Finite Group Databasebeta

← C11×#60702 #14637895

Subgroups — C11×#60702 #14637895

Order 2816.

2008 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3444C211yesmaximal, characteristic, complemented
2C2×C11×#529C211yesmaximal, characteristic, complemented
3C11×#3183C214yesmaximal, complemented
4C11×#3181C212yesmaximal, complemented
5C11×#3180C212yesmaximal, complemented
6C11×#3172C212yesmaximal, complemented
7C11×#3171C212yesmaximal, complemented
8C11×#3168C214yesmaximal, complemented
9C11×#3166C211yesmaximal, characteristic, complemented
10C11×#3153C211yesmaximal, characteristic, complemented
11C11×#3142C211yesmaximal, characteristic, complemented
12C11×#3140C211yesmaximal, characteristic, complemented
13C11×#3056C212yesmaximal, complemented
14C11×#3055C212yesmaximal, complemented
15C4×C11×#137C212yesmaximal, complemented
16C4×C11×AGL(1,ℤ/8)C212yesmaximal, complemented
17C2×C4×C11×M16C211yesmaximal, characteristic, complemented
18C2×C11×#137C2212yes—
19C2×C11×AGL(1,ℤ/8)C2212yes—
20C22×C11×M16C2212yes—
21C11×#533C2211yescharacteristic
22C11×#533C2211yescharacteristic, complemented
23C11×#533C2211yescharacteristic, complemented
24C11×#532C2211yescharacteristic
25C11×#532C2211yescharacteristic, complemented
26C11×#532C2211yescharacteristic, complemented
27C11×#529—21no—
28C11×#529—21no—
29C11×#529—21no—
30C11×#529—21no—
31C11×#529—21no—
32C11×#529—21no—
33C11×#529—21no—
34C11×#529—21no—
35C11×#529C2212yes—
36C11×#529C2212yes—
37C11×#529C2212yes—
38C11×#529C2212yes—
39C11×#529C2212yescomplemented
40C11×#529C2212yescomplemented
41C2×C11×#126—21no—
42C2×C11×#125C2211yescharacteristic
43C2×C11×#124C2211yescharacteristic
44C11×#525—21no—
45C11×#525—21no—
46C11×#525C2212yes—
47C2×C11×#123—21no—
48C2×C11×C22⋊Q8C2211yescharacteristic
49C2×C11×#121C2211yescharacteristic
50C4×C11×#41—21no—
51C4×C11×#41—21no—
52C4×C11×#41C2212yes—
53C2×C4×Q8×C11C2211yescharacteristic
54C2×C4×D4×C11—21no—
55C2×C4×D4×C11C2211yescharacteristic
56C2×C11×#117—21no—
57C22×C42×C11C2211yescharacteristic
58C11×#501C2212yescomplemented
59C11×#501C2212yescomplemented
60C11×#499C2214yescomplemented
61C11×#497C2212yescomplemented
62C11×#496C2212yescomplemented
63C11×#495C2214yescomplemented
64C11×#491C2212yescomplemented
65C11×#490C2212yescomplemented
66C11×#489C2212yescomplemented
67C11×#489C2212yescomplemented
68C11×#488C2214yescomplemented
69C11×#488C2214yescomplemented
70C11×#470C2214yescomplemented
71C11×#469C2214yes—
72C11×#468C2214yes—
73C11×#468C2214yescomplemented
74C11×#467C2214yescomplemented
75C11×#466C2214yes—
76C11×#465C2214yes—
77C11×#465C2214yescomplemented
78C11×#442C2214yescomplemented
79C11×#441C2214yescomplemented
80C11×#440C2214yescomplemented
81C11×#440C2214yescomplemented
82C4×C11×Q16C2214yescomplemented
83C4×C11×SD16C2214yescomplemented
84C4×C11×SD16C2214yescomplemented
85C4×C11×D8C2214yescomplemented
86C11×#428C2212yes—
87C11×#428C2212yes—
88C11×#419C2212yes—
89C11×#418C2212yes—
90C11×#417C2212yes—
91C11×#417C2212yes—
92C4×C11×M16C2211yescharacteristic
93C4×C11×M16C2212yes—
94C4×C11×M16C2211yescharacteristic
