Finite Group Databasebeta

← C11×#61343 #14638536

Subgroups — C11×#61343 #14638536

Order 2816.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3510C211yesmaximal, characteristic, complemented
2C11×#3501C211yesmaximal, characteristic, complemented
3C11×#3376C212yesmaximal, complemented
4C11×#3376C212yesmaximal, complemented
5C11×#3373C212yesmaximal, complemented
6C11×#3370C212yesmaximal, complemented
7C11×#3370C212yesmaximal, complemented
8C11×#3367C212yesmaximal, complemented
9C11×#3361C212yesmaximal, complemented
10C11×#3360C212yesmaximal, complemented
11C11×#3140C211yesmaximal, characteristic, complemented
12C11×#3137C211yesmaximal, characteristic, complemented
13C11×#3136C211yesmaximal, characteristic, complemented
14C11×#3082C211yesmaximal, characteristic, complemented
15C11×#3081C211yesmaximal, characteristic, complemented
16C11×#3076C211yesmaximal, characteristic, complemented
17C11×#3042C211yesmaximal, characteristic, complemented
18C11×#3041C211yesmaximal, characteristic
19C2×C11×#463C211yesmaximal, characteristic, complemented
20C11×#2962C211yesmaximal, characteristic, complemented
21C11×#2949C211yesmaximal, characteristic, complemented
22C11×#2948C211yesmaximal, characteristic, complemented
23C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
24C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
25C22×C11×SD16C2211yescharacteristic
26C22×C11×D8C2211yescharacteristic
27C11×#559C2212yescomplemented
28C11×#559C2212yescomplemented
29C11×#556C2212yescomplemented
30C11×#556C2212yescomplemented
31C11×#554—21no—
32C11×#554—21no—
33C11×#554—21no—
34C11×#554C2212yescomplemented
35C11×#554C2212yescomplemented
36C11×#554C2212yescomplemented
37C11×#551—22no—
38C11×#551—22no—
39D4×Q8×C11—21no—
40D4×Q8×C11C2212yescomplemented
41C11×#544C2211yescharacteristic
42C11×#544C2211yescharacteristic
43C11×#543—22no—
44C11×#542—21no—
45C11×#542—21no—
46C11×#536C2211yescharacteristic
47C11×#535C2211yescharacteristic
48C11×#533C2211yescharacteristic
49C11×#533C2211yescharacteristic
50C11×#529—21no—
51C11×#529—21no—
52C2×C11×#124C2211yescharacteristic
53C2×C11×C22⋊Q8—22no—
54C11×#519C2211yescharacteristic
55C11×#518C2211yescharacteristic
56C11×#518C2211yescharacteristic
57C11×#518C2211yescharacteristic
58C4×C11×#41C2211yescharacteristic
59C2×C4×D4×C11C2211yescharacteristic
60C11×#491C2212yescomplemented
61C11×#490C2212yescomplemented
62C11×#489C2212yescomplemented
63C11×#489C2212yescomplemented
64C11×#489C2212yescomplemented
65C11×#489C2212yescomplemented
66C11×#488C2212yescomplemented
67C11×#488C2212yescomplemented
68C11×#488C2212yescomplemented
69C11×#488C2212yescomplemented
70C11×#487C2212yescomplemented
71C11×#486C2212yescomplemented
72C11×#479C2211yescharacteristic, complemented
73C11×#479C2211yescharacteristic, complemented
74C11×#479C2212yescomplemented
75C11×#479C2212yescomplemented
76C11×#478C2211yescharacteristic, complemented
77C11×#478C2211yescharacteristic, complemented
78C11×#478C2212yescomplemented
79C11×#478C2212yescomplemented
80C11×#477C2211yescharacteristic, complemented
81C11×#477C2212yescomplemented
82C11×#476C2211yescharacteristic, complemented
83C11×#476C2212yescomplemented
84C11×#475C2211yescharacteristic, complemented
85C11×#475C2212yescomplemented
86C11×#474C2211yescharacteristic, complemented
87C11×#474C2212yescomplemented
88C11×#463C2212yes—
89C11×#463C2212yes—
90C11×#463C2212yes—
91C11×#463C2212yes—
92C11×#463C2212yes—
93C11×#463C2212yes—
94C11×#463C2212yescomplemented
95C11×#463C2212yescomplemented
96C11×#461C2212yescomplemented
97C11×#461C2212yescomplemented
98C11×#459C2212yes—
99C11×#459C2212yes—
100C11×#446C2212yescomplemented
101C11×#446C2212yescomplemented
102C11×#446C2212yescomplemented
103C8×Q8×C11C2212yescomplemented
104C11×#442C2212yes—
105C11×#442C2212yes—
106C11×#442C2212yescomplemented
107C11×#440C2212yescomplemented
108C11×#440C2212yescomplemented
109C11×#440C2212yescomplemented
