Finite Group Databasebeta

← C11×#61671 #14638864

Subgroups — C11×#61671 #14638864

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3546C211yesmaximal, characteristic, complemented
2C11×#3497C211yesmaximal, characteristic, complemented
3C11×#3320C212yesmaximal, complemented
4C11×#3313C212yesmaximal, complemented
5C11×#3309C212yesmaximal, complemented
6C11×#3308C212yesmaximal, complemented
7C11×#3271C212yesmaximal, complemented
8C11×#3268C212yesmaximal, complemented
9C11×#3266C212yesmaximal, complemented
10C11×#3265C212yesmaximal, complemented
11C11×#3219C211yesmaximal, characteristic, complemented
12C11×#3214C211yesmaximal, characteristic, complemented
13C11×#3203C212yesmaximal, complemented
14C11×#3198C212yesmaximal, complemented
15C11×#3117C211yesmaximal, characteristic, complemented
16C11×#3112C211yesmaximal, characteristic, complemented
17C11×#3013C212yesmaximal, complemented
18C11×#3010C212yesmaximal, complemented
19C11×#2980C211yesmaximal, characteristic, complemented
20C2×C11×2−1+4C2212yescomplemented
21C2×C11×#137C2212yescomplemented
22C2×C11×AGL(1,ℤ/8)C2212yes—
23C2×C11×#135C2212yescomplemented
24C22×C11×SD16C2212yes—
25C11×#560—22no—
26C11×#556C2211yescharacteristic
27C11×#553C2212yes—
28C11×#550—21no—
29C11×#550—21no—
30C11×#550C2211yescharacteristic
31C11×#550C2212yescomplemented
32D4×Q8×C11—21no—
33D4×Q8×C11C2212yescomplemented
34C11×#548—22no—
35C11×#548C2212yes—
36C11×#548C2212yescomplemented
37C11×#547C2211yescharacteristic
38C11×#546—21no—
39C11×#546C2212yes—
40D42×C11C2211yescharacteristic
41C11×#542—21no—
42C11×#538—22no—
43C11×#537—21no—
44C11×#537—21no—
45C11×#537C2212yes—
46C11×#537C2212yescomplemented
47C11×#535—21no—
48C11×#535C2212yes—
49C11×#532—22no—
50C11×#532C2211yescharacteristic
51C11×#532C2211yescharacteristic
52C11×#532C2211yescharacteristic, complemented
53C11×#529C2211yescharacteristic
54C2×C4×Q8×C11C2211yescharacteristic, complemented
55C11×#497C2211yescharacteristic
56C11×#496C2212yes—
57C11×#496C2211yescharacteristic
58C11×#491C2211yescharacteristic, complemented
59C11×#490C2211yescharacteristic, complemented
60C11×#489C2212yescomplemented
61C11×#485C2212yescomplemented
62C11×#484C2211yescharacteristic, complemented
63C11×#484C2212yescomplemented
64C11×#482C2212yescomplemented
65C11×#481C2211yescharacteristic
66C11×#480C2212yescomplemented
67C11×#480C2212yescomplemented
68C11×#479C2212yescomplemented
69C11×#477C2212yescomplemented
70C11×#469C2212yescomplemented
71C11×#468C2212yes—
72C11×#468C2212yes—
73C11×#468C2212yescomplemented
74C11×#467C2212yescomplemented
75C11×#466C2212yes—
76C11×#466C2212yes—
77C11×#465C2212yescomplemented
78C11×#464C2212yes—
79C11×#464C2212yescomplemented
80C11×#463C2212yes—
81C11×#461C2212yescomplemented
82C11×#460C2212yes—
83C11×#459C2212yescomplemented
84C11×#452C2212yescomplemented
85C11×#452C2212yescomplemented
86C11×#452C2212yescomplemented
87C11×#451C2212yescomplemented
88C11×#451C2211yescharacteristic, complemented
89C11×#450C2212yes—
90C11×#449C2212yes—
91C11×#449C2212yes—
92C11×#449C2212yes—
93C11×#449C2212yescomplemented
94C11×#449C2212yescomplemented
95C11×#449C2212yescomplemented
96C11×#449C2212yescomplemented
97C11×#448C2212yes—
98C11×#448C2211yescharacteristic
99C11×#448C2212yes—
100C11×#448C2212yescomplemented
101C11×#448C2212yescomplemented
102C11×#447C2212yes—
103C11×#441C2212yescomplemented
104C11×#440C2212yes—
105C11×#440C2212yescomplemented
106C11×#440C2212yescomplemented
107C11×#435C2212yes—
108C11×#435C2212yescomplemented
109C11×#435C2212yescomplemented
110C11×#435C2212yescomplemented
