Finite Group Databasebeta

← C11×#60598 #14637791

Subgroups — C11×#60598 #14637791

Order 2816.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3512C211yesmaximal, characteristic, complemented
2C4×C11×2−1+4C211yesmaximal, characteristic, complemented
3C11×#3127C212yesmaximal, complemented
4C11×#3126C212yesmaximal, complemented
5C11×#3120C212yesmaximal, complemented
6C11×#3119C212yesmaximal, complemented
7C11×#3117C212yesmaximal, complemented
8C11×#3111C212yesmaximal, complemented
9C11×#3108C212yesmaximal, complemented
10C11×#3102C212yesmaximal, complemented
11C11×#3099C211yesmaximal, characteristic, complemented
12C11×#3098C211yesmaximal, characteristic, complemented
13C11×#3080C211yesmaximal, characteristic, complemented
14C2×C11×#479C211yesmaximal, characteristic, complemented
15C11×#3037C211yesmaximal, characteristic, complemented
16C11×#3035C211yesmaximal, characteristic, complemented
17C11×#3013C211yesmaximal, characteristic, complemented
18C11×#3013C211yesmaximal, characteristic, complemented
19C11×#2952C211yesmaximal, characteristic, complemented
20C11×#2951C211yesmaximal, characteristic, complemented
21C11×#2947C211yesmaximal, characteristic, complemented
22C11×#2947C211yesmaximal, characteristic, complemented
23C11×#2925C211yesmaximal, characteristic, complemented
24C2×C11×2−1+4C2211yescharacteristic
25C2×C11×#137C2211yescharacteristic
26C2×C11×#137C2211yescharacteristic
27C2×C11×#135C2211yescharacteristic
28C2×C11×#135C2211yescharacteristic
29C11×#553—22no—
30C11×#553—22no—
31C11×#553—21no—
32C11×#553—21no—
33C11×#552—21no—
34C11×#552—21no—
35C11×#541C2212yes—
36C11×#540C2212yes—
37C11×#537C2211yescharacteristic
38C11×#537C2211yescharacteristic
39C11×#532C2211yescharacteristic
40C11×#529C2212yes—
41C11×#529C2212yes—
42C2×C11×#125C2211yescharacteristic
43C11×#520—22no—
44C11×#520—21no—
45C11×#520C2211yescharacteristic
46C11×#520C2212yes—
47C11×#520C2211yescharacteristic
48C11×#520C2211yescharacteristic
49C11×#520C2211yescharacteristic
50C11×#519—21no—
51C11×#519C2211yescharacteristic
52C11×#519C2212yes—
53C4×C11×#41—22no—
54C4×C11×#41—21no—
55C4×C11×#41C2211yescharacteristic
56C4×C11×#41C2212yes—
57C4×C11×#41C2211yescharacteristic
58C2×C4×Q8×C11—21no—
59C2×C4×Q8×C11C2211yescharacteristic
60C2×C4×Q8×C11C2212yes—
61C11×#485C2212yes—
62C11×#485C2212yes—
63C11×#484C2212yes—
64C11×#483C2212yes—
65C11×#482C2212yes—
66C11×#482C2212yes—
67C11×#481C2212yes—
68C11×#480C2212yes—
69C11×#479C2212yes—
70C11×#479C2212yes—
71C11×#479C2212yes—
72C11×#479C2212yes—
73C11×#479C2212yes—
74C11×#479C2212yes—
75C11×#478C2212yes—
76C11×#478C2212yes—
77C11×#464C2211yescharacteristic
78C11×#464C2211yescharacteristic
79C11×#464C2212yes—
80C11×#464C2212yes—
81C11×#463C2211yescharacteristic
82C11×#463C2211yescharacteristic
83C11×#462C2211yescharacteristic
84C11×#462C2212yes—
85C11×#461C2211yescharacteristic
86C11×#460C2211yescharacteristic
87C11×#460C2212yes—
88C11×#459C2211yescharacteristic
89C11×#452C2212yes—
90C11×#452C2212yes—
91C11×#451C2212yes—
92C11×#451C2212yes—
93C11×#449C2212yes—
94C11×#449C2212yes—
95C11×#448C2212yes—
96C11×#448C2212yes—
97C11×#442C2212yes—
98C11×#441C2212yes—
99C11×#441C2212yes—
100C11×#441C2212yes—
101C11×#440C2212yes—
102C11×#440C2212yes—
103C11×#440C2212yes—
104C11×#440C2212yes—
105C4×C11×Q16C2212yes—
106C4×C11×Q16C2212yes—
107C4×C11×Q16C2212yes—
108C4×C11×SD16C2212yes—
109C4×C11×SD16C2212yes—
110C4×C11×SD16C2212yes—
111C4×C11×SD16C2212yes—
112C4×C11×D8C2212yes—
113C11×#433C2212yes—
114C11×#433C2212yes—
115C11×#432C2212yes—
116C11×#431C2212yes—
