Finite Group Databasebeta

← C11×#61647 #14638840

Subgroups — C11×#61647 #14638840

Order 2816.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3536C211yesmaximal, characteristic, complemented
2C11×#3485C211yesmaximal, characteristic, complemented
3C11×#3331C212yesmaximal, complemented
4C11×#3330C212yesmaximal, complemented
5C11×#3314C212yesmaximal, complemented
6C11×#3306C212yesmaximal, complemented
7C11×#3275C212yesmaximal, complemented
8C11×#3273C212yesmaximal, complemented
9C11×#3269C212yesmaximal, complemented
10C11×#3267C212yesmaximal, complemented
11C11×#3225C212yesmaximal, complemented
12C11×#3201C212yesmaximal, complemented
13C11×#3196C211yesmaximal, characteristic, complemented
14C11×#3194C211yesmaximal, characteristic, complemented
15C11×#3118C212yesmaximal, complemented
16C11×#3012C212yesmaximal, complemented
17C11×#3007C211yesmaximal, characteristic, complemented
18C11×#3006C211yesmaximal, characteristic, complemented
19C11×#2978C211yesmaximal, characteristic, complemented
20C2×C11×H(5,𝔽2)C2211yescharacteristic, complemented
21C22×C11×#41C2211yescharacteristic
22C2×C11×#137C2212yescomplemented
23C2×C11×AGL(1,ℤ/8)C2212yescomplemented
24C2×C11×AGL(1,ℤ/8)C2212yescomplemented
25C2×C11×#135C2212yescomplemented
26C11×#562—22no—
27C11×#554C2212yescomplemented
28C11×#548C2212yescomplemented
29C11×#547—21no—
30C11×#547—21no—
31C11×#547C2212yes—
32C11×#547C2212yescomplemented
33C11×#547C2212yescomplemented
34C11×#546—21no—
35C11×#546—21no—
36C11×#546—22no—
37C11×#546C2212yes—
38C11×#546C2212yescomplemented
39C11×#546C2212yescomplemented
40C11×#543—21no—
41C11×#542C2212yescomplemented
42C11×#539—21no—
43C11×#538—21no—
44C11×#537—21no—
45C11×#537C2212yes—
46C11×#536C2211yescharacteristic, complemented
47C11×#536C2211yescharacteristic, complemented
48C11×#534—22no—
49C11×#525C2211yescharacteristic
50C11×#525C2211yescharacteristic
51C2×C11×#123—22no—
52C2×C11×C22⋊Q8C2211yescharacteristic, complemented
53C2×C11×#121C2211yescharacteristic, complemented
54C11×#518C2211yescharacteristic, complemented
55C11×#497C2212yescomplemented
56C11×#495C2212yescomplemented
57C11×#489C2212yescomplemented
58C11×#487C2212yescomplemented
59C11×#485C2212yescomplemented
60C11×#484C2211yescharacteristic, complemented
61C11×#484C2212yescomplemented
62C11×#483C2211yescharacteristic, complemented
63C11×#483C2212yescomplemented
64C11×#482C2212yescomplemented
65C11×#481C2211yescharacteristic, complemented
66C11×#480C2211yescharacteristic, complemented
67C11×#476C2212yescomplemented
68C11×#474C2212yescomplemented
69C11×#470C2212yescomplemented
70C11×#470C2212yescomplemented
71C11×#469C2212yescomplemented
72C11×#468C2212yescomplemented
73C11×#468C2212yescomplemented
74C11×#468C2212yescomplemented
75C11×#467C2212yescomplemented
76C11×#465C2212yescomplemented
77C11×#464C2212yescomplemented
78C11×#463C2212yescomplemented
79C11×#463C2212yescomplemented
80C11×#463C2212yescomplemented
81C11×#462C2212yescomplemented
82C11×#461C2212yescomplemented
83C11×#452C2212yescomplemented
84C11×#452C2212yescomplemented
85C11×#452C2212yescomplemented
86C11×#452C2212yescomplemented
87C11×#452C2212yescomplemented
88C11×#452C2212yescomplemented
89C11×#451C2211yescharacteristic, complemented
90C11×#451C2212yescomplemented
91C11×#450C2211yescharacteristic, complemented
92C11×#450C2212yescomplemented
93C11×#450C2212yescomplemented
94C11×#449C2212yes—
95C11×#449C2212yescomplemented
96C11×#449C2212yescomplemented
97C11×#449C2212yescomplemented
98C11×#448C2211yescharacteristic, complemented
99C11×#448C2212yescomplemented
100C11×#447C2212yes—
101C11×#447C2211yescharacteristic, complemented
102C11×#447C2212yescomplemented
103C11×#442C2212yescomplemented
104C11×#440C2212yescomplemented
105C4×C11×SD16C2212yescomplemented
106C4×C11×D8C2212yescomplemented
107C11×#436C2212yescomplemented
108C11×#436C2212yescomplemented
109C11×#435C2212yescomplemented
