Finite Group Databasebeta

← #14734997

Subgroups — #14734997

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079806C211yesmaximal, characteristic, complemented
2#13079603C211yesmaximal, characteristic, complemented
3#13079080C211yesmaximal, characteristic, complemented
4#13067933C214yesmaximal, complemented
5#13067909C214yesmaximal, complemented
6#13067240C211yesmaximal, characteristic, complemented
7#13067218C211yesmaximal, characteristic, complemented
8#13067214C211yesmaximal, characteristic, complemented
9C2×C11×#562C211yesmaximal, characteristic, complemented
10C11×#562—22no—
11C11×#562—22no—
12C11×#562—22no—
13C11×#562C2214yes—
14C2×C11×#125C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C11×#124C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×#121—21no—
22C2×C11×#121—21no—
23C2×#66995—21no—
24C2×#66985—21no—
25#10623008C2211yescharacteristic
26#10622840—21no—
27#10622830—21no—
28#10622680C2212yescomplemented
29#10622679—22no—
30#10622678C2212yescomplemented
31#10622673C2212yescomplemented
32#10622672—22no—
33#10622671C2212yescomplemented
34#10622671C2212yescomplemented
35#10622670—22no—
36#10622668C2212yescomplemented
37#10622581—21no—
38#10622580—21no—
39#10622539C2211yescharacteristic
40#10622539C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42#10622181C2214yescomplemented
43#10622178C2214yescomplemented
44#10622178C2214yescomplemented
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C2×#4339—21no—
54C11×#125—21no—
55C11×#125—21no—
56C11×#125D412yes—
57C11×#125C2312yes—
58C11×#124—21no—
59C11×#124—21no—
60C11×#124—21no—
61C11×#124—21no—
62C11×#124D412yes—
63C11×#124D412yes—
64C11×#124C2312yes—
65C11×#124C2312yes—
66C11×#123—24no—
67C11×#123—24no—
68C11×#123—24no—
69C11×#123—24no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×#121—24no—
75C11×#121—24no—
76C11×#121—24no—
77C11×#121—24no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11C2311yescharacteristic
91C2×#4326—22no—
92#66995—44no—
93C2×#4325—22no—
94C2×#4325—22no—
95C2×#4324—22no—
96#66985—44no—
97C2×#4323—22no—
98C2×#4323—22no—
99#66983—21no—
100#66983—21no—
101C2×#4318—21no—
102#66928—21no—
103#66927C2311yescharacteristic
104C4×D44—21no—
105C4×D44—21no—
106#66922C2311yescharacteristic
107#66899—22no—
108#66896—22no—
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)—21no—
111#66873—22no—
112#66873—22no—
113#66872—22no—
114#66871—22no—
115C4⋊(C11⋊C8)—21no—
116C4⋊(C11⋊C8)—21no—
117#66867C2312yes—
118#66867C2312yes—
119#66867C2312yes—
120C4×C11⋊C8—21no—
121#18993—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—42no—
127C2×Q8×C11—81no—
128C2×Q8×C11C2×D412yes—
129C2×Q8×C11C2×D412yes—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—42no—
135C2×D4×C11—81no—
136C2×D4×C11—82no—
137C2×D4×C11—82no—
138C2×D4×C11C2×D412yes—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—82no—
147C22×C4×C11—82no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C2×C22⋊D11—41no—
152#4339—42no—
153#4339—42no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×C4×D11—41no—
158C2×Dic22—21no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2411yescharacteristic
183#4326—44no—
184#4325—44no—
185#4325—82no—
186#4324—44no—
187#4323—44no—
188#4323—82no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193#4318—24no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×#562D1111yescharacteristic, complemented
198#3234—111no—
199#3213—111no—
200#3153—111no—
201#1661—114no—
202#1656—114no—
203#1533—111no—
204#1528—111no—
205#1527—111no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11#12011yescharacteristic
215C22×D11—41no—
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—81no—
219Q8×C11—81no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—81no—
223D4×C11—81no—
224D4×C11—84no—
225D4×C11—84no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—84no—
238C2×C4×C11—84no—
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C22⋊D11—82no—
246C2×Dic11—41no—
247D44—41no—
248D44—42no—
249D44—41no—
250D44—42no—
251C4×D11—82no—
252Dic22—41no—
253Dic22—41no—
254C11⋊C8—24no—
255C11⋊C8—42no—
256C11⋊C8—42no—
257C2×#137—221no—
258C2×AGL(1,ℤ/8)—221no—
259#562—22no—
260#562—22no—
261#562—22no—
262#562C2×D1114yes—
263#532—111no—
264C2×#125C2×D1111yescharacteristic
265C2×#124C2×D1111yescharacteristic
266C2×#124C2×D1111yescharacteristic
267C2×#123—21no—
268C2×#123—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8—21no—
271C2×#121—21no—
272C2×#121—21no—
273#501—112no—
274#497—112no—
275#496—112no—
276#496—112no—
277#495—222no—
278#490—112no—
279#489—112no—
280#481—221no—
281#480—221no—
282#478—222no—
283#463—222no—
284#448—221no—
285#447—221no—
