Finite Group Databasebeta

← C11×#24218 #14601411

Subgroups — C11×#24218 #14601411

Order 2816.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic, complemented
2C2×C11×#463C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic, complemented
4C2×C11×#449C211yesmaximal, characteristic, complemented
5C2×C11×#447C211yesmaximal, characteristic, complemented
6C11×#2324C211yesmaximal, characteristic, complemented
7C11×#2042C211yesmaximal, characteristic, complemented
8C11×#2041C211yesmaximal, characteristic, complemented
9C11×#2012C211yesmaximal, characteristic, complemented
10C11×#2011C211yesmaximal, 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×SD16C2211yescharacteristic, complemented
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C22×C11×D8C2211yescharacteristic, complemented
22C11×#535—24no—
23C11×#535—24no—
24C2×C11×#127C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C2×C11×#124C2211yescharacteristic
28C2×C11×#121—21no—
29C2×C11×#121—21no—
30C2×C11×#121C2211yescharacteristic
31C2×C11×#120—21no—
32C2×C11×#120—21no—
33C2×C4×D4×C11C2211yescharacteristic, complemented
34C2×C11×#117C2211yescharacteristic
35C11×#463—24no—
36C11×#459—24no—
37C11×#449—24no—
38C11×#447—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×#390—21no—
56C11×#390C2211yescharacteristic, complemented
57C11×#389C2211yescharacteristic, complemented
58C11×#388—21no—
59C11×#386—21no—
60C11×#385—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×D4×C11—21no—
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
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11—21no—
91C23×C4×C11—21no—
92C23×C4×C11C2311yescharacteristic
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—41no—
96C2×C11×D8—22no—
97C2×C11×D8—22no—
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—22no—
101C2×C11×D8—22no—
102C2×C11×D8—41no—
103C2×C11×D8—41no—
104C2×C11×D8—41no—
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×#127—22no—
110C11×#127—22no—
111C11×#127—22no—
112C11×#127D414yescomplemented
113C11×#124—22no—
114C11×#124—22no—
115C11×#124—22no—
116C11×#124D414yescomplemented
117C11×#121—28no—
118C11×#121—28no—
119C11×#121—22no—
120C11×#121D414yescomplemented
121C11×#120—28no—
122C11×#120—28no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C11×#117—22no—
126C11×#117—22no—
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⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4D411yescharacteristic
143C2×C11×C22⋊C4D411yescharacteristic
144C2×C42×C11—21no—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C11×C4⋊C8—22no—
148C11×C4⋊C8—22no—
149C11×#103—22no—
150C11×#103—22no—
151C11×#103—41no—
152C11×#102—22no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—41no—
159C11×#102—41no—
160C11×#102—41no—
161C11×C22⋊C8—22no—
162C11×C22⋊C8—22no—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24218C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—24no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—81no—
175C24×C11—81no—
176C24×C11—81no—
177C24×C11—81no—
178C24×C11C2×D411yescharacteristic
179C11×#41—44no—
180C11×#41—44no—
181C11×#41—44no—
182C11×#41—44no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11C2×D412yes—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—24no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
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—21no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11—21no—
216C2×D4×C11—44no—
217C2×D4×C11—44no—
218C2×D4×C11—44no—
219C2×D4×C11—44no—
220C2×D4×C11—42no—
221C2×D4×C11—42no—
222C2×D4×C11—42no—
223C2×D4×C11—42no—
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×C11—81no—
232C2×D4×C11—81no—
233C2×D4×C11—81no—
234C2×D4×C11C2×D412yes—
235C2×D4×C11C2×D412yes—
236C2×D4×C11C2×D412yes—
237C2×D4×C11C2×D412yes—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—24no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—42no—
248C22×C4×C11—42no—
249C22×C4×C11—42no—
250C22×C4×C11—81no—
251C22×C4×C11—81no—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D412yes—