110C11×#435C2212yescomplemented
111C11×#433C2212yescomplemented
112C11×#417C2212yescomplemented
113C11×#417C2212yescomplemented
114C11×#417C2212yescomplemented
115C2×C11×#102C2212yescomplemented
116C11×#408C2212yescomplemented
117C11×#407C2211yescharacteristic, complemented
118C11×#407C2211yescharacteristic, complemented
119C11×H(5,𝔽2)—44no—
120C2×C11×#41—21no—
121C2×C11×#41—22no—
122C2×C11×#41—21no—
123C2×C11×#41—21no—
124C2×C11×#41—44no—
125C2×C11×#41C2312yes—
126C2×C11×#41C2312yes—
127C2×C11×#41C2312yes—
128C2×C11×#41C2311yescharacteristic
129C2×C11×#41C2312yes—
130C2×C11×#41C2311yescharacteristic
131C22×Q8×C11C2311yescharacteristic
132C22×Q8×C11C2311yescharacteristic
133C22×D4×C11—21no—
134C22×D4×C11—21no—
135C22×D4×C11—22no—
136C22×D4×C11—21no—
137C22×D4×C11C2311yescharacteristic
138C22×D4×C11C2312yes—
139C22×D4×C11C2311yescharacteristic
140C23×C4×C11—21no—
141C23×C4×C11C2311yescharacteristic
142C11×#137—44no—
143C11×AGL(1,ℤ/8)—44no—
144C11×AGL(1,ℤ/8)—44no—
145C11×#135—44no—
146C2×C11×Q16C2312yes—
147C2×C11×Q16C2312yes—
148C2×C11×Q16C2312yes—
149C2×C11×SD16C2312yes—
150C2×C11×SD16C2312yes—
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2312yes—
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2312yes—
155C2×C11×D8C2312yes—
156C2×C11×D8C2312yes—
157C2×C11×D8C2312yes—
158C2×C11×M16C2312yes—
159C2×C11×M16C2312yes—
160C2×C11×M16C2312yes—
161C22×C8×C11C2312yes—
162C11×C4⋊Q8—21no—
163C11×C4⋊Q8C2312yes—
164C11×C4⋊Q8C2312yes—
165C11×#126—22no—
166C11×#125—22no—
167C11×#124—21no—
168C11×#124—22no—
169C11×#124—22no—
170C11×#124C2312yes—
171C11×#124C2312yes—
172C11×#123—22no—
173C11×#123—21no—
174C11×#123—22no—
175C11×#123—22no—
176C11×#123—22no—
177C11×#123—22no—
178C11×#123—22no—
179C11×#123—22no—
180C11×#123—22no—
181C11×#123—22no—
182C11×#123—22no—
183C11×#123—22no—
184C11×#123—22no—
185C11×#123D412yes—
186C11×C22⋊Q8—22no—
187C11×C22⋊Q8—21no—
188C11×C22⋊Q8—21no—
189C11×C22⋊Q8—21no—
190C11×C22⋊Q8—21no—
191C11×C22⋊Q8—22no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—22no—
194C11×C22⋊Q8—22no—
195C11×C22⋊Q8—22no—
196C11×C22⋊Q8D411yescharacteristic
197C11×C22⋊Q8D411yescharacteristic
198C11×C22⋊Q8C2312yes—
199C11×C22⋊Q8C2312yes—
200C11×C22⋊Q8C2311yescharacteristic
201C11×C22⋊Q8C2311yescharacteristic
202C11×C22⋊Q8C2312yes—
203C11×C22⋊Q8C2312yes—
204C11×C22⋊Q8C2312yes—
205C11×#121—22no—
206C11×#121—22no—
207C11×#121—22no—
208C11×#121—22no—
209C11×#121—22no—
210C11×#121—22no—
211C11×#121—21no—
212C11×#121—21no—
213C11×#121—22no—
214C11×#121—22no—
215C11×#121—22no—
216C11×#121D411yescharacteristic
217C11×#121D411yescharacteristic
218C11×#121C2312yes—
219C11×#121C2312yes—
220C11×#121C2311yescharacteristic
221C11×#121C2311yescharacteristic
222C11×#121C2312yes—
223C11×#120—21no—
224C11×#120—22no—
225C11×#120—22no—
226C11×#120—22no—
227C11×#120D412yes—
228C4×Q8×C11C2312yes—
229C4×D4×C11—22no—
230C4×D4×C11—21no—
231C4×D4×C11—21no—
232C4×D4×C11—21no—
233C4×D4×C11—21no—
234C4×D4×C11—22no—
235C4×D4×C11C2312yes—
236C4×D4×C11C2312yes—
237C4×D4×C11C2312yes—
238C4×D4×C11C2312yes—
239C4×D4×C11C2312yes—
240C11×#117C2311yescharacteristic
241C11×#117C2311yescharacteristic
242C2×C11×C4⋊C4—21no—
243C2×C11×C4⋊C4—22no—
244C2×C11×C4⋊C4—22no—
245C2×C11×C4⋊C4C2311yescharacteristic
246C2×C11×C4⋊C4C2311yescharacteristic
247C2×C11×C4⋊C4C2312yes—
248C2×C11×C22⋊C4—21no—
249C2×C11×C22⋊C4—21no—
250C2×C11×C22⋊C4—22no—
251C2×C11×C22⋊C4—22no—
252C2×C11×C22⋊C4—22no—
253C2×C11×C22⋊C4—22no—
254C11×#107C2312yes—
255C11×#107C2312yes—
256C11×#106C2312yes—
257C11×#106C2312yes—
258C11×C4⋊C8C2312yes—
259C11×C4⋊C8C2312yes—
260C11×#103C2312yes—
261C11×#103C2312yes—
262C11×#103C2312yes—
263C11×#103C2312yes—
264C11×#103C2312yes—
265C11×#103C2312yes—
266C11×#103C2312yes—
267C11×#103C2312yes—
268C11×#102C2312yes—
269C11×#102C2312yes—
270C11×#102C2312yes—
271C11×#102C2312yes—
272C11×#102C2312yes—
273C11×#102C2312yes—
