Finite Group Databasebeta

← C11×#24451 #14601644

Subgroups — C11×#24451 #14601644

Order 2816.

1580 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#550C211yesmaximal, characteristic, complemented
2C2×C11×#469C211yesmaximal, characteristic, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C2×C11×#449C211yesmaximal, characteristic, complemented
5C2×C11×#417C211yesmaximal, characteristic, complemented
6C11×#2416C211yesmaximal, characteristic, complemented
7C11×#2041C211yesmaximal, characteristic, complemented
8C11×#2034C211yesmaximal, characteristic, complemented
9C11×#2011C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic, complemented
12C11×#1874C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic, complemented
14C11×#1865C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#550—24no—
23C11×#550—24no—
24C2×C11×#127—21no—
25C2×C11×#127C2211yescharacteristic
26C2×C11×#121—21no—
27C2×C11×#121—21no—
28C2×C11×#121—21no—
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic
32C2×C11×#121C2211yescharacteristic
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C4×D4×C11—21no—
35C2×C4×D4×C11C2211yescharacteristic
36C22×C11×C4⋊C4C2211yescharacteristic
37C11×#469—24no—
38C11×#449—24no—
39C11×#449—24no—
40C2×C11×#106C2211yescharacteristic
41C11×#417—24no—
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C11×C22⋊C8C2211yescharacteristic
55C11×#396—21no—
56C11×#394—21no—
57C11×#390C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#386—21no—
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—22no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C2×C11×#41—41no—
76C2×C11×#41D414yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11D411yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C22×D4×C11C2311yescharacteristic
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11—21no—
91C23×C4×C11—21no—
92C23×C4×C11—21no—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C2×C11×SD16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—22no—
101C2×C11×D8—41no—
102C2×C11×D8—41no—
103C2×C11×D8—41no—
104C2×C11×M16—22no—
105C2×C11×M16—22no—
106C2×C11×M16—41no—
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C11×#127—28no—
112C11×#127—22no—
113C11×#127—22no—
114C11×#121—28no—
115C11×#121—28no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—41no—
123C11×#121—44no—
124C11×#121D414yescomplemented
125C4×Q8×C11—22no—
126C4×Q8×C11—22no—
127C4×D4×C11—28no—
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—22no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—41no—
135C2×C11×C4⋊C4D411yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
147C2×C11×C22⋊C4D411yescharacteristic
148C2×C11×C22⋊C4D411yescharacteristic
149C2×C42×C11—21no—
150C2×C42×C11C2311yescharacteristic
151C11×#106—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103D414yescomplemented
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—22no—
159C11×#102—22no—
160C11×#102—22no—
161C11×#102—41no—
162C11×C22⋊C8—22no—
163C11×C22⋊C8—22no—
164C11×C22⋊C8—41no—
165C11×#95—21no—
166C11×#95—21no—
167#24451C1111yesmaximal, characteristic, direct product factor, Sylow
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11C2×D411yescharacteristic
172C24×C11C2×D411yescharacteristic
173C11×#41—28no—
174C11×#41—44no—
175C11×#41—44no—
176C11×#41—44no—
177C11×#41—44no—
178C11×#41—44no—
179C11×#41—44no—
180C11×#41—44no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11C2×D412yes—
185C2×Q8×C11C2×D412yes—
186C2×Q8×C11#4112yes—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—22no—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—24no—
194C2×D4×C11—22no—
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—21no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—41no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—42no—
217C2×D4×C11—42no—
