Finite Group Databasebeta

← C11×#24220 #14601413

Subgroups — C11×#24220 #14601413

Order 2816.

1556 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#464C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic, complemented
4C2×C11×#452C211yesmaximal, characteristic, complemented
5C2×C11×#450C211yesmaximal, characteristic, complemented
6C11×#2323C211yesmaximal, characteristic, complemented
7C11×#2042C211yesmaximal, characteristic, complemented
8C11×#2041C211yesmaximal, characteristic, complemented
9C11×#2015C211yesmaximal, characteristic, complemented
10C11×#2014C211yesmaximal, characteristic, complemented
11C11×#1983C211yesmaximal, characteristic, complemented
12C11×#1982C211yesmaximal, characteristic, complemented
13C11×#1798C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic, complemented
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic, complemented
22C11×#535—24no—
23C11×#535—24no—
24C2×C11×#127C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C2×C11×#124C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×#121—21no—
30C2×C11×#121—21no—
31C2×C11×#120—21no—
32C2×C11×#120—21no—
33C2×C4×Q8×C11C2211yescharacteristic, complemented
34C2×C11×#117C2211yescharacteristic
35C11×#464—24no—
36C11×#460—24no—
37C11×#452—24no—
38C11×#450—24no—
39C2×C11×C4⋊C8C2211yescharacteristic, complemented
40C2×C11×C4⋊C8C2211yescharacteristic, complemented
41C2×C11×#103C2211yescharacteristic, complemented
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#103C2211yescharacteristic, complemented
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52C2×C11×#102C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C11×C22⋊C8C2211yescharacteristic
55C11×#391C2211yescharacteristic, complemented
56C11×#389—21no—
57C11×#389C2211yescharacteristic, complemented
58C11×#388—21no—
59C11×#388—21no—
60C11×#387—21no—
61C11×#380C2211yescharacteristic
62C4×C11×C4⋊C4C2211yescharacteristic, complemented
63C11×#336C2211yescharacteristic, complemented
64C11×#336C2211yescharacteristic, complemented
65C25×C11—21no—
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—22no—
76C22×D4×C11—22no—
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—22no—
83C22×D4×C11—22no—
84C22×D4×C11—41no—
85C22×D4×C11—41no—
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C22×D4×C11C2311yescharacteristic
89C23×C4×C11—21no—
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—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16—22no—
99C2×C11×SD16—22no—
100C2×C11×SD16—41no—
101C2×C11×SD16—41no—
102C2×C11×SD16—41no—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C11×#127—22no—
108C11×#127—22no—
109C11×#127—22no—
110C11×#127D414yes—
111C11×#124—22no—
112C11×#124—22no—
113C11×#124—22no—
114C11×#124D414yes—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8D414yescomplemented
117C11×#121—28no—
118C11×#121—28no—
119C11×#120—28no—
120C11×#120—28no—
121C4×Q8×C11—22no—
122C4×Q8×C11—22no—
123C11×#117—22no—
124C11×#117—22no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4D411yescharacteristic
129C2×C11×C4⋊C4D411yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4D411yescharacteristic
140C2×C11×C22⋊C4D411yescharacteristic
141C2×C42×C11—21no—
142C2×C42×C11—21no—
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2311yescharacteristic
145C11×C4⋊C8—22no—
146C11×C4⋊C8—22no—
147C11×#103—22no—
148C11×#103—22no—
149C11×#103—41no—
150C11×#102—22no—
151C11×#102—22no—
152C11×#102—22no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—41no—
157C11×#102—41no—
158C11×#102—41no—
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×#95—21no—
162C11×#95—21no—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24220C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—24no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—81no—
174C24×C11—81no—
175C24×C11—81no—
176C24×C11—81no—
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×C11C2×D412yes—
193C2×Q8×C11C2×D412yes—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—24no—
197C2×D4×C11—24no—
198C2×D4×C11—24no—
199C2×D4×C11—24no—
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—21no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11—44no—
216C2×D4×C11—44no—
217C2×D4×C11—44no—
218C2×D4×C11—44no—
219C2×D4×C11—42no—
