Finite Group Databasebeta

← #15625332

Subgroups — #15625332

Order 2816.

2098 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081949C211yesmaximal, characteristic, complemented
2#13079719C218yesmaximal, complemented
3#13079704C218yesmaximal, complemented
4#13079080C212yesmaximal, complemented
5#13079012C212yesmaximal, complemented
6#13078088C212yesmaximal, complemented
7#13078080C212yesmaximal, complemented
8#13077874C212yesmaximal, complemented
9#13077866C212yesmaximal, complemented
10#13077254C211yesmaximal, characteristic, complemented
11C2×C11×#542C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C11×#542—24no—
14C11×#542C2218yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic, complemented
16C2×C11×#126—21no—
17C2×C11×#124—21no—
18C2×C11×#124C2211yescharacteristic, complemented
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic, complemented
24C2×C4×D4×C11C2211yescharacteristic, complemented
25C2×C11×#117C2211yescharacteristic
26C2×#66995C2214yescomplemented
27C2×#66985C2214yescomplemented
28#10623057C2214yescomplemented
29#10623056C2214yescomplemented
30#10623055—24no—
31#10623041—21no—
32#10623041—21no—
33#10623024—21no—
34#10623024—21no—
35#10623008C2212yes—
36#10623008C2212yes—
37#10622820C2212yes—
38#10622706C2214yescomplemented
39#10622702C2218yescomplemented
40#10622701C2214yescomplemented
41#10622673C2214yescomplemented
42#10622672C2218yescomplemented
43#10622671C2214yescomplemented
44#10622663C2214yescomplemented
45#10622660C2218yescomplemented
46#10622659C2214yescomplemented
47#10622653C2214yescomplemented
48#10622650C2218yes—
49#10622649C2214yescomplemented
50#10622644C2214yescomplemented
51#10622641C2218yescomplemented
52#10622640C2214yescomplemented
53#10622632C2214yescomplemented
54#10622629C2218yescomplemented
55#10622628C2214yescomplemented
56#10622613C2218yescomplemented
57#10622579C2214yescomplemented
58#10622579C2214yescomplemented
59#10622537C2212yescomplemented
60C4×#4318C2212yescomplemented
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—48no—
71C2×#4339C2314yes—
72C2×#4339C2314yes—
73C22×D44C2312yes—
74C22×C4×D11—22no—
75C22×Dic22C2312yes—
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8C2314yes—
78C11×#126—28no—
79C11×#124—28no—
80C11×#124—22no—
81C11×#124C2314yes—
82C11×#123—28no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—28no—
85C11×C22⋊Q8C2314yes—
86C11×#121—22no—
87C11×#121C2314yes—
88C4×Q8×C11—22no—
89C4×Q8×C11C2314yes—
90C4×D4×C11—22no—
91C4×D4×C11C2314yes—
92C11×#117D414yes—
93C11×#117C2314yes—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×#4326C2318yes—
112#66995—48no—
113C2×#4325C2318yes—
114C2×#4324C2318yes—
115#66985—48no—
116C2×#4323C2318yes—
117#66983—22no—
118#66983—22no—
119#66983—22no—
120#66983—22no—
121C2×#4318C2314yes—
122#66950—24no—
123#66950—24no—
124#66948—24no—
125#66948—24no—
126#66939—24no—
127#66939—24no—
128#66935—24no—
129#66935—24no—
130#66928C2314yes—
131#66928C2314yes—
132#66927C2312yes—
133#66927C2312yes—
134C4×D44—22no—
135C4×D44—22no—
136C4×D44—22no—
137C4×D44—22no—
138#66922C2312yes—
139#66922C2312yes—
140C22⋊(C11⋊C8)C2314yes—
141C22⋊(C11⋊C8)C2314yes—
142#66874C2318yes—
143#66874C2318yes—
144#66873C2318yes—
145#66873C2318yes—
146C4⋊(C11⋊C8)C2314yes—
147C4⋊(C11⋊C8)C2314yes—
148#66867C2314yes—
149C4×C11⋊C8C2314yes—