95C4×C11×M16C2212yescomplemented
96C4×C11×M16C2212yescomplemented
97C2×C11×#97C2212yescomplemented
98C2×C4×C8×C11C2212yescomplemented
99C2×C11×#41—21no—
100C2×C11×#41—21no—
101C2×C11×#41C2312yes—
102C22×Q8×C11C2311yescharacteristic
103C22×D4×C11—21no—
104C22×D4×C11C2311yescharacteristic
105C23×C4×C11—21no—
106C23×C4×C11D411yescharacteristic
107C23×C4×C11D411yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C11×#137—28no—
110C11×AGL(1,ℤ/8)—28no—
111C2×C11×Q16C2314yes—
112C2×C11×SD16C2314yes—
113C2×C11×SD16C2314yes—
114C2×C11×D8C2314yes—
115C2×C11×M16—28no—
116C2×C11×M16C2312yes—
117C2×C11×M16C2314yes—
118C2×C11×M16C2312yes—
119C22×C8×C11C2314yes—
120C11×C4⋊Q8C2311yescharacteristic
121C11×C4⋊Q8C2311yescharacteristic
122C11×C4⋊Q8C2311yescharacteristic
123C11×#127C2311yescharacteristic
124C11×#126—22no—
125C11×#126—22no—
126C11×#126—22no—
127C11×#126—22no—
128C11×#126—22no—
129C11×#126—22no—
130C11×#125—21no—
131C11×#125—21no—
132C11×#125—21no—
133C11×#125—21no—
134C11×#125C2312yes—
135C11×#125C2312yes—
136C11×#125C2312yes—
137C11×#124—21no—
138C11×#124—21no—
139C11×#124—21no—
140C11×#124—21no—
141C11×#124C2312yes—
142C11×#124C2312yes—
143C11×#124C2312yes—
144C11×#123—22no—
145C11×#123—22no—
146C11×#123—22no—
147C11×#123—22no—
148C11×#123—22no—
149C11×#123—22no—
150C11×#123—22no—
151C11×C22⋊Q8—21no—
152C11×C22⋊Q8—21no—
153C11×C22⋊Q8—21no—
154C11×C22⋊Q8—21no—
155C11×C22⋊Q8—21no—
156C11×C22⋊Q8—21no—
157C11×C22⋊Q8C2312yes—
158C11×C22⋊Q8C2312yes—
159C11×C22⋊Q8C2312yes—
160C11×C22⋊Q8C2312yes—
161C11×#121—21no—
162C11×#121—21no—
163C11×#121—21no—
164C11×#121—21no—
165C11×#121—21no—
166C11×#121—21no—
167C11×#121C2312yes—
168C11×#121C2312yes—
169C11×#121C2312yes—
170C11×#121C2312yes—
171C11×#120—22no—
172C4×Q8×C11—21no—
173C4×Q8×C11—21no—
174C4×Q8×C11—21no—
175C4×Q8×C11—21no—
176C4×Q8×C11—21no—
177C4×Q8×C11—21no—
178C4×Q8×C11C2312yes—
179C4×Q8×C11C2312yes—
180C4×Q8×C11C2312yes—
181C4×Q8×C11C2312yes—
182C4×D4×C11—22no—
183C4×D4×C11—22no—
184C4×D4×C11—22no—
185C4×D4×C11—22no—
186C4×D4×C11—22no—
187C4×D4×C11—22no—
188C4×D4×C11—22no—
189C4×D4×C11—22no—
190C4×D4×C11—22no—
191C4×D4×C11—22no—
192C4×D4×C11—21no—
193C4×D4×C11—21no—
194C4×D4×C11—21no—
195C4×D4×C11—21no—
196C4×D4×C11—21no—
197C4×D4×C11—21no—
198C4×D4×C11C2312yes—
199C4×D4×C11C2312yes—
200C4×D4×C11C2312yes—
201C4×D4×C11C2312yes—
202C11×#117—21no—
203C11×#117—21no—
204C11×#117—22no—
205C11×#117—22no—
206C11×#117—22no—
207C11×#117—22no—
208C11×#117—22no—
209C11×#117—22no—
210C11×#117—22no—
211C11×#117C2312yes—
212C2×C11×C4⋊C4—21no—
213C2×C11×C4⋊C4—21no—
214C2×C11×C4⋊C4—21no—
215C2×C11×C4⋊C4—21no—
216C2×C11×C4⋊C4C2311yescharacteristic
217C2×C11×C4⋊C4C2311yescharacteristic
218C2×C11×C22⋊C4—21no—
219C2×C11×C22⋊C4—21no—
220C2×C11×C22⋊C4—21no—
221C2×C11×C22⋊C4—21no—
222C2×C11×C22⋊C4—21no—
223C2×C42×C11—21no—
224C2×C42×C11—22no—
225C2×C42×C11D411yescharacteristic
226C2×C42×C11D411yescharacteristic
227C2×C42×C11D411yescharacteristic
228C2×C42×C11D411yescharacteristic
229C2×C42×C11D411yescharacteristic
230C2×C42×C11D411yescharacteristic