286#432—111no—
287#432—111no—
288C4×M16—111no—
289#330—114no—
290#329—114no—
291#329—114no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—84no—
301C22×C11—84no—
302C22×C11#45312yes—
303C22×C11C2×#12011yescharacteristic
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—42no—
317Dic11—81no—
318C2×#41—221no—
319C22×Q8C22⋊D1111yescharacteristic
320C22×Q8C22⋊D1111yescharacteristic
321C22×D4—21no—
322C22×D4—21no—
323C22×D4C22⋊D1111yescharacteristic
324C22×D4C22⋊D1111yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327#137—444no—
328AGL(1,ℤ/8)—444no—
329C2×Q16—222no—
330C2×SD16—222no—
331C2×SD16—222no—
332C2×SD16—222no—
333C2×D8—222no—
334C2×D8—222no—
335C2×M16—221no—
336C4⋊Q8—111no—
337#127—111no—
338#125—21no—
339#125—21no—
340#125C22⋊D1112yes—
341#125C22×D1112yes—
342#124—21no—
343#124—21no—
344#124—21no—
345#124—21no—
346#124—221no—
347#124C22⋊D1112yes—
348#124C22⋊D1112yes—
349#124C22×D1112yes—
350#124C22×D1112yes—
351#123—24no—
352#123—24no—
353#123—24no—
354#123—24no—
355C22⋊Q8—24no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359#121—24no—
360#121—24no—
361#121—24no—
362#121—24no—
363#121—221no—
364#121—221no—
365C4×D4—221no—
366C4×D4—221no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4C22⋊D1111yescharacteristic
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C42C22×D1111yescharacteristic
380#107—222no—
381#106—222no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384#103—222no—
385#102—222no—
386#102—222no—
387#102—222no—
388C22⋊C8—221no—
389C22⋊C8—221no—
390#97—112no—
391#97—112no—
392#97—112no—
393C4×C8—221no—
394C2×C11—22no—
395C2×C11—82no—
396C2×C11—82no—
397C2×C11C2×#45311yescharacteristic
398C2×C11#301911yescharacteristic
399C2×C11#302011yescharacteristic
400D11—161no—
401C24—21no—
402C24—21no—
403#41—442no—
404#41—442no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—42no—
408C2×Q8—81no—
409C2×Q8—221no—
410C2×Q8C2×C22⋊D1112yes—
411C2×Q8C2×C22⋊D1112yes—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—81no—
418C2×D4—82no—
419C2×D4—82no—
420C2×D4—221no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—441no—
424C2×D4C2×C22⋊D1112yes—
425C2×D4C2×C22⋊D1112yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—82no—
433C22×C4—82no—
434C22×C4—441no—
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438Q16—444no—
439SD16—444no—
440SD16—444no—
441SD16—882no—
442D8—444no—
443D8—882no—
444M16—224no—
445C2×C8—222no—
446C2×C8—222no—
447C2×C8—222no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4C2×C22⋊D1112yes—
459C4⋊C4C2×C22⋊D1112yes—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C42C2×C22⋊D1111yescharacteristic
473C42C2×C22⋊D1111yescharacteristic
474C42C2×C22⋊D1111yescharacteristic
475C42C23×D1111yescharacteristic
476C11#1899311yescharacteristic, complemented, Sylow
477C23—22no—
478C23—22no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—441no—
486C23#6700611yescharacteristic
487Q8—42no—
488Q8—42no—
489Q8—81no—
490Q8—81no—
491Q8—441no—
492Q8—441no—
493D4—42no—
494D4—42no—
495D4—81no—
496D4—81no—
497D4—84no—
498D4—84no—
499D4—441no—
500D4—442no—
501D4—441no—
502D4—442no—
503D4—882no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—84no—
516C2×C4—84no—
517C2×C4—441no—
518C2×C4—882no—
519C2×C4#6700611yescharacteristic
520C2×C4#6700611yescharacteristic
521C2×C4#6700611yescharacteristic
522C2×C4C22×C22⋊D1111yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C8—224no—
526C8—442no—
527C8—442no—
528C22—21no—
529C22—21no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—84no—
537C22—84no—
538C22—881no—
539C22—881no—
540C22—881no—
541C22#1062285412yes—
542C22C2×#6700611yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—42no—
553C4—881no—
554C2—22no—
555C2—82no—
556C2—82no—
557C2—1761no—
558C2C2×#1062285411yescharacteristic
559C2#1307797311yescharacteristic
560C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#562C2
socleC22×C11C2×#120
hypercenterC2×#562D11
hypocenterC11#18993
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #13079806C2semidirect
2. #13079603C2semidirect
3. #13079080C2semidirect
4. #13067933C2semidirect
5. #13067909C2semidirect
6. #13067240C2semidirect
7. #13067218C2semidirect
8. #13067214C2semidirect
9. C2×C11×#562C2semidirect
28. #10622680C22semidirect
30. #10622678C22semidirect
31. #10622673C22semidirect
33. #10622671C22semidirect
34. #10622671C22semidirect
36. #10622668C22semidirect
42. #10622181C22semidirect
43. #10622178C22semidirect
44. #10622178C22semidirect
197. C2×#562D11semidirect
476. C11#18993semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130796032
#130790802
#130679332
#130679092
#130672402
#130672182
#130672142
C2×C11×#5622
#1899311