Finite Group Databasebeta

← #14926810

Subgroups — #14926810

Order 2816.

2650 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C212yesmaximal
2#13076966C214yesmaximal, complemented
3#13074733C214yesmaximal, complemented
4#13073995C214yesmaximal, complemented
5#13073993C214yesmaximal, complemented
6#13073092C214yesmaximal, complemented
7#13072258C214yesmaximal, complemented
8#13071230C211yesmaximal, characteristic
9#13071228C212yesmaximal
10C2×C22⋊C4×Dic11C211yesmaximal, characteristic
11C11×#2315C211yesmaximal, characteristic
12C24×Dic11C2211yescharacteristic
13C23×Dic22C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2212yes—
22C2×#66941C2214yescomplemented
23C2×#66931—216no—
24C2×#66931C2214yes—
25C2×#66931C2214yes—
26C2×#66931C2214yes—
27C2×#66931C2214yes—
28C11×#385C2214yes—
29C11×#385C2214yes—
30C11×#380C2214yes—
31#10622825C2214yes—
32#10622823C2214yes—
33#10622823C2214yes—
34C2×C11⋊#95C2212yes—
35#10622598C2214yescomplemented
36#10622597C2218yescomplemented
37#10622592C2218yescomplemented
38#10622589C2214yescomplemented
39#10622586C2214yescomplemented
40#10622563C2214yes—
41#10622563C2214yes—
42#10622559C2214yes—
43#10622559C2214yes—
44#10622555C2218yes—
45C22⋊C4×Dic11C2214yes—
46C22⋊C4×Dic11C2214yes—
47#10622270C2218yescomplemented
48#10622269C2218yescomplemented
49#10622260C2218yescomplemented
50#10622259C2218yescomplemented
51C25×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×Dic11—44no—
56C23×Dic11D418yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C22×Dic22—28no—
65C22×Dic22—48no—
66C22×Dic22C2314yes—
67C22×Dic22C2314yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C22⋊C4—28no—
71C2×C11×C22⋊C4Q818yescomplemented
72C2×C11×C22⋊C4C2314yes—
73C2×C11×C22⋊C4C2314yes—
74C2×C11×C22⋊C4C2314yes—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11Q818yescomplemented
77C2×C22⋊Dic11C2314yes—
78C2×C22⋊Dic11C2314yes—
79C2×C22⋊Dic11C2314yes—
80C2×C4⋊Dic11—28no—
81C2×C4⋊Dic11C2314yes—
82C2×C4⋊Dic11C2314yes—
83C2×C4⋊Dic11C2314yes—
84C2×C4⋊Dic11C2314yes—
85C2×Dic11⋊C4—28no—
86C2×Dic11⋊C4—28no—
87C2×Dic11⋊C4C2314yes—
88C2×Dic11⋊C4C2314yes—
89C2×Dic11⋊C4C2314yes—
90C2×Dic11⋊C4C2314yes—
91C2×Dic11⋊C4C2318yes—
92C2×Dic11⋊C4C2318yes—
93C2×C4×Dic11—44no—
94C2×C4×Dic11C2314yes—
95C2×C4×Dic11C2314yes—
96#66941—48no—
97#66931—216no—
98#66931—216no—
99#66931—216no—
100#66931—216no—
101C11×#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106#35011—111nomaximal, Sylow
107C24×C11—42no—
108C24×C11—42no—
109C24×C11C2×D414yes—
110C24×C11C2×Q814yes—
111C24×C11C2×Q814yes—
112C24×C11C2411yescharacteristic
113C24×C11C2412yes—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—42no—
117C22×C4×C11—44no—
118C22×C4×C11—42no—
119C22×C4×C11—44no—
120C22×C4×C11C2×Q818yescomplemented
121C22×C4×C11C2414yes—
122C22×C4×C11C2414yes—
123C22×C4×C11C2414yes—
124C22×Dic11—24no—
125C22×Dic11—28no—
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—42no—
129C22×Dic11—44no—
130C22×Dic11—44no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11—44no—
134C22×Dic11—416no—
135C22×Dic11C2×D414yes—
136C22×Dic11C2×D418yes—
137C22×Dic11C2×D414yes—
138C22×Dic11C2×D418yes—
139C22×Dic11C2×Q818yescomplemented
140C22×Dic11C2414yes—
141C22×Dic11C2414yes—
142C22×Dic11C2412yes—
143C22×Dic11C2411yescharacteristic
144C22×Dic11C2414yes—
145C22×Dic11C2411yescharacteristic
146C2×Dic22—28no—
147C2×Dic22—28no—
148C2×Dic22—216no—
149C2×Dic22—48no—
150C2×Dic22—432no—