111C11×#432C2211yescharacteristic, complemented
112C11×#432C2211yescharacteristic, complemented
113C11×#419C2212yescomplemented
114C11×#417C2212yescomplemented
115C11×#416C2212yescomplemented
116C2×C11×#103C2212yescomplemented
117C11×#408C2212yescomplemented
118C11×#408C2212yescomplemented
119C11×2−1+4—44no—
120C11×2−1+4—44no—
121C2×C11×#41—22no—
122C2×C11×#41—22no—
123C2×C11×#41—22no—
124C2×C11×#41—21no—
125C2×C11×#41—21no—
126C2×C11×#41C2312yes—
127C2×C11×#41C2312yes—
128C2×C11×#41C2312yes—
129C2×C11×#41C2312yes—
130C2×C11×#41C2312yes—
131C22×Q8×C11—22no—
132C22×Q8×C11C2311yescharacteristic
133C22×Q8×C11C2312yes—
134C22×Q8×C11C2312yes—
135C22×D4×C11—21no—
136C22×D4×C11C2312yes—
137C11×#137—44no—
138C11×AGL(1,ℤ/8)—44no—
139C11×#135—44no—
140C2×C11×Q16C2312yes—
141C2×C11×Q16C2312yes—
142C2×C11×SD16—44no—
143C2×C11×SD16C2312yes—
144C2×C11×SD16C2312yes—
145C2×C11×SD16C2312yes—
146C2×C11×SD16C2312yes—
147C2×C11×SD16C2312yes—
148C2×C11×SD16C2312yes—
149C2×C11×SD16C2312yes—
150C2×C11×D8C2312yes—
151C2×C11×D8C2312yes—
152C2×C11×D8C2312yes—
153C2×C11×M16C2312yes—
154C2×C11×M16C2312yes—
155C22×C8×C11C2312yes—
156C22×C8×C11C2312yes—
157C11×C4⋊Q8—22no—
158C11×C4⋊Q8D411yescharacteristic
159C11×C4⋊Q8C2311yescharacteristic
160C11×C4⋊Q8C2311yescharacteristic
161C11×#127—22no—
162C11×#127—21no—
163C11×#127—22no—
164C11×#127D411yescharacteristic
165C11×#127C2311yescharacteristic
166C11×#127C2311yescharacteristic
167C11×#126—22no—
168C11×#126—22no—
169C11×#126—21no—
170C11×#125C2311yescharacteristic
171C11×#124—22no—
172C11×#124—21no—
173C11×#124—22no—
174C11×#124—22no—
175C11×#124—21no—
176C11×#124D412yes—
177C11×#124C2312yes—
178C11×#124C2311yescharacteristic
179C11×#123—21no—
180C11×#123—22no—
181C11×#123—22no—
182C11×#123—22no—
183C11×C22⋊Q8—22no—
184C11×C22⋊Q8—22no—
185C11×C22⋊Q8—22no—
186C11×C22⋊Q8—22no—
187C11×C22⋊Q8—21no—
188C11×C22⋊Q8—22no—
189C11×C22⋊Q8—22no—
190C11×C22⋊Q8C2311yescharacteristic
191C11×C22⋊Q8C2312yes—
192C11×C22⋊Q8C2312yes—
193C11×C22⋊Q8C2312yes—
194C11×#121—22no—
195C11×#121—22no—
196C11×#121—22no—
197C11×#121—22no—
198C11×#121—22no—
199C11×#121—22no—
200C11×#121—22no—
201C11×#121—22no—
202C11×#121—22no—
203C11×#121—21no—
204C11×#121—21no—
205C11×#121—21no—
206C11×#121—21no—
207C11×#121—22no—
208C11×#121—22no—
209C11×#121—22no—
210C11×#121—22no—
211C11×#121D412yes—
212C11×#121D411yescharacteristic
213C11×#121D411yescharacteristic
214C11×#121C2311yescharacteristic
215C11×#121C2312yes—
216C11×#121C2312yes—
217C11×#121C2312yes—
218C11×#121C2312yes—
219C11×#121C2312yes—
220C11×#121C2312yes—
221C11×#120—22no—
222C11×#120—22no—
223C11×#120—22no—
224C11×#120—22no—
225C4×Q8×C11—21no—
226C4×Q8×C11—21no—
227C4×Q8×C11—21no—
228C4×Q8×C11C2312yes—
229C4×Q8×C11C2312yes—
230C4×Q8×C11C2311yescharacteristic
231C4×D4×C11—22no—
232C4×D4×C11—21no—
233C4×D4×C11—22no—
234C4×D4×C11—21no—
235C4×D4×C11—22no—
236C4×D4×C11—22no—
237C4×D4×C11—22no—
238C4×D4×C11—21no—
239C4×D4×C11—21no—
240C4×D4×C11—21no—
241C4×D4×C11C2311yescharacteristic
242C4×D4×C11C2312yes—
243C4×D4×C11C2311yescharacteristic
244C4×D4×C11C2312yes—
245C4×D4×C11C2311yescharacteristic
246C11×#117—21no—
247C11×#117C2312yes—
248C2×C11×C4⋊C4—21no—
249C2×C11×C4⋊C4C2311yescharacteristic
250C2×C11×C4⋊C4C2312yes—
251C2×C11×C22⋊C4—22no—
252C2×C42×C11—21no—
253C2×C42×C11C2311yescharacteristic
254C11×#107C2312yes—
255C11×#107C2312yes—
256C11×#107C2312yes—
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×#103C2312yes—
269C11×#102C2312yes—
270C11×#102C2312yes—
271C11×#102C2312yes—
272C11×#102C2312yes—
