Finite Group Databasebeta

← #14788986

Subgroups — #14788986

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082380C211yesmaximal, characteristic
2#13078088C212yesmaximal, complemented
3C2×#10622674C212yesmaximal, complemented
4#13069845C212yesmaximal, complemented
5#13069662C212yesmaximal, complemented
6#13069444C212yesmaximal, complemented
7#13068608C211yesmaximal, characteristic, complemented
8#13068569C212yesmaximal, complemented
9C4×C11×#124C211yesmaximal, characteristic, complemented
10C2×#67037C2212yes—
11C2×C11×#124C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic, complemented
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66995C2214yescomplemented
15C2×#66983—22no—
16#10623086—22no—
17#10623085—24no—
18D4×D44—22no—
19#10623041C2212yes—
20#10623024—22no—
21#10623008C2212yes—
22C11×#391C2211yescharacteristic, complemented
23C11×#390C2211yescharacteristic
24C11×#388—22no—
25C11×#382C2211yescharacteristic, complemented
26C4×C11×C22⋊C4—22no—
27C43×C11C2211yescharacteristic, complemented
28C2×#66897C2212yes—
29#10622674—28no—
30#10622644—22no—
31#10622641—24no—
32#10622640—22no—
33#10622579C2214yescomplemented
34C2×#66869C2214yescomplemented
35C2×#66869C2214yescomplemented
36#10622537C2212yescomplemented
37#10622168C2212yescomplemented
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11D412yes—
41C22×C22⋊D11—24no—
42#67037—24no—
43#67037—24no—
44#67037—44no—
45C2×#4341—24no—
46C2×D4×D11—24no—
47C2×#4339C2314yes—
48C22×D44—22no—
49C11×#124—22no—
50C11×#124D414yescomplemented
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4D412yes—
61C2×C42×C11—21no—
62C2×C42×C11—21no—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×#4326—24no—
68#66995—28no—
69#66995—44no—
70C2×#4325—24no—
71#66983—24no—
72#66983—24no—
73#66983—22no—
74#66983—22no—
75#66983—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×C4⋊Dic11—22no—
78C2×#4318C2314yes—
79#66950—24no—
80#66948—24no—
81#66939—28no—
82#66935—28no—
83#66928D414yes—
84#66927D412yes—
85C4×D44—22no—
86C4×D44—22no—
87#66922D412yes—
88C11×#95—22no—
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#24224—111nomaximal, Sylow
98C24×C11C2×D412yes—
99C23×D11—24no—
100C2×Q8×C11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11C2×D412yescomplemented
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11C2×D412yes—
107C2×D4×C11#4112yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—44no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—28no—
120C2×C22⋊D11—24no—
121C2×C22⋊D11—48no—
122C2×C22⋊D11—48no—
123C22×Dic11—24no—
124#4341—48no—
125#4341—48no—
126D4×D11—48no—
127D4×D11—48no—
128#4339—24no—
129#4339—24no—
130#4339—24no—
131#4339—24no—
132C2×D44—24no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—84no—
136C2×D44C2×D414yes—
137C2×C4×D11—24no—
138C2×Dic22C2×D414yes—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—44no—
145C42×C11—21no—
146C42×C11—22no—
147C42×C11—42no—
148C42×C11—42no—
149C42×C11—41no—
150C42×C11—41no—
151C42×C11C2×D412yes—
152C42×C11C2×D412yes—
153C42×C11C2×D412yescomplemented
154#4326—48no—
155#4325—48no—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—24no—
159C4⋊Dic11—24no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162#4318—24no—
163#4318—24no—
164C2×C11⋊C8—24no—
165#3496—111no—
166#3037—112no—
167C2×#455—112no—
168C4×#124D1111yescharacteristic, complemented
169#2040—112no—
170#2007—112no—