117C11×#428C2211yescharacteristic
118C11×#428C2211yescharacteristic
119C2×C11×#107C2211yescharacteristic
120C2×C11×#106C2211yescharacteristic
121C11×#423C2211yescharacteristic
122C2×C11×C4⋊C8C2211yescharacteristic
123C11×#417C2211yescharacteristic
124C11×#417C2211yescharacteristic
125C11×#417C2211yescharacteristic
126C11×#417C2211yescharacteristic
127C11×#416C2211yescharacteristic
128C11×#416C2211yescharacteristic
129C2×C11×#103C2211yescharacteristic
130C2×C11×#103C2211yescharacteristic
131C11×#408C2211yescharacteristic
132C11×#408C2211yescharacteristic
133C11×#405C2211yescharacteristic
134C11×#405C2211yescharacteristic
135C11×2−1+4—24no—
136C11×2−1+4—24no—
137C2×C11×#41—21no—
138C2×C11×#41—22no—
139C2×C11×#41C2312yes—
140C2×C11×#41C2311yescharacteristic
141C2×C11×#41C2311yescharacteristic
142C2×C11×#41C2311yescharacteristic
143C2×C11×#41C2311yescharacteristic
144C22×Q8×C11—21no—
145C22×Q8×C11C2312yes—
146C22×Q8×C11C2311yescharacteristic
147C11×#137—24no—
148C11×#137—24no—
149C11×#135—24no—
150C11×#135—24no—
151C2×C11×Q16C2311yescharacteristic
152C2×C11×Q16C2311yescharacteristic
153C2×C11×Q16C2312yes—
154C2×C11×Q16C2312yes—
155C2×C11×SD16C2311yescharacteristic
156C2×C11×SD16C2311yescharacteristic
157C2×C11×SD16C2311yescharacteristic
158C2×C11×SD16C2311yescharacteristic
159C2×C11×SD16C2312yes—
160C2×C11×SD16C2312yes—
161C2×C11×D8C2311yescharacteristic
162C2×C11×D8C2311yescharacteristic
163C2×C11×M16C2311yescharacteristic
164C2×C11×M16C2311yescharacteristic
165C22×C8×C11C2311yescharacteristic
166C22×C8×C11C2311yescharacteristic
167C11×C4⋊Q8C2311yescharacteristic
168C11×#127C2311yescharacteristic
169C11×#126—22no—
170C11×#126—22no—
171C11×#126—22no—
172C11×#126—22no—
173C11×#125—22no—
174C11×#125—22no—
175C11×#125—21no—
176C11×#125—21no—
177C11×#125C2312yes—
178C11×#125C2312yes—
179C11×#124C2311yescharacteristic
180C11×#124C2311yescharacteristic
181C11×#123—22no—
182C11×#123—22no—
183C11×#123—22no—
184C11×#123—22no—
185C11×C22⋊Q8—21no—
186C11×C22⋊Q8—21no—
187C11×C22⋊Q8C2312yes—
188C11×C22⋊Q8C2312yes—
189C11×#121—21no—
190C11×#121—21no—
191C11×#121—22no—
192C11×#121—22no—
193C11×#121—21no—
194C11×#121—21no—
195C11×#121—22no—
196C11×#121—22no—
197C11×#121C2312yes—
198C11×#121C2312yes—
199C4×Q8×C11—21no—
200C4×Q8×C11—21no—
201C4×Q8×C11—22no—
202C4×Q8×C11—21no—
203C4×Q8×C11—22no—
204C4×Q8×C11—22no—
205C4×Q8×C11—21no—
206C4×Q8×C11—22no—
207C4×Q8×C11—21no—
208C4×Q8×C11D411yescharacteristic
209C4×Q8×C11D411yescharacteristic
210C4×Q8×C11C2312yes—
211C4×Q8×C11C2311yescharacteristic
212C4×Q8×C11C2312yes—
213C4×Q8×C11C2312yes—
214C4×Q8×C11C2312yes—
215C4×Q8×C11C2312yes—
216C4×Q8×C11C2311yescharacteristic
217C4×Q8×C11C2312yes—
218C4×Q8×C11C2312yes—
219C4×D4×C11—22no—
220C4×D4×C11—21no—
221C4×D4×C11—21no—
222C4×D4×C11—22no—
223C4×D4×C11—21no—
224C4×D4×C11—22no—
225C4×D4×C11—22no—
226C4×D4×C11—22no—
227C4×D4×C11—22no—
228C4×D4×C11—22no—
229C4×D4×C11—22no—
230C4×D4×C11—22no—
231C4×D4×C11—22no—
232C4×D4×C11—21no—
233C4×D4×C11—21no—
234C4×D4×C11D412yes—
235C4×D4×C11D411yescharacteristic
236C4×D4×C11D412yes—
237C4×D4×C11D411yescharacteristic
238C4×D4×C11C2311yescharacteristic
239C4×D4×C11C2312yes—
240C4×D4×C11C2311yescharacteristic
241C4×D4×C11C2312yes—
242C4×D4×C11C2312yes—
243C11×#117—21no—
244C11×#117—22no—
245C11×#117—21no—
246C11×#117—21no—
247C11×#117—22no—
248C11×#117—22no—
249C11×#117—22no—
250C11×#117—22no—
251C11×#117—21no—
252C11×#117—22no—
253C11×#117—22no—
254C11×#117C2311yescharacteristic
255C11×#117C2312yes—
256C11×#117C2311yescharacteristic
