Finite Group Databasebeta

← C11×#61461 #14638654

Subgroups — C11×#61461 #14638654

Order 2816.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3482C211yesmaximal, characteristic, complemented
2C11×#3475C211yesmaximal, characteristic, complemented
3C11×#3398C211yesmaximal, characteristic, complemented
4C11×#3384C211yesmaximal, characteristic, complemented
5C11×#3372C211yesmaximal, characteristic, complemented
6C11×#3367C211yesmaximal, characteristic, complemented
7C11×#3349C212yesmaximal, complemented
8C11×#3340C211yesmaximal, characteristic, complemented
9C11×#3315C212yesmaximal, complemented
10C11×#3311C212yesmaximal, complemented
11C11×#3303C211yesmaximal, characteristic, complemented
12C11×#3302C211yesmaximal, characteristic, complemented
13C11×#3283C211yesmaximal, characteristic, complemented
14C11×#3267C212yesmaximal, complemented
15C11×#3185C211yesmaximal, characteristic, complemented
16C11×#3181C212yesmaximal, complemented
17C11×#3116C211yesmaximal, characteristic, complemented
18C11×#3116C212yesmaximal, complemented
19C11×#3111C212yesmaximal, complemented
20C11×#3110C211yesmaximal, characteristic, complemented
21C11×#2970C211yesmaximal, characteristic, complemented
22C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
23C11×#2943C212yesmaximal, complemented
24C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C11×#135C2212yes—
26C11×#557C2211yescharacteristic, complemented
27C11×#556C2211yescharacteristic
28C11×#556C2212yes—
29C11×#556C2211yescharacteristic, complemented
30C11×#555C2211yescharacteristic
31C11×#554C2211yescharacteristic
32C11×#553—21no—
33C11×#552—21no—
34C11×#552—22no—
35C11×#552—21no—
36C11×#552C2212yes—
37C11×#551—22no—
38D4×Q8×C11C2211yescharacteristic, complemented
39C11×#548—21no—
40C11×#547C2211yescharacteristic
41C11×#547C2212yes—
42C11×#547C2211yescharacteristic, complemented
43C11×#546C2212yes—
44C11×#533C2211yescharacteristic
45C11×#533C2211yescharacteristic
46C11×#533C2212yescomplemented
47C11×#529—21no—
48C11×#529—22no—
49C11×#529—22no—
50C11×#529C2212yes—
51C11×#525—21no—
52C4×C11×#41C2212yes—
53C4×C11×#41C2211yescharacteristic
54C4×C11×#41C2211yescharacteristic
55C4×C11×#41C2212yescomplemented
56C2×C4×Q8×C11—21no—
57C2×C4×D4×C11C2211yescharacteristic
58C2×C11×#117—21no—
59C11×#501C2212yescomplemented
60C11×#498C2211yescharacteristic, complemented
61C11×#497C2212yes—
62C11×#494C2211yescharacteristic, complemented
63C11×#491C2212yescomplemented
64C11×#489C2212yes—
65C11×#487C2211yescharacteristic, complemented
66C11×#487C2211yescharacteristic, complemented
67C11×#485C2212yes—
68C11×#485C2212yescomplemented
69C11×#485C2212yescomplemented
70C11×#485C2212yescomplemented
71C11×#484C2212yes—
72C11×#482C2212yes—
73C11×#479C2212yescomplemented
74C11×#478C2212yescomplemented
75C11×#477C2211yescharacteristic, complemented
76C11×#477C2212yescomplemented
77C11×#476C2212yes—
78C11×#476C2211yescharacteristic, complemented
79C11×#474C2211yescharacteristic
80C11×#474C2211yescharacteristic
81C11×#470C2212yes—
82C11×#470C2212yes—
83C11×#467C2212yescomplemented
84C11×#467C2212yescomplemented
85C11×#465C2212yes—
86C11×#465C2212yes—
87C11×#464C2212yes—
88C11×#463C2212yes—
89C11×#462C2211yescharacteristic, complemented
90C11×#462C2212yescomplemented
91C11×#461C2212yes—
92C11×#461C2211yescharacteristic
93C11×#461C2211yescharacteristic
94C11×#461C2211yescharacteristic, complemented
95C11×#452C2212yes—
96C11×#452C2212yes—
97C11×#452C2212yes—
98C11×#452C2212yescomplemented
99C11×#450C2212yes—
100C11×#449C2212yes—
101C11×#446C2211yescharacteristic, complemented
102C11×#446C2211yescharacteristic, complemented
103C11×#442C2211yescharacteristic
104C11×#442C2212yes—
105C11×#442C2211yescharacteristic
106C11×#441C2212yescomplemented
107C11×#441C2212yescomplemented
108C11×#441C2212yescomplemented
109C11×#441C2212yescomplemented
110C11×#440C2211yescharacteristic