171#1962—112no—
172#1800—111no—
173#1792—112no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11#12114yes—
179C23×C11C22×D411yescharacteristic
180C22×D11—24no—
181C22×D11—48no—
182C22×D11—84no—
183C22×D11—84no—
184Q8×C11—24no—
185Q8×C11—42no—
186D4×C11—24no—
187D4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—44no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—82no—
205C2×C4×C11#12012yes—
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11#12011yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D412yes—
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11H(5,𝔽2)12yes—
212C22⋊D11—416no—
213C22⋊D11—44no—
214C22⋊D11—44no—
215C2×Dic11—24no—
216C2×Dic11—48no—
217D44—24no—
218D44—24no—
219D44—44no—
220D44—82no—
221D44—84no—
222C4×D11—44no—
223C4×D11—44no—
224Dic22—24no—
225Dic22—24no—
226C11⋊C8—44no—
227C2×H(5,𝔽2)—112no—
228C2×#137—114no—
229#547—222no—
230#546—224no—
231D42—222no—
232#537—112no—
233#534—222no—
234#532—112no—
235C2×#124C2×D1111yescharacteristic
236C2×#121—222no—
237C2×C4×Q8C2×D1111yescharacteristic, complemented
238C2×C4×D4C2×D1111yescharacteristic
239#464—224no—
240#462—222no—
241#460—222no—
242#455—228no—
243#423—112no—
244C2×#104—114no—
245C2×#104—114no—
246#417—114no—
247C2×#100—112no—
248#391C2×D1111yescharacteristic, complemented
249#390C2×D1111yescharacteristic
250#388—22no—
251#382C2×D1111yescharacteristic, complemented
252C4×C22⋊C4—22no—
253C43C2×D1111yescharacteristic, complemented
254#343—112no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—24no—
258C22×C11—44no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—82no—
262C22×C11C2×#12011yescharacteristic
263C22×C11C2×#12111yescharacteristic
264C22×C11#53511yescharacteristic
265C2×D11—44no—
266C2×D11—44no—
267C2×D11—44no—
268C2×D11—168no—
269C4×C11—21no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—81no—
276C4×C11#45512yescomplemented
277C4×C11D4212yes—
278C4×C11#54612yes—
279Dic11—44no—
280H(5,𝔽2)—224no—
281H(5,𝔽2)—224no—
282H(5,𝔽2)—444no—
283C2×#41—114no—
284C2×#41—224no—
285C22×Q8C22×D1111yescharacteristic
286C22×D4—222no—
287C22×D4—224no—
288C22×D4—224no—
289C22×D4C22×D1111yescharacteristic
290C23×C4C22⋊D1112yes—
291#137—228no—
292#137—444no—
293C2×Q16—224no—
294C2×SD16—224no—
295C2×M16—114no—
296C4⋊Q8—112no—
297#127—112no—
298#124—22no—
299#124—114no—
300#124D4414yescomplemented
301#123—228no—
302C22⋊Q8—224no—
303#121—224no—
304#121—224no—
305#121—224no—
306#121—222no—
307#121—224no—
308#121—222no—
309#120—228no—
310C4×Q8—22no—
311C4×Q8—22no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—222no—
315C4×D4—222no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—224no—
323C2×C22⋊C4C22⋊D1112yes—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42C22×D1111yescharacteristic
328C2×C42C22×D1111yescharacteristic
329C2×C42C22×D1111yescharacteristic
330C4⋊C8—222no—
331C4⋊C8—222no—
332#104—228no—
333#104—444no—
334#103—224no—
335#102—224no—
336#100—224no—
337#95—22no—
338#95—22no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—44no—
342C2×C11#240811yescharacteristic
343C2×C11C2×#45511yescharacteristic
344C2×C11#301811yescharacteristic
345D11—84no—
346C24—224no—
347C24C2×C22⋊D1112yes—
348#41—224no—
349#41—224no—
350#41—224no—
351#41—224no—
352#41—448no—
353#41—448no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—114no—
358C2×Q8C2×D4412yescomplemented