110C4×C11×SD16C2212yescomplemented
111C4×C11×SD16C2212yescomplemented
112C4×C11×SD16C2212yescomplemented
113C4×C11×D8C2212yes—
114C4×C11×D8C2212yes—
115C4×C11×D8C2212yescomplemented
116C11×#428C2211yescharacteristic
117C11×#427C2211yescharacteristic
118C11×#427C2211yescharacteristic
119C11×#424C2211yescharacteristic
120C11×#424C2211yescharacteristic
121C2×C11×C4⋊C8C2211yescharacteristic
122C11×#419C2211yescharacteristic
123C11×#419C2211yescharacteristic
124C11×#418C2211yescharacteristic
125C11×#418C2211yescharacteristic
126C11×#418C2211yescharacteristic
127C11×#417C2211yescharacteristic
128C11×#416C2211yescharacteristic
129C11×#416C2211yescharacteristic
130C2×C11×#103C2211yescharacteristic
131C2×C11×#102C2211yescharacteristic
132C11×#405C2211yescharacteristic
133C11×#405C2211yescharacteristic
134C4×C11×M16C2211yescharacteristic
135C2×C11×#41C2311yescharacteristic
136C22×Q8×C11—22no—
137C22×Q8×C11C2311yescharacteristic
138C22×D4×C11C2311yescharacteristic
139C22×D4×C11C2311yescharacteristic
140C23×C4×C11—21no—
141C11×AGL(1,ℤ/8)—24no—
142C2×C11×SD16—24no—
143C2×C11×SD16C2312yes—
144C2×C11×SD16C2312yes—
145C2×C11×SD16C2312yes—
146C2×C11×D8—24no—
147C2×C11×D8C2312yes—
148C2×C11×D8C2312yes—
149C2×C11×D8C2312yes—
150C2×C11×M16C2311yescharacteristic
151C2×C11×M16C2311yescharacteristic
152C22×C8×C11C2311yescharacteristic
153C22×C8×C11C2311yescharacteristic
154C11×C4⋊Q8—21no—
155C11×C4⋊Q8—21no—
156C11×C4⋊Q8D411yescharacteristic
157C11×C4⋊Q8D411yescharacteristic
158C11×C4⋊Q8C2312yes—
159C11×C4⋊Q8C2311yescharacteristic
160C11×C4⋊Q8C2311yescharacteristic
161C11×C4⋊Q8C2312yes—
162C11×C4⋊Q8C2312yes—
163C11×#127C2312yes—
164C11×#126—22no—
165C11×#126—22no—
166C11×#126—22no—
167C11×#126—22no—
168C11×#125—21no—
169C11×#125—21no—
170C11×#125D411yescharacteristic
171C11×#125D411yescharacteristic
172C11×#125C2312yes—
173C11×#125C2312yes—
174C11×#125C2311yescharacteristic
175C11×#125C2311yescharacteristic
176C11×#124—22no—
177C11×#124—22no—
178C11×#124—21no—
179C11×#124—21no—
180C11×#124C2312yes—
181C11×#124C2312yes—
182C11×#124C2312yes—
183C11×#124C2312yes—
184C11×#123—22no—
185C11×#123—22no—
186C11×#123—22no—
187C11×#123—22no—
188C11×#123—22no—
189C11×C22⋊Q8—22no—
190C11×C22⋊Q8—22no—
191C11×C22⋊Q8—22no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—22no—
194C11×C22⋊Q8—21no—
195C11×C22⋊Q8—21no—
196C11×C22⋊Q8—22no—
197C11×C22⋊Q8—22no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8—21no—
200C11×C22⋊Q8—21no—
201C11×C22⋊Q8—22no—
202C11×C22⋊Q8—22no—
203C11×C22⋊Q8—22no—
204C11×C22⋊Q8—22no—
205C11×C22⋊Q8—22no—
206C11×C22⋊Q8—22no—
207C11×C22⋊Q8—22no—
208C11×C22⋊Q8—22no—
209C11×C22⋊Q8D412yes—
210C11×C22⋊Q8D412yes—
211C11×#121—21no—
212C11×#121—21no—
213C11×#120—22no—
214C4×Q8×C11—21no—
215C4×Q8×C11—21no—
216C4×Q8×C11—21no—
217C4×Q8×C11—21no—
218C4×Q8×C11C2311yescharacteristic
219C4×Q8×C11C2311yescharacteristic
220C4×Q8×C11C2312yes—
221C4×Q8×C11C2312yes—
222C4×Q8×C11C2312yes—
223C4×Q8×C11C2312yes—
224C4×D4×C11—21no—
225C4×D4×C11—21no—
226C4×D4×C11—21no—
227C4×D4×C11—21no—
228C4×D4×C11—21no—
229C4×D4×C11—21no—
230C4×D4×C11—21no—
231C4×D4×C11—21no—
232C4×D4×C11—22no—
233C4×D4×C11—22no—
234C4×D4×C11—21no—
235C4×D4×C11—21no—
236C4×D4×C11C2312yes—
237C4×D4×C11C2312yes—
238C4×D4×C11C2311yescharacteristic
239C4×D4×C11C2311yescharacteristic
240C4×D4×C11C2312yes—
241C4×D4×C11C2312yes—
242C4×D4×C11C2312yes—
243C4×D4×C11C2312yes—
244C4×D4×C11C2312yes—
245C4×D4×C11C2312yes—
246C11×#117—22no—
247C11×#117—22no—
248C11×#117—22no—
249C11×#117—21no—
250C11×#117C2311yescharacteristic
251C11×#117C2311yescharacteristic
252C11×#117C2311yescharacteristic
253C11×#117C2311yescharacteristic
254C11×#117C2311yescharacteristic
255C2×C11×C4⋊C4—22no—
256C2×C11×C4⋊C4—22no—
257C2×C11×C4⋊C4—22no—
258C2×C11×C4⋊C4C2311yescharacteristic
259C2×C11×C22⋊C4—21no—
260C2×C11×C22⋊C4—21no—
261C2×C11×C22⋊C4—21no—
262C2×C11×C22⋊C4—22no—
263C2×C11×C22⋊C4—22no—