274C11×#102C2312yes—
275C11×#102C2312yes—
276C11×C22⋊C8C2312yes—
277C11×C22⋊C8C2312yes—
278C11×C22⋊C8C2311yescharacteristic
279C11×C22⋊C8C2311yescharacteristic
280C11×C22⋊C8C2311yescharacteristic
281C11×C22⋊C8C2311yescharacteristic
282C11×C22⋊C8C2312yes—
283C11×C22⋊C8C2312yes—
284C11×#97C2312yes—
285C4×C8×C11C2312yes—
286#61647C1111yesmaximal, characteristic, direct product factor, Sylow
287C24×C11—21no—
288C24×C11—21no—
289C24×C11—22no—
290C24×C11C2×D411yescharacteristic
291C11×#41—24no—
292C11×#41—24no—
293C11×#41—24no—
294C11×#41—42no—
295C11×#41—42no—
296C11×#41—42no—
297C11×#41—42no—
298C11×#41—42no—
299C11×#41—42no—
300C11×#41—42no—
301C11×#41—44no—
302C11×#41—44no—
303C11×#41—44no—
304C11×#41—84no—
305C2×Q8×C11—21no—
306C2×Q8×C11—21no—
307C2×Q8×C11—22no—
308C2×Q8×C11—42no—
309C2×Q8×C11—42no—
310C2×Q8×C11C2×D411yescharacteristic
311C2×Q8×C11C2412yes—
312C2×Q8×C11C2411yescharacteristic
313C2×Q8×C11C2412yes—
314C2×D4×C11—24no—
315C2×D4×C11—24no—
316C2×D4×C11—22no—
317C2×D4×C11—22no—
318C2×D4×C11—22no—
319C2×D4×C11—21no—
320C2×D4×C11—22no—
321C2×D4×C11—21no—
322C2×D4×C11—21no—
323C2×D4×C11—22no—
324C2×D4×C11—22no—
325C2×D4×C11—22no—
326C2×D4×C11—21no—
327C2×D4×C11—22no—
328C2×D4×C11—21no—
329C2×D4×C11—42no—
330C2×D4×C11—42no—
331C2×D4×C11—44no—
332C2×D4×C11—44no—
333C2×D4×C11—48no—
334C2×D4×C11—82no—
335C2×D4×C11C2×D412yes—
336C2×D4×C11C2×D412yes—
337C2×D4×C11C2×D412yes—
338C2×D4×C11C2×D411yescharacteristic
339C2×D4×C11C2411yescharacteristic
340C2×D4×C11C2412yes—
341C2×D4×C11C2412yes—
342C22×C4×C11—21no—
343C22×C4×C11—21no—
344C22×C4×C11—21no—
345C22×C4×C11—21no—
346C22×C4×C11—22no—
347C22×C4×C11—22no—
348C22×C4×C11—22no—
349C22×C4×C11—22no—
350C22×C4×C11—21no—
351C22×C4×C11—22no—
352C22×C4×C11—22no—
353C22×C4×C11—22no—
354C22×C4×C11—22no—
355C22×C4×C11—42no—
356C22×C4×C11—44no—
357C22×C4×C11C2×D411yescharacteristic
358C22×C4×C11C2×D411yescharacteristic
359C22×C4×C11C2×D411yescharacteristic
360C22×C4×C11C2411yescharacteristic
361C22×C4×C11C2411yescharacteristic
362C22×C4×C11C2412yes—
363C22×C4×C11C2411yescharacteristic
364C11×Q16—42no—
365C11×Q16—42no—
366C11×Q16—42no—
367C11×SD16—24no—
368C11×SD16—24no—
369C11×SD16—42no—
370C11×SD16—42no—
371C11×SD16—42no—
372C11×SD16—42no—
373C11×D8—24no—
374C11×D8—24no—
375C11×D8—42no—
376C11×M16—42no—
377C11×M16—42no—
378C11×M16—42no—
379C2×C8×C11—42no—
380C2×C8×C11C2412yes—
381C2×C8×C11C2412yes—
382C2×C8×C11C2412yes—
383C2×C8×C11C2412yes—
384C11×C4⋊C4—21no—
385C11×C4⋊C4—21no—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—22no—
388C11×C4⋊C4—22no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—21no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4C2×D412yes—
399C11×C4⋊C4C2×D412yes—
400C11×C4⋊C4C2×D411yescharacteristic
401C11×C4⋊C4C2×D411yescharacteristic
402C11×C4⋊C4C2412yes—
403C11×C4⋊C4C2412yes—
404C11×C4⋊C4C2411yescharacteristic
405C11×C4⋊C4C2411yescharacteristic
406C11×C22⋊C4—21no—
407C11×C22⋊C4—22no—
408C11×C22⋊C4—22no—
409C11×C22⋊C4—22no—
410C11×C22⋊C4—22no—
411C11×C22⋊C4—21no—
412C11×C22⋊C4—21no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—21no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4C2×D412yes—
427C11×C22⋊C4C2×D412yes—
428C11×C22⋊C4C2×D412yes—
429C11×C22⋊C4C2×D412yes—
430C11×C22⋊C4C2×D412yes—
431C42×C11—21no—
432C42×C11—22no—
433C42×C11C2412yes—
434#3536C2×C1111yescharacteristic, complemented
435#3485C2×C1111yescharacteristic, complemented
436#3331C2×C1112yescomplemented
437#3330C2×C1112yescomplemented
438#3314C2×C1112yescomplemented
439#3306C2×C1112yescomplemented
440#3275C2×C1112yescomplemented
441#3273C2×C1112yescomplemented
442#3269C2×C1112yescomplemented
443#3267C2×C1112yescomplemented
444#3225C2×C1112yescomplemented
445#3201C2×C1112yescomplemented
446#3196C2×C1111yescharacteristic, complemented
447#3194C2×C1111yescharacteristic, complemented
448#3118C2×C1112yescomplemented
449#3012C2×C1112yescomplemented
