Finite Group Databasebeta

← #14788080

Subgroups — #14788080

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3C2×#10622628C211yesmaximal, characteristic, complemented
4#13069798C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069568C211yesmaximal, characteristic, complemented
7#13069543C211yesmaximal, characteristic, complemented
8#13068967C212yesmaximal, complemented
9#13068862C212yesmaximal, complemented
10#13068596C211yesmaximal, characteristic, complemented
11C4×C11×#121C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C2×C11×#121C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×#4323C2212yes—
18C2×#66983—21no—
19C2×#66983C2212yes—
20#10623008—24no—
21#10623008—24no—
22C2×#66928—21no—
23C2×#66927C2211yescharacteristic
24C2×C4×D44—21no—
25C2×C4×D44C2212yes—
26C2×#66922C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#388—21no—
30C11×#386—21no—
31C11×#380C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4—21no—
34C2×#66896C2212yes—
35C2×C22⋊(C11⋊C8)C2212yes—
36#10622628—24no—
37#10622620—24no—
38C2×#66873C2212yes—
39C2×#66873C2212yes—
40C2×#66873C2212yes—
41C2×#66871C2212yes—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—22no—
54C2×#4339—28no—
55C2×#4339—44no—
56C2×#4339—44no—
57C22×D44—21no—
58C22×D44—21no—
59C22×D44C2312yes—
60C22×C4×D11—22no—
61C22×Dic22—21no—
62C11×#121—22no—
63C11×#121—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—44no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C42×C11—21no—
79C2×C42×C11D411yescharacteristic
80C2×C42×C11D411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×#4323—24no—
84C2×#4323—24no—
85C2×#4323—42no—
86#66983—28no—
87#66983—24no—
88#66983—24no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2312yes—
93C22×C11⋊C8C2312yes—
94C22×C11⋊C8C2312yes—
95#66928—28no—
96#66927—22no—
97#66927D414yescomplemented
98C4×D44—28no—
99C4×D44—24no—
100C4×D44—24no—
101#66922—22no—
102#66922D414yescomplemented
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106#66896—24no—
107C22⋊(C11⋊C8)—42no—
108#66873—24no—
109#66873—24no—
110#66873—42no—
111#66871—24no—
112C4⋊(C11⋊C8)—22no—
113C4⋊(C11⋊C8)—22no—
114#24150—111nomaximal, Sylow
115C24×C11—21no—
116C24×C11C2×D411yescharacteristic
117C23×D11—22no—
118C2×D4×C11—24no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11#4112yescomplemented
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11D814yescomplemented
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—28no—
152C2×C22⋊D11—44no—
153C2×C22⋊D11—44no—
154C22×Dic11—22no—
155#4339—432no—
156C2×D44—24no—
157C2×D44—24no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44—22no—
163C2×D44—42no—
164C2×D44—42no—
165C2×D44—42no—
166C2×D44—42no—
167C2×D44C2×D414yes—
168C2×C4×D11—28no—
169C2×C4×D11—44no—
170C2×C4×D11—44no—
171C2×Dic22—24no—
172C2×Dic22—42no—
173C2×Dic22—42no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4#4112yescomplemented
181C11×C22⋊C4—24no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—42no—
191C42×C11C2×D412yes—
192C42×C11C2×D412yes—
193#4323—48no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—28no—
196C4⋊Dic11—24no—
197C4⋊Dic11—22no—
198C4⋊Dic11C2×D414yes—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×#532—111no—
206C2×#474—111no—
207C2×#459—111no—
208C4×#121D1111yescharacteristic, complemented
209#2033—112no—
210#1999—112no—
211#1988—111no—
212#1982—111no—
213#1879—112no—
214#1862—112no—
215#1797—111no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—22no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11C2×D812yes—
230C23×C11C22×D411yescharacteristic
231C22×D11—24no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—42no—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—48no—
