Finite Group Databasebeta

← C11×#62019 #14639212

Subgroups — C11×#62019 #14639212

Order 2816.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3558C211yesmaximal, characteristic
2C11×#3523C211yesmaximal, characteristic, complemented
3C11×#3400C212yesmaximal, complemented
4C11×#3371C212yesmaximal, complemented
5C11×#3311C212yesmaximal, complemented
6C11×#3310C212yesmaximal, complemented
7C11×#3300C212yesmaximal, complemented
8D4×C11×SD16C212yesmaximal, complemented
9C11×#3270C212yesmaximal, complemented
10C11×#3266C212yesmaximal, complemented
11C11×#3258C212yesmaximal, complemented
12C11×#3246C211yesmaximal, characteristic, complemented
13C11×#3222C212yesmaximal, complemented
14C11×#3215C211yesmaximal, characteristic, complemented
15C11×#3121C212yesmaximal, complemented
16C11×#3112C211yesmaximal, characteristic, complemented
17C11×#3043C212yesmaximal, complemented
18C2×C11×#464C211yesmaximal, characteristic, complemented
19C11×#2992C211yesmaximal, characteristic, complemented
20C2×C11×#137C2212yescomplemented
21C22×C11×Q16C2211yescharacteristic, complemented
22C22×C11×SD16C2211yescharacteristic
23C22×C11×SD16C2212yescomplemented
24C11×#562—21no—
25C11×H(3,𝔽4)—21no—
26C11×#559C2212yes—
27C11×#557—21no—
28C11×#557C2211yescharacteristic, complemented
29C11×#557C2211yescharacteristic, complemented
30C11×#556—21no—
31C11×#556C2211yescharacteristic, complemented
32C11×#552—22no—
33C11×#552C2212yescomplemented
34D4×Q8×C11C2211yescharacteristic, complemented
35D4×Q8×C11C2212yescomplemented
36C11×#548C2212yes—
37C11×#546—22no—
38C11×#546C2212yes—
39D42×C11C2212yes—
40C11×#542C2212yes—
41C11×#541—22no—
42C11×#541C2212yescomplemented
43C11×#538—22no—
44C11×#538—21no—
45C11×#535C2212yes—
46C11×#534—21no—
47C11×#533—21no—
48C11×#533C2211yescharacteristic, complemented
49C11×#532C2211yescharacteristic
50C11×#529—21no—
51C11×#529C2211yescharacteristic
52C2×C11×#124C2211yescharacteristic
53C11×#519C2212yescomplemented
54C2×C4×Q8×C11C2211yescharacteristic, complemented
55C11×#497C2212yescomplemented
56C11×#497C2212yescomplemented
57C11×#492C2212yes—
58C11×#490C2212yes—
59C11×#489C2212yescomplemented
60C11×#488C2212yescomplemented
61C11×#485C2212yescomplemented
62C11×#482C2212yes—
63C11×#480C2212yescomplemented
64C11×#479C2212yescomplemented
65C11×#478C2212yescomplemented
66C11×#477C2211yescharacteristic, complemented
67C11×#477C2211yescharacteristic, complemented
68C11×#476C2212yescomplemented
69C11×#475C2212yescomplemented
70C11×#470C2212yescomplemented
71C11×#468C2212yes—
72C11×#467C2212yescomplemented
73C11×#465C2212yes—
74C11×#465C2212yescomplemented
75C11×#465C2212yescomplemented
76C11×#464C2212yescomplemented
77C11×#464C2212yescomplemented
78C11×#464C2212yescomplemented
79C11×#464C2212yescomplemented
80C11×#464C2212yescomplemented
81C11×#464C2212yescomplemented
82C11×#464C2212yescomplemented
83C11×#464C2212yescomplemented
84C11×#462C2212yescomplemented
85C11×#461C2212yescomplemented
86C11×#461C2212yescomplemented
87C11×#460C2212yes—
88C11×#460C2212yes—
89C11×#460C2211yescharacteristic, complemented
90C11×#460C2212yescomplemented
91C11×#460C2211yescharacteristic, complemented
92C11×#452C2212yescomplemented
93C11×#452C2212yescomplemented
94C11×#451C2212yescomplemented
95C11×#451C2212yescomplemented
96C11×#450C2212yes—
97C11×#450C2212yescomplemented
98C11×#450C2212yescomplemented
99C11×#448C2212yes—
100C11×#448C2212yescomplemented
101C11×#446C2212yescomplemented
102C11×#441C2212yescomplemented
103C11×#440C2212yescomplemented
104C11×#440C2212yescomplemented
105C11×#440C2212yescomplemented
106C4×C11×Q16C2212yescomplemented
107C4×C11×SD16C2212yescomplemented
