Finite Group Databasebeta

← #14771890

Subgroups — #14771890

Order 2816.

1126 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×#10622447C211yesmaximal, characteristic
2C2×D11×#107C212yesmaximal, complemented
3C4⋊C4×D44C211yesmaximal, characteristic
4#13071516C211yesmaximal, characteristic
5#13069375C211yesmaximal, characteristic, complemented
6#13068805C212yesmaximal, complemented
7#13068802C212yesmaximal, complemented
8#13068775C211yesmaximal, characteristic, complemented
9#13068644C212yesmaximal, complemented
10C4×#66871C211yesmaximal, characteristic, complemented
11C11×#1947C211yesmaximal, characteristic, complemented
12C22×C8×D11C2212yes—
13C2×#66946—21no—
14C2×C4⋊C4×D11C2212yes—
15C2×C4⋊C4×D11C2212yes—
16C2×C4×D44—21no—
17C2×C4×D44C2211yescharacteristic
18C2×C11×#107C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C11×#384C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C8C2212yes—
23C2×#66882C2212yes—
24#10622602—22no—
25#10622600C2212yes—
26#10622600C2212yes—
27#10622586—21no—
28C2×#66871C2211yescharacteristic
29C2×#66871C2212yes—
30C2×#66871C2212yes—
31C2×#66871C2211yescharacteristic
32#10622548C2211yescharacteristic
33C4×C4⋊Dic11C2211yescharacteristic
34#10622541—21no—
35C2×C4×C11⋊C8C2211yescharacteristic
36D11×#107—28no—
37#10622447C418yescomplemented
38#10622281—22no—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×D44D411yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11—22no—
46C22×C4×D11C2312yes—
47C22×C8×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4D412yes—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—21no—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C2×C8×D11—24no—
70C2×C8×D11—24no—
71C2×C8×D11C2×C418yescomplemented
72#66946—44no—
73C4⋊C4×D11—24no—
74C4⋊C4×D11—24no—
75C4⋊C4×D11—42no—
76C4⋊C4×D11—42no—
77C4×D44—44no—
78C4×D44C2×C414yes—
79C4×D44Q814yes—
80C11×#107—24no—
81C11×C4⋊C8C2×C414yescomplemented
82C11×#95—21no—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86(C2×D11)⋊C8C2×C418yescomplemented
87#66882—24no—
88#66871—24no—
89#66871—22no—
90#66871—42no—
91#66871D414yescomplemented
92C4×C11⋊C8C2×C414yescomplemented
93D4×#107—111nomaximal, Sylow
94C23×D11C2×D412yes—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11C2×D412yes—
105C2×D44C4⋊C414yes—
106C2×D44D814yes—
107C2×D44Q1614yes—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—44no—
113C2×C4×D11—44no—
114C2×C4×D11—44no—
115C2×C4×D11—44no—
116C2×C4×D11—82no—
117C2×C4×D11—82no—
118C2×C4×D11C22×C414yes—
119C2×C4×D11C2×Q814yes—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11C22×C414yes—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—81no—
130C11×C4⋊C4C2×D412yes—
131C42×C11—42no—
132C42×C11C22×C412yes—
133C42×C11C2×Q812yes—
134(C2×D11)⋊C4—44no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4C4⋊C418yes—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—42no—
143C4⋊Dic11—81no—
144C4⋊Dic11C4⋊C414yes—
145C4⋊Dic11C2×D412yes—
146Dic11⋊C4—44no—
147Dic11⋊C4—44no—
148C4×Dic11—42no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8C22×C412yes—
152C2×C11⋊C8C22×C412yes—
153C2×C11⋊C8C2×D412yes—
154C2×C11⋊C8#4112yes—
155C8×D11—216no—
156C2×C8×D4—111no—
157C22×#107—112no—
158D4×C4⋊C4—111no—
159D4×C4⋊C4—111no—
160#1947—111no—
161#1947D1111yescharacteristic, complemented
162#1852—112no—
163#1852—112no—
164#1845—111no—
165#1808—112no—
166C4×#107—111no—
167C23×C11C22×D411yescharacteristic
