Finite Group Databasebeta

← C11×#61677 #14638870

Subgroups — C11×#61677 #14638870

Order 2816.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3548C211yesmaximal, characteristic, complemented
2C11×#3500C211yesmaximal, characteristic, complemented
3C11×#3316C212yesmaximal, complemented
4C11×#3314C212yesmaximal, complemented
5C11×#3308C212yesmaximal, complemented
6C11×#3306C212yesmaximal, complemented
7C11×#3271C212yesmaximal, complemented
8C11×#3269C212yesmaximal, complemented
9C11×#3268C212yesmaximal, complemented
10C11×#3267C212yesmaximal, complemented
11C11×#3215C211yesmaximal, characteristic, complemented
12C11×#3213C211yesmaximal, characteristic, complemented
13C11×#3201C212yesmaximal, complemented
14C11×#3198C212yesmaximal, complemented
15C11×#3116C211yesmaximal, characteristic, complemented
16C11×#3115C211yesmaximal, characteristic, complemented
17C11×#3013C212yesmaximal, complemented
18C11×#3012C212yesmaximal, complemented
19C11×#2980C211yesmaximal, characteristic, complemented
20C2×C11×2−1+4C2211yescharacteristic
21C2×C11×H(5,𝔽2)C2211yescharacteristic
22C2×C11×#137C2212yescomplemented
23C2×C11×AGL(1,ℤ/8)C2212yes—
24C2×C11×#135C2212yes—
25C2×C11×#135C2212yescomplemented
26C11×#562—21no—
27C11×#562—21no—
28C11×#554—21no—
29C11×#554C2212yescomplemented
30C11×#550—21no—
31C11×#550C2212yescomplemented
32C11×#548C2212yes—
33C11×#548C2212yes—
34C11×#547C2212yescomplemented
35C11×#547C2212yescomplemented
36C11×#546—22no—
37C11×#546—22no—
38C11×#546C2212yes—
39C11×#546C2212yes—
40C11×#540—22no—
41C11×#537—22no—
42C11×#537C2212yes—
43C11×#537C2212yescomplemented
44C11×#536—21no—
45C11×#536C2211yescharacteristic
46C11×#535—21no—
47C11×#535C2211yescharacteristic
48C11×#533C2211yescharacteristic, complemented
49C11×#532—21no—
50C11×#532C2211yescharacteristic
51C11×#532C2211yescharacteristic, complemented
52C2×C11×#124—21no—
53C2×C11×#124C2211yescharacteristic
54C4×C11×#41C2211yescharacteristic
55C11×#497C2212yescomplemented
56C11×#496C2212yescomplemented
57C11×#489C2212yescomplemented
58C11×#489C2212yescomplemented
59C11×#485C2212yescomplemented
60C11×#484C2212yescomplemented
61C11×#483C2212yescomplemented
62C11×#482C2212yescomplemented
63C11×#481C2212yescomplemented
64C11×#480C2212yescomplemented
65C11×#477C2211yescharacteristic, complemented
66C11×#476C2211yescharacteristic, complemented
67C11×#475C2211yescharacteristic, complemented
68C11×#474C2211yescharacteristic, complemented
69C11×#470C2212yescomplemented
70C11×#469C2212yescomplemented
71C11×#468C2212yescomplemented
72C11×#468C2212yescomplemented
73C11×#467C2212yescomplemented
74C11×#466C2212yescomplemented
75C11×#465C2212yescomplemented
76C11×#465C2212yescomplemented
77C11×#464C2212yescomplemented
78C11×#464C2212yescomplemented
79C11×#463C2212yescomplemented
80C11×#463C2212yescomplemented
81C11×#462C2211yescharacteristic, complemented
82C11×#461C2211yescharacteristic, complemented
83C11×#460C2211yescharacteristic, complemented
84C11×#459C2211yescharacteristic, complemented
85C11×#452C2212yes—
86C11×#452C2212yes—
87C11×#452C2212yescomplemented
88C11×#452C2212yescomplemented
89C11×#452C2212yescomplemented
90C11×#451C2212yescomplemented
91C11×#451C2212yescomplemented
92C11×#450C2212yes—
93C11×#450C2212yes—
94C11×#449C2212yes—
95C11×#449C2212yes—
96C11×#449C2212yescomplemented
97C11×#449C2212yescomplemented
98C11×#449C2212yescomplemented
99C11×#448C2212yescomplemented
100C11×#448C2212yescomplemented
101C11×#447C2212yes—
102C11×#447C2212yes—
103C11×#442C2212yescomplemented
104C11×#441C2212yescomplemented
105C11×#440C2212yescomplemented
106C11×#440C2212yescomplemented
107C11×#435C2212yescomplemented
108C11×#435C2212yescomplemented
