Finite Group Databasebeta

← C11×#24449 #14601642

Subgroups — C11×#24449 #14601642

Order 2816.

1452 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#548C211yesmaximal, characteristic
2C2×C11×#470C211yesmaximal, characteristic, complemented
3C2×C11×#452C211yesmaximal, characteristic, complemented
4C2×C11×#451C211yesmaximal, characteristic, complemented
5C2×C11×#417C211yesmaximal, characteristic, complemented
6C11×#2417C211yesmaximal, characteristic, complemented
7C11×#2042C211yesmaximal, characteristic, complemented
8C11×#2034C211yesmaximal, characteristic, complemented
9C11×#2015C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1872C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic, complemented
14C11×#1865C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#548—24no—
23C11×#548—24no—
24C2×C11×#124—21no—
25C2×C11×#124C2211yescharacteristic
26C2×C11×C22⋊Q8—21no—
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#121—21no—
31C2×C11×#121C2211yescharacteristic
32C2×C4×Q8×C11C2211yescharacteristic
33C2×C4×D4×C11—21no—
34C2×C4×D4×C11C2211yescharacteristic
35C22×C11×C4⋊C4C2211yescharacteristic
36C11×#470—24no—
37C11×#452—24no—
38C11×#451—24no—
39C2×C11×#106C2211yescharacteristic
40C11×#417—24no—
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#398—21no—
55C11×#396—21no—
56C11×#391C2211yescharacteristic
57C11×#389C2211yescharacteristic
58C11×#386—21no—
59C11×#380—21no—
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41D414yes—
71C22×Q8×C11—22no—
72C22×Q8×C11—22no—
73C22×Q8×C11—21no—
74C22×Q8×C11—22no—
75C22×Q8×C11—22no—
76C22×Q8×C11—41no—
77C22×Q8×C11—41no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11D411yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C2×C11×Q16—22no—
91C2×C11×Q16—22no—
92C2×C11×Q16—22no—
93C2×C11×Q16—22no—
94C2×C11×Q16—22no—
95C2×C11×Q16—41no—
96C2×C11×SD16—22no—
97C2×C11×SD16—41no—
98C2×C11×SD16—41no—
99C2×C11×M16—22no—
100C2×C11×M16—22no—
101C2×C11×M16—41no—
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#124—28no—
107C11×#124—22no—
108C11×#124—22no—
109C11×C22⋊Q8—28no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—41no—
115C11×C22⋊Q8D414yes—
116C11×#121—28no—
117C11×#121—22no—
118C11×#121—22no—
119C4×Q8×C11—22no—
120C4×Q8×C11—22no—
121C4×D4×C11—28no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—22no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—41no—
132C2×C11×C4⋊C4D411yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—21no—
144C2×C11×C22⋊C4D411yescharacteristic
145C2×C11×C22⋊C4D411yescharacteristic
146C2×C42×C11—21no—
147C2×C42×C11C2311yescharacteristic
148C11×#106—22no—
149C11×#103—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—41no—
155C11×#103D414yescomplemented
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—22no—
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—41no—
162C11×#95—21no—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24449C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11C2×D411yescharacteristic
169C24×C11C2×D411yescharacteristic
170C11×#41—28no—
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—44no—
174C2×Q8×C11—24no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
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—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—42no—
190C2×Q8×C11—42no—
191C2×Q8×C11—44no—
192C2×Q8×C11—44no—
193C2×Q8×C11—44no—
194C2×Q8×C11—44no—
195C2×Q8×C11C2×D412yes—
196C2×Q8×C11C2×D412yes—
197C2×Q8×C11C2×D412yes—
198C2×Q8×C11#4112yes—
199C2×D4×C11—24no—
200C2×D4×C11—22no—
201C2×D4×C11—24no—
202C2×D4×C11—22no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—41no—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11C2×D412yes—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—24no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—24no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—42no—
