Finite Group Databasebeta

← C11×#24389 #14601582

Subgroups — C11×#24389 #14601582

Order 2816.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C2×C11×#470C211yesmaximal, characteristic, complemented
3C2×C11×#468C211yesmaximal, characteristic, complemented
4C2×C11×#452C211yesmaximal, characteristic, complemented
5C2×C11×#407C211yesmaximal, characteristic, complemented
6C11×#2848C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2034C211yesmaximal, characteristic, complemented
9C11×#2001C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1895C211yesmaximal, characteristic, complemented
12C11×#1894C211yesmaximal, characteristic, complemented
13C11×#1873C211yesmaximal, characteristic, complemented
14C11×#1854C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic, complemented
19C22×C11×SD16C2211yescharacteristic, complemented
20C22×C11×M16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#525—24no—
23C11×#525—24no—
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic
32C2×C11×#120—21no—
33C2×C4×D4×C11—21no—
34C2×C4×D4×C11—21no—
35C2×C11×#117C2211yescharacteristic
36C11×#470—24no—
37C11×#468—24no—
38C11×#452—24no—
39C2×C11×#107C2211yescharacteristic, complemented
40C2×C11×#106C2211yescharacteristic, complemented
41C2×C11×#103C2211yescharacteristic, complemented
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#103C2211yescharacteristic, complemented
44C2×C11×#103C2211yescharacteristic, complemented
45C2×C11×#103C2211yescharacteristic, complemented
46C2×C11×#102C2211yescharacteristic, complemented
47C2×C11×#102C2211yescharacteristic, complemented
48C2×C11×#102C2211yescharacteristic, complemented
49C11×#407—24no—
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#385—21no—
55C11×#385—21no—
56C11×#385—21no—
57C11×#380C2211yescharacteristic
58C11×#380C2211yescharacteristic
59C11×#380C2211yescharacteristic
60C11×#379—21no—
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C11×#340C2211yescharacteristic, complemented
64C11×#340C2211yescharacteristic, complemented
65C25×C11D411yescharacteristic
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C22×Q8×C11C2311yescharacteristic
73C22×Q8×C11C2311yescharacteristic
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11—22no—
80C23×C4×C11—22no—
81C23×C4×C11—22no—
82C23×C4×C11—22no—
83C23×C4×C11—41no—
84C23×C4×C11—41no—
85C23×C4×C11D411yescharacteristic
86C23×C4×C11D411yescharacteristic
87C23×C4×C11D411yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C2×C11×Q16—22no—
92C2×C11×Q16—22no—
93C2×C11×Q16—41no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16—41no—
97C2×C11×M16—22no—
98C2×C11×M16—22no—
99C2×C11×M16—22no—
100C2×C11×M16—22no—
101C2×C11×M16—41no—
102C2×C11×M16—41no—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C11×#123—28no—
108C11×C22⋊Q8—22no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—41no—
116C11×C22⋊Q8—41no—
117C11×C22⋊Q8D414yes—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121D414yes—
122C11×#120—28no—
123C4×D4×C11—28no—
124C4×D4×C11—28no—
125C11×#117—22no—
126C11×#117—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—21no—
132C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4—21no—
147C2×C11×C22⋊C4—21no—
148C2×C42×C11—21no—
149C11×#107—22no—
150C11×#106—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—22no—
155C11×#103—41no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—41no—
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—22no—
162C11×C22⋊C8D414yescomplemented
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24389C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—21no—
171C24×C11—41no—
172C24×C11—41no—
173C24×C11—41no—
174C24×C11—41no—
175C24×C11C2×D411yescharacteristic
176C24×C11C2×D411yescharacteristic
177C24×C11C2×D411yescharacteristic
178C11×#41—44no—
179C11×#41—44no—
180C11×#41—44no—
181C11×#41—44no—
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—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—21no—
192C2×Q8×C11—21no—
