Finite Group Databasebeta

← C11×#61083 #14638276

Subgroups — C11×#61083 #14638276

Order 2816.

2674 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#578C211yesmaximal, characteristic, complemented
2C2×C11×#577C211yesmaximal, characteristic, complemented
3C11×#3500C211yesmaximal, characteristic, complemented
4C11×#3499C211yesmaximal, characteristic, complemented
5C11×#3270C214yesmaximal, complemented
6C11×#3269C214yesmaximal, complemented
7C11×#3267C214yesmaximal, complemented
8C11×#3266C214yesmaximal, complemented
9C2×C11×#497C211yesmaximal, characteristic, complemented
10C11×#3059C211yesmaximal, characteristic, complemented
11C11×#3057C211yesmaximal, characteristic, complemented
12C11×#3040C211yesmaximal, characteristic, complemented
13C11×#3039C211yesmaximal, characteristic, complemented
14C11×#3011C211yesmaximal, characteristic, complemented
15C11×#3011C211yesmaximal, characteristic, complemented
16C11×#3010C211yesmaximal, characteristic, complemented
17C11×#3009C211yesmaximal, characteristic, complemented
18C11×#2943C211yesmaximal, characteristic, complemented
19C11×#2932C211yesmaximal, characteristic, complemented
20C2×C11×2−1+4C2211yescharacteristic
21C2×C11×2−1+4C2211yescharacteristic
22C2×C11×2−1+4C2211yescharacteristic, complemented
23C2×C11×H(5,𝔽2)C2211yescharacteristic
24C11×#578—28no—
25C11×#577—28no—
26C2×C11×#137C2211yescharacteristic
27C2×C11×#137C2211yescharacteristic
28C2×C11×#137C2212yes—
29C2×C11×#137C2212yescomplemented
30C2×C11×#137C2211yescharacteristic, complemented
31C2×C11×#137C2212yescomplemented
32C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
33C2×C11×AGL(1,ℤ/8)C2212yes—
34C2×C11×#135C2212yes—
35C2×C11×#135C2211yescharacteristic
36C2×C11×#135C2212yescomplemented
37C22×C11×Q16C2211yescharacteristic, complemented
38C22×C11×Q16C2212yescomplemented
39C22×C11×Q16C2211yescharacteristic, complemented
40C22×C11×SD16C2211yescharacteristic
41C22×C11×SD16C2212yes—
42C22×C11×SD16C2211yescharacteristic
43C2×C11×#131C2211yescharacteristic
44C2×C11×#131C2211yescharacteristic, complemented
45D4×Q8×C11C2214yescomplemented
46C11×#548C2214yes—
47C11×#547—24no—
48C11×#547C2214yescomplemented
49C11×#546—24no—
50C11×#546C2214yes—
51C11×#536—21no—
52C11×#536—21no—
53C11×#536—21no—
54C11×#536C2211yescharacteristic
55C11×#536C2211yescharacteristic
56C11×#536C2211yescharacteristic, complemented
57C11×#535—21no—
58C11×#535C2211yescharacteristic
59C11×#532—21no—
60C11×#532—21no—
61C11×#532C2211yescharacteristic
62C2×C11×C4⋊Q8—21no—
63C2×C11×C4⋊Q8C2211yescharacteristic, complemented
64C2×C11×#124—21no—
65C2×C11×#124C2211yescharacteristic
66C4×C11×#41C2211yescharacteristic
67C4×C11×#41C2211yescharacteristic, complemented
68C11×#497C2214yescomplemented
69C11×#497C2214yescomplemented
70C11×#470C2214yescomplemented
71C11×#468C2214yescomplemented
72C11×#467C2214yescomplemented
73C11×#465C2214yescomplemented
74C11×#464C2214yescomplemented
75C11×#463C2214yescomplemented
76C11×#462C2214yescomplemented
77C11×#461C2214yescomplemented
78C11×#452C2214yes—
79C11×#452C2214yescomplemented
80C11×#452C2214yescomplemented
81C11×#451C2214yescomplemented
82C11×#451C2214yescomplemented
83C11×#450C2214yes—
84C11×#449C2214yescomplemented
85C11×#448C2214yescomplemented
86C11×#442C2212yescomplemented
87C11×#441C2212yescomplemented
88C11×#440C2212yescomplemented
89C11×#440C2212yescomplemented
90C11×#435C2214yescomplemented
91C11×#435C2214yescomplemented
92C11×#427C2211yescharacteristic, complemented
93C11×#423C2211yescharacteristic, complemented