151C11×C4⋊C4—44no—
152C11×C4⋊C4—44no—
153C11×C22⋊C4—28no—
154C11×C22⋊C4—28no—
155C11×C22⋊C4C2×Q8116yescomplemented
156C22⋊Dic11—28no—
157C22⋊Dic11—28no—
158C22⋊Dic11C2×Q8116yescomplemented
159C4⋊Dic11—28no—
160C4⋊Dic11—28no—
161C4⋊Dic11—44no—
162C4⋊Dic11—44no—
163Dic11⋊C4—28no—
164Dic11⋊C4—28no—
165Dic11⋊C4—28no—
166Dic11⋊C4—28no—
167Dic11⋊C4—48no—
168Dic11⋊C4—48no—
169C4×Dic11—28no—
170C4×Dic11—44no—
171C22×C22⋊Q8—112no—
172#2857—114no—
173#2659—114no—
174#2583—114no—
175#2583—114no—
176#2502—114no—
177#2434—114no—
178#2315—112no—
179#2315—111no—
180#2315D1111yescharacteristic
181C2×C4×C22⋊C4—111no—
182C23×C11—24no—
183C23×C11—22no—
184C23×C11—24no—
185C23×C11—22no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11—48no—
189C23×C11—48no—
190C23×C11C4⋊Q8116yescomplemented
191C23×C11C22×D412yes—
192C23×C11C22×D414yes—
193C23×C11C22×Q814yes—
194C23×C11C22×Q812yes—
195C23×C11C22×Q814yes—
196C23×C11C22×Q812yes—
197C23×C11C2511yescharacteristic
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—28no—
203C2×C4×C11—28no—
204C2×C4×C11—48no—
205C2×C4×C11—48no—
206C2×C4×C11—48no—
207C2×C4×C11C22×Q818yes—
208C2×Dic11—24no—
209C2×Dic11—22no—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—216no—
213C2×Dic11—28no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—28no—
217C2×Dic11—28no—
218C2×Dic11—44no—
219C2×Dic11—48no—
220C2×Dic11—48no—
221C2×Dic11—48no—
222C2×Dic11—48no—
223C2×Dic11C22×D412yes—
224C2×Dic11C22×D414yes—
225C2×Dic11C22×D412yes—
226C2×Dic11C22×Q818yes—
227C2×Dic11H(5,𝔽2)14yes—
228Dic22—416no—
229Dic22—416no—
230C23×Q8—112no—
231C24×C4—111no—
232C2×C4⋊Q8—114no—
233C2×C22⋊Q8—114no—
234C2×C22⋊Q8—114no—
235C2×C22⋊Q8—114no—
236C2×C22⋊Q8—114no—
237C2×C22⋊Q8—2216no—
238C22×C4⋊C4—112no—
239C22×C4⋊C4—112no—
240C22×C4⋊C4—112no—
241C22×C22⋊C4—111no—
242C22×C22⋊C4—112no—
243C22×C22⋊C4C2×D1112yes—
244C22×C22⋊C4C2×D1111yescharacteristic
245C22×C42—112no—
246#398—118no—
247#398—118no—
248#395—118no—
249#395—118no—
250#391—118no—
251#389—114no—
252#389—114no—
253#389—118no—
254#385—114no—
255#385—114no—
256#385—114no—
257#385—114no—
258#385—114no—
259#385—114no—
260#385C2×D1114yes—
261#385C2×D1114yes—
262#384—114no—
263#380—114no—
264#380—118no—
265#380C2×D1114yes—
266C4×C22⋊C4—114no—
267C4×C22⋊C4—114no—
268C2×#95—112no—
269C22×C11—24no—
270C22×C11—22no—
271C22×C11—24no—
272C22×C11—22no—
273C22×C11—24no—
274C22×C11—28no—
275C22×C11—28no—
276C22×C11—24no—
277C22×C11—416no—
278C22×C11C2×C4⋊Q814yes—
279C22×C11C2×C4⋊Q818yes—
280C22×C11C23×D411yescharacteristic
281C22×C11C23×Q811yescharacteristic
282C22×C11C23×Q811yescharacteristic
283C22×C11C2×H(5,𝔽2)12yes—
284C22×C11#58512yes—
285C4×C11—28no—
286C4×C11—44no—
287C4×C11—44no—
288Dic11—24no—
289Dic11—22no—
290Dic11—28no—
291Dic11—44no—
292Dic11—44no—
293Dic11#53414yes—
294C25C22×D1111yescharacteristic
295C22×Q8—114no—
296C22×Q8—114no—
297C22×Q8—228no—
298C22×Q8—448no—
299C23×C4—112no—
300C23×C4—111no—
301C23×C4—118no—
302C23×C4—112no—
303C23×C4—112no—
304C23×C4—111no—
305C23×C4—112no—
306C23×C4—112no—
307C23×C4—444no—
308C23×C4C22×D1112yes—
309C23×C4C22×D1112yes—
310C23×C4C22×D1112yes—
311C4⋊Q8—448no—
312C22⋊Q8—2216no—
313C22⋊Q8—2216no—
314C22⋊Q8—2216no—
315C22⋊Q8—2216no—
316C2×C4⋊C4—114no—
317C2×C4⋊C4—114no—
318C2×C4⋊C4—114no—
319C2×C4⋊C4—114no—
320C2×C4⋊C4—114no—
321C2×C4⋊C4—114no—
322C2×C4⋊C4—118no—
323C2×C4⋊C4—114no—
324C2×C4⋊C4—118no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4—228no—