257C11×#117C2312yes—
258C2×C11×C4⋊C4—21no—
259C2×C11×C4⋊C4—22no—
260C2×C11×C4⋊C4—21no—
261C2×C11×C4⋊C4—21no—
262C2×C11×C4⋊C4—21no—
263C2×C11×C4⋊C4—22no—
264C2×C11×C4⋊C4—21no—
265C2×C11×C4⋊C4—21no—
266C2×C11×C4⋊C4C2311yescharacteristic
267C2×C11×C4⋊C4C2312yes—
268C2×C11×C4⋊C4C2311yescharacteristic
269C2×C11×C4⋊C4C2311yescharacteristic
270C2×C42×C11—21no—
271C2×C42×C11—22no—
272C2×C42×C11—22no—
273C2×C42×C11—21no—
274C2×C42×C11C2311yescharacteristic
275C2×C42×C11C2312yes—
276C11×#107C2312yes—
277C11×#107C2312yes—
278C11×#107C2312yes—
279C11×#107C2312yes—
280C11×#106C2312yes—
281C11×#106C2312yes—
282C11×#106C2312yes—
283C11×#106C2312yes—
284C11×C4⋊C8C2311yescharacteristic
285C11×C4⋊C8C2311yescharacteristic
286C11×C4⋊C8C2311yescharacteristic
287C11×C4⋊C8C2311yescharacteristic
288C11×C4⋊C8C2312yes—
289C11×C4⋊C8C2312yes—
290C11×#103C2312yes—
291C11×#103C2312yes—
292C11×#103C2312yes—
293C11×#103C2312yes—
294C11×#103C2311yescharacteristic
295C11×#103C2311yescharacteristic
296C11×#103C2311yescharacteristic
297C11×#103C2311yescharacteristic
298C11×#103C2312yes—
299C11×#103C2312yes—
300C11×#103C2312yes—
301C11×#103C2312yes—
302C11×#102C2311yescharacteristic
303C11×#102C2311yescharacteristic
304C11×#102C2311yescharacteristic
305C11×#102C2311yescharacteristic
306C11×#102C2312yes—
307C11×#102C2312yes—
308C11×#102C2312yes—
309C11×#102C2312yes—
310C11×C22⋊C8C2312yes—
311C11×C22⋊C8C2312yes—
312C11×C22⋊C8C2312yes—
313C11×C22⋊C8C2312yes—
314C11×#97C2312yes—
315C11×#97C2312yes—
316C4×C8×C11C2312yes—
317C4×C8×C11C2312yes—
318#60598C1111yesmaximal, characteristic, direct product factor, Sylow
319C11×#41—216no—
320C11×#41—28no—
321C11×#41—24no—
322C11×#41—24no—
323C11×#41—22no—
324C11×#41—22no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41#4114yes—
331C2×Q8×C11—28no—
332C2×Q8×C11—24no—
333C2×Q8×C11—24no—
334C2×Q8×C11—22no—
335C2×Q8×C11—21no—
336C2×Q8×C11—22no—
337C2×Q8×C11C2×D411yescharacteristic
338C2×Q8×C11#4114yes—
339C2×Q8×C11C2411yescharacteristic
340C2×Q8×C11C2411yescharacteristic
341C2×Q8×C11C2411yescharacteristic
342C2×Q8×C11C2412yes—
343C2×D4×C11—22no—
344C2×D4×C11—21no—
345C2×D4×C11—21no—
346C2×D4×C11—21no—
347C2×D4×C11—22no—
348C2×D4×C11—22no—
349C2×D4×C11—21no—
350C2×D4×C11—21no—
351C2×D4×C11C2×D412yes—
352C2×D4×C11C2×D411yescharacteristic
353C2×D4×C11C2411yescharacteristic
354C2×D4×C11C2411yescharacteristic
355C2×D4×C11C2411yescharacteristic
356C22×C4×C11—22no—
357C22×C4×C11—21no—
358C22×C4×C11—22no—
359C22×C4×C11—21no—
360C22×C4×C11—22no—
361C22×C4×C11—21no—
362C22×C4×C11—21no—
363C22×C4×C11—21no—
364C22×C4×C11—21no—
365C22×C4×C11—21no—
366C22×C4×C11—21no—
367C22×C4×C11—22no—
368C22×C4×C11—21no—
369C22×C4×C11—22no—
370C22×C4×C11—22no—
371C22×C4×C11C2×D411yescharacteristic
372C22×C4×C11C2×D412yes—
373C22×C4×C11C2×D411yescharacteristic
374C22×C4×C11C2×D412yes—
375C22×C4×C11C2412yes—
376C22×C4×C11C2411yescharacteristic
377C11×Q16—22no—
378C11×Q16—22no—
379C11×Q16—24no—
380C11×Q16—24no—
381C11×SD16—22no—
382C11×SD16—22no—
383C11×SD16—24no—
384C11×SD16—24no—
385C11×SD16—22no—
386C11×SD16—22no—
387C11×D8—22no—
388C11×D8—22no—
389C11×M16—22no—
390C11×M16—22no—
391C2×C8×C11—22no—
392C2×C8×C11—22no—
393C2×C8×C11C2411yescharacteristic
394C2×C8×C11C2411yescharacteristic
395C2×C8×C11C2412yes—
396C2×C8×C11C2412yes—
397C2×C8×C11C2411yescharacteristic
398C2×C8×C11C2411yescharacteristic
399C11×C4⋊C4—22no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—21no—
406C11×C4⋊C4—21no—
407C11×C4⋊C4—21no—
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⋊C4—21no—
416C11×C4⋊C4—22no—