220C2×D4×C11—42no—
221C2×D4×C11—42no—
222C2×D4×C11—42no—
223C2×D4×C11—81no—
224C2×D4×C11—81no—
225C2×D4×C11—81no—
226C2×D4×C11—81no—
227C2×D4×C11—81no—
228C2×D4×C11—81no—
229C2×D4×C11—81no—
230C2×D4×C11—81no—
231C2×D4×C11C2×D412yes—
232C2×D4×C11C2×D412yes—
233C2×D4×C11C2×D412yes—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—24no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—42no—
245C22×C4×C11—42no—
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D412yes—
252C22×C4×C11#4112yes—
253C22×C4×C11C2411yescharacteristic
254C11×Q16—44no—
255C11×SD16—44no—
256C11×SD16—44no—
257C11×SD16—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×C11—21no—
269C2×C8×C11—21no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—24no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—42no—
279C11×C4⋊C4—81no—
280C11×C4⋊C4C2×D412yes—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—24no—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—22no—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—81no—
289C42×C11—21no—
290C42×C11—21no—
291C42×C11—42no—
292C42×C11—81no—
293C42×C11C2×D412yes—
294C42×C11C2×D412yes—
295C2×#535C2×C1111yescharacteristic
296C2×#464C2×C1111yescharacteristic, complemented
297C2×#460C2×C1111yescharacteristic, complemented
298C2×#452C2×C1111yescharacteristic, complemented
299C2×#450C2×C1111yescharacteristic, complemented
300#2323C2×C1111yescharacteristic, complemented
301#2042C2×C1111yescharacteristic, complemented
302#2041C2×C1111yescharacteristic, complemented
303#2015C2×C1111yescharacteristic, complemented
304#2014C2×C1111yescharacteristic, complemented
305#1983C2×C1111yescharacteristic, complemented
306#1982C2×C1111yescharacteristic, complemented
307#1798C2×C1111yescharacteristic, complemented
308#1788C2×C1111yescharacteristic, complemented
309#1786C2×C1111yescharacteristic, complemented
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—48no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—84no—
339C23×C11—84no—
340C23×C11—84no—
341C23×C11—84no—
342C23×C11—84no—
343C23×C11—84no—
344C23×C11#12112yes—
345C23×C11C22×D411yescharacteristic
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—22no—
349Q8×C11—22no—
350Q8×C11—41no—
351Q8×C11—41no—
352Q8×C11—41no—
353Q8×C11—41no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—22no—
359D4×C11—22no—
360D4×C11—48no—
361D4×C11—48no—
362D4×C11—41no—
363D4×C11—41no—
364D4×C11—41no—
365D4×C11—41no—
366D4×C11—41no—
367D4×C11—41no—
368D4×C11—84no—
369D4×C11—84no—
370D4×C11—84no—
371D4×C11—84no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
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—21no—
383C2×C4×C11—21no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—48no—
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#12012yes—
405C2×C4×C11#12012yes—
406C2×C4×C11#12112yes—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C2×#4111yescharacteristic
411C2×C4×C11H(5,𝔽2)11yescharacteristic
412C2×C4×C11H(5,𝔽2)11yescharacteristic
413C8×C11—41no—
414C8×C11—41no—
415C8×C11—41no—
416C8×C11—41no—
417C22×#41C22×C1111yescharacteristic
418C23×D4C22×C1111yescharacteristic
419C22×Q16C22×C1111yescharacteristic, complemented
420C22×SD16C22×C1111yescharacteristic
421C22×SD16C22×C1111yescharacteristic
422C22×SD16C22×C1111yescharacteristic, complemented
423#535—24no—
424#535—24no—
425C2×#127C22×C1111yescharacteristic
426C2×#127C22×C1111yescharacteristic
427C2×#124C22×C1111yescharacteristic
428C2×#124C22×C1111yescharacteristic
429C2×C22⋊Q8C22×C1111yescharacteristic
430C2×#121—21no—
431C2×#121—21no—
432C2×#120—21no—
433C2×#120—21no—
434C2×C4×Q8C22×C1111yescharacteristic, complemented
435C2×#117C22×C1111yescharacteristic
436#464—24no—
437#460—24no—
438#452—24no—
439#450—24no—
440C2×C4⋊C8C22×C1111yescharacteristic, complemented
441C2×C4⋊C8C22×C1111yescharacteristic, complemented
442C2×#103C22×C1111yescharacteristic, complemented
443C2×#103C22×C1111yescharacteristic, complemented
444C2×#103C22×C1111yescharacteristic, complemented
445C2×#102C22×C1111yescharacteristic
446C2×#102C22×C1111yescharacteristic
447C2×#102C22×C1111yescharacteristic
448C2×#102C22×C1111yescharacteristic
449C2×#102C22×C1111yescharacteristic
450C2×#102C22×C1111yescharacteristic
451C2×#102C22×C1111yescharacteristic, complemented
