Finite Group Databasebeta

← #14789004

Subgroups — #14789004

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 522 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#13069845C212yesmaximal, complemented
5#13069657C212yesmaximal, complemented
6#13069448C212yesmaximal, complemented
7#13068608C211yesmaximal, characteristic, complemented
8#13068569C212yesmaximal, complemented
9C11×#2328C211yesmaximal, characteristic, complemented
10C2×#67037C2212yes—
11C2×C11×#127C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic, complemented
14C2×#66985C2214yescomplemented
15C2×#66983—22no—
16#10623086—22no—
17#10623085—24no—
18D4×D44—22no—
19#10623041C2212yes—
20#10623024—22no—
21#10623008C2212yes—
22C11×#390C2211yescharacteristic
23C11×#390C2211yescharacteristic, complemented
24C11×#386—22no—
25C11×#386—22no—
26C11×#382C2211yescharacteristic, complemented
27C11×#376C2211yescharacteristic, 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—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D412yes—
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×#4324—24no—
67#66985—28no—
68#66985—44no—
69C2×#4323—24no—
70#66983—24no—
71#66983—24no—
72#66983—22no—
73#66983—22no—
74#66983—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×C4⋊Dic11—22no—
77C2×#4318C2314yes—
78#66950—24no—
79#66948—24no—
80#66939—28no—
81#66935—28no—
82#66928D414yescomplemented
83#66927D412yescomplemented
84C4×D44—22no—
85C4×D44—22no—
86#66922D412yescomplemented
87C11×#95—21no—
88C11×#95—21no—
89C11×#95—22no—
90#66897—24no—
91#66874—24no—
92#66873—24no—
93#66869—28no—
94#66869—44no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—22no—
97#24226—111nomaximal, Sylow
98C24×C11—21no—
99C24×C11C2×D412yes—
100C23×D11—24no—
101C2×D4×C11—28no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—82no—
108C2×D4×C11—82no—
109C2×D4×C11C2×D412yes—
110C2×D4×C11C2×D412yescomplemented
111C2×D4×C11#4112yes—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—82no—
119C22×C4×C11—82no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—28no—
125C2×C22⋊D11—24no—
126C2×C22⋊D11—48no—
127C2×C22⋊D11—48no—
128C22×Dic11—24no—
129#4341—48no—
130#4341—48no—
131D4×D11—48no—
132D4×D11—48no—
133#4339—24no—
134#4339—24no—
135#4339—24no—
136#4339—24no—
137C2×D44—24no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—84no—
141C2×D44C2×D414yes—
142C2×C4×D11—24no—
143C2×Dic22C2×D414yes—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—82no—
150C11×C22⋊C4—82no—
151C42×C11—21no—
152C42×C11—22no—
153C42×C11C2×D412yes—
154C42×C11C2×D412yes—
155C42×C11C2×D412yescomplemented
156#4324—48no—
157#4323—48no—
158(C2×D11)⋊C4—28no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161C4⋊Dic11—24no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164#4318—24no—
165#4318—24no—
166C2×C11⋊C8—24no—
167#3496—111no—
168#3036—112no—
169C2×#453—112no—
170#2328D1111yescharacteristic, complemented
171#2040—112no—
172#2006—112no—
173#1963—112no—
174#1800—111no—
175#1792—112no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11#12114yes—
186C23×C11C22×D411yescharacteristic
187C22×D11—24no—
188C22×D11—48no—
189C22×D11—84no—
190C22×D11—84no—
191D4×C11—24no—
192D4×C11—24no—
193D4×C11—24no—
194D4×C11—42no—
195D4×C11—88no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—44no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—82no—
210C2×C4×C11—84no—
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12012yes—
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D412yes—
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)12yes—
218C22⋊D11—416no—
219C22⋊D11—44no—
220C22⋊D11—44no—
221C2×Dic11—24no—
222C2×Dic11—48no—
223D44—24no—
224D44—24no—
225D44—44no—
226D44—82no—
227D44—84no—
228C4×D11—44no—
229C4×D11—44no—
230Dic22—24no—
231Dic22—24no—
232C11⋊C8—44no—
233C2×H(5,𝔽2)—112no—
234C2×AGL(1,ℤ/8)—114no—
235#547—222no—
236#546—224no—
237D42—222no—
238#537—112no—
239#534—222no—
240#532—112no—
241C2×#127C2×D1111yescharacteristic
242C2×#121—222no—
243C2×C4×D4C2×D1111yescharacteristic
244C2×C4×D4C2×D1111yescharacteristic, complemented
245#463—224no—
246#461—222no—
247#459—222no—
248#453—228no—
249#423—112no—
250C2×#104—114no—
251C2×#104—114no—
252#417—114no—
253C2×#100—112no—
254#390C2×D1111yescharacteristic
255#390C2×D1111yescharacteristic, complemented
256#386—22no—
257#386—22no—
258#382C2×D1111yescharacteristic, complemented
259#376C2×D1111yescharacteristic, complemented
260#343—112no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—24no—
