Finite Group Databasebeta

← #14788968

Subgroups — #14788968

Order 2816.

1586 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082380C211yesmaximal, characteristic, complemented
2#13078080C212yesmaximal, complemented
3C2×#10622690C212yesmaximal, complemented
4#13069840C212yesmaximal, complemented
5#13069657C212yesmaximal, complemented
6#13069444C212yesmaximal, complemented
7#13068608C211yesmaximal, characteristic, complemented
8#13068569C212yesmaximal, complemented
9C4×C11×#127C211yesmaximal, characteristic, complemented
10C2×#67037C2212yes—
11C2×C11×#127C2211yescharacteristic
12C2×C4×D4×C11—22no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic, complemented
15C2×#66985C2214yescomplemented
16C2×#66983—22no—
17#10623086—22no—
18#10623085—24no—
19D4×D44—22no—
20#10623041C2212yes—
21#10623024—22no—
22#10623008C2212yes—
23C11×#390—22no—
24C11×#390C2211yescharacteristic
25C11×#390C2211yescharacteristic, complemented
26C11×#384C2211yescharacteristic, complemented
27C43×C11C2211yescharacteristic, complemented
28C2×#66897C2212yes—
29#10622690—28no—
30#10622632—22no—
31#10622629—24no—
32#10622628—22no—
33#10622579C2214yescomplemented
34C2×#66869C2214yescomplemented
35C2×#66869C2214yescomplemented
36#10622537C2212yescomplemented
37#10622168C2212yescomplemented
38C22×D4×C11—22no—
39C22×D4×C11C2311yescharacteristic
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D412yes—
43C22×C22⋊D11—24no—
44#67037—24no—
45#67037—24no—
46#67037—44no—
47C2×#4341—24no—
48C2×D4×D11—24no—
49C2×#4339C2314yes—
50C22×D44—22no—
51C11×#127—22no—
52C11×#127D414yescomplemented
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11—48no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4D412yes—
65C2×C42×C11—21no—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×#4324—24no—
71#66985—28no—
72#66985—44no—
73C2×#4323—24no—
74#66983—24no—
75#66983—24no—
76#66983—22no—
77#66983—22no—
78#66983—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×C4⋊Dic11—22no—
81C2×#4318C2314yes—
82#66950—24no—
83#66948—24no—
84#66939—28no—
85#66935—28no—
86#66928D414yescomplemented
87#66927D412yescomplemented
88C4×D44—22no—
89C4×D44—22no—
90#66922D412yescomplemented
91#66897—24no—
92#66874—24no—
93#66873—24no—
94#66869—28no—
95#66869—44no—
96C4⋊(C11⋊C8)—22no—
97C4⋊(C11⋊C8)—22no—
98#24222—111nomaximal, Sylow
99C24×C11—21no—
100C24×C11C2×D412yes—
101C23×D11—24no—
102C2×D4×C11—28no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—21no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—44no—
109C2×D4×C11—44no—
110C2×D4×C11C2×D412yes—
111C2×D4×C11C2×D412yescomplemented
112C2×D4×C11#4112yes—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—44no—
119C22×C4×C11—44no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—28no—
127C2×C22⋊D11—24no—
128C2×C22⋊D11—48no—
129C2×C22⋊D11—48no—
130C22×Dic11—24no—
131#4341—48no—
132#4341—48no—
133D4×D11—48no—
134D4×D11—48no—
135#4339—24no—
136#4339—24no—
137#4339—24no—
138#4339—24no—
139C2×D44—24no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—84no—
143C2×D44C2×D414yes—
144C2×C4×D11—24no—
145C2×Dic22C2×D414yes—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—44no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—42no—
153C42×C11—24no—
154C42×C11—21no—
155C42×C11—22no—
156C42×C11—42no—
157C42×C11C2×D412yes—
158C42×C11C2×D412yes—
159C42×C11C2×D412yescomplemented
160#4324—48no—
161#4323—48no—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—24no—
165C4⋊Dic11—24no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168#4318—24no—
169#4318—24no—
170C2×C11⋊C8—24no—
171#3496—111no—
172#3036—112no—
173C2×#453—112no—
