Finite Group Databasebeta

← C11×#61676 #14638869

Subgroups — C11×#61676 #14638869

Order 2816.

2024 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3551C211yesmaximal, characteristic, complemented
2C11×#3499C211yesmaximal, characteristic, complemented
3C11×#3320C212yesmaximal, complemented
4C11×#3315C212yesmaximal, complemented
5C11×#3312C212yesmaximal, complemented
6C11×#3307C212yesmaximal, complemented
7C11×#3270C212yesmaximal, complemented
8C11×#3269C212yesmaximal, complemented
9C11×#3267C212yesmaximal, complemented
10C11×#3266C212yesmaximal, complemented
11C11×#3218C212yesmaximal, complemented
12C11×#3202C211yesmaximal, characteristic, complemented
13C11×#3201C212yesmaximal, complemented
14C11×#3200C211yesmaximal, characteristic, complemented
15C11×#3111C212yesmaximal, complemented
16C11×#3013C212yesmaximal, complemented
17C11×#3011C211yesmaximal, characteristic, complemented
18C11×#3010C211yesmaximal, characteristic, complemented
19C11×#2980C211yesmaximal, characteristic, complemented
20C2×C11×2−1+4C2211yescharacteristic
21C2×C11×2−1+4C2211yescharacteristic, complemented
22C2×C11×#137C2212yes—
23C2×C11×#137C2211yescharacteristic, complemented
24C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C11×#135C2212yes—
26C22×C11×Q16C2211yescharacteristic, complemented
27C22×C11×SD16C2211yescharacteristic
28C11×#563—21no—
29C11×#560—21no—
30C11×#555—21no—
31C11×#553C2212yes—
32C11×#552C2212yes—
33C11×#551—21no—
34D4×Q8×C11C2212yes—
35D4×Q8×C11C2212yescomplemented
36C11×#548C2212yes—
37C11×#547—22no—
38C11×#547—22no—
39C11×#547C2212yes—
40C11×#547C2212yescomplemented
41C11×#546C2212yes—
42C11×#540—22no—
43C11×#538—22no—
44C11×#537C2212yes—
45C11×#536—21no—
46C11×#536—21no—
47C11×#536C2211yescharacteristic
48C11×#536C2211yescharacteristic
49C11×#536C2211yescharacteristic, complemented
50C11×#535C2211yescharacteristic
51C11×#532—21no—
52C11×#532C2211yescharacteristic
53C2×C11×C4⋊Q8—21no—
54C2×C11×C4⋊Q8C2211yescharacteristic, complemented
55C11×#529C2212yes—
56C4×C11×#41C2211yescharacteristic, complemented
57C11×#497C2212yes—
58C11×#497C2212yes—
59C11×#491C2212yescomplemented
60C11×#491C2212yescomplemented
61C11×#485C2212yes—
62C11×#485C2212yescomplemented
63C11×#485C2212yescomplemented
64C11×#484C2212yescomplemented
65C11×#483C2212yescomplemented
66C11×#482C2212yes—
67C11×#479C2212yescomplemented
68C11×#478C2212yescomplemented
69C11×#470C2212yes—
70C11×#470C2212yescomplemented
71C11×#468C2212yes—
72C11×#468C2212yes—
73C11×#467C2212yes—
74C11×#467C2212yescomplemented
75C11×#465C2212yes—
76C11×#465C2212yes—
77C11×#464C2212yes—
78C11×#463C2212yes—
79C11×#462C2212yescomplemented
80C11×#462C2212yescomplemented
81C11×#461C2212yes—
82C11×#461C2212yes—
83C11×#452C2212yes—
84C11×#452C2212yes—
85C11×#452C2212yes—
86C11×#452C2212yescomplemented
87C11×#452C2212yescomplemented
88C11×#451C2212yes—
89C11×#451C2212yescomplemented
90C11×#451C2212yescomplemented
91C11×#451C2212yescomplemented
92C11×#451C2212yescomplemented
93C11×#450C2212yes—
94C11×#449C2212yes—
95C11×#449C2212yes—
96C11×#449C2212yes—
97C11×#448C2212yes—
98C11×#448C2212yes—
99C11×#448C2212yes—
100C11×#448C2212yes—
101C11×#442C2212yes—
102C11×#441C2212yescomplemented
103C11×#440C2212yes—
104C11×#440C2212yescomplemented
105C11×#435C2212yes—
106C11×#435C2212yes—
107C11×#435C2212yescomplemented
108C11×#435C2212yescomplemented
109C11×#432C2212yescomplemented
110C11×#419C2211yescharacteristic
111C11×#419C2211yescharacteristic, complemented
