Finite Group Databasebeta

← C11×#24428 #14601621

Subgroups — C11×#24428 #14601621

Order 2816.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic, complemented
2C2×C11×#466C211yesmaximal, characteristic, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C2×C11×#447C211yesmaximal, characteristic, complemented
5C2×C11×#416C211yesmaximal, characteristic, complemented
6C11×#2414C211yesmaximal, characteristic, complemented
7C11×#2042C211yesmaximal, characteristic, complemented
8C11×#2036C211yesmaximal, characteristic, complemented
9C11×#2012C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1875C211yesmaximal, characteristic, complemented
13C11×#1869C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic, complemented
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic, complemented
22C11×#546—24no—
23C11×#546—24no—
24C2×C11×#124C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121—21no—
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic, complemented
31C2×C11×#120—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic, complemented
35C22×C11×C22⋊C4—21no—
36C11×#466—24no—
37C11×#449—24no—
38C11×#447—24no—
39C2×C11×#107C2211yescharacteristic, complemented
40C11×#416—24no—
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×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C11×#394—21no—
55C11×#392—21no—
56C11×#390—21no—
57C11×#390C2211yescharacteristic, complemented
58C11×#389C2211yescharacteristic, complemented
59C11×#388—21no—
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, 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—41no—
70C2×C11×#41—41no—
71C2×C11×#41D414yescomplemented
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—21no—
74C22×D4×C11—21no—
75C22×D4×C11—22no—
76C22×D4×C11—22no—
77C22×D4×C11—22no—
78C22×D4×C11—22no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—41no—
83C22×D4×C11—41no—
84C22×D4×C11D411yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C2×C11×SD16—22no—
93C2×C11×SD16—41no—
94C2×C11×SD16—41no—
95C2×C11×D8—22no—
96C2×C11×D8—22no—
97C2×C11×D8—22no—
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—41no—
101C22×C8×C11—22no—
102C22×C8×C11—22no—
103C22×C8×C11—41no—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C11×#124—22no—
109C11×#124—22no—
110C11×#123—28no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×#121—28no—
114C11×#121—22no—
115C11×#121—22no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—41no—
119C11×#121D414yescomplemented
120C11×#120—28no—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C11×#117—22no—
126C11×#117—41no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4D411yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C22⋊C4—28no—
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⋊C4—21no—
144C2×C11×C22⋊C4—21no—
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4D411yescharacteristic
147C2×C11×C22⋊C4D411yescharacteristic
148C2×C42×C11—21no—
149C2×C42×C11C2311yescharacteristic
150C11×#107—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—22no—
159C11×#102—41no—
160C11×#102D414yescomplemented
161C11×C22⋊C8—22no—
162C11×C22⋊C8—22no—
163C11×C22⋊C8—41no—
164C11×#95—21no—
165C11×#95—21no—
166#24428C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11—24no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—42no—
175C24×C11—81no—
176C24×C11—81no—
177C24×C11C2×D411yescharacteristic
178C24×C11C2×D411yescharacteristic
179C11×#41—28no—
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—22no—
191C2×D4×C11—24no—
192C2×D4×C11—22no—
193C2×D4×C11—24no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
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—41no—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—44no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—42no—
216C2×D4×C11—42no—
217C2×D4×C11—44no—
218C2×D4×C11—42no—
219C2×D4×C11—42no—
220C2×D4×C11—81no—
221C2×D4×C11—81no—
222C2×D4×C11—81no—
223C2×D4×C11—81no—
224C2×D4×C11—81no—
225C2×D4×C11C2×D412yes—
226C2×D4×C11C2×D412yes—
227C2×D4×C11C2×D412yes—
228C2×D4×C11#4112yes—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—24no—
