311yescharacteristic
122C22×C8×C11—21no—
123C11×#127—22no—
124C11×#127—21no—
125C11×#124—22no—
126C11×#124—21no—
127C11×#124—22no—
128C11×#124—41no—
129C11×#123—22no—
130C11×#123—21no—
131C11×C22⋊Q8—22no—
132C11×C22⋊Q8—21no—
133C11×C22⋊Q8—21no—
134C11×C22⋊Q8—21no—
135C11×C22⋊Q8—21no—
136C11×C22⋊Q8—21no—
137C11×C22⋊Q8—21no—
138C11×C22⋊Q8D411yescharacteristic
139C11×C22⋊Q8D411yescharacteristic
140C11×#121—22no—
141C11×#121—22no—
142C11×#121—22no—
143C11×#121—22no—
144C11×#121—22no—
145C11×#121—21no—
146C11×#121—21no—
147C11×#121—21no—
148C11×#121—21no—
149C11×#121—21no—
150C11×#121—21no—
151C11×#121—22no—
152C11×#121—21no—
153C11×#121—21no—
154C11×#121D411yescharacteristic
155C11×#121D411yescharacteristic
156C11×#120—22no—
157C11×#120—22no—
158C11×#120—22no—
159C11×#120—21no—
160C11×#120—22no—
161C4×Q8×C11—21no—
162C4×D4×C11—22no—
163C4×D4×C11—22no—
164C4×D4×C11—21no—
165C4×D4×C11—22no—
166C4×D4×C11—21no—
167C4×D4×C11—21no—
168C11×#117—21no—
169C11×#117C2311yescharacteristic
170C2×C11×C4⋊C4—21no—
171C2×C11×C4⋊C4—21no—
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×#103—21no—
196C11×#103—21no—
197C11×#102—21no—
198C11×#102—21no—
199C11×#102—21no—
200C11×#100—22no—
201C11×#100—41no—
202C11×C22⋊C8—21no—
203C11×C22⋊C8—21no—
204C11×#95—22no—
205C11×#95—22no—
206#24467C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—22no—
208C24×C11—21no—
209C24×C11C2×D411yescharacteristic
210C24×C11C2×D412yes—
211C11×#41—21no—
212C11×#41—21no—
213C11×#41—22no—
214C11×#41—22no—
215C11×#41—21no—
216C11×#41—21no—
217C11×#41—21no—
218C11×#41—21no—
219C11×#41—21no—
220C11×#41—21no—
221C11×#41—21no—
222C11×#41—21no—
223C11×#41—42no—
224C11×#41—42no—
225C11×#41—41no—
226C11×#41—41no—
227C11×#41—42no—
228C11×#41—42no—
229C11×#41—42no—
230C11×#41—42no—
231C11×#41—42no—
232C11×#41—42no—
233C11×#41C2×D412yes—
234C11×#41#4112yes—
235C2×Q8×C11—21no—
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—41no—
244C2×Q8×C11C2×D411yescharacteristic
245C2×Q8×C11C2×D411yescharacteristic
246C2×Q8×C11C2×D411yescharacteristic
247C2×D4×C11—21no—
248C2×D4×C11—22no—
249C2×D4×C11—22no—
250C2×D4×C11—22no—
251C2×D4×C11—22no—
252C2×D4×C11—21no—
253C2×D4×C11—21no—
254C2×D4×C11—21no—
255C2×D4×C11—21no—
256C2×D4×C11—21no—
257C2×D4×C11—22no—
258C2×D4×C11—22no—
259C2×D4×C11—22no—
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—41no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11—42no—
273C2×D4×C11—42no—
274C2×D4×C11—44no—
275C2×D4×C11—44no—
276C2×D4×C11—42no—
277C2×D4×C11—42no—
278C2×D4×C11—44no—
279C2×D4×C11—84no—
280C2×D4×C11C2×D411yescharacteristic
281C2×D4×C11C2×D411yescharacteristic
282C2×D4×C11C2×D411yescharacteristic
283C22×C4×C11—21no—
284C22×C4×C11—21no—
285C22×C4×C11—21no—
286C22×C4×C11—21no—
287C22×C4×C11—21no—
288C22×C4×C11—22no—
289C22×C4×C11—21no—
290C22×C4×C11—21no—
291C22×C4×C11—21no—
292C22×C4×C11—22no—
293C22×C4×C11—21no—
294C22×C4×C11—21no—
295C22×C4×C11—21no—
296C22×C4×C11—21no—
297C22×C4×C11—21no—
298C22×C4×C11—21no—
299C22×C4×C11—42no—
300C22×C4×C11—42no—
301C22×C4×C11—42no—
302C22×C4×C11—42no—
303C22×C4×C11—42no—
304C22×C4×C11C2×D411yescharacteristic
305C22×C4×C11C2×D411yescharacteristic
306C22×C4×C11C2×D411yescharacteristic
307C22×C4×C11C2×D411yescharacteristic
308C22×C4×C11C2×D411yescharacteristic
309C22×C4×C11C2×D412yes—
310C22×C4×C11C2411yescharacteristic
311C11×Q16—42no—
312C11×Q16—42no—
313C11×Q16—42no—
314C11×SD16—42no—
315C11×SD16—42no—
316C11×SD16—42no—
317C11×M16—21no—
318C11×M16—21no—
319C11×M16—21no—
320C11×M16—21no—
321C11×M16—21no—
322C11×M16—21no—
323C11×M16—21no—