450#3007C2×C1111yescharacteristic, complemented
451#3006C2×C1111yescharacteristic, complemented
452#2978C2×C1111yescharacteristic, complemented
453C23×C11—24no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—21no—
457C23×C11—41no—
458C23×C11—41no—
459C23×C11—41no—
460C23×C11—44no—
461C23×C11—42no—
462C23×C11—81no—
463C23×C11—81no—
464C23×C11—81no—
465C23×C11—81no—
466C23×C11—82no—
467C23×C11—82no—
468C23×C11C22×D411yescharacteristic
469C23×C11C22×D411yescharacteristic
470C23×C11C22×D412yes—
471C23×C11C22×D411yescharacteristic
472Q8×C11—22no—
473Q8×C11—22no—
474Q8×C11—22no—
475Q8×C11—22no—
476Q8×C11—22no—
477Q8×C11—41no—
478Q8×C11—42no—
479Q8×C11—81no—
480Q8×C11—82no—
481D4×C11—24no—
482D4×C11—22no—
483D4×C11—22no—
484D4×C11—22no—
485D4×C11—22no—
486D4×C11—41no—
487D4×C11—42no—
488D4×C11—42no—
489D4×C11—42no—
490D4×C11—44no—
491D4×C11—44no—
492D4×C11—44no—
493D4×C11—44no—
494D4×C11—42no—
495D4×C11—44no—
496D4×C11—81no—
497D4×C11—81no—
498D4×C11—81no—
499D4×C11—82no—
500D4×C11—82no—
501D4×C11—82no—
502D4×C11H(5,𝔽2)14yes—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—21no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—44no—
519C2×C4×C11—44no—
520C2×C4×C11—44no—
521C2×C4×C11—42no—
522C2×C4×C11—42no—
523C2×C4×C11—42no—
524C2×C4×C11—82no—
525C2×C4×C11—82no—
526C2×C4×C11—82no—
527C2×C4×C11—82no—
528C2×C4×C11—81no—
529C2×C4×C11—81no—
530C2×C4×C11—82no—
531C2×C4×C11C22×D412yes—
532C2×C4×C11C22×D411yescharacteristic
533C2×C4×C11C22×D412yes—
534C2×C4×C11C22×D411yescharacteristic
535C2×C4×C11C22×D411yescharacteristic
536C2×C4×C11C22×D412yes—
537C2×C4×C11C2511yescharacteristic
538C8×C11—22no—
539C8×C11—22no—
540C8×C11—22no—
541C8×C11—22no—
542C2×H(5,𝔽2)C22×C1111yescharacteristic, complemented
543C22×#41C22×C1111yescharacteristic
544C2×#137C22×C1112yescomplemented
545C2×AGL(1,ℤ/8)C22×C1112yescomplemented
546C2×AGL(1,ℤ/8)C22×C1112yescomplemented
547C2×#135C22×C1112yescomplemented
548#562—22no—
549#554C22×C1112yescomplemented
550#548C22×C1112yescomplemented
551#547—21no—
552#547—21no—
553#547C22×C1112yes—
554#547C22×C1112yescomplemented
555#547C22×C1112yescomplemented
556#546—21no—
557#546—21no—
558#546—22no—
559#546C22×C1112yes—
560#546C22×C1112yescomplemented
561#546C22×C1112yescomplemented
562#543—21no—
563#542C22×C1112yescomplemented
564#539—21no—
565#538—21no—
566#537—21no—
567#537C22×C1112yes—
568#536C22×C1111yescharacteristic, complemented
569#536C22×C1111yescharacteristic, complemented
570#534—22no—
571#525C22×C1111yescharacteristic
572#525C22×C1111yescharacteristic
573C2×#123—22no—
574C2×C22⋊Q8C22×C1111yescharacteristic, complemented
575C2×#121C22×C1111yescharacteristic, complemented
576#518C22×C1111yescharacteristic, complemented
577#497C22×C1112yescomplemented
578#495C22×C1112yescomplemented
579#489C22×C1112yescomplemented
580#487C22×C1112yescomplemented
581#485C22×C1112yescomplemented
582#484C22×C1111yescharacteristic, complemented
583#484C22×C1112yescomplemented
584#483C22×C1111yescharacteristic, complemented
585#483C22×C1112yescomplemented
586#482C22×C1112yescomplemented
587#481C22×C1111yescharacteristic, complemented
588#480C22×C1111yescharacteristic, complemented
589#476C22×C1112yescomplemented
590#474C22×C1112yescomplemented
591#470C22×C1112yescomplemented
592#470C22×C1112yescomplemented
593#469C22×C1112yescomplemented
594#468C22×C1112yescomplemented
595#468C22×C1112yescomplemented
596#468C22×C1112yescomplemented
597#467C22×C1112yescomplemented
598#465C22×C1112yescomplemented
599#464C22×C1112yescomplemented
600#463C22×C1112yescomplemented
601#463C22×C1112yescomplemented
602#463C22×C1112yescomplemented
603#462C22×C1112yescomplemented
604#461C22×C1112yescomplemented
605#452C22×C1112yescomplemented
606#452C22×C1112yescomplemented
607#452C22×C1112yescomplemented
608#452C22×C1112yescomplemented
609#452C22×C1112yescomplemented
610#452C22×C1112yescomplemented