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—114no—
362C2×D4—224no—
363C2×D4—228no—
364C2×D4—224no—
365C2×D4—222no—
366C2×D4—222no—
367C2×D4—448no—
368C2×D4—448no—
369C2×D4—448no—
370C2×D4—448no—
371C2×D4—884no—
372C2×D4C2×D4412yes—
373C2×D4#433912yes—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—44no—
381C22×C4—224no—
382C22×C4—224no—
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1112yes—
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C23×D1111yescharacteristic
387Q16—448no—
388SD16—448no—
389M16—224no—
390M16—224no—
391C2×C8—224no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—42no—
395C4⋊C4—224no—
396C4⋊C4—222no—
397C4⋊C4—222no—
398C22⋊C4—28no—
399C22⋊C4—24no—
400C22⋊C4—44no—
401C22⋊C4—228no—
402C22⋊C4—224no—
403C22⋊C4—224no—
404C42—21no—
405C42—22no—
406C42—42no—
407C42—42no—
408C42—41no—
409C42—41no—
410C42C2×D4412yescomplemented
411C42D4×D1112yes—
412C42D4×D1112yes—
413C11#2422411yescharacteristic, complemented, Sylow
414C23—22no—
415C23—22no—
416C23—42no—
417C23—42no—
418C23—224no—
419C23—448no—
420C23—884no—
421C23—884no—
422C23#6698314yes—
423C23C22×C22⋊D1111yescharacteristic
424Q8—24no—
425Q8—42no—
426Q8—224no—
427Q8—224no—
428D4—24no—
429D4—24no—
430D4—224no—
431D4—224no—
432D4—4416no—
433D4—444no—
434D4—444no—
435D4—444no—
436D4—882no—
437D4—884no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—82no—
455C2×C4—224no—
456C2×C4—448no—
457C2×C4—444no—
458C2×C4—444no—
459C2×C4#6699011yescharacteristic
460C2×C4#6699012yes—
461C2×C4#6699011yescharacteristic
462C2×C4C22×D4411yescharacteristic
463C2×C4C2×#433911yescharacteristic
464C2×C4C2×D4×D1112yes—
465C2×C4#6704212yes—
466C8—444no—
467C22—21no—
468C22—21no—
469C22—24no—
470C22—44no—
471C22—42no—
472C22—42no—
473C22—82no—
474C22—444no—
475C22—444no—
476C22—444no—
477C22—1768no—
478C22C2×#6698311yescharacteristic
479C22C2×#6699011yescharacteristic
480C22#1062336111yescharacteristic
481C4—21no—
482C4—22no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—81no—
488C4—444no—
489C4#1062267412yescomplemented
490C4D4×D4412yes—
491C4#1062308112yes—
492C2—21no—
493C2—21no—
494C2—44no—
495C2—884no—
496C2#1307197211yescharacteristic
497C2C2×#1062267411yescharacteristic
498C2#1307796411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#124C2
socleC22×C11C2×#120
prime radical#13082380C2
hypercenterC4×#124D11
hypocenterC11#24224
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
2. #13078088C2semidirect
3. C2×#10622674C2semidirect
4. #13069845C2semidirect
5. #13069662C2semidirect
6. #13069444C2semidirect
7. #13068608C2semidirect
8. #13068569C2semidirect
9. C4×C11×#124C2semidirect
12. C2×C4×Q8×C11C22semidirect
14. C2×#66995C22semidirect
22. C11×#391C22semidirect
25. C11×#382C22semidirect
27. C43×C11C22semidirect
33. #10622579C22semidirect
34. C2×#66869C22semidirect
35. C2×#66869C22semidirect
36. #10622537C22semidirect
37. #10622168C22semidirect
50. C11×#124D4semidirect
103. C2×Q8×C11C2×D4semidirect
153. C42×C11C2×D4semidirect
168. C4×#124D11semidirect
237. C2×C4×Q8C2×D11semidirect
248. #391C2×D11semidirect
251. #382C2×D11semidirect
253. C43C2×D11semidirect
276. C4×C11#455semidirect
300. #124D44semidirect
358. C2×Q8C2×D44semidirect
410. C42C2×D44semidirect
413. C11#24224semidirect
489. C4#10622674semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130780882
C2×#106226742
#130698452
#130696622
#130694442
#130686082
#130685692
C4×C11×#1242
#2422411