417C11×C4⋊C4—22no—
418C11×C4⋊C4—21no—
419C11×C4⋊C4—21no—
420C11×C4⋊C4C2×D411yescharacteristic
421C11×C4⋊C4C2×D411yescharacteristic
422C11×C4⋊C4C2×D412yes—
423C11×C4⋊C4C2×D412yes—
424C11×C4⋊C4C2411yescharacteristic
425C11×C4⋊C4C2412yes—
426C11×C4⋊C4C2411yescharacteristic
427C11×C4⋊C4C2412yes—
428C11×C4⋊C4C2412yes—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—21no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—21no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—21no—
436C11×C22⋊C4—21no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—22no—
440C11×C22⋊C4—22no—
441C11×C22⋊C4—22no—
442C11×C22⋊C4—21no—
443C11×C22⋊C4—21no—
444C11×C22⋊C4C2×D412yes—
445C11×C22⋊C4C2×D412yes—
446C11×C22⋊C4C2×D412yes—
447C42×C11—22no—
448C42×C11—21no—
449C42×C11—22no—
450C42×C11—21no—
451C42×C11—22no—
452C42×C11—22no—
453C42×C11—22no—
454C42×C11—22no—
455C42×C11—21no—
456C42×C11—22no—
457C42×C11—22no—
458C42×C11C2×D412yes—
459C42×C11C2×D411yescharacteristic
460C42×C11C2×D412yes—
461C42×C11C2×D411yescharacteristic
462C42×C11C2412yes—
463C42×C11C2411yescharacteristic
464C42×C11C2411yescharacteristic
465#3512C2×C1111yescharacteristic, complemented
466C4×2−1+4C2×C1111yescharacteristic, complemented
467#3127C2×C1112yescomplemented
468#3126C2×C1112yescomplemented
469#3120C2×C1112yescomplemented
470#3119C2×C1112yescomplemented
471#3117C2×C1112yescomplemented
472#3111C2×C1112yescomplemented
473#3108C2×C1112yescomplemented
474#3102C2×C1112yescomplemented
475#3099C2×C1111yescharacteristic, complemented
476#3098C2×C1111yescharacteristic, complemented
477#3080C2×C1111yescharacteristic, complemented
478C2×#479C2×C1111yescharacteristic, complemented
479#3037C2×C1111yescharacteristic, complemented
480#3035C2×C1111yescharacteristic, complemented
481#3013C2×C1111yescharacteristic, complemented
482#3013C2×C1111yescharacteristic, complemented
483#2952C2×C1111yescharacteristic, complemented
484#2951C2×C1111yescharacteristic, complemented
485#2947C2×C1111yescharacteristic, complemented
486#2947C2×C1111yescharacteristic, complemented
487#2925C2×C1111yescharacteristic, complemented
488C23×C11—21no—
489C23×C11—21no—
490C23×C11—21no—
491C23×C11C22×D412yes—
492C23×C11C22×D411yescharacteristic
493Q8×C11—28no—
494Q8×C11—22no—
495Q8×C11—24no—
496Q8×C11—21no—
497Q8×C11—22no—
498Q8×C11—21no—
499Q8×C11—21no—
500Q8×C11—21no—
501Q8×C11—21no—
502Q8×C11C2×#4112yes—
503Q8×C11C2×#4114yes—
504D4×C11—28no—
505D4×C11—24no—
506D4×C11—24no—
507D4×C11—22no—
508D4×C11—21no—
509D4×C11—21no—
510D4×C11—21no—
511D4×C11—21no—
512D4×C11—21no—
513D4×C11—42no—
514D4×C11—42no—
515D4×C11—81no—
516D4×C11—81no—
517D4×C11—82no—
518D4×C11—82no—
519D4×C11C2×#4112yes—
520C2×C4×C11—28no—
521C2×C4×C11—28no—
522C2×C4×C11—24no—
523C2×C4×C11—22no—
524C2×C4×C11—21no—
525C2×C4×C11—24no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—22no—
531C2×C4×C11—21no—
532C2×C4×C11—21no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—42no—
536C2×C4×C11—41no—
537C2×C4×C11—42no—
538C2×C4×C11—41no—
539C2×C4×C11—42no—
540C2×C4×C11—42no—
541C2×C4×C11—42no—
542C2×C4×C11—82no—
543C2×C4×C11—82no—
544C2×C4×C11—81no—
545C2×C4×C11—82no—
546C2×C4×C11—81no—
547C2×C4×C11—82no—
548C2×C4×C11—81no—
549C2×C4×C11—81no—
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C22×D412yes—
552C2×C4×C11C22×D411yescharacteristic
553C2×C4×C11C22×D412yes—
554C2×C4×C11C22×D412yes—
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11C22×D411yescharacteristic
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C2×#4112yes—
559C2×C4×C11C2×#4112yes—