264C2×C11×C22⋊C4—22no—
265C2×C42×C11—21no—
266C2×C42×C11C2311yescharacteristic
267C11×#107C2311yescharacteristic
268C11×#107C2311yescharacteristic
269C11×#107C2311yescharacteristic
270C11×#107C2311yescharacteristic
271C11×#107C2312yes—
272C11×#106C2311yescharacteristic
273C11×#106C2311yescharacteristic
274C11×#106C2311yescharacteristic
275C11×#106C2311yescharacteristic
276C11×#106C2312yes—
277C11×C4⋊C8C2311yescharacteristic
278C11×C4⋊C8C2311yescharacteristic
279C11×C4⋊C8C2311yescharacteristic
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2312yes—
282C11×C4⋊C8C2312yes—
283C11×C4⋊C8C2312yes—
284C11×C4⋊C8C2312yes—
285C11×#103C2311yescharacteristic
286C11×#103C2312yes—
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2312yes—
291C11×#103C2312yes—
292C11×#103C2311yescharacteristic
293C11×#103C2312yes—
294C11×#103C2311yescharacteristic
295C11×#103C2311yescharacteristic
296C11×#102C2311yescharacteristic
297C11×#102C2312yes—
298C11×#102C2312yes—
299C11×#102C2312yes—
300C11×#102C2312yes—
301C11×#102C2312yes—
302C11×#102C2312yes—
303C11×#102C2311yescharacteristic
304C11×#102C2312yes—
305C11×#102C2311yescharacteristic
306C11×#102C2311yescharacteristic
307C11×#102C2312yes—
308C11×#102C2312yes—
309C11×#97C2312yes—
310C11×#97C2312yes—
311C11×#97C2312yes—
312C4×C8×C11C2312yes—
313C4×C8×C11C2312yes—
314C4×C8×C11C2312yes—
315#61343C1111yesmaximal, characteristic, direct product factor, Sylow
316C24×C11—21no—
317C24×C11—21no—
318C11×#41—22no—
319C11×#41—22no—
320C2×Q8×C11—21no—
321C2×Q8×C11—21no—
322C2×Q8×C11—21no—
323C2×Q8×C11—22no—
324C2×Q8×C11—22no—
325C2×Q8×C11—22no—
326C2×Q8×C11—22no—
327C2×Q8×C11—84no—
328C2×Q8×C11C2×D412yes—
329C2×Q8×C11C2×D412yes—
330C2×Q8×C11C2412yes—
331C2×Q8×C11C2411yescharacteristic
332C2×D4×C11—21no—
333C2×D4×C11—21no—
334C2×D4×C11—21no—
335C2×D4×C11—22no—
336C2×D4×C11—22no—
337C2×D4×C11—22no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11#4114yes—
341C2×D4×C11C2412yes—
342C2×D4×C11C2411yescharacteristic
343C2×D4×C11C2412yes—
344C22×C4×C11—21no—
345C22×C4×C11—21no—
346C22×C4×C11—21no—
347C22×C4×C11—22no—
348C22×C4×C11—21no—
349C22×C4×C11—21no—
350C22×C4×C11—22no—
351C22×C4×C11—22no—
352C22×C4×C11—22no—
353C22×C4×C11—22no—
354C22×C4×C11—22no—
355C22×C4×C11—22no—
356C22×C4×C11—22no—
357C22×C4×C11—82no—
358C22×C4×C11C2×D411yescharacteristic
359C22×C4×C11C2×D411yescharacteristic
360C22×C4×C11C2411yescharacteristic
361C11×SD16—24no—
362C11×SD16—24no—
363C11×SD16—24no—
364C11×D8—24no—
365C11×D8—24no—
366C11×D8—24no—
367C11×M16—22no—
368C11×M16—22no—
369C2×C8×C11—22no—
370C2×C8×C11—22no—
371C2×C8×C11C2412yes—
372C2×C8×C11C2411yescharacteristic
373C2×C8×C11C2411yescharacteristic
374C2×C8×C11C2412yes—
375C2×C8×C11C2411yescharacteristic
376C2×C8×C11C2411yescharacteristic
377C11×C4⋊C4—21no—
378C11×C4⋊C4—21no—
379C11×C4⋊C4—21no—
380C11×C4⋊C4—22no—
381C11×C4⋊C4—22no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—22no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4—22no—
386C11×C4⋊C4—21no—
387C11×C4⋊C4—21no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—21no—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4C2×D412yes—
397C11×C4⋊C4C2×D412yes—
398C11×C4⋊C4C2×D412yes—
399C11×C4⋊C4C2×D412yes—
400C11×C4⋊C4C2×D411yescharacteristic
401C11×C4⋊C4C2×D411yescharacteristic
402C11×C4⋊C4C2×D411yescharacteristic
403C11×C4⋊C4C2×D411yescharacteristic
404C11×C4⋊C4C2×D412yes—
405C11×C4⋊C4C2×D412yes—
406C11×C4⋊C4C2412yes—
407C11×C4⋊C4C2411yescharacteristic
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2411yescharacteristic
411C11×C4⋊C4C2411yescharacteristic
412C11×C4⋊C4C2411yescharacteristic
413C11×C22⋊C4—21no—
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⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—21no—
429C11×C22⋊C4—21no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4C2×D412yes—
435C11×C22⋊C4C2×D412yes—
436C42×C11—21no—
437C42×C11—21no—
438C42×C11—21no—