111C11×#440C2212yes—
112C11×#440C2212yes—
113C11×#440C2212yes—
114C11×#440C2211yescharacteristic
115C11×#440C2212yescomplemented
116C11×#440C2212yescomplemented
117C4×C11×SD16C2211yescharacteristic
118C4×C11×SD16C2211yescharacteristic
119C4×C11×D8C2211yescharacteristic
120C4×C11×D8C2211yescharacteristic
121C11×#435C2212yes—
122C11×#435C2212yes—
123C8×D4×C11C2211yescharacteristic, complemented
124C8×D4×C11C2211yescharacteristic, complemented
125C11×#432C2211yescharacteristic
126C11×#432C2212yescomplemented
127C11×#428C2211yescharacteristic
128C11×#427C2212yescomplemented
129C11×#418C2211yescharacteristic
130C11×#417C2211yescharacteristic
131C11×#416C2212yes—
132C11×#416C2212yescomplemented
133C4×C11×M16C2211yescharacteristic
134C2×C11×#97C2212yescomplemented
135C2×C11×#41D411yescharacteristic
136C2×C11×#41C2312yes—
137C2×C11×#41C2311yescharacteristic
138C2×C11×#41C2312yes—
139C22×Q8×C11—21no—
140C22×D4×C11C2311yescharacteristic
141C23×C4×C11—21no—
142C11×AGL(1,ℤ/8)—24no—
143C11×#135—28no—
144C2×C11×Q16C2312yes—
145C2×C11×Q16C2312yes—
146C2×C11×Q16C2312yes—
147C2×C11×SD16C2311yescharacteristic
148C2×C11×SD16C2312yes—
149C2×C11×SD16C2312yes—
150C2×C11×SD16C2311yescharacteristic
151C2×C11×SD16C2312yes—
152C2×C11×D8C2311yescharacteristic
153C2×C11×D8C2311yescharacteristic
154C2×C11×M16C2311yescharacteristic
155C2×C11×M16C2311yescharacteristic
156C22×C8×C11C2312yes—
157C22×C8×C11C2312yes—
158C11×C4⋊Q8C2312yes—
159C11×C4⋊Q8C2311yescharacteristic
160C11×C4⋊Q8C2311yescharacteristic
161C11×C4⋊Q8C2312yes—
162C11×C4⋊Q8C2311yescharacteristic
163C11×C4⋊Q8C2311yescharacteristic
164C11×#126—22no—
165C11×#126—22no—
166C11×#126—22no—
167C11×#126—22no—
168C11×#126—22no—
169C11×#126—22no—
170C11×#125—22no—
171C11×#125—21no—
172C11×#125—22no—
173C11×#125—21no—
174C11×#125—21no—
175C11×#125—22no—
176C11×#125C2312yes—
177C11×#124—22no—
178C11×#124—21no—
179C11×#124—22no—
180C11×#124C2312yes—
181C11×#123—22no—
182C11×#123—22no—
183C11×#123—22no—
184C11×#123—22no—
185C11×#123—22no—
186C11×#123—22no—
187C11×#123—22no—
188C11×C22⋊Q8—21no—
189C11×C22⋊Q8—21no—
190C11×C22⋊Q8—21no—
191C11×C22⋊Q8—21no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—21no—
194C11×C22⋊Q8—22no—
195C11×C22⋊Q8—22no—
196C11×C22⋊Q8C2312yes—
197C11×C22⋊Q8C2312yes—
198C11×C22⋊Q8C2312yes—
199C11×C22⋊Q8C2312yes—
200C11×C22⋊Q8C2312yes—
201C11×#121—21no—
202C11×#121—21no—
203C11×#121—22no—
204C11×#121—21no—
205C11×#121—22no—
206C11×#121C2312yes—
207C11×#120—22no—
208C4×Q8×C11—21no—
209C4×Q8×C11—22no—
210C4×Q8×C11—21no—
211C4×Q8×C11—21no—
212C4×Q8×C11—22no—
213C4×Q8×C11—21no—
214C4×Q8×C11D411yescharacteristic
215C4×Q8×C11C2312yes—
216C4×Q8×C11C2311yescharacteristic
217C4×Q8×C11C2312yes—
218C4×Q8×C11C2311yescharacteristic
219C4×Q8×C11C2312yes—
220C4×Q8×C11C2312yes—
221C4×Q8×C11C2311yescharacteristic
222C4×D4×C11—22no—
223C4×D4×C11—21no—
224C4×D4×C11—21no—
225C4×D4×C11—22no—
226C4×D4×C11—22no—
227C4×D4×C11—22no—
228C4×D4×C11—22no—
229C4×D4×C11—21no—
230C4×D4×C11—21no—
231C4×D4×C11D412yes—
232C4×D4×C11D411yescharacteristic
233C4×D4×C11C2311yescharacteristic
234C4×D4×C11C2311yescharacteristic
235C4×D4×C11C2311yescharacteristic
236C4×D4×C11C2311yescharacteristic
237C4×D4×C11C2311yescharacteristic
238C4×D4×C11C2312yes—
239C4×D4×C11C2311yescharacteristic
240C4×D4×C11C2312yes—
241C4×D4×C11C2312yes—
242C4×D4×C11C2311yescharacteristic
243C11×#117—21no—
244C11×#117—21no—
245C11×#117—22no—
246C11×#117—21no—
247C11×#117—21no—
248C11×#117—22no—
249C11×#117—22no—
250C11×#117—22no—
251C11×#117—21no—
252C11×#117—22no—
253C11×#117D411yescharacteristic
254C11×#117D412yes—
255C11×#117C2312yes—
256C11×#117C2311yescharacteristic
257C11×#117C2312yes—
258C2×C11×C4⋊C4—21no—
259C2×C11×C4⋊C4—21no—
260C2×C11×C4⋊C4—22no—
261C2×C11×C4⋊C4—21no—
262C2×C11×C4⋊C4C2311yescharacteristic
263C2×C11×C22⋊C4—21no—
264C2×C11×C22⋊C4—22no—
265C2×C42×C11—22no—