560C2×C4×C11C2511yescharacteristic
561C8×C11—21no—
562C8×C11—21no—
563C8×C11—21no—
564C8×C11—21no—
565C8×C11—22no—
566C8×C11—22no—
567C2×2−1+4C22×C1111yescharacteristic
568C2×#137C22×C1111yescharacteristic
569C2×#137C22×C1111yescharacteristic
570C2×#135C22×C1111yescharacteristic
571C2×#135C22×C1111yescharacteristic
572#553—22no—
573#553—22no—
574#553—21no—
575#553—21no—
576#552—21no—
577#552—21no—
578#541C22×C1112yes—
579#540C22×C1112yes—
580#537C22×C1111yescharacteristic
581#537C22×C1111yescharacteristic
582#532C22×C1111yescharacteristic
583#529C22×C1112yes—
584#529C22×C1112yes—
585C2×#125C22×C1111yescharacteristic
586#520—22no—
587#520—21no—
588#520C22×C1112yes—
589#520C22×C1111yescharacteristic
590#520C22×C1111yescharacteristic
591#520C22×C1111yescharacteristic
592#520C22×C1111yescharacteristic
593#519—21no—
594#519C22×C1112yes—
595#519C22×C1111yescharacteristic
596C4×#41—22no—
597C4×#41—21no—
598C4×#41C22×C1111yescharacteristic
599C4×#41C22×C1112yes—
600C4×#41C22×C1111yescharacteristic
601C2×C4×Q8—21no—
602C2×C4×Q8C22×C1111yescharacteristic
603C2×C4×Q8C22×C1112yes—
604#485C22×C1112yes—
605#485C22×C1112yes—
606#484C22×C1112yes—
607#483C22×C1112yes—
608#482C22×C1112yes—
609#482C22×C1112yes—
610#481C22×C1112yes—
611#480C22×C1112yes—
612#479C22×C1112yes—
613#479C22×C1112yes—
614#479C22×C1112yes—
615#479C22×C1112yes—
616#479C22×C1112yes—
617#479C22×C1112yes—
618#478C22×C1112yes—
619#478C22×C1112yes—
620#464C22×C1112yes—
621#464C22×C1111yescharacteristic
622#464C22×C1112yes—
623#464C22×C1111yescharacteristic
624#463C22×C1111yescharacteristic
625#463C22×C1111yescharacteristic
626#462C22×C1112yes—
627#462C22×C1111yescharacteristic
628#461C22×C1111yescharacteristic
629#460C22×C1112yes—
630#460C22×C1111yescharacteristic
631#459C22×C1111yescharacteristic
632#452C22×C1112yes—
633#452C22×C1112yes—
634#451C22×C1112yes—
635#451C22×C1112yes—
636#449C22×C1112yes—
637#449C22×C1112yes—
638#448C22×C1112yes—
639#448C22×C1112yes—
640#442C22×C1112yes—
641#441C22×C1112yes—
642#441C22×C1112yes—
643#441C22×C1112yes—
644#440C22×C1112yes—
645#440C22×C1112yes—
646#440C22×C1112yes—
647#440C22×C1112yes—
648C4×Q16C22×C1112yes—
649C4×Q16C22×C1112yes—
650C4×Q16C22×C1112yes—
651C4×SD16C22×C1112yes—
652C4×SD16C22×C1112yes—
653C4×SD16C22×C1112yes—
654C4×SD16C22×C1112yes—
655C4×D8C22×C1112yes—
656#433C22×C1112yes—
657#433C22×C1112yes—
658#432C22×C1112yes—
659#431C22×C1112yes—
660#428C22×C1111yescharacteristic
661#428C22×C1111yescharacteristic
662C2×#107C22×C1111yescharacteristic
663C2×#106C22×C1111yescharacteristic
664#423C22×C1111yescharacteristic
665C2×C4⋊C8C22×C1111yescharacteristic
666#417C22×C1111yescharacteristic
667#417C22×C1111yescharacteristic
668#417C22×C1111yescharacteristic
669#417C22×C1111yescharacteristic
670#416C22×C1111yescharacteristic
671#416C22×C1111yescharacteristic
672C2×#103C22×C1111yescharacteristic
673C2×#103C22×C1111yescharacteristic
674#408C22×C1111yescharacteristic
675#408C22×C1111yescharacteristic
676#405C22×C1111yescharacteristic
677#405C22×C1111yescharacteristic
678C22×C11—21no—
679C22×C11—21no—
680C22×C11—22no—
681C22×C11—22no—
682C22×C11—22no—
683C22×C11—22no—
684C22×C11—41no—
685C22×C11—41no—
686C22×C11—41no—
687C22×C11—41no—
688C22×C11—41no—
689C22×C11—41no—
690C22×C11—41no—
691C22×C11—41no—
692C22×C11#52512yes—
693C22×C11C23×D411yescharacteristic
694C4×C11—21no—
695C4×C11—22no—
696C4×C11—21no—
697C4×C11—21no—
698C4×C11—22no—
699C4×C11—21no—
700C4×C11—24no—
701C4×C11—22no—
702C4×C11—22no—
703C4×C11—42no—
704C4×C11—41no—
705C4×C11—42no—
706C4×C11—41no—