94C11×#419C2211yescharacteristic, complemented
95C11×#419C2211yescharacteristic, complemented
96C11×#419C2211yescharacteristic, complemented
97C11×#418C2211yescharacteristic
98C11×#416C2211yescharacteristic
99C11×#416C2211yescharacteristic, complemented
100C11×#408C2211yescharacteristic
101C11×#408C2211yescharacteristic, complemented
102C2×C11×#97C2211yescharacteristic, complemented
103C11×2−1+4—24no—
104C11×2−1+4—24no—
105C11×2−1+4—24no—
106C11×2−1+4—42no—
107C11×2−1+4—42no—
108C11×2−1+4—42no—
109C11×H(5,𝔽2)—24no—
110C11×H(5,𝔽2)—42no—
111C2×C11×#41—21no—
112C2×C11×#41—21no—
113C2×C11×#41—21no—
114C2×C11×#41—21no—
115C2×C11×#41—22no—
116C2×C11×#41—22no—
117C2×C11×#41—22no—
118C2×C11×#41C2312yes—
119C2×C11×#41C2312yes—
120C2×C11×#41C2312yes—
121C2×C11×#41C2312yes—
122C2×C11×#41C2311yescharacteristic
123C2×C11×#41C2311yescharacteristic
124C2×C11×#41C2311yescharacteristic
125C2×C11×#41C2311yescharacteristic
126C22×Q8×C11—21no—
127C22×Q8×C11—21no—
128C22×Q8×C11—21no—
129C22×Q8×C11C2311yescharacteristic
130C22×Q8×C11C2311yescharacteristic
131C22×Q8×C11C2311yescharacteristic
132C22×Q8×C11C2312yes—
133C22×Q8×C11C2312yes—
134C22×Q8×C11C2312yes—
135C22×D4×C11—21no—
136C22×D4×C11—22no—
137C22×D4×C11C2311yescharacteristic
138C22×D4×C11C2312yes—
139C11×#137—24no—
140C11×#137—24no—
141C11×#137—24no—
142C11×#137—28no—
143C11×#137—28no—
144C11×#137—28no—
145C11×AGL(1,ℤ/8)—24no—
146C11×AGL(1,ℤ/8)—28no—
147C11×#135—28no—
148C11×#135—28no—
149C11×#135D418yescomplemented
150C2×C11×Q16—28no—
151C2×C11×Q16—24no—
152C2×C11×Q16—42no—
153C2×C11×Q16C2312yes—
154C2×C11×Q16C2312yes—
155C2×C11×Q16C2312yes—
156C2×C11×Q16C2312yes—
157C2×C11×Q16C2312yes—
158C2×C11×Q16C2314yes—
159C2×C11×Q16C2311yescharacteristic
160C2×C11×SD16—28no—
161C2×C11×SD16—24no—
162C2×C11×SD16—42no—
163C2×C11×SD16C2312yes—
164C2×C11×SD16C2312yes—
165C2×C11×SD16C2312yes—
166C2×C11×SD16C2312yes—
167C2×C11×SD16C2312yes—
168C2×C11×SD16C2312yes—
169C2×C11×SD16C2314yes—
170C2×C11×SD16C2311yescharacteristic
171C2×C11×SD16C2311yescharacteristic
172C2×C11×D8C2312yes—
173C2×C11×D8C2311yescharacteristic
174C11×#131—24no—
175C11×#131—24no—
176C2×C11×M16C2311yescharacteristic
177C2×C11×M16C2311yescharacteristic
178C2×C11×M16C2312yes—
179C2×C11×M16C2312yes—
180C22×C8×C11C2311yescharacteristic
181C22×C8×C11C2312yes—
182C22×C8×C11C2312yes—
183C22×C8×C11C2311yescharacteristic
184C11×C4⋊Q8—21no—
185C11×C4⋊Q8—21no—
186C11×C4⋊Q8—21no—
187C11×C4⋊Q8—24no—
188C11×C4⋊Q8—21no—
189C11×C4⋊Q8—21no—
190C11×C4⋊Q8D411yescharacteristic
191C11×C4⋊Q8C2314yes—
192C11×#127—21no—
193C11×#127D411yescharacteristic
194C11×#124—21no—
195C11×#124—21no—
196C11×#124—21no—
197C11×#124—21no—
198C11×#124—24no—
199C11×#124—21no—
200C11×#124—21no—
201C11×#124D411yescharacteristic
202C11×#124D411yescharacteristic
203C11×#124C2314yes—
204C11×#123—22no—
205C11×#123—22no—
206C11×#123—22no—
207C11×#123—24no—
208C11×#123—24no—
209C11×#123—24no—
210C11×C22⋊Q8—24no—
211C11×C22⋊Q8—24no—
212C11×C22⋊Q8—24no—
213C11×C22⋊Q8C2314yes—
214C11×C22⋊Q8C2314yes—
215C11×C22⋊Q8C2314yes—
216C11×#121—24no—
217C11×#121—24no—
218C11×#121—24no—
219C11×#121D414yes—
220C11×#121C2314yes—
221C11×#120—24no—
222C11×#120—22no—
223C4×Q8×C11C2312yes—
224C4×Q8×C11C2312yes—
225C4×D4×C11—24no—
226C4×D4×C11—22no—
227C4×D4×C11—22no—
228C4×D4×C11—24no—
229C4×D4×C11C2312yes—
230C4×D4×C11C2312yes—
231C4×D4×C11C2314yes—
232C11×#117—21no—
233C11×#117—21no—
234C11×#117C2311yescharacteristic
235C11×#117C2311yescharacteristic
236C2×C11×C4⋊C4—22no—
237C2×C11×C4⋊C4—24no—