266C2×C42×C11—21no—
267C2×C42×C11—22no—
268C2×C42×C11C2311yescharacteristic
269C2×C42×C11C2312yes—
270C11×#107C2311yescharacteristic
271C11×#107C2312yes—
272C11×#107C2312yes—
273C11×#107C2312yes—
274C11×#107C2311yescharacteristic
275C11×#106C2312yes—
276C11×#106C2312yes—
277C11×#106C2312yes—
278C11×#106C2311yescharacteristic
279C11×#106C2311yescharacteristic
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2311yescharacteristic
282C11×C4⋊C8C2312yes—
283C11×C4⋊C8C2312yes—
284C11×#103C2312yes—
285C11×#103C2312yes—
286C11×#103C2311yescharacteristic
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2312yes—
291C11×#103C2312yes—
292C11×#103C2311yescharacteristic
293C11×#103C2312yes—
294C11×#103C2312yes—
295C11×#102C2311yescharacteristic
296C11×#102C2312yes—
297C11×#102C2311yescharacteristic
298C11×#102C2312yes—
299C11×#102C2311yescharacteristic
300C11×#102C2312yes—
301C11×#102C2311yescharacteristic
302C11×#102C2311yescharacteristic
303C11×#102C2311yescharacteristic
304C11×C22⋊C8C2312yes—
305C11×C22⋊C8C2312yes—
306C11×C22⋊C8C2312yes—
307C11×#97C2312yes—
308C11×#97C2312yes—
309C11×#97C2311yescharacteristic
310C11×#97C2312yes—
311C11×#97C2311yescharacteristic
312C4×C8×C11C2311yescharacteristic
313C4×C8×C11C2311yescharacteristic
314#61461C1111yesmaximal, characteristic, direct product factor, Sylow
315C24×C11—21no—
316C11×#41—24no—
317C11×#41—24no—
318C11×#41—22no—
319C11×#41—42no—
320C11×#41—42no—
321C11×#41—42no—
322C11×#41—41no—
323C2×Q8×C11—22no—
324C2×Q8×C11—21no—
325C2×Q8×C11—21no—
326C2×Q8×C11—44no—
327C2×Q8×C11C2×D411yescharacteristic
328C2×Q8×C11C2412yes—
329C2×Q8×C11C2411yescharacteristic
330C2×Q8×C11C2412yes—
331C2×D4×C11—22no—
332C2×D4×C11—22no—
333C2×D4×C11—21no—
334C2×D4×C11—22no—
335C2×D4×C11—22no—
336C2×D4×C11—21no—
337C2×D4×C11—41no—
338C2×D4×C11C2×D411yescharacteristic
339C2×D4×C11C2×D412yes—
340C2×D4×C11C2411yescharacteristic
341C2×D4×C11C2411yescharacteristic
342C2×D4×C11C2411yescharacteristic
343C22×C4×C11—21no—
344C22×C4×C11—21no—
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—21no—
352C22×C4×C11—21no—
353C22×C4×C11—21no—
354C22×C4×C11—22no—
355C22×C4×C11—44no—
356C22×C4×C11C2×D411yescharacteristic
357C22×C4×C11C2×D411yescharacteristic
358C22×C4×C11C2×D412yes—
359C22×C4×C11C2×D412yes—
360C22×C4×C11C2411yescharacteristic
361C22×C4×C11C2412yes—
362C11×Q16—24no—
363C11×Q16—42no—
364C11×Q16—42no—
365C11×SD16—22no—
366C11×SD16—24no—
367C11×SD16—24no—
368C11×SD16—22no—
369C11×SD16—42no—
370C11×D8—22no—
371C11×D8#4114yescomplemented
372C11×M16—22no—
373C11×M16—41no—
374C2×C8×C11—24no—
375C2×C8×C11—42no—
376C2×C8×C11C2411yescharacteristic
377C2×C8×C11C2411yescharacteristic
378C2×C8×C11C2411yescharacteristic
379C2×C8×C11C2412yes—
380C2×C8×C11C2412yes—
381C2×C8×C11C2411yescharacteristic
382C11×C4⋊C4—21no—
383C11×C4⋊C4—21no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4—22no—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—21no—
388C11×C4⋊C4—22no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—21no—
392C11×C4⋊C4—21no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—22no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4C2×D411yescharacteristic
406C11×C4⋊C4C2×D411yescharacteristic
407C11×C4⋊C4C2×D412yes—
408C11×C4⋊C4C2×D412yes—
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2411yescharacteristic
411C11×C4⋊C4C2412yes—
412C11×C4⋊C4C2412yes—
413C11×C4⋊C4C2411yescharacteristic
414C11×C4⋊C4C2411yescharacteristic
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—21no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—21no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—21no—
427C11×C22⋊C4—21no—
428C11×C22⋊C4—21no—
429C11×C22⋊C4—21no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—21no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4C2×D412yes—
435C11×C22⋊C4C2×D412yes—
436C11×C22⋊C4C2×D412yes—
437C42×C11—22no—
438C42×C11—22no—