108C11×#435C2212yescomplemented
109C11×#435C2212yescomplemented
110C8×D4×C11C2212yescomplemented
111C11×#433C2212yescomplemented
112C11×#432C2211yescharacteristic, complemented
113C11×#424C2212yescomplemented
114C2×C11×C4⋊C8C2211yescharacteristic, complemented
115C11×#418C2212yescomplemented
116C11×#416C2212yescomplemented
117C2×C11×#103C2211yescharacteristic, complemented
118C2×C11×#102C2211yescharacteristic
119C2×C11×#41—21no—
120C2×C11×#41C2312yes—
121C22×Q8×C11C2311yescharacteristic
122C22×Q8×C11C2312yes—
123C22×Q8×C11C2311yescharacteristic
124C22×D4×C11—22no—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C11×#137—44no—
128C2×C11×Q16—42no—
129C2×C11×Q16C2312yes—
130C2×C11×Q16C2312yes—
131C2×C11×Q16C2312yes—
132C2×C11×Q16C2312yes—
133C2×C11×SD16—42no—
134C2×C11×SD16—44no—
135C2×C11×SD16C2312yes—
136C2×C11×SD16C2312yes—
137C2×C11×SD16C2312yes—
138C2×C11×SD16C2312yes—
139C2×C11×SD16C2312yes—
140C2×C11×SD16C2312yes—
141C2×C11×SD16C2312yes—
142C2×C11×SD16C2312yes—
143C2×C11×M16C2312yes—
144C22×C8×C11C2311yescharacteristic
145C22×C8×C11C2311yescharacteristic
146C22×C8×C11C2312yes—
147C11×C4⋊Q8—21no—
148C11×C4⋊Q8—21no—
149C11×C4⋊Q8—22no—
150C11×C4⋊Q8C2312yes—
151C11×C4⋊Q8C2311yescharacteristic
152C11×C4⋊Q8C2311yescharacteristic
153C11×C4⋊Q8C2311yescharacteristic
154C11×#127C2312yes—
155C11×#127C2311yescharacteristic
156C11×#126—22no—
157C11×#126—22no—
158C11×#126—22no—
159C11×#126—22no—
160C11×#126—22no—
161C11×#126D412yes—
162C11×#125—21no—
163C11×#125—22no—
164C11×#125—22no—
165C11×#125—22no—
166C11×#125—22no—
167C11×#125—22no—
168C11×#125—21no—
169C11×#125D411yescharacteristic
170C11×#125C2312yes—
171C11×#124—22no—
172C11×#124—21no—
173C11×#124—22no—
174C11×#124—22no—
175C11×#124—21no—
176C11×#124—21no—
177C11×#124—21no—
178C11×#124D411yescharacteristic
179C11×#124C2312yes—
180C11×#124C2312yes—
181C11×#124C2312yes—
182C11×#123—22no—
183C11×#123—22no—
184C11×#123—22no—
185C11×#123—22no—
186C11×#123—22no—
187C11×#123D412yes—
188C11×C22⋊Q8—21no—
189C11×C22⋊Q8—22no—
190C11×C22⋊Q8—22no—
191C11×C22⋊Q8—22no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—22no—
194C11×C22⋊Q8D411yescharacteristic
195C11×C22⋊Q8C2312yes—
196C11×C22⋊Q8C2312yes—
197C11×C22⋊Q8C2312yes—
198C11×C22⋊Q8C2312yes—
199C11×#121—22no—
200C11×#121—21no—
201C11×#121—22no—
202C11×#121—22no—
203C11×#121—22no—
204C11×#121—22no—
205C11×#121D411yescharacteristic
206C11×#121C2312yes—
207C11×#121C2312yes—
208C11×#120—22no—
209C11×#120—22no—
210C11×#120—22no—
211C11×#120—22no—
212C11×#120—22no—
213C4×Q8×C11—21no—
214C4×Q8×C11—22no—
215C4×Q8×C11—22no—
216C4×Q8×C11—21no—
217C4×Q8×C11—21no—
218C4×Q8×C11—21no—
219C4×Q8×C11—21no—
220C4×Q8×C11—21no—
221C4×Q8×C11C2311yescharacteristic
222C4×Q8×C11C2311yescharacteristic
223C4×Q8×C11C2311yescharacteristic
224C4×Q8×C11C2311yescharacteristic
225C4×Q8×C11C2312yes—
226C4×Q8×C11C2312yes—
227C4×Q8×C11C2312yes—
228C4×Q8×C11C2312yes—
229C4×Q8×C11C2311yescharacteristic
230C4×D4×C11—22no—
231C4×D4×C11—21no—
232C4×D4×C11—22no—
233C4×D4×C11—22no—
234C4×D4×C11—21no—
235C4×D4×C11C2312yes—
236C4×D4×C11C2312yes—
237C4×D4×C11C2312yes—
238C4×D4×C11C2311yescharacteristic
239C11×#117—21no—
240C11×#117—22no—
241C11×#117—22no—
242C11×#117—22no—
243C11×#117C2312yes—
244C11×#117C2312yes—
245C2×C11×C4⋊C4—21no—
246C2×C11×C4⋊C4C2311yescharacteristic
247C2×C11×C22⋊C4—21no—
248C2×C11×C22⋊C4—21no—
249C2×C11×C22⋊C4—22no—
250C2×C42×C11—21no—
251C2×C42×C11C2311yescharacteristic
252C11×#107C2312yes—
253C11×#107C2312yes—
254C11×#106C2312yes—
255C11×#106C2312yes—
256C11×C4⋊C8C2312yes—
257C11×C4⋊C8C2312yes—
258C11×C4⋊C8C2311yescharacteristic
259C11×C4⋊C8C2312yes—
260C11×C4⋊C8C2312yes—
