Finite Group Databasebeta

← #14764319

Subgroups — #14764319

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622446C211yesmaximal, characteristic
2#13071021C211yesmaximal, characteristic
3#13071012C211yesmaximal, characteristic
4#13069379C211yesmaximal, characteristic, complemented
5#13069377C211yesmaximal, characteristic, complemented
6#13069375C211yesmaximal, characteristic, complemented
7#13068818C212yesmaximal
8#13068812C212yesmaximal
9#13068779C212yesmaximal, complemented
10#13068745C212yesmaximal, complemented
11C11×#1947C211yesmaximal, characteristic, complemented
12C2×#66945C2212yes—
13C2×C42×D11C2211yescharacteristic
14C2×C11×#107C2212yes—
15C2×C11×C4⋊C8C2211yescharacteristic
16C11×#384C2211yescharacteristic
17C4×C11×C4⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C8C2212yes—
19C2×#66882C2212yes—
20C2×C8×Dic11C2212yes—
21#10622600—21no—
22#10622600—21no—
23#10622600C2211yescharacteristic
24#10622600C2211yescharacteristic
25#10622590C2211yescharacteristic
26#10622590C2211yescharacteristic
27#10622590C2212yes—
28C4⋊C4×Dic11—21no—
29C4⋊C4×Dic11—21no—
30C2×#66872C2212yes—
31C2×#66872C2212yes—
32C4×(C2×D11)⋊C4—21no—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35#10622545—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622446C418yescomplemented
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⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4×Dic11—21no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69#66945—42no—
70#66945—42no—
71C42×D11C2×C414yes—
72C42×D11Q814yes—
73C11×#107—42no—
74C11×C4⋊C8C2×C414yes—
75C11×#95—21no—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C11⋊#95—21no—
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—
87C8×Dic11C2×C418yes—
88#66872—42no—
89#66872—42no—
90C4⋊(C11⋊C8)C2×C414yes—
91#21985—111nomaximal, Sylow
92C23×D11C2×D411yescharacteristic
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—22no—
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—21no—
111C2×C4×D11—41no—
112C2×C4×D11—41no—
113C2×C4×D11C4⋊C414yes—
114C2×C4×D11C4⋊C414yes—
115C2×C4×D11C22×C412yes—
116C2×C4×D11C2×Q812yes—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11C22×C414yes—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—42no—
128C42×C11—42no—
129C42×C11C22×C412yes—
130C42×C11C2×Q812yes—
131(C2×D11)⋊C4—44no—
132(C2×D11)⋊C4—42no—
133(C2×D11)⋊C4—42no—
134C4⋊Dic11—21no—
135C4⋊Dic11—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—42no—
141C4⋊Dic11—42no—
142C4×Dic11—44no—
143C4×Dic11—42no—
144C4×Dic11C4⋊C414yes—
145C4×Dic11C4⋊C414yes—
146C4×Dic11C22×C412yes—
147C4×Dic11C2×Q812yes—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8C22×C414yes—
151C2×#431—111no—
152#2285—111no—
153#2283—111no—
154#1948—111no—
155#1948—111no—
156#1947—111no—
157#1947D1111yescharacteristic, complemented
158#1854—112no—
159#1854—112no—
160#1846—112no—
161#1835—112no—
162C23×C11C22×D411yescharacteristic
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
167C22×D11—21no—
168C22×D11—21no—
169C22×D11C2×C4⋊C412yes—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11C2×C4⋊C412yes—
182C2×C4×C11C2×C4⋊C412yes—
183C2×C4×C11#13512yes—
184C2×C4×C11#13512yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×Q811yescharacteristic
187C2×C4×C11H(5,𝔽2)11yescharacteristic
188C2×C4×C11H(5,𝔽2)11yescharacteristic
189C2×C4×C112−1+411yescharacteristic
190C2×C4×C112−1+411yescharacteristic
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—42no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11C2×C4⋊C412yes—
207C2×Dic11C2×C4⋊C412yes—
208C2×Dic11C2×C4⋊C412yes—
209C4×D11—22no—