273C11×#102C2312yes—
274C11×#102C2312yes—
275C11×#102C2312yes—
276C11×C22⋊C8C2311yescharacteristic
277C11×C22⋊C8C2312yes—
278C11×C22⋊C8C2311yescharacteristic
279C11×C22⋊C8C2312yes—
280C11×C22⋊C8C2312yes—
281C11×C22⋊C8C2312yes—
282C11×C22⋊C8C2312yes—
283C11×#97C2312yes—
284C11×#97C2311yescharacteristic
285C11×#97C2311yescharacteristic
286#61671C1111yesmaximal, characteristic, direct product factor, Sylow
287C24×C11—22no—
288C11×#41—24no—
289C11×#41—24no—
290C11×#41—42no—
291C11×#41—42no—
292C11×#41—42no—
293C11×#41—42no—
294C11×#41—42no—
295C11×#41—42no—
296C11×#41—48no—
297C11×#41—48no—
298C11×#41—42no—
299C11×#41—42no—
300C11×#41—48no—
301C11×#41—82no—
302C11×#41—82no—
303C2×Q8×C11—24no—
304C2×Q8×C11—21no—
305C2×Q8×C11—21no—
306C2×Q8×C11—22no—
307C2×Q8×C11—22no—
308C2×Q8×C11—24no—
309C2×Q8×C11—24no—
310C2×Q8×C11—42no—
311C2×Q8×C11—42no—
312C2×Q8×C11—48no—
313C2×Q8×C11C2×D412yes—
314C2×Q8×C11C2412yes—
315C2×Q8×C11C2411yescharacteristic
316C2×Q8×C11C2412yes—
317C2×D4×C11—22no—
318C2×D4×C11—22no—
319C2×D4×C11—22no—
320C2×D4×C11—21no—
321C2×D4×C11—22no—
322C2×D4×C11—22no—
323C2×D4×C11—22no—
324C2×D4×C11—22no—
325C2×D4×C11—22no—
326C2×D4×C11—22no—
327C2×D4×C11—22no—
328C2×D4×C11—21no—
329C2×D4×C11—21no—
330C2×D4×C11—21no—
331C2×D4×C11—21no—
332C2×D4×C11—22no—
333C2×D4×C11—42no—
334C2×D4×C11—42no—
335C2×D4×C11—82no—
336C2×D4×C11C2×D412yes—
337C2×D4×C11C2×D411yescharacteristic
338C2×D4×C11C2×D411yescharacteristic
339C2×D4×C11C2×D412yes—
340C2×D4×C11C2×D412yes—
341C2×D4×C11C2×D412yes—
342C2×D4×C11C2412yes—
343C2×D4×C11C2411yescharacteristic
344C2×D4×C11C2412yes—
345C22×C4×C11—21no—
346C22×C4×C11—22no—
347C22×C4×C11—22no—
348C22×C4×C11—21no—
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—22no—
356C22×C4×C11C2×D411yescharacteristic
357C22×C4×C11C2×D411yescharacteristic
358C22×C4×C11C2411yescharacteristic
359C22×C4×C11C2412yes—
360C22×C4×C11C2412yes—
361C11×Q16—24no—
362C11×Q16—42no—
363C11×SD16—24no—
364C11×SD16—24no—
365C11×SD16—24no—
366C11×SD16—42no—
367C11×SD16—42no—
368C11×SD16—42no—
369C11×SD16—42no—
370C11×D8—42no—
371C11×D8—42no—
372C11×D8—42no—
373C11×M16—42no—
374C11×M16—42no—
375C2×C8×C11—42no—
376C2×C8×C11—42no—
377C2×C8×C11C2412yes—
378C2×C8×C11C2412yes—
379C2×C8×C11C2412yes—
380C2×C8×C11C2412yes—
381C11×C4⋊C4—22no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—21no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4—21no—
386C11×C4⋊C4—21no—
387C11×C4⋊C4—21no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—21no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—21no—
395C11×C4⋊C4C2×D411yescharacteristic
396C11×C4⋊C4C2×D412yes—
397C11×C4⋊C4C2×D411yescharacteristic
398C11×C4⋊C4C2412yes—
399C11×C4⋊C4C2411yescharacteristic
400C11×C4⋊C4C2411yescharacteristic
401C11×C4⋊C4C2412yes—
402C11×C22⋊C4—22no—
403C11×C22⋊C4—22no—
404C11×C22⋊C4—21no—
405C11×C22⋊C4—22no—
406C11×C22⋊C4—22no—
407C11×C22⋊C4—21no—
408C11×C22⋊C4—22no—
409C11×C22⋊C4—21no—
410C11×C22⋊C4—21no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—21no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4C2×D412yes—
421C11×C22⋊C4C2×D412yes—
422C11×C22⋊C4C2×D412yes—
423C11×C22⋊C4C2×D412yes—
424C42×C11—22no—
425C42×C11—22no—
426C42×C11—21no—
427C42×C11—22no—
428C42×C11C2×D411yescharacteristic
429C42×C11C2×D411yescharacteristic
430C42×C11C2411yescharacteristic
431C42×C11C2411yescharacteristic
432#3546C2×C1111yescharacteristic, complemented
433#3497C2×C1111yescharacteristic, complemented
434#3320C2×C1112yescomplemented
435#3313C2×C1112yescomplemented
436#3309C2×C1112yescomplemented