258C22×C4×C11#4112yes—
259C22×C4×C11C2411yescharacteristic
260C11×SD16—44no—
261C11×D8—44no—
262C11×D8—44no—
263C11×D8—44no—
264C2×C8×C11—21no—
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—21no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—81no—
284C11×C4⋊C4C2×D412yes—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—24no—
292C11×C22⋊C4—42no—
293C11×C22⋊C4—81no—
294C11×C22⋊C4—81no—
295C11×C22⋊C4—81no—
296C42×C11—21no—
297C42×C11—21no—
298C42×C11—81no—
299C42×C11C2×D412yes—
300C42×C11C2×D412yes—
301C2×#535C2×C1111yescharacteristic, complemented
302C2×#463C2×C1111yescharacteristic, complemented
303C2×#459C2×C1111yescharacteristic, complemented
304C2×#449C2×C1111yescharacteristic, complemented
305C2×#447C2×C1111yescharacteristic, complemented
306#2324C2×C1111yescharacteristic, complemented
307#2042C2×C1111yescharacteristic, complemented
308#2041C2×C1111yescharacteristic, complemented
309#2012C2×C1111yescharacteristic, complemented
310#2011C2×C1111yescharacteristic, complemented
311#1983C2×C1111yescharacteristic, complemented
312#1982C2×C1111yescharacteristic, complemented
313#1798C2×C1111yescharacteristic, complemented
314#1788C2×C1111yescharacteristic, complemented
315#1786C2×C1111yescharacteristic, complemented
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
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—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—41no—
350C23×C11—41no—
351C23×C11—84no—
352C23×C11—84no—
353C23×C11—84no—
354C23×C11—84no—
355C23×C11—84no—
356C23×C11—84no—
357C23×C11#12112yes—
358C23×C11C22×D411yescharacteristic
359Q8×C11—22no—
360Q8×C11—22no—
361Q8×C11—41no—
362Q8×C11—41no—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—22no—
369D4×C11—22no—
370D4×C11—22no—
371D4×C11—48no—
372D4×C11—48no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—41no—
377D4×C11—41no—
378D4×C11—41no—
379D4×C11—41no—
380D4×C11—41no—
381D4×C11—84no—
382D4×C11—84no—
383D4×C11—84no—
384D4×C11—84no—
385D4×C11—84no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—48no—
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—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—84no—
416C2×C4×C11#12012yes—
417C2×C4×C11#12012yes—
418C2×C4×C11#12112yes—
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C2×#4111yescharacteristic
423C2×C4×C11H(5,𝔽2)11yescharacteristic
424C2×C4×C11H(5,𝔽2)11yescharacteristic
425C8×C11—41no—
426C8×C11—41no—
427C8×C11—41no—
428C8×C11—41no—
429C22×#41C22×C1111yescharacteristic
430C23×D4C22×C1111yescharacteristic
431C22×SD16C22×C1111yescharacteristic, complemented
432C22×D8C22×C1111yescharacteristic
433C22×D8C22×C1111yescharacteristic
434C22×D8C22×C1111yescharacteristic, complemented
435#535—24no—
436#535—24no—
437C2×#127C22×C1111yescharacteristic
438C2×#127C22×C1111yescharacteristic
439C2×#124C22×C1111yescharacteristic
440C2×#124C22×C1111yescharacteristic
441C2×#121—21no—
442C2×#121—21no—
443C2×#121C22×C1111yescharacteristic
444C2×#120—21no—
445C2×#120—21no—
446C2×C4×D4C22×C1111yescharacteristic, complemented
447C2×#117C22×C1111yescharacteristic
448#463—24no—
449#459—24no—
450#449—24no—
451#447—24no—
452C2×C4⋊C8C22×C1111yescharacteristic, complemented
453C2×C4⋊C8C22×C1111yescharacteristic, complemented
454C2×#103C22×C1111yescharacteristic, complemented
455C2×#103C22×C1111yescharacteristic, complemented
456C2×#103C22×C1111yescharacteristic, complemented
457C2×#102C22×C1111yescharacteristic
458C2×#102C22×C1111yescharacteristic
459C2×#102C22×C1111yescharacteristic
460C2×#102C22×C1111yescharacteristic
461C2×#102C22×C1111yescharacteristic
462C2×#102C22×C1111yescharacteristic
463C2×#102C22×C1111yescharacteristic, complemented
464C2×#102C22×C1111yescharacteristic, complemented
465C2×#102C22×C1111yescharacteristic, complemented
466C2×C22⋊C8C22×C1111yescharacteristic
467C2×C22⋊C8C22×C1111yescharacteristic
468#390—21no—
469#390C22×C1111yescharacteristic, complemented
470#389C22×C1111yescharacteristic, complemented
471#388—21no—
472#386—21no—
473#385—21no—
474#380C22×C1111yescharacteristic
