Finite Group Databasebeta

← C11×#24247 #14601440

Subgroups — C11×#24247 #14601440

Order 2816.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 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×C4×C11×SD16C211yesmaximal, characteristic, complemented
6C11×#2536C211yesmaximal, characteristic, complemented
7C11×#2035C211yesmaximal, characteristic, complemented
8C11×#2034C211yesmaximal, characteristic, complemented
9C11×#2001C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1958C211yesmaximal, characteristic, complemented
12C11×#1954C211yesmaximal, characteristic, complemented
13C11×#1804C211yesmaximal, 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—
38C4×C11×SD16—24no—
39C2×C11×#106C2211yescharacteristic, 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×C4×C8×C11C2211yescharacteristic, complemented
56C11×#398—21no—
57C11×#394—21no—
58C11×#388—21no—
59C11×#388—21no—
60C11×#382C2211yescharacteristic, 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⋊C4D411yescharacteristic
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—28no—
132C2×C11×C22⋊C4—21no—
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⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4D411yescharacteristic
142C2×C11×C22⋊C4D411yescharacteristic
143C2×C42×C11—21no—
144C2×C42×C11C2311yescharacteristic
145C11×#106—22no—
146C11×C4⋊C8—22no—
147C11×#103—22no—
148C11×#103—22no—
149C11×#103—22no—
150C11×#103—41no—
151C11×#102—22no—
152C11×#102—22no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—41no—
157C11×C22⋊C8—22no—
158C11×C22⋊C8—22no—
159C11×C22⋊C8—41no—
160C11×C22⋊C8—41no—
161C4×C8×C11—22no—
162C11×#95—21no—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24247C1111yesmaximal, 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⋊C4C2×D412yes—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—24no—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—22no—
286C11×C22⋊C4—42no—
287C11×C22⋊C4—42no—
288C11×C22⋊C4—42no—
289C11×C22⋊C4—42no—
290C42×C11—42no—
291C42×C11C2×D412yes—
292C42×C11C2×D412yes—
293C2×#546C2×C1111yescharacteristic
294C2×#464C2×C1111yescharacteristic, complemented
295C2×#452C2×C1111yescharacteristic, complemented
296C2×#450C2×C1111yescharacteristic, complemented
297C2×C4×SD16C2×C1111yescharacteristic, complemented
298#2536C2×C1111yescharacteristic, complemented
299#2035C2×C1111yescharacteristic, complemented
300#2034C2×C1111yescharacteristic, complemented
301#2001C2×C1111yescharacteristic, complemented
302#2000C2×C1111yescharacteristic, complemented
303#1958C2×C1111yescharacteristic, complemented
304#1954C2×C1111yescharacteristic, complemented
305#1804C2×C1111yescharacteristic, complemented
306#1788C2×C1111yescharacteristic, complemented
307#1786C2×C1111yescharacteristic, complemented
308C23×C11—21no—
309C23×C11—22no—
310C23×C11—21no—
311C23×C11—22no—
312C23×C11—21no—
313C23×C11—22no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—22no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—48no—
326C23×C11—48no—
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—84no—
338C23×C11—84no—
339C23×C11—84no—
340C23×C11—84no—
341C23×C11—84no—
342C23×C11#13512yes—
343C23×C11C22×D411yescharacteristic
344Q8×C11—22no—
345Q8×C11—22no—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—41no—
349Q8×C11—41no—
350Q8×C11—41no—
351Q8×C11—41no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—44no—
358D4×C11—48no—
359D4×C11—48no—
360D4×C11—41no—
361D4×C11—41no—
362D4×C11—84no—
