Finite Group Databasebeta

← #14810755

Subgroups — #14810755

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic22C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic
3C2×#10622667C211yesmaximal, characteristic
4#13069757C212yesmaximal, complemented
5#13069752C212yesmaximal
6#13069568C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068974C212yesmaximal
9#13068960C212yesmaximal, complemented
10#13068449C211yesmaximal, characteristic, complemented
11C11×#2592C211yesmaximal, characteristic
12C2×C11×#124C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×Q8×Dic11—21no—
15C22×#4326C2211yescharacteristic
16C22×#4324C2211yescharacteristic
17Q8×Dic22—24no—
18Q8×Dic22—24no—
19C2×#66941—22no—
20C2×#66941—21no—
21C2×#66922C2212yes—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25C11×#397—21no—
26C11×#393—21no—
27C11×#391C2212yes—
28C11×#390C2212yes—
29C11×#388—22no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2212yes—
33C2×#66896C2211yescharacteristic
34C2×#66896C2212yes—
35#10622668—24no—
36#10622667—24no—
37C2×#66874C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C22×Dic22—22no—
49C22×Dic22—21no—
50C22×Dic22C2311yescharacteristic
51C11×#124—22no—
52C11×#124—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—21no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65Q8×Dic11—28no—
66C2×#4326—22no—
67C2×#4326—24no—
68C2×#4324—22no—
69C2×#4324—24no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—21no—
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81#66941—216no—
82#66941—28no—
83#66922—22no—
84#66922—24no—
85#66922—24no—
86#66922D414yes—
87C4×Dic22—24no—
88C4×Dic22—22no—
89C4×Dic22—24no—
90C4×Dic22D414yes—
91C11×#95—21no—
92C11×#95—22no—
93C11×#95—22no—
94#66899—22no—
95#66899—24no—
96#66896—22no—
97#66896—24no—
98#66874—24no—
99C4⋊(C11⋊C8)—22no—
100#66867—22no—
101#25942—111nomaximal, Sylow
102C24×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—24no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—22no—
122C22×Dic11—21no—
123C2×Dic22—28no—
124C2×Dic22—24no—
125C2×Dic22—21no—
126C2×Dic22—22no—
127C2×Dic22—81no—
128C2×Dic22—81no—
129C2×Dic22—82no—
130C2×Dic22—82no—
131C2×Dic22C2×D412yes—
132C2×Dic22#4114yes—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C22⋊C4—42no—
138C11×C22⋊C4—42no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—82no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—81no—
144C42×C11C2×D412yes—
145C42×C11C2×D412yes—
146#4326—44no—
147#4324—44no—
148C4⋊Dic11—28no—
149C4⋊Dic11—24no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11C2×D414yes—
153C4⋊Dic11C2×D412yes—
154Dic11⋊C4—28no—
155Dic11⋊C4—24no—
156C4×Dic11—28no—
157C4×Dic11—24no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×Q82—111no—
166C2×#489—111no—
167C2×#464—111no—
168#2592D1111yescharacteristic
169#2024—112no—
170#2023—112no—
171#1988—111no—
172#1985—111no—
173#1880—112no—
174#1878—112no—
175#1763—111no—
176C23×C11—41no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11C22×D411yescharacteristic
182Q8×C11—28no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—42no—
186D4×C11—41no—
187D4×C11—41no—
188D4×C11—42no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11#12012yes—
203C2×C4×C11#12012yes—
204C2×C4×C11#13714yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4112yes—
208C2×C4×C112−1+412yes—
209C2×Dic11—22no—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—22no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217Dic22—22no—
218Dic22—24no—
219Dic22—84no—
220Dic22—88no—
221Dic22#12414yes—
222C11⋊C8—41no—
223C11⋊C8—41no—
224C11⋊C8—42no—
225C22×Q16—111no—
226C22×SD16—111no—
227Q82—224no—
228Q82—224no—
229C2×C4⋊Q8—111no—
230C2×C4⋊Q8—112no—
231C2×C4⋊Q8—222no—
232C2×C4⋊Q8—221no—
233C2×#124C2×D1111yescharacteristic
234C2×C4×Q8—111no—
235C2×C4×Q8—112no—
236C2×C4×Q8—221no—
237C2×C4×Q8C2×D1111yescharacteristic
238#489—224no—
239#464—224no—
240C2×C4⋊C8—111no—
241C2×#103—112no—
242C2×#103—111no—
243C2×#103—112no—
244C2×#102—112no—
245C2×#102—111no—
246C2×#97—111no—
247#397—21no—
248#393—21no—
249#391C2×D1112yes—
250#390C2×D1112yes—
251#388—22no—
252C4×C4⋊C4C2×D1111yescharacteristic
253#340—112no—
254#340—112no—
255#340—112no—
256#336—112no—
257#336—112no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11C2×#12011yescharacteristic
264C22×C11#54812yes—
265C22×C11C2×#13712yes—
266C22×C11#57611yescharacteristic
