Finite Group Databasebeta

← #14764347

Subgroups — #14764347

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622318C211yesmaximal, characteristic
2#13071022C211yesmaximal, characteristic
3#13071021C211yesmaximal, characteristic
4#13069378C212yesmaximal, complemented
5#13069373C212yesmaximal, complemented
6#13068818C212yesmaximal
7#13068816C212yesmaximal
8#13068785C211yesmaximal, characteristic, complemented
9#13068784C211yesmaximal, characteristic, complemented
10#13068751C211yesmaximal, characteristic, complemented
11C11×#1836C211yesmaximal, characteristic, complemented
12C2×#66945—21no—
13C2×#66945C2211yescharacteristic
14C2×#66945C2211yescharacteristic
15C2×C42×D11C2211yescharacteristic
16C2×C11×#97C2211yescharacteristic
17C11×#384C2211yescharacteristic
18C11×#382C2211yescharacteristic
19C2×(C2×D11)⋊C8C2212yes—
20C2×#66882C2212yes—
21C2×#66881C2212yes—
22C2×Dic11⋊C8C2212yes—
23#10622600—21no—
24#10622600C2212yes—
25#10622590—21no—
26#10622589C2211yescharacteristic
27#10622589C2211yescharacteristic
28C4⋊C4×Dic11—21no—
29C4⋊C4×Dic11C2212yes—
30C2×#66872C2212yes—
31C2×#66871C2212yes—
32#10622549C2211yescharacteristic
33#10622548C2211yescharacteristic
34C2×#66867C2211yescharacteristic
35#10622318C418yescomplemented
36#10622280—21no—
37#10622280—21no—
38#10622262—21no—
39#10622262—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73#66945—42no—
74#66945—42no—
75#66945—44no—
76C42×D11C2×C414yes—
77C42×D11Q814yes—
78C11×#97C2×C414yes—
79C11×#95—21no—
80C11×#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85(C2×D11)⋊C8C2×C418yes—
86#66882—42no—
87#66881—42no—
88Dic11⋊C8C2×C418yes—
89#66872—42no—
90#66871—42no—
91#66867C2×C414yes—
92#21988—111nomaximal, Sylow
93C23×D11C2×D411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×C4×D11C4⋊C414yes—
113C2×C4×D11C4⋊C414yes—
114C2×C4×D11C22×C412yes—
115C2×C4×D11C2×Q812yes—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11C22×C414yes—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—42no—
124C42×C11C22×C412yes—
125C42×C11C2×Q812yes—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—44no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—42no—
134C4⋊Dic11—42no—
135Dic11⋊C4—42no—
136Dic11⋊C4—42no—
137Dic11⋊C4—42no—
138Dic11⋊C4—42no—
139C4×Dic11—42no—
140C4×Dic11—42no—
141C4×Dic11—44no—
142C4×Dic11C4⋊C414yes—
143C4×Dic11C4⋊C414yes—
144C4×Dic11C22×C412yes—
145C4×Dic11C2×Q812yes—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8C22×C414yes—
149C2×#432—111no—
150#2285—111no—
151#2285—111no—
152#1948—112no—
153#1947—112no—
154#1854—112no—
155#1854—112no—
156#1847—111no—
157#1847—111no—
158#1836—111no—
159#1836D1111yescharacteristic, complemented
160C23×C11C22×D411yescharacteristic
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
167C22×D11C2×C4⋊C412yes—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11C2×C4⋊C412yes—
182C2×C4×C11C2×C4⋊C412yes—
183C2×C4×C11C23×C411yescharacteristic
184C2×C4×C11C22×Q811yescharacteristic
185C2×C4×C11H(5,𝔽2)12yes—
186C2×C4×C112−1+412yes—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200C2×Dic11C2×C4⋊C412yes—
201C2×Dic11C2×C4⋊C412yes—
202C2×Dic11C2×C4⋊C412yes—
203C2×Dic11AGL(1,ℤ/8)12yes—
204C2×Dic11#13712yes—
205C4×D11—24no—
206C4×D11—24no—
207C4×D11—28no—
208C4×D11—44no—
209C8×C11—24no—
210C11⋊C8—24no—
211C2×#117—111no—
212C2×#117—111no—
213C2×#117—221no—
214C22×C42—111no—
215#432—118no—
216C2×#107—112no—
217C2×#107—112no—
218C2×#106—112no—
219C2×#106—112no—
220C2×C4⋊C8—112no—
221C2×C22⋊C8—112no—
222C2×#97—111no—
223C2×#97C2×D1111yescharacteristic
224#384—111no—
225#384—111no—
226#384—111no—
227#384C2×D1111yescharacteristic
228#382—111no—
229#382—221no—
230#382C2×D1111yescharacteristic
231#380—112no—
232#380—221no—
233#380—221no—
234#380—221no—
235C4×C4⋊C4—112no—
236C4×C4⋊C4—221no—
237C4×C4⋊C4—221no—
238C4×C4⋊C4—221no—
239#340—112no—
240#340—112no—
241#340C2×D1112yes—
242#340C2×D1112yes—
243C22×C11C22×C4⋊C411yescharacteristic
244C22×C11#53511yescharacteristic
245C22×C11#53611yescharacteristic
246C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
247C22×C11C2×#13711yescharacteristic
248C22×C11#57511yescharacteristic
249C22×C11#57511yescharacteristic
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—41no—
254C2×D11—41no—
255C2×D11—41no—