261C11×C4⋊C8C2311yescharacteristic
262C11×#103C2312yes—
263C11×#103C2312yes—
264C11×#103C2312yes—
265C11×#103C2312yes—
266C11×#103C2312yes—
267C11×#103C2312yes—
268C11×#103C2312yes—
269C11×#103C2312yes—
270C11×#102C2312yes—
271C11×#102C2312yes—
272C11×#102C2312yes—
273C11×#102C2312yes—
274C11×#102C2312yes—
275C11×#102C2312yes—
276C11×#102C2312yes—
277C11×#102C2312yes—
278C11×C22⋊C8C2312yes—
279C11×C22⋊C8C2312yes—
280C11×C22⋊C8C2312yes—
281C11×#97C2312yes—
282C11×#97C2312yes—
283C4×C8×C11C2312yes—
284#62019C1111yesmaximal, characteristic, direct product factor, Sylow
285C24×C11—21no—
286C24×C11—22no—
287C11×#41—42no—
288C11×#41—42no—
289C11×#41—82no—
290C2×Q8×C11—21no—
291C2×Q8×C11—22no—
292C2×Q8×C11—21no—
293C2×Q8×C11—21no—
294C2×Q8×C11—21no—
295C2×Q8×C11—22no—
296C2×Q8×C11—24no—
297C2×Q8×C11—41no—
298C2×Q8×C11—42no—
299C2×Q8×C11—41no—
300C2×Q8×C11—41no—
301C2×Q8×C11C2×D411yescharacteristic
302C2×Q8×C11C2412yes—
303C2×Q8×C11C2412yes—
304C2×Q8×C11C2411yescharacteristic
305C2×Q8×C11C2411yescharacteristic
306C2×D4×C11—22no—
307C2×D4×C11—22no—
308C2×D4×C11—22no—
309C2×D4×C11—22no—
310C2×D4×C11—21no—
311C2×D4×C11—21no—
312C2×D4×C11—21no—
313C2×D4×C11—22no—
314C2×D4×C11—22no—
315C2×D4×C11—41no—
316C2×D4×C11—42no—
317C2×D4×C11—41no—
318C2×D4×C11—42no—
319C2×D4×C11—84no—
320C2×D4×C11C2×D412yes—
321C2×D4×C11C2×D411yescharacteristic
322C2×D4×C11C2412yes—
323C2×D4×C11C2412yes—
324C22×C4×C11—21no—
325C22×C4×C11—21no—
326C22×C4×C11—22no—
327C22×C4×C11—21no—
328C22×C4×C11—22no—
329C22×C4×C11—22no—
330C22×C4×C11—22no—
331C22×C4×C11C2×D411yescharacteristic
332C22×C4×C11C2×D411yescharacteristic
333C22×C4×C11C2411yescharacteristic
334C22×C4×C11C2412yes—
335C11×Q16—24no—
336C11×Q16—42no—
337C11×Q16—42no—
338C11×Q16—42no—
339C11×SD16—24no—
340C11×SD16—24no—
341C11×SD16—42no—
342C11×SD16—42no—
343C11×SD16—42no—
344C11×SD16—42no—
345C11×SD16—42no—
346C11×SD16—42no—
347C11×M16—42no—
348C2×C8×C11—41no—
349C2×C8×C11—42no—
350C2×C8×C11—41no—
351C2×C8×C11C2412yes—
352C2×C8×C11C2412yes—
353C2×C8×C11C2412yes—
354C2×C8×C11C2412yes—
355C11×C4⋊C4—21no—
356C11×C4⋊C4—21no—
357C11×C4⋊C4—21no—
358C11×C4⋊C4—21no—
359C11×C4⋊C4—21no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—22no—
362C11×C4⋊C4—22no—
363C11×C4⋊C4—21no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—21no—
366C11×C4⋊C4—22no—
367C11×C4⋊C4—21no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—21no—
370C11×C4⋊C4—22no—
371C11×C4⋊C4—22no—
372C11×C4⋊C4—22no—
373C11×C4⋊C4—22no—
374C11×C4⋊C4—22no—
375C11×C4⋊C4—22no—
376C11×C4⋊C4C2×D412yes—
377C11×C4⋊C4C2×D412yes—
378C11×C4⋊C4C2×D412yes—
379C11×C4⋊C4C2×D411yescharacteristic
380C11×C4⋊C4C2×D412yes—
381C11×C4⋊C4C2×D411yescharacteristic
382C11×C4⋊C4C2412yes—
383C11×C4⋊C4C2411yescharacteristic
384C11×C4⋊C4C2411yescharacteristic
385C11×C4⋊C4C2412yes—
386C11×C22⋊C4—22no—
387C11×C22⋊C4—22no—
388C11×C22⋊C4—22no—
389C11×C22⋊C4—22no—
390C11×C22⋊C4—22no—
391C11×C22⋊C4—22no—
392C11×C22⋊C4—22no—
393C11×C22⋊C4—22no—
394C11×C22⋊C4—22no—
395C11×C22⋊C4—22no—
396C11×C22⋊C4—22no—
397C11×C22⋊C4—22no—
398C11×C22⋊C4—22no—
399C11×C22⋊C4—22no—
400C11×C22⋊C4—22no—
401C11×C22⋊C4C2×D412yes—
402C11×C22⋊C4C2×D412yes—
403C11×C22⋊C4C2×D412yes—
404C11×C22⋊C4C2×D412yes—
405C11×C22⋊C4C2×D412yes—
406C42×C11—21no—
407C42×C11—21no—
408C42×C11—21no—
409C42×C11—21no—
410C42×C11—22no—
411C42×C11—22no—
412C42×C11—22no—
413C42×C11—22no—
414C42×C11—22no—
415C42×C11C2×D411yescharacteristic
416C42×C11C2×D411yescharacteristic
417C42×C11C2412yes—
418C42×C11C2411yescharacteristic
419C42×C11C2411yescharacteristic
420#3558C2×C1111yescharacteristic
421#3523C2×C1111yescharacteristic, complemented