475C4×C4⋊C4C22×C1111yescharacteristic, complemented
476#336C22×C1111yescharacteristic, complemented
477#336C22×C1111yescharacteristic, complemented
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—816no—
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×C11—81no—
510C22×C11—81no—
511C22×C11—81no—
512C22×C11—81no—
513C22×C11—81no—
514C22×C11C2×#12011yescharacteristic
515C22×C11C2×#12111yescharacteristic
516C22×C11#53511yescharacteristic
517C22×C11#57611yescharacteristic
518C22×C11#57611yescharacteristic
519C22×C11#57611yescharacteristic
520C22×C11#57711yescharacteristic
521C4×C11—22no—
522C4×C11—22no—
523C4×C11—22no—
524C4×C11—42no—
525C4×C11—41no—
526C4×C11—41no—
527C4×C11—42no—
528C4×C11—81no—
529C4×C11—81no—
530C4×C11D4211yescharacteristic
531C4×C11D4211yescharacteristic
532C4×C11#54611yescharacteristic
533C4×C11#54611yescharacteristic
534C25—21no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—22no—
538C2×#41—22no—
539C2×#41—41no—
540C2×#41—41no—
541C22×Q8C23×C1111yescharacteristic
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—22no—
545C22×D4—22no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—41no—
554C22×D4—41no—
555C22×D4C23×C1111yescharacteristic
556C22×D4C23×C1111yescharacteristic
557C22×D4C23×C1111yescharacteristic
558C22×D4C23×C1111yescharacteristic
559C23×C4—21no—
560C23×C4—21no—
561C23×C4C23×C1111yescharacteristic
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—41no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—22no—
568C2×D8—22no—
569C2×D8—22no—
570C2×D8—22no—
571C2×D8—41no—
572C2×D8—41no—
573C2×D8—41no—
574C22×C8C23×C1111yescharacteristic
575C22×C8C23×C1111yescharacteristic
576C22×C8C23×C1111yescharacteristic
577C22×C8C23×C1111yescharacteristic
578#127—22no—
579#127—22no—
580#127—22no—
581#127D4×C1114yescomplemented
582#124—22no—
583#124—22no—
584#124—22no—
585#124D4×C1114yescomplemented
586#121—28no—
587#121—28no—
588#121—22no—
589#121D4×C1114yescomplemented
590#120—28no—
591#120—28no—
592C4×D4—22no—
593C4×D4—22no—
594#117—22no—
595#117—22no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4D4×C1111yescharacteristic
598C2×C4⋊C4D4×C1111yescharacteristic
599C2×C4⋊C4C23×C1111yescharacteristic
600C2×C4⋊C4C23×C1111yescharacteristic
601C2×C4⋊C4C23×C1111yescharacteristic
602C2×C22⋊C4—21no—
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⋊C4D4×C1111yescharacteristic
612C2×C22⋊C4D4×C1111yescharacteristic
613C2×C42—21no—
614C2×C42C23×C1111yescharacteristic
615C2×C42C23×C1111yescharacteristic
616C4⋊C8—22no—
617C4⋊C8—22no—
618#103—22no—
619#103—22no—
620#103—41no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—41no—
628#102—41no—
629#102—41no—
630C22⋊C8—22no—
631C22⋊C8—22no—
632#95—21no—
633#95—21no—
634#95—21no—
635C2×C11—42no—
636C2×C11—82no—
637C2×C11—82no—
638C2×C11—82no—
639C2×C11—82no—
640C2×C11#240811yescharacteristic
641C2×C11#300811yescharacteristic
642C2×C11#301211yescharacteristic
643C2×C11#304111yescharacteristic
644C2×C11#304511yescharacteristic
645C2×C11#322011yescharacteristic
646C2×C11#322411yescharacteristic
647C24—24no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×D4×C1111yescharacteristic
659#41—44no—
660#41—44no—
661#41—44no—
662#41—44no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8C2×D4×C1112yes—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
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—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4C2×D4×C1112yes—
715C2×D4C2×D4×C1112yes—
716C2×D4C2×D4×C1112yes—
717C2×D4C2×D4×C1112yes—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—24no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4C2×D4×C1111yescharacteristic
733C22×C4C2×D4×C1111yescharacteristic
734C22×C4C2×D4×C1111yescharacteristic
735C22×C4C2×D4×C1111yescharacteristic
736C22×C4C2×D4×C1111yescharacteristic
737C22×C4C2×D4×C1112yes—
738C22×C4C11×#4112yes—
739C22×C4C24×C1111yescharacteristic
740SD16—44no—
741D8—44no—
742D8—44no—
743D8—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C4⋊C4—22no—