112C11×#417C2212yescomplemented
113C11×#416C2211yescharacteristic
114C11×#416C2211yescharacteristic, complemented
115C2×C11×#103C2212yescomplemented
116C11×#408C2211yescharacteristic
117C11×#408C2211yescharacteristic
118C11×#408C2212yescomplemented
119C11×2−1+4—42no—
120C11×2−1+4—42no—
121C11×2−1+4—42no—
122C11×2−1+4—42no—
123C2×C11×#41—21no—
124C2×C11×#41—21no—
125C2×C11×#41—21no—
126C2×C11×#41—21no—
127C2×C11×#41—22no—
128C2×C11×#41C2311yescharacteristic
129C2×C11×#41C2311yescharacteristic
130C2×C11×#41C2312yes—
131C2×C11×#41C2311yescharacteristic
132C2×C11×#41C2312yes—
133C2×C11×#41C2311yescharacteristic
134C2×C11×#41C2311yescharacteristic
135C22×Q8×C11—21no—
136C22×Q8×C11—21no—
137C22×Q8×C11C2311yescharacteristic
138C22×Q8×C11C2312yes—
139C22×Q8×C11C2311yescharacteristic
140C22×Q8×C11C2311yescharacteristic
141C22×Q8×C11C2311yescharacteristic
142C22×Q8×C11C2311yescharacteristic
143C22×D4×C11C2311yescharacteristic
144C11×#137—42no—
145C11×#137—44no—
146C11×AGL(1,ℤ/8)—42no—
147C11×#135—44no—
148C2×C11×Q16—42no—
149C2×C11×Q16C2312yes—
150C2×C11×Q16C2312yes—
151C2×C11×Q16C2312yes—
152C2×C11×Q16C2312yes—
153C2×C11×Q16C2312yes—
154C2×C11×SD16—42no—
155C2×C11×SD16C2312yes—
156C2×C11×SD16C2312yes—
157C2×C11×SD16C2312yes—
158C2×C11×SD16C2312yes—
159C2×C11×SD16C2312yes—
160C2×C11×SD16C2312yes—
161C2×C11×D8C2312yes—
162C2×C11×M16C2311yescharacteristic
163C2×C11×M16C2311yescharacteristic
164C2×C11×M16C2312yes—
165C22×C8×C11C2311yescharacteristic
166C22×C8×C11C2311yescharacteristic
167C22×C8×C11C2312yes—
168C11×C4⋊Q8—21no—
169C11×C4⋊Q8—21no—
170C11×C4⋊Q8—21no—
171C11×C4⋊Q8—22no—
172C11×C4⋊Q8—22no—
173C11×C4⋊Q8—21no—
174C11×C4⋊Q8—21no—
175C11×C4⋊Q8D411yescharacteristic
176C11×C4⋊Q8C2312yes—
177C11×C4⋊Q8C2312yes—
178C11×#127—21no—
179C11×#127D411yescharacteristic
180C11×#126—22no—
181C11×#126—22no—
182C11×#126—22no—
183C11×#125—22no—
184C11×#125C2312yes—
185C11×#124—21no—
186C11×#124—21no—
187C11×#124—21no—
188C11×#124—21no—
189C11×#124—22no—
190C11×#124D411yescharacteristic
191C11×#124D411yescharacteristic
192C11×#124C2312yes—
193C11×#123—21no—
194C11×#123—21no—
195C11×#123—21no—
196C11×#123—21no—
197C11×#123—22no—
198C11×#123—22no—
199C11×#123—22no—
200C11×#123—22no—
201C11×#123—22no—
202C11×#123—22no—
203C11×#123—22no—
204C11×#123—22no—
205C11×#123—22no—
206C11×C22⋊Q8—22no—
207C11×C22⋊Q8—22no—
208C11×C22⋊Q8—22no—
209C11×C22⋊Q8—22no—
210C11×C22⋊Q8—22no—
211C11×C22⋊Q8—22no—
212C11×C22⋊Q8C2312yes—
213C11×C22⋊Q8C2312yes—
214C11×C22⋊Q8C2312yes—
215C11×C22⋊Q8C2312yes—
216C11×C22⋊Q8C2312yes—
217C11×C22⋊Q8C2312yes—
218C11×C22⋊Q8C2312yes—
219C11×#121—22no—
220C11×#121—22no—
221C11×#121—22no—
222C11×#121—22no—
223C11×#121—22no—
224C11×#121—22no—
225C11×#121—22no—
226C11×#121—22no—
227C11×#121D412yes—
228C11×#121D412yes—
229C11×#121C2312yes—
230C11×#121C2312yes—
231C11×#121C2312yes—
232C11×#120—21no—
233C11×#120—21no—
234C11×#120—22no—
235C4×Q8×C11C2312yes—
236C4×Q8×C11C2312yes—
237C4×D4×C11—22no—
238C4×D4×C11—22no—
239C4×D4×C11—22no—
240C4×D4×C11—22no—
241C4×D4×C11—22no—
242C4×D4×C11—22no—
243C4×D4×C11C2312yes—
244C4×D4×C11C2312yes—
245C4×D4×C11C2312yes—
246C4×D4×C11C2312yes—
247C11×#117—22no—
248C11×#117—21no—
249C11×#117—22no—
250C11×#117C2311yescharacteristic
251C11×#117C2311yescharacteristic
252C11×#117C2311yescharacteristic
253C2×C11×C4⋊C4—22no—
254C2×C11×C4⋊C4—22no—
255C2×C11×C4⋊C4—22no—
256C2×C11×C4⋊C4C2312yes—
257C2×C11×C22⋊C4—22no—
258C2×C42×C11—21no—
259C2×C42×C11C2311yescharacteristic