109C11×#435C2212yescomplemented
110C11×#435C2212yescomplemented
111C11×#432C2211yescharacteristic, complemented
112C11×#432C2211yescharacteristic, complemented
113C11×#417C2212yes—
114C11×#417C2212yescomplemented
115C2×C11×#103C2212yescomplemented
116C2×C11×#102C2212yes—
117C11×#408C2212yes—
118C11×#408C2212yescomplemented
119C11×2−1+4—42no—
120C11×2−1+4—42no—
121C11×H(5,𝔽2)—42no—
122C11×H(5,𝔽2)—42no—
123C2×C11×#41—21no—
124C2×C11×#41—21no—
125C2×C11×#41—22no—
126C2×C11×#41—22no—
127C2×C11×#41—21no—
128C2×C11×#41C2311yescharacteristic
129C2×C11×#41C2312yes—
130C2×C11×#41C2312yes—
131C2×C11×#41C2312yes—
132C2×C11×#41C2312yes—
133C2×C11×#41C2311yescharacteristic
134C2×C11×#41C2311yescharacteristic
135C22×Q8×C11—21no—
136C22×Q8×C11C2312yes—
137C22×Q8×C11C2311yescharacteristic
138C22×D4×C11—21no—
139C22×D4×C11—22no—
140C22×D4×C11C2312yes—
141C22×D4×C11C2311yescharacteristic
142C11×#137—44no—
143C11×AGL(1,ℤ/8)—44no—
144C11×#135—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—
160C22×C8×C11C2312yes—
161C22×C8×C11C2312yes—
162C11×C4⋊Q8—21no—
163C11×C4⋊Q8D411yescharacteristic
164C11×C4⋊Q8C2311yescharacteristic
165C11×C4⋊Q8C2311yescharacteristic
166C11×C4⋊Q8C2311yescharacteristic
167C11×#127—21no—
168C11×#127—22no—
169C11×#127D411yescharacteristic
170C11×#127C2311yescharacteristic
171C11×#125—22no—
172C11×#125—21no—
173C11×#124—21no—
174C11×#124—21no—
175C11×#124—22no—
176C11×#124—22no—
177C11×#124—21no—
178C11×#124—21no—
179C11×#124—21no—
180C11×#124D411yescharacteristic
181C11×#124D411yescharacteristic
182C11×#124C2312yes—
183C11×#124C2312yes—
184C11×#123—22no—
185C11×#123—22no—
186C11×#123—22no—
187C11×#123—22no—
188C11×#123—22no—
189C11×#123—22no—
190C11×#123—22no—
191C11×C22⋊Q8—22no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—21no—
194C11×C22⋊Q8—22no—
195C11×C22⋊Q8—22no—
196C11×C22⋊Q8—22no—
197C11×C22⋊Q8—22no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8C2312yes—
200C11×C22⋊Q8C2312yes—
201C11×C22⋊Q8C2312yes—
202C11×C22⋊Q8C2312yes—
203C11×C22⋊Q8C2312yes—
204C11×#121—22no—
205C11×#121—22no—
206C11×#121—22no—
207C11×#121—22no—
208C11×#121—22no—
209C11×#121—22no—
210C11×#121—22no—
211C11×#121—22no—
212C11×#121—22no—
213C11×#121—21no—
214C11×#121—22no—
215C11×#121—22no—
216C11×#121—22no—
217C11×#121—22no—
218C11×#121D412yes—
219C11×#121D412yes—
220C11×#121C2312yes—
221C11×#121C2312yes—
222C11×#121C2312yes—
223C11×#121C2312yes—
224C11×#121C2312yes—
225C11×#120—22no—
226C11×#120—22no—
227C11×#120—22no—
228C4×Q8×C11—21no—
229C4×Q8×C11C2311yescharacteristic
230C4×Q8×C11C2311yescharacteristic
231C4×Q8×C11C2312yes—
232C4×D4×C11—22no—
233C4×D4×C11—21no—
234C4×D4×C11—21no—
235C4×D4×C11—22no—
236C4×D4×C11—22no—
237C4×D4×C11—22no—
238C4×D4×C11—21no—
239C4×D4×C11C2311yescharacteristic
240C4×D4×C11C2311yescharacteristic
241C4×D4×C11C2312yes—
242C4×D4×C11C2312yes—
243C4×D4×C11C2312yes—
244C11×#117—21no—
245C11×#117—21no—
246C11×#117C2311yescharacteristic
247C2×C11×C4⋊C4—22no—
248C2×C11×C4⋊C4C2312yes—
249C2×C11×C4⋊C4C2312yes—
250C2×C11×C22⋊C4—21no—
251C2×C11×C22⋊C4—21no—
252C2×C11×C22⋊C4—22no—
253C2×C11×C22⋊C4—22no—
254C2×C42×C11—21no—
255C2×C42×C11C2311yescharacteristic
256C11×#107C2312yes—
257C11×#107C2312yes—
258C11×#106C2312yes—
259C11×#106C2312yes—
260C11×C4⋊C8C2311yescharacteristic
261C11×C4⋊C8C2311yescharacteristic
262C11×C4⋊C8C2311yescharacteristic
263C11×C4⋊C8C2311yescharacteristic
264C11×#103C2312yes—
265C11×#103C2312yes—
266C11×#103C2312yes—
267C11×#103C2312yes—
268C11×#103C2312yes—
269C11×#103C2312yes—
270C11×#103C2312yes—
271C11×#103C2312yes—
272C11×#102C2312yes—
273C11×#102C2312yes—
274C11×#102C2312yes—
275C11×#102C2312yes—
276C11×#102C2312yes—