238C2×C11×C22⋊C4—22no—
239C2×C11×C22⋊C4—24no—
240C2×C42×C11—21no—
241C2×C42×C11—21no—
242C2×C42×C11C2311yescharacteristic
243C11×#107C2312yes—
244C11×#106C2312yes—
245C11×C4⋊C8C2314yes—
246C11×#103C2312yes—
247C11×#103C2312yes—
248C11×#103C2314yes—
249C11×#103C2314yes—
250C11×#103C2314yes—
251C11×#102C2312yes—
252C11×#102C2312yes—
253C11×#102C2314yes—
254C11×C22⋊C8C2314yes—
255C11×C22⋊C8C2314yes—
256C11×#97C2312yes—
257C11×#97C2312yes—
258#61083C1111yesmaximal, characteristic, direct product factor, Sylow
259C24×C11—22no—
260C24×C11—21no—
261C11×#41—22no—
262C11×#41—22no—
263C11×#41—22no—
264C11×#41—22no—
265C11×#41—22no—
266C11×#41—22no—
267C11×#41—24no—
268C11×#41—24no—
269C11×#41—24no—
270C11×#41—24no—
271C11×#41—42no—
272C11×#41—42no—
273C11×#41—42no—
274C11×#41—42no—
275C11×#41—44no—
276C11×#41—44no—
277C11×#41—44no—
278C11×#41—44no—
279C11×#41—48no—
280C11×#41—48no—
281C11×#41—48no—
282C11×#41C2×D414yes—
283C11×#41C2×D414yes—
284C2×Q8×C11—22no—
285C2×Q8×C11—22no—
286C2×Q8×C11—22no—
287C2×Q8×C11—21no—
288C2×Q8×C11—21no—
289C2×Q8×C11—21no—
290C2×Q8×C11—24no—
291C2×Q8×C11—24no—
292C2×Q8×C11—24no—
293C2×Q8×C11—22no—
294C2×Q8×C11—22no—
295C2×Q8×C11—22no—
296C2×Q8×C11—22no—
297C2×Q8×C11—22no—
298C2×Q8×C11—22no—
299C2×Q8×C11—42no—
300C2×Q8×C11—42no—
301C2×Q8×C11—42no—
302C2×Q8×C11—44no—
303C2×Q8×C11—44no—
304C2×Q8×C11—44no—
305C2×Q8×C11C2×D411yescharacteristic
306C2×Q8×C11C2×D411yescharacteristic
307C2×Q8×C11C2412yes—
308C2×Q8×C11C2412yes—
309C2×Q8×C11C2412yes—
310C2×Q8×C11C2411yescharacteristic
311C2×Q8×C11C2411yescharacteristic
312C2×D4×C11—21no—
313C2×D4×C11—21no—
314C2×D4×C11—24no—
315C2×D4×C11—22no—
316C2×D4×C11—22no—
317C2×D4×C11—22no—
318C2×D4×C11—22no—
319C2×D4×C11—24no—
320C2×D4×C11—22no—
321C2×D4×C11—22no—
322C2×D4×C11—21no—
323C2×D4×C11—22no—
324C2×D4×C11—42no—
325C2×D4×C11—44no—
326C2×D4×C11—48no—
327C2×D4×C11C2×D412yes—
328C2×D4×C11C2×D412yes—
329C2×D4×C11C2×D411yescharacteristic
330C2×D4×C11C2×D411yescharacteristic
331C2×D4×C11C2×D414yes—
332C2×D4×C11C2412yes—
333C2×D4×C11C2411yescharacteristic
334C2×D4×C11C2411yescharacteristic
335C22×C4×C11—21no—
336C22×C4×C11—21no—
337C22×C4×C11—21no—
338C22×C4×C11—21no—
339C22×C4×C11—21no—
340C22×C4×C11—22no—
341C22×C4×C11—22no—
342C22×C4×C11—22no—
343C22×C4×C11—22no—
344C22×C4×C11—22no—
345C22×C4×C11—22no—
346C22×C4×C11—22no—
347C22×C4×C11—22no—
348C22×C4×C11—22no—
349C22×C4×C11C2×D412yes—
350C22×C4×C11C2412yes—
351C22×C4×C11C2412yes—
352C22×C4×C11C2411yescharacteristic
353C11×Q16—24no—
354C11×Q16—24no—
355C11×Q16—24no—
356C11×Q16—24no—
357C11×Q16—24no—
358C11×Q16—44no—
359C11×Q16C2×D414yes—
360C11×SD16—24no—
361C11×SD16—24no—
362C11×SD16—24no—
363C11×SD16—24no—
364C11×SD16—24no—
365C11×SD16—24no—
366C11×SD16—44no—
367C11×SD16C2×D414yes—
368C11×SD16C2×D414yes—
369C11×D8—24no—
370C11×D8C2×D414yes—
371C11×M16—24no—
372C11×M16—24no—
373C11×M16—22no—
374C11×M16—22no—
375C2×C8×C11—24no—
376C2×C8×C11—24no—
377C2×C8×C11—22no—
378C2×C8×C11C2×D414yes—
379C2×C8×C11C2412yes—
380C2×C8×C11C2412yes—
381C2×C8×C11C2412yes—
382C2×C8×C11C2411yescharacteristic
383C2×C8×C11C2411yescharacteristic
384C11×C4⋊C4—24no—
385C11×C4⋊C4—24no—
386C11×C4⋊C4—24no—
387C11×C4⋊C4—24no—
388C11×C4⋊C4—22no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—24no—
391C11×C4⋊C4C2×D414yes—
392C11×C4⋊C4C2412yes—
393C11×C4⋊C4C2412yes—
394C11×C22⋊C4—24no—
395C11×C22⋊C4—21no—
396C11×C22⋊C4—21no—
397C11×C22⋊C4—24no—
398C11×C22⋊C4—24no—
399C11×C22⋊C4—24no—
400C11×C22⋊C4—24no—
401C11×C22⋊C4—24no—
402C11×C22⋊C4—22no—
