Finite Group Databasebeta

← C11×#24259 #14601452

Subgroups — C11×#24259 #14601452

Order 2816.

1566 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic
2C2×C11×#464C211yesmaximal, characteristic, complemented
3C2×C11×#452C211yesmaximal, characteristic, complemented
4C2×C11×#450C211yesmaximal, characteristic, complemented
5C2×C11×#440C211yesmaximal, characteristic, complemented
6C11×#2538C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#2001C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1959C211yesmaximal, characteristic, complemented
12C11×#1955C211yesmaximal, characteristic, complemented
13C11×#1802C211yesmaximal, 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
21C11×#546—24no—
22C11×#546—24no—
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic, complemented
28C2×C11×#121—21no—
29C2×C11×#121C2211yescharacteristic
30C2×C11×#120—21no—
31C2×C4×Q8×C11C2211yescharacteristic, complemented
32C2×C4×D4×C11C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C22×C11×C22⋊C4—21no—
35C11×#464—24no—
36C11×#452—24no—
37C11×#450—24no—
38C11×#440—24no—
39C2×C11×#107C2211yescharacteristic, complemented
40C2×C11×C4⋊C8C2211yescharacteristic, complemented
41C2×C11×#103C2211yescharacteristic, complemented
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#103C2211yescharacteristic, complemented
44C2×C11×#103C2211yescharacteristic, complemented
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C2×C11×C22⋊C8C2211yescharacteristic, complemented
55C2×C11×#97C2211yescharacteristic, complemented
56C11×#396—21no—
57C11×#396—21no—
58C11×#390—21no—
59C11×#389—21no—
60C11×#384C2211yescharacteristic, complemented
61C11×#380C2211yescharacteristic
62C11×#380C2211yescharacteristic, complemented
63C11×#340C2211yescharacteristic, complemented
64C11×#340C2211yescharacteristic, 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—21no—
76C22×D4×C11—22no—
77C22×D4×C11—22no—
78C22×D4×C11—22no—
79C22×D4×C11—22no—
80C22×D4×C11—21no—
81C22×D4×C11—41no—
82C22×D4×C11—41no—
83C22×D4×C11D411yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
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—41no—
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16—41no—
98C2×C11×SD16D414yescomplemented
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C11×#124—22no—
104C11×#124D414yes—
105C11×#123—28no—
106C11×C22⋊Q8—22no—
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8—22no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—41no—
111C11×C22⋊Q8—41no—
112C11×#121—28no—
113C11×#121—22no—
114C11×#121—22no—
115C11×#120—28no—
116C4×Q8×C11—22no—
117C4×Q8×C11—22no—
118C4×D4×C11—22no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11D414yes—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4D411yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C22⋊C4—28no—
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⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4D411yescharacteristic
144C2×C11×C22⋊C4D411yescharacteristic
145C2×C42×C11—21no—
146C2×C42×C11C2311yescharacteristic
147C11×#107—22no—
148C11×C4⋊C8—22no—
149C11×#103—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103—41no—
153C11×#102—22no—
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—41no—
162C11×C22⋊C8—41no—
163C11×#97—22no—
164C11×#95—21no—
165C11×#95—21no—
166#24259C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11—24no—
169C24×C11—21no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—81no—
175C24×C11—81no—
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×C11C2×D412yes—
193C2×Q8×C11C2×D412yes—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—22no—
197C2×D4×C11—24no—
198C2×D4×C11—22no—
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—41no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—44no—
211C2×D4×C11—44no—
212C2×D4×C11—44no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—44no—
216C2×D4×C11—81no—
217C2×D4×C11—81no—
218C2×D4×C11C2×D412yes—
219C2×D4×C11C2×D412yes—
220C2×D4×C11C2×D412yes—
221C2×D4×C11#4112yes—
222C22×C4×C11—24no—
223C22×C4×C11—21no—
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—21no—