174C4×#127D1111yescharacteristic, complemented
175#2039—112no—
176#2006—112no—
177#1962—112no—
178#1800—111no—
179#1792—112no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11#12114yes—
190C23×C11C22×D411yescharacteristic
191C22×D11—24no—
192C22×D11—48no—
193C22×D11—84no—
194C22×D11—84no—
195D4×C11—24no—
196D4×C11—24no—
197D4×C11—24no—
198D4×C11—416no—
199D4×C11—42no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—44no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—82no—
214C2×C4×C11—82no—
215C2×C4×C11—82no—
216C2×C4×C11#12012yes—
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D412yes—
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)12yes—
223C22⋊D11—416no—
224C22⋊D11—44no—
225C22⋊D11—44no—
226C2×Dic11—24no—
227C2×Dic11—48no—
228D44—24no—
229D44—24no—
230D44—44no—
231D44—82no—
232D44—84no—
233C4×D11—44no—
234C4×D11—44no—
235Dic22—24no—
236Dic22—24no—
237C11⋊C8—44no—
238C2×H(5,𝔽2)—112no—
239C2×AGL(1,ℤ/8)—114no—
240#547—222no—
241#546—224no—
242D42—222no—
243#537—112no—
244#534—222no—
245#532—112no—
246C2×#127C2×D1111yescharacteristic
247C2×#121—222no—
248C2×C4×D4—22no—
249C2×C4×D4C2×D1111yescharacteristic
250C2×C4×D4C2×D1111yescharacteristic, complemented
251#463—224no—
252#461—222no—
253#459—222no—
254#453—228no—
255#423—112no—
256C2×#104—114no—
257C2×#104—114no—
258#417—114no—
259C2×#100—112no—
260#390—22no—
261#390C2×D1111yescharacteristic
262#390C2×D1111yescharacteristic, complemented
263#384C2×D1111yescharacteristic, complemented
264C43C2×D1111yescharacteristic, complemented
265#343—112no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—24no—
269C22×C11—44no—
270C22×C11—44no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11C2×#12011yescharacteristic
279C22×C11C2×#12111yescharacteristic
280C22×C11#53511yescharacteristic
281C2×D11—44no—
282C2×D11—44no—
283C2×D11—44no—
284C2×D11—168no—
285C4×C11—24no—
286C4×C11—21no—
287C4×C11—22no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11—81no—
291C4×C11#45312yescomplemented
292C4×C11D4212yes—
293C4×C11#54612yes—
294Dic11—44no—
295H(5,𝔽2)—224no—
296H(5,𝔽2)—224no—
297H(5,𝔽2)—444no—
298C2×#41—114no—
299C2×#41—224no—
300C22×D4—22no—
301C22×D4—222no—
302C22×D4—224no—
303C22×D4—224no—
304C22×D4C22×D1111yescharacteristic
305C22×D4C22×D1111yescharacteristic
306C23×C4—21no—
307C23×C4C22⋊D1112yes—
308AGL(1,ℤ/8)—228no—
309AGL(1,ℤ/8)—444no—
310C2×SD16—224no—
311C2×D8—224no—
312C2×M16—114no—
313C4⋊Q8—112no—
314#127—22no—
315#127—112no—
316#127D4414yescomplemented
317#124—114no—
318#123—228no—
319C22⋊Q8—224no—
320#121—224no—
321#121—224no—
322#121—224no—
323#121—222no—
324#121—224no—
325#121—222no—
326#120—228no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—48no—
332C4×D4—222no—
333C4×D4—222no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C4⋊C4C22×D1111yescharacteristic
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—224no—
342C2×C22⋊C4C22⋊D1112yes—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42C22×D1111yescharacteristic
346C2×C42C22×D1111yescharacteristic
347C2×C42C22×D1111yescharacteristic
348C4⋊C8—222no—
349C4⋊C8—222no—
350#104—228no—
351#104—444no—
352#103—224no—
353#102—224no—
354#100—224no—
355C2×C11—21no—
356C2×C11—21no—
357C2×C11—44no—
358C2×C11—82no—
359C2×C11#240811yescharacteristic
360C2×C11C2×#45311yescharacteristic
361C2×C11#301811yescharacteristic
362D11—84no—
363C24—21no—
364C24—224no—
365C24C2×C22⋊D1112yes—
366#41—224no—
367#41—224no—
368#41—224no—
369#41—224no—
370#41—448no—
371#41—448no—
372C2×Q8—114no—
373C2×D4—28no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—44no—
380C2×D4—44no—
381C2×D4—114no—
382C2×D4—224no—