260C11×#107C2312yes—
261C11×#107C2312yes—
262C11×#106C2312yes—
263C11×#106C2312yes—
264C11×C4⋊C8C2312yes—
265C11×C4⋊C8C2312yes—
266C11×#103C2312yes—
267C11×#103C2312yes—
268C11×#103C2312yes—
269C11×#103C2312yes—
270C11×#103C2312yes—
271C11×#103C2312yes—
272C11×#103C2312yes—
273C11×#103C2312yes—
274C11×#103C2312yes—
275C11×#103C2312yes—
276C11×#103C2312yes—
277C11×#103C2312yes—
278C11×#102C2312yes—
279C11×#102C2312yes—
280C11×#102C2312yes—
281C11×#102C2312yes—
282C11×C22⋊C8C2312yes—
283C11×C22⋊C8C2312yes—
284C11×C22⋊C8C2312yes—
285C11×C22⋊C8C2312yes—
286C11×C22⋊C8C2312yes—
287C11×C22⋊C8C2312yes—
288C11×#97C2312yes—
289C11×#97C2312yes—
290#61676C1111yesmaximal, characteristic, direct product factor, Sylow
291C24×C11—21no—
292C11×#41—22no—
293C11×#41—22no—
294C11×#41—24no—
295C11×#41—22no—
296C11×#41—22no—
297C11×#41—41no—
298C11×#41—41no—
299C11×#41—41no—
300C11×#41—41no—
301C11×#41—41no—
302C11×#41—41no—
303C11×#41—42no—
304C11×#41—44no—
305C11×#41—44no—
306C11×#41—42no—
307C11×#41—42no—
308C11×#41—44no—
309C11×#41—44no—
310C11×#41—48no—
311C2×Q8×C11—21no—
312C2×Q8×C11—21no—
313C2×Q8×C11—22no—
314C2×Q8×C11—21no—
315C2×Q8×C11—21no—
316C2×Q8×C11—21no—
317C2×Q8×C11—22no—
318C2×Q8×C11—22no—
319C2×Q8×C11—24no—
320C2×Q8×C11—42no—
321C2×Q8×C11—41no—
322C2×Q8×C11—41no—
323C2×Q8×C11—41no—
324C2×Q8×C11—41no—
325C2×Q8×C11—41no—
326C2×Q8×C11—41no—
327C2×Q8×C11—44no—
328C2×Q8×C11—44no—
329C2×Q8×C11—41no—
330C2×Q8×C11—41no—
331C2×Q8×C11C2×D411yescharacteristic
332C2×Q8×C11C2×D411yescharacteristic
333C2×Q8×C11C2411yescharacteristic
334C2×Q8×C11C2411yescharacteristic
335C2×Q8×C11C2412yes—
336C2×Q8×C11C2412yes—
337C2×Q8×C11C2411yescharacteristic
338C2×D4×C11—21no—
339C2×D4×C11—21no—
340C2×D4×C11—22no—
341C2×D4×C11—21no—
342C2×D4×C11—22no—
343C2×D4×C11—22no—
344C2×D4×C11—22no—
345C2×D4×C11—22no—
346C2×D4×C11—21no—
347C2×D4×C11—41no—
348C2×D4×C11—41no—
349C2×D4×C11C2×D412yes—
350C2×D4×C11C2×D412yes—
351C2×D4×C11C2×D411yescharacteristic
352C2×D4×C11C2×D411yescharacteristic
353C2×D4×C11C2×D412yes—
354C2×D4×C11C2×D411yescharacteristic
355C2×D4×C11C2×D411yescharacteristic
356C2×D4×C11C2412yes—
357C2×D4×C11C2411yescharacteristic
358C22×C4×C11—21no—
359C22×C4×C11—21no—
360C22×C4×C11—21no—
361C22×C4×C11—21no—
362C22×C4×C11—22no—
363C22×C4×C11—21no—
364C22×C4×C11—22no—
365C22×C4×C11—21no—
366C22×C4×C11—22no—
367C22×C4×C11—21no—
368C22×C4×C11—21no—
369C22×C4×C11—22no—
370C22×C4×C11—22no—
371C22×C4×C11—22no—
372C22×C4×C11C2×D412yes—
373C22×C4×C11C2411yescharacteristic
374C22×C4×C11C2412yes—
375C22×C4×C11C2411yescharacteristic
376C22×C4×C11C2411yescharacteristic
377C11×Q16—24no—
378C11×Q16—42no—
379C11×Q16—42no—
380C11×Q16—42no—
381C11×Q16—42no—
382C11×SD16—24no—
383C11×SD16—24no—
384C11×SD16—42no—
385C11×SD16—42no—
386C11×SD16—42no—
387C11×SD16—42no—
388C11×D8—24no—
389C11×M16—41no—
390C11×M16—42no—
391C11×M16—41no—
392C2×C8×C11—41no—
393C2×C8×C11—41no—
394C2×C8×C11—42no—
395C2×C8×C11C2412yes—
396C2×C8×C11C2412yes—
397C2×C8×C11C2412yes—
398C2×C8×C11C2412yes—
399C11×C4⋊C4—22no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—22no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4—22no—
414C11×C4⋊C4—22no—
415C11×C4⋊C4C2×D412yes—
416C11×C4⋊C4C2×D412yes—
417C11×C4⋊C4C2412yes—
418C11×C4⋊C4C2412yes—
419C11×C4⋊C4C2412yes—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—21no—
423C11×C22⋊C4—21no—
424C11×C22⋊C4—21no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—22no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4C2×D412yes—