277C11×#102C2312yes—
278C11×#102C2312yes—
279C11×#102C2312yes—
280C11×C22⋊C8C2312yes—
281C11×C22⋊C8C2312yes—
282C11×C22⋊C8C2312yes—
283C11×C22⋊C8C2312yes—
284C11×C22⋊C8C2312yes—
285C11×C22⋊C8C2312yes—
286C11×#97C2312yes—
287C11×#97C2312yes—
288#61677C1111yesmaximal, characteristic, direct product factor, Sylow
289C24×C11—22no—
290C24×C11—21no—
291C11×#41—22no—
292C11×#41—22no—
293C11×#41—24no—
294C11×#41—24no—
295C11×#41—41no—
296C11×#41—41no—
297C11×#41—41no—
298C11×#41—41no—
299C11×#41—42no—
300C11×#41—42no—
301C11×#41—44no—
302C11×#41—44no—
303C11×#41—42no—
304C11×#41—42no—
305C11×#41—42no—
306C11×#41—42no—
307C11×#41—48no—
308C11×#41—82no—
309C11×#41—84no—
310C2×Q8×C11—21no—
311C2×Q8×C11—22no—
312C2×Q8×C11—21no—
313C2×Q8×C11—21no—
314C2×Q8×C11—24no—
315C2×Q8×C11—42no—
316C2×Q8×C11—41no—
317C2×Q8×C11—41no—
318C2×Q8×C11—44no—
319C2×Q8×C11C2×D411yescharacteristic
320C2×Q8×C11C2×D411yescharacteristic
321C2×Q8×C11C2412yes—
322C2×Q8×C11C2412yes—
323C2×Q8×C11C2411yescharacteristic
324C2×D4×C11—21no—
325C2×D4×C11—24no—
326C2×D4×C11—22no—
327C2×D4×C11—22no—
328C2×D4×C11—22no—
329C2×D4×C11—22no—
330C2×D4×C11—22no—
331C2×D4×C11—22no—
332C2×D4×C11—22no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11—21no—
336C2×D4×C11—22no—
337C2×D4×C11—21no—
338C2×D4×C11—21no—
339C2×D4×C11—42no—
340C2×D4×C11—41no—
341C2×D4×C11—41no—
342C2×D4×C11—44no—
343C2×D4×C11—48no—
344C2×D4×C11C2×D412yes—
345C2×D4×C11C2×D412yes—
346C2×D4×C11C2×D412yes—
347C2×D4×C11C2×D412yes—
348C2×D4×C11C2×D411yescharacteristic
349C2×D4×C11C2×D411yescharacteristic
350C2×D4×C11C2412yes—
351C2×D4×C11C2412yes—
352C2×D4×C11C2411yescharacteristic
353C22×C4×C11—21no—
354C22×C4×C11—21no—
355C22×C4×C11—22no—
356C22×C4×C11—22no—
357C22×C4×C11—22no—
358C22×C4×C11—22no—
359C22×C4×C11—22no—
360C22×C4×C11—22no—
361C22×C4×C11—21no—
362C22×C4×C11—21no—
363C22×C4×C11—22no—
364C22×C4×C11—22no—
365C22×C4×C11C2×D411yescharacteristic
366C22×C4×C11C2×D411yescharacteristic
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2412yes—
369C22×C4×C11C2412yes—
370C11×Q16—24no—
371C11×Q16—42no—
372C11×Q16—42no—
373C11×SD16—24no—
374C11×SD16—24no—
375C11×SD16—42no—
376C11×SD16—42no—
377C11×SD16—42no—
378C11×SD16—42no—
379C11×D8—24no—
380C11×D8—42no—
381C11×D8—42no—
382C11×M16—42no—
383C11×M16—42no—
384C2×C8×C11—42no—
385C2×C8×C11—42no—
386C2×C8×C11C2412yes—
387C2×C8×C11C2412yes—
388C2×C8×C11C2412yes—
389C2×C8×C11C2412yes—
390C11×C4⋊C4—21no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4C2×D412yes—
405C11×C4⋊C4C2×D412yes—
406C11×C4⋊C4C2412yes—
407C11×C4⋊C4C2412yes—
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2411yescharacteristic
410C11×C22⋊C4—22no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—21no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
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—21no—
423C11×C22⋊C4—21no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4C2×D412yes—
429C11×C22⋊C4C2×D412yes—
430C11×C22⋊C4C2×D412yes—
431C11×C22⋊C4C2×D412yes—
432C42×C11—21no—
433C42×C11—21no—
434C42×C11—21no—
435C42×C11—22no—
436C42×C11C2×D411yescharacteristic
437C42×C11C2×D411yescharacteristic
438C42×C11C2411yescharacteristic
439C42×C11C2411yescharacteristic
440#3548C2×C1111yescharacteristic, complemented
441#3500C2×C1111yescharacteristic, complemented
442#3316C2×C1112yescomplemented
443#3314C2×C1112yescomplemented
444#3308C2×C1112yescomplemented
445#3306C2×C1112yescomplemented
446#3271C2×C1112yescomplemented
447#3269C2×C1112yescomplemented
448#3268C2×C1112yescomplemented
449#3267C2×C1112yescomplemented
450#3215C2×C1111yescharacteristic, complemented
451#3213C2×C1111yescharacteristic, complemented