439C42×C11—21no—
440C42×C11—22no—
441C42×C11—22no—
442C42×C11—22no—
443C42×C11—21no—
444C42×C11—22no—
445C42×C11—21no—
446C42×C11C2×D412yes—
447C42×C11C2×D412yes—
448C42×C11C2×D411yescharacteristic
449C42×C11C2×D411yescharacteristic
450C42×C11C2411yescharacteristic
451C42×C11C2411yescharacteristic
452C42×C11C2412yes—
453#3482C2×C1111yescharacteristic, complemented
454#3475C2×C1111yescharacteristic, complemented
455#3398C2×C1111yescharacteristic, complemented
456#3384C2×C1111yescharacteristic, complemented
457#3372C2×C1111yescharacteristic, complemented
458#3367C2×C1111yescharacteristic, complemented
459#3349C2×C1112yescomplemented
460#3340C2×C1111yescharacteristic, complemented
461#3315C2×C1112yescomplemented
462#3311C2×C1112yescomplemented
463#3303C2×C1111yescharacteristic, complemented
464#3302C2×C1111yescharacteristic, complemented
465#3283C2×C1111yescharacteristic, complemented
466#3267C2×C1112yescomplemented
467#3185C2×C1111yescharacteristic, complemented
468#3181C2×C1112yescomplemented
469#3116C2×C1111yescharacteristic, complemented
470#3116C2×C1112yescomplemented
471#3111C2×C1112yescomplemented
472#3110C2×C1111yescharacteristic, complemented
473#2970C2×C1111yescharacteristic, complemented
474C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
475#2943C2×C1112yescomplemented
476C23×C11—21no—
477C23×C11—21no—
478C23×C11—21no—
479C23×C11—42no—
480C23×C11—42no—
481C23×C11—81no—
482C23×C11C22×D411yescharacteristic
483C23×C11C22×D412yes—
484Q8×C11—22no—
485Q8×C11—21no—
486Q8×C11—22no—
487Q8×C11—22no—
488Q8×C11—22no—
489Q8×C11—22no—
490Q8×C11—21no—
491Q8×C11—44no—
492Q8×C11—42no—
493Q8×C11—81no—
494D4×C11—22no—
495D4×C11—21no—
496D4×C11—21no—
497D4×C11—21no—
498D4×C11—21no—
499D4×C11—42no—
500D4×C11—42no—
501D4×C11—44no—
502D4×C11—44no—
503D4×C11—42no—
504D4×C11—82no—
505D4×C11C2×#4112yes—
506D4×C11C2×#4112yes—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—21no—
510C2×C4×C11—22no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—21no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—21no—
518C2×C4×C11—21no—
519C2×C4×C11—22no—
520C2×C4×C11—21no—
521C2×C4×C11—42no—
522C2×C4×C11—41no—
523C2×C4×C11—42no—
524C2×C4×C11—44no—
525C2×C4×C11—44no—
526C2×C4×C11—42no—
527C2×C4×C11—42no—
528C2×C4×C11—42no—
529C2×C4×C11—42no—
530C2×C4×C11—44no—
531C2×C4×C11—42no—
532C2×C4×C11—42no—
533C2×C4×C11—42no—
534C2×C4×C11—42no—
535C2×C4×C11—82no—
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C22×D412yes—
539C2×C4×C11C22×D411yescharacteristic
540C2×C4×C11C22×D412yes—
541C2×C4×C11C22×D412yes—
542C2×C4×C11C22×D411yescharacteristic
543C2×C4×C11C22×D411yescharacteristic
544C2×C4×C11C2511yescharacteristic
545C8×C11—22no—
546C8×C11—21no—
547C8×C11—21no—
548C8×C11—22no—
549C8×C11—21no—
550C8×C11C2×#4112yes—
551C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
552C2×#135C22×C1112yes—
553#557C22×C1111yescharacteristic, complemented
554#556C22×C1111yescharacteristic
555#556C22×C1112yes—
556#556C22×C1111yescharacteristic, complemented
557#555C22×C1111yescharacteristic
558#554C22×C1111yescharacteristic
559#553—21no—
560#552—21no—
561#552—22no—
562#552—21no—
563#552C22×C1112yes—
564#551—22no—
565D4×Q8C22×C1111yescharacteristic, complemented
566#548—21no—
567#547C22×C1111yescharacteristic
568#547C22×C1112yes—
569#547C22×C1111yescharacteristic, complemented
570#546C22×C1112yes—
571#533C22×C1111yescharacteristic
572#533C22×C1111yescharacteristic
573#533C22×C1112yescomplemented
574#529—21no—
575#529—22no—
576#529—22no—
577#529C22×C1112yes—
578#525—21no—
579C4×#41C22×C1112yes—
580C4×#41C22×C1111yescharacteristic
581C4×#41C22×C1111yescharacteristic
582C4×#41C22×C1112yescomplemented
583C2×C4×Q8—21no—
584C2×C4×D4C22×C1111yescharacteristic
585C2×#117—21no—
586#501C22×C1112yescomplemented
587#498C22×C1111yescharacteristic, complemented
588#497C22×C1112yes—
589#494C22×C1111yescharacteristic, complemented