327C2×C4⋊C4—228no—
328C2×C4⋊C4—228no—
329C2×C4⋊C4C22×D1114yes—
330C2×C4⋊C4C22×D1114yes—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—118no—
333C2×C22⋊C4—114no—
334C2×C22⋊C4—114no—
335C2×C22⋊C4—114no—
336C2×C22⋊C4—228no—
337C2×C22⋊C4Dic2218yescomplemented
338C2×C22⋊C4C22×D1114yes—
339C2×C22⋊C4C22×D1114yes—
340C2×C22⋊C4C22×D1114yes—
341C2×C42—114no—
342C2×C42—114no—
343C2×C42—444no—
344#95—118no—
345#95—118no—
346#95—118no—
347#95—118no—
348#95C22×D1118yes—
349C2×C11—28no—
350C2×C11—24no—
351C2×C11C22×C4⋊Q811yescharacteristic
352C2×C11C2×#53411yescharacteristic
353C2×C11#344911yescharacteristic
354C2×C11#350112yes—
355C2×C11#350112yes—
356C24—42no—
357C24—42no—
358C24C2×Dic2214yes—
359C24D4×D1114yes—
360C24Q8×D1114yes—
361C24C23×D1112yes—
362C24C23×D1111yescharacteristic
363C2×Q8—228no—
364C2×Q8—228no—
365C2×Q8—2216no—
366C2×Q8—448no—
367C2×Q8—4432no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—42no—
371C22×C4—44no—
372C22×C4—42no—
373C22×C4—44no—
374C22×C4—111no—
375C22×C4—118no—
376C22×C4—114no—
377C22×C4—114no—
378C22×C4—112no—
379C22×C4—111no—
380C22×C4—118no—
381C22×C4—114no—
382C22×C4—118no—
383C22×C4—114no—
384C22×C4—114no—
385C22×C4—224no—
386C22×C4—228no—
387C22×C4—224no—
388C22×C4—224no—
389C22×C4—4416no—
390C22×C4—442no—
391C22×C4—444no—
392C22×C4—442no—
393C22×C4—444no—
394C22×C4—442no—
395C22×C4—444no—
396C22×C4C2×Dic2218yescomplemented
397C22×C4C23×D1114yes—
398C22×C4C23×D1114yes—
399C22×C4C23×D1114yes—
400C4⋊C4—44no—
401C4⋊C4—44no—
402C4⋊C4—228no—
403C4⋊C4—228no—
404C4⋊C4—228no—
405C4⋊C4—228no—
406C4⋊C4—228no—
407C4⋊C4—228no—
408C4⋊C4—448no—
409C4⋊C4—444no—
410C4⋊C4—448no—
411C4⋊C4—444no—
412C22⋊C4—28no—
413C22⋊C4—28no—
414C22⋊C4—1116no—
415C22⋊C4—228no—
416C22⋊C4—228no—
417C22⋊C4C2×Dic22116yescomplemented
418C42—228no—
419C42—444no—
420C11#3501111yescharacteristic, complemented, Sylow
421C23—22no—
422C23—24no—
423C23—22no—
424C23—24no—
425C23—44no—
426C23—48no—
427C23—44no—
428C23—48no—
429C23#66941116yescomplemented
430C23C22×Dic2214yes—
431C23C22×Dic2212yes—
432C23C2×D4×D1112yes—
433C23C2×D4×D1114yes—
434C23C2×Q8×D1114yes—
435C23C2×Q8×D1112yes—
436C23C24×D1111yescharacteristic
437Q8—4416no—
438Q8—4416no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—28no—
444C2×C4—28no—
445C2×C4—48no—
446C2×C4—48no—
447C2×C4—48no—
448C2×C4—112no—
449C2×C4—114no—
450C2×C4—112no—
451C2×C4—114no—
452C2×C4—118no—
453C2×C4—2216no—
454C2×C4—228no—
455C2×C4—224no—
456C2×C4—222no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—228no—
462C2×C4—228no—
463C2×C4—444no—
464C2×C4—448no—
465C2×C4—448no—
466C2×C4—448no—
467C2×C4—448no—
468C2×C4C22×Dic2218yes—
469C22—24no—
470C22—28no—
471C22—24no—
472C22—28no—
473C22—24no—
474C22—22no—
475C22—24no—
476C22—22no—
477C22—416no—
478C22C2×#6694118yes—
479C22C2×#6694114yes—
480C22C23×Dic2211yescharacteristic
481C22C22×D4×D1111yescharacteristic
482C22C22×Q8×D1111yescharacteristic
483C22D11×H(5,𝔽2)12yes—
484C22#1062345512yes—
485C4—28no—
486C4—44no—
487C4—44no—
488C4—114no—
489C4—228no—
490C4—224no—
491C4—222no—
492C4—444no—
493C4—444no—
494C2—24no—
495C2—28no—
496C2C22×#6694111yescharacteristic
497C2D11×#53411yescharacteristic
498C2#1308194211yescharacteristic
499C2#1308241412yes—
500C2#1308241612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2315C2
prime radicalC25×C11C23
hypercenter#2315D11
hypocenterC11#35011
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2315