439C42×C11—22no—
440C42×C11—22no—
441C42×C11—21no—
442C42×C11—21no—
443C42×C11C2×D411yescharacteristic
444C42×C11C2×D411yescharacteristic
445C42×C11C2411yescharacteristic
446C42×C11C2412yes—
447C42×C11C2412yes—
448C42×C11C2411yescharacteristic
449#3510C2×C1111yescharacteristic, complemented
450#3501C2×C1111yescharacteristic, complemented
451#3376C2×C1112yescomplemented
452#3376C2×C1112yescomplemented
453#3373C2×C1112yescomplemented
454#3370C2×C1112yescomplemented
455#3370C2×C1112yescomplemented
456#3367C2×C1112yescomplemented
457#3361C2×C1112yescomplemented
458#3360C2×C1112yescomplemented
459#3140C2×C1111yescharacteristic, complemented
460#3137C2×C1111yescharacteristic, complemented
461#3136C2×C1111yescharacteristic, complemented
462#3082C2×C1111yescharacteristic, complemented
463#3081C2×C1111yescharacteristic, complemented
464#3076C2×C1111yescharacteristic, complemented
465#3042C2×C1111yescharacteristic, complemented
466#3041C2×C1111yescharacteristic
467C2×#463C2×C1111yescharacteristic, complemented
468#2962C2×C1111yescharacteristic, complemented
469#2949C2×C1111yescharacteristic, complemented
470#2948C2×C1111yescharacteristic, complemented
471C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
472C23×C11—22no—
473C23×C11—24no—
474C23×C11—22no—
475C23×C11—21no—
476C23×C11—42no—
477C23×C11—81no—
478C23×C11—81no—
479C23×C11—81no—
480C23×C11—81no—
481C23×C11C22×D411yescharacteristic
482Q8×C11—22no—
483Q8×C11—21no—
484Q8×C11—22no—
485Q8×C11—21no—
486Q8×C11—42no—
487Q8×C11—42no—
488Q8×C11—42no—
489Q8×C11—42no—
490Q8×C11—81no—
491Q8×C11—82no—
492Q8×C11—82no—
493D4×C11—24no—
494D4×C11—22no—
495D4×C11—21no—
496D4×C11—22no—
497D4×C11—22no—
498D4×C11—21no—
499D4×C11—42no—
500D4×C11—42no—
501D4×C11—82no—
502D4×C11—82no—
503D4×C11C2×#4114yes—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—22no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—22no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—44no—
516C2×C4×C11—42no—
517C2×C4×C11—42no—
518C2×C4×C11—81no—
519C2×C4×C11—82no—
520C2×C4×C11—82no—
521C2×C4×C11—82no—
522C2×C4×C11—81no—
523C2×C4×C11—82no—
524C2×C4×C11—82no—
525C2×C4×C11—82no—
526C2×C4×C11—82no—
527C2×C4×C11—81no—
528C2×C4×C11C22×D411yescharacteristic
529C2×C4×C11C22×D411yescharacteristic
530C2×C4×C11C22×D412yes—
531C2×C4×C11C22×D412yes—
532C2×C4×C11C22×D411yescharacteristic
533C2×C4×C11C22×D411yescharacteristic
534C2×C4×C11C22×D412yes—
535C2×C4×C11C22×D412yes—
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C2×#4112yes—
538C2×C4×C112−1+412yes—
539C2×C4×C11C2511yescharacteristic
540C8×C11—21no—
541C8×C11—21no—
542C8×C11—21no—
543C8×C11—21no—
544C8×C11—22no—
545C8×C11—22no—
546C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
547C22×SD16C22×C1111yescharacteristic
548C22×D8C22×C1111yescharacteristic
549#559C22×C1112yescomplemented
550#559C22×C1112yescomplemented
551#556C22×C1112yescomplemented
552#556C22×C1112yescomplemented
553#554—21no—
554#554—21no—
555#554—21no—
556#554C22×C1112yescomplemented
557#554C22×C1112yescomplemented
558#554C22×C1112yescomplemented
559#551—22no—
560#551—22no—
561D4×Q8—21no—
562D4×Q8C22×C1112yescomplemented
563#544C22×C1111yescharacteristic
564#544C22×C1111yescharacteristic
565#543—22no—
566#542—21no—
567#542—21no—
568#536C22×C1111yescharacteristic
569#535C22×C1111yescharacteristic
570#533C22×C1111yescharacteristic
571#533C22×C1111yescharacteristic
572#529—21no—
573#529—21no—
574C2×#124C22×C1111yescharacteristic
575C2×C22⋊Q8—22no—
576#519C22×C1111yescharacteristic
577#518C22×C1111yescharacteristic
578#518C22×C1111yescharacteristic
579#518C22×C1111yescharacteristic
580C4×#41C22×C1111yescharacteristic
581C2×C4×D4C22×C1111yescharacteristic
582#491C22×C1112yescomplemented
583#490C22×C1112yescomplemented
584#489C22×C1112yescomplemented
585#489C22×C1112yescomplemented
586#489C22×C1112yescomplemented
587#489C22×C1112yescomplemented
588#488C22×C1112yescomplemented