234C22×C4×C11—42no—
235C22×C4×C11—42no—
236C22×C4×C11—42no—
237C22×C4×C11—42no—
238C22×C4×C11—42no—
239C22×C4×C11—81no—
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2411yescharacteristic
247C11×Q16—44no—
248C11×Q16—44no—
249C11×SD16—44no—
250C11×M16—44no—
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×C11—21no—
262C2×C8×C11C2×D412yes—
263C11×C4⋊C4—24no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4—22no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—42no—
273C11×C4⋊C4—42no—
274C11×C4⋊C4—42no—
275C11×C4⋊C4—81no—
276C11×C4⋊C4C2×D412yes—
277C11×C4⋊C4C2×D412yes—
278C11×C22⋊C4—24no—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—22no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—42no—
285C11×C22⋊C4—42no—
286C11×C22⋊C4—81no—
287C42×C11—24no—
288C42×C11—21no—
289C42×C11—21no—
290C2×#548C2×C1111yescharacteristic
291C2×#470C2×C1111yescharacteristic, complemented
292C2×#452C2×C1111yescharacteristic, complemented
293C2×#451C2×C1111yescharacteristic, complemented
294C2×#417C2×C1111yescharacteristic, complemented
295#2417C2×C1111yescharacteristic, complemented
296#2042C2×C1111yescharacteristic, complemented
297#2034C2×C1111yescharacteristic, complemented
298#2015C2×C1111yescharacteristic, complemented
299#2000C2×C1111yescharacteristic, complemented
300#1878C2×C1111yescharacteristic, complemented
301#1872C2×C1111yescharacteristic, complemented
302#1870C2×C1111yescharacteristic, complemented
303#1865C2×C1111yescharacteristic, complemented
304#1787C2×C1111yescharacteristic, complemented
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—22no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11#12012yes—
325C23×C11#13712yes—
326C23×C11C22×D411yescharacteristic
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—48no—
333Q8×C11—41no—
334Q8×C11—41no—
335Q8×C11—41no—
336Q8×C11—41no—
337Q8×C11—41no—
338Q8×C11—41no—
339Q8×C11#12114yes—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—48no—
343D4×C11—44no—
344D4×C11—48no—
345D4×C11—41no—
346D4×C11—41no—
347C2×C4×C11—22no—
348C2×C4×C11—21no—
349C2×C4×C11—22no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—21no—
361C2×C4×C11—22no—
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—48no—
369C2×C4×C11—48no—
370C2×C4×C11—41no—
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—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—84no—
390C2×C4×C11#12012yes—
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C2×#4111yescharacteristic
395C2×C4×C11H(5,𝔽2)11yescharacteristic
396C2×C4×C11H(5,𝔽2)11yescharacteristic
397C8×C11—22no—
398C8×C11—41no—
399C8×C11—41no—
400C8×C11—41no—
401C22×#41C22×C1111yescharacteristic
402C23×Q8C22×C1111yescharacteristic
403C22×Q16C22×C1111yescharacteristic
404C22×Q16C22×C1111yescharacteristic
405C22×SD16C22×C1111yescharacteristic
406C22×M16C22×C1111yescharacteristic
407#548—24no—
408#548—24no—
409C2×#124—21no—
410C2×#124C22×C1111yescharacteristic
411C2×C22⋊Q8—21no—
412C2×C22⋊Q8C22×C1111yescharacteristic
413C2×C22⋊Q8C22×C1111yescharacteristic
414C2×C22⋊Q8C22×C1111yescharacteristic
415C2×#121—21no—
416C2×#121C22×C1111yescharacteristic
417C2×C4×Q8C22×C1111yescharacteristic
418C2×C4×D4—21no—
419C2×C4×D4C22×C1111yescharacteristic
420C22×C4⋊C4C22×C1111yescharacteristic
421#470—24no—
422#452—24no—
423#451—24no—
424C2×#106C22×C1111yescharacteristic
425#417—24no—
426C2×#103C22×C1111yescharacteristic
427C2×#103C22×C1111yescharacteristic
428C2×#103C22×C1111yescharacteristic
429C2×#103C22×C1111yescharacteristic
430C2×#103C22×C1111yescharacteristic
431C2×#103C22×C1111yescharacteristic