707C4×C11—42no—
708C4×C11—41no—
709C4×C11—41no—
710C4×C11#52512yes—
711C4×C11C22×#4111yescharacteristic
712C4×C11C22×#4111yescharacteristic
7132−1+4—24no—
7142−1+4—24no—
715C2×#41—21no—
716C2×#41—22no—
717C2×#41C23×C1112yes—
718C2×#41C23×C1111yescharacteristic
719C2×#41C23×C1111yescharacteristic
720C2×#41C23×C1111yescharacteristic
721C2×#41C23×C1111yescharacteristic
722C22×Q8—21no—
723C22×Q8C23×C1112yes—
724C22×Q8C23×C1111yescharacteristic
725#137—24no—
726#137—24no—
727#135—24no—
728#135—24no—
729C2×Q16C23×C1111yescharacteristic
730C2×Q16C23×C1111yescharacteristic
731C2×Q16C23×C1112yes—
732C2×Q16C23×C1112yes—
733C2×SD16C23×C1111yescharacteristic
734C2×SD16C23×C1111yescharacteristic
735C2×SD16C23×C1111yescharacteristic
736C2×SD16C23×C1111yescharacteristic
737C2×SD16C23×C1112yes—
738C2×SD16C23×C1112yes—
739C2×D8C23×C1111yescharacteristic
740C2×D8C23×C1111yescharacteristic
741C2×M16C23×C1111yescharacteristic
742C2×M16C23×C1111yescharacteristic
743C22×C8C23×C1111yescharacteristic
744C22×C8C23×C1111yescharacteristic
745C4⋊Q8C23×C1111yescharacteristic
746#127C23×C1111yescharacteristic
747#126—22no—
748#126—22no—
749#126—22no—
750#126—22no—
751#125—22no—
752#125—22no—
753#125—21no—
754#125—21no—
755#125C23×C1112yes—
756#125C23×C1112yes—
757#124C23×C1111yescharacteristic
758#124C23×C1111yescharacteristic
759#123—22no—
760#123—22no—
761#123—22no—
762#123—22no—
763C22⋊Q8—21no—
764C22⋊Q8—21no—
765C22⋊Q8C23×C1112yes—
766C22⋊Q8C23×C1112yes—
767#121—21no—
768#121—21no—
769#121—22no—
770#121—22no—
771#121—21no—
772#121—21no—
773#121—22no—
774#121—22no—
775#121C23×C1112yes—
776#121C23×C1112yes—
777C4×Q8—21no—
778C4×Q8—21no—
779C4×Q8—22no—
780C4×Q8—21no—
781C4×Q8—22no—
782C4×Q8—22no—
783C4×Q8—21no—
784C4×Q8—22no—
785C4×Q8—21no—
786C4×Q8D4×C1111yescharacteristic
787C4×Q8D4×C1111yescharacteristic
788C4×Q8C23×C1112yes—
789C4×Q8C23×C1111yescharacteristic
790C4×Q8C23×C1112yes—
791C4×Q8C23×C1112yes—
792C4×Q8C23×C1112yes—
793C4×Q8C23×C1112yes—
794C4×Q8C23×C1111yescharacteristic
795C4×Q8C23×C1112yes—
796C4×Q8C23×C1112yes—
797C4×D4—22no—
798C4×D4—21no—
799C4×D4—21no—
800C4×D4—22no—
801C4×D4—21no—
802C4×D4—22no—
803C4×D4—22no—
804C4×D4—22no—
805C4×D4—22no—
806C4×D4—22no—
807C4×D4—22no—
808C4×D4—22no—
809C4×D4—22no—
810C4×D4—21no—
811C4×D4—21no—
812C4×D4D4×C1112yes—
813C4×D4D4×C1111yescharacteristic
814C4×D4D4×C1112yes—
815C4×D4D4×C1111yescharacteristic
816C4×D4C23×C1111yescharacteristic
817C4×D4C23×C1112yes—
818C4×D4C23×C1111yescharacteristic
819C4×D4C23×C1112yes—
820C4×D4C23×C1112yes—
821#117—21no—
822#117—22no—
823#117—21no—
824#117—21no—
825#117—22no—
826#117—22no—
827#117—22no—
828#117—22no—
829#117—21no—
830#117—22no—
831#117—22no—
832#117C23×C1111yescharacteristic
833#117C23×C1112yes—
834#117C23×C1111yescharacteristic
835#117C23×C1112yes—
836C2×C4⋊C4—21no—
837C2×C4⋊C4—22no—
838C2×C4⋊C4—21no—
839C2×C4⋊C4—21no—
840C2×C4⋊C4—21no—
841C2×C4⋊C4—22no—
842C2×C4⋊C4—21no—
843C2×C4⋊C4—21no—
844C2×C4⋊C4C23×C1111yescharacteristic
845C2×C4⋊C4C23×C1112yes—
846C2×C4⋊C4C23×C1111yescharacteristic
847C2×C4⋊C4C23×C1111yescharacteristic
848C2×C42—21no—
849C2×C42—22no—
850C2×C42—22no—
851C2×C42—21no—
852C2×C42C23×C1111yescharacteristic
853C2×C42C23×C1112yes—
854#107C23×C1112yes—
855#107C23×C1112yes—
856#107C23×C1112yes—
857#107C23×C1112yes—
858#106C23×C1112yes—
859#106C23×C1112yes—
860#106C23×C1112yes—
861#106C23×C1112yes—
862C4⋊C8C23×C1111yescharacteristic
863C4⋊C8C23×C1111yescharacteristic
864C4⋊C8C23×C1111yescharacteristic
865C4⋊C8C23×C1111yescharacteristic
866C4⋊C8C23×C1112yes—