231C2×C42×C11C2311yescharacteristic
232C2×C42×C11C2311yescharacteristic
233C2×C42×C11C2311yescharacteristic
234C2×C42×C11C2311yescharacteristic
235C2×C42×C11C2311yescharacteristic
236C2×C42×C11C2311yescharacteristic
237C11×#107C2314yes—
238C11×#107C2314yes—
239C11×#106C2314yes—
240C11×#106C2314yes—
241C11×#103C2314yes—
242C11×#103C2314yes—
243C11×#103C2314yes—
244C11×#103C2314yes—
245C11×#102C2314yes—
246C11×#102C2314yes—
247C11×#102C2314yes—
248C11×#102C2314yes—
249C11×#97C2312yes—
250C11×#97C2312yes—
251C11×#97C2314yes—
252C4×C8×C11C2312yes—
253C4×C8×C11C2314yes—
254C4×C8×C11C2312yes—
255#60702C1111yesmaximal, characteristic, direct product factor, Sylow
256C24×C11—21no—
257C24×C11C2×D411yescharacteristic
258C11×#41—24no—
259C11×#41—24no—
260C11×#41—44no—
261C11×#41—44no—
262C2×Q8×C11—21no—
263C2×Q8×C11—21no—
264C2×Q8×C11—21no—
265C2×Q8×C11—24no—
266C2×Q8×C11C2412yes—
267C2×Q8×C11C2412yes—
268C2×D4×C11—22no—
269C2×D4×C11—22no—
270C2×D4×C11—22no—
271C2×D4×C11—22no—
272C2×D4×C11—22no—
273C2×D4×C11—21no—
274C2×D4×C11—21no—
275C2×D4×C11—21no—
276C2×D4×C11—24no—
277C2×D4×C11—44no—
278C2×D4×C11C2412yes—
279C2×D4×C11C2412yes—
280C22×C4×C11—24no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11—44no—
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2×D411yescharacteristic
299C22×C4×C11C2×D411yescharacteristic
300C22×C4×C11C2×D411yescharacteristic
301C22×C4×C11C2×D411yescharacteristic
302C22×C4×C11C2×D411yescharacteristic
303C22×C4×C11C2×D411yescharacteristic
304C22×C4×C11C2×D411yescharacteristic
305C22×C4×C11C2×D411yescharacteristic
306C22×C4×C11C2×D411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2411yescharacteristic
310C11×Q16—28no—
311C11×SD16—28no—
312C11×SD16—28no—
313C11×D8—28no—
314C11×M16—28no—
315C11×M16—24no—
316C11×M16#4118yescomplemented
317C2×C8×C11—28no—
318C2×C8×C11C2414yes—
319C2×C8×C11C2414yes—
320C11×C4⋊C4—22no—
321C11×C4⋊C4—22no—
322C11×C4⋊C4—22no—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—22no—
327C11×C4⋊C4—22no—
328C11×C4⋊C4—21no—
329C11×C4⋊C4—21no—
330C11×C4⋊C4—21no—
331C11×C4⋊C4—21no—
332C11×C4⋊C4—21no—
333C11×C4⋊C4—21no—
334C11×C4⋊C4—22no—
335C11×C4⋊C4—22no—
336C11×C4⋊C4—22no—
337C11×C4⋊C4—22no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—22no—
340C11×C4⋊C4C2412yes—
341C11×C4⋊C4C2412yes—
342C11×C4⋊C4C2412yes—
343C11×C4⋊C4C2412yes—
344C11×C22⋊C4—22no—
345C11×C22⋊C4—22no—
346C11×C22⋊C4—22no—
347C11×C22⋊C4—22no—
348C11×C22⋊C4—22no—
349C11×C22⋊C4—22no—
350C11×C22⋊C4—22no—
351C11×C22⋊C4—22no—
352C11×C22⋊C4—22no—
353C11×C22⋊C4—22no—
354C11×C22⋊C4—22no—
355C11×C22⋊C4—22no—
356C11×C22⋊C4—22no—
357C11×C22⋊C4—22no—
358C11×C22⋊C4—22no—
359C11×C22⋊C4—22no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—22no—
363C42×C11—22no—
364C42×C11—22no—
365C42×C11—22no—
366C42×C11—22no—
367C42×C11—22no—
368C42×C11C2×D411yescharacteristic
369C42×C11C2×D411yescharacteristic
370C42×C11C2×D411yescharacteristic
371C42×C11C2×D411yescharacteristic
372C42×C11C2×D411yescharacteristic
373C42×C11C2×D411yescharacteristic
374C42×C11C2×D411yescharacteristic
375C42×C11C2×D411yescharacteristic