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—42no—
243C22×C4×C11—42no—
244C22×C4×C11—81no—
245C22×C4×C11—81no—
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C11×Q16—44no—
252C11×SD16—28no—
253C11×SD16—44no—
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×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11C2×D412yes—
266C11×C4⋊C4—24no—
267C11×C4⋊C4—22no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—42no—
276C11×C4⋊C4—42no—
277C11×C4⋊C4—42no—
278C11×C4⋊C4—42no—
279C11×C4⋊C4—81no—
280C11×C4⋊C4C2×D412yes—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—24no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—42no—
289C11×C22⋊C4—42no—
290C11×C22⋊C4—81no—
291C11×C22⋊C4—81no—
292C42×C11—42no—
293C42×C11C2×D412yes—
294C42×C11C2×D412yes—
295C2×#546C2×C1111yescharacteristic
296C2×#464C2×C1111yescharacteristic, complemented
297C2×#452C2×C1111yescharacteristic, complemented
298C2×#450C2×C1111yescharacteristic, complemented
299C2×#440C2×C1111yescharacteristic, complemented
300#2538C2×C1111yescharacteristic, complemented
301#2036C2×C1111yescharacteristic, complemented
302#2033C2×C1111yescharacteristic, complemented
303#2001C2×C1111yescharacteristic, complemented
304#2000C2×C1111yescharacteristic, complemented
305#1959C2×C1111yescharacteristic, complemented
306#1955C2×C1111yescharacteristic, complemented
307#1802C2×C1111yescharacteristic, complemented
308#1788C2×C1111yescharacteristic, complemented
309#1786C2×C1111yescharacteristic, complemented
310C23×C11—21no—
311C23×C11—22no—
312C23×C11—21no—
313C23×C11—22no—
314C23×C11—21no—
315C23×C11—22no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—22no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—48no—
328C23×C11—48no—
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—41no—
339C23×C11—84no—
340C23×C11—84no—
341C23×C11—84no—
342C23×C11—84no—
343C23×C11—84no—
344C23×C11#13712yes—
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—44no—
360D4×C11—48no—
361D4×C11—48no—
362D4×C11—41no—
363D4×C11—41no—
364D4×C11—84no—
365D4×C11#12114yes—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—22no—
371C2×C4×C11—21no—
372C2×C4×C11—22no—
373C2×C4×C11—21no—
374C2×C4×C11—22no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—48no—
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—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—84no—
404C2×C4×C11#12012yes—
405C2×C4×C11#12012yes—
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C2×#4111yescharacteristic
410C2×C4×C11H(5,𝔽2)11yescharacteristic
411C2×C4×C11H(5,𝔽2)11yescharacteristic
412C8×C11—22no—
413C8×C11—41no—
414C8×C11—41no—
415C8×C11—41no—
416C22×#41C22×C1111yescharacteristic
417C23×D4C22×C1111yescharacteristic
418C22×Q16C22×C1111yescharacteristic, complemented
419C22×SD16C22×C1111yescharacteristic
420C22×SD16C22×C1111yescharacteristic
421#546—24no—
422#546—24no—
423C2×#124C22×C1111yescharacteristic
424C2×#123—21no—
425C2×C22⋊Q8C22×C1111yescharacteristic
426C2×C22⋊Q8C22×C1111yescharacteristic
427C2×C22⋊Q8C22×C1111yescharacteristic, complemented
428C2×#121—21no—
429C2×#121C22×C1111yescharacteristic
430C2×#120—21no—
431C2×C4×Q8C22×C1111yescharacteristic, complemented
432C2×C4×D4C22×C1111yescharacteristic
433C2×C4×D4C22×C1111yescharacteristic
434C22×C22⋊C4—21no—
435#464—24no—
436#452—24no—
437#450—24no—
438#440—24no—
439C2×#107C22×C1111yescharacteristic, complemented
440C2×C4⋊C8C22×C1111yescharacteristic, complemented
441C2×#103C22×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×C22⋊C8C22×C1111yescharacteristic
452C2×C22⋊C8C22×C1111yescharacteristic
453C2×C22⋊C8C22×C1111yescharacteristic, complemented
454C2×C22⋊C8C22×C1111yescharacteristic, complemented
455C2×#97C22×C1111yescharacteristic, complemented
456#396—21no—
457#396—21no—
458#390—21no—
459#389—21no—
460#384C22×C1111yescharacteristic, complemented
461#380C22×C1111yescharacteristic
462#380C22×C1111yescharacteristic, complemented
463#340C22×C1111yescharacteristic, complemented
464#340C22×C1111yescharacteristic, complemented
465C22×C11—24no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—41no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—41no—