589#488C22×C1112yescomplemented
590#488C22×C1112yescomplemented
591#488C22×C1112yescomplemented
592#487C22×C1112yescomplemented
593#486C22×C1112yescomplemented
594#479C22×C1111yescharacteristic, complemented
595#479C22×C1111yescharacteristic, complemented
596#479C22×C1112yescomplemented
597#479C22×C1112yescomplemented
598#478C22×C1111yescharacteristic, complemented
599#478C22×C1111yescharacteristic, complemented
600#478C22×C1112yescomplemented
601#478C22×C1112yescomplemented
602#477C22×C1111yescharacteristic, complemented
603#477C22×C1112yescomplemented
604#476C22×C1111yescharacteristic, complemented
605#476C22×C1112yescomplemented
606#475C22×C1111yescharacteristic, complemented
607#475C22×C1112yescomplemented
608#474C22×C1111yescharacteristic, complemented
609#474C22×C1112yescomplemented
610#463C22×C1112yes—
611#463C22×C1112yes—
612#463C22×C1112yes—
613#463C22×C1112yes—
614#463C22×C1112yes—
615#463C22×C1112yes—
616#463C22×C1112yescomplemented
617#463C22×C1112yescomplemented
618#461C22×C1112yescomplemented
619#461C22×C1112yescomplemented
620#459C22×C1112yes—
621#459C22×C1112yes—
622#446C22×C1112yescomplemented
623#446C22×C1112yescomplemented
624#446C22×C1112yescomplemented
625C8×Q8C22×C1112yescomplemented
626#442C22×C1112yes—
627#442C22×C1112yes—
628#442C22×C1112yescomplemented
629#440C22×C1112yescomplemented
630#440C22×C1112yescomplemented
631#440C22×C1112yescomplemented
632C4×SD16C22×C1112yescomplemented
633C4×SD16C22×C1112yescomplemented
634C4×SD16C22×C1112yescomplemented
635C4×D8C22×C1112yes—
636C4×D8C22×C1112yes—
637C4×D8C22×C1112yescomplemented
638#428C22×C1111yescharacteristic
639#427C22×C1111yescharacteristic
640#427C22×C1111yescharacteristic
641#424C22×C1111yescharacteristic
642#424C22×C1111yescharacteristic
643C2×C4⋊C8C22×C1111yescharacteristic
644#419C22×C1111yescharacteristic
645#419C22×C1111yescharacteristic
646#418C22×C1111yescharacteristic
647#418C22×C1111yescharacteristic
648#418C22×C1111yescharacteristic
649#417C22×C1111yescharacteristic
650#416C22×C1111yescharacteristic
651#416C22×C1111yescharacteristic
652C2×#103C22×C1111yescharacteristic
653C2×#102C22×C1111yescharacteristic
654#405C22×C1111yescharacteristic
655#405C22×C1111yescharacteristic
656C4×M16C22×C1111yescharacteristic
657C22×C11—21no—
658C22×C11—21no—
659C22×C11—24no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—41no—
663C22×C11—42no—
664C22×C11—41no—
665C22×C11—42no—
666C22×C11—41no—
667C22×C11—42no—
668C22×C11—84no—
669C22×C11—162no—
670C22×C11#54812yes—
671C22×C11C23×D411yescharacteristic
672C4×C11—21no—
673C4×C11—21no—
674C4×C11—22no—
675C4×C11—22no—
676C4×C11—21no—
677C4×C11—21no—
678C4×C11—22no—
679C4×C11—22no—
680C4×C11—41no—
681C4×C11—41no—
682C4×C11—41no—
683C4×C11—42no—
684C4×C11—41no—
685C4×C11—41no—
686C4×C11—41no—
687C4×C11—41no—
688C4×C11—42no—
689C4×C11#54812yes—
690C4×C11C22×#4111yescharacteristic
691C4×C11C2×2−1+411yescharacteristic
692C2×#41C23×C1111yescharacteristic
693C22×Q8—22no—
694C22×Q8C23×C1111yescharacteristic
695C22×D4C23×C1111yescharacteristic
696C22×D4C23×C1111yescharacteristic
697C23×C4—21no—
698AGL(1,ℤ/8)—24no—
699C2×SD16—24no—
700C2×SD16C23×C1112yes—
701C2×SD16C23×C1112yes—
702C2×SD16C23×C1112yes—
703C2×D8—24no—
704C2×D8C23×C1112yes—
705C2×D8C23×C1112yes—
706C2×D8C23×C1112yes—
707C2×M16C23×C1111yescharacteristic
708C2×M16C23×C1111yescharacteristic
709C22×C8C23×C1111yescharacteristic
710C22×C8C23×C1111yescharacteristic
711C4⋊Q8—21no—
712C4⋊Q8—21no—
713C4⋊Q8D4×C1111yescharacteristic
714C4⋊Q8D4×C1111yescharacteristic
715C4⋊Q8C23×C1112yes—
716C4⋊Q8C23×C1111yescharacteristic
717C4⋊Q8C23×C1111yescharacteristic
718C4⋊Q8C23×C1112yes—
719C4⋊Q8C23×C1112yes—
720#127C23×C1112yes—
721#126—22no—
722#126—22no—
723#126—22no—
724#126—22no—
725#125—21no—
726#125—21no—
727#125D4×C1111yescharacteristic
728#125D4×C1111yescharacteristic
729#125C23×C1111yescharacteristic
730#125C23×C1111yescharacteristic
731#125C23×C1112yes—