241D4×C11—41no—
242D4×C11—41no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—28no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—44no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—84no—
269C2×C4×C11#12012yes—
270C2×C4×C11#12012yes—
271C2×C4×C11C2×D812yes—
272C2×C4×C11C2×D812yes—
273C2×C4×C11AGL(1,ℤ/8)12yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C22⋊D11—416no—
281C2×Dic11—24no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284D44—24no—
285D44—24no—
286D44—48no—
287D44—42no—
288D44—42no—
289D44—48no—
290C4×D11—416no—
291Dic22—48no—
292C11⋊C8—42no—
293C11⋊C8—42no—
294C22×#41—221no—
295C22×D8—112no—
296#532—224no—
297#532—224no—
298C2×C4⋊Q8—111no—
299C2×#127—111no—
300C2×#124—221no—
301C2×#121—112no—
302C2×#121—221no—
303C2×#121C2×D1111yescharacteristic
304C2×C4×D4—21no—
305C2×C4×D4—112no—
306C2×C4×D4—221no—
307C2×C4×D4C2×D1111yescharacteristic
308C22×C42C2×D1111yescharacteristic
309#474—224no—
310#459—224no—
311C2×#107—112no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8—111no—
314C2×#102—112no—
315C2×#102—112no—
316C2×#102—112no—
317C2×#102—112no—
318C2×C22⋊C8—112no—
319#390C2×D1111yescharacteristic
320#389C2×D1111yescharacteristic
321#388—21no—
322#386—21no—
323#380C2×D1111yescharacteristic
324C4×C4⋊C4C2×D1111yescharacteristic
325C4×C22⋊C4—21no—
326#340—112no—
327#340—112no—
328#336—112no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11C2×#12011yescharacteristic
344C22×C11#52511yescharacteristic
345C22×C11#53711yescharacteristic
346C22×C11C22×D811yescharacteristic
347C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57511yescharacteristic
350C2×D11—44no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—82no—
354C2×D11—82no—
355C2×D11—82no—
356C2×D11—82no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—42no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—81no—
363C4×C11—81no—
364C4×C11#44714yes—
365C4×C11#54611yescharacteristic
366C4×C11#54711yescharacteristic
367C4×C11#54811yescharacteristic
368C4×C11#55011yescharacteristic
369Dic11—44no—
370C2×#41—228no—
371C2×#41—444no—
372C2×#41—444no—
373C22×Q8—221no—
374C22×D4—21no—
375C22×D4—112no—
376C22×D4—222no—
377C22×D4—221no—
378C22×D4—221no—
379C22×D4C22×D1111yescharacteristic
380C23×C4—21no—
381C23×C4—222no—
382C23×C4C22⋊D1111yescharacteristic
383C23×C4C22⋊D1111yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C2×D8—224no—
386C2×D8—224no—
387C2×D8—442no—
388C22×C8—112no—
389C22×C8—112no—
390C4⋊Q8—114no—
391C4⋊Q8—222no—
392#127—114no—
393#127—222no—
394#124—228no—
395#121—22no—
396#121—22no—
397#121—224no—
398#121—224no—
399#121—228no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—44no—
403C4×D4—224no—
404C4×D4—224no—
405C4×D4—228no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4—222no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—21no—
422C2×C42C22⋊D1111yescharacteristic
423C2×C42C22⋊D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426#107—224no—
427C4⋊C8—222no—
428C4⋊C8—222no—
429#102—224no—
430#102—224no—
431#102—224no—
432#102—442no—
433C22⋊C8—442no—
434#95—21no—
435#95—21no—
436#95—21no—
437C2×C11—42no—
438C2×C11—82no—
439C2×C11#240711yescharacteristic
440C2×C11C2×#44711yescharacteristic
441C2×C11#300511yescharacteristic
442C2×C11#310011yescharacteristic
443C2×C11#311511yescharacteristic
444C2×C11#324511yescharacteristic
445C2×C11#325111yescharacteristic
446D11—84no—
447C24—21no—
448C24—222no—
449C24C2×C22⋊D1111yescharacteristic
450#41—4432no—
451C2×Q8—224no—
452C2×Q8—442no—
453C2×Q8—442no—
454C2×D4—24no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—114no—
463C2×D4—228no—
464C2×D4—224no—
465C2×D4—224no—
466C2×D4—222no—
467C2×D4—222no—