363D4×C11#12114yes—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—22no—
369C2×C4×C11—21no—
370C2×C4×C11—22no—
371C2×C4×C11—21no—
372C2×C4×C11—22no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—48no—
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—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—84no—
402C2×C4×C11#12012yes—
403C2×C4×C11#12012yes—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C2×#4111yescharacteristic
408C2×C4×C11H(5,𝔽2)11yescharacteristic
409C2×C4×C11H(5,𝔽2)11yescharacteristic
410C8×C11—22no—
411C8×C11—41no—
412C8×C11—41no—
413C8×C11—41no—
414C22×#41C22×C1111yescharacteristic
415C23×D4C22×C1111yescharacteristic
416C22×Q16C22×C1111yescharacteristic, complemented
417C22×SD16C22×C1111yescharacteristic
418C22×SD16C22×C1111yescharacteristic
419#546—24no—
420#546—24no—
421C2×#124C22×C1111yescharacteristic
422C2×#123—21no—
423C2×C22⋊Q8C22×C1111yescharacteristic
424C2×C22⋊Q8C22×C1111yescharacteristic
425C2×C22⋊Q8C22×C1111yescharacteristic, complemented
426C2×#121—21no—
427C2×#121C22×C1111yescharacteristic
428C2×#120—21no—
429C2×C4×Q8C22×C1111yescharacteristic, complemented
430C2×C4×D4C22×C1111yescharacteristic
431C2×C4×D4C22×C1111yescharacteristic
432C22×C22⋊C4—21no—
433#464—24no—
434#452—24no—
435#450—24no—
436C4×SD16—24no—
437C2×#106C22×C1111yescharacteristic, complemented
438C2×C4⋊C8C22×C1111yescharacteristic, complemented
439C2×#103C22×C1111yescharacteristic, complemented
440C2×#103C22×C1111yescharacteristic, complemented
441C2×#103C22×C1111yescharacteristic, complemented
442C2×#103C22×C1111yescharacteristic, complemented
443C2×#102C22×C1111yescharacteristic
444C2×#102C22×C1111yescharacteristic
445C2×#102C22×C1111yescharacteristic
446C2×#102C22×C1111yescharacteristic
447C2×#102C22×C1111yescharacteristic
448C2×#102C22×C1111yescharacteristic
449C2×C22⋊C8C22×C1111yescharacteristic
450C2×C22⋊C8C22×C1111yescharacteristic
451C2×C22⋊C8C22×C1111yescharacteristic, complemented
452C2×C22⋊C8C22×C1111yescharacteristic, complemented
453C2×C4×C8C22×C1111yescharacteristic, complemented
454#398—21no—
455#394—21no—
456#388—21no—
457#388—21no—
458#382C22×C1111yescharacteristic, complemented
459#380C22×C1111yescharacteristic
460#380C22×C1111yescharacteristic, complemented
461#340C22×C1111yescharacteristic, complemented
462#340C22×C1111yescharacteristic, complemented
463C22×C11—24no—
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—41no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—41no—
471C22×C11—41no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—41no—
476C22×C11—42no—
477C22×C11—41no—
478C22×C11—42no—
479C22×C11—41no—
480C22×C11—42no—
481C22×C11—41no—
482C22×C11—42no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—41no—
487C22×C11—816no—
488C22×C11—81no—
489C22×C11—81no—
490C22×C11—81no—
491C22×C11—81no—
492C22×C11C2×#12011yescharacteristic
493C22×C11D4211yescharacteristic
494C22×C11#54611yescharacteristic
495C22×C11C2×#13511yescharacteristic
496C22×C11#57511yescharacteristic
497C22×C11#57711yescharacteristic
498C22×C11#57711yescharacteristic
499C4×C11—22no—
500C4×C11—22no—
501C4×C11—41no—
502C4×C11—41no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—81no—
507C4×C11—81no—
508C4×C11—81no—
509C4×C11C2×#12111yescharacteristic
510C4×C11#53511yescharacteristic
511C4×C11D4211yescharacteristic
512C4×C11#54611yescharacteristic
513C25—21no—
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—41no—
519C2×#41—41no—
520C22×Q8C23×C1111yescharacteristic