437#3308C2×C1112yescomplemented
438#3271C2×C1112yescomplemented
439#3268C2×C1112yescomplemented
440#3266C2×C1112yescomplemented
441#3265C2×C1112yescomplemented
442#3219C2×C1111yescharacteristic, complemented
443#3214C2×C1111yescharacteristic, complemented
444#3203C2×C1112yescomplemented
445#3198C2×C1112yescomplemented
446#3117C2×C1111yescharacteristic, complemented
447#3112C2×C1111yescharacteristic, complemented
448#3013C2×C1112yescomplemented
449#3010C2×C1112yescomplemented
450#2980C2×C1111yescharacteristic, complemented
451C23×C11—21no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—82no—
455C23×C11—82no—
456C23×C11—82no—
457C23×C11C22×D412yes—
458C23×C11C22×D412yes—
459C23×C11C22×D411yescharacteristic
460Q8×C11—24no—
461Q8×C11—22no—
462Q8×C11—22no—
463Q8×C11—22no—
464Q8×C11—22no—
465Q8×C11—42no—
466Q8×C11—44no—
467Q8×C11—44no—
468Q8×C11—42no—
469Q8×C11H(5,𝔽2)14yes—
470D4×C11—22no—
471D4×C11—22no—
472D4×C11—22no—
473D4×C11—22no—
474D4×C11—22no—
475D4×C11—41no—
476D4×C11—42no—
477D4×C11—42no—
478D4×C11—42no—
479D4×C11—42no—
480D4×C11—41no—
481D4×C11—44no—
482D4×C11—44no—
483D4×C11—42no—
484D4×C11—42no—
485D4×C11—44no—
486D4×C11—81no—
487D4×C11—81no—
488D4×C11—82no—
489D4×C11—82no—
490D4×C11—82no—
491D4×C11—81no—
492D4×C11—82no—
493D4×C11—82no—
494D4×C11—82no—
495D4×C11—82no—
496D4×C11—82no—
497C2×C4×C11—24no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—21no—
509C2×C4×C11—22no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—44no—
513C2×C4×C11—44no—
514C2×C4×C11—44no—
515C2×C4×C11—44no—
516C2×C4×C11—42no—
517C2×C4×C11—44no—
518C2×C4×C11—82no—
519C2×C4×C11—82no—
520C2×C4×C11—81no—
521C2×C4×C11—82no—
522C2×C4×C11C22×D411yescharacteristic
523C2×C4×C11C22×D411yescharacteristic
524C2×C4×C11C22×D411yescharacteristic
525C2×C4×C11C22×D412yes—
526C2×C4×C11C22×D411yescharacteristic
527C2×C4×C11C22×D411yescharacteristic
528C2×C4×C11C22×D412yes—
529C2×C4×C11C2511yescharacteristic
530C8×C11—22no—
531C8×C11—22no—
532C8×C11—22no—
533C8×C11—22no—
534C2×2−1+4C22×C1112yescomplemented
535C2×#137C22×C1112yescomplemented
536C2×AGL(1,ℤ/8)C22×C1112yes—
537C2×#135C22×C1112yescomplemented
538C22×SD16C22×C1112yes—
539#560—22no—
540#556C22×C1111yescharacteristic
541#553C22×C1112yes—
542#550—21no—
543#550—21no—
544#550C22×C1111yescharacteristic
545#550C22×C1112yescomplemented
546D4×Q8—21no—
547D4×Q8C22×C1112yescomplemented
548#548—22no—
549#548C22×C1112yes—
550#548C22×C1112yescomplemented
551#547C22×C1111yescharacteristic
552#546—21no—
553#546C22×C1112yes—
554D42C22×C1111yescharacteristic
555#542—21no—
556#538—22no—
557#537—21no—
558#537—21no—
559#537C22×C1112yes—
560#537C22×C1112yescomplemented
561#535—21no—
562#535C22×C1112yes—
563#532—22no—
564#532C22×C1111yescharacteristic
565#532C22×C1111yescharacteristic
566#532C22×C1111yescharacteristic, complemented
567#529C22×C1111yescharacteristic
568C2×C4×Q8C22×C1111yescharacteristic, complemented
569#497C22×C1111yescharacteristic
570#496C22×C1112yes—
571#496C22×C1111yescharacteristic
572#491C22×C1111yescharacteristic, complemented
573#490C22×C1111yescharacteristic, complemented
574#489C22×C1112yescomplemented
575#485C22×C1112yescomplemented
576#484C22×C1111yescharacteristic, complemented
577#484C22×C1112yescomplemented
578#482C22×C1112yescomplemented
579#481C22×C1111yescharacteristic
580#480C22×C1112yescomplemented
581#480C22×C1112yescomplemented
582#479C22×C1112yescomplemented
583#477C22×C1112yescomplemented
584#469C22×C1112yescomplemented
585#468C22×C1112yes—
586#468C22×C1112yes—
587#468C22×C1112yescomplemented
588#467C22×C1112yescomplemented