403C11×C22⋊C4—22no—
404C11×C22⋊C4C2×D414yes—
405C11×C22⋊C4C2×D414yes—
406C42×C11—21no—
407C42×C11—21no—
408C42×C11—22no—
409C42×C11—22no—
410C42×C11C2×D411yescharacteristic
411C42×C11C2×D411yescharacteristic
412C42×C11C2412yes—
413C2×#578C2×C1111yescharacteristic, complemented
414C2×#577C2×C1111yescharacteristic, complemented
415#3500C2×C1111yescharacteristic, complemented
416#3499C2×C1111yescharacteristic, complemented
417#3270C2×C1114yescomplemented
418#3269C2×C1114yescomplemented
419#3267C2×C1114yescomplemented
420#3266C2×C1114yescomplemented
421C2×#497C2×C1111yescharacteristic, complemented
422#3059C2×C1111yescharacteristic, complemented
423#3057C2×C1111yescharacteristic, complemented
424#3040C2×C1111yescharacteristic, complemented
425#3039C2×C1111yescharacteristic, complemented
426#3011C2×C1111yescharacteristic, complemented
427#3011C2×C1111yescharacteristic, complemented
428#3010C2×C1111yescharacteristic, complemented
429#3009C2×C1111yescharacteristic, complemented
430#2943C2×C1111yescharacteristic, complemented
431#2932C2×C1111yescharacteristic, complemented
432C23×C11—21no—
433C23×C11—21no—
434C23×C11—22no—
435C23×C11—44no—
436C23×C11—42no—
437C23×C11—82no—
438C23×C11—84no—
439C23×C11C22×D412yes—
440C23×C11C22×D412yes—
441C23×C11C22×D411yescharacteristic
442Q8×C11—22no—
443Q8×C11—22no—
444Q8×C11—21no—
445Q8×C11—21no—
446Q8×C11—22no—
447Q8×C11—22no—
448Q8×C11—22no—
449Q8×C11—22no—
450Q8×C11—22no—
451Q8×C11—22no—
452Q8×C11—44no—
453Q8×C11—44no—
454Q8×C11—44no—
455Q8×C11—42no—
456Q8×C11—42no—
457Q8×C11—42no—
458Q8×C11C22×D412yes—
459Q8×C11C22×D412yes—
460D4×C11—24no—
461D4×C11—24no—
462D4×C11—24no—
463D4×C11—24no—
464D4×C11—22no—
465D4×C11—22no—
466D4×C11—22no—
467D4×C11—21no—
468D4×C11—21no—
469D4×C11—22no—
470D4×C11—44no—
471D4×C11—44no—
472D4×C11—44no—
473D4×C11—44no—
474D4×C11—44no—
475D4×C11—44no—
476D4×C11—42no—
477D4×C11—84no—
478D4×C11C22×D412yes—
479D4×C11C22×D412yes—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—24no—
483C2×C4×C11—24no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—42no—
494C2×C4×C11—44no—
495C2×C4×C11—44no—
496C2×C4×C11—44no—
497C2×C4×C11—44no—
498C2×C4×C11—44no—
499C2×C4×C11—44no—
500C2×C4×C11—44no—
501C2×C4×C11—44no—
502C2×C4×C11—42no—
503C2×C4×C11—42no—
504C2×C4×C11—42no—
505C2×C4×C11—82no—
506C2×C4×C11C22×D412yes—
507C2×C4×C11C22×D412yes—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C22×D411yescharacteristic
511C2×C4×C11C22×D412yes—
512C2×C4×C11H(5,𝔽2)12yes—
513C2×C4×C11C2511yescharacteristic
514C8×C11—22no—
515C8×C11—22no—
516C8×C11—22no—
517C8×C11C22×D412yes—
518C8×C11C22×D412yes—
519C2×2−1+4C22×C1111yescharacteristic
520C2×2−1+4C22×C1111yescharacteristic
521C2×2−1+4C22×C1111yescharacteristic, complemented
522C2×H(5,𝔽2)C22×C1111yescharacteristic
523#578—28no—
524#577—28no—
525C2×#137C22×C1111yescharacteristic
526C2×#137C22×C1111yescharacteristic
527C2×#137C22×C1112yes—
528C2×#137C22×C1112yescomplemented
529C2×#137C22×C1111yescharacteristic, complemented
530C2×#137C22×C1112yescomplemented
531C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
532C2×AGL(1,ℤ/8)C22×C1112yes—
533C2×#135C22×C1112yes—
534C2×#135C22×C1111yescharacteristic
535C2×#135C22×C1112yescomplemented
536C22×Q16C22×C1111yescharacteristic, complemented
537C22×Q16C22×C1112yescomplemented
538C22×Q16C22×C1111yescharacteristic, complemented
539C22×SD16C22×C1111yescharacteristic
540C22×SD16C22×C1112yes—
541C22×SD16C22×C1111yescharacteristic
542C2×#131C22×C1111yescharacteristic