422#3400C2×C1112yescomplemented
423#3371C2×C1112yescomplemented
424#3311C2×C1112yescomplemented
425#3310C2×C1112yescomplemented
426#3300C2×C1112yescomplemented
427D4×SD16C2×C1112yescomplemented
428#3270C2×C1112yescomplemented
429#3266C2×C1112yescomplemented
430#3258C2×C1112yescomplemented
431#3246C2×C1111yescharacteristic, complemented
432#3222C2×C1112yescomplemented
433#3215C2×C1111yescharacteristic, complemented
434#3121C2×C1112yescomplemented
435#3112C2×C1111yescharacteristic, complemented
436#3043C2×C1112yescomplemented
437C2×#464C2×C1111yescharacteristic, complemented
438#2992C2×C1111yescharacteristic, complemented
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—42no—
442C23×C11—81no—
443C23×C11—82no—
444C23×C11—82no—
445C23×C11—81no—
446C23×C11—82no—
447C23×C11C22×D412yes—
448C23×C11C22×D411yescharacteristic
449Q8×C11—21no—
450Q8×C11—22no—
451Q8×C11—21no—
452Q8×C11—22no—
453Q8×C11—21no—
454Q8×C11—22no—
455Q8×C11—22no—
456Q8×C11—41no—
457Q8×C11—44no—
458Q8×C11—42no—
459Q8×C11—42no—
460Q8×C11—81no—
461Q8×C11—81no—
462Q8×C11H(5,𝔽2)12yes—
463D4×C11—24no—
464D4×C11—22no—
465D4×C11—22no—
466D4×C11—22no—
467D4×C11—22no—
468D4×C11—41no—
469D4×C11—44no—
470D4×C11—81no—
471D4×C11—82no—
472D4×C11—82no—
473D4×C11—81no—
474D4×C11—82no—
475D4×C11—81no—
476D4×C11—82no—
477D4×C11—82no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—41no—
492C2×C4×C11—42no—
493C2×C4×C11—44no—
494C2×C4×C11—42no—
495C2×C4×C11—82no—
496C2×C4×C11—82no—
497C2×C4×C11—82no—
498C2×C4×C11—81no—
499C2×C4×C11C22×D411yescharacteristic
500C2×C4×C11C22×D411yescharacteristic
501C2×C4×C11C22×D411yescharacteristic
502C2×C4×C11C22×D412yes—
503C2×C4×C11C22×D412yes—
504C2×C4×C11C22×D412yes—
505C2×C4×C11C22×D411yescharacteristic
506C2×C4×C11C22×D411yescharacteristic
507C2×C4×C11C2511yescharacteristic
508C8×C11—22no—
509C8×C11—22no—
510C8×C11—22no—
511C8×C11—22no—
512C2×#137C22×C1112yescomplemented
513C22×Q16C22×C1111yescharacteristic, complemented
514C22×SD16C22×C1111yescharacteristic
515C22×SD16C22×C1112yescomplemented
516#562—21no—
517H(3,𝔽4)—21no—
518#559C22×C1112yes—
519#557—21no—
520#557C22×C1111yescharacteristic, complemented
521#557C22×C1111yescharacteristic, complemented
522#556—21no—
523#556C22×C1111yescharacteristic, complemented
524#552—22no—
525#552C22×C1112yescomplemented
526D4×Q8C22×C1111yescharacteristic, complemented
527D4×Q8C22×C1112yescomplemented
528#548C22×C1112yes—
529#546—22no—
530#546C22×C1112yes—
531D42C22×C1112yes—
532#542C22×C1112yes—
533#541—22no—
534#541C22×C1112yescomplemented
535#538—22no—
536#538—21no—
537#535C22×C1112yes—
538#534—21no—
539#533—21no—
540#533C22×C1111yescharacteristic, complemented
541#532C22×C1111yescharacteristic
542#529—21no—
543#529C22×C1111yescharacteristic
544C2×#124C22×C1111yescharacteristic
545#519C22×C1112yescomplemented
546C2×C4×Q8C22×C1111yescharacteristic, complemented
547#497C22×C1112yescomplemented
548#497C22×C1112yescomplemented
549#492C22×C1112yes—
550#490C22×C1112yes—
551#489C22×C1112yescomplemented
552#488C22×C1112yescomplemented
553#485C22×C1112yescomplemented
554#482C22×C1112yes—
555#480C22×C1112yescomplemented
556#479C22×C1112yescomplemented
557#478C22×C1112yescomplemented
558#477C22×C1111yescharacteristic, complemented
559#477C22×C1111yescharacteristic, complemented
560#476C22×C1112yescomplemented
561#475C22×C1112yescomplemented
562#470C22×C1112yescomplemented
563#468C22×C1112yes—
564#467C22×C1112yescomplemented
565#465C22×C1112yes—
566#465C22×C1112yescomplemented
567#465C22×C1112yescomplemented
568#464C22×C1112yescomplemented
569#464C22×C1112yescomplemented
570#464C22×C1112yescomplemented
571#464C22×C1112yescomplemented