218C2×D4×C11—42no—
219C2×D4×C11—42no—
220C2×D4×C11—42no—
221C2×D4×C11—42no—
222C2×D4×C11—42no—
223C2×D4×C11—81no—
224C2×D4×C11—81no—
225C2×D4×C11—81no—
226C2×D4×C11—81no—
227C2×D4×C11—81no—
228C2×D4×C11—81no—
229C2×D4×C11—81no—
230C2×D4×C11C2×D412yes—
231C2×D4×C11C2×D412yes—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—24no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—24no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—42no—
250C22×C4×C11—42no—
251C22×C4×C11—42no—
252C22×C4×C11—42no—
253C22×C4×C11—42no—
254C22×C4×C11—42no—
255C22×C4×C11—81no—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C11×SD16—44no—
264C11×D8—44no—
265C11×D8—44no—
266C11×M16—44no—
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—
276C2×C8×C11—21no—
277C2×C8×C11—21no—
278C2×C8×C11C2×D412yes—
279C11×C4⋊C4—24no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—42no—
288C11×C4⋊C4—42no—
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2×D412yes—
291C11×C22⋊C4—24no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—42no—
296C11×C22⋊C4—42no—
297C11×C22⋊C4—42no—
298C11×C22⋊C4—42no—
299C11×C22⋊C4—81no—
300C42×C11—24no—
301C42×C11—21no—
302C42×C11—21no—
303C2×#550C2×C1111yescharacteristic, complemented
304C2×#469C2×C1111yescharacteristic, complemented
305C2×#449C2×C1111yescharacteristic, complemented
306C2×#449C2×C1111yescharacteristic, complemented
307C2×#417C2×C1111yescharacteristic, complemented
308#2416C2×C1111yescharacteristic, complemented
309#2041C2×C1111yescharacteristic, complemented
310#2034C2×C1111yescharacteristic, complemented
311#2011C2×C1111yescharacteristic, complemented
312#1999C2×C1111yescharacteristic, complemented
313#1880C2×C1111yescharacteristic, complemented
314#1874C2×C1111yescharacteristic, complemented
315#1870C2×C1111yescharacteristic, complemented
316#1865C2×C1111yescharacteristic, complemented
317#1788C2×C1111yescharacteristic, complemented
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
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—41no—
352C23×C11#12012yes—
353C23×C11C22×D411yescharacteristic
354Q8×C11—22no—
355Q8×C11—22no—
356Q8×C11—22no—
357Q8×C11#12114yescomplemented
358D4×C11—22no—
359D4×C11—22no—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—44no—
363D4×C11—48no—
364D4×C11—48no—
365D4×C11—48no—
366D4×C11—41no—
367D4×C11—41no—
368D4×C11—41no—
369D4×C11—41no—
370D4×C11—41no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—41no—
374D4×C11—84no—
375D4×C11—84no—
376D4×C11—84no—
377D4×C11—84no—
378D4×C11—84no—
379C2×C4×C11—21no—
380C2×C4×C11—22no—
381C2×C4×C11—21no—
382C2×C4×C11—22no—
383C2×C4×C11—21no—
384C2×C4×C11—22no—
385C2×C4×C11—21no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
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—22no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—48no—
399C2×C4×C11—48no—
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—84no—
415C2×C4×C11#12012yes—
416C2×C4×C11AGL(1,ℤ/8)12yes—
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
428C22×#41C22×C1111yescharacteristic
429C22×SD16C22×C1111yescharacteristic
430C22×D8C22×C1111yescharacteristic
431C22×D8C22×C1111yescharacteristic
432C22×M16C22×C1111yescharacteristic
433#550—24no—
434#550—24no—
435C2×#127—21no—
436C2×#127C22×C1111yescharacteristic
437C2×#121—21no—
438C2×#121—21no—
439C2×#121—21no—
440C2×#121C22×C1111yescharacteristic
441C2×#121C22×C1111yescharacteristic
442C2×#121C22×C1111yescharacteristic
443C2×#121C22×C1111yescharacteristic
444C2×C4×Q8C22×C1111yescharacteristic
445C2×C4×D4—21no—
446C2×C4×D4C22×C1111yescharacteristic
447C22×C4⋊C4C22×C1111yescharacteristic
448#469—24no—
449#449—24no—
450#449—24no—
451C2×#106C22×C1111yescharacteristic
452#417—24no—
453C2×#103C22×C1111yescharacteristic
454C2×#103C22×C1111yescharacteristic
455C2×#103C22×C1111yescharacteristic