376C42×C11C2×D411yescharacteristic
377C42×C11C2×D411yescharacteristic
378C42×C11C2×D411yescharacteristic
379C42×C11C2×D411yescharacteristic
380C42×C11C2411yescharacteristic
381C42×C11C2411yescharacteristic
382C42×C11C2411yescharacteristic
383C42×C11C2411yescharacteristic
384#3444C2×C1111yescharacteristic, complemented
385C2×#529C2×C1111yescharacteristic, complemented
386#3183C2×C1114yescomplemented
387#3181C2×C1112yescomplemented
388#3180C2×C1112yescomplemented
389#3172C2×C1112yescomplemented
390#3171C2×C1112yescomplemented
391#3168C2×C1114yescomplemented
392#3166C2×C1111yescharacteristic, complemented
393#3153C2×C1111yescharacteristic, complemented
394#3142C2×C1111yescharacteristic, complemented
395#3140C2×C1111yescharacteristic, complemented
396#3056C2×C1112yescomplemented
397#3055C2×C1112yescomplemented
398C4×#137C2×C1112yescomplemented
399C4×AGL(1,ℤ/8)C2×C1112yescomplemented
400C2×C4×M16C2×C1111yescharacteristic, complemented
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—41no—
406C23×C11—42no—
407C23×C11—42no—
408C23×C11—42no—
409C23×C11C22×D411yescharacteristic
410C23×C11C22×D411yescharacteristic
411C23×C11C22×D411yescharacteristic
412Q8×C11—22no—
413Q8×C11—24no—
414Q8×C11—22no—
415Q8×C11—42no—
416Q8×C11—42no—
417Q8×C11—42no—
418D4×C11—22no—
419D4×C11—24no—
420D4×C11—22no—
421D4×C11—42no—
422D4×C11—42no—
423D4×C11—44no—
424D4×C11—44no—
425D4×C11—44no—
426D4×C11—44no—
427D4×C11—44no—
428D4×C11—42no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—44no—
453C2×C4×C11—44no—
454C2×C4×C11—42no—
455C2×C4×C11—42no—
456C2×C4×C11—42no—
457C2×C4×C11—44no—
458C2×C4×C11—44no—
459C2×C4×C11—44no—
460C2×C4×C11C22×D411yescharacteristic
461C2×C4×C11C22×D411yescharacteristic
462C2×C4×C11C22×D411yescharacteristic
463C2×C4×C11C22×D411yescharacteristic
464C2×C4×C11C22×D411yescharacteristic
465C2×C4×C11C22×D411yescharacteristic
466C2×C4×C11C22×D411yescharacteristic
467C2×C4×C11C22×D411yescharacteristic
468C2×C4×C11C22×D411yescharacteristic
469C2×C4×C11C22×D411yescharacteristic
470C2×C4×C11C22×D411yescharacteristic
471C2×C4×C11C2×#4114yes—
472C2×C4×C11C2511yescharacteristic
473C8×C11—24no—
474C8×C11C2×#4118yes—
475C2×#137C22×C1112yes—
476C2×AGL(1,ℤ/8)C22×C1112yes—
477C22×M16C22×C1112yes—
478#533C22×C1111yescharacteristic
479#533C22×C1111yescharacteristic, complemented
480#533C22×C1111yescharacteristic, complemented
481#532C22×C1111yescharacteristic
482#532C22×C1111yescharacteristic, complemented
483#532C22×C1111yescharacteristic, complemented
484#529—21no—
485#529—21no—
486#529—21no—
487#529—21no—
488#529—21no—
489#529—21no—
490#529—21no—
491#529—21no—
492#529C22×C1112yes—
493#529C22×C1112yes—
494#529C22×C1112yes—
495#529C22×C1112yes—
496#529C22×C1112yescomplemented
497#529C22×C1112yescomplemented
498C2×#126—21no—
499C2×#125C22×C1111yescharacteristic
500C2×#124C22×C1111yescharacteristic
501#525—21no—
502#525—21no—
503#525C22×C1112yes—
504C2×#123—21no—
505C2×C22⋊Q8C22×C1111yescharacteristic
506C2×#121C22×C1111yescharacteristic
507C4×#41—21no—
508C4×#41—21no—
509C4×#41C22×C1112yes—