452#3201C2×C1112yescomplemented
453#3198C2×C1112yescomplemented
454#3116C2×C1111yescharacteristic, complemented
455#3115C2×C1111yescharacteristic, complemented
456#3013C2×C1112yescomplemented
457#3012C2×C1112yescomplemented
458#2980C2×C1111yescharacteristic, complemented
459C23×C11—21no—
460C23×C11—22no—
461C23×C11—22no—
462C23×C11—44no—
463C23×C11—42no—
464C23×C11—81no—
465C23×C11—82no—
466C23×C11—81no—
467C23×C11—82no—
468C23×C11C22×D412yes—
469C23×C11C22×D411yescharacteristic
470C23×C11C22×D412yes—
471Q8×C11—21no—
472Q8×C11—22no—
473Q8×C11—22no—
474Q8×C11—22no—
475Q8×C11—22no—
476Q8×C11—41no—
477Q8×C11—41no—
478Q8×C11—44no—
479Q8×C11—42no—
480Q8×C11—42no—
481Q8×C11—81no—
482Q8×C11H(5,𝔽2)12yes—
483D4×C11—24no—
484D4×C11—21no—
485D4×C11—22no—
486D4×C11—22no—
487D4×C11—22no—
488D4×C11—22no—
489D4×C11—41no—
490D4×C11—42no—
491D4×C11—42no—
492D4×C11—41no—
493D4×C11—42no—
494D4×C11—42no—
495D4×C11—44no—
496D4×C11—44no—
497D4×C11—42no—
498D4×C11—42no—
499D4×C11—44no—
500D4×C11—81no—
501D4×C11—82no—
502D4×C11—82no—
503D4×C11—82no—
504D4×C11—82no—
505D4×C11—82no—
506D4×C11—82no—
507D4×C11—82no—
508D4×C11H(5,𝔽2)12yes—
509C2×C4×C11—24no—
510C2×C4×C11—21no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—21no—
516C2×C4×C11—21no—
517C2×C4×C11—21no—
518C2×C4×C11—21no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—44no—
526C2×C4×C11—44no—
527C2×C4×C11—44no—
528C2×C4×C11—44no—
529C2×C4×C11—42no—
530C2×C4×C11—81no—
531C2×C4×C11—81no—
532C2×C4×C11—82no—
533C2×C4×C11—82no—
534C2×C4×C11—82no—
535C2×C4×C11—82no—
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C22×D411yescharacteristic
539C2×C4×C11C22×D411yescharacteristic
540C2×C4×C11C22×D411yescharacteristic
541C2×C4×C11C22×D412yes—
542C2×C4×C11C22×D412yes—
543C2×C4×C11C2511yescharacteristic
544C8×C11—22no—
545C8×C11—22no—
546C8×C11—22no—
547C8×C11—22no—
548C2×2−1+4C22×C1111yescharacteristic
549C2×H(5,𝔽2)C22×C1111yescharacteristic
550C2×#137C22×C1112yescomplemented
551C2×AGL(1,ℤ/8)C22×C1112yes—
552C2×#135C22×C1112yes—
553C2×#135C22×C1112yescomplemented
554#562—21no—
555#562—21no—
556#554—21no—
557#554C22×C1112yescomplemented
558#550—21no—
559#550C22×C1112yescomplemented
560#548C22×C1112yes—
561#548C22×C1112yes—
562#547C22×C1112yescomplemented
563#547C22×C1112yescomplemented
564#546—22no—
565#546—22no—
566#546C22×C1112yes—
567#546C22×C1112yes—
568#540—22no—
569#537—22no—
570#537C22×C1112yes—
571#537C22×C1112yescomplemented
572#536—21no—
573#536C22×C1111yescharacteristic
574#535—21no—
575#535C22×C1111yescharacteristic
576#533C22×C1111yescharacteristic, complemented
577#532—21no—
578#532C22×C1111yescharacteristic
579#532C22×C1111yescharacteristic, complemented
580C2×#124—21no—
581C2×#124C22×C1111yescharacteristic
582C4×#41C22×C1111yescharacteristic
583#497C22×C1112yescomplemented
584#496C22×C1112yescomplemented
585#489C22×C1112yescomplemented
586#489C22×C1112yescomplemented
587#485C22×C1112yescomplemented
588#484C22×C1112yescomplemented
589#483C22×C1112yescomplemented
590#482C22×C1112yescomplemented
591#481C22×C1112yescomplemented
592#480C22×C1112yescomplemented
593#477C22×C1111yescharacteristic, complemented
594#476C22×C1111yescharacteristic, complemented
595#475C22×C1111yescharacteristic, complemented
596#474C22×C1111yescharacteristic, complemented
597#470C22×C1112yescomplemented
598#469C22×C1112yescomplemented
599#468C22×C1112yescomplemented
600#468C22×C1112yescomplemented
601#467C22×C1112yescomplemented
602#466C22×C1112yescomplemented
603#465C22×C1112yescomplemented
604#465C22×C1112yescomplemented
605#464C22×C1112yescomplemented
606#464C22×C1112yescomplemented
607#463C22×C1112yescomplemented
608#463C22×C1112yescomplemented