572#464C22×C1112yescomplemented
573#464C22×C1112yescomplemented
574#464C22×C1112yescomplemented
575#464C22×C1112yescomplemented
576#462C22×C1112yescomplemented
577#461C22×C1112yescomplemented
578#461C22×C1112yescomplemented
579#460C22×C1112yes—
580#460C22×C1112yes—
581#460C22×C1111yescharacteristic, complemented
582#460C22×C1111yescharacteristic, complemented
583#460C22×C1112yescomplemented
584#452C22×C1112yescomplemented
585#452C22×C1112yescomplemented
586#451C22×C1112yescomplemented
587#451C22×C1112yescomplemented
588#450C22×C1112yes—
589#450C22×C1112yescomplemented
590#450C22×C1112yescomplemented
591#448C22×C1112yes—
592#448C22×C1112yescomplemented
593#446C22×C1112yescomplemented
594#441C22×C1112yescomplemented
595#440C22×C1112yescomplemented
596#440C22×C1112yescomplemented
597#440C22×C1112yescomplemented
598C4×Q16C22×C1112yescomplemented
599C4×SD16C22×C1112yescomplemented
600#435C22×C1112yescomplemented
601#435C22×C1112yescomplemented
602C8×D4C22×C1112yescomplemented
603#433C22×C1112yescomplemented
604#432C22×C1111yescharacteristic, complemented
605#424C22×C1112yescomplemented
606C2×C4⋊C8C22×C1111yescharacteristic, complemented
607#418C22×C1112yescomplemented
608#416C22×C1112yescomplemented
609C2×#103C22×C1111yescharacteristic, complemented
610C2×#102C22×C1111yescharacteristic
611C22×C11—21no—
612C22×C11—21no—
613C22×C11—22no—
614C22×C11—22no—
615C22×C11—22no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11—42no—
621C22×C11—42no—
622C22×C11—162no—
623C22×C11—164no—
624C22×C11#57712yes—
625C22×C11C23×D411yescharacteristic
626C4×C11—21no—
627C4×C11—21no—
628C4×C11—22no—
629C4×C11—22no—
630C4×C11—21no—
631C4×C11—22no—
632C4×C11—21no—
633C4×C11—21no—
634C4×C11—22no—
635C4×C11—42no—
636C4×C11—42no—
637C4×C11—41no—
638C4×C11—42no—
639C4×C11—41no—
640C4×C11—41no—
641C4×C11—42no—
642C4×C11C2×H(5,𝔽2)11yescharacteristic
643C4×C11#58511yescharacteristic
644C2×#41—21no—
645C2×#41C23×C1112yes—
646C22×Q8C23×C1111yescharacteristic
647C22×Q8C23×C1112yes—
648C22×Q8C23×C1111yescharacteristic
649C22×D4—22no—
650C22×D4C23×C1111yescharacteristic
651C22×D4C23×C1112yes—
652#137—44no—
653C2×Q16—42no—
654C2×Q16C23×C1112yes—
655C2×Q16C23×C1112yes—
656C2×Q16C23×C1112yes—
657C2×Q16C23×C1112yes—
658C2×SD16—42no—
659C2×SD16—44no—
660C2×SD16C23×C1112yes—
661C2×SD16C23×C1112yes—
662C2×SD16C23×C1112yes—
663C2×SD16C23×C1112yes—
664C2×SD16C23×C1112yes—
665C2×SD16C23×C1112yes—
666C2×SD16C23×C1112yes—
667C2×SD16C23×C1112yes—
668C2×M16C23×C1112yes—
669C22×C8C23×C1111yescharacteristic
670C22×C8C23×C1112yes—
671C22×C8C23×C1111yescharacteristic
672C4⋊Q8—21no—
673C4⋊Q8—21no—
674C4⋊Q8—22no—
675C4⋊Q8C23×C1111yescharacteristic
676C4⋊Q8C23×C1112yes—
677C4⋊Q8C23×C1111yescharacteristic
678C4⋊Q8C23×C1111yescharacteristic
679#127C23×C1111yescharacteristic
680#127C23×C1112yes—
681#126—22no—
682#126—22no—
683#126—22no—
684#126—22no—
685#126—22no—
686#126D4×C1112yes—
687#125—21no—
688#125—22no—
689#125—22no—
690#125—22no—
691#125—22no—
692#125—22no—
693#125—21no—
694#125D4×C1111yescharacteristic
695#125C23×C1112yes—
696#124—22no—
697#124—21no—
698#124—22no—
699#124—22no—
700#124—21no—
701#124—21no—
702#124—21no—
703#124D4×C1111yescharacteristic
704#124C23×C1112yes—
705#124C23×C1112yes—
706#124C23×C1112yes—
707#123—22no—
708#123—22no—
709#123—22no—
710#123—22no—
711#123—22no—
712#123D4×C1112yes—
713C22⋊Q8—21no—
714C22⋊Q8—22no—
715C22⋊Q8—22no—
716C22⋊Q8—22no—
717C22⋊Q8—22no—
718C22⋊Q8—22no—
719C22⋊Q8D4×C1111yescharacteristic
720C22⋊Q8C23×C1112yes—
721C22⋊Q8C23×C1112yes—
722C22⋊Q8C23×C1112yes—
723C22⋊Q8C23×C1112yes—
724#121—22no—
725#121—21no—
726#121—22no—
727#121—22no—
728#121—22no—
729#121—22no—