590#491C22×C1112yescomplemented
591#489C22×C1112yes—
592#487C22×C1111yescharacteristic, complemented
593#487C22×C1111yescharacteristic, complemented
594#485C22×C1112yes—
595#485C22×C1112yescomplemented
596#485C22×C1112yescomplemented
597#485C22×C1112yescomplemented
598#484C22×C1112yes—
599#482C22×C1112yes—
600#479C22×C1112yescomplemented
601#478C22×C1112yescomplemented
602#477C22×C1111yescharacteristic, complemented
603#477C22×C1112yescomplemented
604#476C22×C1112yes—
605#476C22×C1111yescharacteristic, complemented
606#474C22×C1111yescharacteristic
607#474C22×C1111yescharacteristic
608#470C22×C1112yes—
609#470C22×C1112yes—
610#467C22×C1112yescomplemented
611#467C22×C1112yescomplemented
612#465C22×C1112yes—
613#465C22×C1112yes—
614#464C22×C1112yes—
615#463C22×C1112yes—
616#462C22×C1111yescharacteristic, complemented
617#462C22×C1112yescomplemented
618#461C22×C1111yescharacteristic
619#461C22×C1111yescharacteristic
620#461C22×C1112yes—
621#461C22×C1111yescharacteristic, complemented
622#452C22×C1112yes—
623#452C22×C1112yes—
624#452C22×C1112yes—
625#452C22×C1112yescomplemented
626#450C22×C1112yes—
627#449C22×C1112yes—
628#446C22×C1111yescharacteristic, complemented
629#446C22×C1111yescharacteristic, complemented
630#442C22×C1111yescharacteristic
631#442C22×C1112yes—
632#442C22×C1111yescharacteristic
633#441C22×C1112yescomplemented
634#441C22×C1112yescomplemented
635#441C22×C1112yescomplemented
636#441C22×C1112yescomplemented
637#440C22×C1112yes—
638#440C22×C1112yes—
639#440C22×C1111yescharacteristic
640#440C22×C1112yes—
641#440C22×C1111yescharacteristic
642#440C22×C1112yescomplemented
643#440C22×C1112yescomplemented
644C4×SD16C22×C1111yescharacteristic
645C4×SD16C22×C1111yescharacteristic
646C4×D8C22×C1111yescharacteristic
647C4×D8C22×C1111yescharacteristic
648#435C22×C1112yes—
649#435C22×C1112yes—
650C8×D4C22×C1111yescharacteristic, complemented
651C8×D4C22×C1111yescharacteristic, complemented
652#432C22×C1111yescharacteristic
653#432C22×C1112yescomplemented
654#428C22×C1111yescharacteristic
655#427C22×C1112yescomplemented
656#418C22×C1111yescharacteristic
657#417C22×C1111yescharacteristic
658#416C22×C1112yes—
659#416C22×C1112yescomplemented
660C4×M16C22×C1111yescharacteristic
661C2×#97C22×C1112yescomplemented
662C22×C11—22no—
663C22×C11—21no—
664C22×C11—22no—
665C22×C11—21no—
666C22×C11—22no—
667C22×C11—22no—
668C22×C11—21no—
669C22×C11—22no—
670C22×C11—41no—
671C22×C11—41no—
672C22×C11—41no—
673C22×C11—41no—
674C22×C11—41no—
675C22×C11—41no—
676C22×C11—41no—
677C22×C11—84no—
678C22×C11C23×D411yescharacteristic
679C4×C11—21no—
680C4×C11—22no—
681C4×C11—21no—
682C4×C11—22no—
683C4×C11—21no—
684C4×C11—21no—
685C4×C11—22no—
686C4×C11—41no—
687C4×C11—42no—
688C4×C11—42no—
689C4×C11—41no—
690C4×C11—42no—
691C4×C11—41no—
692C4×C11—41no—
693C4×C11—42no—
694C4×C11—41no—
695C4×C11#57512yes—
696C4×C11C22×#4111yescharacteristic
697C4×C11#58511yescharacteristic
698C2×#41D4×C1111yescharacteristic
699C2×#41C23×C1112yes—
700C2×#41C23×C1111yescharacteristic
701C2×#41C23×C1112yes—
702C22×Q8—21no—
703C22×D4C23×C1111yescharacteristic
704C23×C4—21no—
705AGL(1,ℤ/8)—24no—
706#135—28no—
707C2×Q16C23×C1112yes—
708C2×Q16C23×C1112yes—
709C2×Q16C23×C1112yes—
710C2×SD16C23×C1112yes—
711C2×SD16C23×C1112yes—
712C2×SD16C23×C1111yescharacteristic
713C2×SD16C23×C1111yescharacteristic
714C2×SD16C23×C1112yes—
715C2×D8C23×C1111yescharacteristic
716C2×D8C23×C1111yescharacteristic
717C2×M16C23×C1111yescharacteristic
718C2×M16C23×C1111yescharacteristic
719C22×C8C23×C1112yes—
720C22×C8C23×C1112yes—
721C4⋊Q8C23×C1111yescharacteristic
722C4⋊Q8C23×C1111yescharacteristic
723C4⋊Q8C23×C1112yes—
724C4⋊Q8C23×C1111yescharacteristic
725C4⋊Q8C23×C1111yescharacteristic
726C4⋊Q8C23×C1112yes—
727#126—22no—
728#126—22no—
729#126—22no—
730#126—22no—
731#126—22no—
732#126—22no—
733#125—22no—
734#125—21no—
735#125—22no—