168C22×D11—22no—
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11C2×C4⋊C414yes—
173C22×D11C2×D814yes—
174C22×D11C2×Q1614yes—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11C2×C4⋊C412yes—
187C2×C4×C11C2×C4⋊C412yes—
188C2×C4×C11C2×D812yes—
189C2×C4×C11C2×Q1612yes—
190C2×C4×C11C23×C411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C22×Q811yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11H(5,𝔽2)11yescharacteristic
195C2×C4×C112−1+411yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11C2×C4⋊C414yes—
208D44#107116yescomplemented
209C4×D11—24no—
210C4×D11—24no—
211C4×D11—24no—
212C4×D11—24no—
213C4×D11—88no—
214C4×D11—88no—
215C8×C11—24no—
216C11⋊C8—22no—
217C11⋊C8C4×D414yescomplemented
218C23×C8—112no—
219C2×C4×D4—111no—
220C2×C4×D4—221no—
221C2×C4×D4—221no—
222C22×C4⋊C4—112no—
223C22×C4⋊C4—112no—
224C8×D4—118no—
225C2×#107—111no—
226C2×#107—112no—
227C2×#107—111no—
228C2×#107—112no—
229C2×#107—112no—
230C2×#107—228no—
231C2×#107C2×D1112yes—
232C2×C4⋊C8C2×D1111yescharacteristic
233C2×C22⋊C8—112no—
234C2×C4×C8—111no—
235#389—221no—
236#389—221no—
237#385—222no—
238#385—222no—
239#384—111no—
240#384C2×D1111yescharacteristic
241#380—112no—
242#380—112no—
243C4×C4⋊C4—111no—
244C4×C4⋊C4C2×D1111yescharacteristic
245#340—112no—
246#340—111no—
247#340—111no—
248#340C2×D1112yes—
249C22×C11C22×C4⋊C411yescharacteristic
250C22×C11D4211yescharacteristic
251C22×C11#54711yescharacteristic
252C22×C11C22×D811yescharacteristic
253C22×C11C22×Q1611yescharacteristic
254C22×C11#57611yescharacteristic
255C22×C11#57811yescharacteristic
256C2×D11—24no—
257C2×D11—24no—
258C2×D11—24no—
259C2×D11—24no—
260C2×D11—24no—
261C2×D11—24no—
262C2×D11C2×#10718yescomplemented
263C4×C11—22no—
264C4×C11—42no—
265C4×C11—81no—
266C4×C11—82no—
267C4×C11C2×#10714yescomplemented
268C4×C11C2×C4×D411yescharacteristic
269C4×C11#52011yescharacteristic
270C4×C11D4×Q811yescharacteristic
271C4×C11#55411yescharacteristic
272Dic11—24no—
273Dic11—42no—
274Dic11—81no—
275Dic11—82no—
276C22×D4—111no—
277C23×C4—112no—
278C23×C4—222no—
279C23×C4—222no—
280C22×C8—111no—
281C22×C8—111no—
282C22×C8—118no—
283C22×C8—224no—
284C22×C8—224no—
285C22×C8C22×D1112yes—
286C4×D4—114no—
287C4×D4—114no—
288C4×D4—444no—
289C4×D4—444no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—112no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—224no—
297C2×C4⋊C4—224no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—442no—
303C2×C4⋊C4—442no—
304C2×C4⋊C4C22×D1112yes—
305C2×C4⋊C4C22×D1111yescharacteristic
306C2×C4⋊C4C22×D1111yescharacteristic
307C2×C22⋊C4—112no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C42—21no—
311C2×C42—221no—
312C2×C42C22×D1111yescharacteristic
313#107—24no—
314#107—114no—
315#107—222no—
316#107—224no—
317#107—224no—
318#107—442no—
319C4⋊C8C4×D1114yescomplemented
320C22⋊C8—118no—
321C4×C8—114no—
322#95—21no—
323#95—222no—
324#95—222no—
325#95—221no—
326C2×C11D4×C4⋊C411yescharacteristic
327C2×C11C22×#10711yescharacteristic
328C2×C11#291311yescharacteristic
329C2×C11D4×D811yescharacteristic
330C2×C11D4×Q1611yescharacteristic
331C2×C11#333411yescharacteristic
332C2×C11#333811yescharacteristic
333D11—28no—
334C24—112no—
335C2×D4—114no—
336C2×D4—114no—
337C2×D4—114no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—112no—
342C22×C4—114no—
343C22×C4—114no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—222no—
351C22×C4—444no—