264C22×C11—44no—
265C22×C11—44no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11C2×#12011yescharacteristic
274C22×C11C2×#12111yescharacteristic
275C22×C11#53511yescharacteristic
276C2×D11—44no—
277C2×D11—44no—
278C2×D11—44no—
279C2×D11—168no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—81no—
286C4×C11—81no—
287C4×C11D4212yes—
288C4×C11#54612yes—
289Dic11—44no—
290H(5,𝔽2)—224no—
291H(5,𝔽2)—224no—
292H(5,𝔽2)—444no—
293C2×#41—114no—
294C2×#41—224no—
295C22×D4—22no—
296C22×D4—222no—
297C22×D4—224no—
298C22×D4—224no—
299C22×D4C22×D1111yescharacteristic
300C22×D4C22×D1111yescharacteristic
301C23×C4—21no—
302C23×C4C22⋊D1112yes—
303AGL(1,ℤ/8)—228no—
304AGL(1,ℤ/8)—444no—
305C2×SD16—224no—
306C2×D8—224no—
307C2×M16—114no—
308C4⋊Q8—112no—
309#127—22no—
310#127—112no—
311#127D4414yescomplemented
312#124—114no—
313#123—228no—
314C22⋊Q8—224no—
315#121—224no—
316#121—224no—
317#121—224no—
318#121—222no—
319#121—224no—
320#121—222no—
321#120—228no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—222no—
327C4×D4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4C22×D1111yescharacteristic
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—224no—
335C2×C22⋊C4C22⋊D1112yes—
336C2×C42C22×D1111yescharacteristic
337C2×C42C22×D1111yescharacteristic
338C2×C42C22×D1111yescharacteristic
339C4⋊C8—222no—
340C4⋊C8—222no—
341#104—228no—
342#104—444no—
343#103—224no—
344#102—224no—
345#100—224no—
346#95—21no—
347#95—21no—
348#95—22no—
349C2×C11—21no—
350C2×C11—21no—
351C2×C11—44no—
352C2×C11—82no—
353C2×C11#240811yescharacteristic
354C2×C11#301911yescharacteristic
355C2×C11#302111yescharacteristic
356D11—84no—
357C24—21no—
358C24—224no—
359C24C2×C22⋊D1112yes—
360#41—224no—
361#41—224no—
362#41—224no—
363#41—224no—
364#41—448no—
365#41—448no—
366C2×Q8—114no—
367C2×D4—28no—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—82no—
374C2×D4—82no—
375C2×D4—114no—
376C2×D4—224no—
377C2×D4—228no—
378C2×D4—224no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—448no—
382C2×D4—448no—
383C2×D4—448no—
384C2×D4—448no—
385C2×D4—884no—
386C2×D4C2×D4412yes—
387C2×D4C2×D4412yescomplemented
388C2×D4#433912yes—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—42no—
395C22×C4—82no—
396C22×C4—82no—
397C22×C4—224no—
398C22×C4—224no—
399C22×C4C2×C22⋊D1112yes—
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C23×D1111yescharacteristic
403SD16—448no—
404D8—448no—
405M16—224no—
406M16—224no—
407C2×C8—224no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—224no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C22⋊C4—24no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—82no—
417C22⋊C4—82no—
418C22⋊C4—228no—
419C22⋊C4—224no—
420C22⋊C4—224no—
421C42—21no—
422C42—22no—
423C42C2×D4412yescomplemented
424C42D4×D1112yes—
425C42D4×D1112yes—
426C11#2422611yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—22no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—41no—
435C23—41no—
436C23—224no—
437C23—448no—
438C23—884no—
439C23—884no—
440C23#6698314yes—
441C23C22×C22⋊D1111yescharacteristic
442Q8—224no—
443Q8—224no—
444D4—24no—
445D4—24no—
446D4—24no—
447D4—42no—
448D4—88no—
449D4—224no—
450D4—224no—
451D4—444no—
452D4—4416no—
453D4—444no—
454D4—444no—
455D4—882no—
456D4—884no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—44no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—84no—
472C2×C4—224no—
473C2×C4—448no—
474C2×C4—444no—
475C2×C4—444no—
476C2×C4#6699012yes—
477C2×C4#6699011yescharacteristic
478C2×C4#6699011yescharacteristic
479C2×C4C22×D4411yescharacteristic
480C2×C4C2×#433911yescharacteristic
481C2×C4C2×D4×D1112yes—
482C2×C4#6704212yes—
483C8—444no—
484C22—21no—
485C22—21no—
486C22—24no—
487C22—44no—
488C22—44no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—82no—
493C22—82no—
494C22—81no—
495C22—81no—
496C22—444no—
497C22—444no—
498C22—444no—
499C22—1768no—
500C22C2×#6698311yescharacteristic
501C22C2×#6699011yescharacteristic
502C22#1062336111yescharacteristic
503C4—21no—
504C4—21no—
505C4—22no—
506C4—42no—
507C4—42no—
508C4—81no—
509C4—81no—
510C4—444no—
511C4D4×D4412yes—
512C4#1062308112yes—
513C2—21no—
514C2—21no—
515C2—44no—
516C2—82no—
517C2—884no—
518C2#1307197211yescharacteristic
519C2#1307797211yescharacteristic
520C2#1307798711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2328C2
socleC22×C11C2×#120
hypercenter#2328D11
hypocenterC11#24226
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2328