383C2×D4—228no—
384C2×D4—224no—
385C2×D4—222no—
386C2×D4—222no—
387C2×D4—448no—
388C2×D4—448no—
389C2×D4—448no—
390C2×D4—448no—
391C2×D4—884no—
392C2×D4C2×D4412yes—
393C2×D4C2×D4412yescomplemented
394C2×D4#433912yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—44no—
401C22×C4—44no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—224no—
405C22×C4—224no—
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C2×C22⋊D1112yes—
408C22×C4C2×C22⋊D1111yescharacteristic
409C22×C4C23×D1111yescharacteristic
410SD16—448no—
411D8—448no—
412M16—224no—
413M16—224no—
414C2×C8—224no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—44no—
418C4⋊C4—224no—
419C4⋊C4—222no—
420C4⋊C4—222no—
421C22⋊C4—24no—
422C22⋊C4—44no—
423C22⋊C4—44no—
424C22⋊C4—42no—
425C22⋊C4—228no—
426C22⋊C4—224no—
427C22⋊C4—224no—
428C42—24no—
429C42—21no—
430C42—22no—
431C42—42no—
432C42C2×D4412yescomplemented
433C42D4×D1112yes—
434C42D4×D1112yes—
435C11#2422211yescharacteristic, complemented, Sylow
436C23—22no—
437C23—22no—
438C23—22no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—41no—
444C23—41no—
445C23—224no—
446C23—448no—
447C23—884no—
448C23—884no—
449C23#6698314yes—
450C23C22×C22⋊D1111yescharacteristic
451Q8—224no—
452Q8—224no—
453D4—24no—
454D4—24no—
455D4—24no—
456D4—416no—
457D4—42no—
458D4—224no—
459D4—224no—
460D4—4416no—
461D4—444no—
462D4—444no—
463D4—444no—
464D4—882no—
465D4—884no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—224no—
483C2×C4—448no—
484C2×C4—444no—
485C2×C4—444no—
486C2×C4#6699012yes—
487C2×C4#6699011yescharacteristic
488C2×C4#6699011yescharacteristic
489C2×C4C22×D4411yescharacteristic
490C2×C4C2×#433911yescharacteristic
491C2×C4C2×D4×D1112yes—
492C2×C4#6704212yes—
493C8—444no—
494C22—21no—
495C22—21no—
496C22—24no—
497C22—44no—
498C22—44no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—82no—
503C22—82no—
504C22—81no—
505C22—81no—
506C22—444no—
507C22—444no—
508C22—444no—
509C22—1768no—
510C22C2×#6698311yescharacteristic
511C22C2×#6699011yescharacteristic
512C22#1062336111yescharacteristic
513C4—24no—
514C4—21no—
515C4—22no—
516C4—42no—
517C4—42no—
518C4—81no—
519C4—444no—
520C4#1062269012yescomplemented
521C4D4×D4412yes—
522C4#1062308112yes—
523C2—21no—
524C2—21no—
525C2—44no—
526C2—82no—
527C2—884no—
528C2#1307197211yescharacteristic
529C2C2×#1062269011yescharacteristic
530C2#1307796411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#127C2
socleC22×C11C2×#120
hypercenterC4×#127D11
hypocenterC11#24222
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. #13082380C2semidirect
2. #13078080C2semidirect
3. C2×#10622690C2semidirect
4. #13069840C2semidirect
5. #13069657C2semidirect
6. #13069444C2semidirect
7. #13068608C2semidirect
8. #13068569C2semidirect
9. C4×C11×#127C2semidirect
14. C2×C4×D4×C11C22semidirect
15. C2×#66985C22semidirect
25. C11×#390C22semidirect
26. C11×#384C22semidirect
27. C43×C11C22semidirect
33. #10622579C22semidirect
34. C2×#66869C22semidirect
35. C2×#66869C22semidirect
36. #10622537C22semidirect
37. #10622168C22semidirect
52. C11×#127D4semidirect
86. #66928D4semidirect
87. #66927D4semidirect
90. #66922D4semidirect
111. C2×D4×C11C2×D4semidirect
159. C42×C11C2×D4semidirect
174. C4×#127D11semidirect
250. C2×C4×D4C2×D11semidirect
262. #390C2×D11semidirect
263. #384C2×D11semidirect
264. C43C2×D11semidirect
291. C4×C11#453semidirect
316. #127D44semidirect
393. C2×D4C2×D44semidirect
432. C42C2×D44semidirect
435. C11#24222semidirect
520. C4#10622690semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130780802
C2×#106226902
#130698402
#130696572
#130694442
#130686082
#130685692
C4×C11×#1272
#2422211