438C11×C22⋊C4C2×D412yes—
439C11×C22⋊C4C2×D412yes—
440C11×C22⋊C4C2×D412yes—
441C42×C11—21no—
442C42×C11—22no—
443C42×C11—21no—
444C42×C11—22no—
445C42×C11—21no—
446C42×C11C2×D411yescharacteristic
447C42×C11C2×D411yescharacteristic
448C42×C11C2412yes—
449#3551C2×C1111yescharacteristic, complemented
450#3499C2×C1111yescharacteristic, complemented
451#3320C2×C1112yescomplemented
452#3315C2×C1112yescomplemented
453#3312C2×C1112yescomplemented
454#3307C2×C1112yescomplemented
455#3270C2×C1112yescomplemented
456#3269C2×C1112yescomplemented
457#3267C2×C1112yescomplemented
458#3266C2×C1112yescomplemented
459#3218C2×C1112yescomplemented
460#3202C2×C1111yescharacteristic, complemented
461#3201C2×C1112yescomplemented
462#3200C2×C1111yescharacteristic, complemented
463#3111C2×C1112yescomplemented
464#3013C2×C1112yescomplemented
465#3011C2×C1111yescharacteristic, complemented
466#3010C2×C1111yescharacteristic, complemented
467#2980C2×C1111yescharacteristic, complemented
468C23×C11—21no—
469C23×C11—22no—
470C23×C11—81no—
471C23×C11—82no—
472C23×C11C22×D411yescharacteristic
473C23×C11C22×D412yes—
474C23×C11C22×D411yescharacteristic
475C23×C11C22×D411yescharacteristic
476Q8×C11—21no—
477Q8×C11—22no—
478Q8×C11—21no—
479Q8×C11—21no—
480Q8×C11—22no—
481Q8×C11—22no—
482Q8×C11—22no—
483Q8×C11—21no—
484Q8×C11—21no—
485Q8×C11—41no—
486Q8×C11—41no—
487Q8×C11—44no—
488Q8×C11—42no—
489Q8×C11—42no—
490Q8×C11—42no—
491Q8×C11—42no—
492Q8×C11—81no—
493Q8×C11H(5,𝔽2)12yes—
494D4×C11—24no—
495D4×C11—21no—
496D4×C11—22no—
497D4×C11—22no—
498D4×C11—42no—
499D4×C11—42no—
500D4×C11—41no—
501D4×C11—41no—
502D4×C11—42no—
503D4×C11—41no—
504D4×C11—41no—
505D4×C11—42no—
506D4×C11—44no—
507D4×C11—42no—
508D4×C11—81no—
509D4×C11—82no—
510D4×C11—82no—
511D4×C11—82no—
512D4×C11—82no—
513D4×C11H(5,𝔽2)12yes—
514C2×C4×C11—24no—
515C2×C4×C11—21no—
516C2×C4×C11—21no—
517C2×C4×C11—21no—
518C2×C4×C11—22no—
519C2×C4×C11—21no—
520C2×C4×C11—22no—
521C2×C4×C11—21no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—22no—
531C2×C4×C11—42no—
532C2×C4×C11—42no—
533C2×C4×C11—44no—
534C2×C4×C11—42no—
535C2×C4×C11—44no—
536C2×C4×C11—42no—
537C2×C4×C11—42no—
538C2×C4×C11—44no—
539C2×C4×C11—42no—
540C2×C4×C11—42no—
541C2×C4×C11—82no—
542C2×C4×C11—82no—
543C2×C4×C11—82no—
544C2×C4×C11—81no—
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C22×D412yes—
547C2×C4×C11C22×D412yes—
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C22×D412yes—
551C2×C4×C11C2511yescharacteristic
552C8×C11—22no—
553C8×C11—22no—
554C8×C11—22no—
555C8×C11—22no—
556C2×2−1+4C22×C1111yescharacteristic
557C2×2−1+4C22×C1111yescharacteristic, complemented
558C2×#137C22×C1112yes—
559C2×#137C22×C1111yescharacteristic, complemented
560C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
561C2×#135C22×C1112yes—
562C22×Q16C22×C1111yescharacteristic, complemented
563C22×SD16C22×C1111yescharacteristic
564#563—21no—
565#560—21no—
566#555—21no—
567#553C22×C1112yes—
568#552C22×C1112yes—
569#551—21no—
570D4×Q8C22×C1112yes—
571D4×Q8C22×C1112yescomplemented
572#548C22×C1112yes—
573#547—22no—
574#547—22no—
575#547C22×C1112yes—
576#547C22×C1112yescomplemented
577#546C22×C1112yes—
578#540—22no—
579#538—22no—
580#537C22×C1112yes—
581#536—21no—
582#536—21no—
583#536C22×C1111yescharacteristic
584#536C22×C1111yescharacteristic
585#536C22×C1111yescharacteristic, complemented
586#535C22×C1111yescharacteristic
587#532—21no—
588#532C22×C1111yescharacteristic