521C22×Q8C23×C1111yescharacteristic
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—22no—
527C22×D4—22no—
528C22×D4—21no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4D4×C1111yescharacteristic
532C22×D4C23×C1111yescharacteristic
533C22×D4C23×C1111yescharacteristic
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C23×C1111yescharacteristic
537C23×C4C23×C1111yescharacteristic
538C2×Q16—22no—
539C2×Q16—22no—
540C2×Q16—41no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—41no—
546C2×SD16D4×C1114yescomplemented
547C22×C8C23×C1111yescharacteristic
548C22×C8C23×C1111yescharacteristic
549C22×C8C23×C1111yescharacteristic
550C22×C8C23×C1111yescharacteristic
551#124—22no—
552#124D4×C1114yes—
553#123—28no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560#121—28no—
561#121—22no—
562#121—22no—
563#120—28no—
564C4×Q8—22no—
565C4×Q8—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4D4×C1114yes—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4D4×C1111yescharacteristic
575C2×C4⋊C4C23×C1111yescharacteristic
576C2×C4⋊C4C23×C1111yescharacteristic
577C2×C4⋊C4C23×C1111yescharacteristic
578C2×C4⋊C4C23×C1111yescharacteristic
579C2×C22⋊C4—28no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C1111yescharacteristic
590C2×C22⋊C4D4×C1111yescharacteristic
591C2×C42—21no—
592C2×C42C23×C1111yescharacteristic
593#106—22no—
594C4⋊C8—22no—
595#103—22no—
596#103—22no—
597#103—22no—
598#103—41no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—22no—
604#102—41no—
605C22⋊C8—22no—
606C22⋊C8—22no—
607C22⋊C8—41no—
608C22⋊C8—41no—
609C4×C8—22no—
610#95—21no—
611#95—21no—
612#95—21no—
613#95—21no—
614C2×C11—42no—
615C2×C11—44no—
616C2×C11—81no—
617C2×C11—82no—
618C2×C11#240811yescharacteristic
619C2×C11#300211yescharacteristic
620C2×C11#300911yescharacteristic
621C2×C11#327511yescharacteristic
622C2×C11#328211yescharacteristic
623C2×C11#329611yescharacteristic
624C2×C11#332311yescharacteristic
625C24—21no—
626C24—24no—
627C24—21no—
628C24—42no—
629C24—42no—
630C24—42no—
631C24—42no—
632C24—81no—
633C24—81no—
634C24C2×D4×C1111yescharacteristic
635C24C2×D4×C1111yescharacteristic
636#41—44no—
637#41—44no—
638#41—44no—
639#41—44no—
640C2×Q8—21no—
641C2×Q8—21no—
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×Q8C2×D4×C1112yes—
651C2×Q8C2×D4×C1112yes—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—41no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—44no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4C2×D4×C1112yes—
677C2×D4C2×D4×C1112yes—
678C2×D4C2×D4×C1112yes—
679C2×D4C11×#4112yes—
680C22×C4—24no—
681C22×C4—21no—
682C22×C4—21no—
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—24no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—81no—
703C22×C4—81no—
704C22×C4C2×D4×C1111yescharacteristic
705C22×C4C2×D4×C1111yescharacteristic
706C22×C4C2×D4×C1111yescharacteristic
707C22×C4C2×D4×C1111yescharacteristic
708C22×C4C24×C1111yescharacteristic
709Q16—44no—
710SD16—28no—
711SD16—44no—
712C2×C8—21no—
713C2×C8—21no—
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×C8C2×D4×C1112yes—
724C4⋊C4—24no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4C2×D4×C1112yes—
737C22⋊C4—24no—
738C22⋊C4—24no—
739C22⋊C4—22no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—22no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C42—42no—
749C42C2×D4×C1112yes—
750C42C2×D4×C1112yes—
751C11#2424711yescharacteristic, direct product factor, Sylow
752C23—21no—