468C2×D4—222no—
469C2×D4—222no—
470C2×D4—222no—
471C2×D4—442no—
472C2×D4—442no—
473C2×D4—444no—
474C2×D4—444no—
475C2×D4—442no—
476C2×D4—442no—
477C2×D4#433912yescomplemented
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—228no—
496C22×C4—222no—
497C22×C4—444no—
498C22×C4—444no—
499C22×C4#432314yescomplemented
500C22×C4C2×C22⋊D1111yescharacteristic
501C22×C4C2×C22⋊D1111yescharacteristic
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506D8—448no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—222no—
512C2×C8—222no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—114no—
520C4⋊C4—224no—
521C4⋊C4—222no—
522C4⋊C4#433912yescomplemented
523C22⋊C4—24no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—228no—
529C22⋊C4—228no—
530C42—22no—
531C42—22no—
532C42—21no—
533C42—21no—
534C42—42no—
535C42D4×D1112yes—
536C42D4×D1112yes—
537C11#2415011yescharacteristic, complemented, Sylow
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—22no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—224no—
552C23—442no—
553C23—442no—
554C23—442no—
555C23—442no—
556C23—442no—
557C23—442no—
558C23C2×#432312yes—
559C23C22×C22⋊D1111yescharacteristic
560Q8—448no—
561D4—22no—
562D4—22no—
563D4—48no—
564D4—41no—
565D4—41no—
566D4—224no—
567D4—224no—
568D4—448no—
569D4—4416no—
570D4—442no—
571D4—442no—
572D4—448no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—28no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—44no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—84no—
599C2×C4—224no—
600C2×C4—4416no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4C2×#432312yes—
604C2×C4C2×#432312yes—
605C2×C4#6699012yes—
606C2×C4#6699012yes—
607C2×C4#6700212yes—
608C2×C4C2×#433911yescharacteristic
609C2×C4C2×#433911yescharacteristic
610C2×C4C2×D4×D1111yescharacteristic
611C2×C4C2×D4×D1111yescharacteristic
612C2×C4#6704211yescharacteristic
613C2×C4#6704311yescharacteristic
614C8—442no—
615C8—442no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—444no—
631C22—444no—
632C22—444no—
633C22—882no—
634C22—882no—
635C22—882no—
636C22—882no—
637C22#1062332211yescharacteristic
638C22C22×#432311yescharacteristic
639C22C2×#6699011yescharacteristic
640C22C2×#6700211yescharacteristic
641C22#1062335311yescharacteristic
642C22#1062335311yescharacteristic
643C22#1062336411yescharacteristic
644C4—22no—
645C4—22no—
646C4—42no—
647C4—41no—
648C4—41no—
649C4—81no—
650C4—81no—
651C4—444no—
652C4#1062264914yes—
653C4#1062308111yescharacteristic
654C4#1062308211yescharacteristic
655C4#1062308311yescharacteristic
656C4#1062308411yescharacteristic
657C2—42no—
658C2—82no—
659C2—884no—
660C2#1307196111yescharacteristic
661C2C2×#1062264911yescharacteristic
662C2#1307785611yescharacteristic
663C2#1307861611yescharacteristic
664C2#1307876711yescharacteristic
665C2#1307992311yescharacteristic
666C2#1307997811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
hypercenterC4×#121D11
hypocenterC11#24150
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. C2×#10622620C2semidirect
3. C2×#10622628C2semidirect
4. #13069798C2semidirect
5. #13069612C2semidirect
6. #13069568C2semidirect
7. #13069543C2semidirect
8. #13068967C2semidirect
9. #13068862C2semidirect
10. #13068596C2semidirect
11. C4×C11×#121C2semidirect
97. #66927D4semidirect
102. #66922D4semidirect
126. C2×D4×C11#41semidirect
144. C22×C4×C11D8semidirect
180. C11×C4⋊C4#41semidirect
208. C4×#121D11semidirect
477. C2×D4#4339semidirect
499. C22×C4#4323semidirect
522. C4⋊C4#4339semidirect
537. C11#24150semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106226202
C2×#106226282
#130697982
#130696122
#130695682
#130695432
#130689672
#130688622
#130685962
C4×C11×#1212
#2415011