736#125—21no—
737#125—21no—
738#125—22no—
739#125C23×C1112yes—
740#124—22no—
741#124—21no—
742#124—22no—
743#124C23×C1112yes—
744#123—22no—
745#123—22no—
746#123—22no—
747#123—22no—
748#123—22no—
749#123—22no—
750#123—22no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8—21no—
754C22⋊Q8—21no—
755C22⋊Q8—22no—
756C22⋊Q8—21no—
757C22⋊Q8—22no—
758C22⋊Q8—22no—
759C22⋊Q8C23×C1112yes—
760C22⋊Q8C23×C1112yes—
761C22⋊Q8C23×C1112yes—
762C22⋊Q8C23×C1112yes—
763C22⋊Q8C23×C1112yes—
764#121—21no—
765#121—21no—
766#121—22no—
767#121—21no—
768#121—22no—
769#121C23×C1112yes—
770#120—22no—
771C4×Q8—21no—
772C4×Q8—22no—
773C4×Q8—21no—
774C4×Q8—21no—
775C4×Q8—22no—
776C4×Q8—21no—
777C4×Q8D4×C1111yescharacteristic
778C4×Q8C23×C1112yes—
779C4×Q8C23×C1111yescharacteristic
780C4×Q8C23×C1112yes—
781C4×Q8C23×C1111yescharacteristic
782C4×Q8C23×C1112yes—
783C4×Q8C23×C1112yes—
784C4×Q8C23×C1111yescharacteristic
785C4×D4—22no—
786C4×D4—21no—
787C4×D4—21no—
788C4×D4—22no—
789C4×D4—22no—
790C4×D4—22no—
791C4×D4—22no—
792C4×D4—21no—
793C4×D4—21no—
794C4×D4D4×C1112yes—
795C4×D4D4×C1111yescharacteristic
796C4×D4C23×C1111yescharacteristic
797C4×D4C23×C1111yescharacteristic
798C4×D4C23×C1111yescharacteristic
799C4×D4C23×C1111yescharacteristic
800C4×D4C23×C1111yescharacteristic
801C4×D4C23×C1112yes—
802C4×D4C23×C1111yescharacteristic
803C4×D4C23×C1112yes—
804C4×D4C23×C1112yes—
805C4×D4C23×C1111yescharacteristic
806#117—21no—
807#117—21no—
808#117—22no—
809#117—21no—
810#117—21no—
811#117—22no—
812#117—22no—
813#117—22no—
814#117—21no—
815#117—22no—
816#117D4×C1111yescharacteristic
817#117D4×C1112yes—
818#117C23×C1112yes—
819#117C23×C1111yescharacteristic
820#117C23×C1112yes—
821C2×C4⋊C4—21no—
822C2×C4⋊C4—21no—
823C2×C4⋊C4—22no—
824C2×C4⋊C4—21no—
825C2×C4⋊C4C23×C1111yescharacteristic
826C2×C22⋊C4—21no—
827C2×C22⋊C4—22no—
828C2×C42—22no—
829C2×C42—21no—
830C2×C42—22no—
831C2×C42C23×C1111yescharacteristic
832C2×C42C23×C1112yes—
833#107C23×C1112yes—
834#107C23×C1112yes—
835#107C23×C1111yescharacteristic
836#107C23×C1111yescharacteristic
837#107C23×C1112yes—
838#106C23×C1111yescharacteristic
839#106C23×C1112yes—
840#106C23×C1111yescharacteristic
841#106C23×C1112yes—
842#106C23×C1112yes—
843C4⋊C8C23×C1111yescharacteristic
844C4⋊C8C23×C1111yescharacteristic
845C4⋊C8C23×C1112yes—
846C4⋊C8C23×C1112yes—
847#103C23×C1112yes—
848#103C23×C1112yes—
849#103C23×C1112yes—
850#103C23×C1112yes—
851#103C23×C1111yescharacteristic
852#103C23×C1111yescharacteristic
853#103C23×C1112yes—
854#103C23×C1112yes—
855#103C23×C1112yes—
856#103C23×C1112yes—
857#103C23×C1112yes—
858#102C23×C1111yescharacteristic
859#102C23×C1112yes—
860#102C23×C1111yescharacteristic
861#102C23×C1112yes—
862#102C23×C1111yescharacteristic
863#102C23×C1111yescharacteristic
864#102C23×C1111yescharacteristic
865#102C23×C1111yescharacteristic
866#102C23×C1112yes—
867C22⋊C8C23×C1112yes—
868C22⋊C8C23×C1112yes—
869C22⋊C8C23×C1112yes—
870#97C23×C1111yescharacteristic
871#97C23×C1112yes—
872#97C23×C1112yes—
873#97C23×C1112yes—
874#97C23×C1111yescharacteristic
875C4×C8C23×C1111yescharacteristic
876C4×C8C23×C1111yescharacteristic
877C2×C11—42no—
878C2×C11—41no—
879C2×C11—42no—
880C2×C11—42no—
881C2×C11—81no—
882C2×C11D4×#4111yescharacteristic
883C2×C11C2×#57511yescharacteristic
884C2×C11#358611yescharacteristic
885C24—21no—
886#41—24no—
887#41—24no—
888#41—22no—
889#41—42no—
890#41—42no—
891#41—42no—
892#41—41no—
893C2×Q8—22no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—44no—
897C2×Q8C2×D4×C1111yescharacteristic
898C2×Q8C24×C1112yes—
899C2×Q8C24×C1111yescharacteristic
900C2×Q8C24×C1112yes—
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—21no—
904C2×D4—22no—
905C2×D4—22no—
906C2×D4—21no—
907C2×D4—41no—
908C2×D4C2×D4×C1111yescharacteristic
909C2×D4C2×D4×C1112yes—
910C2×D4C24×C1111yescharacteristic
911C2×D4C24×C1111yescharacteristic
912C2×D4C24×C1111yescharacteristic