589#466C22×C1112yes—
590#466C22×C1112yes—
591#465C22×C1112yescomplemented
592#464C22×C1112yes—
593#464C22×C1112yescomplemented
594#463C22×C1112yes—
595#461C22×C1112yescomplemented
596#460C22×C1112yes—
597#459C22×C1112yescomplemented
598#452C22×C1112yescomplemented
599#452C22×C1112yescomplemented
600#452C22×C1112yescomplemented
601#451C22×C1111yescharacteristic, complemented
602#451C22×C1112yescomplemented
603#450C22×C1112yes—
604#449C22×C1112yes—
605#449C22×C1112yes—
606#449C22×C1112yes—
607#449C22×C1112yescomplemented
608#449C22×C1112yescomplemented
609#449C22×C1112yescomplemented
610#449C22×C1112yescomplemented
611#448C22×C1111yescharacteristic
612#448C22×C1112yes—
613#448C22×C1112yes—
614#448C22×C1112yescomplemented
615#448C22×C1112yescomplemented
616#447C22×C1112yes—
617#441C22×C1112yescomplemented
618#440C22×C1112yes—
619#440C22×C1112yescomplemented
620#440C22×C1112yescomplemented
621#435C22×C1112yes—
622#435C22×C1112yescomplemented
623#435C22×C1112yescomplemented
624#435C22×C1112yescomplemented
625#432C22×C1111yescharacteristic, complemented
626#432C22×C1111yescharacteristic, complemented
627#419C22×C1112yescomplemented
628#417C22×C1112yescomplemented
629#416C22×C1112yescomplemented
630C2×#103C22×C1112yescomplemented
631#408C22×C1112yescomplemented
632#408C22×C1112yescomplemented
633C22×C11—21no—
634C22×C11—22no—
635C22×C11—22no—
636C22×C11—21no—
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—21no—
640C22×C11—22no—
641C22×C11—22no—
642C22×C11—41no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—41no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—41no—
651C22×C11—164no—
652C22×C11C23×D411yescharacteristic
653C4×C11—21no—
654C4×C11—21no—
655C4×C11—21no—
656C4×C11—21no—
657C4×C11—24no—
658C4×C11—21no—
659C4×C11—22no—
660C4×C11—22no—
661C4×C11—41no—
662C4×C11—42no—
663C4×C11—42no—
664C4×C11—41no—
665C4×C11—42no—
666C4×C11—41no—
667C4×C11C2×H(5,𝔽2)12yes—
6682−1+4—44no—
6692−1+4—44no—
670C2×#41—22no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—21no—
674C2×#41—21no—
675C2×#41C23×C1112yes—
676C2×#41C23×C1112yes—
677C2×#41C23×C1112yes—
678C2×#41C23×C1112yes—
679C2×#41C23×C1112yes—
680C22×Q8—22no—
681C22×Q8C23×C1111yescharacteristic
682C22×Q8C23×C1112yes—
683C22×Q8C23×C1112yes—
684C22×D4—21no—
685C22×D4C23×C1112yes—
686#137—44no—
687AGL(1,ℤ/8)—44no—
688#135—44no—
689C2×Q16C23×C1112yes—
690C2×Q16C23×C1112yes—
691C2×SD16—44no—
692C2×SD16C23×C1112yes—
693C2×SD16C23×C1112yes—
694C2×SD16C23×C1112yes—
695C2×SD16C23×C1112yes—
696C2×SD16C23×C1112yes—
697C2×SD16C23×C1112yes—
698C2×SD16C23×C1112yes—
699C2×D8C23×C1112yes—
700C2×D8C23×C1112yes—
701C2×D8C23×C1112yes—
702C2×M16C23×C1112yes—
703C2×M16C23×C1112yes—
704C22×C8C23×C1112yes—
705C22×C8C23×C1112yes—
706C4⋊Q8—22no—
707C4⋊Q8D4×C1111yescharacteristic
708C4⋊Q8C23×C1111yescharacteristic
709C4⋊Q8C23×C1111yescharacteristic
710#127—22no—
711#127—21no—
712#127—22no—
713#127D4×C1111yescharacteristic
714#127C23×C1111yescharacteristic
715#127C23×C1111yescharacteristic
716#126—22no—
717#126—22no—
718#126—21no—
719#125C23×C1111yescharacteristic
720#124—22no—
721#124—21no—
722#124—22no—
723#124—22no—
724#124—21no—
725#124D4×C1112yes—
726#124C23×C1111yescharacteristic
727#124C23×C1112yes—
728#123—21no—
729#123—22no—
730#123—22no—
731#123—22no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—22no—
735C22⋊Q8—22no—
736C22⋊Q8—21no—
737C22⋊Q8—22no—
738C22⋊Q8—22no—
739C22⋊Q8C23×C1111yescharacteristic
740C22⋊Q8C23×C1112yes—
741C22⋊Q8C23×C1112yes—
742C22⋊Q8C23×C1112yes—
743#121—22no—
744#121—22no—
745#121—22no—
