Finite Group Databasebeta

← C11×#24368 #14601561

Subgroups — C11×#24368 #14601561

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic, complemented
2C2×C11×#464C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic, complemented
4C2×C11×#448C211yesmaximal, characteristic, complemented
5C11×#2431C211yesmaximal, characteristic
6Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
7C11×#2056C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#2015C211yesmaximal, characteristic, complemented
10C11×#2014C211yesmaximal, characteristic, complemented
11C11×#1895C211yesmaximal, characteristic, complemented
12C11×#1880C211yesmaximal, characteristic, complemented
13C11×#1878C211yesmaximal, characteristic, complemented
14C11×#1851C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C2×C11×#137—24no—
19C2×C11×#137—24no—
20C2×C11×#137—24no—
21C22×C11×Q16C2211yescharacteristic
22C22×C11×Q16C2211yescharacteristic
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×SD16C2211yescharacteristic
26C22×C11×SD16C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic
28C2×C11×#127C2211yescharacteristic
29C2×C11×#124C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C4×Q8×C11C2211yescharacteristic
32C2×C4×Q8×C11C2211yescharacteristic
33C11×#464—24no—
34C11×#460—24no—
35C11×#448—24no—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C11×#392—21no—
48C11×#392—21no—
49C11×#391—21no—
50C11×#391—21no—
51C11×#391C2211yescharacteristic
52C11×#391C2211yescharacteristic
53C11×#391C2211yescharacteristic
54C11×#390C2211yescharacteristic
55C11×#386—21no—
56C11×#386—21no—
57C11×#380—21no—
58C11×#380C2211yescharacteristic
59C4×C11×C22⋊C4—21no—
60C4×C11×C22⋊C4C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C22×Q8×C11—21no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—22no—
75C22×Q8×C11—41no—
76C22×Q8×C11—41no—
77C22×Q8×C11D414yescomplemented
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11—21no—
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11—21no—
89C23×C4×C11C2311yescharacteristic
90C11×#137—232no—
91C2×C11×Q16—22no—
92C2×C11×Q16—22no—
93C2×C11×Q16—22no—
94C2×C11×Q16—22no—
95C2×C11×Q16—22no—
96C2×C11×Q16D414yescomplemented
97C2×C11×SD16—22no—
98C2×C11×SD16—22no—
99C2×C11×SD16—22no—
100C2×C11×SD16—22no—
101C2×C11×SD16—22no—
102C2×C11×SD16—22no—
103C2×C11×SD16—22no—
104C2×C11×SD16—22no—
105C2×C11×SD16—22no—
106C2×C11×SD16—41no—
107C2×C11×SD16—41no—
108C2×C11×SD16D414yescomplemented
109C2×C11×M16—22no—
110C2×C11×M16—22no—
111C2×C11×M16—22no—
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C22×C8×C11C2311yescharacteristic
115C22×C8×C11C2311yescharacteristic
116C11×#127—22no—
117C11×#127—41no—
118C11×#124—22no—
119C11×#124—41no—
120C11×#121—22no—
121C11×#121—22no—
122C4×Q8×C11—22no—
123C4×Q8×C11—22no—
124C4×Q8×C11—41no—
125C4×Q8×C11—41no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4D411yescharacteristic
138C2×C11×C22⋊C4D411yescharacteristic
139C2×C42×C11—21no—
140C2×C42×C11—21no—
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2311yescharacteristic
143C11×C4⋊C8—22no—
144C11×C4⋊C8—22no—
145C11×#103—22no—
146C11×#103—22no—
147C11×#103—22no—
148C11×#103—41no—
149C11×#102—22no—
150C11×#102—22no—
151C11×#102—22no—
152C11×#102—41no—
153C11×C22⋊C8—22no—
154C11×#95—21no—
155C11×#95—21no—
156C11×#95—21no—
157C11×#95—21no—
158C11×#95—21no—
159C11×#95—21no—
160C11×#95—21no—
161C11×#95D411yescharacteristic
162C11×#95D411yescharacteristic
163#24368C1111yesmaximal, characteristic, direct product factor, Sylow
164C24×C11—21no—
165C24×C11—21no—
166C24×C11C2×D411yescharacteristic
167C11×#41—28no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—44no—
171C2×Q8×C11—24no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—28no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—42no—