589C2×C4⋊Q8—21no—
590C2×C4⋊Q8C22×C1111yescharacteristic, complemented
591#529C22×C1112yes—
592C4×#41C22×C1111yescharacteristic, complemented
593#497C22×C1112yes—
594#497C22×C1112yes—
595#491C22×C1112yescomplemented
596#491C22×C1112yescomplemented
597#485C22×C1112yes—
598#485C22×C1112yescomplemented
599#485C22×C1112yescomplemented
600#484C22×C1112yescomplemented
601#483C22×C1112yescomplemented
602#482C22×C1112yes—
603#479C22×C1112yescomplemented
604#478C22×C1112yescomplemented
605#470C22×C1112yes—
606#470C22×C1112yescomplemented
607#468C22×C1112yes—
608#468C22×C1112yes—
609#467C22×C1112yes—
610#467C22×C1112yescomplemented
611#465C22×C1112yes—
612#465C22×C1112yes—
613#464C22×C1112yes—
614#463C22×C1112yes—
615#462C22×C1112yescomplemented
616#462C22×C1112yescomplemented
617#461C22×C1112yes—
618#461C22×C1112yes—
619#452C22×C1112yes—
620#452C22×C1112yes—
621#452C22×C1112yes—
622#452C22×C1112yescomplemented
623#452C22×C1112yescomplemented
624#451C22×C1112yes—
625#451C22×C1112yescomplemented
626#451C22×C1112yescomplemented
627#451C22×C1112yescomplemented
628#451C22×C1112yescomplemented
629#450C22×C1112yes—
630#449C22×C1112yes—
631#449C22×C1112yes—
632#449C22×C1112yes—
633#448C22×C1112yes—
634#448C22×C1112yes—
635#448C22×C1112yes—
636#448C22×C1112yes—
637#442C22×C1112yes—
638#441C22×C1112yescomplemented
639#440C22×C1112yes—
640#440C22×C1112yescomplemented
641#435C22×C1112yes—
642#435C22×C1112yes—
643#435C22×C1112yescomplemented
644#435C22×C1112yescomplemented
645#432C22×C1112yescomplemented
646#419C22×C1111yescharacteristic
647#419C22×C1111yescharacteristic, complemented
648#417C22×C1112yescomplemented
649#416C22×C1111yescharacteristic
650#416C22×C1111yescharacteristic, complemented
651C2×#103C22×C1112yescomplemented
652#408C22×C1111yescharacteristic
653#408C22×C1111yescharacteristic
654#408C22×C1112yescomplemented
655C22×C11—22no—
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—21no—
661C22×C11—22no—
662C22×C11—21no—
663C22×C11—22no—
664C22×C11—21no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—162no—
670C22×C11C23×D411yescharacteristic
671C4×C11—22no—
672C4×C11—22no—
673C4×C11—21no—
674C4×C11—22no—
675C4×C11—22no—
676C4×C11—21no—
677C4×C11—21no—
678C4×C11—42no—
679C4×C11—42no—
680C4×C11—42no—
681C4×C11—41no—
682C4×C11—41no—
683C4×C11—42no—
684C4×C11—42no—
685C4×C11C2×H(5,𝔽2)11yescharacteristic
686C4×C11C2×H(5,𝔽2)11yescharacteristic
6872−1+4—42no—
6882−1+4—42no—
6892−1+4—42no—
6902−1+4—42no—
691C2×#41—21no—
692C2×#41—21no—
693C2×#41—21no—
694C2×#41—21no—
695C2×#41—22no—
696C2×#41C23×C1111yescharacteristic
697C2×#41C23×C1111yescharacteristic
698C2×#41C23×C1112yes—
699C2×#41C23×C1111yescharacteristic
700C2×#41C23×C1112yes—
701C2×#41C23×C1111yescharacteristic
702C2×#41C23×C1111yescharacteristic
703C22×Q8—21no—
704C22×Q8—21no—
705C22×Q8C23×C1111yescharacteristic
706C22×Q8C23×C1112yes—
707C22×Q8C23×C1111yescharacteristic
708C22×Q8C23×C1111yescharacteristic
709C22×Q8C23×C1111yescharacteristic
710C22×Q8C23×C1111yescharacteristic
711C22×D4C23×C1111yescharacteristic
712#137—42no—
713#137—44no—
714AGL(1,ℤ/8)—42no—
715#135—44no—
716C2×Q16—42no—
717C2×Q16C23×C1112yes—
718C2×Q16C23×C1112yes—
719C2×Q16C23×C1112yes—
720C2×Q16C23×C1112yes—
721C2×Q16C23×C1112yes—
722C2×SD16—42no—
723C2×SD16C23×C1112yes—
724C2×SD16C23×C1112yes—
725C2×SD16C23×C1112yes—
726C2×SD16C23×C1112yes—
727C2×SD16C23×C1112yes—
728C2×SD16C23×C1112yes—
729C2×D8C23×C1112yes—
730C2×M16C23×C1111yescharacteristic