432C2×#103C22×C1111yescharacteristic
433C2×#102C22×C1111yescharacteristic
434C2×#102C22×C1111yescharacteristic
435C2×#102C22×C1111yescharacteristic
436C2×C22⋊C8C22×C1111yescharacteristic
437C2×C22⋊C8C22×C1111yescharacteristic
438C2×C22⋊C8C22×C1111yescharacteristic
439#398—21no—
440#396—21no—
441#391C22×C1111yescharacteristic
442#389C22×C1111yescharacteristic
443#386—21no—
444#380—21no—
445#380C22×C1111yescharacteristic
446#340C22×C1111yescharacteristic
447#340C22×C1111yescharacteristic
448#336C22×C1111yescharacteristic
449#336C22×C1111yescharacteristic
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11—41no—
463C22×C11—41no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11—81no—
471C22×C11C2×#12011yescharacteristic
472C22×C11D4211yescharacteristic
473C22×C11#54611yescharacteristic
474C22×C11C2×#13711yescharacteristic
475C22×C11#57511yescharacteristic
476C22×C11#57711yescharacteristic
477C22×C11#57811yescharacteristic
478C4×C11—22no—
479C4×C11—24no—
480C4×C11—41no—
481C4×C11—42no—
482C4×C11—41no—
483C4×C11—42no—
484C4×C11—41no—
485C4×C11—42no—
486C4×C11—81no—
487C4×C11—81no—
488C4×C11—81no—
489C4×C11C2×#12111yescharacteristic
490C4×C11#53411yescharacteristic
491C4×C11D4211yescharacteristic
492C4×C11#54611yescharacteristic
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41D4×C1114yes—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—21no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8C23×C1111yescharacteristic
507C22×Q8C23×C1111yescharacteristic
508C22×Q8C23×C1111yescharacteristic
509C22×D4—21no—
510C22×D4—21no—
511C22×D4D4×C1111yescharacteristic
512C22×D4C23×C1111yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C23×C1111yescharacteristic
517C23×C4C23×C1111yescharacteristic
518C2×Q16—22no—
519C2×Q16—22no—
520C2×Q16—22no—
521C2×Q16—22no—
522C2×Q16—22no—
523C2×Q16—41no—
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—41no—
530C22×C8C23×C1111yescharacteristic
531C22×C8C23×C1111yescharacteristic
532C22×C8C23×C1111yescharacteristic
533C22×C8C23×C1111yescharacteristic
534#124—28no—
535#124—22no—
536#124—22no—
537C22⋊Q8—28no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—41no—
543C22⋊Q8D4×C1114yes—
544#121—28no—
545#121—22no—
546#121—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×D4—28no—
550C4×D4—22no—
551C4×D4—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4D4×C1111yescharacteristic
561C2×C4⋊C4C23×C1111yescharacteristic
562C2×C4⋊C4C23×C1111yescharacteristic
563C2×C4⋊C4C23×C1111yescharacteristic
564C2×C4⋊C4C23×C1111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4D4×C1111yescharacteristic
573C2×C22⋊C4D4×C1111yescharacteristic
574C2×C42—21no—
575C2×C42C23×C1111yescharacteristic
576#106—22no—
577#103—22no—
578#103—22no—
579#103—22no—
580#103—22no—
581#103—22no—
582#103—41no—
583#103D4×C1114yescomplemented
584#102—22no—
585#102—22no—
586#102—22no—
587C22⋊C8—22no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590#95—21no—
591#95—21no—
592#95—21no—
593#95—21no—
594C2×C11—42no—
595C2×C11—42no—
596C2×C11—82no—
597C2×C11#241011yescharacteristic
598C2×C11#300711yescharacteristic
599C2×C11#301311yescharacteristic
600C2×C11#327011yescharacteristic
601C2×C11#327511yescharacteristic
602C2×C11#331611yescharacteristic
603C2×C11#332711yescharacteristic
604C24—21no—
605C24C2×D4×C1111yescharacteristic
606C24C2×D4×C1111yescharacteristic
607#41—28no—
608#41—44no—
609#41—44no—
610#41—44no—
611C2×Q8—24no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—42no—
627C2×Q8—42no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—44no—
631C2×Q8—44no—
632C2×Q8C2×D4×C1112yes—
633C2×Q8C2×D4×C1112yes—
634C2×Q8C2×D4×C1112yes—
635C2×Q8C11×#4112yes—
636C2×D4—24no—
637C2×D4—22no—
638C2×D4—24no—