193C2×Q8×C11C2×D412yes—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—24no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—42no—
203C2×D4×C11—42no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11—42no—
208C2×D4×C11C2×D412yes—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—24no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
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—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—41no—
238C22×C4×C11—41no—
239C22×C4×C11—41no—
240C22×C4×C11—44no—
241C22×C4×C11—44no—
242C22×C4×C11—44no—
243C22×C4×C11—44no—
244C22×C4×C11—42no—
245C22×C4×C11—42no—
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D412yes—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D412yes—
252C22×C4×C11#4112yes—
253C22×C4×C11C2411yescharacteristic
254C11×Q16—44no—
255C11×SD16—44no—
256C11×M16—44no—
257C11×M16—44no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11C2×D412yes—
269C2×C8×C11C2×D412yes—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—42no—
281C11×C4⋊C4—42no—
282C11×C4⋊C4—42no—
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2×D412yes—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—42no—
291C11×C22⋊C4—42no—
292C11×C22⋊C4—42no—
293C11×C22⋊C4—42no—
294C11×C22⋊C4—42no—
295C11×C22⋊C4—42no—
296C42×C11—24no—
297C2×#525C2×C1111yescharacteristic
298C2×#470C2×C1111yescharacteristic, complemented
299C2×#468C2×C1111yescharacteristic, complemented
300C2×#452C2×C1111yescharacteristic, complemented
301C2×#407C2×C1111yescharacteristic, complemented
302#2848C2×C1111yescharacteristic, complemented
303#2036C2×C1111yescharacteristic, complemented
304#2034C2×C1111yescharacteristic, complemented
305#2001C2×C1111yescharacteristic, complemented
306#2000C2×C1111yescharacteristic, complemented
307#1895C2×C1111yescharacteristic, complemented
308#1894C2×C1111yescharacteristic, complemented
309#1873C2×C1111yescharacteristic, complemented
310#1854C2×C1111yescharacteristic, complemented
311#1788C2×C1111yescharacteristic, complemented
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—22no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11#12012yes—
345C23×C11#12112yes—
346C23×C11#13712yes—
347C23×C11C22×D411yescharacteristic
348Q8×C11—22no—
349Q8×C11—22no—
350Q8×C11—41no—
351Q8×C11—41no—
352Q8×C11—41no—
353Q8×C11—41no—
354Q8×C11—41no—
355Q8×C11—41no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—48no—
359D4×C11—48no—
360D4×C11—48no—
361D4×C11—41no—
362D4×C11—41no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—21no—
378C2×C4×C11—22no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—44no—
382C2×C4×C11—44no—
383C2×C4×C11—44no—
384C2×C4×C11—48no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11#12012yes—
408C2×C4×C11#12112yes—
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C2×#4111yescharacteristic
413C2×C4×C11H(5,𝔽2)11yescharacteristic
414C2×C4×C11H(5,𝔽2)11yescharacteristic
415C8×C11—22no—
416C8×C11—22no—
417C8×C11—41no—
418C8×C11—41no—
419C22×#41C22×C1111yescharacteristic
420C24×C4C22×C1111yescharacteristic
421C22×Q16C22×C1111yescharacteristic, complemented
422C22×SD16C22×C1111yescharacteristic, complemented
423C22×M16C22×C1111yescharacteristic
424C22×M16C22×C1111yescharacteristic
425#525—24no—
426#525—24no—
427C2×#123—21no—
428C2×C22⋊Q8C22×C1111yescharacteristic
429C2×C22⋊Q8C22×C1111yescharacteristic
430C2×C22⋊Q8C22×C1111yescharacteristic
431C2×C22⋊Q8C22×C1111yescharacteristic
432C2×C22⋊Q8C22×C1111yescharacteristic
433C2×#121C22×C1111yescharacteristic
434C2×#121C22×C1111yescharacteristic
435C2×#120—21no—
436C2×C4×D4—21no—
437C2×C4×D4—21no—
438C2×#117C22×C1111yescharacteristic
439#470—24no—
440#468—24no—
441#452—24no—
442C2×#107C22×C1111yescharacteristic, complemented
443C2×#106C22×C1111yescharacteristic, complemented
444C2×#103C22×C1111yescharacteristic, complemented
445C2×#103C22×C1111yescharacteristic, complemented
446C2×#103C22×C1111yescharacteristic, complemented
447C2×#103C22×C1111yescharacteristic, complemented
448C2×#103C22×C1111yescharacteristic, complemented
449C2×#102C22×C1111yescharacteristic, complemented