731C2×M16C23×C1112yes—
732C2×M16C23×C1111yescharacteristic
733C22×C8C23×C1111yescharacteristic
734C22×C8C23×C1111yescharacteristic
735C22×C8C23×C1112yes—
736C4⋊Q8—21no—
737C4⋊Q8—21no—
738C4⋊Q8—21no—
739C4⋊Q8—22no—
740C4⋊Q8—22no—
741C4⋊Q8—21no—
742C4⋊Q8—21no—
743C4⋊Q8D4×C1111yescharacteristic
744C4⋊Q8C23×C1112yes—
745C4⋊Q8C23×C1112yes—
746#127—21no—
747#127D4×C1111yescharacteristic
748#126—22no—
749#126—22no—
750#126—22no—
751#125—22no—
752#125C23×C1112yes—
753#124—21no—
754#124—21no—
755#124—21no—
756#124—21no—
757#124—22no—
758#124D4×C1111yescharacteristic
759#124D4×C1111yescharacteristic
760#124C23×C1112yes—
761#123—21no—
762#123—21no—
763#123—21no—
764#123—21no—
765#123—22no—
766#123—22no—
767#123—22no—
768#123—22no—
769#123—22no—
770#123—22no—
771#123—22no—
772#123—22no—
773#123—22no—
774C22⋊Q8—22no—
775C22⋊Q8—22no—
776C22⋊Q8—22no—
777C22⋊Q8—22no—
778C22⋊Q8—22no—
779C22⋊Q8—22no—
780C22⋊Q8C23×C1112yes—
781C22⋊Q8C23×C1112yes—
782C22⋊Q8C23×C1112yes—
783C22⋊Q8C23×C1112yes—
784C22⋊Q8C23×C1112yes—
785C22⋊Q8C23×C1112yes—
786C22⋊Q8C23×C1112yes—
787#121—22no—
788#121—22no—
789#121—22no—
790#121—22no—
791#121—22no—
792#121—22no—
793#121—22no—
794#121—22no—
795#121D4×C1112yes—
796#121D4×C1112yes—
797#121C23×C1112yes—
798#121C23×C1112yes—
799#121C23×C1112yes—
800#120—21no—
801#120—21no—
802#120—22no—
803C4×Q8C23×C1112yes—
804C4×Q8C23×C1112yes—
805C4×D4—22no—
806C4×D4—22no—
807C4×D4—22no—
808C4×D4—22no—
809C4×D4—22no—
810C4×D4—22no—
811C4×D4C23×C1112yes—
812C4×D4C23×C1112yes—
813C4×D4C23×C1112yes—
814C4×D4C23×C1112yes—
815#117—22no—
816#117—21no—
817#117—22no—
818#117C23×C1111yescharacteristic
819#117C23×C1111yescharacteristic
820#117C23×C1111yescharacteristic
821C2×C4⋊C4—22no—
822C2×C4⋊C4—22no—
823C2×C4⋊C4—22no—
824C2×C4⋊C4C23×C1112yes—
825C2×C22⋊C4—22no—
826C2×C42—21no—
827C2×C42C23×C1111yescharacteristic
828#107C23×C1112yes—
829#107C23×C1112yes—
830#106C23×C1112yes—
831#106C23×C1112yes—
832C4⋊C8C23×C1112yes—
833C4⋊C8C23×C1112yes—
834#103C23×C1112yes—
835#103C23×C1112yes—
836#103C23×C1112yes—
837#103C23×C1112yes—
838#103C23×C1112yes—
839#103C23×C1112yes—
840#103C23×C1112yes—
841#103C23×C1112yes—
842#103C23×C1112yes—
843#103C23×C1112yes—
844#103C23×C1112yes—
845#103C23×C1112yes—
846#102C23×C1112yes—
847#102C23×C1112yes—
848#102C23×C1112yes—
849#102C23×C1112yes—
850C22⋊C8C23×C1112yes—
851C22⋊C8C23×C1112yes—
852C22⋊C8C23×C1112yes—
853C22⋊C8C23×C1112yes—
854C22⋊C8C23×C1112yes—
855C22⋊C8C23×C1112yes—
856#97C23×C1112yes—
857#97C23×C1112yes—
858C2×C11—41no—
859C2×C11—42no—
860C2×C11—41no—
861C2×C11—41no—
862C2×C11—42no—
863C2×C11—82no—
864C2×C11#348411yescharacteristic
865C2×C11#358612yes—
866C24—21no—
867#41—22no—
868#41—22no—
869#41—24no—
870#41—22no—
871#41—22no—
872#41—41no—
873#41—41no—
874#41—41no—
875#41—41no—
876#41—41no—
877#41—41no—
878#41—42no—
879#41—44no—
880#41—44no—
881#41—42no—
882#41—42no—
883#41—44no—
884#41—44no—
885#41—48no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—22no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—22no—
893C2×Q8—22no—
894C2×Q8—24no—
895C2×Q8—42no—
896C2×Q8—41no—
897C2×Q8—41no—
898C2×Q8—41no—
899C2×Q8—41no—
900C2×Q8—41no—
901C2×Q8—41no—
902C2×Q8—44no—
903C2×Q8—44no—
904C2×Q8—41no—
905C2×Q8—41no—
906C2×Q8C2×D4×C1111yescharacteristic
907C2×Q8C2×D4×C1111yescharacteristic
908C2×Q8C24×C1111yescharacteristic
909C2×Q8C24×C1111yescharacteristic
910C2×Q8C24×C1112yes—
911C2×Q8C24×C1112yes—
912C2×Q8C24×C1111yescharacteristic