456C2×#102C22×C1111yescharacteristic
457C2×#102C22×C1111yescharacteristic
458C2×#102C22×C1111yescharacteristic
459C2×#102C22×C1111yescharacteristic
460C2×#102C22×C1111yescharacteristic
461C2×#102C22×C1111yescharacteristic
462C2×#102C22×C1111yescharacteristic
463C2×C22⋊C8C22×C1111yescharacteristic
464C2×C22⋊C8C22×C1111yescharacteristic
465C2×C22⋊C8C22×C1111yescharacteristic
466#396—21no—
467#394—21no—
468#390C22×C1111yescharacteristic
469#389C22×C1111yescharacteristic
470#386—21no—
471#380C22×C1111yescharacteristic
472#340C22×C1111yescharacteristic
473#340C22×C1111yescharacteristic
474#336C22×C1111yescharacteristic
475#336C22×C1111yescharacteristic
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—41no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—41no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—81no—
497C22×C11—81no—
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×C11C2×#12011yescharacteristic
512C22×C11D4211yescharacteristic
513C22×C11#54611yescharacteristic
514C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
515C22×C11#57511yescharacteristic
516C22×C11#57611yescharacteristic
517C22×C11#57711yescharacteristic
518C4×C11—22no—
519C4×C11—24no—
520C4×C11—22no—
521C4×C11—41no—
522C4×C11—41no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—81no—
526C4×C11—81no—
527C4×C11C2×#12111yescharacteristic
528C4×C11#53411yescharacteristic
529C4×C11D4211yescharacteristic
530C4×C11#54611yescharacteristic
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—22no—
538C2×#41—41no—
539C2×#41—41no—
540C2×#41—41no—
541C2×#41—41no—
542C2×#41D4×C1114yescomplemented
543C22×Q8C23×C1111yescharacteristic
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4D4×C1111yescharacteristic
553C22×D4C23×C1111yescharacteristic
554C22×D4C23×C1111yescharacteristic
555C22×D4C23×C1111yescharacteristic
556C23×C4—21no—
557C23×C4—21no—
558C23×C4—21no—
559C23×C4C23×C1111yescharacteristic
560C23×C4C23×C1111yescharacteristic
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—41no—
568C2×D8—41no—
569C2×D8—41no—
570C2×M16—22no—
571C2×M16—22no—
572C2×M16—41no—
573C22×C8C23×C1111yescharacteristic
574C22×C8C23×C1111yescharacteristic
575C22×C8C23×C1111yescharacteristic
576C22×C8C23×C1111yescharacteristic
577#127—28no—
578#127—22no—
579#127—22no—
580#121—28no—
581#121—28no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—41no—
589#121—44no—
590#121D4×C1114yescomplemented
591C4×Q8—22no—
592C4×Q8—22no—
593C4×D4—28no—
594C4×D4—22no—
595C4×D4—22no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4D4×C1111yescharacteristic
602C2×C4⋊C4C23×C1111yescharacteristic
603C2×C4⋊C4C23×C1111yescharacteristic
604C2×C4⋊C4C23×C1111yescharacteristic
605C2×C4⋊C4C23×C1111yescharacteristic
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#106—22no—
618#103—22no—
619#103—22no—
620#103D4×C1114yescomplemented
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—41no—
628C22⋊C8—22no—
629C22⋊C8—22no—
630C22⋊C8—41no—
631#95—21no—
632#95—21no—
633C2×C11—42no—
634C2×C11—81no—
635C2×C11—82no—
636C2×C11—82no—
637C2×C11—161no—
638C2×C11#241011yescharacteristic
639C2×C11#300611yescharacteristic
640C2×C11#301211yescharacteristic
641C2×C11#327111yescharacteristic
642C2×C11#327411yescharacteristic
643C2×C11#330911yescharacteristic
644C2×C11#333211yescharacteristic
645C24—21no—
646C24—21no—
647C24—21no—
648C24C2×D4×C1111yescharacteristic
649C24C2×D4×C1111yescharacteristic
650#41—28no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656#41—44no—
657#41—44no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8C2×D4×C1112yes—
662C2×Q8C2×D4×C1112yes—
663C2×Q8C11×#4112yes—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—22no—
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—21no—
687C2×D4—21no—
688C2×D4—41no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C1112yes—