256C2×D11—41no—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—81no—
260C4×C11—81no—
261C4×C11—82no—
262C4×C11#52012yes—
263C4×C11#54412yes—
264Dic11—22no—
265Dic11—22no—
266Dic11—81no—
267Dic11—82no—
268Dic11—81no—
269Dic11#42814yes—
270C23×C4—111no—
271C23×C4—111no—
272C23×C4—111no—
273C22×C8—112no—
274C22×C8C22×D1112yes—
275#117—442no—
276#117—442no—
277#117—444no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4C22×D1111yescharacteristic
290C2×C4⋊C4C22×D1111yescharacteristic
291C2×C4⋊C4C22×D1112yes—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—222no—
295C2×C42—111no—
296C2×C42—111no—
297C2×C42—111no—
298C2×C42—114no—
299C2×C42—114no—
300C2×C42—221no—
301C2×C42—221no—
302C2×C42—222no—
303C2×C42C22×D1111yescharacteristic
304#107—442no—
305#107—442no—
306#106—442no—
307#106—442no—
308C4⋊C8—118no—
309C22⋊C8—118no—
310#97—114no—
311#97C4×D1114yes—
312#95—21no—
313#95—21no—
314#95—222no—
315#95—222no—
316#95—221no—
317#95—221no—
318C2×C11#231711yescharacteristic
319C2×C11C2×#42811yescharacteristic
320C2×C11#291111yescharacteristic
321C2×C11#321411yescharacteristic
322C2×C11#321611yescharacteristic
323C2×C11#323511yescharacteristic
324C2×C11#323711yescharacteristic
325D11—42no—
326C24—111no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—114no—
334C22×C4—112no—
335C22×C4—112no—
336C22×C4—114no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—441no—
345C22×C4—441no—
346C22×C4D4×D1111yescharacteristic
347C22×C4D4×D1111yescharacteristic
348C22×C4C23×D1111yescharacteristic
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—114no—
352C2×C8—222no—
353C2×C8—222no—
354C2×C8C2×C4×D1114yes—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—24no—
358C4⋊C4—42no—
359C4⋊C4—42no—
360C4⋊C4—222no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C4⋊C4—222no—
364C4⋊C4—442no—
365C4⋊C4—442no—
366C4⋊C4—442no—
367C4⋊C4—442no—
368C4⋊C4—442no—
369C4⋊C4—442no—
370C22⋊C4—444no—
371C22⋊C4—442no—
372C22⋊C4—442no—
373C42—114no—
374C42—114no—
375C42—112no—
376C42—112no—
377C42—444no—
378C42—442no—
379C42—442no—
380C42C2×C4×D1112yes—
381C42Q8×D1112yes—
382C11#2198811yescharacteristic, complemented, Sylow
383C23—112no—
384C23—221no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23C2×D4×D1111yescharacteristic
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—112no—
405C2×C4—112no—
406C2×C4—112no—
407C2×C4—112no—
408C2×C4—112no—
409C2×C4—228no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—224no—
415C2×C4—224no—
416C2×C4—444no—
417C2×C4—442no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—442no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—442no—
426C2×C4C4⋊C4×D1112yes—
427C2×C4C4⋊C4×D1112yes—
428C2×C4C22×C4×D1111yescharacteristic
429C2×C4C2×Q8×D1111yescharacteristic
430C2×C4#6704212yes—
431C2×C4#6704312yes—
432C8—24no—
433C8—224no—
434C22—222no—
435C22—222no—
436C22—222no—
437C22—441no—
438C22—441no—
439C22—441no—
440C22—441no—
441C22C2×C4⋊C4×D1111yescharacteristic
442C22#1062320511yescharacteristic
443C22#1062320611yescharacteristic
444C22D11×AGL(1,ℤ/8)11yescharacteristic
445C22#1062330411yescharacteristic
446C22D11×#13711yescharacteristic
447C22#1062330811yescharacteristic
448C4—22no—
449C4—22no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4—114no—
454C4—222no—
455C4—222no—
456C4—882no—
457C4—881no—
458C4—881no—
459C4#1062305412yes—
460C4#1062322012yes—
461C2—442no—
462C2#1307124111yescharacteristic
463C2D11×#42811yescharacteristic
464C2#1307720311yescharacteristic
465C2#1307961211yescharacteristic
466C2#1307962811yescharacteristic
467C2#1307980911yescharacteristic
468C2#1307982511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1836C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1836D11
hypocenterC11#21988
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
4. #13069378C2semidirect
5. #13069373C2semidirect
8. #13068785C2semidirect
9. #13068784C2semidirect
10. #13068751C2semidirect
11. C11×#1836C2semidirect
35. #10622318C4semidirect
159. #1836D11semidirect
382. C11#21988semidirect

Maximal subgroups

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

subgroupindex
C2×#106223182
#130710222
#130710212
#130693782
#130693732
#130688182
#130688162
#130687852
#130687842
#130687512
C11×#18362
#2198811