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—22no—
916C2×D4—21no—
917C2×D4—22no—
918C2×D4—22no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—21no—
922C2×D4—41no—
923C2×D4—41no—
924C2×D4C2×D4×C1112yes—
925C2×D4C2×D4×C1112yes—
926C2×D4C2×D4×C1111yescharacteristic
927C2×D4C2×D4×C1111yescharacteristic
928C2×D4C2×D4×C1112yes—
929C2×D4C2×D4×C1111yescharacteristic
930C2×D4C2×D4×C1111yescharacteristic
931C2×D4C24×C1112yes—
932C2×D4C24×C1111yescharacteristic
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—22no—
938C22×C4—21no—
939C22×C4—22no—
940C22×C4—21no—
941C22×C4—22no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4C2×D4×C1112yes—
948C22×C4C24×C1111yescharacteristic
949C22×C4C24×C1112yes—
950C22×C4C24×C1111yescharacteristic
951C22×C4C24×C1111yescharacteristic
952Q16—24no—
953Q16—42no—
954Q16—42no—
955Q16—42no—
956Q16—42no—
957SD16—24no—
958SD16—24no—
959SD16—42no—
960SD16—42no—
961SD16—42no—
962SD16—42no—
963D8—24no—
964M16—41no—
965M16—41no—
966M16—42no—
967C2×C8—41no—
968C2×C8—41no—
969C2×C8—42no—
970C2×C8C24×C1112yes—
971C2×C8C24×C1112yes—
972C2×C8C24×C1112yes—
973C2×C8C24×C1112yes—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4C2×D4×C1112yes—
991C4⋊C4C2×D4×C1112yes—
992C4⋊C4C24×C1112yes—
993C4⋊C4C24×C1112yes—
994C4⋊C4C24×C1112yes—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—21no—
998C22⋊C4—21no—
999C22⋊C4—21no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4C2×D4×C1112yes—
1013C22⋊C4C2×D4×C1112yes—
1014C22⋊C4C2×D4×C1112yes—
1015C22⋊C4C2×D4×C1112yes—
1016C42—21no—
1017C42—22no—
1018C42—21no—
1019C42—22no—
1020C42—21no—
1021C42C2×D4×C1111yescharacteristic
1022C42C2×D4×C1111yescharacteristic
1023C42C24×C1112yes—
1024C11#6167611yescharacteristic, direct product factor, Sylow
1025C23—21no—
1026C23—22no—
1027C23—81no—
1028C23—82no—
1029C23C22×D4×C1111yescharacteristic
1030C23C22×D4×C1111yescharacteristic
1031C23C22×D4×C1112yes—
1032C23C22×D4×C1111yescharacteristic
1033Q8—21no—
1034Q8—22no—
1035Q8—21no—
1036Q8—21no—
1037Q8—22no—
1038Q8—22no—
1039Q8—22no—
1040Q8—21no—
1041Q8—21no—
1042Q8—41no—
1043Q8—41no—
1044Q8—44no—
1045Q8—42no—
1046Q8—42no—
1047Q8—42no—
1048Q8—42no—
1049Q8—81no—
1050Q8C11×H(5,𝔽2)12yes—
1051D4—24no—
1052D4—21no—
1053D4—22no—
1054D4—22no—
1055D4—42no—
1056D4—42no—
1057D4—41no—
1058D4—41no—
1059D4—42no—
1060D4—41no—
1061D4—41no—
1062D4—42no—
1063D4—44no—
1064D4—42no—
1065D4—81no—
1066D4—82no—
1067D4—82no—
1068D4—82no—
1069D4—82no—
1070D4C11×H(5,𝔽2)12yes—
1071C2×C4—24no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—42no—
1089C2×C4—42no—
1090C2×C4—44no—
1091C2×C4—42no—
1092C2×C4—44no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—44no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—82no—
1099C2×C4—82no—
1100C2×C4—82no—
1101C2×C4—81no—
1102C2×C4C22×D4×C1111yescharacteristic
1103C2×C4C22×D4×C1112yes—
1104C2×C4C22×D4×C1112yes—
1105C2×C4C22×D4×C1111yescharacteristic
1106C2×C4C22×D4×C1111yescharacteristic
1107C2×C4C22×D4×C1112yes—
1108C2×C4C25×C1111yescharacteristic
1109C8—22no—
1110C8—22no—
1111C8—22no—
1112C8—22no—
1113C22—21no—
1114C22—22no—
1115C22—21no—
1116C22—22no—
1117C22—21no—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—162no—
1128C22C23×D4×C1111yescharacteristic
1129C4—21no—
1130C4—22no—
1131C4—22no—
1132C4—21no—
1133C4—21no—
1134C4—22no—
1135C4—22no—
1136C4—41no—
1137C4—41no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4C2×C11×H(5,𝔽2)11yescharacteristic
1144C4C2×C11×H(5,𝔽2)11yescharacteristic