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—22no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—22no—
925C22×C4—44no—
926C22×C4C2×D4×C1111yescharacteristic
927C22×C4C2×D4×C1111yescharacteristic
928C22×C4C2×D4×C1112yes—
929C22×C4C2×D4×C1112yes—
930C22×C4C24×C1111yescharacteristic
931C22×C4C24×C1112yes—
932Q16—24no—
933Q16—42no—
934Q16—42no—
935SD16—24no—
936SD16—24no—
937SD16—22no—
938SD16—22no—
939SD16—42no—
940D8—22no—
941D8C11×#4114yescomplemented
942M16—22no—
943M16—41no—
944C2×C8—24no—
945C2×C8—42no—
946C2×C8C24×C1111yescharacteristic
947C2×C8C24×C1111yescharacteristic
948C2×C8C24×C1111yescharacteristic
949C2×C8C24×C1112yes—
950C2×C8C24×C1112yes—
951C2×C8C24×C1111yescharacteristic
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—21no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—21no—
968C4⋊C4—22no—
969C4⋊C4—21no—
970C4⋊C4—22no—
971C4⋊C4—21no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—21no—
975C4⋊C4C2×D4×C1111yescharacteristic
976C4⋊C4C2×D4×C1111yescharacteristic
977C4⋊C4C2×D4×C1112yes—
978C4⋊C4C2×D4×C1112yes—
979C4⋊C4C24×C1111yescharacteristic
980C4⋊C4C24×C1112yes—
981C4⋊C4C24×C1111yescharacteristic
982C4⋊C4C24×C1112yes—
983C4⋊C4C24×C1111yescharacteristic
984C4⋊C4C24×C1111yescharacteristic
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—21no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—21no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—21no—
997C22⋊C4—21no—
998C22⋊C4—21no—
999C22⋊C4—21no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—21no—
1003C22⋊C4—22no—
1004C22⋊C4C2×D4×C1112yes—
1005C22⋊C4C2×D4×C1112yes—
1006C22⋊C4C2×D4×C1112yes—
1007C42—22no—
1008C42—22no—
1009C42—21no—
1010C42—22no—
1011C42—22no—
1012C42—22no—
1013C42—21no—
1014C42—22no—
1015C42—21no—
1016C42C2×D4×C1112yes—
1017C42C2×D4×C1112yes—
1018C42C2×D4×C1111yescharacteristic
1019C42C2×D4×C1111yescharacteristic
1020C42C24×C1111yescharacteristic
1021C42C24×C1111yescharacteristic
1022C42C24×C1112yes—
1023C11#6146111yescharacteristic, direct product factor, Sylow
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—42no—
1028C23—42no—
1029C23—81no—
1030C23C22×D4×C1111yescharacteristic
1031C23C22×D4×C1112yes—
1032Q8—22no—
1033Q8—21no—
1034Q8—22no—
1035Q8—22no—
1036Q8—22no—
1037Q8—22no—
1038Q8—21no—
1039Q8—44no—
1040Q8—42no—
1041Q8—81no—
1042D4—22no—
1043D4—21no—
1044D4—21no—
1045D4—21no—
1046D4—21no—
1047D4—42no—
1048D4—42no—
1049D4—44no—
1050D4—44no—
1051D4—42no—
1052D4—82no—
1053D4C2×C11×#4112yes—
1054D4C2×C11×#4112yes—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—42no—
1070C2×C4—41no—
1071C2×C4—42no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—42no—
1075C2×C4—42no—
1076C2×C4—42no—
1077C2×C4—42no—
1078C2×C4—44no—
1079C2×C4—42no—
1080C2×C4—42no—
1081C2×C4—42no—
1082C2×C4—42no—
1083C2×C4—82no—
1084C2×C4C22×D4×C1111yescharacteristic
1085C2×C4C22×D4×C1111yescharacteristic
1086C2×C4C22×D4×C1112yes—
1087C2×C4C22×D4×C1111yescharacteristic
1088C2×C4C22×D4×C1112yes—
1089C2×C4C22×D4×C1112yes—
1090C2×C4C22×D4×C1111yescharacteristic
1091C2×C4C22×D4×C1111yescharacteristic
1092C2×C4C25×C1111yescharacteristic
1093C8—22no—
1094C8—21no—
1095C8—21no—
1096C8—22no—
1097C8—21no—
1098C8C2×C11×#4112yes—
1099C22—22no—
1100C22—21no—
1101C22—22no—
1102C22—22no—
1103C22—21no—
1104C22—22no—
1105C22—22no—
1106C22—21no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22—41no—
1114C22—84no—
1115C22C23×D4×C1111yescharacteristic
1116C4—22no—
1117C4—21no—
1118C4—21no—
1119C4—22no—
1120C4—21no—
1121C4—22no—
1122C4—21no—
1123C4—42no—
1124C4—41no—
1125C4—42no—
1126C4—41no—
1127C4—41no—
1128C4—42no—
1129C4—41no—
1130C4—41no—
1131C4—42no—
1132C4C11×#57512yes—
1133C4C22×C11×#4111yescharacteristic
1134C4C11×#58511yescharacteristic
1135C2—41no—
1136C2—42no—
1137C2—42no—
1138C2—42no—
1139C2—81no—
1140C2D4×C11×#4111yescharacteristic
1141C2C2×C11×#57511yescharacteristic