609#462C22×C1111yescharacteristic, complemented
610#461C22×C1111yescharacteristic, complemented
611#460C22×C1111yescharacteristic, complemented
612#459C22×C1111yescharacteristic, complemented
613#452C22×C1112yes—
614#452C22×C1112yes—
615#452C22×C1112yescomplemented
616#452C22×C1112yescomplemented
617#452C22×C1112yescomplemented
618#451C22×C1112yescomplemented
619#451C22×C1112yescomplemented
620#450C22×C1112yes—
621#450C22×C1112yes—
622#449C22×C1112yes—
623#449C22×C1112yes—
624#449C22×C1112yescomplemented
625#449C22×C1112yescomplemented
626#449C22×C1112yescomplemented
627#448C22×C1112yescomplemented
628#448C22×C1112yescomplemented
629#447C22×C1112yes—
630#447C22×C1112yes—
631#442C22×C1112yescomplemented
632#441C22×C1112yescomplemented
633#440C22×C1112yescomplemented
634#440C22×C1112yescomplemented
635#435C22×C1112yescomplemented
636#435C22×C1112yescomplemented
637#435C22×C1112yescomplemented
638#435C22×C1112yescomplemented
639#432C22×C1111yescharacteristic, complemented
640#432C22×C1111yescharacteristic, complemented
641#417C22×C1112yes—
642#417C22×C1112yescomplemented
643C2×#103C22×C1112yescomplemented
644C2×#102C22×C1112yes—
645#408C22×C1112yes—
646#408C22×C1112yescomplemented
647C22×C11—21no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—21no—
651C22×C11—22no—
652C22×C11—22no—
653C22×C11—21no—
654C22×C11—22no—
655C22×C11—22no—
656C22×C11—22no—
657C22×C11—41no—
658C22×C11—41no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—164no—
666C22×C11—162no—
667C22×C11C23×D411yescharacteristic
668C4×C11—21no—
669C4×C11—21no—
670C4×C11—21no—
671C4×C11—21no—
672C4×C11—21no—
673C4×C11—22no—
674C4×C11—22no—
675C4×C11—22no—
676C4×C11—42no—
677C4×C11—42no—
678C4×C11—41no—
679C4×C11—41no—
680C4×C11—42no—
681C4×C11—42no—
682C4×C11C2×H(5,𝔽2)11yescharacteristic
683C4×C11C2×H(5,𝔽2)11yescharacteristic
6842−1+4—42no—
6852−1+4—42no—
686H(5,𝔽2)—42no—
687H(5,𝔽2)—42no—
688C2×#41—21no—
689C2×#41—21no—
690C2×#41—22no—
691C2×#41—22no—
692C2×#41—21no—
693C2×#41C23×C1111yescharacteristic
694C2×#41C23×C1112yes—
695C2×#41C23×C1112yes—
696C2×#41C23×C1112yes—
697C2×#41C23×C1112yes—
698C2×#41C23×C1111yescharacteristic
699C2×#41C23×C1111yescharacteristic
700C22×Q8—21no—
701C22×Q8C23×C1112yes—
702C22×Q8C23×C1111yescharacteristic
703C22×D4—21no—
704C22×D4—22no—
705C22×D4C23×C1112yes—
706C22×D4C23×C1111yescharacteristic
707#137—44no—
708AGL(1,ℤ/8)—44no—
709#135—44no—
710#135—44no—
711C2×Q16C23×C1112yes—
712C2×Q16C23×C1112yes—
713C2×Q16C23×C1112yes—
714C2×SD16C23×C1112yes—
715C2×SD16C23×C1112yes—
716C2×SD16C23×C1112yes—
717C2×SD16C23×C1112yes—
718C2×SD16C23×C1112yes—
719C2×SD16C23×C1112yes—
720C2×D8C23×C1112yes—
721C2×D8C23×C1112yes—
722C2×D8C23×C1112yes—
723C2×M16C23×C1112yes—
724C2×M16C23×C1112yes—
725C22×C8C23×C1112yes—
726C22×C8C23×C1112yes—
727C4⋊Q8—21no—
728C4⋊Q8D4×C1111yescharacteristic
729C4⋊Q8C23×C1111yescharacteristic
730C4⋊Q8C23×C1111yescharacteristic
731C4⋊Q8C23×C1111yescharacteristic
732#127—21no—
733#127—22no—
734#127D4×C1111yescharacteristic
735#127C23×C1111yescharacteristic
736#125—22no—
737#125—21no—
738#124—21no—
739#124—21no—
740#124—22no—
741#124—22no—
742#124—21no—
743#124—21no—
744#124—21no—
745#124D4×C1111yescharacteristic
746#124D4×C1111yescharacteristic
747#124C23×C1112yes—
748#124C23×C1112yes—
749#123—22no—
750#123—22no—
751#123—22no—
752#123—22no—
753#123—22no—
754#123—22no—
755#123—22no—
756C22⋊Q8—22no—
757C22⋊Q8—22no—
758C22⋊Q8—21no—
759C22⋊Q8—22no—
760C22⋊Q8—22no—
761C22⋊Q8—22no—
762C22⋊Q8—22no—
763C22⋊Q8—22no—
764C22⋊Q8C23×C1112yes—
765C22⋊Q8C23×C1112yes—
766C22⋊Q8C23×C1112yes—
767C22⋊Q8C23×C1112yes—
768C22⋊Q8C23×C1112yes—
769#121—22no—
770#121—22no—
771#121—22no—
772#121—22no—