746#121—22no—
747#121—22no—
748#121—22no—
749#121—22no—
750#121—22no—
751#121—22no—
752#121—21no—
753#121—21no—
754#121—21no—
755#121—21no—
756#121—22no—
757#121—22no—
758#121—22no—
759#121—22no—
760#121D4×C1112yes—
761#121D4×C1111yescharacteristic
762#121D4×C1111yescharacteristic
763#121C23×C1111yescharacteristic
764#121C23×C1112yes—
765#121C23×C1112yes—
766#121C23×C1112yes—
767#121C23×C1112yes—
768#121C23×C1112yes—
769#121C23×C1112yes—
770#120—22no—
771#120—22no—
772#120—22no—
773#120—22no—
774C4×Q8—21no—
775C4×Q8—21no—
776C4×Q8—21no—
777C4×Q8C23×C1112yes—
778C4×Q8C23×C1112yes—
779C4×Q8C23×C1111yescharacteristic
780C4×D4—22no—
781C4×D4—21no—
782C4×D4—22no—
783C4×D4—21no—
784C4×D4—22no—
785C4×D4—22no—
786C4×D4—22no—
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—21no—
790C4×D4C23×C1111yescharacteristic
791C4×D4C23×C1112yes—
792C4×D4C23×C1111yescharacteristic
793C4×D4C23×C1112yes—
794C4×D4C23×C1111yescharacteristic
795#117—21no—
796#117C23×C1112yes—
797C2×C4⋊C4—21no—
798C2×C4⋊C4C23×C1111yescharacteristic
799C2×C4⋊C4C23×C1112yes—
800C2×C22⋊C4—22no—
801C2×C42—21no—
802C2×C42C23×C1111yescharacteristic
803#107C23×C1112yes—
804#107C23×C1112yes—
805#107C23×C1112yes—
806#106C23×C1112yes—
807C4⋊C8C23×C1112yes—
808C4⋊C8C23×C1112yes—
809#103C23×C1112yes—
810#103C23×C1112yes—
811#103C23×C1112yes—
812#103C23×C1112yes—
813#103C23×C1112yes—
814#103C23×C1112yes—
815#103C23×C1112yes—
816#103C23×C1112yes—
817#103C23×C1112yes—
818#102C23×C1112yes—
819#102C23×C1112yes—
820#102C23×C1112yes—
821#102C23×C1112yes—
822#102C23×C1112yes—
823#102C23×C1112yes—
824#102C23×C1112yes—
825C22⋊C8C23×C1111yescharacteristic
826C22⋊C8C23×C1112yes—
827C22⋊C8C23×C1111yescharacteristic
828C22⋊C8C23×C1112yes—
829C22⋊C8C23×C1112yes—
830C22⋊C8C23×C1112yes—
831C22⋊C8C23×C1112yes—
832#97C23×C1112yes—
833#97C23×C1111yescharacteristic
834#97C23×C1111yescharacteristic
835C2×C11—41no—
836C2×C11—42no—
837C2×C11—42no—
838C2×C11—82no—
839C2×C11—82no—
840C2×C11—81no—
841C2×C11#348411yescharacteristic
842C2×C11#358511yescharacteristic
843C2×C11#358611yescharacteristic
844C24—22no—
845#41—24no—
846#41—24no—
847#41—42no—
848#41—42no—
849#41—42no—
850#41—42no—
851#41—42no—
852#41—42no—
853#41—48no—
854#41—48no—
855#41—42no—
856#41—42no—
857#41—48no—
858#41—82no—
859#41—82no—
860C2×Q8—24no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—22no—
864C2×Q8—22no—
865C2×Q8—24no—
866C2×Q8—24no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—48no—
870C2×Q8C2×D4×C1112yes—
871C2×Q8C24×C1112yes—
872C2×Q8C24×C1111yescharacteristic
873C2×Q8C24×C1112yes—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—22no—
877C2×D4—21no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—22no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—22no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—82no—
893C2×D4C2×D4×C1112yes—
894C2×D4C2×D4×C1111yescharacteristic
895C2×D4C2×D4×C1111yescharacteristic
896C2×D4C2×D4×C1112yes—
897C2×D4C2×D4×C1112yes—
898C2×D4C2×D4×C1112yes—
899C2×D4C24×C1112yes—
900C2×D4C24×C1111yescharacteristic
901C2×D4C24×C1112yes—
902C22×C4—21no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—21no—
906C22×C4—22no—
907C22×C4—21no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4C2×D4×C1111yescharacteristic
914C22×C4C2×D4×C1111yescharacteristic
915C22×C4C24×C1111yescharacteristic
916C22×C4C24×C1112yes—
917C22×C4C24×C1112yes—
918Q16—24no—
919Q16—42no—
920SD16—24no—
921SD16—24no—
922SD16—24no—
923SD16—42no—
924SD16—42no—
925SD16—42no—
926SD16—42no—
927D8—42no—
928D8—42no—
929D8—42no—
930M16—42no—
931M16—42no—