452C2×#102C22×C1111yescharacteristic, complemented
453C2×#102C22×C1111yescharacteristic, complemented
454C2×C22⋊C8C22×C1111yescharacteristic
455C2×C22⋊C8C22×C1111yescharacteristic
456#391C22×C1111yescharacteristic, complemented
457#389—21no—
458#389C22×C1111yescharacteristic, complemented
459#388—21no—
460#388—21no—
461#387—21no—
462#380C22×C1111yescharacteristic
463C4×C4⋊C4C22×C1111yescharacteristic, complemented
464#336C22×C1111yescharacteristic, complemented
465#336C22×C1111yescharacteristic, complemented
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—41no—
470C22×C11—41no—
471C22×C11—41no—
472C22×C11—41no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—816no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11—81no—
489C22×C11—81no—
490C22×C11—81no—
491C22×C11—81no—
492C22×C11—81no—
493C22×C11—81no—
494C22×C11—81no—
495C22×C11C2×#12011yescharacteristic
496C22×C11C2×#12111yescharacteristic
497C22×C11#53511yescharacteristic
498C22×C11#57611yescharacteristic
499C22×C11#57711yescharacteristic
500C22×C11#57711yescharacteristic
501C22×C11#57711yescharacteristic
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—22no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—41no—
508C4×C11—41no—
509C4×C11—42no—
510C4×C11—81no—
511C4×C11—81no—
512C4×C11D4211yescharacteristic
513C4×C11D4211yescharacteristic
514C4×C11#54611yescharacteristic
515C4×C11#54611yescharacteristic
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—41no—
522C2×#41—41no—
523C22×Q8C23×C1111yescharacteristic
524C22×Q8C23×C1111yescharacteristic
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—22no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4C23×C1111yescharacteristic
538C22×D4C23×C1111yescharacteristic
539C22×D4C23×C1111yescharacteristic
540C23×C4—21no—
541C23×C4C23×C1111yescharacteristic
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—41no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C22×C8C23×C1111yescharacteristic
555C22×C8C23×C1111yescharacteristic
556C22×C8C23×C1111yescharacteristic
557C22×C8C23×C1111yescharacteristic
558#127—22no—
559#127—22no—
560#127—22no—
561#127D4×C1114yes—
562#124—22no—
563#124—22no—
564#124—22no—
565#124D4×C1114yes—
566C22⋊Q8—22no—
567C22⋊Q8D4×C1114yescomplemented
568#121—28no—
569#121—28no—
570#120—28no—
571#120—28no—
572C4×Q8—22no—
573C4×Q8—22no—
574#117—22no—
575#117—22no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4D4×C1111yescharacteristic
580C2×C4⋊C4D4×C1111yescharacteristic
581C2×C4⋊C4C23×C1111yescharacteristic
582C2×C4⋊C4C23×C1111yescharacteristic
583C2×C4⋊C4C23×C1111yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C1111yescharacteristic
591C2×C22⋊C4D4×C1111yescharacteristic
592C2×C42—21no—
593C2×C42—21no—
594C2×C42C23×C1111yescharacteristic
595C2×C42C23×C1111yescharacteristic
596C4⋊C8—22no—
597C4⋊C8—22no—
598#103—22no—
599#103—22no—
600#103—41no—
601#102—22no—
602#102—22no—
603#102—22no—
604#102—22no—
605#102—22no—
606#102—22no—
607#102—41no—
608#102—41no—
609#102—41no—
610C22⋊C8—22no—
611C22⋊C8—22no—
612#95—21no—
613#95—21no—
614#95—21no—
615#95—21no—
616#95—21no—
617C2×C11—42no—
618C2×C11—82no—
619C2×C11—82no—
620C2×C11—82no—
621C2×C11#240811yescharacteristic
622C2×C11#300911yescharacteristic
623C2×C11#301211yescharacteristic
624C2×C11#304311yescharacteristic
625C2×C11#304511yescharacteristic
626C2×C11#322211yescharacteristic
627C2×C11#322411yescharacteristic
628C24—24no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—42no—
633C24—42no—
634C24—81no—
635C24—81no—
636C24—81no—
637C24—81no—
638C24C2×D4×C1111yescharacteristic
639#41—44no—
640#41—44no—
641#41—44no—
642#41—44no—
643C2×Q8—21no—
644C2×Q8—21no—
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×Q8C2×D4×C1112yes—
654C2×Q8C2×D4×C1112yes—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—81no—
685C2×D4—81no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4—81no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4C2×D4×C1112yes—
693C2×D4C2×D4×C1112yes—
694C2×D4C2×D4×C1112yes—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—24no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4C2×D4×C1111yescharacteristic
708C22×C4C2×D4×C1111yescharacteristic
709C22×C4C2×D4×C1111yescharacteristic
710C22×C4C2×D4×C1111yescharacteristic