237C22×C4×C11—24no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—42no—
247C22×C4×C11—42no—
248C22×C4×C11—81no—
249C22×C4×C11—81no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2411yescharacteristic
257C11×SD16—44no—
258C11×D8—44no—
259C11×D8—44no—
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—
270C2×C8×C11—21no—
271C2×C8×C11—44no—
272C2×C8×C11C2×D412yes—
273C11×C4⋊C4—24no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—81no—
282C11×C4⋊C4C2×D412yes—
283C11×C4⋊C4C2×D412yes—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—24no—
291C11×C22⋊C4—42no—
292C11×C22⋊C4—42no—
293C11×C22⋊C4—42no—
294C11×C22⋊C4—42no—
295C11×C22⋊C4—81no—
296C11×C22⋊C4—81no—
297C42×C11—21no—
298C42×C11—21no—
299C42×C11—42no—
300C2×#546C2×C1111yescharacteristic, complemented
301C2×#466C2×C1111yescharacteristic, complemented
302C2×#449C2×C1111yescharacteristic, complemented
303C2×#447C2×C1111yescharacteristic, complemented
304C2×#416C2×C1111yescharacteristic, complemented
305#2414C2×C1111yescharacteristic, complemented
306#2042C2×C1111yescharacteristic, complemented
307#2036C2×C1111yescharacteristic, complemented
308#2012C2×C1111yescharacteristic, complemented
309#2000C2×C1111yescharacteristic, complemented
310#1879C2×C1111yescharacteristic, complemented
311#1875C2×C1111yescharacteristic, complemented
312#1869C2×C1111yescharacteristic, complemented
313#1862C2×C1111yescharacteristic, complemented
314#1786C2×C1111yescharacteristic, complemented
315C23×C11—21no—
316C23×C11—22no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—22no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—22no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—22no—
331C23×C11—48no—
332C23×C11—48no—
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—84no—
351C23×C11—84no—
352C23×C11—84no—
353C23×C11—84no—
354C23×C11—84no—
355C23×C11#12012yes—
356C23×C11#13512yes—
357C23×C11C22×D411yescharacteristic
358Q8×C11—22no—
359Q8×C11—22no—
360Q8×C11—41no—
361Q8×C11—41no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—44no—
368D4×C11—48no—
369D4×C11—48no—
370D4×C11—41no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—84no—
377D4×C11—84no—
378D4×C11—84no—
379D4×C11#12114yes—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—21no—
391C2×C4×C11—22no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—48no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—84no—
416C2×C4×C11#12012yes—
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C2×#4111yescharacteristic
421C2×C4×C11H(5,𝔽2)11yescharacteristic
422C2×C4×C11H(5,𝔽2)11yescharacteristic
423C8×C11—22no—
424C8×C11—41no—
425C8×C11—41no—
426C8×C11—41no—
427C22×#41C22×C1111yescharacteristic
428C23×D4C22×C1111yescharacteristic
429C22×SD16C22×C1111yescharacteristic, complemented
430C22×D8C22×C1111yescharacteristic
431C22×D8C22×C1111yescharacteristic
432C23×C8C22×C1111yescharacteristic, complemented
433#546—24no—
434#546—24no—
435C2×#124C22×C1111yescharacteristic
436C2×#123—21no—
437C2×C22⋊Q8C22×C1111yescharacteristic
438C2×#121—21no—
439C2×#121C22×C1111yescharacteristic
440C2×#121C22×C1111yescharacteristic
441C2×#121C22×C1111yescharacteristic, complemented
442C2×#120—21no—
443C2×C4×D4C22×C1111yescharacteristic
444C2×C4×D4C22×C1111yescharacteristic
445C2×#117C22×C1111yescharacteristic, complemented
446C22×C22⋊C4—21no—
447#466—24no—
448#449—24no—
449#447—24no—
450C2×#107C22×C1111yescharacteristic, complemented
451#416—24no—
452C2×#103C22×C1111yescharacteristic, complemented
453C2×#103C22×C1111yescharacteristic, complemented
454C2×#103C22×C1111yescharacteristic, complemented
455C2×#102C22×C1111yescharacteristic
456C2×#102C22×C1111yescharacteristic
457C2×#102C22×C1111yescharacteristic
458C2×#102C22×C1111yescharacteristic
459C2×#102C22×C1111yescharacteristic
460C2×#102C22×C1111yescharacteristic
461C2×#102C22×C1111yescharacteristic, complemented
462C2×C22⋊C8C22×C1111yescharacteristic
463C2×C22⋊C8C22×C1111yescharacteristic
464C2×C22⋊C8C22×C1111yescharacteristic, complemented
465#394—21no—
466#392—21no—
467#390—21no—