150#60810—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C23×D11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11—24no—
156C2×Q8×C11—24no—
157C2×Q8×C11—82no—
158C2×Q8×C11C2412yes—
159C2×D4×C11—24no—
160C2×D4×C11—21no—
161C2×D4×C11—24no—
162C2×D4×C11—82no—
163C2×D4×C11C2412yes—
164C22×C4×C11—24no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—24no—
169C22×C4×C11—82no—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—24no—
179C2×C22⋊D11—24no—
180C2×C22⋊D11—48no—
181C22×Dic11—22no—
182#4339—28no—
183#4339—28no—
184#4339—44no—
185#4339—44no—
186#4339—48no—
187#4339—48no—
188C2×D44—22no—
189C2×D44—22no—
190C2×D44—22no—
191C2×D44—22no—
192C2×D44—22no—
193C2×D44—44no—
194C2×D44C2414yes—
195C2×C4×D11—24no—
196C2×C4×D11—24no—
197C2×C4×D11—48no—
198C2×Dic22—22no—
199C2×Dic22—44no—
200C2×Dic22C2414yes—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4C2×D414yes—
207C11×C4⋊C4C2×D414yes—
208C11×C4⋊C4C2412yes—
209C11×C4⋊C4C2412yes—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4C2×D414yes—
216C11×C22⋊C4C2×D414yes—
217C42×C11—24no—
218C42×C11C2×D412yes—
219C42×C11C2×D412yes—
220C42×C11C2412yes—
221C42×C11C2412yes—
222#4326—48no—
223#4325—48no—
224#4324—48no—
225#4323—48no—
226(C2×D11)⋊C4—24no—
227(C2×D11)⋊C4—24no—
228(C2×D11)⋊C4—24no—
229(C2×D11)⋊C4—24no—
230C4⋊Dic11—22no—
231C4⋊Dic11—22no—
232C4⋊Dic11—22no—
233C4⋊Dic11—22no—
234#4318—28no—
235C2×C11⋊C8C2418yes—
236C2×#542D1111yescharacteristic, complemented
237#3449—111no—
238#3225—118no—
239#3224—118no—
240#3153—112no—
241#3141—112no—
242#3037—112no—
243#3036—112no—
244#3007—112no—
245#3006—112no—
246#2921—111no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11C22×D412yes—
255C23×C11C22×D411yescharacteristic
256C22×D11—24no—
257C22×D11—44no—
258C22×D11—82no—
259C22×D11—82no—
260Q8×C11—24no—
261Q8×C11—42no—
262Q8×C11—84no—
263D4×C11—24no—
264D4×C11—42no—
265D4×C11—84no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—84no—
280C2×C4×C11C22×D412yes—
281C2×C4×C11C22×D412yes—
282C2×C4×C11C22×D412yes—
283C2×C4×C11C22×D412yes—
284C2×C4×C11C22×D412yes—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11H(5,𝔽2)14yes—
287C2×C4×C11C2511yescharacteristic
288C22⋊D11—48no—
289C22⋊D11—48no—
290C2×Dic11—24no—
291C2×Dic11—44no—
292D44—24no—
293D44—24no—
294D44—44no—
295D44—82no—
296D44—82no—
297D44—82no—
298D44—82no—
299C4×D11—48no—
300C4×D11—48no—
301Dic22—24no—
302Dic22—24no—
303Dic22—44no—
304C11⋊C8—28no—
305C22×#41—112no—
306C2×#137—114no—
307C2×AGL(1,ℤ/8)—114no—
308#542—24no—
309#542C2×D1118yescomplemented
310#537—221no—
311#537—221no—
312#536—114no—
313#535—114no—
314#534—221no—
315#534—221no—
316#532—112no—
317#532—112no—
318C2×C4⋊Q8C2×D1111yescharacteristic, complemented
319C2×#126—21no—
320C2×#124—21no—
321C2×#124C2×D1111yescharacteristic, complemented
322#525—224no—
323C2×#123—21no—
324C2×C22⋊Q8—21no—
325C2×C22⋊Q8C2×D1111yescharacteristic
326C2×#121C2×D1111yescharacteristic
327C2×C4×Q8C2×D1111yescharacteristic, complemented
328C2×C4×D4C2×D1111yescharacteristic, complemented
329C2×#117C2×D1111yescharacteristic
330#497—114no—
331#496—114no—
332#495—118no—
333#489—118no—
334#487—114no—
335#486—114no—
336#464—118no—
337#463—118no—
338#462—114no—
339#461—114no—
340#460—114no—
341#459—114no—
342#452—118no—
343#451—114no—
344#450—114no—
345#449—118no—
346#448—114no—