324C11×M16—42no—
325C11×M16C2×D412yescomplemented
326C2×C8×C11—21no—
327C2×C8×C11—21no—
328C2×C8×C11—21no—
329C2×C8×C11—21no—
330C2×C8×C11—42no—
331C11×C4⋊C4—22no—
332C11×C4⋊C4—22no—
333C11×C4⋊C4—21no—
334C11×C4⋊C4—21no—
335C11×C4⋊C4—21no—
336C11×C4⋊C4—21no—
337C11×C4⋊C4—21no—
338C11×C4⋊C4—21no—
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—21no—
350C11×C22⋊C4—21no—
351C11×C22⋊C4—21no—
352C11×C22⋊C4—22no—
353C11×C22⋊C4—22no—
354C11×C22⋊C4—21no—
355C11×C22⋊C4—44no—
356C11×C22⋊C4—44no—
357C11×C22⋊C4—41no—
358C11×C22⋊C4—41no—
359C42×C11—22no—
360C42×C11—21no—
361C42×C11—21no—
362C42×C11—21no—
363C42×C11—21no—
364C42×C11—42no—
365C42×C11C2×D412yescomplemented
366#3488C2×C1111yescharacteristic
367#3056C2×C1111yescharacteristic, complemented
368C2×#455C2×C1111yescharacteristic, complemented
369#3007C2×C1111yescharacteristic, complemented
370C22×#104C2×C1111yescharacteristic, complemented
371#2850C2×C1111yescharacteristic, complemented
372#2040C2×C1111yescharacteristic, complemented
373#2037C2×C1111yescharacteristic, complemented
374#2007C2×C1111yescharacteristic, complemented
375#2004C2×C1111yescharacteristic, complemented
376#1900C2×C1111yescharacteristic, complemented
377#1896C2×C1111yescharacteristic, complemented
378#1882C2×C1111yescharacteristic, complemented
379#1860C2×C1111yescharacteristic, complemented
380#1792C2×C1111yescharacteristic, complemented
381C23×C11—21no—
382C23×C11—21no—
383C23×C11—21no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—21no—
387C23×C11—21no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—41no—
391C23×C11—42no—
392C23×C11—44no—
393C23×C11—42no—
394C23×C11—42no—
395C23×C11—42no—
396C23×C11—81no—
397C23×C11—82no—
398C23×C11—82no—
399C23×C11#12011yescharacteristic
400C23×C11#12011yescharacteristic
401C23×C11C22×D411yescharacteristic
402Q8×C11—21no—
403Q8×C11—21no—
404Q8×C11—21no—
405Q8×C11—21no—
406Q8×C11—21no—
407Q8×C11—42no—
408Q8×C11—41no—
409Q8×C11—41no—
410Q8×C11—41no—
411Q8×C11—41no—
412Q8×C11#12112yes—
413D4×C11—22no—
414D4×C11—22no—
415D4×C11—21no—
416D4×C11—21no—
417D4×C11—21no—
418D4×C11—21no—
419D4×C11—21no—
420D4×C11—42no—
421D4×C11—42no—
422D4×C11—44no—
423D4×C11—42no—
424D4×C11—44no—
425D4×C11—41no—
426D4×C11—41no—
427D4×C11—41no—
428D4×C11—41no—
429D4×C11—44no—
430D4×C11—42no—
431D4×C11—41no—
432D4×C11—41no—
433D4×C11—41no—
434D4×C11—41no—
435D4×C11—81no—
436D4×C11—82no—
437D4×C11—82no—
438D4×C11—82no—
439D4×C11—82no—
440D4×C11#12112yes—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—21no—
450C2×C4×C11—22no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—22no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—42no—
462C2×C4×C11—42no—
463C2×C4×C11—42no—
464C2×C4×C11—44no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—48no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—42no—
475C2×C4×C11—42no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—82no—
481C2×C4×C11#12011yescharacteristic
482C2×C4×C11#12011yescharacteristic
483C2×C4×C11C22×D411yescharacteristic
484C2×C4×C11C22×D411yescharacteristic
485C2×C4×C11C22×D411yescharacteristic
486C2×C4×C11C2×#4111yescharacteristic
487C2×C4×C11H(5,𝔽2)11yescharacteristic
488C2×C4×C11H(5,𝔽2)11yescharacteristic
489C8×C11—22no—
490C8×C11—41no—
491C8×C11—41no—
492C8×C11—41no—
493C2×H(5,𝔽2)C22×C1111yescharacteristic
494C22×#41C22×C1111yescharacteristic
495C2×#137C22×C1111yescharacteristic
496C2×#137C22×C1111yescharacteristic, complemented
497C2×#137C22×C1111yescharacteristic, complemented
498C22×M16C22×C1111yescharacteristic, complemented
499#550—21no—