867C4⋊C8C23×C1112yes—
868#103C23×C1112yes—
869#103C23×C1112yes—
870#103C23×C1112yes—
871#103C23×C1112yes—
872#103C23×C1111yescharacteristic
873#103C23×C1111yescharacteristic
874#103C23×C1111yescharacteristic
875#103C23×C1111yescharacteristic
876#103C23×C1112yes—
877#103C23×C1112yes—
878#103C23×C1112yes—
879#103C23×C1112yes—
880#102C23×C1111yescharacteristic
881#102C23×C1111yescharacteristic
882#102C23×C1111yescharacteristic
883#102C23×C1111yescharacteristic
884#102C23×C1112yes—
885#102C23×C1112yes—
886#102C23×C1112yes—
887#102C23×C1112yes—
888C22⋊C8C23×C1112yes—
889C22⋊C8C23×C1112yes—
890C22⋊C8C23×C1112yes—
891C22⋊C8C23×C1112yes—
892#97C23×C1112yes—
893#97C23×C1112yes—
894C4×C8C23×C1112yes—
895C4×C8C23×C1112yes—
896C2×C11—22no—
897C2×C11—42no—
898C2×C11—42no—
899C2×C11—81no—
900C2×C11—81no—
901C2×C11C2×#52511yescharacteristic
902C2×C11#358411yescharacteristic
903C2×C11#358611yescharacteristic
904#41—216no—
905#41—28no—
906#41—24no—
907#41—24no—
908#41—22no—
909#41—22no—
910#41—22no—
911#41—22no—
912#41—22no—
913#41—22no—
914#41—22no—
915#41C11×#4114yes—
916C2×Q8—28no—
917C2×Q8—24no—
918C2×Q8—24no—
919C2×Q8—22no—
920C2×Q8—21no—
921C2×Q8—22no—
922C2×Q8C2×D4×C1111yescharacteristic
923C2×Q8C11×#4114yes—
924C2×Q8C24×C1111yescharacteristic
925C2×Q8C24×C1111yescharacteristic
926C2×Q8C24×C1111yescharacteristic
927C2×Q8C24×C1112yes—
928C2×D4—22no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—22no—
933C2×D4—22no—
934C2×D4—21no—
935C2×D4—21no—
936C2×D4C2×D4×C1112yes—
937C2×D4C2×D4×C1111yescharacteristic
938C2×D4C24×C1111yescharacteristic
939C2×D4C24×C1111yescharacteristic
940C2×D4C24×C1111yescharacteristic
941C22×C4—22no—
942C22×C4—21no—
943C22×C4—22no—
944C22×C4—21no—
945C22×C4—22no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—22no—
953C22×C4—21no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4C2×D4×C1111yescharacteristic
957C22×C4C2×D4×C1112yes—
958C22×C4C2×D4×C1111yescharacteristic
959C22×C4C2×D4×C1112yes—
960C22×C4C24×C1112yes—
961C22×C4C24×C1111yescharacteristic
962Q16—22no—
963Q16—22no—
964Q16—24no—
965Q16—24no—
966SD16—22no—
967SD16—22no—
968SD16—24no—
969SD16—24no—
970SD16—22no—
971SD16—22no—
972D8—22no—
973D8—22no—
974M16—22no—
975M16—22no—
976C2×C8—22no—
977C2×C8—22no—
978C2×C8C24×C1111yescharacteristic
979C2×C8C24×C1111yescharacteristic
980C2×C8C24×C1112yes—
981C2×C8C24×C1112yes—
982C2×C8C24×C1111yescharacteristic
983C2×C8C24×C1111yescharacteristic
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—21no—
989C4⋊C4—22no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—21no—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4C2×D4×C1111yescharacteristic
1006C4⋊C4C2×D4×C1111yescharacteristic
1007C4⋊C4C2×D4×C1112yes—
1008C4⋊C4C2×D4×C1112yes—
1009C4⋊C4C24×C1111yescharacteristic
1010C4⋊C4C24×C1112yes—
1011C4⋊C4C24×C1111yescharacteristic
1012C4⋊C4C24×C1112yes—
1013C4⋊C4C24×C1112yes—
1014C22⋊C4—22no—
1015C22⋊C4—21no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—21no—
1019C22⋊C4—22no—
1020C22⋊C4—21no—
1021C22⋊C4—21no—
1022C22⋊C4—21no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—21no—
1028C22⋊C4—21no—
1029C22⋊C4C2×D4×C1112yes—
1030C22⋊C4C2×D4×C1112yes—
1031C22⋊C4C2×D4×C1112yes—
1032C42—22no—
1033C42—21no—
1034C42—22no—
1035C42—21no—
1036C42—22no—
1037C42—22no—
1038C42—22no—
1039C42—22no—
1040C42—21no—
1041C42—22no—
1042C42—22no—
1043C42C2×D4×C1112yes—
1044C42C2×D4×C1111yescharacteristic
1045C42C2×D4×C1112yes—
1046C42C2×D4×C1111yescharacteristic
1047C42C24×C1112yes—
1048C42C24×C1111yescharacteristic
1049C42C24×C1111yescharacteristic