510C2×C4×Q8C22×C1111yescharacteristic
511C2×C4×D4—21no—
512C2×C4×D4C22×C1111yescharacteristic
513C2×#117—21no—
514C22×C42C22×C1111yescharacteristic
515#501C22×C1112yescomplemented
516#501C22×C1112yescomplemented
517#499C22×C1114yescomplemented
518#497C22×C1112yescomplemented
519#496C22×C1112yescomplemented
520#495C22×C1114yescomplemented
521#491C22×C1112yescomplemented
522#490C22×C1112yescomplemented
523#489C22×C1112yescomplemented
524#489C22×C1112yescomplemented
525#488C22×C1114yescomplemented
526#488C22×C1114yescomplemented
527#470C22×C1114yescomplemented
528#469C22×C1114yes—
529#468C22×C1114yes—
530#468C22×C1114yescomplemented
531#467C22×C1114yescomplemented
532#466C22×C1114yes—
533#465C22×C1114yes—
534#465C22×C1114yescomplemented
535#442C22×C1114yescomplemented
536#441C22×C1114yescomplemented
537#440C22×C1114yescomplemented
538#440C22×C1114yescomplemented
539C4×Q16C22×C1114yescomplemented
540C4×SD16C22×C1114yescomplemented
541C4×SD16C22×C1114yescomplemented
542C4×D8C22×C1114yescomplemented
543#428C22×C1112yes—
544#428C22×C1112yes—
545#419C22×C1112yes—
546#418C22×C1112yes—
547#417C22×C1112yes—
548#417C22×C1112yes—
549C4×M16C22×C1111yescharacteristic
550C4×M16C22×C1111yescharacteristic
551C4×M16C22×C1112yes—
552C4×M16C22×C1112yescomplemented
553C4×M16C22×C1112yescomplemented
554C2×#97C22×C1112yescomplemented
555C2×C4×C8C22×C1112yescomplemented
556C22×C11—21no—
557C22×C11—21no—
558C22×C11—21no—
559C22×C11—21no—
560C22×C11—21no—
561C22×C11—21no—
562C22×C11—21no—
563C22×C11—44no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—84no—
571C22×C11#53212yes—
572C22×C11#57512yes—
573C22×C11C23×D411yescharacteristic
574C4×C11—21no—
575C4×C11—21no—
576C4×C11—21no—
577C4×C11—21no—
578C4×C11—21no—
579C4×C11—21no—
580C4×C11—21no—
581C4×C11—21no—
582C4×C11—21no—
583C4×C11—42no—
584C4×C11—42no—
585C4×C11—42no—
586C4×C11—42no—
587C4×C11—42no—
588C4×C11—42no—
589C4×C11#53212yes—
590C4×C11#57512yes—
591C4×C11C22×#4112yes—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41C23×C1112yes—
595C22×Q8C23×C1111yescharacteristic
596C22×D4—21no—
597C22×D4C23×C1111yescharacteristic
598C23×C4—21no—
599C23×C4D4×C1111yescharacteristic
600C23×C4D4×C1111yescharacteristic
601C23×C4C23×C1111yescharacteristic
602#137—28no—
603AGL(1,ℤ/8)—28no—
604C2×Q16C23×C1114yes—
605C2×SD16C23×C1114yes—
606C2×SD16C23×C1114yes—
607C2×D8C23×C1114yes—
608C2×M16—28no—
609C2×M16C23×C1112yes—
610C2×M16C23×C1114yes—
611C2×M16C23×C1112yes—
612C22×C8C23×C1114yes—
613C4⋊Q8C23×C1111yescharacteristic
614C4⋊Q8C23×C1111yescharacteristic
615C4⋊Q8C23×C1111yescharacteristic
616#127C23×C1111yescharacteristic
617#126—22no—
618#126—22no—
619#126—22no—
620#126—22no—
621#126—22no—
622#126—22no—
623#125—21no—
624#125—21no—
625#125—21no—
626#125—21no—
627#125C23×C1112yes—
628#125C23×C1112yes—
629#125C23×C1112yes—
630#124—21no—
631#124—21no—
632#124—21no—
633#124—21no—
634#124C23×C1112yes—
635#124C23×C1112yes—
636#124C23×C1112yes—
637#123—22no—
638#123—22no—
639#123—22no—
640#123—22no—
641#123—22no—
642#123—22no—
643#123—22no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8—21no—