732#125C23×C1112yes—
733#124—22no—
734#124—22no—
735#124—21no—
736#124—21no—
737#124C23×C1112yes—
738#124C23×C1112yes—
739#124C23×C1112yes—
740#124C23×C1112yes—
741#123—22no—
742#123—22no—
743#123—22no—
744#123—22no—
745#123—22no—
746C22⋊Q8—22no—
747C22⋊Q8—22no—
748C22⋊Q8—22no—
749C22⋊Q8—22no—
750C22⋊Q8—22no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8—22no—
756C22⋊Q8—21no—
757C22⋊Q8—21no—
758C22⋊Q8—22no—
759C22⋊Q8—22no—
760C22⋊Q8—22no—
761C22⋊Q8—22no—
762C22⋊Q8—22no—
763C22⋊Q8—22no—
764C22⋊Q8—22no—
765C22⋊Q8—22no—
766C22⋊Q8D4×C1112yes—
767C22⋊Q8D4×C1112yes—
768#121—21no—
769#121—21no—
770#120—22no—
771C4×Q8—21no—
772C4×Q8—21no—
773C4×Q8—21no—
774C4×Q8—21no—
775C4×Q8C23×C1111yescharacteristic
776C4×Q8C23×C1111yescharacteristic
777C4×Q8C23×C1112yes—
778C4×Q8C23×C1112yes—
779C4×Q8C23×C1112yes—
780C4×Q8C23×C1112yes—
781C4×D4—21no—
782C4×D4—21no—
783C4×D4—21no—
784C4×D4—21no—
785C4×D4—21no—
786C4×D4—21no—
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—22no—
790C4×D4—22no—
791C4×D4—21no—
792C4×D4—21no—
793C4×D4C23×C1112yes—
794C4×D4C23×C1112yes—
795C4×D4C23×C1111yescharacteristic
796C4×D4C23×C1111yescharacteristic
797C4×D4C23×C1112yes—
798C4×D4C23×C1112yes—
799C4×D4C23×C1112yes—
800C4×D4C23×C1112yes—
801C4×D4C23×C1112yes—
802C4×D4C23×C1112yes—
803#117—22no—
804#117—22no—
805#117—22no—
806#117—21no—
807#117C23×C1111yescharacteristic
808#117C23×C1111yescharacteristic
809#117C23×C1111yescharacteristic
810#117C23×C1111yescharacteristic
811#117C23×C1111yescharacteristic
812C2×C4⋊C4—22no—
813C2×C4⋊C4—22no—
814C2×C4⋊C4—22no—
815C2×C4⋊C4C23×C1111yescharacteristic
816C2×C22⋊C4—21no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—21no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C42—21no—
823C2×C42C23×C1111yescharacteristic
824#107C23×C1111yescharacteristic
825#107C23×C1111yescharacteristic
826#107C23×C1111yescharacteristic
827#107C23×C1111yescharacteristic
828#107C23×C1112yes—
829#106C23×C1111yescharacteristic
830#106C23×C1111yescharacteristic
831#106C23×C1111yescharacteristic
832#106C23×C1111yescharacteristic
833#106C23×C1112yes—
834C4⋊C8C23×C1111yescharacteristic
835C4⋊C8C23×C1111yescharacteristic
836C4⋊C8C23×C1111yescharacteristic
837C4⋊C8C23×C1111yescharacteristic
838C4⋊C8C23×C1112yes—
839C4⋊C8C23×C1112yes—
840C4⋊C8C23×C1112yes—
841C4⋊C8C23×C1112yes—
842#103C23×C1112yes—
843#103C23×C1112yes—
844#103C23×C1111yescharacteristic
845#103C23×C1111yescharacteristic
846#103C23×C1111yescharacteristic
847#103C23×C1111yescharacteristic
848#103C23×C1112yes—
849#103C23×C1112yes—
850#103C23×C1112yes—
851#103C23×C1112yes—
852#103C23×C1112yes—
853#102C23×C1112yes—
854#102C23×C1112yes—
855#102C23×C1111yescharacteristic
856#102C23×C1111yescharacteristic
857#102C23×C1111yescharacteristic
858#102C23×C1111yescharacteristic
859#102C23×C1112yes—
860#102C23×C1112yes—
861#102C23×C1112yes—
862#102C23×C1112yes—
863#102C23×C1112yes—
864#102C23×C1112yes—
865#102C23×C1112yes—
866#97C23×C1112yes—
867#97C23×C1112yes—
868#97C23×C1112yes—
869C4×C8C23×C1112yes—
870C4×C8C23×C1112yes—
871C4×C8C23×C1112yes—
872C2×C11—22no—
873C2×C11—44no—
874C2×C11—81no—
875C2×C11—82no—
876C2×C11C2×#54811yescharacteristic
877C2×C11#358411yescharacteristic
878C2×C11#358511yescharacteristic
879C24—21no—
880C24—21no—
881#41—22no—
882#41—22no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—22no—
887C2×Q8—22no—
888C2×Q8—22no—
889C2×Q8—22no—
890C2×Q8—84no—
891C2×Q8C2×D4×C1112yes—
892C2×Q8C2×D4×C1112yes—
893C2×Q8C24×C1112yes—
894C2×Q8C24×C1111yescharacteristic
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—22no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—22no—
903C2×D4C11×#4114yes—
904C2×D4C24×C1112yes—
905C2×D4C24×C1111yescharacteristic
906C2×D4C24×C1112yes—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—22no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—82no—
921C22×C4C2×D4×C1111yescharacteristic