708C2×D4C2×D4×C1112yes—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—24no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—81no—
733C22×C4C2×D4×C1111yescharacteristic
734C22×C4C2×D4×C1111yescharacteristic
735C22×C4C2×D4×C1111yescharacteristic
736C22×C4C2×D4×C1112yes—
737C22×C4C2×D4×C1112yes—
738C22×C4C2×D4×C1111yescharacteristic
739C22×C4C24×C1111yescharacteristic
740SD16—44no—
741D8—44no—
742D8—44no—
743M16—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×C8C2×D4×C1112yes—
756C4⋊C4—24no—
757C4⋊C4—22no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—42no—
765C4⋊C4—42no—
766C4⋊C4C2×D4×C1112yes—
767C4⋊C4C2×D4×C1112yes—
768C22⋊C4—24no—
769C22⋊C4—22no—
770C22⋊C4—24no—
771C22⋊C4—22no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—81no—
777C42—24no—
778C42—21no—
779C42—21no—
780C11#2445111yescharacteristic, direct product factor, Sylow
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
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—
815C23C11×#12012yes—
816C23C22×D4×C1111yescharacteristic
817Q8—22no—
818Q8—22no—
819Q8—22no—
820Q8C11×#12114yescomplemented
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—44no—
826D4—48no—
827D4—48no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—84no—
838D4—84no—
839D4—84no—
840D4—84no—
841D4—84no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
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—84no—
878C2×C4C11×#12012yes—
879C2×C4C11×AGL(1,ℤ/8)12yes—
880C2×C4C22×D4×C1111yescharacteristic
881C2×C4C22×D4×C1111yescharacteristic
882C2×C4C22×D4×C1111yescharacteristic
883C2×C4C2×C11×#4111yescharacteristic
884C2×C4C11×H(5,𝔽2)11yescharacteristic
885C2×C4C11×H(5,𝔽2)11yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22C2×C11×#12011yescharacteristic
926C22D42×C1111yescharacteristic
927C22C11×#54611yescharacteristic
928C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
929C22C11×#57511yescharacteristic
930C22C11×#57611yescharacteristic
931C22C11×#57711yescharacteristic
932C4—22no—
933C4—24no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4C2×C11×#12111yescharacteristic
942C4C11×#53411yescharacteristic
943C4D42×C1111yescharacteristic
944C4C11×#54611yescharacteristic
945C2—42no—
946C2—81no—
947C2—82no—
948C2—82no—
949C2—161no—
950C2C11×#241011yescharacteristic
951C2C11×#300611yescharacteristic
952C2C11×#301211yescharacteristic
953C2C11×#327111yescharacteristic
954C2C11×#327411yescharacteristic
955C2C11×#330911yescharacteristic
956C2C11×#333211yescharacteristic
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×#550C2semidirect
2. C2×C11×#469C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#449C2semidirect
5. C2×C11×#417C2semidirect
6. C11×#2416C2semidirect
7. C11×#2041C2semidirect
8. C11×#2034C2semidirect
9. C11×#2011C2semidirect
10. C11×#1999C2semidirect
11. C11×#1880C2semidirect
12. C11×#1874C2semidirect
13. C11×#1870C2semidirect
14. C11×#1865C2semidirect
15. C11×#1788C2semidirect
76. C2×C11×#41D4semidirect
124. C11×#121D4semidirect
154. C11×#103D4semidirect
167. #24451C11direct (N × H)
303. C2×#550C2×C11semidirect
304. C2×#469C2×C11semidirect
305. C2×#449C2×C11semidirect
306. C2×#449C2×C11semidirect
307. C2×#417C2×C11semidirect
308. #2416C2×C11semidirect
309. #2041C2×C11semidirect
310. #2034C2×C11semidirect
311. #2011C2×C11semidirect
312. #1999C2×C11semidirect
313. #1880C2×C11semidirect
314. #1874C2×C11semidirect
315. #1870C2×C11semidirect
316. #1865C2×C11semidirect
317. #1788C2×C11semidirect
357. Q8×C11#121semidirect
542. C2×#41D4×C11semidirect
590. #121D4×C11semidirect
620. #103D4×C11semidirect
780. C11#24451direct (N × H)
820. Q8C11×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5502
C2×C11×#4692
C2×C11×#4492
C2×C11×#4172
C11×#24162
C11×#20412
C11×#20342
C11×#20112
C11×#19992
C11×#18802
C11×#18742
C11×#18702
C11×#18652
C11×#17882
#2445111