647C22⋊Q8—21no—
648C22⋊Q8—21no—
649C22⋊Q8—21no—
650C22⋊Q8C23×C1112yes—
651C22⋊Q8C23×C1112yes—
652C22⋊Q8C23×C1112yes—
653C22⋊Q8C23×C1112yes—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—21no—
658#121—21no—
659#121—21no—
660#121C23×C1112yes—
661#121C23×C1112yes—
662#121C23×C1112yes—
663#121C23×C1112yes—
664#120—22no—
665C4×Q8—21no—
666C4×Q8—21no—
667C4×Q8—21no—
668C4×Q8—21no—
669C4×Q8—21no—
670C4×Q8—21no—
671C4×Q8C23×C1112yes—
672C4×Q8C23×C1112yes—
673C4×Q8C23×C1112yes—
674C4×Q8C23×C1112yes—
675C4×D4—22no—
676C4×D4—22no—
677C4×D4—22no—
678C4×D4—22no—
679C4×D4—22no—
680C4×D4—22no—
681C4×D4—22no—
682C4×D4—22no—
683C4×D4—22no—
684C4×D4—22no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690C4×D4—21no—
691C4×D4C23×C1112yes—
692C4×D4C23×C1112yes—
693C4×D4C23×C1112yes—
694C4×D4C23×C1112yes—
695#117—21no—
696#117—21no—
697#117—22no—
698#117—22no—
699#117—22no—
700#117—22no—
701#117—22no—
702#117—22no—
703#117—22no—
704#117C23×C1112yes—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—21no—
709C2×C4⋊C4C23×C1111yescharacteristic
710C2×C4⋊C4C23×C1111yescharacteristic
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C42—21no—
717C2×C42—22no—
718C2×C42D4×C1111yescharacteristic
719C2×C42D4×C1111yescharacteristic
720C2×C42D4×C1111yescharacteristic
721C2×C42D4×C1111yescharacteristic
722C2×C42D4×C1111yescharacteristic
723C2×C42D4×C1111yescharacteristic
724C2×C42C23×C1111yescharacteristic
725C2×C42C23×C1111yescharacteristic
726C2×C42C23×C1111yescharacteristic
727C2×C42C23×C1111yescharacteristic
728C2×C42C23×C1111yescharacteristic
729C2×C42C23×C1111yescharacteristic
730#107C23×C1114yes—
731#107C23×C1114yes—
732#106C23×C1114yes—
733#106C23×C1114yes—
734#103C23×C1114yes—
735#103C23×C1114yes—
736#103C23×C1114yes—
737#103C23×C1114yes—
738#102C23×C1114yes—
739#102C23×C1114yes—
740#102C23×C1114yes—
741#102C23×C1114yes—
742#97C23×C1114yes—
743#97C23×C1112yes—
744#97C23×C1112yes—
745C4×C8C23×C1114yes—
746C4×C8C23×C1112yes—
747C4×C8C23×C1112yes—
748C2×C11—22no—
749C2×C11—22no—
750C2×C11—41no—
751C2×C11—82no—
752C2×C11—82no—
753C2×C11C2×#53211yescharacteristic
754C2×C11C2×#57511yescharacteristic
755C2×C11C2×#57511yescharacteristic
756C24—21no—
757C24C2×D4×C1111yescharacteristic
758#41—24no—
759#41—24no—
760#41—44no—
761#41—44no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—24no—
766C2×Q8C24×C1112yes—
767C2×Q8C24×C1112yes—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—44no—
778C2×D4C24×C1112yes—
779C2×D4C24×C1112yes—
780C22×C4—24no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—44no—
792C22×C4C2×D4×C1111yescharacteristic
793C22×C4C2×D4×C1111yescharacteristic
794C22×C4C2×D4×C1111yescharacteristic
795C22×C4C2×D4×C1111yescharacteristic
796C22×C4C2×D4×C1111yescharacteristic
797C22×C4C2×D4×C1111yescharacteristic
798C22×C4C2×D4×C1111yescharacteristic
799C22×C4C2×D4×C1111yescharacteristic
800C22×C4C2×D4×C1111yescharacteristic
801C22×C4C2×D4×C1111yescharacteristic
802C22×C4C2×D4×C1111yescharacteristic
803C22×C4C2×D4×C1111yescharacteristic
804C22×C4C2×D4×C1111yescharacteristic