773#121—22no—
774#121—22no—
775#121—22no—
776#121—22no—
777#121—22no—
778#121—21no—
779#121—22no—
780#121—22no—
781#121—22no—
782#121—22no—
783#121D4×C1112yes—
784#121D4×C1112yes—
785#121C23×C1112yes—
786#121C23×C1112yes—
787#121C23×C1112yes—
788#121C23×C1112yes—
789#121C23×C1112yes—
790#120—22no—
791#120—22no—
792#120—22no—
793C4×Q8—21no—
794C4×Q8C23×C1111yescharacteristic
795C4×Q8C23×C1111yescharacteristic
796C4×Q8C23×C1112yes—
797C4×D4—22no—
798C4×D4—21no—
799C4×D4—21no—
800C4×D4—22no—
801C4×D4—22no—
802C4×D4—22no—
803C4×D4—21no—
804C4×D4C23×C1111yescharacteristic
805C4×D4C23×C1111yescharacteristic
806C4×D4C23×C1112yes—
807C4×D4C23×C1112yes—
808C4×D4C23×C1112yes—
809#117—21no—
810#117—21no—
811#117C23×C1111yescharacteristic
812C2×C4⋊C4—22no—
813C2×C4⋊C4C23×C1112yes—
814C2×C4⋊C4C23×C1112yes—
815C2×C22⋊C4—21no—
816C2×C22⋊C4—21no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C42—21no—
820C2×C42C23×C1111yescharacteristic
821#107C23×C1112yes—
822#107C23×C1112yes—
823#106C23×C1112yes—
824#106C23×C1112yes—
825C4⋊C8C23×C1111yescharacteristic
826C4⋊C8C23×C1111yescharacteristic
827C4⋊C8C23×C1111yescharacteristic
828C4⋊C8C23×C1111yescharacteristic
829#103C23×C1112yes—
830#103C23×C1112yes—
831#103C23×C1112yes—
832#103C23×C1112yes—
833#103C23×C1112yes—
834#103C23×C1112yes—
835#103C23×C1112yes—
836#103C23×C1112yes—
837#102C23×C1112yes—
838#102C23×C1112yes—
839#102C23×C1112yes—
840#102C23×C1112yes—
841#102C23×C1112yes—
842#102C23×C1112yes—
843#102C23×C1112yes—
844#102C23×C1112yes—
845C22⋊C8C23×C1112yes—
846C22⋊C8C23×C1112yes—
847C22⋊C8C23×C1112yes—
848C22⋊C8C23×C1112yes—
849C22⋊C8C23×C1112yes—
850C22⋊C8C23×C1112yes—
851#97C23×C1112yes—
852#97C23×C1112yes—
853C2×C11—42no—
854C2×C11—41no—
855C2×C11—42no—
856C2×C11—42no—
857C2×C11—82no—
858C2×C11—82no—
859C2×C11#348411yescharacteristic
860C2×C11#358511yescharacteristic
861C2×C11#358611yescharacteristic
862C24—22no—
863C24—21no—
864#41—22no—
865#41—22no—
866#41—24no—
867#41—24no—
868#41—41no—
869#41—41no—
870#41—41no—
871#41—41no—
872#41—42no—
873#41—42no—
874#41—44no—
875#41—44no—
876#41—42no—
877#41—42no—
878#41—42no—
879#41—42no—
880#41—48no—
881#41—82no—
882#41—84no—
883C2×Q8—21no—
884C2×Q8—22no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—24no—
888C2×Q8—42no—
889C2×Q8—41no—
890C2×Q8—41no—
891C2×Q8—44no—
892C2×Q8C2×D4×C1111yescharacteristic
893C2×Q8C2×D4×C1111yescharacteristic
894C2×Q8C24×C1112yes—
895C2×Q8C24×C1112yes—
896C2×Q8C24×C1111yescharacteristic
897C2×D4—21no—
898C2×D4—24no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—22no—
906C2×D4—22no—
907C2×D4—22no—
908C2×D4—21no—
909C2×D4—22no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—42no—
913C2×D4—41no—
914C2×D4—41no—
915C2×D4—44no—
916C2×D4—48no—
917C2×D4C2×D4×C1112yes—
918C2×D4C2×D4×C1112yes—
919C2×D4C2×D4×C1112yes—
920C2×D4C2×D4×C1112yes—
921C2×D4C2×D4×C1111yescharacteristic
922C2×D4C2×D4×C1111yescharacteristic
923C2×D4C24×C1112yes—
924C2×D4C24×C1112yes—
925C2×D4C24×C1111yescharacteristic
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4C2×D4×C1111yescharacteristic
939C22×C4C2×D4×C1111yescharacteristic
940C22×C4C24×C1111yescharacteristic
941C22×C4C24×C1112yes—
942C22×C4C24×C1112yes—
943Q16—24no—
944Q16—42no—
945Q16—42no—
946SD16—24no—
947SD16—24no—
948SD16—42no—
949SD16—42no—
950SD16—42no—
951SD16—42no—
952D8—24no—
953D8—42no—
954D8—42no—
955M16—42no—
956M16—42no—
957C2×C8—42no—
958C2×C8—42no—
959C2×C8C24×C1112yes—
960C2×C8C24×C1112yes—
961C2×C8C24×C1112yes—
962C2×C8C24×C1112yes—
963C4⋊C4—21no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4C2×D4×C1112yes—
978C4⋊C4C2×D4×C1112yes—
979C4⋊C4C24×C1112yes—
980C4⋊C4C24×C1112yes—