611#451C22×C1111yescharacteristic, complemented
612#451C22×C1112yescomplemented
613#450C22×C1112yescomplemented
614#450C22×C1111yescharacteristic, complemented
615#450C22×C1112yescomplemented
616#449C22×C1112yes—
617#449C22×C1112yescomplemented
618#449C22×C1112yescomplemented
619#449C22×C1112yescomplemented
620#448C22×C1111yescharacteristic, complemented
621#448C22×C1112yescomplemented
622#447C22×C1112yes—
623#447C22×C1111yescharacteristic, complemented
624#447C22×C1112yescomplemented
625#442C22×C1112yescomplemented
626#440C22×C1112yescomplemented
627C4×SD16C22×C1112yescomplemented
628C4×D8C22×C1112yescomplemented
629#436C22×C1112yescomplemented
630#436C22×C1112yescomplemented
631#435C22×C1112yescomplemented
632#435C22×C1112yescomplemented
633#433C22×C1112yescomplemented
634#417C22×C1112yescomplemented
635#417C22×C1112yescomplemented
636#417C22×C1112yescomplemented
637C2×#102C22×C1112yescomplemented
638#408C22×C1112yescomplemented
639#407C22×C1111yescharacteristic, complemented
640#407C22×C1111yescharacteristic, complemented
641C22×C11—21no—
642C22×C11—22no—
643C22×C11—21no—
644C22×C11—21no—
645C22×C11—21no—
646C22×C11—22no—
647C22×C11—21no—
648C22×C11—21no—
649C22×C11—21no—
650C22×C11—21no—
651C22×C11—21no—
652C22×C11—22no—
653C22×C11—24no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—41no—
658C22×C11—41no—
659C22×C11—42no—
660C22×C11—41no—
661C22×C11—42no—
662C22×C11—84no—
663C22×C11—82no—
664C22×C11—164no—
665C22×C11—162no—
666C22×C11C23×D411yescharacteristic
667C4×C11—22no—
668C4×C11—22no—
669C4×C11—21no—
670C4×C11—21no—
671C4×C11—21no—
672C4×C11—22no—
673C4×C11—42no—
674C4×C11—42no—
675C4×C11—41no—
676C4×C11—41no—
677C4×C11—41no—
678C4×C11—42no—
679C4×C11—42no—
680C4×C11C2×H(5,𝔽2)12yes—
681H(5,𝔽2)—44no—
682C2×#41—21no—
683C2×#41—22no—
684C2×#41—21no—
685C2×#41—21no—
686C2×#41—44no—
687C2×#41C23×C1112yes—
688C2×#41C23×C1112yes—
689C2×#41C23×C1112yes—
690C2×#41C23×C1111yescharacteristic
691C2×#41C23×C1112yes—
692C2×#41C23×C1111yescharacteristic
693C22×Q8C23×C1111yescharacteristic
694C22×Q8C23×C1111yescharacteristic
695C22×D4—21no—
696C22×D4—21no—
697C22×D4—22no—
698C22×D4—21no—
699C22×D4C23×C1111yescharacteristic
700C22×D4C23×C1112yes—
701C22×D4C23×C1111yescharacteristic
702C23×C4—21no—
703C23×C4C23×C1111yescharacteristic
704#137—44no—
705AGL(1,ℤ/8)—44no—
706AGL(1,ℤ/8)—44no—
707#135—44no—
708C2×Q16C23×C1112yes—
709C2×Q16C23×C1112yes—
710C2×Q16C23×C1112yes—
711C2×SD16C23×C1112yes—
712C2×SD16C23×C1112yes—
713C2×SD16C23×C1112yes—
714C2×SD16C23×C1112yes—
715C2×SD16C23×C1112yes—
716C2×SD16C23×C1112yes—
717C2×D8C23×C1112yes—
718C2×D8C23×C1112yes—
719C2×D8C23×C1112yes—
720C2×M16C23×C1112yes—
721C2×M16C23×C1112yes—
722C2×M16C23×C1112yes—
723C22×C8C23×C1112yes—
724C4⋊Q8—21no—
725C4⋊Q8C23×C1112yes—
726C4⋊Q8C23×C1112yes—
727#126—22no—
728#125—22no—
729#124—21no—
730#124—22no—
731#124—22no—
732#124C23×C1112yes—
733#124C23×C1112yes—
734#123—22no—
735#123—21no—
736#123—22no—
737#123—22no—
738#123—22no—
739#123—22no—
740#123—22no—
741#123—22no—
742#123—22no—
743#123—22no—
744#123—22no—
745#123—22no—
746#123—22no—
747#123D4×C1112yes—
748C22⋊Q8—22no—
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8—22no—
756C22⋊Q8—22no—
757C22⋊Q8—22no—
758C22⋊Q8D4×C1111yescharacteristic
759C22⋊Q8D4×C1111yescharacteristic
760C22⋊Q8C23×C1112yes—
761C22⋊Q8C23×C1112yes—
762C22⋊Q8C23×C1111yescharacteristic
763C22⋊Q8C23×C1111yescharacteristic
764C22⋊Q8C23×C1112yes—
765C22⋊Q8C23×C1112yes—
766C22⋊Q8C23×C1112yes—
767#121—22no—
768#121—22no—
769#121—22no—
770#121—22no—
771#121—22no—
772#121—22no—
773#121—21no—
774#121—21no—
775#121—22no—
776#121—22no—
777#121—22no—
778#121D4×C1111yescharacteristic
779#121D4×C1111yescharacteristic
780#121C23×C1112yes—
781#121C23×C1112yes—
782#121C23×C1111yescharacteristic
783#121C23×C1111yescharacteristic
784#121C23×C1112yes—
785#120—21no—
786#120—22no—
787#120—22no—
788#120—22no—