500#548—21no—
501#546—21no—
502#546—22no—
503D42—22no—
504D42—21no—
505#537—21no—
506#537C22×C1111yescharacteristic
507#535—21no—
508#535C22×C1111yescharacteristic
509C2×#124C22×C1111yescharacteristic, complemented
510#525—21no—
511#525C22×C1111yescharacteristic
512C2×C22⋊Q8C22×C1111yescharacteristic, complemented
513C2×#121—21no—
514C2×#121C22×C1111yescharacteristic
515#520C22×C1111yescharacteristic
516C22×C42C22×C1111yescharacteristic, complemented
517#470—21no—
518#468—21no—
519#467—21no—
520#465—21no—
521#455—24no—
522#452—21no—
523#452—21no—
524#451—21no—
525#450—21no—
526#428C22×C1111yescharacteristic, complemented
527C2×#104—24no—
528C2×#104C22×C1111yescharacteristic
529C2×#104C22×C1111yescharacteristic
530C2×#104C22×C1111yescharacteristic, complemented
531C2×#104C22×C1111yescharacteristic, complemented
532C2×#104C22×C1111yescharacteristic, complemented
533C2×#104C22×C1111yescharacteristic, complemented
534#419C22×C1111yescharacteristic, complemented
535#417C22×C1111yescharacteristic
536#417C22×C1111yescharacteristic, complemented
537#417C22×C1111yescharacteristic, complemented
538C2×#100C22×C1111yescharacteristic, complemented
539C2×#100C22×C1111yescharacteristic, complemented
540#407C22×C1111yescharacteristic, complemented
541#391C22×C1111yescharacteristic, complemented
542#390C22×C1111yescharacteristic, complemented
543#388—22no—
544#386—22no—
545#382C22×C1111yescharacteristic, complemented
546#343C22×C1111yescharacteristic, complemented
547#343C22×C1111yescharacteristic, complemented
548#339C22×C1111yescharacteristic, complemented
549#339C22×C1111yescharacteristic, complemented
550C22×C11—21no—
551C22×C11—21no—
552C22×C11—21no—
553C22×C11—21no—
554C22×C11—21no—
555C22×C11—22no—
556C22×C11—21no—
557C22×C11—21no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—41no—
561C22×C11—41no—
562C22×C11—41no—
563C22×C11—41no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—41no—
567C22×C11—41no—
568C22×C11—41no—
569C22×C11—42no—
570C22×C11—41no—
571C22×C11—84no—
572C22×C11—82no—
573C22×C11—82no—
574C22×C11—164no—
575C22×C11#45512yescomplemented
576C22×C11C2×#12011yescharacteristic
577C22×C11D4211yescharacteristic
578C22×C11#54611yescharacteristic
579C4×C11—21no—
580C4×C11—21no—
581C4×C11—22no—
582C4×C11—42no—
583C4×C11—42no—
584C4×C11—41no—
585C4×C11—41no—
586C4×C11—42no—
587C4×C11—41no—
588C4×C11—41no—
589C4×C11—81no—
590C4×C11—81no—
591C4×C11C2×#12111yescharacteristic
592C4×C11#53411yescharacteristic
593C4×C11D4211yescharacteristic
594C4×C11#54611yescharacteristic
595H(5,𝔽2)—22no—
596H(5,𝔽2)—22no—
597H(5,𝔽2)—41no—
598H(5,𝔽2)—41no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—22no—
604C2×#41—22no—
605C2×#41—41no—
606C2×#41—41no—
607C2×#41D4×C1111yescharacteristic
608C2×#41D4×C1111yescharacteristic
609C2×#41C23×C1111yescharacteristic
610C2×#41C23×C1111yescharacteristic
611C2×#41C23×C1111yescharacteristic
612C22×Q8D4×C1111yescharacteristic
613C22×Q8C23×C1111yescharacteristic
614C22×D4—21no—
615C22×D4—22no—
616C22×D4—22no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C1111yescharacteristic
620C22×D4D4×C1112yes—
621C22×D4C23×C1111yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4C23×C1111yescharacteristic
625#137—22no—
626#137—22no—
627#137—22no—
628#137—41no—
629#137—41no—
630#137—41no—
631C2×Q16—21no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×SD16—21no—
637C2×M16—21no—
638C2×M16—22no—
639C2×M16—41no—
640C2×M16C23×C1111yescharacteristic
641C2×M16C23×C1111yescharacteristic
642C2×M16C23×C1111yescharacteristic
643C2×M16C23×C1111yescharacteristic
