Finite Group Databasebeta

← C11×#24391 #14601584

Subgroups — C11×#24391 #14601584

Order 2816.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic, complemented
2C2×C11×#468C211yesmaximal, characteristic, complemented
3C2×C11×#466C211yesmaximal, characteristic, complemented
4C2×C11×#449C211yesmaximal, characteristic, complemented
5C2×C11×#408C211yesmaximal, characteristic, complemented
6C11×#2615C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#2000C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1895C211yesmaximal, characteristic, complemented
12C11×#1892C211yesmaximal, characteristic, complemented
13C11×#1874C211yesmaximal, characteristic, complemented
14C11×#1852C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic
22C11×#537—24no—
23C11×#537—24no—
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121—21no—
28C2×C11×#121—21no—
29C2×C11×#121—21no—
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic
32C2×C11×#121C2211yescharacteristic
33C2×C11×#121C2211yescharacteristic
34C2×C11×#121C2211yescharacteristic
35C22×C11×C4⋊C4C2211yescharacteristic
36C11×#468—24no—
37C11×#466—24no—
38C11×#449—24no—
39C2×C11×#107C2211yescharacteristic
40C2×C11×#107C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C11×#408—24no—
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#393—21no—
55C11×#392—21no—
56C11×#392—21no—
57C11×#392—21no—
58C11×#380C2211yescharacteristic
59C11×#380C2211yescharacteristic
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#340C2211yescharacteristic
64C11×#340C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—22no—
72C2×C11×#41—22no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C2×C11×#41—41no—
76C2×C11×#41—41no—
77C22×Q8×C11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11—21no—
85C22×D4×C11D411yescharacteristic
86C22×D4×C11D411yescharacteristic
87C22×D4×C11D411yescharacteristic
88C22×D4×C11C2311yescharacteristic
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11—21no—
91C23×C4×C11—21no—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C2×C11×SD16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16—41no—
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—41no—
101C2×C11×M16—22no—
102C2×C11×M16—22no—
103C2×C11×M16—41no—
104C22×C8×C11—22no—
105C22×C8×C11—22no—
106C22×C8×C11—41no—
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C11×C22⋊Q8—28no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8D414yescomplemented
116C11×#121—28no—
117C11×#121—28no—
118C11×#121—28no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—22no—
123C11×#121—22no—
124C11×#121—22no—
125C11×#121—22no—
126C11×#121—41no—
127C11×#121—41no—
128C11×#121D414yescomplemented
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—22no—
133C2×C11×C4⋊C4—22no—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4—21no—
149C11×#107—22no—
150C11×#107—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—41no—
154C11×#102—22no—
155C11×#102—22no—
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#24391C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11—21no—
169C24×C11C2×D411yescharacteristic
170C24×C11C2×D411yescharacteristic
171C24×C11C2×D411yescharacteristic
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C11×#41—44no—
176C11×#41—44no—
177C11×#41—44no—
178C11×#41—44no—
179C11×#41—44no—
180C2×Q8×C11—22no—
181C2×Q8×C11—22no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—41no—
188C2×Q8×C11C2×D412yes—
189C2×D4×C11—24no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
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—21no—
208C2×D4×C11—21no—
209C2×D4×C11—41no—
210C2×D4×C11—41no—
211C2×D4×C11—41no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—42no—