639C2×D4—22no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4C2×D4×C1112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—24no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—81no—
677C22×C4C2×D4×C1111yescharacteristic
678C22×C4C2×D4×C1111yescharacteristic
679C22×C4C2×D4×C1111yescharacteristic
680C22×C4C2×D4×C1111yescharacteristic
681C22×C4C2×D4×C1112yes—
682C22×C4C2×D4×C1112yes—
683C22×C4C24×C1111yescharacteristic
684Q16—44no—
685Q16—44no—
686SD16—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C1112yes—
700C4⋊C4—24no—
701C4⋊C4—24no—
702C4⋊C4—22no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—81no—
713C4⋊C4C2×D4×C1112yes—
714C4⋊C4C2×D4×C1112yes—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—81no—
724C42—24no—
725C42—21no—
726C42—21no—
727C11#2444911yescharacteristic, direct product factor, Sylow
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23C11×#12012yes—
748C23C11×#13712yes—
749C23C22×D4×C1111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—22no—
755Q8—48no—
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760Q8—41no—
761Q8—41no—
762Q8C11×#12114yes—
763D4—22no—
764D4—22no—
765D4—48no—
766D4—44no—
767D4—48no—
768D4—41no—
769D4—41no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—48no—
792C2×C4—48no—
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×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—84no—
813C2×C4C11×#12012yes—
814C2×C4C22×D4×C1111yescharacteristic
815C2×C4C22×D4×C1111yescharacteristic
816C2×C4C22×D4×C1111yescharacteristic
817C2×C4C2×C11×#4111yescharacteristic
818C2×C4C11×H(5,𝔽2)11yescharacteristic
819C2×C4C11×H(5,𝔽2)11yescharacteristic
820C8—22no—
821C8—41no—
822C8—41no—
823C8—41no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22C2×C11×#12011yescharacteristic
846C22D42×C1111yescharacteristic
847C22C11×#54611yescharacteristic
848C22C2×C11×#13711yescharacteristic
849C22C11×#57511yescharacteristic
850C22C11×#57711yescharacteristic
851C22C11×#57811yescharacteristic
852C4—22no—
853C4—24no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—42no—
858C4—41no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4C2×C11×#12111yescharacteristic
864C4C11×#53411yescharacteristic
865C4D42×C1111yescharacteristic
866C4C11×#54611yescharacteristic
867C2—42no—
868C2—42no—
869C2—82no—
870C2C11×#241011yescharacteristic
871C2C11×#300711yescharacteristic
872C2C11×#301311yescharacteristic
873C2C11×#327011yescharacteristic
874C2C11×#327511yescharacteristic
875C2C11×#331611yescharacteristic
876C2C11×#332711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#548C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#470C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C11×#451C2semidirect
5. C2×C11×#417C2semidirect
6. C11×#2417C2semidirect
7. C11×#2042C2semidirect
8. C11×#2034C2semidirect
9. C11×#2015C2semidirect
10. C11×#2000C2semidirect
11. C11×#1878C2semidirect
12. C11×#1872C2semidirect
13. C11×#1870C2semidirect
14. C11×#1865C2semidirect
15. C11×#1787C2semidirect
155. C11×#103D4semidirect
166. #24449C11direct (N × H)
291. C2×#470C2×C11semidirect
292. C2×#452C2×C11semidirect
293. C2×#451C2×C11semidirect
294. C2×#417C2×C11semidirect
295. #2417C2×C11semidirect
296. #2042C2×C11semidirect
297. #2034C2×C11semidirect
298. #2015C2×C11semidirect
299. #2000C2×C11semidirect
300. #1878C2×C11semidirect
301. #1872C2×C11semidirect
302. #1870C2×C11semidirect
303. #1865C2×C11semidirect
304. #1787C2×C11semidirect
583. #103D4×C11semidirect
727. C11#24449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5482
C2×C11×#4702
C2×C11×#4522
C2×C11×#4512
C2×C11×#4172
C11×#24172
C11×#20422
C11×#20342
C11×#20152
C11×#20002
C11×#18782
C11×#18722
C11×#18702
C11×#18652
C11×#17872
#2444911