730#121D4×C1111yescharacteristic
731#121C23×C1112yes—
732#121C23×C1112yes—
733#120—22no—
734#120—22no—
735#120—22no—
736#120—22no—
737#120—22no—
738C4×Q8—21no—
739C4×Q8—22no—
740C4×Q8—22no—
741C4×Q8—21no—
742C4×Q8—21no—
743C4×Q8—21no—
744C4×Q8—21no—
745C4×Q8—21no—
746C4×Q8C23×C1111yescharacteristic
747C4×Q8C23×C1111yescharacteristic
748C4×Q8C23×C1111yescharacteristic
749C4×Q8C23×C1111yescharacteristic
750C4×Q8C23×C1112yes—
751C4×Q8C23×C1112yes—
752C4×Q8C23×C1112yes—
753C4×Q8C23×C1112yes—
754C4×Q8C23×C1111yescharacteristic
755C4×D4—22no—
756C4×D4—21no—
757C4×D4—22no—
758C4×D4—22no—
759C4×D4—21no—
760C4×D4C23×C1112yes—
761C4×D4C23×C1112yes—
762C4×D4C23×C1112yes—
763C4×D4C23×C1111yescharacteristic
764#117—21no—
765#117—22no—
766#117—22no—
767#117—22no—
768#117C23×C1112yes—
769#117C23×C1112yes—
770C2×C4⋊C4—21no—
771C2×C4⋊C4C23×C1111yescharacteristic
772C2×C22⋊C4—21no—
773C2×C22⋊C4—21no—
774C2×C22⋊C4—22no—
775C2×C42—21no—
776C2×C42C23×C1111yescharacteristic
777#107C23×C1112yes—
778#107C23×C1112yes—
779#106C23×C1112yes—
780#106C23×C1112yes—
781C4⋊C8C23×C1112yes—
782C4⋊C8C23×C1112yes—
783C4⋊C8C23×C1111yescharacteristic
784C4⋊C8C23×C1112yes—
785C4⋊C8C23×C1112yes—
786C4⋊C8C23×C1111yescharacteristic
787#103C23×C1112yes—
788#103C23×C1112yes—
789#103C23×C1112yes—
790#103C23×C1112yes—
791#103C23×C1112yes—
792#103C23×C1112yes—
793#103C23×C1112yes—
794#103C23×C1112yes—
795#102C23×C1112yes—
796#102C23×C1112yes—
797#102C23×C1112yes—
798#102C23×C1112yes—
799#102C23×C1112yes—
800#102C23×C1112yes—
801#102C23×C1112yes—
802#102C23×C1112yes—
803C22⋊C8C23×C1112yes—
804C22⋊C8C23×C1112yes—
805C22⋊C8C23×C1112yes—
806#97C23×C1112yes—
807#97C23×C1112yes—
808C4×C8C23×C1112yes—
809C2×C11—22no—
810C2×C11—42no—
811C2×C11—82no—
812C2×C11—82no—
813C2×C11#348811yescharacteristic
814C2×C11C2×#57711yescharacteristic
815C2×C11#358611yescharacteristic
816C24—21no—
817C24—22no—
818#41—42no—
819#41—42no—
820#41—82no—
821C2×Q8—21no—
822C2×Q8—22no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—22no—
827C2×Q8—24no—
828C2×Q8—41no—
829C2×Q8—42no—
830C2×Q8—41no—
831C2×Q8—41no—
832C2×Q8C2×D4×C1111yescharacteristic
833C2×Q8C24×C1112yes—
834C2×Q8C24×C1112yes—
835C2×Q8C24×C1111yescharacteristic
836C2×Q8C24×C1111yescharacteristic
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—41no—
847C2×D4—42no—
848C2×D4—41no—
849C2×D4—42no—
850C2×D4—84no—
851C2×D4C2×D4×C1112yes—
852C2×D4C2×D4×C1111yescharacteristic
853C2×D4C24×C1112yes—
854C2×D4C24×C1112yes—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4C2×D4×C1111yescharacteristic
863C22×C4C2×D4×C1111yescharacteristic
864C22×C4C24×C1111yescharacteristic
865C22×C4C24×C1112yes—
866Q16—24no—
867Q16—42no—
868Q16—42no—
869Q16—42no—
870SD16—24no—
871SD16—24no—
872SD16—42no—
873SD16—42no—
874SD16—42no—
875SD16—42no—
876SD16—42no—
877SD16—42no—
878M16—42no—
879C2×C8—41no—
880C2×C8—42no—
881C2×C8—41no—
882C2×C8C24×C1112yes—
883C2×C8C24×C1112yes—
884C2×C8C24×C1112yes—
885C2×C8C24×C1112yes—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—22no—
894C4⋊C4—21no—
895C4⋊C4—22no—
896C4⋊C4—21no—
897C4⋊C4—22no—
898C4⋊C4—21no—
899C4⋊C4—22no—
900C4⋊C4—21no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—22no—
905C4⋊C4—22no—
906C4⋊C4—22no—
907C4⋊C4C2×D4×C1112yes—
908C4⋊C4C2×D4×C1112yes—
909C4⋊C4C2×D4×C1112yes—
910C4⋊C4C2×D4×C1111yescharacteristic
911C4⋊C4C2×D4×C1112yes—
912C4⋊C4C2×D4×C1111yescharacteristic
913C4⋊C4C24×C1112yes—
914C4⋊C4C24×C1111yescharacteristic
915C4⋊C4C24×C1111yescharacteristic
916C4⋊C4C24×C1112yes—
917C22⋊C4—22no—
918C22⋊C4—22no—
919C22⋊C4—22no—
920C22⋊C4—22no—
921C22⋊C4—22no—
922C22⋊C4—22no—
923C22⋊C4—22no—
924C22⋊C4—22no—