543C2×#131C22×C1111yescharacteristic, complemented
544D4×Q8C22×C1114yescomplemented
545#548C22×C1114yes—
546#547—24no—
547#547C22×C1114yescomplemented
548#546—24no—
549#546C22×C1114yes—
550#536—21no—
551#536—21no—
552#536—21no—
553#536C22×C1111yescharacteristic
554#536C22×C1111yescharacteristic
555#536C22×C1111yescharacteristic, complemented
556#535—21no—
557#535C22×C1111yescharacteristic
558#532—21no—
559#532—21no—
560#532C22×C1111yescharacteristic
561C2×C4⋊Q8—21no—
562C2×C4⋊Q8C22×C1111yescharacteristic, complemented
563C2×#124—21no—
564C2×#124C22×C1111yescharacteristic
565C4×#41C22×C1111yescharacteristic
566C4×#41C22×C1111yescharacteristic, complemented
567#497C22×C1114yescomplemented
568#497C22×C1114yescomplemented
569#470C22×C1114yescomplemented
570#468C22×C1114yescomplemented
571#467C22×C1114yescomplemented
572#465C22×C1114yescomplemented
573#464C22×C1114yescomplemented
574#463C22×C1114yescomplemented
575#462C22×C1114yescomplemented
576#461C22×C1114yescomplemented
577#452C22×C1114yes—
578#452C22×C1114yescomplemented
579#452C22×C1114yescomplemented
580#451C22×C1114yescomplemented
581#451C22×C1114yescomplemented
582#450C22×C1114yes—
583#449C22×C1114yescomplemented
584#448C22×C1114yescomplemented
585#442C22×C1112yescomplemented
586#441C22×C1112yescomplemented
587#440C22×C1112yescomplemented
588#440C22×C1112yescomplemented
589#435C22×C1114yescomplemented
590#435C22×C1114yescomplemented
591#427C22×C1111yescharacteristic, complemented
592#423C22×C1111yescharacteristic, complemented
593#419C22×C1111yescharacteristic, complemented
594#419C22×C1111yescharacteristic, complemented
595#419C22×C1111yescharacteristic, complemented
596#418C22×C1111yescharacteristic
597#416C22×C1111yescharacteristic
598#416C22×C1111yescharacteristic, complemented
599#408C22×C1111yescharacteristic
600#408C22×C1111yescharacteristic, complemented
601C2×#97C22×C1111yescharacteristic, complemented
602C22×C11—22no—
603C22×C11—24no—
604C22×C11—24no—
605C22×C11—22no—
606C22×C11—22no—
607C22×C11—22no—
608C22×C11—22no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11—44no—
612C22×C11—42no—
613C22×C11—162no—
614C22×C11—164no—
615C22×C11D4212yes—
616C22×C11C23×D411yescharacteristic
617C4×C11—22no—
618C4×C11—22no—
619C4×C11—22no—
620C4×C11—22no—
621C4×C11—22no—
622C4×C11—22no—
623C4×C11—42no—
624C4×C11—42no—
625C4×C11—42no—
626C4×C11—42no—
627C4×C11—42no—
628C4×C11D4212yes—
629C4×C11C23×D411yescharacteristic
630C4×C11C2×H(5,𝔽2)11yescharacteristic
6312−1+4—24no—
6322−1+4—24no—
6332−1+4—24no—
6342−1+4—42no—
6352−1+4—42no—
6362−1+4—42no—
637H(5,𝔽2)—24no—
638H(5,𝔽2)—42no—
639C2×#41—21no—
640C2×#41—21no—
641C2×#41—21no—
642C2×#41—21no—
643C2×#41—22no—
644C2×#41—22no—
645C2×#41—22no—
646C2×#41C23×C1112yes—
647C2×#41C23×C1112yes—
648C2×#41C23×C1112yes—
649C2×#41C23×C1112yes—
650C2×#41C23×C1111yescharacteristic
651C2×#41C23×C1111yescharacteristic
652C2×#41C23×C1111yescharacteristic
653C2×#41C23×C1111yescharacteristic
654C22×Q8—21no—
655C22×Q8—21no—
656C22×Q8—21no—
657C22×Q8C23×C1111yescharacteristic
658C22×Q8C23×C1111yescharacteristic
659C22×Q8C23×C1111yescharacteristic
660C22×Q8C23×C1112yes—
661C22×Q8C23×C1112yes—
662C22×Q8C23×C1112yes—
663C22×D4—21no—
664C22×D4—22no—
665C22×D4C23×C1111yescharacteristic
666C22×D4C23×C1112yes—
667#137—24no—
668#137—24no—
669#137—24no—
670#137—28no—
671#137—28no—
672#137—28no—
673AGL(1,ℤ/8)—24no—
674AGL(1,ℤ/8)—28no—
675#135—28no—
676#135—28no—
677#135D4×C1118yescomplemented
678C2×Q16—28no—
679C2×Q16—24no—
680C2×Q16—42no—
681C2×Q16C23×C1112yes—