Complements

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

NH ≅ G/Ntype
1. #13082380C2semidirect
2. #13078080C2semidirect
3. C2×#10622690C2semidirect
4. #13069845C2semidirect
5. #13069657C2semidirect
6. #13069448C2semidirect
7. #13068608C2semidirect
8. #13068569C2semidirect
9. C11×#2328C2semidirect
13. C2×C4×D4×C11C22semidirect
14. C2×#66985C22semidirect
23. C11×#390C22semidirect
26. C11×#382C22semidirect
27. C11×#376C22semidirect
33. #10622579C22semidirect
34. C2×#66869C22semidirect
35. C2×#66869C22semidirect
36. #10622537C22semidirect
37. #10622168C22semidirect
52. C11×#127D4semidirect
82. #66928D4semidirect
83. #66927D4semidirect
86. #66922D4semidirect
110. C2×D4×C11C2×D4semidirect
155. C42×C11C2×D4semidirect
170. #2328D11semidirect
244. C2×C4×D4C2×D11semidirect
255. #390C2×D11semidirect
258. #382C2×D11semidirect
259. #376C2×D11semidirect
311. #127D44semidirect
387. C2×D4C2×D44semidirect
423. C42C2×D44semidirect
426. C11#24226semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130780802
C2×#106226902
#130698452
#130696572
#130694482
#130686082
#130685692
C11×#23282
#2422611