217C2×D4×C11—81no—
218C2×D4×C11—81no—
219C2×D4×C11—81no—
220C2×D4×C11—81no—
221C2×D4×C11—81no—
222C2×D4×C11—81no—
223C2×D4×C11—81no—
224C2×D4×C11—81no—
225C2×D4×C11—81no—
226C2×D4×C11—81no—
227C2×D4×C11C2×D412yes—
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—24no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—24no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—42no—
251C22×C4×C11—42no—
252C22×C4×C11—81no—
253C22×C4×C11—81no—
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D412yes—
260C22×C4×C11#4112yes—
261C22×C4×C11C2411yescharacteristic
262C11×SD16—44no—
263C11×D8—44no—
264C11×M16—44no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C2×C8×C11—21no—
275C2×C8×C11—44no—
276C2×C8×C11C2×D412yes—
277C2×C8×C11C2×D412yes—
278C11×C4⋊C4—24no—
279C11×C4⋊C4—24no—
280C11×C4⋊C4—24no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2×D412yes—
291C11×C22⋊C4—24no—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—24no—
295C11×C22⋊C4—42no—
296C11×C22⋊C4—42no—
297C11×C22⋊C4—42no—
298C11×C22⋊C4—81no—
299C11×C22⋊C4—81no—
300C11×C22⋊C4—81no—
301C2×#537C2×C1111yescharacteristic, complemented
302C2×#468C2×C1111yescharacteristic, complemented
303C2×#466C2×C1111yescharacteristic, complemented
304C2×#449C2×C1111yescharacteristic, complemented
305C2×#408C2×C1111yescharacteristic, complemented
306#2615C2×C1111yescharacteristic, complemented
307#2036C2×C1111yescharacteristic, complemented
308#2033C2×C1111yescharacteristic, complemented
309#2000C2×C1111yescharacteristic, complemented
310#1999C2×C1111yescharacteristic, complemented
311#1895C2×C1111yescharacteristic, complemented
312#1892C2×C1111yescharacteristic, complemented
313#1874C2×C1111yescharacteristic, complemented
314#1852C2×C1111yescharacteristic, complemented
315#1788C2×C1111yescharacteristic, complemented
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—22no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—21no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11#12012yes—
350C23×C11#12112yes—
351C23×C11C22×D411yescharacteristic
352Q8×C11—22no—
353Q8×C11—22no—
354Q8×C11—44no—
355Q8×C11—41no—
356Q8×C11—41no—
357D4×C11—22no—
358D4×C11—22no—
359D4×C11—44no—
360D4×C11—44no—
361D4×C11—44no—
362D4×C11—48no—
363D4×C11—41no—
364D4×C11—41no—
365D4×C11—41no—
366D4×C11—41no—
367D4×C11—41no—
368D4×C11—41no—
369D4×C11—84no—
370D4×C11—84no—
371D4×C11—84no—
372D4×C11—84no—
373D4×C11—84no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—48no—
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—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—84no—
413C2×C4×C11#12012yes—
414C2×C4×C11#12112yes—
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C2×#4111yescharacteristic
419C2×C4×C11H(5,𝔽2)11yescharacteristic
420C2×C4×C11H(5,𝔽2)11yescharacteristic
421C8×C11—22no—
422C8×C11—22no—
423C8×C11—41no—
424C8×C11—41no—
425C22×#41C22×C1111yescharacteristic
426C22×#41C22×C1111yescharacteristic
427C22×SD16C22×C1111yescharacteristic
428C22×D8C22×C1111yescharacteristic
429C22×M16C22×C1111yescharacteristic
430C23×C8C22×C1111yescharacteristic
431#537—24no—
432#537—24no—
433C2×C22⋊Q8—21no—
434C2×C22⋊Q8C22×C1111yescharacteristic
435C2×C22⋊Q8C22×C1111yescharacteristic
436C2×#121—21no—
437C2×#121—21no—
438C2×#121—21no—
439C2×#121C22×C1111yescharacteristic
440C2×#121C22×C1111yescharacteristic
441C2×#121C22×C1111yescharacteristic
442C2×#121C22×C1111yescharacteristic
443C2×#121C22×C1111yescharacteristic
444C22×C4⋊C4C22×C1111yescharacteristic
445#468—24no—
446#466—24no—
447#449—24no—
448C2×#107C22×C1111yescharacteristic
449C2×#107C22×C1111yescharacteristic
450C2×#103C22×C1111yescharacteristic
451C2×#103C22×C1111yescharacteristic