682C2×Q16C23×C1112yes—
683C2×Q16C23×C1112yes—
684C2×Q16C23×C1112yes—
685C2×Q16C23×C1112yes—
686C2×Q16C23×C1114yes—
687C2×Q16C23×C1111yescharacteristic
688C2×SD16—28no—
689C2×SD16—24no—
690C2×SD16—42no—
691C2×SD16C23×C1112yes—
692C2×SD16C23×C1112yes—
693C2×SD16C23×C1112yes—
694C2×SD16C23×C1112yes—
695C2×SD16C23×C1112yes—
696C2×SD16C23×C1112yes—
697C2×SD16C23×C1114yes—
698C2×SD16C23×C1111yescharacteristic
699C2×SD16C23×C1111yescharacteristic
700C2×D8C23×C1112yes—
701C2×D8C23×C1111yescharacteristic
702#131—24no—
703#131—24no—
704C2×M16C23×C1111yescharacteristic
705C2×M16C23×C1112yes—
706C2×M16C23×C1111yescharacteristic
707C2×M16C23×C1112yes—
708C22×C8C23×C1112yes—
709C22×C8C23×C1112yes—
710C22×C8C23×C1111yescharacteristic
711C22×C8C23×C1111yescharacteristic
712C4⋊Q8—21no—
713C4⋊Q8—21no—
714C4⋊Q8—21no—
715C4⋊Q8—24no—
716C4⋊Q8—21no—
717C4⋊Q8—21no—
718C4⋊Q8D4×C1111yescharacteristic
719C4⋊Q8C23×C1114yes—
720#127—21no—
721#127D4×C1111yescharacteristic
722#124—21no—
723#124—21no—
724#124—21no—
725#124—21no—
726#124—24no—
727#124—21no—
728#124—21no—
729#124D4×C1111yescharacteristic
730#124D4×C1111yescharacteristic
731#124C23×C1114yes—
732#123—22no—
733#123—22no—
734#123—22no—
735#123—24no—
736#123—24no—
737#123—24no—
738C22⋊Q8—24no—
739C22⋊Q8—24no—
740C22⋊Q8—24no—
741C22⋊Q8C23×C1114yes—
742C22⋊Q8C23×C1114yes—
743C22⋊Q8C23×C1114yes—
744#121—24no—
745#121—24no—
746#121—24no—
747#121D4×C1114yes—
748#121C23×C1114yes—
749#120—24no—
750#120—22no—
751C4×Q8C23×C1112yes—
752C4×Q8C23×C1112yes—
753C4×D4—24no—
754C4×D4—22no—
755C4×D4—22no—
756C4×D4—24no—
757C4×D4C23×C1112yes—
758C4×D4C23×C1112yes—
759C4×D4C23×C1114yes—
760#117—21no—
761#117—21no—
762#117C23×C1111yescharacteristic
763#117C23×C1111yescharacteristic
764C2×C4⋊C4—22no—
765C2×C4⋊C4—24no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—24no—
768C2×C42—21no—
769C2×C42—21no—
770C2×C42C23×C1111yescharacteristic
771#107C23×C1112yes—
772#106C23×C1112yes—
773C4⋊C8C23×C1114yes—
774#103C23×C1112yes—
775#103C23×C1112yes—
776#103C23×C1114yes—
777#103C23×C1114yes—
778#103C23×C1114yes—
779#102C23×C1112yes—
780#102C23×C1112yes—
781#102C23×C1114yes—
782C22⋊C8C23×C1114yes—
783C22⋊C8C23×C1114yes—
784#97C23×C1112yes—
785#97C23×C1112yes—
786C2×C11—22no—
787C2×C11—42no—
788C2×C11—42no—
789C2×C11—42no—
790C2×C11—42no—
791C2×C11—82no—
792C2×C11C2×D4211yescharacteristic
793C2×C11#358612yes—
794C24—22no—
795C24—21no—
796#41—22no—
797#41—22no—
798#41—22no—
799#41—22no—
800#41—22no—
801#41—22no—
802#41—24no—
803#41—24no—
804#41—24no—
805#41—24no—
806#41—42no—
807#41—42no—
808#41—42no—
809#41—42no—
810#41—44no—
811#41—44no—
812#41—44no—
813#41—44no—
814#41—48no—
815#41—48no—
816#41—48no—
817#41C2×D4×C1114yes—
818#41C2×D4×C1114yes—
819C2×Q8—22no—
820C2×Q8—22no—
821C2×Q8—22no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—24no—
826C2×Q8—24no—
827C2×Q8—24no—
828C2×Q8—22no—
829C2×Q8—22no—
830C2×Q8—22no—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—22no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—44no—
838C2×Q8—44no—
839C2×Q8—44no—
840C2×Q8C2×D4×C1111yescharacteristic
841C2×Q8C2×D4×C1111yescharacteristic
842C2×Q8C24×C1112yes—
843C2×Q8C24×C1112yes—
844C2×Q8C24×C1112yes—
845C2×Q8C24×C1111yescharacteristic
846C2×Q8C24×C1111yescharacteristic
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—24no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—24no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—21no—
858C2×D4—22no—
859C2×D4—42no—
860C2×D4—44no—
861C2×D4—48no—
862C2×D4C2×D4×C1112yes—
