Finite Group Databasebeta

← #14764157

Subgroups — #14764157

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊C8C211yesmaximal, characteristic
2#13071021C211yesmaximal, characteristic
3#13071012C211yesmaximal, characteristic
4#13069387C212yesmaximal, complemented
5#13069381C212yesmaximal, complemented
6#13069379C211yesmaximal, characteristic, complemented
7#13069377C211yesmaximal, characteristic, complemented
8#13069375C211yesmaximal, characteristic, complemented
9#13068642C212yesmaximal
10#13068640C212yesmaximal
11C11×#1947C211yesmaximal, characteristic, complemented
12C22×C8×D11C2212yes—
13C2×#66945—21no—
14C2×C42×D11C2211yescharacteristic
15C2×C11×#107C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C11×#384C2211yescharacteristic
18C4×C11×C4⋊C4C2211yescharacteristic
19C2×#66882C2212yes—
20C2×Dic11⋊C8C2212yes—
21#10622600—21no—
22#10622600C2211yescharacteristic
23#10622600C2212yes—
24#10622600C2211yescharacteristic
25#10622590—21no—
26#10622590C2211yescharacteristic
27#10622590C2211yescharacteristic
28C4⋊C4×Dic11—21no—
29C4⋊C4×Dic11C2212yes—
30C2×#66872C2212yes—
31C2×#66872C2212yes—
32C4×(C2×D11)⋊C4—21no—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35#10622545—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37D11×C4⋊C8C418yescomplemented
38#10622277—21no—
39#10622264—21no—
40C11×#340C2212yes—
41#10622189C2212yes—
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⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2312yes—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69C2×C8×D11—42no—
70C2×C8×D11—42no—
71C2×C8×D11C2×C418yes—
72#66945—44no—
73C42×D11C2×C414yes—
74C42×D11Q814yes—
75C11×#107—42no—
76C11×C4⋊C8C2×C414yes—
77C11×#95—21no—
78C11⋊#95—21no—
79C11⋊#95—21no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66882—42no—
88Dic11⋊C8C2×C418yes—
89#66872—42no—
90#66872—42no—
91C4⋊(C11⋊C8)C2×C414yes—
92#21962—111nomaximal, Sylow
93C23×D11C2×D411yescharacteristic
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
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—21no—
111C2×C4×D11—21no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11C4⋊C414yes—
115C2×C4×D11C4⋊C414yes—
116C2×C4×D11C22×C412yes—
117C2×C4×D11C2×Q812yes—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11C22×C414yes—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—42no—
129C42×C11—42no—
130C42×C11C22×C412yes—
131C42×C11C2×Q812yes—
132(C2×D11)⋊C4—44no—
133(C2×D11)⋊C4—42no—
134(C2×D11)⋊C4—42no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—42no—
142C4⋊Dic11—42no—
143C4×Dic11—44no—
144C4×Dic11—42no—
145C4×Dic11C4⋊C414yes—
146C4×Dic11C4⋊C414yes—
147C4×Dic11C22×C412yes—
148C4×Dic11C2×Q812yes—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8C22×C414yes—
152C8×D11—48no—
153C22×C4⋊C8—111no—
154#2285—111no—
155#2283—111no—
156#1949—112no—
157#1949—112no—
158#1948—111no—
159#1948—111no—
160#1947—111no—
161#1947D1111yescharacteristic, complemented
162#1808—112no—
163#1807—112no—
164C23×C11C22×D411yescharacteristic
165C22×D11—21no—
166C22×D11—21no—
167C22×D11—21no—
168C22×D11—21no—
169C22×D11C2×C4⋊C412yes—
170C22×D11AGL(1,ℤ/8)12yes—
171C22×D11#13712yes—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11C2×C4⋊C412yes—
184C2×C4×C11C2×C4⋊C412yes—
185C2×C4×C11#13512yes—
186C2×C4×C11#13512yes—
187C2×C4×C11C23×C411yescharacteristic
188C2×C4×C11C22×Q811yescharacteristic
189C2×C4×C11H(5,𝔽2)11yescharacteristic
190C2×C4×C11H(5,𝔽2)11yescharacteristic
191C2×C4×C112−1+411yescharacteristic
192C2×C4×C112−1+411yescharacteristic
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11C2×C4⋊C412yes—
209C2×Dic11C2×C4⋊C412yes—
210C2×Dic11C2×C4⋊C412yes—
211C4×D11—28no—
212C4×D11—22no—
213C4×D11—22no—
214C4×D11—22no—
215C4×D11—22no—
216C4×D11—28no—
217C8×C11—24no—
218C11⋊C8—24no—
219C23×C8—112no—
220C2×#117—221no—
221C22×C42—111no—
222C2×#107—112no—
223C2×#107C2×D1112yes—
224C2×#106—112no—
225C2×#106—112no—
226C2×C4⋊C8—112no—
227C2×C4⋊C8—111no—
228C2×C4⋊C8—118no—
229C2×C4⋊C8C2×D1111yescharacteristic
230#384—111no—
231#384C2×D1111yescharacteristic
232#383—221no—
233#382—111no—
234#382—111no—
235#382—221no—
236#381—221no—
237#380—111no—
238#380—112no—
239#380—111no—
240#380—221no—
241C4×C4⋊C4—112no—
242C4×C4⋊C4—111no—
243C4×C4⋊C4—221no—
244C4×C4⋊C4C2×D1111yescharacteristic
245C4×C22⋊C4—221no—
246#376—221no—
247#340—112no—
248#340—112no—
249#340—112no—
250#340C2×D1112yes—
251C22×C11C22×C4⋊C411yescharacteristic
252C22×C11#53711yescharacteristic
253C22×C11#53711yescharacteristic
254C22×C11C2×#13511yescharacteristic
255C22×C11C2×#13511yescharacteristic