932C2×C8—42no—
933C2×C8—42no—
934C2×C8C24×C1112yes—
935C2×C8C24×C1112yes—
936C2×C8C24×C1112yes—
937C2×C8C24×C1112yes—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—21no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—21no—
950C4⋊C4—22no—
951C4⋊C4—21no—
952C4⋊C4C2×D4×C1111yescharacteristic
953C4⋊C4C2×D4×C1112yes—
954C4⋊C4C2×D4×C1111yescharacteristic
955C4⋊C4C24×C1112yes—
956C4⋊C4C24×C1111yescharacteristic
957C4⋊C4C24×C1111yescharacteristic
958C4⋊C4C24×C1112yes—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—21no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—21no—
965C22⋊C4—22no—
966C22⋊C4—21no—
967C22⋊C4—21no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—22no—
977C22⋊C4C2×D4×C1112yes—
978C22⋊C4C2×D4×C1112yes—
979C22⋊C4C2×D4×C1112yes—
980C22⋊C4C2×D4×C1112yes—
981C42—22no—
982C42—22no—
983C42—21no—
984C42—22no—
985C42C2×D4×C1111yescharacteristic
986C42C2×D4×C1111yescharacteristic
987C42C24×C1111yescharacteristic
988C42C24×C1111yescharacteristic
989C11#6167111yescharacteristic, direct product factor, Sylow
990C23—21no—
991C23—22no—
992C23—22no—
993C23—82no—
994C23—82no—
995C23—82no—
996C23C22×D4×C1112yes—
997C23C22×D4×C1112yes—
998C23C22×D4×C1111yescharacteristic
999Q8—24no—
1000Q8—22no—
1001Q8—22no—
1002Q8—22no—
1003Q8—22no—
1004Q8—42no—
1005Q8—44no—
1006Q8—44no—
1007Q8—42no—
1008Q8C11×H(5,𝔽2)14yes—
1009D4—22no—
1010D4—22no—
1011D4—22no—
1012D4—22no—
1013D4—22no—
1014D4—41no—
1015D4—42no—
1016D4—42no—
1017D4—42no—
1018D4—42no—
1019D4—41no—
1020D4—44no—
1021D4—44no—
1022D4—42no—
1023D4—42no—
1024D4—44no—
1025D4—81no—
1026D4—81no—
1027D4—82no—
1028D4—82no—
1029D4—82no—
1030D4—81no—
1031D4—82no—
1032D4—82no—
1033D4—82no—
1034D4—82no—
1035D4—82no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—42no—
1056C2×C4—44no—
1057C2×C4—82no—
1058C2×C4—82no—
1059C2×C4—81no—
1060C2×C4—82no—
1061C2×C4C22×D4×C1111yescharacteristic
1062C2×C4C22×D4×C1111yescharacteristic
1063C2×C4C22×D4×C1111yescharacteristic
1064C2×C4C22×D4×C1112yes—
1065C2×C4C22×D4×C1111yescharacteristic
1066C2×C4C22×D4×C1111yescharacteristic
1067C2×C4C22×D4×C1112yes—
1068C2×C4C25×C1111yescharacteristic
1069C8—22no—
1070C8—22no—
1071C8—22no—
1072C8—22no—
1073C22—21no—
1074C22—22no—
1075C22—22no—
1076C22—21no—
1077C22—22no—
1078C22—22no—
1079C22—21no—
1080C22—22no—
1081C22—22no—
1082C22—42no—
1083C22—42no—
1084C22—41no—
1085C22—41no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—41no—
1091C22—164no—
1092C22C23×D4×C1111yescharacteristic
1093C4—24no—
1094C4—21no—
1095C4—22no—
1096C4—22no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—21no—
1101C4—42no—
1102C4—41no—
1103C4—41no—
1104C4—42no—
1105C4—42no—
1106C4—41no—
1107C4C2×C11×H(5,𝔽2)12yes—
1108C2—42no—
1109C2—41no—
1110C2—42no—
1111C2—81no—
1112C2—82no—
1113C2—82no—
1114C2C11×#348411yescharacteristic
1115C2C11×#358511yescharacteristic
1116C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#532 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3546C2semidirect
2. C11×#3497C2semidirect
3. C11×#3320C2semidirect
4. C11×#3313C2semidirect
5. C11×#3309C2semidirect
6. C11×#3308C2semidirect
7. C11×#3271C2semidirect
8. C11×#3268C2semidirect
9. C11×#3266C2semidirect
10. C11×#3265C2semidirect
11. C11×#3219C2semidirect
12. C11×#3214C2semidirect
13. C11×#3203C2semidirect
14. C11×#3198C2semidirect
15. C11×#3117C2semidirect
16. C11×#3112C2semidirect
17. C11×#3013C2semidirect
18. C11×#3010C2semidirect
19. C11×#2980C2semidirect
20. C2×C11×2−1+4C22semidirect
21. C2×C11×#137C22semidirect
23. C2×C11×#135C22semidirect
31. C11×#550C22semidirect