789#120D4×C1112yes—
790C4×Q8C23×C1112yes—
791C4×D4—22no—
792C4×D4—21no—
793C4×D4—21no—
794C4×D4—21no—
795C4×D4—21no—
796C4×D4—22no—
797C4×D4C23×C1112yes—
798C4×D4C23×C1112yes—
799C4×D4C23×C1112yes—
800C4×D4C23×C1112yes—
801C4×D4C23×C1112yes—
802#117C23×C1111yescharacteristic
803#117C23×C1111yescharacteristic
804C2×C4⋊C4—21no—
805C2×C4⋊C4—22no—
806C2×C4⋊C4—22no—
807C2×C4⋊C4C23×C1111yescharacteristic
808C2×C4⋊C4C23×C1111yescharacteristic
809C2×C4⋊C4C23×C1112yes—
810C2×C22⋊C4—21no—
811C2×C22⋊C4—21no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816#107C23×C1112yes—
817#107C23×C1112yes—
818#106C23×C1112yes—
819#106C23×C1112yes—
820C4⋊C8C23×C1112yes—
821C4⋊C8C23×C1112yes—
822#103C23×C1112yes—
823#103C23×C1112yes—
824#103C23×C1112yes—
825#103C23×C1112yes—
826#103C23×C1112yes—
827#103C23×C1112yes—
828#103C23×C1112yes—
829#103C23×C1112yes—
830#102C23×C1112yes—
831#102C23×C1112yes—
832#102C23×C1112yes—
833#102C23×C1112yes—
834#102C23×C1112yes—
835#102C23×C1112yes—
836#102C23×C1112yes—
837#102C23×C1112yes—
838C22⋊C8C23×C1112yes—
839C22⋊C8C23×C1112yes—
840C22⋊C8C23×C1111yescharacteristic
841C22⋊C8C23×C1111yescharacteristic
842C22⋊C8C23×C1111yescharacteristic
843C22⋊C8C23×C1111yescharacteristic
844C22⋊C8C23×C1112yes—
845C22⋊C8C23×C1112yes—
846#97C23×C1112yes—
847C4×C8C23×C1112yes—
848C2×C11—41no—
849C2×C11—41no—
850C2×C11—41no—
851C2×C11—42no—
852C2×C11—44no—
853C2×C11—82no—
854C2×C11—81no—
855C2×C11#348411yescharacteristic
856C2×C11#358511yescharacteristic
857C2×C11#358611yescharacteristic
858C24—21no—
859C24—21no—
860C24—22no—
861C24C2×D4×C1111yescharacteristic
862#41—24no—
863#41—24no—
864#41—24no—
865#41—42no—
866#41—42no—
867#41—42no—
868#41—42no—
869#41—42no—
870#41—42no—
871#41—42no—
872#41—44no—
873#41—44no—
874#41—44no—
875#41—84no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—22no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8C2×D4×C1111yescharacteristic
882C2×Q8C24×C1112yes—
883C2×Q8C24×C1111yescharacteristic
884C2×Q8C24×C1112yes—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—21no—
891C2×D4—22no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—22no—
895C2×D4—22no—
896C2×D4—22no—
897C2×D4—21no—
898C2×D4—22no—
899C2×D4—21no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—48no—
905C2×D4—82no—
906C2×D4C2×D4×C1112yes—
907C2×D4C2×D4×C1112yes—
908C2×D4C2×D4×C1112yes—
909C2×D4C2×D4×C1111yescharacteristic
910C2×D4C24×C1111yescharacteristic
911C2×D4C24×C1112yes—
912C2×D4C24×C1112yes—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—21no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—42no—
927C22×C4—44no—
928C22×C4C2×D4×C1111yescharacteristic
929C22×C4C2×D4×C1111yescharacteristic
930C22×C4C2×D4×C1111yescharacteristic
931C22×C4C24×C1111yescharacteristic
932C22×C4C24×C1111yescharacteristic
933C22×C4C24×C1112yes—
934C22×C4C24×C1111yescharacteristic
935Q16—42no—
936Q16—42no—
937Q16—42no—
938SD16—24no—
939SD16—24no—
940SD16—42no—
941SD16—42no—
942SD16—42no—
943SD16—42no—
944D8—24no—
945D8—24no—
946D8—42no—
947M16—42no—
948M16—42no—
949M16—42no—
950C2×C8—42no—
951C2×C8C24×C1112yes—
952C2×C8C24×C1112yes—
953C2×C8C24×C1112yes—
954C2×C8C24×C1112yes—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—21no—
964C4⋊C4—22no—
965C4⋊C4—21no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4C2×D4×C1112yes—
970C4⋊C4C2×D4×C1112yes—
971C4⋊C4C2×D4×C1111yescharacteristic
972C4⋊C4C2×D4×C1111yescharacteristic
973C4⋊C4C24×C1112yes—
974C4⋊C4C24×C1112yes—
975C4⋊C4C24×C1111yescharacteristic
976C4⋊C4C24×C1111yescharacteristic
977C22⋊C4—21no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—21no—
983C22⋊C4—21no—
984C22⋊C4—22no—
985C22⋊C4—21no—
986C22⋊C4—21no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4C2×D4×C1112yes—
998C22⋊C4C2×D4×C1112yes—
999C22⋊C4C2×D4×C1112yes—
1000C22⋊C4C2×D4×C1112yes—
1001C22⋊C4C2×D4×C1112yes—
1002C42—21no—
1003C42—22no—
1004C42C24×C1112yes—