347#447—114no—
348#433—118no—
349#423—112no—
350#417—114no—
351#417—114no—
352#407—112no—
353C4×M16—112no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—82no—
363C22×C11—84no—
364C22×C11#53512yes—
365C22×C11C23×D411yescharacteristic
366C2×D11—44no—
367C2×D11—44no—
368C2×D11—44no—
369C2×D11—88no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11#53512yes—
379C4×C11C2×H(5,𝔽2)12yes—
380Dic11—44no—
381C2×#41—114no—
382C2×#41—114no—
383C2×#41—222no—
384C2×#41—222no—
385C2×#41—448no—
386C22×Q8—21no—
387C22×Q8—112no—
388C22×Q8C22×D1111yescharacteristic
389C22×D4—21no—
390C22×D4—112no—
391C22×D4—222no—
392C22×D4C22×D1111yescharacteristic
393C23×C4—21no—
394C23×C4—222no—
395C23×C4C22×D1111yescharacteristic
396#137—448no—
397AGL(1,ℤ/8)—448no—
398C2×Q16—118no—
399C2×SD16—118no—
400C2×SD16—118no—
401C2×D8—118no—
402C2×M16—114no—
403C4⋊Q8—22no—
404C4⋊Q8—112no—
405C4⋊Q8—112no—
406C4⋊Q8C22×D1114yes—
407#127—112no—
408#127—112no—
409#126—28no—
410#124—28no—
411#124—22no—
412#124—114no—
413#124—114no—
414#124C22×D1114yes—
415#123—28no—
416#123—224no—
417#123—224no—
418C22⋊Q8—22no—
419C22⋊Q8—28no—
420C22⋊Q8—224no—
421C22⋊Q8—224no—
422C22⋊Q8C22×D1114yes—
423#121—22no—
424#121—222no—
425#121—222no—
426#121—222no—
427#121—222no—
428#121—224no—
429#121—224no—
430#121C22×D1114yes—
431#120—224no—
432#120—224no—
433C4×Q8—22no—
434C4×Q8C22×D1114yes—
435C4×D4—22no—
436C4×D4—222no—
437C4×D4—222no—
438C4×D4—222no—
439C4×D4—222no—
440C4×D4C22×D1114yes—
441#117C22⋊D1114yes—
442#117C22×D1114yes—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4C22⋊D1111yescharacteristic
447C2×C4⋊C4C22⋊D1111yescharacteristic
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C4⋊C4C22×D1111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4C22⋊D1111yescharacteristic
456C2×C22⋊C4C22⋊D1111yescharacteristic
457C2×C42—21no—
458C2×C42C22×D1111yescharacteristic
459C2×C42C22×D1111yescharacteristic
460C4⋊C8—114no—
461C4⋊C8—114no—
462#103—118no—
463#103—118no—
464#102—118no—
465#102—118no—
466C22⋊C8—114no—
467C22⋊C8—114no—
468#97—114no—
469C4×C8—114no—
470C2×C11—22no—
471C2×C11—42no—
472C2×C11—82no—
473C2×C11C2×#53511yescharacteristic
474C2×C11#358511yescharacteristic
475C2×C11#358611yescharacteristic
476D11—84no—
477C24—21no—
478C24—222no—
479C24C2×C22⋊D1111yescharacteristic
480#41—228no—
481#41—228no—
482#41—444no—
483#41—444no—
484#41—448no—
485#41—448no—
486C2×Q8—21no—
487C2×Q8—24no—
488C2×Q8—24no—
489C2×Q8—82no—
490C2×Q8—114no—
491C2×Q8—222no—
492C2×Q8—444no—
493C2×Q8C23×D1112yes—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—21no—
497C2×D4—82no—
498C2×D4—114no—
499C2×D4—224no—
500C2×D4—224no—
501C2×D4—222no—
502C2×D4—222no—
503C2×D4—222no—
504C2×D4—222no—
505C2×D4—222no—
506C2×D4—444no—
507C2×D4—448no—
508C2×D4C23×D1112yes—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—82no—
515C22×C4—222no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—448no—
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C2×C22⋊D1112yes—
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C23×D1112yes—
526C22×C4C23×D1111yescharacteristic
527Q16—448no—
528SD16—448no—
529SD16—448no—
530D8—448no—
531M16—228no—
532C2×C8—118no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—222no—
539C4⋊C4—222no—
540C4⋊C4—222no—
541C4⋊C4—222no—
542C4⋊C4C2×C22⋊D1114yes—