187C2×Q8×C11—42no—
188C2×Q8×C11—44no—
189C2×Q8×C11—44no—
190C2×Q8×C11—44no—
191C2×Q8×C11C2×D412yes—
192C2×Q8×C11C2×D412yes—
193C2×Q8×C11C2×D412yes—
194C2×Q8×C11C2×D412yes—
195C2×Q8×C11C2×D412yes—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—42no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—81no—
216C2×D4×C11—81no—
217C2×D4×C11—81no—
218C2×D4×C11—81no—
219C2×D4×C11C2×D412yes—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—24no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—42no—
232C22×C4×C11—42no—
233C22×C4×C11—42no—
234C22×C4×C11—42no—
235C22×C4×C11—42no—
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11#4112yes—
243C22×C4×C11C2411yescharacteristic
244C11×Q16—28no—
245C11×Q16—28no—
246C11×SD16—28no—
247C11×SD16—28no—
248C11×SD16—44no—
249C11×SD16—44no—
250C11×M16—28no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11C2×D412yes—
262C2×C8×C11C2×D412yes—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—42no—
270C11×C4⋊C4—42no—
271C11×C22⋊C4—22no—
272C11×C22⋊C4—41no—
273C11×C22⋊C4—42no—
274C11×C22⋊C4—42no—
275C11×C22⋊C4—42no—
276C11×C22⋊C4—42no—
277C11×C22⋊C4—81no—
278C11×C22⋊C4—81no—
279C42×C11—21no—
280C42×C11—21no—
281C42×C11—21no—
282C42×C11—21no—
283C42×C11—42no—
284C42×C11—42no—
285C22×#137C2×C1111yescharacteristic, complemented
286C2×#464C2×C1111yescharacteristic, complemented
287C2×#460C2×C1111yescharacteristic, complemented
288C2×#448C2×C1111yescharacteristic, complemented
289#2431C2×C1111yescharacteristic
290Q8×C22⋊C4C2×C1111yescharacteristic, complemented
291#2056C2×C1111yescharacteristic, complemented
292#2055C2×C1111yescharacteristic, complemented
293#2015C2×C1111yescharacteristic, complemented
294#2014C2×C1111yescharacteristic, complemented
295#1895C2×C1111yescharacteristic, complemented
296#1880C2×C1111yescharacteristic, complemented
297#1878C2×C1111yescharacteristic, complemented
298#1851C2×C1111yescharacteristic, complemented
299#1788C2×C1111yescharacteristic, complemented
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—22no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11#12112yes—
321C23×C11C22×D411yescharacteristic
322Q8×C11—22no—
323Q8×C11—22no—
324Q8×C11—22no—
325Q8×C11—22no—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—48no—
330Q8×C11—41no—
331Q8×C11—41no—
332Q8×C11—41no—
333Q8×C11—41no—
334Q8×C11#12014yes—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—48no—
338D4×C11—41no—
339D4×C11—41no—
340D4×C11—41no—
341D4×C11—41no—
342D4×C11—41no—
343D4×C11—41no—
344D4×C11—84no—
345D4×C11—84no—
346D4×C11—84no—
347C2×C4×C11—22no—
348C2×C4×C11—21no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—22no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—48no—
370C2×C4×C11—48no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11#12112yes—
385C2×C4×C11#13712yescomplemented
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C2×#4111yescharacteristic
390C2×C4×C11H(5,𝔽2)11yescharacteristic
391C2×C4×C11H(5,𝔽2)11yescharacteristic
392C8×C11—22no—
393C8×C11—22no—
394C8×C11—41no—
395C8×C11—41no—
396C22×#41C22×C1111yescharacteristic
397C23×Q8C22×C1111yescharacteristic
398C2×#137—24no—
399C2×#137—24no—
400C2×#137—24no—
401C22×Q16C22×C1111yescharacteristic
402C22×Q16C22×C1111yescharacteristic
403C22×SD16C22×C1111yescharacteristic
404C22×SD16C22×C1111yescharacteristic
405C22×SD16C22×C1111yescharacteristic
406C22×SD16C22×C1111yescharacteristic
407C22×M16C22×C1111yescharacteristic
408C2×#127C22×C1111yescharacteristic
409C2×#124C22×C1111yescharacteristic
410C2×#121C22×C1111yescharacteristic
411C2×C4×Q8C22×C1111yescharacteristic
412C2×C4×Q8C22×C1111yescharacteristic
413#464—24no—
414#460—24no—
415#448—24no—
416C2×C4⋊C8C22×C1111yescharacteristic
417C2×C4⋊C8C22×C1111yescharacteristic