452C2×#103C22×C1111yescharacteristic
453C2×#102C22×C1111yescharacteristic
454C2×#102C22×C1111yescharacteristic
455C2×#102C22×C1111yescharacteristic
456C2×#102C22×C1111yescharacteristic
457C2×#102C22×C1111yescharacteristic
458#408—24no—
459C2×C22⋊C8C22×C1111yescharacteristic
460C2×C22⋊C8C22×C1111yescharacteristic
461C2×C22⋊C8C22×C1111yescharacteristic
462C2×C22⋊C8C22×C1111yescharacteristic
463#393—21no—
464#392—21no—
465#392—21no—
466#392—21no—
467#380C22×C1111yescharacteristic
468#380C22×C1111yescharacteristic
469#380C22×C1111yescharacteristic
470#340C22×C1111yescharacteristic
471#340C22×C1111yescharacteristic
472#340C22×C1111yescharacteristic
473#340C22×C1111yescharacteristic
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
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—42no—
489C22×C11—41no—
490C22×C11—41no—
491C22×C11—41no—
492C22×C11—41no—
493C22×C11—42no—
494C22×C11—41no—
495C22×C11—42no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—81no—
499C22×C11—81no—
500C22×C11—81no—
501C22×C11—81no—
502C22×C11—81no—
503C22×C11—81no—
504C22×C11—81no—
505C22×C11—81no—
506C22×C11—81no—
507C22×C11—81no—
508C22×C11—81no—
509C22×C11C2×#12011yescharacteristic
510C22×C11C2×#12111yescharacteristic
511C22×C11#53411yescharacteristic
512C22×C11#57611yescharacteristic
513C22×C11#57611yescharacteristic
514C22×C11#57711yescharacteristic
515C22×C11#57811yescharacteristic
516C4×C11—22no—
517C4×C11—22no—
518C4×C11—41no—
519C4×C11—42no—
520C4×C11—42no—
521C4×C11—42no—
522C4×C11—81no—
523C4×C11—81no—
524C4×C11—81no—
525C4×C11D4211yescharacteristic
526C4×C11D4211yescharacteristic
527C4×C11#54611yescharacteristic
528C4×C11#54611yescharacteristic
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—41no—
538C2×#41—41no—
539C2×#41—41no—
540C2×#41—41no—
541C22×Q8D4×C1111yescharacteristic
542C22×Q8C23×C1111yescharacteristic
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—21no—
549C22×D4D4×C1111yescharacteristic
550C22×D4D4×C1111yescharacteristic
551C22×D4D4×C1111yescharacteristic
552C22×D4C23×C1111yescharacteristic
553C22×D4C23×C1111yescharacteristic
554C23×C4—21no—
555C23×C4—21no—
556C23×C4C23×C1111yescharacteristic
557C23×C4C23×C1111yescharacteristic
558C23×C4C23×C1111yescharacteristic
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—41no—
565C2×M16—22no—
566C2×M16—22no—
567C2×M16—41no—
568C22×C8—22no—
569C22×C8—22no—
570C22×C8—41no—
571C22×C8C23×C1111yescharacteristic
572C22×C8C23×C1111yescharacteristic
573C22×C8C23×C1111yescharacteristic
574C22×C8C23×C1111yescharacteristic
575C22⋊Q8—28no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8D4×C1114yescomplemented
580#121—28no—
581#121—28no—
582#121—28no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—41no—
591#121—41no—
592#121D4×C1114yescomplemented
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4C23×C1111yescharacteristic
599C2×C4⋊C4C23×C1111yescharacteristic
600C2×C4⋊C4C23×C1111yescharacteristic
601C2×C4⋊C4C23×C1111yescharacteristic
602C2×C4⋊C4C23×C1111yescharacteristic
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613#107—22no—
614#107—22no—
615#103—22no—
616#103—22no—
617#103—41no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—22no—
622#102—41no—
623C22⋊C8—22no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8D4×C1114yescomplemented
627#95—21no—
628#95—21no—
629#95—21no—
630C2×C11—42no—
631C2×C11—42no—
632C2×C11—81no—
633C2×C11—82no—
634C2×C11—161no—
635C2×C11#241011yescharacteristic
636C2×C11#300811yescharacteristic
637C2×C11#301311yescharacteristic
638C2×C11#306111yescharacteristic
639C2×C11#306211yescharacteristic
640C2×C11#319811yescharacteristic
641C2×C11#320311yescharacteristic
642C24—21no—
643C24—21no—