711C22×C4C2×D4×C1111yescharacteristic
712C22×C4C2×D4×C1112yes—
713C22×C4C11×#4112yes—
714C22×C4C24×C1111yescharacteristic
715Q16—44no—
716SD16—44no—
717SD16—44no—
718SD16—44no—
719C2×C8—21no—
720C2×C8—21no—
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—
731C4⋊C4—22no—
732C4⋊C4—22no—
733C4⋊C4—24no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—42no—
740C4⋊C4—81no—
741C4⋊C4C2×D4×C1112yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—81no—
750C42—21no—
751C42—21no—
752C42—42no—
753C42—81no—
754C42C2×D4×C1112yes—
755C42C2×D4×C1112yes—
756C11#2422011yescharacteristic, direct product factor, Sylow
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—48no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23C11×#12112yes—
792C23C22×D4×C1111yescharacteristic
793Q8—22no—
794Q8—22no—
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—84no—
816D4—84no—
817D4—84no—
818D4—84no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—48no—
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×C4C11×#12012yes—
852C2×C4C11×#12012yes—
853C2×C4C11×#12112yes—
854C2×C4C22×D4×C1111yescharacteristic
855C2×C4C22×D4×C1111yescharacteristic
856C2×C4C22×D4×C1111yescharacteristic
857C2×C4C2×C11×#4111yescharacteristic
858C2×C4C11×H(5,𝔽2)11yescharacteristic
859C2×C4C11×H(5,𝔽2)11yescharacteristic
860C8—41no—
861C8—41no—
862C8—41no—
863C8—41no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—816no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22C2×C11×#12011yescharacteristic
894C22C2×C11×#12111yescharacteristic
895C22C11×#53511yescharacteristic
896C22C11×#57611yescharacteristic
897C22C11×#57711yescharacteristic
898C22C11×#57711yescharacteristic
899C22C11×#57711yescharacteristic
900C4—22no—
901C4—22no—
902C4—22no—
903C4—42no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—81no—
909C4—81no—
910C4D42×C1111yescharacteristic
911C4D42×C1111yescharacteristic
912C4C11×#54611yescharacteristic
913C4C11×#54611yescharacteristic
914C2—42no—
915C2—82no—
916C2—82no—
917C2—82no—
918C2C11×#240811yescharacteristic
919C2C11×#300911yescharacteristic
920C2C11×#301211yescharacteristic
921C2C11×#304311yescharacteristic
922C2C11×#304511yescharacteristic
923C2C11×#322211yescharacteristic
924C2C11×#322411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#464C2semidirect
3. C2×C11×#460C2semidirect
4. C2×C11×#452C2semidirect
5. C2×C11×#450C2semidirect
6. C11×#2323C2semidirect
7. C11×#2042C2semidirect
8. C11×#2041C2semidirect
9. C11×#2015C2semidirect
10. C11×#2014C2semidirect
11. C11×#1983C2semidirect
12. C11×#1982C2semidirect
13. C11×#1798C2semidirect
14. C11×#1788C2semidirect
15. C11×#1786C2semidirect
18. C22×C11×Q16C22semidirect
21. C22×C11×SD16C22semidirect
33. C2×C4×Q8×C11C22semidirect
39. C2×C11×C4⋊C8C22semidirect
40. C2×C11×C4⋊C8C22semidirect
41. C2×C11×#103C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#103C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×#102C22semidirect
55. C11×#391C22semidirect
57. C11×#389C22semidirect
62. C4×C11×C4⋊C4C22semidirect
63. C11×#336C22semidirect
64. C11×#336C22semidirect
116. C11×C22⋊Q8D4semidirect
166. #24220C11direct (N × H)
296. C2×#464C2×C11semidirect
297. C2×#460C2×C11semidirect
298. C2×#452C2×C11semidirect
299. C2×#450C2×C11semidirect
300. #2323C2×C11semidirect
301. #2042C2×C11semidirect
302. #2041C2×C11semidirect
303. #2015C2×C11semidirect
304. #2014C2×C11semidirect
305. #1983C2×C11semidirect
306. #1982C2×C11semidirect
307. #1798C2×C11semidirect
308. #1788C2×C11semidirect
309. #1786C2×C11semidirect
419. C22×Q16C22×C11semidirect
422. C22×SD16C22×C11semidirect
434. C2×C4×Q8C22×C11semidirect
440. C2×C4⋊C8C22×C11semidirect
441. C2×C4⋊C8C22×C11semidirect
442. C2×#103C22×C11semidirect
443. C2×#103C22×C11semidirect
444. C2×#103C22×C11semidirect
451. C2×#102C22×C11semidirect
452. C2×#102C22×C11semidirect
453. C2×#102C22×C11semidirect
456. #391C22×C11semidirect
458. #389C22×C11semidirect
463. C4×C4⋊C4C22×C11semidirect
464. #336C22×C11semidirect
465. #336C22×C11semidirect
567. C22⋊Q8D4×C11semidirect
756. C11#24220direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4642
C2×C11×#4602
C2×C11×#4522
C2×C11×#4502
C11×#23232
C11×#20422
C11×#20412
C11×#20152
C11×#20142
C11×#19832
C11×#19822
C11×#17982
C11×#17882
C11×#17862
#2422011