644C22×C8—21no—
645#127—22no—
646#127—21no—
647#124—22no—
648#124—21no—
649#124—22no—
650#124—41no—
651#123—22no—
652#123—21no—
653C22⋊Q8—22no—
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—22no—
666#121—22no—
667#121—21no—
668#121—21no—
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121D4×C1111yescharacteristic
677#121D4×C1111yescharacteristic
678#120—22no—
679#120—22no—
680#120—22no—
681#120—21no—
682#120—22no—
683C4×Q8—21no—
684C4×D4—22no—
685C4×D4—22no—
686C4×D4—21no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—21no—
690#117—21no—
691#117C23×C1111yescharacteristic
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4C23×C1111yescharacteristic
695C2×C4⋊C4C23×C1111yescharacteristic
696C2×C22⋊C4—22no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4D4×C1112yes—
701C2×C42—22no—
702C2×C42—21no—
703C2×C42—41no—
704C2×C42C23×C1111yescharacteristic
705C2×C42C23×C1111yescharacteristic
706#107—21no—
707#106—21no—
708#104—22no—
709#104—22no—
710#104—22no—
711#104—22no—
712#104—41no—
713#104D4×C1114yescomplemented
714#103—21no—
715#103—21no—
716#103—21no—
717#103—21no—
718#103—21no—
719#102—21no—
720#102—21no—
721#102—21no—
722#100—22no—
723#100—41no—
724C22⋊C8—21no—
725C22⋊C8—21no—
726#95—22no—
727#95—22no—
728C2×C11—21no—
729C2×C11—21no—
730C2×C11—22no—
731C2×C11—41no—
732C2×C11—42no—
733C2×C11—81no—
734C2×C11—82no—
735C2×C11—81no—
736C2×C11#241011yescharacteristic
737C2×C11C2×#45511yescharacteristic
738C2×C11#301811yescharacteristic
739C24—22no—
740C24—21no—
741C24C2×D4×C1111yescharacteristic
742C24C2×D4×C1112yes—
743#41—21no—
744#41—21no—
745#41—22no—
746#41—22no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—42no—
756#41—42no—
757#41—41no—
758#41—41no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41C2×D4×C1112yes—
766#41C11×#4112yes—
767C2×Q8—21no—
768C2×Q8—22no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—41no—
776C2×Q8C2×D4×C1111yescharacteristic
777C2×Q8C2×D4×C1111yescharacteristic
778C2×Q8C2×D4×C1111yescharacteristic
779C2×D4—21no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—41no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—44no—
811C2×D4—84no—
812C2×D4C2×D4×C1111yescharacteristic
813C2×D4C2×D4×C1111yescharacteristic
814C2×D4C2×D4×C1111yescharacteristic
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4C2×D4×C1111yescharacteristic
837C22×C4C2×D4×C1111yescharacteristic
838C22×C4C2×D4×C1111yescharacteristic
839C22×C4C2×D4×C1111yescharacteristic
840C22×C4C2×D4×C1111yescharacteristic
841C22×C4C2×D4×C1112yes—
842C22×C4C24×C1111yescharacteristic
843Q16—42no—
844Q16—42no—
845Q16—42no—
846SD16—42no—
847SD16—42no—
848SD16—42no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—42no—
857M16C2×D4×C1112yescomplemented
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—42no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4C2×D4×C1111yescharacteristic
874C4⋊C4C2×D4×C1111yescharacteristic
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—22no—
885C22⋊C4—22no—
886C22⋊C4—21no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—41no—
890C22⋊C4—41no—
891C42—22no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—42no—
897C42C2×D4×C1112yescomplemented
898C11#2446711yescharacteristic, direct product factor, Sylow
899C23—21no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23C11×#12011yescharacteristic
918C23C11×#12011yescharacteristic
919C23C22×D4×C1111yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8C11×#12112yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—44no—