922C22×C4C2×D4×C1111yescharacteristic
923C22×C4C24×C1111yescharacteristic
924SD16—24no—
925SD16—24no—
926SD16—24no—
927D8—24no—
928D8—24no—
929D8—24no—
930M16—22no—
931M16—22no—
932C2×C8—22no—
933C2×C8—22no—
934C2×C8C24×C1112yes—
935C2×C8C24×C1111yescharacteristic
936C2×C8C24×C1111yescharacteristic
937C2×C8C24×C1112yes—
938C2×C8C24×C1111yescharacteristic
939C2×C8C24×C1111yescharacteristic
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4C2×D4×C1112yes—
960C4⋊C4C2×D4×C1112yes—
961C4⋊C4C2×D4×C1112yes—
962C4⋊C4C2×D4×C1112yes—
963C4⋊C4C2×D4×C1111yescharacteristic
964C4⋊C4C2×D4×C1111yescharacteristic
965C4⋊C4C2×D4×C1111yescharacteristic
966C4⋊C4C2×D4×C1111yescharacteristic
967C4⋊C4C2×D4×C1112yes—
968C4⋊C4C2×D4×C1112yes—
969C4⋊C4C24×C1112yes—
970C4⋊C4C24×C1111yescharacteristic
971C4⋊C4C24×C1111yescharacteristic
972C4⋊C4C24×C1111yescharacteristic
973C4⋊C4C24×C1111yescharacteristic
974C4⋊C4C24×C1111yescharacteristic
975C4⋊C4C24×C1111yescharacteristic
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—21no—
992C22⋊C4—21no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4C2×D4×C1112yes—
998C22⋊C4C2×D4×C1112yes—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—22no—
1003C42—22no—
1004C42—21no—
1005C42—21no—
1006C42C2×D4×C1111yescharacteristic
1007C42C2×D4×C1111yescharacteristic
1008C42C24×C1111yescharacteristic
1009C42C24×C1112yes—
1010C42C24×C1112yes—
1011C42C24×C1111yescharacteristic
1012C11#6134311yescharacteristic, direct product factor, Sylow
1013C23—22no—
1014C23—24no—
1015C23—22no—
1016C23—21no—
1017C23—42no—
1018C23—81no—
1019C23—81no—
1020C23—81no—
1021C23—81no—
1022C23C22×D4×C1111yescharacteristic
1023Q8—22no—
1024Q8—21no—
1025Q8—22no—
1026Q8—21no—
1027Q8—42no—
1028Q8—42no—
1029Q8—42no—
1030Q8—42no—
1031Q8—81no—
1032Q8—82no—
1033Q8—82no—
1034D4—24no—
1035D4—22no—
1036D4—21no—
1037D4—22no—
1038D4—22no—
1039D4—21no—
1040D4—42no—
1041D4—42no—
1042D4—82no—
1043D4—82no—
1044D4C2×C11×#4114yes—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—44no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—81no—
1060C2×C4—82no—
1061C2×C4—82no—
1062C2×C4—82no—
1063C2×C4—81no—
1064C2×C4—82no—
1065C2×C4—82no—
1066C2×C4—82no—
1067C2×C4—82no—
1068C2×C4—81no—
1069C2×C4C22×D4×C1111yescharacteristic
1070C2×C4C22×D4×C1111yescharacteristic
1071C2×C4C22×D4×C1112yes—
1072C2×C4C22×D4×C1112yes—
1073C2×C4C22×D4×C1111yescharacteristic
1074C2×C4C22×D4×C1111yescharacteristic
1075C2×C4C22×D4×C1112yes—
1076C2×C4C22×D4×C1112yes—
1077C2×C4C22×D4×C1111yescharacteristic
1078C2×C4C2×C11×#4112yes—
1079C2×C4C11×2−1+412yes—
1080C2×C4C25×C1111yescharacteristic
1081C8—21no—
1082C8—21no—
1083C8—21no—
1084C8—21no—
1085C8—22no—
1086C8—22no—
1087C22—21no—
1088C22—21no—
1089C22—24no—
1090C22—42no—
1091C22—42no—
1092C22—41no—
1093C22—42no—
1094C22—41no—
1095C22—42no—
1096C22—41no—
1097C22—42no—
1098C22—84no—
1099C22—162no—
1100C22C11×#54812yes—
1101C22C23×D4×C1111yescharacteristic
1102C4—21no—
1103C4—21no—
1104C4—22no—
1105C4—22no—
1106C4—21no—
1107C4—21no—
1108C4—22no—
1109C4—22no—
1110C4—41no—
1111C4—42no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—42no—
1116C4—41no—
1117C4—41no—
1118C4—41no—
1119C4C11×#54812yes—
1120C4C22×C11×#4111yescharacteristic
1121C4C2×C11×2−1+411yescharacteristic
1122C2—22no—
1123C2—44no—
1124C2—82no—
1125C2—81no—
1126C2C2×C11×#54811yescharacteristic
1127C2C11×#358411yescharacteristic
1128C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3041C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3510C2semidirect
2. C11×#3501C2semidirect
3. C11×#3376C2semidirect
4. C11×#3376C2semidirect
5. C11×#3373C2semidirect
6. C11×#3370C2semidirect
7. C11×#3370C2semidirect
8. C11×#3367C2semidirect
9. C11×#3361C2semidirect
10. C11×#3360C2semidirect
11. C11×#3140C2semidirect
12. C11×#3137C2semidirect
13. C11×#3136C2semidirect
14. C11×#3082C2semidirect
15. C11×#3081C2semidirect
16. C11×#3076C2semidirect
17. C11×#3042C2semidirect