805C22×C4C2×D4×C1111yescharacteristic
806C22×C4C2×D4×C1111yescharacteristic
807C22×C4C24×C1111yescharacteristic
808C22×C4C24×C1111yescharacteristic
809C22×C4C24×C1111yescharacteristic
810Q16—28no—
811SD16—28no—
812SD16—28no—
813D8—28no—
814M16—24no—
815M16—28no—
816M16C11×#4118yescomplemented
817C2×C8—28no—
818C2×C8C24×C1114yes—
819C2×C8C24×C1114yes—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4C24×C1112yes—
841C4⋊C4C24×C1112yes—
842C4⋊C4C24×C1112yes—
843C4⋊C4C24×C1112yes—
844C22⋊C4—22no—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C22⋊C4—22no—
848C22⋊C4—22no—
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—22no—
852C22⋊C4—22no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C42—22no—
864C42—22no—
865C42—22no—
866C42—22no—
867C42—22no—
868C42C2×D4×C1111yescharacteristic
869C42C2×D4×C1111yescharacteristic
870C42C2×D4×C1111yescharacteristic
871C42C2×D4×C1111yescharacteristic
872C42C2×D4×C1111yescharacteristic
873C42C2×D4×C1111yescharacteristic
874C42C2×D4×C1111yescharacteristic
875C42C2×D4×C1111yescharacteristic
876C42C2×D4×C1111yescharacteristic
877C42C2×D4×C1111yescharacteristic
878C42C2×D4×C1111yescharacteristic
879C42C2×D4×C1111yescharacteristic
880C42C24×C1111yescharacteristic
881C42C24×C1111yescharacteristic
882C42C24×C1111yescharacteristic
883C42C24×C1111yescharacteristic
884C11#6070211yescharacteristic, direct product factor, Sylow
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—41no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23C22×D4×C1111yescharacteristic
894C23C22×D4×C1111yescharacteristic
895C23C22×D4×C1111yescharacteristic
896Q8—22no—
897Q8—24no—
898Q8—22no—
899Q8—42no—
900Q8—42no—
901Q8—42no—
902D4—22no—
903D4—24no—
904D4—22no—
905D4—42no—
906D4—42no—
907D4—44no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—42no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—44no—
937C2×C4—44no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—44no—
943C2×C4—44no—
944C2×C4C22×D4×C1111yescharacteristic
945C2×C4C22×D4×C1111yescharacteristic
946C2×C4C22×D4×C1111yescharacteristic
947C2×C4C22×D4×C1111yescharacteristic
948C2×C4C22×D4×C1111yescharacteristic
949C2×C4C22×D4×C1111yescharacteristic
950C2×C4C22×D4×C1111yescharacteristic
951C2×C4C22×D4×C1111yescharacteristic
952C2×C4C22×D4×C1111yescharacteristic
953C2×C4C22×D4×C1111yescharacteristic
954C2×C4C22×D4×C1111yescharacteristic
955C2×C4C2×C11×#4114yes—
956C2×C4C25×C1111yescharacteristic
957C8—24no—
958C8C2×C11×#4118yes—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—44no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—84no—
974C22C11×#53212yes—
975C22C11×#57512yes—
976C22C23×D4×C1111yescharacteristic
977C4—21no—
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4C11×#53212yes—
993C4C11×#57512yes—
994C4C22×C11×#4112yes—
995C2—22no—
996C2—22no—
997C2—41no—
998C2—82no—
999C2—82no—
1000C2C2×C11×#53211yescharacteristic
1001C2C2×C11×#57511yescharacteristic
1002C2C2×C11×#57511yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3444C2semidirect
2. C2×C11×#529C2semidirect
3. C11×#3183C2semidirect