468#390C22×C1111yescharacteristic, complemented
469#389C22×C1111yescharacteristic, complemented
470#388—21no—
471#380C22×C1111yescharacteristic
472#340C22×C1111yescharacteristic, complemented
473#340C22×C1111yescharacteristic, complemented
474#336C22×C1111yescharacteristic, complemented
475#336C22×C1111yescharacteristic, complemented
476C22×C11—22no—
477C22×C11—24no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—41no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—41no—
489C22×C11—42no—
490C22×C11—41no—
491C22×C11—42no—
492C22×C11—41no—
493C22×C11—42no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—816no—
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×C11C2×#12011yescharacteristic
513C22×C11D4211yescharacteristic
514C22×C11#54611yescharacteristic
515C22×C11C2×#13511yescharacteristic
516C22×C11#57511yescharacteristic
517C22×C11#57611yescharacteristic
518C22×C11#57611yescharacteristic
519C4×C11—22no—
520C4×C11—41no—
521C4×C11—42no—
522C4×C11—41no—
523C4×C11—41no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—81no—
527C4×C11—81no—
528C4×C11C2×#12111yescharacteristic
529C4×C11#53411yescharacteristic
530C4×C11D4211yescharacteristic
531C4×C11#54611yescharacteristic
532C25—21no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—41no—
537C2×#41—41no—
538C2×#41D4×C1114yescomplemented
539C22×Q8C23×C1111yescharacteristic
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—22no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—41no—
550C22×D4—41no—
551C22×D4D4×C1111yescharacteristic
552C22×D4C23×C1111yescharacteristic
553C22×D4C23×C1111yescharacteristic
554C22×D4C23×C1111yescharacteristic
555C23×C4—21no—
556C23×C4—21no—
557C23×C4C23×C1111yescharacteristic
558C23×C4C23×C1111yescharacteristic
559C2×SD16—22no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—41no—
568C22×C8—22no—
569C22×C8—22no—
570C22×C8—41no—
571C22×C8C23×C1111yescharacteristic
572C22×C8C23×C1111yescharacteristic
573C22×C8C23×C1111yescharacteristic
574C22×C8C23×C1111yescharacteristic
575#124—22no—
576#124—22no—
577#123—28no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580#121—28no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—41no—
586#121D4×C1114yescomplemented
587#120—28no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592#117—22no—
593#117—41no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4D4×C1111yescharacteristic
597C2×C4⋊C4C23×C1111yescharacteristic
598C2×C4⋊C4C23×C1111yescharacteristic
599C2×C4⋊C4C23×C1111yescharacteristic
600C2×C4⋊C4C23×C1111yescharacteristic
601C2×C22⋊C4—28no—
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⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4D4×C1111yescharacteristic
614C2×C22⋊C4D4×C1111yescharacteristic
615C2×C42—21no—
616C2×C42C23×C1111yescharacteristic
617#107—22no—
618#103—22no—
619#103—22no—
620#103—22no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—41no—
627#102D4×C1114yescomplemented
628C22⋊C8—22no—
629C22⋊C8—22no—
630C22⋊C8—41no—
631#95—21no—
632#95—21no—
633C2×C11—42no—
634C2×C11—42no—
635C2×C11—44no—
636C2×C11—82no—
637C2×C11—161no—
638C2×C11#241011yescharacteristic
639C2×C11#300211yescharacteristic
640C2×C11#300811yescharacteristic
641C2×C11#326811yescharacteristic
642C2×C11#328011yescharacteristic
643C2×C11#329711yescharacteristic
644C2×C11#331911yescharacteristic
645C24—21no—
646C24—24no—
647C24—21no—
648C24—21no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24C2×D4×C1111yescharacteristic
656C24C2×D4×C1111yescharacteristic
657#41—28no—
658#41—44no—
659#41—44no—
660#41—44no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8C2×D4×C1112yes—
667C2×D4—24no—
668C2×D4—22no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C1112yes—
704C2×D4C2×D4×C1112yes—
705C2×D4C2×D4×C1112yes—
706C2×D4C11×#4112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—81no—
727C22×C4—81no—
728C22×C4C2×D4×C1111yescharacteristic
729C22×C4C2×D4×C1111yescharacteristic
730C22×C4C2×D4×C1111yescharacteristic
731C22×C4C2×D4×C1111yescharacteristic
732C22×C4C2×D4×C1112yes—
733C22×C4C2×D4×C1112yes—
734C22×C4C24×C1111yescharacteristic
735SD16—44no—