863C2×D4C2×D4×C1112yes—
864C2×D4C2×D4×C1111yescharacteristic
865C2×D4C2×D4×C1111yescharacteristic
866C2×D4C2×D4×C1114yes—
867C2×D4C24×C1112yes—
868C2×D4C24×C1111yescharacteristic
869C2×D4C24×C1111yescharacteristic
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4C2×D4×C1112yes—
885C22×C4C24×C1112yes—
886C22×C4C24×C1112yes—
887C22×C4C24×C1111yescharacteristic
888Q16—24no—
889Q16—24no—
890Q16—24no—
891Q16—24no—
892Q16—24no—
893Q16—44no—
894Q16C2×D4×C1114yes—
895SD16—24no—
896SD16—24no—
897SD16—24no—
898SD16—24no—
899SD16—24no—
900SD16—24no—
901SD16—44no—
902SD16C2×D4×C1114yes—
903SD16C2×D4×C1114yes—
904D8—24no—
905D8C2×D4×C1114yes—
906M16—22no—
907M16—22no—
908M16—24no—
909M16—24no—
910C2×C8—22no—
911C2×C8—24no—
912C2×C8—24no—
913C2×C8C2×D4×C1114yes—
914C2×C8C24×C1112yes—
915C2×C8C24×C1112yes—
916C2×C8C24×C1112yes—
917C2×C8C24×C1111yescharacteristic
918C2×C8C24×C1111yescharacteristic
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—24no—
926C4⋊C4C2×D4×C1114yes—
927C4⋊C4C24×C1112yes—
928C4⋊C4C24×C1112yes—
929C22⋊C4—24no—
930C22⋊C4—21no—
931C22⋊C4—21no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4C2×D4×C1114yes—
940C22⋊C4C2×D4×C1114yes—
941C42—21no—
942C42—21no—
943C42—22no—
944C42—22no—
945C42C2×D4×C1111yescharacteristic
946C42C2×D4×C1111yescharacteristic
947C42C24×C1112yes—
948C11#6108311yescharacteristic, direct product factor, Sylow
949C23—21no—
950C23—21no—
951C23—22no—
952C23—44no—
953C23—42no—
954C23—82no—
955C23—84no—
956C23C22×D4×C1112yes—
957C23C22×D4×C1112yes—
958C23C22×D4×C1111yescharacteristic
959Q8—22no—
960Q8—22no—
961Q8—21no—
962Q8—21no—
963Q8—22no—
964Q8—22no—
965Q8—22no—
966Q8—22no—
967Q8—22no—
968Q8—22no—
969Q8—44no—
970Q8—44no—
971Q8—44no—
972Q8—42no—
973Q8—42no—
974Q8—42no—
975Q8C22×D4×C1112yes—
976Q8C22×D4×C1112yes—
977D4—24no—
978D4—24no—
979D4—24no—
980D4—24no—
981D4—22no—
982D4—22no—
983D4—22no—
984D4—21no—
985D4—21no—
986D4—22no—
987D4—44no—
988D4—44no—
989D4—44no—
990D4—44no—
991D4—44no—
992D4—44no—
993D4—42no—
994D4—84no—
995D4C22×D4×C1112yes—
996D4C22×D4×C1112yes—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—42no—
1011C2×C4—44no—
1012C2×C4—44no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—44no—
1018C2×C4—44no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—82no—
1023C2×C4C22×D4×C1112yes—
1024C2×C4C22×D4×C1112yes—
1025C2×C4C22×D4×C1112yes—
1026C2×C4C22×D4×C1112yes—
1027C2×C4C22×D4×C1111yescharacteristic
1028C2×C4C22×D4×C1112yes—
1029C2×C4C11×H(5,𝔽2)12yes—
1030C2×C4C25×C1111yescharacteristic
1031C8—22no—
1032C8—22no—
1033C8—22no—
1034C8C22×D4×C1112yes—
1035C8C22×D4×C1112yes—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—24no—
1042C22—24no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—44no—
1047C22—162no—
1048C22—164no—
1049C22D42×C1112yes—
1050C22C23×D4×C1111yescharacteristic
1051C4—22no—
1052C4—22no—
1053C4—22no—
1054C4—22no—
1055C4—22no—
1056C4—22no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4D42×C1112yes—
1063C4C23×D4×C1111yescharacteristic
1064C4C2×C11×H(5,𝔽2)11yescharacteristic
1065C2—22no—
1066C2—42no—
1067C2—42no—
1068C2—42no—
1069C2—42no—
1070C2—82no—
1071C2C2×D42×C1111yescharacteristic
1072C2C11×#358612yes—
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. C2×C11×#578C2semidirect
2. C2×C11×#577C2semidirect
3. C11×#3500C2semidirect
4. C11×#3499C2semidirect
5. C11×#3270C2semidirect
6. C11×#3269C2semidirect
7. C11×#3267C2semidirect
8. C11×#3266C2semidirect
9. C2×C11×#497C2semidirect
10. C11×#3059C2semidirect
11. C11×#3057C2semidirect