418C2×#103C22×C1111yescharacteristic
419C2×#103C22×C1111yescharacteristic
420C2×#103C22×C1111yescharacteristic
421C2×#103C22×C1111yescharacteristic
422C2×#102C22×C1111yescharacteristic
423C2×#102C22×C1111yescharacteristic
424C2×#102C22×C1111yescharacteristic
425C2×#102C22×C1111yescharacteristic
426C2×C22⋊C8C22×C1111yescharacteristic
427#392—21no—
428#392—21no—
429#391—21no—
430#391—21no—
431#391C22×C1111yescharacteristic
432#391C22×C1111yescharacteristic
433#391C22×C1111yescharacteristic
434#390C22×C1111yescharacteristic
435#386—21no—
436#386—21no—
437#380—21no—
438#380C22×C1111yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4C22×C1111yescharacteristic
441#340C22×C1111yescharacteristic
442#340C22×C1111yescharacteristic
443#336C22×C1111yescharacteristic
444#336C22×C1111yescharacteristic
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11C2×#12111yescharacteristic
467C22×C11D4211yescharacteristic
468C22×C11D4211yescharacteristic
469C22×C11C2×#13711yescharacteristic
470C22×C11#57511yescharacteristic
471C22×C11#57711yescharacteristic
472C22×C11#57711yescharacteristic
473C4×C11—22no—
474C4×C11—24no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—41no—
479C4×C11—41no—
480C4×C11—41no—
481C4×C11—81no—
482C4×C11—81no—
483C4×C11—81no—
484C4×C11C2×#12011yescharacteristic
485C4×C11#53411yescharacteristic
486C4×C11#54611yescharacteristic
487C4×C11#54611yescharacteristic
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8—21no—
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—22no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8D4×C1114yescomplemented
501C22×Q8C23×C1111yescharacteristic
502C22×Q8C23×C1111yescharacteristic
503C22×Q8C23×C1111yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4C23×C1111yescharacteristic
509C22×D4C23×C1111yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C23×C1111yescharacteristic
513#137—232no—
514C2×Q16—22no—
515C2×Q16—22no—
516C2×Q16—22no—
517C2×Q16—22no—
518C2×Q16—22no—
519C2×Q16D4×C1114yescomplemented
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16D4×C1114yescomplemented
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—22no—
535C22×C8C23×C1111yescharacteristic
536C22×C8C23×C1111yescharacteristic
537C22×C8C23×C1111yescharacteristic
538C22×C8C23×C1111yescharacteristic
539#127—22no—
540#127—41no—
541#124—22no—
542#124—41no—
543#121—22no—
544#121—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—41no—
548C4×Q8—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4C23×C1111yescharacteristic
552C2×C4⋊C4C23×C1111yescharacteristic
553C2×C4⋊C4C23×C1111yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4D4×C1111yescharacteristic
561C2×C22⋊C4D4×C1111yescharacteristic
562C2×C42—21no—
563C2×C42—21no—
564C2×C42C23×C1111yescharacteristic
565C2×C42C23×C1111yescharacteristic
566C4⋊C8—22no—
567C4⋊C8—22no—
568#103—22no—
569#103—22no—
570#103—22no—
571#103—41no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576C22⋊C8—22no—
577#95—21no—
578#95—21no—
579#95—21no—
580#95—21no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95D4×C1111yescharacteristic
585#95D4×C1111yescharacteristic
586C2×C11—42no—
587C2×C11—82no—
588C2×C11—161no—
589C2×C11#241011yescharacteristic
590C2×C11#303711yescharacteristic
591C2×C11#304311yescharacteristic
592C2×C11#326611yescharacteristic
593C2×C11#327111yescharacteristic
594C2×C11#327511yescharacteristic
595C2×C11#327811yescharacteristic
596C24—21no—
597C24—21no—
598C24C2×D4×C1111yescharacteristic
599#41—28no—
600#41—44no—
601#41—44no—
602#41—44no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—28no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—42no—
619C2×Q8—42no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8C2×D4×C1112yes—
624C2×Q8C2×D4×C1112yes—
625C2×Q8C2×D4×C1112yes—