948D4—42no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—81no—
954D4—82no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4C11×#12112yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4C11×#12011yescharacteristic
1000C2×C4C11×#12011yescharacteristic
1001C2×C4C22×D4×C1111yescharacteristic
1002C2×C4C22×D4×C1111yescharacteristic
1003C2×C4C22×D4×C1111yescharacteristic
1004C2×C4C2×C11×#4111yescharacteristic
1005C2×C4C11×H(5,𝔽2)11yescharacteristic
1006C2×C4C11×H(5,𝔽2)11yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C11×#45512yescomplemented
1037C22C2×C11×#12011yescharacteristic
1038C22D42×C1111yescharacteristic
1039C22C11×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×C11×#12111yescharacteristic
1053C4C11×#53411yescharacteristic
1054C4D42×C1111yescharacteristic
1055C4C11×#54611yescharacteristic
1056C2—21no—
1057C2—21no—
1058C2—22no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C11×#241011yescharacteristic
1065C2C2×C11×#45511yescharacteristic
1066C2C11×#301811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3488C2
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×#455C2semidirect
4. C11×#3007C2semidirect
5. C22×C11×#104C2semidirect
6. C11×#2850C2semidirect
7. C11×#2040C2semidirect
8. C11×#2037C2semidirect
9. C11×#2007C2semidirect
10. C11×#2004C2semidirect
11. C11×#1900C2semidirect
12. C11×#1896C2semidirect
13. C11×#1882C2semidirect
14. C11×#1860C2semidirect
15. C11×#1792C2semidirect
19. C2×C11×#137C22semidirect
20. C2×C11×#137C22semidirect
21. C22×C11×M16C22semidirect
32. C2×C11×#124C22semidirect
35. C2×C11×C22⋊Q8C22semidirect
39. C22×C42×C11C22semidirect
49. C11×#428C22semidirect
53. C2×C11×#104C22semidirect
54. C2×C11×#104C22semidirect
55. C2×C11×#104C22semidirect
56. C2×C11×#104C22semidirect
57. C11×#419C22semidirect
59. C11×#417C22semidirect
60. C11×#417C22semidirect
61. C2×C11×#100C22semidirect
62. C2×C11×#100C22semidirect
63. C11×#407C22semidirect
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. #24467C11direct (N × H)
325. C11×M16C2×D4semidirect
365. C42×C11C2×D4semidirect
367. #3056C2×C11semidirect
368. C2×#455C2×C11semidirect
369. #3007C2×C11semidirect
370. C22×#104C2×C11semidirect
371. #2850C2×C11semidirect
372. #2040C2×C11semidirect
373. #2037C2×C11semidirect
374. #2007C2×C11semidirect
375. #2004C2×C11semidirect
376. #1900C2×C11semidirect
377. #1896C2×C11semidirect
378. #1882C2×C11semidirect
379. #1860C2×C11semidirect
380. #1792C2×C11semidirect
496. C2×#137C22×C11semidirect
497. C2×#137C22×C11semidirect
498. C22×M16C22×C11semidirect
509. C2×#124C22×C11semidirect
512. C2×C22⋊Q8C22×C11semidirect
516. C22×C42C22×C11semidirect
526. #428C22×C11semidirect
530. C2×#104C22×C11semidirect
531. C2×#104C22×C11semidirect
532. C2×#104C22×C11semidirect
533. C2×#104C22×C11semidirect
534. #419C22×C11semidirect
536. #417C22×C11semidirect
537. #417C22×C11semidirect
538. C2×#100C22×C11semidirect
539. C2×#100C22×C11semidirect
540. #407C22×C11semidirect
541. #391C22×C11semidirect
542. #390C22×C11semidirect
545. #382C22×C11semidirect
546. #343C22×C11semidirect
547. #343C22×C11semidirect
548. #339C22×C11semidirect
549. #339C22×C11semidirect
575. C22×C11#455semidirect
713. #104D4×C11semidirect
857. M16C2×D4×C11semidirect
897. C42C2×D4×C11semidirect
898. C11#24467direct (N × H)
1036. C22C11×#455semidirect

Maximal subgroups

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

subgroupindex
C11×#34882
C11×#30562
C2×C11×#4552
C11×#30072
C22×C11×#1042
C11×#28502
C11×#20402
C11×#20372
C11×#20072
C11×#20042
C11×#19002
C11×#18962
C11×#18822
C11×#18602
C11×#17922
#2446711