981C4⋊C4C24×C1111yescharacteristic
982C4⋊C4C24×C1111yescharacteristic
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
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—21no—
996C22⋊C4—21no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4C2×D4×C1112yes—
1002C22⋊C4C2×D4×C1112yes—
1003C22⋊C4C2×D4×C1112yes—
1004C22⋊C4C2×D4×C1112yes—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—22no—
1009C42C2×D4×C1111yescharacteristic
1010C42C2×D4×C1111yescharacteristic
1011C42C24×C1111yescharacteristic
1012C42C24×C1111yescharacteristic
1013C11#6167711yescharacteristic, direct product factor, Sylow
1014C23—21no—
1015C23—22no—
1016C23—22no—
1017C23—44no—
1018C23—42no—
1019C23—81no—
1020C23—82no—
1021C23—81no—
1022C23—82no—
1023C23C22×D4×C1112yes—
1024C23C22×D4×C1111yescharacteristic
1025C23C22×D4×C1112yes—
1026Q8—21no—
1027Q8—22no—
1028Q8—22no—
1029Q8—22no—
1030Q8—22no—
1031Q8—41no—
1032Q8—41no—
1033Q8—44no—
1034Q8—42no—
1035Q8—42no—
1036Q8—81no—
1037Q8C11×H(5,𝔽2)12yes—
1038D4—24no—
1039D4—21no—
1040D4—22no—
1041D4—22no—
1042D4—22no—
1043D4—22no—
1044D4—41no—
1045D4—42no—
1046D4—42no—
1047D4—41no—
1048D4—42no—
1049D4—42no—
1050D4—44no—
1051D4—44no—
1052D4—42no—
1053D4—42no—
1054D4—44no—
1055D4—81no—
1056D4—82no—
1057D4—82no—
1058D4—82no—
1059D4—82no—
1060D4—82no—
1061D4—82no—
1062D4—82no—
1063D4C11×H(5,𝔽2)12yes—
1064C2×C4—24no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—44no—
1081C2×C4—44no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—42no—
1085C2×C4—81no—
1086C2×C4—81no—
1087C2×C4—82no—
1088C2×C4—82no—
1089C2×C4—82no—
1090C2×C4—82no—
1091C2×C4C22×D4×C1111yescharacteristic
1092C2×C4C22×D4×C1111yescharacteristic
1093C2×C4C22×D4×C1111yescharacteristic
1094C2×C4C22×D4×C1111yescharacteristic
1095C2×C4C22×D4×C1111yescharacteristic
1096C2×C4C22×D4×C1112yes—
1097C2×C4C22×D4×C1112yes—
1098C2×C4C25×C1111yescharacteristic
1099C8—22no—
1100C8—22no—
1101C8—22no—
1102C8—22no—
1103C22—21no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—21no—
1108C22—22no—
1109C22—22no—
1110C22—21no—
1111C22—22no—
1112C22—22no—
1113C22—41no—
1114C22—41no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—164no—
1122C22—162no—
1123C22C23×D4×C1111yescharacteristic
1124C4—21no—
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—21no—
1129C4—21no—
1130C4—21no—
1131C4—21no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—41no—
1137C4—41no—
1138C4C2×C11×H(5,𝔽2)11yescharacteristic
1139C4C2×C11×H(5,𝔽2)11yescharacteristic
1140C2—41no—
1141C2—42no—
1142C2—42no—
1143C2—42no—
1144C2—82no—
1145C2—82no—
1146C2C11×#348411yescharacteristic
1147C2C11×#358511yescharacteristic
1148C2C11×#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×#3548C2semidirect
2. C11×#3500C2semidirect
3. C11×#3316C2semidirect
4. C11×#3314C2semidirect
5. C11×#3308C2semidirect
6. C11×#3306C2semidirect
7. C11×#3271C2semidirect
8. C11×#3269C2semidirect
9. C11×#3268C2semidirect
10. C11×#3267C2semidirect
11. C11×#3215C2semidirect
12. C11×#3213C2semidirect
13. C11×#3201C2semidirect
14. C11×#3198C2semidirect
15. C11×#3116C2semidirect
16. C11×#3115C2semidirect
17. C11×#3013C2semidirect
18. C11×#3012C2semidirect
19. C11×#2980C2semidirect
22. C2×C11×#137C22semidirect
25. C2×C11×#135C22semidirect
29. C11×#554C22semidirect
31. C11×#550C22semidirect
34. C11×#547C22semidirect
35. C11×#547C22semidirect
43. C11×#537C22semidirect
48. C11×#533C22semidirect
51. C11×#532C22semidirect
55. C11×#497C22semidirect
56. C11×#496C22semidirect
57. C11×#489C22semidirect
58. C11×#489C22semidirect
59. C11×#485C22semidirect
60. C11×#484C22semidirect
61. C11×#483C22semidirect
62. C11×#482C22semidirect
63. C11×#481C22semidirect
64. C11×#480C22semidirect