352C22×C4—444no—
353C22×C4—444no—
354C22×C4—444no—
355C22×C4—882no—
356C22×C4—882no—
357C22×C4D4×D1111yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4C23×D1111yescharacteristic
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—112no—
363C2×C8—112no—
364C2×C8—112no—
365C2×C8—112no—
366C2×C8—2216no—
367C2×C8—221no—
368C2×C8—221no—
369C2×C8C2×C4×D1114yes—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—42no—
376C4⋊C4—81no—
377C4⋊C4—114no—
378C4⋊C4—112no—
379C4⋊C4—221no—
380C4⋊C4—222no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—444no—
385C4⋊C4—444no—
386C4⋊C4—442no—
387C4⋊C4—881no—
388C4⋊C4D4×D1112yes—
389C22⋊C4—118no—
390C22⋊C4—444no—
391C22⋊C4—444no—
392C42—42no—
393C42—442no—
394C42C2×C4×D1112yes—
395C42Q8×D1112yes—
396C11D4×#10711yescharacteristic, complemented, Sylow
397C23—114no—
398C23—114no—
399C23—114no—
400C23—222no—
401C23—222no—
402C23—222no—
403C23—222no—
404C23C2×D4×D1111yescharacteristic
405D4—1116no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—114no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—224no—
421C2×C4—224no—
422C2×C4—224no—
423C2×C4—224no—
424C2×C4—222no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—441no—
431C2×C4—442no—
432C2×C4—441no—
433C2×C4—888no—
434C2×C4—888no—
435C2×C4C4⋊C4×D1112yes—
436C2×C4C4⋊C4×D1112yes—
437C2×C4D8×D1112yes—
438C2×C4Q16×D1112yes—
439C2×C4C22×C4×D1111yescharacteristic
440C2×C4C2×D4×D1111yescharacteristic
441C2×C4C2×Q8×D1111yescharacteristic
442C2×C4#6704011yescharacteristic
443C2×C4#41×D1111yescharacteristic
444C2×C4#6704211yescharacteristic
445C8—24no—
446C8—114no—
447C8—222no—
448C22—118no—
449C22—224no—
450C22—224no—
451C22—224no—
452C22—224no—
453C22—224no—
454C22—224no—
455C22C2×C4⋊C4×D1111yescharacteristic
456C22#1062314011yescharacteristic
457C22#1062316211yescharacteristic
458C22C2×D8×D1111yescharacteristic
459C22C2×Q16×D1111yescharacteristic
460C22#1062330511yescharacteristic
461C22#1062331011yescharacteristic
462C4—22no—
463C4—42no—
464C4—81no—
465C4—82no—
466C4—224no—
467C4—442no—
468C4—881no—
469C4—882no—
470C4D11×#10714yescomplemented
471C4C4×D4×D1111yescharacteristic
472C4#1062310511yescharacteristic
473C4#1062322111yescharacteristic
474C4#1062325811yescharacteristic
475C2—228no—
476C2#1307151711yescharacteristic
477C2C2×D11×#10711yescharacteristic
478C2#1307721511yescharacteristic
479C2#1308028811yescharacteristic
480C2#1308036311yescharacteristic
481C2#1308096211yescharacteristic
482C2#1308100711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1947D11
hypocenterC11D4×#107
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. C2×D11×#107C2semidirect
5. #13069375C2semidirect
6. #13068805C2semidirect
7. #13068802C2semidirect
8. #13068775C2semidirect
9. #13068644C2semidirect
10. C4×#66871C2semidirect
11. C11×#1947C2semidirect
37. #10622447C4semidirect
71. C2×C8×D11C2×C4semidirect
81. C11×C4⋊C8C2×C4semidirect
86. (C2×D11)⋊C8C2×C4semidirect
91. #66871D4semidirect
92. C4×C11⋊C8C2×C4semidirect
161. #1947D11semidirect
208. D44#107semidirect
217. C11⋊C8C4×D4semidirect
262. C2×D11C2×#107semidirect
267. C4×C11C2×#107semidirect
319. C4⋊C8C4×D11semidirect
396. C11D4×#107semidirect
470. C4D11×#107semidirect

Maximal subgroups

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

subgroupindex
C2×#106224472
C2×D11×#1072
C4⋊C4×D442
#130715162
#130693752
#130688052
#130688022
#130687752
#130686442
C4×#668712
C11×#19472
D4×#10711