543C4⋊C4C2×C22⋊D1114yes—
544C4⋊C4C23×D1112yes—
545C4⋊C4C23×D1112yes—
546C22⋊C4—24no—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C22⋊C4—224no—
554C22⋊C4—224no—
555C22⋊C4C2×C22⋊D1114yes—
556C22⋊C4C2×C22⋊D1114yes—
557C42—24no—
558C42C2×C22⋊D1112yes—
559C42C2×C22⋊D1112yes—
560C42C23×D1112yes—
561C42C23×D1112yes—
562C11#6081011yescharacteristic, complemented, Sylow
563C23—22no—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—224no—
571C23—444no—
572C23—882no—
573C23—882no—
574C23C22×C22⋊D1112yes—
575C23C22×C22⋊D1111yescharacteristic
576Q8—24no—
577Q8—42no—
578Q8—84no—
579Q8—224no—
580Q8—224no—
581Q8—444no—
582D4—24no—
583D4—42no—
584D4—84no—
585D4—224no—
586D4—224no—
587D4—444no—
588D4—448no—
589D4—448no—
590D4—882no—
591D4—882no—
592D4—882no—
593D4—882no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—84no—
608C2×C4—224no—
609C2×C4—448no—
610C2×C4—444no—
611C2×C4—448no—
612C2×C4#6704214yes—
613C2×C4C22×C22⋊D1112yes—
614C2×C4C22×C22⋊D1112yes—
615C2×C4C22×C22⋊D1112yes—
616C2×C4C22×C22⋊D1112yes—
617C2×C4C22×C22⋊D1112yes—
618C2×C4C22×C22⋊D1111yescharacteristic
619C2×C4C24×D1111yescharacteristic
620C8—228no—
621C22—21no—
622C22—21no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—82no—
630C22—84no—
631C22—444no—
632C22—444no—
633C22—444no—
634C22—888no—
635C22#1062336112yes—
636C22C23×C22⋊D1111yescharacteristic
637C4—22no—
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—444no—
646C4#1062336112yes—
647C4C2×#6704212yes—
648C2—22no—
649C2—42no—
650C2—82no—
651C2—884no—
652C2C2×#1062336111yescharacteristic
653C2#1308339611yescharacteristic
654C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#542C2
socleC22×C11C23×D4
hypercenterC2×#542D11
hypocenterC11#60810
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #13081949C2semidirect
2. #13079719C2semidirect
3. #13079704C2semidirect
4. #13079080C2semidirect
5. #13079012C2semidirect
6. #13078088C2semidirect
7. #13078080C2semidirect
8. #13077874C2semidirect
9. #13077866C2semidirect
10. #13077254C2semidirect
11. C2×C11×#542C2semidirect
14. C11×#542C22semidirect
15. C2×C11×C4⋊Q8C22semidirect
18. C2×C11×#124C22semidirect
23. C2×C4×Q8×C11C22semidirect
24. C2×C4×D4×C11C22semidirect
26. C2×#66995C22semidirect
27. C2×#66985C22semidirect
28. #10623057C22semidirect
29. #10623056C22semidirect
38. #10622706C22semidirect
39. #10622702C22semidirect
40. #10622701C22semidirect
41. #10622673C22semidirect
42. #10622672C22semidirect
43. #10622671C22semidirect
44. #10622663C22semidirect
45. #10622660C22semidirect
46. #10622659C22semidirect
47. #10622653C22semidirect
49. #10622649C22semidirect
50. #10622644C22semidirect
51. #10622641C22semidirect
52. #10622640C22semidirect
53. #10622632C22semidirect
54. #10622629C22semidirect
55. #10622628C22semidirect
56. #10622613C22semidirect
57. #10622579C22semidirect
58. #10622579C22semidirect
59. #10622537C22semidirect
60. C4×#4318C22semidirect
236. C2×#542D11semidirect
309. #542C2×D11semidirect
318. C2×C4⋊Q8C2×D11semidirect
321. C2×#124C2×D11semidirect
327. C2×C4×Q8C2×D11semidirect
328. C2×C4×D4C2×D11semidirect
562. C11#60810semidirect

Maximal subgroups

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

subgroupindex
#130819492
#130797192
#130797042
#130790802
#130790122
#130780882
#130780802
#130778742
#130778662
#130772542
C2×C11×#5422
#6081011