267C22×C11#57711yescharacteristic
268C4×C11—22no—
269C4×C11—24no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—82no—
273C4×C11—81no—
274C4×C11C2×#12411yescharacteristic
275C4×C11#53611yescharacteristic
276C4×C11#54812yes—
277Dic11—24no—
278Dic11—44no—
279Dic11—42no—
280C22×Q8—111no—
281C22×Q8—222no—
282C22×Q8—221no—
283C22×Q8C22⋊D1111yescharacteristic
284C22×Q8C22×D1111yescharacteristic
285C22×D4C22×D1111yescharacteristic
286C2×Q16—224no—
287C2×Q16—222no—
288C2×SD16—224no—
289C2×SD16—222no—
290C22×C8—111no—
291C22×C8—111no—
292C22×C8—112no—
293C4⋊Q8—114no—
294C4⋊Q8—224no—
295C4⋊Q8—224no—
296C4⋊Q8—2216no—
297C4⋊Q8—228no—
298C4⋊Q8—222no—
299#124—22no—
300#124—22no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×Q8—114no—
304C4×Q8—224no—
305C4×Q8—224no—
306C4×Q8—228no—
307C4×Q8—222no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4C22⋊D1112yes—
315C2×C4⋊C4C22⋊D1111yescharacteristic
316C2×C4⋊C4C22×D1112yes—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C42—21no—
322C2×C42—222no—
323C2×C42—221no—
324C2×C42C22×D1112yes—
325C2×C42C22×D1111yescharacteristic
326C4⋊C8—222no—
327#103—224no—
328#103—222no—
329#103—224no—
330#102—222no—
331#102—224no—
332#97—222no—
333#95—21no—
334#95—22no—
335#95—22no—
336C2×C11—161no—
337C2×C11#243611yescharacteristic
338C2×C11#300411yescharacteristic
339C2×C11#301211yescharacteristic
340C2×C11#336912yes—
341C2×C11#337512yes—
342C24—21no—
343C2×Q8—22no—
344C2×Q8—24no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—112no—
350C2×Q8—114no—
351C2×Q8—228no—
352C2×Q8—224no—
353C2×Q8—221no—
354C2×Q8—222no—
355C2×Q8—881no—
356C2×Q8—881no—
357C2×Q8—882no—
358C2×Q8—882no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—22no—
362C2×D4—22no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—221no—
366C22×C4—222no—
367C22×C4—221no—
368C22×C4C2×C22⋊D1112yes—
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1112yes—
372C22×C4C23×D1111yescharacteristic
373Q16—444no—
374SD16—444no—
375C2×C8—222no—
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—222no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—222no—
382C4⋊C4—24no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—112no—
387C4⋊C4—114no—
388C4⋊C4—228no—
389C4⋊C4—228no—
390C4⋊C4—224no—
391C4⋊C4—224no—
392C4⋊C4—222no—
393C4⋊C4—221no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—44no—
397C22⋊C4—82no—
398C42—22no—
399C42—22no—
400C42—81no—
401C42—228no—
402C42—224no—
403C42D4×D1112yes—
404C42D4×D1112yes—
405C11#2594211yescharacteristic, complemented, Sylow
406C23—41no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23—41no—
411C23C22×C22⋊D1111yescharacteristic
412Q8—28no—
413Q8—41no—
414Q8—41no—
415Q8—42no—
416Q8—114no—
417Q8—222no—
418Q8—224no—
419Q8—884no—
420Q8—888no—
421D4—41no—
422D4—41no—
423D4—42no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—222no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—222no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—442no—
444C2×C4—441no—
445C2×C4#6699012yes—
446C2×C4#6699012yes—
447C2×C4#6700414yes—
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4C2×D4×D1111yescharacteristic
450C2×C4#41×D1112yes—
451C2×C4#6704312yes—
452C8—441no—
453C8—441no—
454C8—442no—
455C22—82no—
456C22—82no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22C2×#6699011yescharacteristic
461C22C2×#6700412yes—
462C22#1062336212yes—
463C22#1062336611yescharacteristic
464C22#1062336811yescharacteristic
465C4—22no—
466C4—24no—
467C4—22no—
468C4—42no—
469C4—82no—
470C4—81no—
471C4—224no—
472C4—444no—
473C4—442no—
474C4D11×#12411yescharacteristic
475C4#1062320611yescharacteristic
476C4#1062320812yes—
477C2—161no—
478C2#1307227111yescharacteristic
479C2#1307784911yescharacteristic
480C2#1307791711yescharacteristic
481C2#1308135212yes—
482C2#1308142612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2592C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2592D11
hypocenterC11#25942
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2592

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic22C2semidirect
4. #13069757C2semidirect
6. #13069568C2semidirect
7. #13069557C2semidirect
9. #13068960C2semidirect
10. #13068449C2semidirect
405. C11#25942semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic222
C2×#106226682
C2×#106226672
#130697572
#130697522
#130695682
#130695572
#130689742
#130689602
#130684492
C11×#25922
#2594211