1005C11#6164711yescharacteristic, direct product factor, Sylow
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—21no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—44no—
1014C23—42no—
1015C23—81no—
1016C23—81no—
1017C23—81no—
1018C23—81no—
1019C23—82no—
1020C23—82no—
1021C23C22×D4×C1111yescharacteristic
1022C23C22×D4×C1111yescharacteristic
1023C23C22×D4×C1112yes—
1024C23C22×D4×C1111yescharacteristic
1025Q8—22no—
1026Q8—22no—
1027Q8—22no—
1028Q8—22no—
1029Q8—22no—
1030Q8—41no—
1031Q8—42no—
1032Q8—81no—
1033Q8—82no—
1034D4—24no—
1035D4—22no—
1036D4—22no—
1037D4—22no—
1038D4—22no—
1039D4—41no—
1040D4—42no—
1041D4—42no—
1042D4—42no—
1043D4—44no—
1044D4—44no—
1045D4—44no—
1046D4—44no—
1047D4—42no—
1048D4—44no—
1049D4—81no—
1050D4—81no—
1051D4—81no—
1052D4—82no—
1053D4—82no—
1054D4—82no—
1055D4C11×H(5,𝔽2)14yes—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—42no—
1075C2×C4—42no—
1076C2×C4—42no—
1077C2×C4—82no—
1078C2×C4—82no—
1079C2×C4—82no—
1080C2×C4—82no—
1081C2×C4—81no—
1082C2×C4—81no—
1083C2×C4—82no—
1084C2×C4C22×D4×C1112yes—
1085C2×C4C22×D4×C1111yescharacteristic
1086C2×C4C22×D4×C1112yes—
1087C2×C4C22×D4×C1111yescharacteristic
1088C2×C4C22×D4×C1111yescharacteristic
1089C2×C4C22×D4×C1112yes—
1090C2×C4C25×C1111yescharacteristic
1091C8—22no—
1092C8—22no—
1093C8—22no—
1094C8—22no—
1095C22—21no—
1096C22—21no—
1097C22—21no—
1098C22—22no—
1099C22—24no—
1100C22—21no—
1101C22—22no—
1102C22—21no—
1103C22—21no—
1104C22—21no—
1105C22—22no—
1106C22—21no—
1107C22—21no—
1108C22—42no—
1109C22—42no—
1110C22—41no—
1111C22—42no—
1112C22—42no—
1113C22—41no—
1114C22—41no—
1115C22—42no—
1116C22—84no—
1117C22—82no—
1118C22—164no—
1119C22—162no—
1120C22C23×D4×C1111yescharacteristic
1121C4—21no—
1122C4—21no—
1123C4—21no—
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—41no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—41no—
1133C4—41no—
1134C4C2×C11×H(5,𝔽2)12yes—
1135C2—41no—
1136C2—41no—
1137C2—41no—
1138C2—42no—
1139C2—44no—
1140C2—81no—
1141C2—82no—
1142C2C11×#348411yescharacteristic
1143C2C11×#358511yescharacteristic
1144C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#3536C2semidirect
2. C11×#3485C2semidirect
3. C11×#3331C2semidirect
4. C11×#3330C2semidirect
5. C11×#3314C2semidirect
6. C11×#3306C2semidirect
7. C11×#3275C2semidirect
8. C11×#3273C2semidirect
9. C11×#3269C2semidirect
10. C11×#3267C2semidirect
11. C11×#3225C2semidirect
12. C11×#3201C2semidirect
13. C11×#3196C2semidirect
14. C11×#3194C2semidirect
15. C11×#3118C2semidirect
16. C11×#3012C2semidirect
17. C11×#3007C2semidirect
18. C11×#3006C2semidirect
19. C11×#2978C2semidirect
20. C2×C11×H(5,𝔽2)C22semidirect
22. C2×C11×#137C22semidirect
23. C2×C11×AGL(1,ℤ/8)C22semidirect
24. C2×C11×AGL(1,ℤ/8)C22semidirect
25. C2×C11×#135C22semidirect
27. C11×#554C22semidirect
28. C11×#548C22semidirect
32. C11×#547C22semidirect
33. C11×#547C22semidirect
38. C11×#546C22semidirect
39. C11×#546C22semidirect
41. C11×#542C22semidirect
46. C11×#536C22semidirect
47. C11×#536C22semidirect
52. C2×C11×C22⋊Q8C22semidirect
53. C2×C11×#121C22semidirect
54. C11×#518C22semidirect
55. C11×#497C22semidirect
56. C11×#495C22semidirect
57. C11×#489C22semidirect
58. C11×#487C22semidirect
59. C11×#485C22semidirect
60. C11×#484C22semidirect
61. C11×#484C22semidirect
62. C11×#483C22semidirect
63. C11×#483C22semidirect
64. C11×#482C22semidirect
65. C11×#481C22semidirect
66. C11×#480C22semidirect
67. C11×#476C22semidirect
68. C11×#474C22semidirect
69. C11×#470C22semidirect
70. C11×#470C22semidirect
71. C11×#469C22semidirect
72. C11×#468C22semidirect
73. C11×#468C22semidirect
74. C11×#468C22semidirect
75. C11×#467C22semidirect
76. C11×#465C22semidirect
77. C11×#464C22semidirect
78. C11×#463C22semidirect
79. C11×#463C22semidirect
80. C11×#463C22semidirect
81. C11×#462C22semidirect
82. C11×#461C22semidirect
83. C11×#452C22semidirect
84. C11×#452C22semidirect