1142C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3482C2semidirect
2. C11×#3475C2semidirect
3. C11×#3398C2semidirect
4. C11×#3384C2semidirect
5. C11×#3372C2semidirect
6. C11×#3367C2semidirect
7. C11×#3349C2semidirect
8. C11×#3340C2semidirect
9. C11×#3315C2semidirect
10. C11×#3311C2semidirect
11. C11×#3303C2semidirect
12. C11×#3302C2semidirect
13. C11×#3283C2semidirect
14. C11×#3267C2semidirect
15. C11×#3185C2semidirect
16. C11×#3181C2semidirect
17. C11×#3116C2semidirect
18. C11×#3116C2semidirect
19. C11×#3111C2semidirect
20. C11×#3110C2semidirect
21. C11×#2970C2semidirect
22. C4×C11×AGL(1,ℤ/8)C2semidirect
23. C11×#2943C2semidirect
26. C11×#557C22semidirect
29. C11×#556C22semidirect
38. D4×Q8×C11C22semidirect
42. C11×#547C22semidirect
46. C11×#533C22semidirect
55. C4×C11×#41C22semidirect
59. C11×#501C22semidirect
60. C11×#498C22semidirect
62. C11×#494C22semidirect
63. C11×#491C22semidirect
65. C11×#487C22semidirect
66. C11×#487C22semidirect
68. C11×#485C22semidirect
69. C11×#485C22semidirect
70. C11×#485C22semidirect
73. C11×#479C22semidirect
74. C11×#478C22semidirect
75. C11×#477C22semidirect
76. C11×#477C22semidirect
78. C11×#476C22semidirect
83. C11×#467C22semidirect
84. C11×#467C22semidirect
89. C11×#462C22semidirect
90. C11×#462C22semidirect
94. C11×#461C22semidirect
98. C11×#452C22semidirect
101. C11×#446C22semidirect
102. C11×#446C22semidirect
106. C11×#441C22semidirect
107. C11×#441C22semidirect
108. C11×#441C22semidirect
109. C11×#441C22semidirect
115. C11×#440C22semidirect
116. C11×#440C22semidirect
123. C8×D4×C11C22semidirect
124. C8×D4×C11C22semidirect
126. C11×#432C22semidirect
128. C11×#427C22semidirect
132. C11×#416C22semidirect
134. C2×C11×#97C22semidirect
314. #61461C11direct (N × H)
371. C11×D8#41semidirect
453. #3482C2×C11semidirect
454. #3475C2×C11semidirect
455. #3398C2×C11semidirect
456. #3384C2×C11semidirect
457. #3372C2×C11semidirect
458. #3367C2×C11semidirect
459. #3349C2×C11semidirect
460. #3340C2×C11semidirect
461. #3315C2×C11semidirect
462. #3311C2×C11semidirect
463. #3303C2×C11semidirect
464. #3302C2×C11semidirect
465. #3283C2×C11semidirect
466. #3267C2×C11semidirect
467. #3185C2×C11semidirect
468. #3181C2×C11semidirect
469. #3116C2×C11semidirect
470. #3116C2×C11semidirect
471. #3111C2×C11semidirect
472. #3110C2×C11semidirect
473. #2970C2×C11semidirect
474. C4×AGL(1,ℤ/8)C2×C11semidirect
475. #2943C2×C11semidirect
553. #557C22×C11semidirect
556. #556C22×C11semidirect
565. D4×Q8C22×C11semidirect
569. #547C22×C11semidirect
573. #533C22×C11semidirect
582. C4×#41C22×C11semidirect
586. #501C22×C11semidirect
587. #498C22×C11semidirect
589. #494C22×C11semidirect
590. #491C22×C11semidirect
592. #487C22×C11semidirect
593. #487C22×C11semidirect
595. #485C22×C11semidirect
596. #485C22×C11semidirect
597. #485C22×C11semidirect
600. #479C22×C11semidirect
601. #478C22×C11semidirect
602. #477C22×C11semidirect
603. #477C22×C11semidirect
605. #476C22×C11semidirect
610. #467C22×C11semidirect
611. #467C22×C11semidirect
616. #462C22×C11semidirect
617. #462C22×C11semidirect
621. #461C22×C11semidirect
625. #452C22×C11semidirect
628. #446C22×C11semidirect
629. #446C22×C11semidirect
633. #441C22×C11semidirect
634. #441C22×C11semidirect
635. #441C22×C11semidirect
636. #441C22×C11semidirect
642. #440C22×C11semidirect
643. #440C22×C11semidirect
650. C8×D4C22×C11semidirect
651. C8×D4C22×C11semidirect
653. #432C22×C11semidirect
655. #427C22×C11semidirect
659. #416C22×C11semidirect
661. C2×#97C22×C11semidirect
941. D8C11×#41semidirect
1023. C11#61461direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34822
C11×#34752
C11×#33982
C11×#33842
C11×#33722
C11×#33672
C11×#33492
C11×#33402
C11×#33152
C11×#33112
C11×#33032
C11×#33022
C11×#32832
C11×#32672
C11×#31852
C11×#31812
C11×#31162
C11×#31112
C11×#31102
C11×#29702
C4×C11×AGL(1,ℤ/8)2
C11×#29432
#6146111