474C22×C11—41no—
475C22×C11—42no—
476C22×C11—41no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—41no—
480C22×C11—42no—
481C22×C11—41no—
482C22×C11—42no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—42no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—41no—
489C22×C11—816no—
490C22×C11—81no—
491C22×C11—81no—
492C22×C11—81no—
493C22×C11—81no—
494C22×C11C2×#12011yescharacteristic
495C22×C11D4211yescharacteristic
496C22×C11#54611yescharacteristic
497C22×C11C2×#13711yescharacteristic
498C22×C11#57511yescharacteristic
499C22×C11#57611yescharacteristic
500C22×C11#57711yescharacteristic
501C4×C11—22no—
502C4×C11—22no—
503C4×C11—41no—
504C4×C11—41no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—81no—
509C4×C11—81no—
510C4×C11—81no—
511C4×C11C2×#12111yescharacteristic
512C4×C11#53511yescharacteristic
513C4×C11D4211yescharacteristic
514C4×C11#54611yescharacteristic
515C25—21no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C22×Q8C23×C1111yescharacteristic
523C22×Q8C23×C1111yescharacteristic
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—22no—
528C22×D4—22no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4D4×C1111yescharacteristic
534C22×D4C23×C1111yescharacteristic
535C22×D4C23×C1111yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C23×C1111yescharacteristic
539C23×C4C23×C1111yescharacteristic
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—41no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—41no—
548C2×SD16D4×C1114yescomplemented
549C22×C8C23×C1111yescharacteristic
550C22×C8C23×C1111yescharacteristic
551C22×C8C23×C1111yescharacteristic
552C22×C8C23×C1111yescharacteristic
553#124—22no—
554#124D4×C1114yes—
555#123—28no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562#121—28no—
563#121—22no—
564#121—22no—
565#120—28no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4D4×C1114yes—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4D4×C1111yescharacteristic
579C2×C4⋊C4C23×C1111yescharacteristic
580C2×C4⋊C4C23×C1111yescharacteristic
581C2×C4⋊C4C23×C1111yescharacteristic
582C2×C4⋊C4C23×C1111yescharacteristic
583C2×C22⋊C4—28no—
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⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4D4×C1111yescharacteristic
594C2×C22⋊C4D4×C1111yescharacteristic
595C2×C42—21no—
596C2×C42C23×C1111yescharacteristic
597#107—22no—
598C4⋊C8—22no—
599#103—22no—
600#103—22no—
601#103—22no—
602#103—41no—
603#102—22no—
604#102—22no—
605#102—22no—
606#102—22no—
607#102—22no—
608#102—41no—
609C22⋊C8—22no—
610C22⋊C8—22no—
611C22⋊C8—41no—
612C22⋊C8—41no—
613#97—22no—
614#95—21no—
615#95—21no—
616C2×C11—42no—
617C2×C11—44no—
618C2×C11—81no—
619C2×C11—82no—
620C2×C11#240811yescharacteristic
621C2×C11#300711yescharacteristic
622C2×C11#301211yescharacteristic
623C2×C11#326611yescharacteristic
624C2×C11#326811yescharacteristic
625C2×C11#331111yescharacteristic
626C2×C11#331411yescharacteristic
627C24—21no—
628C24—24no—
629C24—21no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—81no—
635C24—81no—
636C24C2×D4×C1111yescharacteristic
637C24C2×D4×C1111yescharacteristic
638#41—44no—
639#41—44no—
640#41—44no—
641#41—44no—
642C2×Q8—21no—
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×Q8C2×D4×C1112yes—
653C2×Q8C2×D4×C1112yes—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—44no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4C2×D4×C1112yes—
679C2×D4C2×D4×C1112yes—
680C2×D4C2×D4×C1112yes—
681C2×D4C11×#4112yes—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
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—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—81no—
705C22×C4—81no—
706C22×C4C2×D4×C1111yescharacteristic
707C22×C4C2×D4×C1111yescharacteristic
708C22×C4C2×D4×C1111yescharacteristic
709C22×C4C2×D4×C1111yescharacteristic
710C22×C4C24×C1111yescharacteristic
711Q16—44no—
712SD16—28no—
713SD16—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8C2×D4×C1112yes—
726C4⋊C4—24no—
727C4⋊C4—22no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4—81no—
740C4⋊C4C2×D4×C1112yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—22no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—81no—