450C2×#102C22×C1111yescharacteristic, complemented
451C2×#102C22×C1111yescharacteristic, complemented
452#407—24no—
453C2×C22⋊C8C22×C1111yescharacteristic
454C2×C22⋊C8C22×C1111yescharacteristic
455C2×C22⋊C8C22×C1111yescharacteristic
456C2×C22⋊C8C22×C1111yescharacteristic
457#385—21no—
458#385—21no—
459#385—21no—
460#380C22×C1111yescharacteristic
461#380C22×C1111yescharacteristic
462#380C22×C1111yescharacteristic
463#379—21no—
464#340C22×C1111yescharacteristic, complemented
465#340C22×C1111yescharacteristic, complemented
466#340C22×C1111yescharacteristic, complemented
467#340C22×C1111yescharacteristic, complemented
468C22×C11—22no—
469C22×C11—22no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—416no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—41no—
489C22×C11—41no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—81no—
494C22×C11—81no—
495C22×C11—81no—
496C22×C11—81no—
497C22×C11C2×#12011yescharacteristic
498C22×C11C2×#12111yescharacteristic
499C22×C11#53411yescharacteristic
500C22×C11C2×#13711yescharacteristic
501C22×C11#57511yescharacteristic
502C22×C11#57511yescharacteristic
503C22×C11#57511yescharacteristic
504C4×C11—22no—
505C4×C11—22no—
506C4×C11—41no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—81no—
511C4×C11—81no—
512C4×C11—81no—
513C4×C11—81no—
514C4×C11D4211yescharacteristic
515C4×C11D4211yescharacteristic
516C4×C11#54611yescharacteristic
517C4×C11#54611yescharacteristic
518C25D4×C1111yescharacteristic
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—41no—
524C2×#41—41no—
525C22×Q8C23×C1111yescharacteristic
526C22×Q8C23×C1111yescharacteristic
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4C23×C1111yescharacteristic
531C23×C4—21no—
532C23×C4—22no—
533C23×C4—22no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—41no—
537C23×C4—41no—
538C23×C4D4×C1111yescharacteristic
539C23×C4D4×C1111yescharacteristic
540C23×C4D4×C1111yescharacteristic
541C23×C4C23×C1111yescharacteristic
542C23×C4C23×C1111yescharacteristic
543C23×C4C23×C1111yescharacteristic
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—41no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—22no—
553C2×M16—22no—
554C2×M16—41no—
555C2×M16—41no—
556C22×C8C23×C1111yescharacteristic
557C22×C8C23×C1111yescharacteristic
558C22×C8C23×C1111yescharacteristic
559C22×C8C23×C1111yescharacteristic
560#123—28no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8D4×C1114yes—
571#121—22no—
572#121—22no—
573#121—22no—
574#121D4×C1114yes—
575#120—28no—
576C4×D4—28no—
577C4×D4—28no—
578#117—22no—
579#117—22no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4C23×C1111yescharacteristic
586C2×C4⋊C4C23×C1111yescharacteristic
587C2×C4⋊C4C23×C1111yescharacteristic
588C2×C4⋊C4C23×C1111yescharacteristic
589C2×C4⋊C4C23×C1111yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C42—21no—
602#107—22no—
603#106—22no—
604#103—22no—
605#103—22no—
606#103—22no—
607#103—22no—
608#103—41no—
609#102—22no—
610#102—22no—
611#102—41no—
612C22⋊C8—22no—
613C22⋊C8—22no—
614C22⋊C8—22no—
615C22⋊C8D4×C1114yescomplemented
616#95—21no—
617#95—21no—
618#95—21no—
619C2×C11—42no—
620C2×C11—42no—
621C2×C11—42no—
622C2×C11—82no—
623C2×C11#241011yescharacteristic
624C2×C11#300511yescharacteristic
625C2×C11#300711yescharacteristic
626C2×C11#305411yescharacteristic
627C2×C11#305611yescharacteristic
628C2×C11#319611yescharacteristic
629C2×C11#319711yescharacteristic
630C24—22no—
631C24—22no—
632C24—22no—
633C24—21no—
634C24—41no—
635C24—41no—
636C24—41no—
637C24—41no—
638C24C2×D4×C1111yescharacteristic
639C24C2×D4×C1111yescharacteristic
640C24C2×D4×C1111yescharacteristic
641#41—44no—
642#41—44no—
643#41—44no—
644#41—44no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8C2×D4×C1112yes—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4C2×D4×C1112yes—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4C2×D4×C1111yescharacteristic
710C22×C4C2×D4×C1111yescharacteristic
711C22×C4C2×D4×C1112yes—
712C22×C4C2×D4×C1112yes—
713C22×C4C2×D4×C1111yescharacteristic
714C22×C4C2×D4×C1112yes—