626C2×Q8C2×D4×C1112yes—
627C2×Q8C2×D4×C1112yes—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4—81no—
650C2×D4—81no—
651C2×D4C2×D4×C1112yes—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C2×D4×C1111yescharacteristic
669C22×C4C2×D4×C1111yescharacteristic
670C22×C4C2×D4×C1111yescharacteristic
671C22×C4C2×D4×C1111yescharacteristic
672C22×C4C2×D4×C1112yes—
673C22×C4C2×D4×C1111yescharacteristic
674C22×C4C11×#4112yes—
675C22×C4C24×C1111yescharacteristic
676Q16—28no—
677Q16—28no—
678SD16—28no—
679SD16—28no—
680SD16—44no—
681SD16—44no—
682M16—28no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8C2×D4×C1112yes—
694C2×C8C2×D4×C1112yes—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C22⋊C4—22no—
704C22⋊C4—41no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—42no—
716C42—42no—
717C11#2436811yescharacteristic, direct product factor, Sylow
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23C11×#12112yes—
739C23C22×D4×C1111yescharacteristic
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—22no—
744Q8—22no—
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752Q8C11×#12014yes—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763D4—84no—
764D4—84no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—48no—
788C2×C4—48no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4C11×#12112yes—
803C2×C4C11×#13712yescomplemented
804C2×C4C22×D4×C1111yescharacteristic
805C2×C4C22×D4×C1111yescharacteristic
806C2×C4C22×D4×C1111yescharacteristic
807C2×C4C2×C11×#4111yescharacteristic
808C2×C4C11×H(5,𝔽2)11yescharacteristic
809C2×C4C11×H(5,𝔽2)11yescharacteristic
810C8—22no—
811C8—22no—
812C8—41no—
813C8—41no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22C2×C11×#12111yescharacteristic
836C22D42×C1111yescharacteristic
837C22D42×C1111yescharacteristic
838C22C2×C11×#13711yescharacteristic
839C22C11×#57511yescharacteristic
840C22C11×#57711yescharacteristic
841C22C11×#57711yescharacteristic
842C4—22no—
843C4—24no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4C2×C11×#12011yescharacteristic
854C4C11×#53411yescharacteristic
855C4C11×#54611yescharacteristic
856C4C11×#54611yescharacteristic
857C2—42no—
858C2—82no—
859C2—161no—
860C2C11×#241011yescharacteristic
861C2C11×#303711yescharacteristic
862C2C11×#304311yescharacteristic
863C2C11×#326611yescharacteristic
864C2C11×#327111yescharacteristic
865C2C11×#327511yescharacteristic
866C2C11×#327811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2431C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#137C2semidirect
2. C2×C11×#464C2semidirect
3. C2×C11×#460C2semidirect
4. C2×C11×#448C2semidirect
6. Q8×C11×C22⋊C4C2semidirect
7. C11×#2056C2semidirect
8. C11×#2055C2semidirect
9. C11×#2015C2semidirect
10. C11×#2014C2semidirect
11. C11×#1895C2semidirect
12. C11×#1880C2semidirect
13. C11×#1878C2semidirect
14. C11×#1851C2semidirect
15. C11×#1788C2semidirect
77. C22×Q8×C11D4semidirect
96. C2×C11×Q16D4semidirect
108. C2×C11×SD16D4semidirect
163. #24368C11direct (N × H)
285. C22×#137C2×C11semidirect
286. C2×#464C2×C11semidirect
287. C2×#460C2×C11semidirect
288. C2×#448C2×C11semidirect
290. Q8×C22⋊C4C2×C11semidirect
291. #2056C2×C11semidirect
292. #2055C2×C11semidirect
293. #2015C2×C11semidirect
294. #2014C2×C11semidirect
295. #1895C2×C11semidirect
296. #1880C2×C11semidirect
297. #1878C2×C11semidirect
298. #1851C2×C11semidirect
299. #1788C2×C11semidirect
385. C2×C4×C11#137semidirect
500. C22×Q8D4×C11semidirect
519. C2×Q16D4×C11semidirect
531. C2×SD16D4×C11semidirect
717. C11#24368direct (N × H)
803. C2×C4C11×#137semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C2×C11×#4642
C2×C11×#4602
C2×C11×#4482
C11×#24312
Q8×C11×C22⋊C42
C11×#20562
C11×#20552
C11×#20152
C11×#20142
C11×#18952
C11×#18802
C11×#18782
C11×#18512
C11×#17882
#2436811