753C23—22no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—48no—
770C23—48no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—84no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23C11×#13512yes—
787C23C22×D4×C1111yescharacteristic
788Q8—22no—
789Q8—22no—
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—44no—
802D4—48no—
803D4—48no—
804D4—41no—
805D4—41no—
806D4—84no—
807D4C11×#12114yes—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
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—84no—
846C2×C4C11×#12012yes—
847C2×C4C11×#12012yes—
848C2×C4C22×D4×C1111yescharacteristic
849C2×C4C22×D4×C1111yescharacteristic
850C2×C4C22×D4×C1111yescharacteristic
851C2×C4C2×C11×#4111yescharacteristic
852C2×C4C11×H(5,𝔽2)11yescharacteristic
853C2×C4C11×H(5,𝔽2)11yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—816no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22C2×C11×#12011yescharacteristic
888C22D42×C1111yescharacteristic
889C22C11×#54611yescharacteristic
890C22C2×C11×#13511yescharacteristic
891C22C11×#57511yescharacteristic
892C22C11×#57711yescharacteristic
893C22C11×#57711yescharacteristic
894C4—22no—
895C4—22no—
896C4—41no—
897C4—41no—
898C4—42no—
899C4—42no—
900C4—42no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4C2×C11×#12111yescharacteristic
905C4C11×#53511yescharacteristic
906C4D42×C1111yescharacteristic
907C4C11×#54611yescharacteristic
908C2—42no—
909C2—44no—
910C2—81no—
911C2—82no—
912C2C11×#240811yescharacteristic
913C2C11×#300211yescharacteristic
914C2C11×#300911yescharacteristic
915C2C11×#327511yescharacteristic
916C2C11×#328211yescharacteristic
917C2C11×#329611yescharacteristic
918C2C11×#332311yescharacteristic
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×C4×C11×SD16C2semidirect
6. C11×#2536C2semidirect
7. C11×#2035C2semidirect
8. C11×#2034C2semidirect
9. C11×#2001C2semidirect
10. C11×#2000C2semidirect
11. C11×#1958C2semidirect
12. C11×#1954C2semidirect
13. C11×#1804C2semidirect
14. C11×#1788C2semidirect
15. C11×#1786C2semidirect
18. C22×C11×Q16C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
31. C2×C4×Q8×C11C22semidirect
39. C2×C11×#106C22semidirect
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×C4×C8×C11C22semidirect
60. C11×#382C22semidirect
62. C11×#380C22semidirect
63. C11×#340C22semidirect
64. C11×#340C22semidirect
98. C2×C11×SD16D4semidirect
166. #24247C11direct (N × H)
294. C2×#464C2×C11semidirect
295. C2×#452C2×C11semidirect
296. C2×#450C2×C11semidirect
297. C2×C4×SD16C2×C11semidirect
298. #2536C2×C11semidirect
299. #2035C2×C11semidirect
300. #2034C2×C11semidirect
301. #2001C2×C11semidirect
302. #2000C2×C11semidirect
303. #1958C2×C11semidirect
304. #1954C2×C11semidirect
305. #1804C2×C11semidirect
306. #1788C2×C11semidirect
307. #1786C2×C11semidirect
416. C22×Q16C22×C11semidirect
425. C2×C22⋊Q8C22×C11semidirect
429. C2×C4×Q8C22×C11semidirect
437. C2×#106C22×C11semidirect
438. C2×C4⋊C8C22×C11semidirect
439. C2×#103C22×C11semidirect
440. C2×#103C22×C11semidirect
441. C2×#103C22×C11semidirect
442. C2×#103C22×C11semidirect
451. C2×C22⋊C8C22×C11semidirect
452. C2×C22⋊C8C22×C11semidirect
453. C2×C4×C8C22×C11semidirect
458. #382C22×C11semidirect
460. #380C22×C11semidirect
461. #340C22×C11semidirect
462. #340C22×C11semidirect
546. C2×SD16D4×C11semidirect
751. C11#24247direct (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×C4×C11×SD162
C11×#25362
C11×#20352
C11×#20342
C11×#20012
C11×#20002
C11×#19582
C11×#19542
C11×#18042
C11×#17882
C11×#17862
#2424711