644C24C2×D4×C1111yescharacteristic
645C24C2×D4×C1111yescharacteristic
646C24C2×D4×C1111yescharacteristic
647#41—44no—
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—22no—
656C2×Q8—22no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—41no—
663C2×Q8C2×D4×C1112yes—
664C2×D4—24no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—41no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—81no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C2×D4×C1112yes—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—24no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C1111yescharacteristic
730C22×C4C2×D4×C1111yescharacteristic
731C22×C4C2×D4×C1112yes—
732C22×C4C2×D4×C1112yes—
733C22×C4C2×D4×C1111yescharacteristic
734C22×C4C2×D4×C1112yes—
735C22×C4C11×#4112yes—
736C22×C4C24×C1111yescharacteristic
737SD16—44no—
738D8—44no—
739M16—44no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—44no—
751C2×C8C2×D4×C1112yes—
752C2×C8C2×D4×C1112yes—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4C2×D4×C1112yes—
765C4⋊C4C2×D4×C1112yes—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—81no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C11#2439111yescharacteristic, direct product factor, Sylow
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C11×#12012yes—
811C23C11×#12112yes—
812C23C22×D4×C1111yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4C11×#12012yes—
875C2×C4C11×#12112yes—
876C2×C4C22×D4×C1111yescharacteristic
877C2×C4C22×D4×C1111yescharacteristic
878C2×C4C22×D4×C1111yescharacteristic
879C2×C4C2×C11×#4111yescharacteristic
880C2×C4C11×H(5,𝔽2)11yescharacteristic
881C2×C4C11×H(5,𝔽2)11yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22C2×C11×#12011yescharacteristic
922C22C2×C11×#12111yescharacteristic
923C22C11×#53411yescharacteristic
924C22C11×#57611yescharacteristic
925C22C11×#57611yescharacteristic
926C22C11×#57711yescharacteristic
927C22C11×#57811yescharacteristic
928C4—22no—
929C4—22no—
930C4—41no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4D42×C1111yescharacteristic
938C4D42×C1111yescharacteristic
939C4C11×#54611yescharacteristic
940C4C11×#54611yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2C11×#241011yescharacteristic
947C2C11×#300811yescharacteristic
948C2C11×#301311yescharacteristic
949C2C11×#306111yescharacteristic
950C2C11×#306211yescharacteristic
951C2C11×#319811yescharacteristic
952C2C11×#320311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#537C2semidirect
2. C2×C11×#468C2semidirect
3. C2×C11×#466C2semidirect
4. C2×C11×#449C2semidirect
5. C2×C11×#408C2semidirect
6. C11×#2615C2semidirect
7. C11×#2036C2semidirect
8. C11×#2033C2semidirect
9. C11×#2000C2semidirect
10. C11×#1999C2semidirect
11. C11×#1895C2semidirect
12. C11×#1892C2semidirect
13. C11×#1874C2semidirect
14. C11×#1852C2semidirect
15. C11×#1788C2semidirect
115. C11×C22⋊Q8D4semidirect
128. C11×#121D4semidirect
162. C11×C22⋊C8D4semidirect
166. #24391C11direct (N × H)
301. C2×#537C2×C11semidirect
302. C2×#468C2×C11semidirect
303. C2×#466C2×C11semidirect
304. C2×#449C2×C11semidirect
305. C2×#408C2×C11semidirect
306. #2615C2×C11semidirect
307. #2036C2×C11semidirect
308. #2033C2×C11semidirect
309. #2000C2×C11semidirect
310. #1999C2×C11semidirect
311. #1895C2×C11semidirect
312. #1892C2×C11semidirect
313. #1874C2×C11semidirect
314. #1852C2×C11semidirect
315. #1788C2×C11semidirect
579. C22⋊Q8D4×C11semidirect
592. #121D4×C11semidirect
626. C22⋊C8D4×C11semidirect
776. C11#24391direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C2×C11×#4682
C2×C11×#4662
C2×C11×#4492
C2×C11×#4082
C11×#26152
C11×#20362
C11×#20332
C11×#20002
C11×#19992
C11×#18952
C11×#18922
C11×#18742
C11×#18522
C11×#17882
#2439111