Complements

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

NH ≅ G/Ntype
2. #13076966C2semidirect
3. #13074733C2semidirect
4. #13073995C2semidirect
5. #13073993C2semidirect
6. #13073092C2semidirect
7. #13072258C2semidirect
22. C2×#66941C22semidirect
35. #10622598C22semidirect
36. #10622597C22semidirect
37. #10622592C22semidirect
38. #10622589C22semidirect
39. #10622586C22semidirect
47. #10622270C22semidirect
48. #10622269C22semidirect
49. #10622260C22semidirect
50. #10622259C22semidirect
71. C2×C11×C22⋊C4Q8semidirect
76. C2×C22⋊Dic11Q8semidirect
120. C22×C4×C11C2×Q8semidirect
139. C22×Dic11C2×Q8semidirect
155. C11×C22⋊C4C2×Q8semidirect
158. C22⋊Dic11C2×Q8semidirect
190. C23×C11C4⋊Q8semidirect
337. C2×C22⋊C4Dic22semidirect
396. C22×C4C2×Dic22semidirect
417. C22⋊C4C2×Dic22semidirect
420. C11#35011semidirect
429. C23#66941semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
#130769662
#130747332
#130739952
#130739932
#130730922
#130722582
#130712302
#130712282
C2×C22⋊C4×Dic112
C11×#23152
#3501111