256C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C11C2×#13711yescharacteristic
258C2×D11—22no—
259C2×D11—22no—
260C2×D11—22no—
261C2×D11—22no—
262C2×D11—22no—
263C2×D11—22no—
264C2×D11#42814yes—
265C4×C11—22no—
266C4×C11—81no—
267C4×C11—82no—
268C4×C11—81no—
269C4×C11#42714yes—
270C4×C11#51811yescharacteristic
271C4×C11#51911yescharacteristic
272C4×C11#54411yescharacteristic
273C4×C11#54411yescharacteristic
274Dic11—22no—
275Dic11—22no—
276Dic11—22no—
277Dic11—81no—
278Dic11—82no—
279Dic11—81no—
280C23×C4—111no—
281C23×C4—111no—
282C23×C4—111no—
283C22×C8—112no—
284C22×C8—118no—
285C22×C8—442no—
286C22×C8—442no—
287C22×C8C22×D1112yes—
288#117—444no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—112no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C4⋊C4C22×D1112yes—
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C22⋊C4—222no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C42—21no—
303C2×C42—111no—
304C2×C42—111no—
305C2×C42—111no—
306C2×C42—114no—
307C2×C42—114no—
308C2×C42—222no—
309C2×C42—221no—
310C2×C42C22×D1111yescharacteristic
311#107—42no—
312#107—442no—
313#106—442no—
314#106—442no—
315C4⋊C8—118no—
316C4⋊C8—114no—
317C4⋊C8C4×D1114yes—
318#95—21no—
319#95—221no—
320#95—221no—
321#95—221no—
322#95—221no—
323#95—221no—
324#95—221no—
325#95—222no—
326#95—222no—
327#95—221no—
328C2×C11#231611yescharacteristic
329C2×C11C2×#42711yescharacteristic
330C2×C11C2×#42811yescharacteristic
331C2×C11#324711yescharacteristic
332C2×C11#324711yescharacteristic
333C2×C11#324811yescharacteristic
334C2×C11#324811yescharacteristic
335D11—24no—
336C24—111no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—111no—
341C22×C4—111no—
342C22×C4—111no—
343C22×C4—114no—
344C22×C4—114no—
345C22×C4—112no—
346C22×C4—112no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—222no—
358C22×C4D4×D1111yescharacteristic
359C22×C4D4×D1111yescharacteristic
360C22×C4C23×D1111yescharacteristic
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—114no—
364C2×C8—222no—
365C2×C8—222no—
366C2×C8—448no—
367C2×C8C2×C4×D1114yes—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—222no—
379C4⋊C4—222no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—442no—
383C4⋊C4—442no—
384C22⋊C4—444no—
385C22⋊C4—442no—
386C22⋊C4—442no—
387C42—42no—
388C42—114no—
389C42—114no—
390C42—112no—
391C42—112no—
392C42—444no—
393C42—442no—
394C42C2×C4×D1112yes—
395C42Q8×D1112yes—
396C11#2196211yescharacteristic, complemented, Sylow
397C23—112no—
398C23—112no—
399C23—112no—
400C23—221no—
401C23—221no—
402C23—221no—
403C23—221no—
404C23C2×D4×D1111yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—112no—
417C2×C4—112no—
418C2×C4—112no—
419C2×C4—228no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—222no—
427C2×C4—228no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—442no—
439C2×C4—441no—
440C2×C4C4⋊C4×D1112yes—
441C2×C4C4⋊C4×D1112yes—
442C2×C4#6696512yes—
443C2×C4#6697212yes—
444C2×C4C22×C4×D1111yescharacteristic
445C2×C4#6703711yescharacteristic
446C2×C4C2×Q8×D1111yescharacteristic
447C2×C4#6704011yescharacteristic
448C2×C4#6704211yescharacteristic
449C2×C4#6704311yescharacteristic
450C8—24no—
451C8—224no—
452C22—114no—
453C22—222no—
454C22—222no—
455C22—222no—
456C22—222no—
457C22—222no—
458C22—222no—
459C22C2×C4⋊C4×D1111yescharacteristic
460C22#1062313911yescharacteristic
461C22#1062316011yescharacteristic
462C22C2×#6696511yescharacteristic
463C22C2×#6697211yescharacteristic
464C22D11×AGL(1,ℤ/8)11yescharacteristic
465C22D11×#13711yescharacteristic
466C4—22no—
467C4—81no—
468C4—82no—
469C4—81no—
470C4—222no—
471C4—222no—
472C4—222no—
473C4—881no—
474C4—882no—
475C4—881no—
476C4#1062249314yes—
477C4#1062307611yescharacteristic
478C4#1062310311yescharacteristic
479C4#1062322011yescharacteristic
480C4#1062326011yescharacteristic
481C2—224no—
482C2#1307123111yescharacteristic
483C2C2×#1062249311yescharacteristic
484C2D11×#42811yescharacteristic
485C2#1307993811yescharacteristic
486C2#1307994511yescharacteristic
487C2#1307995111yescharacteristic
488C2#1307995511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1947D11
hypocenterC11#21962
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
4. #13069387C2semidirect
5. #13069381C2semidirect
6. #13069379C2semidirect
7. #13069377C2semidirect
8. #13069375C2semidirect
11. C11×#1947C2semidirect
37. D11×C4⋊C8C4semidirect
161. #1947D11semidirect
396. C11#21962semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊C82
#130710212
#130710122
#130693872
#130693812
#130693792
#130693772
#130693752
#130686422
#130686402
C11×#19472
#2196211