715C22×C4C11×#4112yes—
716C22×C4C24×C1111yescharacteristic
717Q16—44no—
718SD16—44no—
719M16—44no—
720M16—44no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8C2×D4×C1112yes—
732C2×C8C2×D4×C1112yes—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—42no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4C2×D4×C1112yes—
747C4⋊C4C2×D4×C1112yes—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—42no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C42—24no—
760C11#2438911yescharacteristic, direct product factor, Sylow
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23C11×#12012yes—
794C23C11×#12112yes—
795C23C11×#13712yes—
796C23C22×D4×C1111yescharacteristic
797Q8—22no—
798Q8—22no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—48no—
810D4—41no—
811D4—41no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4C11×#12012yes—
857C2×C4C11×#12112yes—
858C2×C4C22×D4×C1111yescharacteristic
859C2×C4C22×D4×C1111yescharacteristic
860C2×C4C22×D4×C1111yescharacteristic
861C2×C4C2×C11×#4111yescharacteristic
862C2×C4C11×H(5,𝔽2)11yescharacteristic
863C2×C4C11×H(5,𝔽2)11yescharacteristic
864C8—22no—
865C8—22no—
866C8—41no—
867C8—41no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—416no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22C2×C11×#12011yescharacteristic
898C22C2×C11×#12111yescharacteristic
899C22C11×#53411yescharacteristic
900C22C2×C11×#13711yescharacteristic
901C22C11×#57511yescharacteristic
902C22C11×#57511yescharacteristic
903C22C11×#57511yescharacteristic
904C4—22no—
905C4—22no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4D42×C1111yescharacteristic
915C4D42×C1111yescharacteristic
916C4C11×#54611yescharacteristic
917C4C11×#54611yescharacteristic
918C2—42no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2C11×#241011yescharacteristic
923C2C11×#300511yescharacteristic
924C2C11×#300711yescharacteristic
925C2C11×#305411yescharacteristic
926C2C11×#305611yescharacteristic
927C2C11×#319611yescharacteristic
928C2C11×#319711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#470C2semidirect
3. C2×C11×#468C2semidirect
4. C2×C11×#452C2semidirect
5. C2×C11×#407C2semidirect
6. C11×#2848C2semidirect
7. C11×#2036C2semidirect
8. C11×#2034C2semidirect
9. C11×#2001C2semidirect
10. C11×#2000C2semidirect
11. C11×#1895C2semidirect
12. C11×#1894C2semidirect
13. C11×#1873C2semidirect
14. C11×#1854C2semidirect
15. C11×#1788C2semidirect
18. C22×C11×Q16C22semidirect
19. C22×C11×SD16C22semidirect
39. C2×C11×#107C22semidirect
40. C2×C11×#106C22semidirect
41. C2×C11×#103C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#103C22semidirect
44. C2×C11×#103C22semidirect
45. C2×C11×#103C22semidirect
46. C2×C11×#102C22semidirect
47. C2×C11×#102C22semidirect
48. C2×C11×#102C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#340C22semidirect
64. C11×#340C22semidirect
162. C11×C22⋊C8D4semidirect
166. #24389C11direct (N × H)
298. C2×#470C2×C11semidirect
299. C2×#468C2×C11semidirect
300. C2×#452C2×C11semidirect
301. C2×#407C2×C11semidirect
302. #2848C2×C11semidirect
303. #2036C2×C11semidirect
304. #2034C2×C11semidirect
305. #2001C2×C11semidirect
306. #2000C2×C11semidirect
307. #1895C2×C11semidirect
308. #1894C2×C11semidirect
309. #1873C2×C11semidirect
310. #1854C2×C11semidirect
311. #1788C2×C11semidirect
421. C22×Q16C22×C11semidirect
422. C22×SD16C22×C11semidirect
442. C2×#107C22×C11semidirect
443. C2×#106C22×C11semidirect
444. C2×#103C22×C11semidirect
445. C2×#103C22×C11semidirect
446. C2×#103C22×C11semidirect
447. C2×#103C22×C11semidirect
448. C2×#103C22×C11semidirect
449. C2×#102C22×C11semidirect
450. C2×#102C22×C11semidirect
451. C2×#102C22×C11semidirect
464. #340C22×C11semidirect
465. #340C22×C11semidirect
466. #340C22×C11semidirect
467. #340C22×C11semidirect
615. C22⋊C8D4×C11semidirect
760. C11#24389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C2×C11×#4702
C2×C11×#4682
C2×C11×#4522
C2×C11×#4072
C11×#28482
C11×#20362
C11×#20342
C11×#20012
C11×#20002
C11×#18952
C11×#18942
C11×#18732
C11×#18542
C11×#17882
#2438911