757C4⋊C4—22no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—81no—
764C4⋊C4C2×D4×C1112yes—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—24no—
772C22⋊C4—42no—
773C22⋊C4—81no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—81no—
779C42C2×D4×C1112yes—
780C42C2×D4×C1112yes—
781C11#2421811yescharacteristic, direct product factor, Sylow
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
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—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23C11×#12112yes—
824C23C22×D4×C1111yescharacteristic
825Q8—22no—
826Q8—22no—
827Q8—41no—
828Q8—41no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—48no—
838D4—48no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4—84no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—48no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—84no—
882C2×C4C11×#12012yes—
883C2×C4C11×#12012yes—
884C2×C4C11×#12112yes—
885C2×C4C22×D4×C1111yescharacteristic
886C2×C4C22×D4×C1111yescharacteristic
887C2×C4C22×D4×C1111yescharacteristic
888C2×C4C2×C11×#4111yescharacteristic
889C2×C4C11×H(5,𝔽2)11yescharacteristic
890C2×C4C11×H(5,𝔽2)11yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—816no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×C11×#12011yescharacteristic
932C22C2×C11×#12111yescharacteristic
933C22C11×#53511yescharacteristic
934C22C11×#57611yescharacteristic
935C22C11×#57611yescharacteristic
936C22C11×#57611yescharacteristic
937C22C11×#57711yescharacteristic
938C4—22no—
939C4—22no—
940C4—22no—
941C4—42no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—81no—
946C4—81no—
947C4D42×C1111yescharacteristic
948C4D42×C1111yescharacteristic
949C4C11×#54611yescharacteristic
950C4C11×#54611yescharacteristic
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—82no—
956C2C11×#240811yescharacteristic
957C2C11×#300811yescharacteristic
958C2C11×#301211yescharacteristic
959C2C11×#304111yescharacteristic
960C2C11×#304511yescharacteristic
961C2C11×#322011yescharacteristic
962C2C11×#322411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C2×C11×#535C2semidirect
2. C2×C11×#463C2semidirect
3. C2×C11×#459C2semidirect
4. C2×C11×#449C2semidirect
5. C2×C11×#447C2semidirect
6. C11×#2324C2semidirect
7. C11×#2042C2semidirect
8. C11×#2041C2semidirect
9. C11×#2012C2semidirect
10. C11×#2011C2semidirect
11. C11×#1983C2semidirect
12. C11×#1982C2semidirect
13. C11×#1798C2semidirect
14. C11×#1788C2semidirect
15. C11×#1786C2semidirect
18. C22×C11×SD16C22semidirect
21. C22×C11×D8C22semidirect
33. C2×C4×D4×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
56. C11×#390C22semidirect
57. C11×#389C22semidirect
62. C4×C11×C4⋊C4C22semidirect
63. C11×#336C22semidirect
64. C11×#336C22semidirect
112. C11×#127D4semidirect
116. C11×#124D4semidirect
120. C11×#121D4semidirect
166. #24218C11direct (N × H)
301. C2×#535C2×C11semidirect
302. C2×#463C2×C11semidirect
303. C2×#459C2×C11semidirect
304. C2×#449C2×C11semidirect
305. C2×#447C2×C11semidirect
306. #2324C2×C11semidirect
307. #2042C2×C11semidirect
308. #2041C2×C11semidirect
309. #2012C2×C11semidirect
310. #2011C2×C11semidirect
311. #1983C2×C11semidirect
312. #1982C2×C11semidirect
313. #1798C2×C11semidirect
314. #1788C2×C11semidirect
315. #1786C2×C11semidirect
431. C22×SD16C22×C11semidirect
434. C22×D8C22×C11semidirect
446. C2×C4×D4C22×C11semidirect
452. C2×C4⋊C8C22×C11semidirect
453. C2×C4⋊C8C22×C11semidirect
454. C2×#103C22×C11semidirect
455. C2×#103C22×C11semidirect
456. C2×#103C22×C11semidirect
463. C2×#102C22×C11semidirect
464. C2×#102C22×C11semidirect
465. C2×#102C22×C11semidirect
469. #390C22×C11semidirect
470. #389C22×C11semidirect
475. C4×C4⋊C4C22×C11semidirect
476. #336C22×C11semidirect
477. #336C22×C11semidirect
581. #127D4×C11semidirect
585. #124D4×C11semidirect
589. #121D4×C11semidirect
781. C11#24218direct (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×#4632
C2×C11×#4592
C2×C11×#4492
C2×C11×#4472
C11×#23242
C11×#20422
C11×#20412
C11×#20122
C11×#20112
C11×#19832
C11×#19822
C11×#17982
C11×#17882
C11×#17862
#2421811