33. D4×Q8×C11C22semidirect
36. C11×#548C22semidirect
46. C11×#537C22semidirect
52. C11×#532C22semidirect
54. C2×C4×Q8×C11C22semidirect
58. C11×#491C22semidirect
59. C11×#490C22semidirect
60. C11×#489C22semidirect
61. C11×#485C22semidirect
62. C11×#484C22semidirect
63. C11×#484C22semidirect
64. C11×#482C22semidirect
66. C11×#480C22semidirect
67. C11×#480C22semidirect
68. C11×#479C22semidirect
69. C11×#477C22semidirect
70. C11×#469C22semidirect
73. C11×#468C22semidirect
74. C11×#467C22semidirect
77. C11×#465C22semidirect
79. C11×#464C22semidirect
81. C11×#461C22semidirect
83. C11×#459C22semidirect
84. C11×#452C22semidirect
85. C11×#452C22semidirect
86. C11×#452C22semidirect
87. C11×#451C22semidirect
88. C11×#451C22semidirect
93. C11×#449C22semidirect
94. C11×#449C22semidirect
95. C11×#449C22semidirect
96. C11×#449C22semidirect
100. C11×#448C22semidirect
101. C11×#448C22semidirect
103. C11×#441C22semidirect
105. C11×#440C22semidirect
106. C11×#440C22semidirect
108. C11×#435C22semidirect
109. C11×#435C22semidirect
110. C11×#435C22semidirect
111. C11×#432C22semidirect
112. C11×#432C22semidirect
113. C11×#419C22semidirect
114. C11×#417C22semidirect
115. C11×#416C22semidirect
116. C2×C11×#103C22semidirect
117. C11×#408C22semidirect
118. C11×#408C22semidirect
286. #61671C11direct (N × H)
432. #3546C2×C11semidirect
433. #3497C2×C11semidirect
434. #3320C2×C11semidirect
435. #3313C2×C11semidirect
436. #3309C2×C11semidirect
437. #3308C2×C11semidirect
438. #3271C2×C11semidirect
439. #3268C2×C11semidirect
440. #3266C2×C11semidirect
441. #3265C2×C11semidirect
442. #3219C2×C11semidirect
443. #3214C2×C11semidirect
444. #3203C2×C11semidirect
445. #3198C2×C11semidirect
446. #3117C2×C11semidirect
447. #3112C2×C11semidirect
448. #3013C2×C11semidirect
449. #3010C2×C11semidirect
450. #2980C2×C11semidirect
534. C2×2−1+4C22×C11semidirect
535. C2×#137C22×C11semidirect
537. C2×#135C22×C11semidirect
545. #550C22×C11semidirect
547. D4×Q8C22×C11semidirect
550. #548C22×C11semidirect
560. #537C22×C11semidirect
566. #532C22×C11semidirect
568. C2×C4×Q8C22×C11semidirect
572. #491C22×C11semidirect
573. #490C22×C11semidirect
574. #489C22×C11semidirect
575. #485C22×C11semidirect
576. #484C22×C11semidirect
577. #484C22×C11semidirect
578. #482C22×C11semidirect
580. #480C22×C11semidirect
581. #480C22×C11semidirect
582. #479C22×C11semidirect
583. #477C22×C11semidirect
584. #469C22×C11semidirect
587. #468C22×C11semidirect
588. #467C22×C11semidirect
591. #465C22×C11semidirect
593. #464C22×C11semidirect
595. #461C22×C11semidirect
597. #459C22×C11semidirect
598. #452C22×C11semidirect
599. #452C22×C11semidirect
600. #452C22×C11semidirect
601. #451C22×C11semidirect
602. #451C22×C11semidirect
607. #449C22×C11semidirect
608. #449C22×C11semidirect
609. #449C22×C11semidirect
610. #449C22×C11semidirect
614. #448C22×C11semidirect
615. #448C22×C11semidirect
617. #441C22×C11semidirect
619. #440C22×C11semidirect
620. #440C22×C11semidirect
622. #435C22×C11semidirect
623. #435C22×C11semidirect
624. #435C22×C11semidirect
625. #432C22×C11semidirect
626. #432C22×C11semidirect
627. #419C22×C11semidirect
628. #417C22×C11semidirect
629. #416C22×C11semidirect
630. C2×#103C22×C11semidirect
631. #408C22×C11semidirect
632. #408C22×C11semidirect
989. C11#61671direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35462
C11×#34972
C11×#33202
C11×#33132
C11×#33092
C11×#33082
C11×#32712
C11×#32682
C11×#32662
C11×#32652
C11×#32192
C11×#32142
C11×#32032
C11×#31982
C11×#31172
C11×#31122
C11×#30132
C11×#30102
C11×#29802
#6167111