4. C11×#3181C2semidirect
5. C11×#3180C2semidirect
6. C11×#3172C2semidirect
7. C11×#3171C2semidirect
8. C11×#3168C2semidirect
9. C11×#3166C2semidirect
10. C11×#3153C2semidirect
11. C11×#3142C2semidirect
12. C11×#3140C2semidirect
13. C11×#3056C2semidirect
14. C11×#3055C2semidirect
15. C4×C11×#137C2semidirect
16. C4×C11×AGL(1,ℤ/8)C2semidirect
17. C2×C4×C11×M16C2semidirect
22. C11×#533C22semidirect
23. C11×#533C22semidirect
25. C11×#532C22semidirect
26. C11×#532C22semidirect
39. C11×#529C22semidirect
40. C11×#529C22semidirect
58. C11×#501C22semidirect
59. C11×#501C22semidirect
60. C11×#499C22semidirect
61. C11×#497C22semidirect
62. C11×#496C22semidirect
63. C11×#495C22semidirect
64. C11×#491C22semidirect
65. C11×#490C22semidirect
66. C11×#489C22semidirect
67. C11×#489C22semidirect
68. C11×#488C22semidirect
69. C11×#488C22semidirect
70. C11×#470C22semidirect
73. C11×#468C22semidirect
74. C11×#467C22semidirect
77. C11×#465C22semidirect
78. C11×#442C22semidirect
79. C11×#441C22semidirect
80. C11×#440C22semidirect
81. C11×#440C22semidirect
82. C4×C11×Q16C22semidirect
83. C4×C11×SD16C22semidirect
84. C4×C11×SD16C22semidirect
85. C4×C11×D8C22semidirect
95. C4×C11×M16C22semidirect
96. C4×C11×M16C22semidirect
97. C2×C11×#97C22semidirect
98. C2×C4×C8×C11C22semidirect
255. #60702C11direct (N × H)
316. C11×M16#41semidirect
384. #3444C2×C11semidirect
385. C2×#529C2×C11semidirect
386. #3183C2×C11semidirect
387. #3181C2×C11semidirect
388. #3180C2×C11semidirect
389. #3172C2×C11semidirect
390. #3171C2×C11semidirect
391. #3168C2×C11semidirect
392. #3166C2×C11semidirect
393. #3153C2×C11semidirect
394. #3142C2×C11semidirect
395. #3140C2×C11semidirect
396. #3056C2×C11semidirect
397. #3055C2×C11semidirect
398. C4×#137C2×C11semidirect
399. C4×AGL(1,ℤ/8)C2×C11semidirect
400. C2×C4×M16C2×C11semidirect
479. #533C22×C11semidirect
480. #533C22×C11semidirect
482. #532C22×C11semidirect
483. #532C22×C11semidirect
496. #529C22×C11semidirect
497. #529C22×C11semidirect
515. #501C22×C11semidirect
516. #501C22×C11semidirect
517. #499C22×C11semidirect
518. #497C22×C11semidirect
519. #496C22×C11semidirect
520. #495C22×C11semidirect
521. #491C22×C11semidirect
522. #490C22×C11semidirect
523. #489C22×C11semidirect
524. #489C22×C11semidirect
525. #488C22×C11semidirect
526. #488C22×C11semidirect
527. #470C22×C11semidirect
530. #468C22×C11semidirect
531. #467C22×C11semidirect
534. #465C22×C11semidirect
535. #442C22×C11semidirect
536. #441C22×C11semidirect
537. #440C22×C11semidirect
538. #440C22×C11semidirect
539. C4×Q16C22×C11semidirect
540. C4×SD16C22×C11semidirect
541. C4×SD16C22×C11semidirect
542. C4×D8C22×C11semidirect
552. C4×M16C22×C11semidirect
553. C4×M16C22×C11semidirect
554. C2×#97C22×C11semidirect
555. C2×C4×C8C22×C11semidirect
816. M16C11×#41semidirect
884. C11#60702direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34442
C2×C11×#5292
C11×#31832
C11×#31812
C11×#31802
C11×#31722
C11×#31712
C11×#31682
C11×#31662
C11×#31532
C11×#31422
C11×#31402
C11×#30562
C11×#30552
C4×C11×#1372
C4×C11×AGL(1,ℤ/8)2
C2×C4×C11×M162
#6070211