65. C11×#477C22semidirect
66. C11×#476C22semidirect
67. C11×#475C22semidirect
68. C11×#474C22semidirect
69. C11×#470C22semidirect
70. C11×#469C22semidirect
71. C11×#468C22semidirect
72. C11×#468C22semidirect
73. C11×#467C22semidirect
74. C11×#466C22semidirect
75. C11×#465C22semidirect
76. C11×#465C22semidirect
77. C11×#464C22semidirect
78. C11×#464C22semidirect
79. C11×#463C22semidirect
80. C11×#463C22semidirect
81. C11×#462C22semidirect
82. C11×#461C22semidirect
83. C11×#460C22semidirect
84. C11×#459C22semidirect
87. C11×#452C22semidirect
88. C11×#452C22semidirect
89. C11×#452C22semidirect
90. C11×#451C22semidirect
91. C11×#451C22semidirect
96. C11×#449C22semidirect
97. C11×#449C22semidirect
98. C11×#449C22semidirect
99. C11×#448C22semidirect
100. C11×#448C22semidirect
103. C11×#442C22semidirect
104. C11×#441C22semidirect
105. C11×#440C22semidirect
106. C11×#440C22semidirect
107. C11×#435C22semidirect
108. C11×#435C22semidirect
109. C11×#435C22semidirect
110. C11×#435C22semidirect
111. C11×#432C22semidirect
112. C11×#432C22semidirect
114. C11×#417C22semidirect
115. C2×C11×#103C22semidirect
118. C11×#408C22semidirect
288. #61677C11direct (N × H)
440. #3548C2×C11semidirect
441. #3500C2×C11semidirect
442. #3316C2×C11semidirect
443. #3314C2×C11semidirect
444. #3308C2×C11semidirect
445. #3306C2×C11semidirect
446. #3271C2×C11semidirect
447. #3269C2×C11semidirect
448. #3268C2×C11semidirect
449. #3267C2×C11semidirect
450. #3215C2×C11semidirect
451. #3213C2×C11semidirect
452. #3201C2×C11semidirect
453. #3198C2×C11semidirect
454. #3116C2×C11semidirect
455. #3115C2×C11semidirect
456. #3013C2×C11semidirect
457. #3012C2×C11semidirect
458. #2980C2×C11semidirect
550. C2×#137C22×C11semidirect
553. C2×#135C22×C11semidirect
557. #554C22×C11semidirect
559. #550C22×C11semidirect
562. #547C22×C11semidirect
563. #547C22×C11semidirect
571. #537C22×C11semidirect
576. #533C22×C11semidirect
579. #532C22×C11semidirect
583. #497C22×C11semidirect
584. #496C22×C11semidirect
585. #489C22×C11semidirect
586. #489C22×C11semidirect
587. #485C22×C11semidirect
588. #484C22×C11semidirect
589. #483C22×C11semidirect
590. #482C22×C11semidirect
591. #481C22×C11semidirect
592. #480C22×C11semidirect
593. #477C22×C11semidirect
594. #476C22×C11semidirect
595. #475C22×C11semidirect
596. #474C22×C11semidirect
597. #470C22×C11semidirect
598. #469C22×C11semidirect
599. #468C22×C11semidirect
600. #468C22×C11semidirect
601. #467C22×C11semidirect
602. #466C22×C11semidirect
603. #465C22×C11semidirect
604. #465C22×C11semidirect
605. #464C22×C11semidirect
606. #464C22×C11semidirect
607. #463C22×C11semidirect
608. #463C22×C11semidirect
609. #462C22×C11semidirect
610. #461C22×C11semidirect
611. #460C22×C11semidirect
612. #459C22×C11semidirect
615. #452C22×C11semidirect
616. #452C22×C11semidirect
617. #452C22×C11semidirect
618. #451C22×C11semidirect
619. #451C22×C11semidirect
624. #449C22×C11semidirect
625. #449C22×C11semidirect
626. #449C22×C11semidirect
627. #448C22×C11semidirect
628. #448C22×C11semidirect
631. #442C22×C11semidirect
632. #441C22×C11semidirect
633. #440C22×C11semidirect
634. #440C22×C11semidirect
635. #435C22×C11semidirect
636. #435C22×C11semidirect
637. #435C22×C11semidirect
638. #435C22×C11semidirect
639. #432C22×C11semidirect
640. #432C22×C11semidirect
642. #417C22×C11semidirect
643. C2×#103C22×C11semidirect
646. #408C22×C11semidirect
1013. C11#61677direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#35002
C11×#33162
C11×#33142
C11×#33082
C11×#33062
C11×#32712
C11×#32692
C11×#32682
C11×#32672
C11×#32152
C11×#32132
C11×#32012
C11×#31982
C11×#31162
C11×#31152
C11×#30132
C11×#30122
C11×#29802
#6167711