1145C2—41no—
1146C2—41no—
1147C2—41no—
1148C2—42no—
1149C2—42no—
1150C2—82no—
1151C2C11×#348411yescharacteristic
1152C2C11×#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. C11×#3551C2semidirect
2. C11×#3499C2semidirect
3. C11×#3320C2semidirect
4. C11×#3315C2semidirect
5. C11×#3312C2semidirect
6. C11×#3307C2semidirect
7. C11×#3270C2semidirect
8. C11×#3269C2semidirect
9. C11×#3267C2semidirect
10. C11×#3266C2semidirect
11. C11×#3218C2semidirect
12. C11×#3202C2semidirect
13. C11×#3201C2semidirect
14. C11×#3200C2semidirect
15. C11×#3111C2semidirect
16. C11×#3013C2semidirect
17. C11×#3011C2semidirect
18. C11×#3010C2semidirect
19. C11×#2980C2semidirect
21. C2×C11×2−1+4C22semidirect
23. C2×C11×#137C22semidirect
26. C22×C11×Q16C22semidirect
35. D4×Q8×C11C22semidirect
40. C11×#547C22semidirect
49. C11×#536C22semidirect
54. C2×C11×C4⋊Q8C22semidirect
56. C4×C11×#41C22semidirect
59. C11×#491C22semidirect
60. C11×#491C22semidirect
62. C11×#485C22semidirect
63. C11×#485C22semidirect
64. C11×#484C22semidirect
65. C11×#483C22semidirect
67. C11×#479C22semidirect
68. C11×#478C22semidirect
70. C11×#470C22semidirect
74. C11×#467C22semidirect
79. C11×#462C22semidirect
80. C11×#462C22semidirect
86. C11×#452C22semidirect
87. C11×#452C22semidirect
89. C11×#451C22semidirect
90. C11×#451C22semidirect
91. C11×#451C22semidirect
92. C11×#451C22semidirect
102. C11×#441C22semidirect
104. C11×#440C22semidirect
107. C11×#435C22semidirect
108. C11×#435C22semidirect
109. C11×#432C22semidirect
111. C11×#419C22semidirect
112. C11×#417C22semidirect
114. C11×#416C22semidirect
115. C2×C11×#103C22semidirect
118. C11×#408C22semidirect
290. #61676C11direct (N × H)
449. #3551C2×C11semidirect
450. #3499C2×C11semidirect
451. #3320C2×C11semidirect
452. #3315C2×C11semidirect
453. #3312C2×C11semidirect
454. #3307C2×C11semidirect
455. #3270C2×C11semidirect
456. #3269C2×C11semidirect
457. #3267C2×C11semidirect
458. #3266C2×C11semidirect
459. #3218C2×C11semidirect
460. #3202C2×C11semidirect
461. #3201C2×C11semidirect
462. #3200C2×C11semidirect
463. #3111C2×C11semidirect
464. #3013C2×C11semidirect
465. #3011C2×C11semidirect
466. #3010C2×C11semidirect
467. #2980C2×C11semidirect
557. C2×2−1+4C22×C11semidirect
559. C2×#137C22×C11semidirect
562. C22×Q16C22×C11semidirect
571. D4×Q8C22×C11semidirect
576. #547C22×C11semidirect
585. #536C22×C11semidirect
590. C2×C4⋊Q8C22×C11semidirect
592. C4×#41C22×C11semidirect
595. #491C22×C11semidirect
596. #491C22×C11semidirect
598. #485C22×C11semidirect
599. #485C22×C11semidirect
600. #484C22×C11semidirect
601. #483C22×C11semidirect
603. #479C22×C11semidirect
604. #478C22×C11semidirect
606. #470C22×C11semidirect
610. #467C22×C11semidirect
615. #462C22×C11semidirect
616. #462C22×C11semidirect
622. #452C22×C11semidirect
623. #452C22×C11semidirect
625. #451C22×C11semidirect
626. #451C22×C11semidirect
627. #451C22×C11semidirect
628. #451C22×C11semidirect
638. #441C22×C11semidirect
640. #440C22×C11semidirect
643. #435C22×C11semidirect
644. #435C22×C11semidirect
645. #432C22×C11semidirect
647. #419C22×C11semidirect
648. #417C22×C11semidirect
650. #416C22×C11semidirect
651. C2×#103C22×C11semidirect
654. #408C22×C11semidirect
1024. C11#61676direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35512
C11×#34992
C11×#33202
C11×#33152
C11×#33122
C11×#33072
C11×#32702
C11×#32692
C11×#32672
C11×#32662
C11×#32182
C11×#32022
C11×#32012
C11×#32002
C11×#31112
C11×#30132
C11×#30112
C11×#30102
C11×#29802
#6167611