925C22⋊C4—22no—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—22no—
930C22⋊C4—22no—
931C22⋊C4—22no—
932C22⋊C4C2×D4×C1112yes—
933C22⋊C4C2×D4×C1112yes—
934C22⋊C4C2×D4×C1112yes—
935C22⋊C4C2×D4×C1112yes—
936C22⋊C4C2×D4×C1112yes—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—22no—
946C42C2×D4×C1111yescharacteristic
947C42C2×D4×C1111yescharacteristic
948C42C24×C1112yes—
949C42C24×C1111yescharacteristic
950C42C24×C1111yescharacteristic
951C11#6201911yescharacteristic, direct product factor, Sylow
952C23—22no—
953C23—22no—
954C23—42no—
955C23—81no—
956C23—82no—
957C23—82no—
958C23—81no—
959C23—82no—
960C23C22×D4×C1112yes—
961C23C22×D4×C1111yescharacteristic
962Q8—21no—
963Q8—22no—
964Q8—21no—
965Q8—22no—
966Q8—21no—
967Q8—22no—
968Q8—22no—
969Q8—41no—
970Q8—44no—
971Q8—42no—
972Q8—42no—
973Q8—81no—
974Q8—81no—
975Q8C11×H(5,𝔽2)12yes—
976D4—24no—
977D4—22no—
978D4—22no—
979D4—22no—
980D4—22no—
981D4—41no—
982D4—44no—
983D4—81no—
984D4—82no—
985D4—82no—
986D4—81no—
987D4—82no—
988D4—81no—
989D4—82no—
990D4—82no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—41no—
1005C2×C4—42no—
1006C2×C4—44no—
1007C2×C4—42no—
1008C2×C4—82no—
1009C2×C4—82no—
1010C2×C4—82no—
1011C2×C4—81no—
1012C2×C4C22×D4×C1111yescharacteristic
1013C2×C4C22×D4×C1111yescharacteristic
1014C2×C4C22×D4×C1111yescharacteristic
1015C2×C4C22×D4×C1112yes—
1016C2×C4C22×D4×C1112yes—
1017C2×C4C22×D4×C1112yes—
1018C2×C4C22×D4×C1111yescharacteristic
1019C2×C4C22×D4×C1111yescharacteristic
1020C2×C4C25×C1111yescharacteristic
1021C8—22no—
1022C8—22no—
1023C8—22no—
1024C8—22no—
1025C22—21no—
1026C22—21no—
1027C22—22no—
1028C22—22no—
1029C22—22no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—162no—
1037C22—164no—
1038C22C11×#57712yes—
1039C22C23×D4×C1111yescharacteristic
1040C4—22no—
1041C4—21no—
1042C4—22no—
1043C4—21no—
1044C4—21no—
1045C4—22no—
1046C4—21no—
1047C4—21no—
1048C4—22no—
1049C4—42no—
1050C4—41no—
1051C4—42no—
1052C4—41no—
1053C4—41no—
1054C4—42no—
1055C4—42no—
1056C4C2×C11×H(5,𝔽2)11yescharacteristic
1057C4C11×#58511yescharacteristic
1058C2—22no—
1059C2—42no—
1060C2—82no—
1061C2—82no—
1062C2C11×#348811yescharacteristic
1063C2C2×C11×#57711yescharacteristic
1064C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3558C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#529 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3523C2semidirect
3. C11×#3400C2semidirect
4. C11×#3371C2semidirect
5. C11×#3311C2semidirect
6. C11×#3310C2semidirect
7. C11×#3300C2semidirect
8. D4×C11×SD16C2semidirect
9. C11×#3270C2semidirect
10. C11×#3266C2semidirect
11. C11×#3258C2semidirect
12. C11×#3246C2semidirect
13. C11×#3222C2semidirect
14. C11×#3215C2semidirect
15. C11×#3121C2semidirect
16. C11×#3112C2semidirect
17. C11×#3043C2semidirect
18. C2×C11×#464C2semidirect
19. C11×#2992C2semidirect
20. C2×C11×#137C22semidirect
21. C22×C11×Q16C22semidirect
23. C22×C11×SD16C22semidirect
28. C11×#557C22semidirect
29. C11×#557C22semidirect
31. C11×#556C22semidirect
33. C11×#552C22semidirect
34. D4×Q8×C11C22semidirect
35. D4×Q8×C11C22semidirect
42. C11×#541C22semidirect
48. C11×#533C22semidirect
53. C11×#519C22semidirect
54. C2×C4×Q8×C11C22semidirect
55. C11×#497C22semidirect
56. C11×#497C22semidirect
59. C11×#489C22semidirect
60. C11×#488C22semidirect
61. C11×#485C22semidirect
63. C11×#480C22semidirect
64. C11×#479C22semidirect
65. C11×#478C22semidirect
66. C11×#477C22semidirect
67. C11×#477C22semidirect
68. C11×#476C22semidirect
69. C11×#475C22semidirect
70. C11×#470C22semidirect
72. C11×#467C22semidirect
74. C11×#465C22semidirect
75. C11×#465C22semidirect
76. C11×#464C22semidirect
77. C11×#464C22semidirect