12. C11×#3040C2semidirect
13. C11×#3039C2semidirect
14. C11×#3011C2semidirect
15. C11×#3011C2semidirect
16. C11×#3010C2semidirect
17. C11×#3009C2semidirect
18. C11×#2943C2semidirect
19. C11×#2932C2semidirect
22. C2×C11×2−1+4C22semidirect
29. C2×C11×#137C22semidirect
30. C2×C11×#137C22semidirect
31. C2×C11×#137C22semidirect
36. C2×C11×#135C22semidirect
37. C22×C11×Q16C22semidirect
38. C22×C11×Q16C22semidirect
39. C22×C11×Q16C22semidirect
44. C2×C11×#131C22semidirect
45. D4×Q8×C11C22semidirect
48. C11×#547C22semidirect
56. C11×#536C22semidirect
63. C2×C11×C4⋊Q8C22semidirect
67. C4×C11×#41C22semidirect
68. C11×#497C22semidirect
69. C11×#497C22semidirect
70. C11×#470C22semidirect
71. C11×#468C22semidirect
72. C11×#467C22semidirect
73. C11×#465C22semidirect
74. C11×#464C22semidirect
75. C11×#463C22semidirect
76. C11×#462C22semidirect
77. C11×#461C22semidirect
79. C11×#452C22semidirect
80. C11×#452C22semidirect
81. C11×#451C22semidirect
82. C11×#451C22semidirect
84. C11×#449C22semidirect
85. C11×#448C22semidirect
86. C11×#442C22semidirect
87. C11×#441C22semidirect
88. C11×#440C22semidirect
89. C11×#440C22semidirect
90. C11×#435C22semidirect
91. C11×#435C22semidirect
92. C11×#427C22semidirect
93. C11×#423C22semidirect
94. C11×#419C22semidirect
95. C11×#419C22semidirect
96. C11×#419C22semidirect
99. C11×#416C22semidirect
101. C11×#408C22semidirect
102. C2×C11×#97C22semidirect
149. C11×#135D4semidirect
258. #61083C11direct (N × H)
413. C2×#578C2×C11semidirect
414. C2×#577C2×C11semidirect
415. #3500C2×C11semidirect
416. #3499C2×C11semidirect
417. #3270C2×C11semidirect
418. #3269C2×C11semidirect
419. #3267C2×C11semidirect
420. #3266C2×C11semidirect
421. C2×#497C2×C11semidirect
422. #3059C2×C11semidirect
423. #3057C2×C11semidirect
424. #3040C2×C11semidirect
425. #3039C2×C11semidirect
426. #3011C2×C11semidirect
427. #3011C2×C11semidirect
428. #3010C2×C11semidirect
429. #3009C2×C11semidirect
430. #2943C2×C11semidirect
431. #2932C2×C11semidirect
521. C2×2−1+4C22×C11semidirect
528. C2×#137C22×C11semidirect
529. C2×#137C22×C11semidirect
530. C2×#137C22×C11semidirect
535. C2×#135C22×C11semidirect
536. C22×Q16C22×C11semidirect
537. C22×Q16C22×C11semidirect
538. C22×Q16C22×C11semidirect
543. C2×#131C22×C11semidirect
544. D4×Q8C22×C11semidirect
547. #547C22×C11semidirect
555. #536C22×C11semidirect
562. C2×C4⋊Q8C22×C11semidirect
566. C4×#41C22×C11semidirect
567. #497C22×C11semidirect
568. #497C22×C11semidirect
569. #470C22×C11semidirect
570. #468C22×C11semidirect
571. #467C22×C11semidirect
572. #465C22×C11semidirect
573. #464C22×C11semidirect
574. #463C22×C11semidirect
575. #462C22×C11semidirect
576. #461C22×C11semidirect
578. #452C22×C11semidirect
579. #452C22×C11semidirect
580. #451C22×C11semidirect
581. #451C22×C11semidirect
583. #449C22×C11semidirect
584. #448C22×C11semidirect
585. #442C22×C11semidirect
586. #441C22×C11semidirect
587. #440C22×C11semidirect
588. #440C22×C11semidirect
589. #435C22×C11semidirect
590. #435C22×C11semidirect
591. #427C22×C11semidirect
592. #423C22×C11semidirect
593. #419C22×C11semidirect
594. #419C22×C11semidirect
595. #419C22×C11semidirect
598. #416C22×C11semidirect
600. #408C22×C11semidirect
601. C2×#97C22×C11semidirect
677. #135D4×C11semidirect
948. C11#61083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5782
C2×C11×#5772
C11×#35002
C11×#34992
C11×#32702
C11×#32692
C11×#32672
C11×#32662
C2×C11×#4972
C11×#30592
C11×#30572
C11×#30402
C11×#30392
C11×#30112
C11×#30102
C11×#30092
C11×#29432
C11×#29322
#6108311