751C22⋊C4—81no—
752C42—42no—
753C42C2×D4×C1112yes—
754C42C2×D4×C1112yes—
755C11#2425911yescharacteristic, direct product factor, Sylow
756C23—21no—
757C23—22no—
758C23—21no—
759C23—22no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—48no—
774C23—48no—
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—
790C23C11×#13712yes—
791C23C22×D4×C1111yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—22no—
795Q8—22no—
796Q8—41no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—44no—
806D4—48no—
807D4—48no—
808D4—41no—
809D4—41no—
810D4—84no—
811D4C11×#12114yes—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
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—84no—
850C2×C4C11×#12012yes—
851C2×C4C11×#12012yes—
852C2×C4C22×D4×C1111yescharacteristic
853C2×C4C22×D4×C1111yescharacteristic
854C2×C4C22×D4×C1111yescharacteristic
855C2×C4C2×C11×#4111yescharacteristic
856C2×C4C11×H(5,𝔽2)11yescharacteristic
857C2×C4C11×H(5,𝔽2)11yescharacteristic
858C8—22no—
859C8—41no—
860C8—41no—
861C8—41no—
862C22—24no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—816no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22C2×C11×#12011yescharacteristic
892C22D42×C1111yescharacteristic
893C22C11×#54611yescharacteristic
894C22C2×C11×#13711yescharacteristic
895C22C11×#57511yescharacteristic
896C22C11×#57611yescharacteristic
897C22C11×#57711yescharacteristic
898C4—22no—
899C4—22no—
900C4—41no—
901C4—41no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—81no—
906C4—81no—
907C4—81no—
908C4C2×C11×#12111yescharacteristic
909C4C11×#53511yescharacteristic
910C4D42×C1111yescharacteristic
911C4C11×#54611yescharacteristic
912C2—42no—
913C2—44no—
914C2—81no—
915C2—82no—
916C2C11×#240811yescharacteristic
917C2C11×#300711yescharacteristic
918C2C11×#301211yescharacteristic
919C2C11×#326611yescharacteristic
920C2C11×#326811yescharacteristic
921C2C11×#331111yescharacteristic
922C2C11×#331411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#546C2
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×#464C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C11×#450C2semidirect
5. C2×C11×#440C2semidirect
6. C11×#2538C2semidirect
7. C11×#2036C2semidirect
8. C11×#2033C2semidirect
9. C11×#2001C2semidirect
10. C11×#2000C2semidirect
11. C11×#1959C2semidirect
12. C11×#1955C2semidirect
13. C11×#1802C2semidirect
14. C11×#1788C2semidirect
15. C11×#1786C2semidirect
18. C22×C11×Q16C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
31. C2×C4×Q8×C11C22semidirect
39. C2×C11×#107C22semidirect
40. C2×C11×C4⋊C8C22semidirect
41. C2×C11×#103C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#103C22semidirect
44. C2×C11×#103C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. C2×C11×C22⋊C8C22semidirect
55. C2×C11×#97C22semidirect
60. C11×#384C22semidirect
62. C11×#380C22semidirect
63. C11×#340C22semidirect
64. C11×#340C22semidirect
98. C2×C11×SD16D4semidirect
166. #24259C11direct (N × H)
296. C2×#464C2×C11semidirect
297. C2×#452C2×C11semidirect
298. C2×#450C2×C11semidirect
299. C2×#440C2×C11semidirect
300. #2538C2×C11semidirect
301. #2036C2×C11semidirect
302. #2033C2×C11semidirect
303. #2001C2×C11semidirect
304. #2000C2×C11semidirect
305. #1959C2×C11semidirect
306. #1955C2×C11semidirect
307. #1802C2×C11semidirect
308. #1788C2×C11semidirect
309. #1786C2×C11semidirect
418. C22×Q16C22×C11semidirect
427. C2×C22⋊Q8C22×C11semidirect
431. C2×C4×Q8C22×C11semidirect
439. C2×#107C22×C11semidirect
440. C2×C4⋊C8C22×C11semidirect
441. C2×#103C22×C11semidirect
442. C2×#103C22×C11semidirect
443. C2×#103C22×C11semidirect
444. C2×#103C22×C11semidirect
453. C2×C22⋊C8C22×C11semidirect
454. C2×C22⋊C8C22×C11semidirect
455. C2×#97C22×C11semidirect
460. #384C22×C11semidirect
462. #380C22×C11semidirect
463. #340C22×C11semidirect
464. #340C22×C11semidirect
548. C2×SD16D4×C11semidirect
755. C11#24259direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5462
C2×C11×#4642
C2×C11×#4522
C2×C11×#4502
C2×C11×#4402
C11×#25382
C11×#20362
C11×#20332
C11×#20012
C11×#20002
C11×#19592
C11×#19552
C11×#18022
C11×#17882
C11×#17862
#2425911