736D8—44no—
737D8—44no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—44no—
750C2×C8C2×D4×C1112yes—
751C4⋊C4—24no—
752C4⋊C4—22no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—81no—
760C4⋊C4C2×D4×C1112yes—
761C4⋊C4C2×D4×C1112yes—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—24no—
769C22⋊C4—42no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—81no—
774C22⋊C4—81no—
775C42—21no—
776C42—21no—
777C42—42no—
778C11#2442811yescharacteristic, direct product factor, Sylow
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—48no—
796C23—48no—
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—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C11×#12012yes—
820C23C11×#13512yes—
821C23C22×D4×C1111yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4C11×#12114yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4C11×#12012yes—
881C2×C4C22×D4×C1111yescharacteristic
882C2×C4C22×D4×C1111yescharacteristic
883C2×C4C22×D4×C1111yescharacteristic
884C2×C4C2×C11×#4111yescharacteristic
885C2×C4C11×H(5,𝔽2)11yescharacteristic
886C2×C4C11×H(5,𝔽2)11yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—41no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×C11×#12011yescharacteristic
928C22D42×C1111yescharacteristic
929C22C11×#54611yescharacteristic
930C22C2×C11×#13511yescharacteristic
931C22C11×#57511yescharacteristic
932C22C11×#57611yescharacteristic
933C22C11×#57611yescharacteristic
934C4—22no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×C11×#12111yescharacteristic
944C4C11×#53411yescharacteristic
945C4D42×C1111yescharacteristic
946C4C11×#54611yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—161no—
952C2C11×#241011yescharacteristic
953C2C11×#300211yescharacteristic
954C2C11×#300811yescharacteristic
955C2C11×#326811yescharacteristic
956C2C11×#328011yescharacteristic
957C2C11×#329711yescharacteristic
958C2C11×#331911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C2×C11×#546C2semidirect
2. C2×C11×#466C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#447C2semidirect
5. C2×C11×#416C2semidirect
6. C11×#2414C2semidirect
7. C11×#2042C2semidirect
8. C11×#2036C2semidirect
9. C11×#2012C2semidirect
10. C11×#2000C2semidirect
11. C11×#1879C2semidirect
12. C11×#1875C2semidirect
13. C11×#1869C2semidirect
14. C11×#1862C2semidirect
15. C11×#1786C2semidirect
18. C22×C11×SD16C22semidirect
21. C23×C8×C11C22semidirect
30. C2×C11×#121C22semidirect
34. C2×C11×#117C22semidirect
39. C2×C11×#107C22semidirect
41. C2×C11×#103C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#103C22semidirect
50. C2×C11×#102C22semidirect
53. C2×C11×C22⋊C8C22semidirect
57. C11×#390C22semidirect
58. C11×#389C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#336C22semidirect
64. C11×#336C22semidirect
71. C2×C11×#41D4semidirect
119. C11×#121D4semidirect
160. C11×#102D4semidirect
166. #24428C11direct (N × H)
300. C2×#546C2×C11semidirect
301. C2×#466C2×C11semidirect
302. C2×#449C2×C11semidirect
303. C2×#447C2×C11semidirect
304. C2×#416C2×C11semidirect
305. #2414C2×C11semidirect
306. #2042C2×C11semidirect
307. #2036C2×C11semidirect
308. #2012C2×C11semidirect
309. #2000C2×C11semidirect
310. #1879C2×C11semidirect
311. #1875C2×C11semidirect
312. #1869C2×C11semidirect
313. #1862C2×C11semidirect
314. #1786C2×C11semidirect
429. C22×SD16C22×C11semidirect
432. C23×C8C22×C11semidirect
441. C2×#121C22×C11semidirect
445. C2×#117C22×C11semidirect
450. C2×#107C22×C11semidirect
452. C2×#103C22×C11semidirect
453. C2×#103C22×C11semidirect
454. C2×#103C22×C11semidirect
461. C2×#102C22×C11semidirect
464. C2×C22⋊C8C22×C11semidirect
468. #390C22×C11semidirect
469. #389C22×C11semidirect
472. #340C22×C11semidirect
473. #340C22×C11semidirect
474. #336C22×C11semidirect
475. #336C22×C11semidirect
538. C2×#41D4×C11semidirect
586. #121D4×C11semidirect
627. #102D4×C11semidirect
778. C11#24428direct (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×#4662
C2×C11×#4492
C2×C11×#4472
C2×C11×#4162
C11×#24142
C11×#20422
C11×#20362
C11×#20122
C11×#20002
C11×#18792
C11×#18752
C11×#18692
C11×#18622
C11×#17862
#2442811