19. C2×C11×#463C2semidirect
20. C11×#2962C2semidirect
21. C11×#2949C2semidirect
22. C11×#2948C2semidirect
23. C4×C11×AGL(1,ℤ/8)C2semidirect
27. C11×#559C22semidirect
28. C11×#559C22semidirect
29. C11×#556C22semidirect
30. C11×#556C22semidirect
34. C11×#554C22semidirect
35. C11×#554C22semidirect
36. C11×#554C22semidirect
40. D4×Q8×C11C22semidirect
60. C11×#491C22semidirect
61. C11×#490C22semidirect
62. C11×#489C22semidirect
63. C11×#489C22semidirect
64. C11×#489C22semidirect
65. C11×#489C22semidirect
66. C11×#488C22semidirect
67. C11×#488C22semidirect
68. C11×#488C22semidirect
69. C11×#488C22semidirect
70. C11×#487C22semidirect
71. C11×#486C22semidirect
72. C11×#479C22semidirect
73. C11×#479C22semidirect
74. C11×#479C22semidirect
75. C11×#479C22semidirect
76. C11×#478C22semidirect
77. C11×#478C22semidirect
78. C11×#478C22semidirect
79. C11×#478C22semidirect
80. C11×#477C22semidirect
81. C11×#477C22semidirect
82. C11×#476C22semidirect
83. C11×#476C22semidirect
84. C11×#475C22semidirect
85. C11×#475C22semidirect
86. C11×#474C22semidirect
87. C11×#474C22semidirect
94. C11×#463C22semidirect
95. C11×#463C22semidirect
96. C11×#461C22semidirect
97. C11×#461C22semidirect
100. C11×#446C22semidirect
101. C11×#446C22semidirect
102. C11×#446C22semidirect
103. C8×Q8×C11C22semidirect
106. C11×#442C22semidirect
107. C11×#440C22semidirect
108. C11×#440C22semidirect
109. C11×#440C22semidirect
110. C4×C11×SD16C22semidirect
111. C4×C11×SD16C22semidirect
112. C4×C11×SD16C22semidirect
115. C4×C11×D8C22semidirect
315. #61343C11direct (N × H)
449. #3510C2×C11semidirect
450. #3501C2×C11semidirect
451. #3376C2×C11semidirect
452. #3376C2×C11semidirect
453. #3373C2×C11semidirect
454. #3370C2×C11semidirect
455. #3370C2×C11semidirect
456. #3367C2×C11semidirect
457. #3361C2×C11semidirect
458. #3360C2×C11semidirect
459. #3140C2×C11semidirect
460. #3137C2×C11semidirect
461. #3136C2×C11semidirect
462. #3082C2×C11semidirect
463. #3081C2×C11semidirect
464. #3076C2×C11semidirect
465. #3042C2×C11semidirect
467. C2×#463C2×C11semidirect
468. #2962C2×C11semidirect
469. #2949C2×C11semidirect
470. #2948C2×C11semidirect
471. C4×AGL(1,ℤ/8)C2×C11semidirect
549. #559C22×C11semidirect
550. #559C22×C11semidirect
551. #556C22×C11semidirect
552. #556C22×C11semidirect
556. #554C22×C11semidirect
557. #554C22×C11semidirect
558. #554C22×C11semidirect
562. D4×Q8C22×C11semidirect
582. #491C22×C11semidirect
583. #490C22×C11semidirect
584. #489C22×C11semidirect
585. #489C22×C11semidirect
586. #489C22×C11semidirect
587. #489C22×C11semidirect
588. #488C22×C11semidirect
589. #488C22×C11semidirect
590. #488C22×C11semidirect
591. #488C22×C11semidirect
592. #487C22×C11semidirect
593. #486C22×C11semidirect
594. #479C22×C11semidirect
595. #479C22×C11semidirect
596. #479C22×C11semidirect
597. #479C22×C11semidirect
598. #478C22×C11semidirect
599. #478C22×C11semidirect
600. #478C22×C11semidirect
601. #478C22×C11semidirect
602. #477C22×C11semidirect
603. #477C22×C11semidirect
604. #476C22×C11semidirect
605. #476C22×C11semidirect
606. #475C22×C11semidirect
607. #475C22×C11semidirect
608. #474C22×C11semidirect
609. #474C22×C11semidirect
616. #463C22×C11semidirect
617. #463C22×C11semidirect
618. #461C22×C11semidirect
619. #461C22×C11semidirect
622. #446C22×C11semidirect
623. #446C22×C11semidirect
624. #446C22×C11semidirect
625. C8×Q8C22×C11semidirect
628. #442C22×C11semidirect
629. #440C22×C11semidirect
630. #440C22×C11semidirect
631. #440C22×C11semidirect
632. C4×SD16C22×C11semidirect
633. C4×SD16C22×C11semidirect
634. C4×SD16C22×C11semidirect
637. C4×D8C22×C11semidirect
1012. C11#61343direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35102
C11×#35012
C11×#33762
C11×#33732
C11×#33702
C11×#33672
C11×#33612
C11×#33602
C11×#31402
C11×#31372
C11×#31362
C11×#30822
C11×#30812
C11×#30762
C11×#30422
C11×#30412
C2×C11×#4632
C11×#29622
C11×#29492
C11×#29482
C4×C11×AGL(1,ℤ/8)2
#6134311