1050C11#6059811yescharacteristic, direct product factor, Sylow
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23C22×D4×C1112yes—
1055C23C22×D4×C1111yescharacteristic
1056Q8—28no—
1057Q8—22no—
1058Q8—24no—
1059Q8—21no—
1060Q8—22no—
1061Q8—21no—
1062Q8—21no—
1063Q8—21no—
1064Q8—21no—
1065Q8C2×C11×#4112yes—
1066Q8C2×C11×#4114yes—
1067D4—28no—
1068D4—24no—
1069D4—24no—
1070D4—22no—
1071D4—21no—
1072D4—21no—
1073D4—21no—
1074D4—21no—
1075D4—21no—
1076D4—42no—
1077D4—42no—
1078D4—81no—
1079D4—81no—
1080D4—82no—
1081D4—82no—
1082D4C2×C11×#4112yes—
1083C2×C4—28no—
1084C2×C4—28no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—42no—
1099C2×C4—41no—
1100C2×C4—42no—
1101C2×C4—41no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—42no—
1105C2×C4—82no—
1106C2×C4—82no—
1107C2×C4—81no—
1108C2×C4—82no—
1109C2×C4—81no—
1110C2×C4—82no—
1111C2×C4—81no—
1112C2×C4—81no—
1113C2×C4C22×D4×C1111yescharacteristic
1114C2×C4C22×D4×C1112yes—
1115C2×C4C22×D4×C1111yescharacteristic
1116C2×C4C22×D4×C1112yes—
1117C2×C4C22×D4×C1112yes—
1118C2×C4C22×D4×C1111yescharacteristic
1119C2×C4C22×D4×C1111yescharacteristic
1120C2×C4C22×D4×C1111yescharacteristic
1121C2×C4C2×C11×#4112yes—
1122C2×C4C2×C11×#4112yes—
1123C2×C4C25×C1111yescharacteristic
1124C8—21no—
1125C8—21no—
1126C8—21no—
1127C8—21no—
1128C8—22no—
1129C8—22no—
1130C22—21no—
1131C22—21no—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22C11×#52512yes—
1145C22C23×D4×C1111yescharacteristic
1146C4—24no—
1147C4—22no—
1148C4—22no—
1149C4—21no—
1150C4—22no—
1151C4—21no—
1152C4—21no—
1153C4—22no—
1154C4—21no—
1155C4—41no—
1156C4—41no—
1157C4—42no—
1158C4—41no—
1159C4—42no—
1160C4—41no—
1161C4—42no—
1162C4C11×#52512yes—
1163C4C22×C11×#4111yescharacteristic
1164C4C22×C11×#4111yescharacteristic
1165C2—22no—
1166C2—42no—
1167C2—42no—
1168C2—81no—
1169C2—81no—
1170C2C2×C11×#52511yescharacteristic
1171C2C11×#358411yescharacteristic
1172C2C11×#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×#3512C2semidirect
2. C4×C11×2−1+4C2semidirect
3. C11×#3127C2semidirect
4. C11×#3126C2semidirect
5. C11×#3120C2semidirect
6. C11×#3119C2semidirect
7. C11×#3117C2semidirect
8. C11×#3111C2semidirect
9. C11×#3108C2semidirect
10. C11×#3102C2semidirect
11. C11×#3099C2semidirect
12. C11×#3098C2semidirect
13. C11×#3080C2semidirect
14. C2×C11×#479C2semidirect
15. C11×#3037C2semidirect
16. C11×#3035C2semidirect
17. C11×#3013C2semidirect
18. C11×#3013C2semidirect
19. C11×#2952C2semidirect
20. C11×#2951C2semidirect
21. C11×#2947C2semidirect
22. C11×#2947C2semidirect
23. C11×#2925C2semidirect
318. #60598C11direct (N × H)
465. #3512C2×C11semidirect
466. C4×2−1+4C2×C11semidirect
467. #3127C2×C11semidirect
468. #3126C2×C11semidirect
469. #3120C2×C11semidirect
470. #3119C2×C11semidirect
471. #3117C2×C11semidirect
472. #3111C2×C11semidirect
473. #3108C2×C11semidirect
474. #3102C2×C11semidirect
475. #3099C2×C11semidirect
476. #3098C2×C11semidirect
477. #3080C2×C11semidirect
478. C2×#479C2×C11semidirect
479. #3037C2×C11semidirect
480. #3035C2×C11semidirect
481. #3013C2×C11semidirect
482. #3013C2×C11semidirect
483. #2952C2×C11semidirect
484. #2951C2×C11semidirect
485. #2947C2×C11semidirect
486. #2947C2×C11semidirect
487. #2925C2×C11semidirect
1050. C11#60598direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35122
C4×C11×2−1+42
C11×#31272
C11×#31262
C11×#31202
C11×#31192
C11×#31172
C11×#31112
C11×#31082
C11×#31022
C11×#30992
C11×#30982
C11×#30802
C2×C11×#4792
C11×#30372
C11×#30352
C11×#30132
C11×#29522
C11×#29512
C11×#29472
C11×#29252
#6059811