85. C11×#452C22semidirect
86. C11×#452C22semidirect
87. C11×#452C22semidirect
88. C11×#452C22semidirect
89. C11×#451C22semidirect
90. C11×#451C22semidirect
91. C11×#450C22semidirect
92. C11×#450C22semidirect
93. C11×#450C22semidirect
95. C11×#449C22semidirect
96. C11×#449C22semidirect
97. C11×#449C22semidirect
98. C11×#448C22semidirect
99. C11×#448C22semidirect
101. C11×#447C22semidirect
102. C11×#447C22semidirect
103. C11×#442C22semidirect
104. C11×#440C22semidirect
105. C4×C11×SD16C22semidirect
106. C4×C11×D8C22semidirect
107. C11×#436C22semidirect
108. C11×#436C22semidirect
109. C11×#435C22semidirect
110. C11×#435C22semidirect
111. C11×#433C22semidirect
112. C11×#417C22semidirect
113. C11×#417C22semidirect
114. C11×#417C22semidirect
115. C2×C11×#102C22semidirect
116. C11×#408C22semidirect
117. C11×#407C22semidirect
118. C11×#407C22semidirect
286. #61647C11direct (N × H)
434. #3536C2×C11semidirect
435. #3485C2×C11semidirect
436. #3331C2×C11semidirect
437. #3330C2×C11semidirect
438. #3314C2×C11semidirect
439. #3306C2×C11semidirect
440. #3275C2×C11semidirect
441. #3273C2×C11semidirect
442. #3269C2×C11semidirect
443. #3267C2×C11semidirect
444. #3225C2×C11semidirect
445. #3201C2×C11semidirect
446. #3196C2×C11semidirect
447. #3194C2×C11semidirect
448. #3118C2×C11semidirect
449. #3012C2×C11semidirect
450. #3007C2×C11semidirect
451. #3006C2×C11semidirect
452. #2978C2×C11semidirect
542. C2×H(5,𝔽2)C22×C11semidirect
544. C2×#137C22×C11semidirect
545. C2×AGL(1,ℤ/8)C22×C11semidirect
546. C2×AGL(1,ℤ/8)C22×C11semidirect
547. C2×#135C22×C11semidirect
549. #554C22×C11semidirect
550. #548C22×C11semidirect
554. #547C22×C11semidirect
555. #547C22×C11semidirect
560. #546C22×C11semidirect
561. #546C22×C11semidirect
563. #542C22×C11semidirect
568. #536C22×C11semidirect
569. #536C22×C11semidirect
574. C2×C22⋊Q8C22×C11semidirect
575. C2×#121C22×C11semidirect
576. #518C22×C11semidirect
577. #497C22×C11semidirect
578. #495C22×C11semidirect
579. #489C22×C11semidirect
580. #487C22×C11semidirect
581. #485C22×C11semidirect
582. #484C22×C11semidirect
583. #484C22×C11semidirect
584. #483C22×C11semidirect
585. #483C22×C11semidirect
586. #482C22×C11semidirect
587. #481C22×C11semidirect
588. #480C22×C11semidirect
589. #476C22×C11semidirect
590. #474C22×C11semidirect
591. #470C22×C11semidirect
592. #470C22×C11semidirect
593. #469C22×C11semidirect
594. #468C22×C11semidirect
595. #468C22×C11semidirect
596. #468C22×C11semidirect
597. #467C22×C11semidirect
598. #465C22×C11semidirect
599. #464C22×C11semidirect
600. #463C22×C11semidirect
601. #463C22×C11semidirect
602. #463C22×C11semidirect
603. #462C22×C11semidirect
604. #461C22×C11semidirect
605. #452C22×C11semidirect
606. #452C22×C11semidirect
607. #452C22×C11semidirect
608. #452C22×C11semidirect
609. #452C22×C11semidirect
610. #452C22×C11semidirect
611. #451C22×C11semidirect
612. #451C22×C11semidirect
613. #450C22×C11semidirect
614. #450C22×C11semidirect
615. #450C22×C11semidirect
617. #449C22×C11semidirect
618. #449C22×C11semidirect
619. #449C22×C11semidirect
620. #448C22×C11semidirect
621. #448C22×C11semidirect
623. #447C22×C11semidirect
624. #447C22×C11semidirect
625. #442C22×C11semidirect
626. #440C22×C11semidirect
627. C4×SD16C22×C11semidirect
628. C4×D8C22×C11semidirect
629. #436C22×C11semidirect
630. #436C22×C11semidirect
631. #435C22×C11semidirect
632. #435C22×C11semidirect
633. #433C22×C11semidirect
634. #417C22×C11semidirect
635. #417C22×C11semidirect
636. #417C22×C11semidirect
637. C2×#102C22×C11semidirect
638. #408C22×C11semidirect
639. #407C22×C11semidirect
640. #407C22×C11semidirect
1005. C11#61647direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35362
C11×#34852
C11×#33312
C11×#33302
C11×#33142
C11×#33062
C11×#32752
C11×#32732
C11×#32692
C11×#32672
C11×#32252
C11×#32012
C11×#31962
C11×#31942
C11×#31182
C11×#30122
C11×#30072
C11×#30062
C11×#29782
#6164711