78. C11×#464C22semidirect
79. C11×#464C22semidirect
80. C11×#464C22semidirect
81. C11×#464C22semidirect
82. C11×#464C22semidirect
83. C11×#464C22semidirect
84. C11×#462C22semidirect
85. C11×#461C22semidirect
86. C11×#461C22semidirect
89. C11×#460C22semidirect
90. C11×#460C22semidirect
91. C11×#460C22semidirect
92. C11×#452C22semidirect
93. C11×#452C22semidirect
94. C11×#451C22semidirect
95. C11×#451C22semidirect
97. C11×#450C22semidirect
98. C11×#450C22semidirect
100. C11×#448C22semidirect
101. C11×#446C22semidirect
102. C11×#441C22semidirect
103. C11×#440C22semidirect
104. C11×#440C22semidirect
105. C11×#440C22semidirect
106. C4×C11×Q16C22semidirect
107. C4×C11×SD16C22semidirect
108. C11×#435C22semidirect
109. C11×#435C22semidirect
110. C8×D4×C11C22semidirect
111. C11×#433C22semidirect
112. C11×#432C22semidirect
113. C11×#424C22semidirect
114. C2×C11×C4⋊C8C22semidirect
115. C11×#418C22semidirect
116. C11×#416C22semidirect
117. C2×C11×#103C22semidirect
284. #62019C11direct (N × H)
421. #3523C2×C11semidirect
422. #3400C2×C11semidirect
423. #3371C2×C11semidirect
424. #3311C2×C11semidirect
425. #3310C2×C11semidirect
426. #3300C2×C11semidirect
427. D4×SD16C2×C11semidirect
428. #3270C2×C11semidirect
429. #3266C2×C11semidirect
430. #3258C2×C11semidirect
431. #3246C2×C11semidirect
432. #3222C2×C11semidirect
433. #3215C2×C11semidirect
434. #3121C2×C11semidirect
435. #3112C2×C11semidirect
436. #3043C2×C11semidirect
437. C2×#464C2×C11semidirect
438. #2992C2×C11semidirect
512. C2×#137C22×C11semidirect
513. C22×Q16C22×C11semidirect
515. C22×SD16C22×C11semidirect
520. #557C22×C11semidirect
521. #557C22×C11semidirect
523. #556C22×C11semidirect
525. #552C22×C11semidirect
526. D4×Q8C22×C11semidirect
527. D4×Q8C22×C11semidirect
534. #541C22×C11semidirect
540. #533C22×C11semidirect
545. #519C22×C11semidirect
546. C2×C4×Q8C22×C11semidirect
547. #497C22×C11semidirect
548. #497C22×C11semidirect
551. #489C22×C11semidirect
552. #488C22×C11semidirect
553. #485C22×C11semidirect
555. #480C22×C11semidirect
556. #479C22×C11semidirect
557. #478C22×C11semidirect
558. #477C22×C11semidirect
559. #477C22×C11semidirect
560. #476C22×C11semidirect
561. #475C22×C11semidirect
562. #470C22×C11semidirect
564. #467C22×C11semidirect
566. #465C22×C11semidirect
567. #465C22×C11semidirect
568. #464C22×C11semidirect
569. #464C22×C11semidirect
570. #464C22×C11semidirect
571. #464C22×C11semidirect
572. #464C22×C11semidirect
573. #464C22×C11semidirect
574. #464C22×C11semidirect
575. #464C22×C11semidirect
576. #462C22×C11semidirect
577. #461C22×C11semidirect
578. #461C22×C11semidirect
581. #460C22×C11semidirect
582. #460C22×C11semidirect
583. #460C22×C11semidirect
584. #452C22×C11semidirect
585. #452C22×C11semidirect
586. #451C22×C11semidirect
587. #451C22×C11semidirect
589. #450C22×C11semidirect
590. #450C22×C11semidirect
592. #448C22×C11semidirect
593. #446C22×C11semidirect
594. #441C22×C11semidirect
595. #440C22×C11semidirect
596. #440C22×C11semidirect
597. #440C22×C11semidirect
598. C4×Q16C22×C11semidirect
599. C4×SD16C22×C11semidirect
600. #435C22×C11semidirect
601. #435C22×C11semidirect
602. C8×D4C22×C11semidirect
603. #433C22×C11semidirect
604. #432C22×C11semidirect
605. #424C22×C11semidirect
606. C2×C4⋊C8C22×C11semidirect
607. #418C22×C11semidirect
608. #416C22×C11semidirect
609. C2×#103C22×C11semidirect
951. C11#62019direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35582
C11×#35232
C11×#34002
C11×#33712
C11×#33112
C11×#33102
C11×#33002
D4×C11×SD162
C11×#32702
C11×#32662
C11×#32582
C11×#32462
C11×#32222
C11×#32152
C11×#31212
C11×#31122
C11×#30432
C2×C11×#4642
C11×#29922
#6201911