210C4×D11—22no—
211C4×D11—22no—
212C4×D11—22no—
213C4×D11—28no—
214C4×D11—44no—
215C8×C11—24no—
216C11⋊C8—24no—
217C2×#117—112no—
218C22×C42—111no—
219#431—118no—
220C2×#107—112no—
221C2×#107C2×D1112yes—
222C2×#106—112no—
223C2×#106—112no—
224C2×C4⋊C8—111no—
225C2×C4⋊C8C2×D1111yescharacteristic
226C2×C22⋊C8—112no—
227C2×C4×C8—112no—
228#384—111no—
229#384C2×D1111yescharacteristic
230#383—221no—
231#382—111no—
232#382—112no—
233#382—111no—
234#381—221no—
235#380—111no—
236#380—111no—
237#380—221no—
238#380—221no—
239C4×C4⋊C4—111no—
240C4×C4⋊C4—221no—
241C4×C4⋊C4—221no—
242C4×C4⋊C4C2×D1111yescharacteristic
243C4×C22⋊C4—221no—
244#376—221no—
245#340—112no—
246#340—112no—
247#340—112no—
248#340C2×D1112yes—
249C22×C11C22×C4⋊C411yescharacteristic
250C22×C11#53511yescharacteristic
251C22×C11#53611yescharacteristic
252C22×C11C2×#13511yescharacteristic
253C22×C11C2×#13511yescharacteristic
254C22×C11#57511yescharacteristic
255C22×C11#57511yescharacteristic
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—22no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C4×C11—22no—
264C4×C11—82no—
265C4×C11—81no—
266C4×C11—81no—
267C4×C11#42714yes—
268C4×C11#52011yescharacteristic
269C4×C11#52011yescharacteristic
270C4×C11#54411yescharacteristic
271C4×C11#54411yescharacteristic
272Dic11—22no—
273Dic11—22no—
274Dic11—22no—
275Dic11—82no—
276Dic11—81no—
277Dic11—81no—
278C23×C4—111no—
279C23×C4—111no—
280C23×C4—111no—
281C22×C8—112no—
282C22×C8C22×D1112yes—
283#117—442no—
284#117—442no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4C22×D1112yes—
293C2×C4⋊C4C22×D1111yescharacteristic
294C2×C4⋊C4C22×D1111yescharacteristic
295C2×C22⋊C4—222no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C42—21no—
299C2×C42—111no—
300C2×C42—111no—
301C2×C42—111no—
302C2×C42—114no—
303C2×C42—114no—
304C2×C42—222no—
305C2×C42—221no—
306C2×C42C22×D1111yescharacteristic
307#107—42no—
308#107—442no—
309#106—442no—
310#106—442no—
311C4⋊C8—114no—
312C4⋊C8C4×D1114yes—
313C22⋊C8—118no—
314C4×C8—118no—
315#95—21no—
316#95—221no—
317#95—221no—
318#95—221no—
319#95—221no—
320#95—221no—
321#95—221no—
322#95—222no—
323#95—222no—
324#95—221no—
325C2×C11#231711yescharacteristic
326C2×C11C2×#42711yescharacteristic
327C2×C11#291111yescharacteristic
328C2×C11#321211yescharacteristic
329C2×C11#321211yescharacteristic
330C2×C11#323311yescharacteristic
331C2×C11#323311yescharacteristic
332D11—42no—
333C24—111no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—111no—
340C22×C4—114no—
341C22×C4—112no—
342C22×C4—112no—
343C22×C4—114no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—222no—
353C22×C4—441no—
354C22×C4—441no—
355C22×C4D4×D1111yescharacteristic
356C22×C4D4×D1111yescharacteristic
357C22×C4C23×D1111yescharacteristic
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—114no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8C2×C4×D1114yes—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—221no—
373C4⋊C4—222no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—222no—
377C4⋊C4—221no—
378C4⋊C4—442no—
379C4⋊C4—442no—
380C22⋊C4—444no—
381C22⋊C4—442no—
382C22⋊C4—442no—
383C42—42no—
384C42—114no—
385C42—114no—
386C42—112no—
387C42—112no—
388C42—444no—
389C42—442no—
390C42C2×C4×D1112yes—
391C42Q8×D1112yes—
392C11#2198511yescharacteristic, complemented, Sylow
393C23—112no—
394C23—221no—
395C23—221no—
396C23—221no—
397C23—221no—
398C23—221no—
399C23—221no—
400C23C2×D4×D1111yescharacteristic
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—112no—
413C2×C4—112no—
414C2×C4—112no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—222no—
422C2×C4—228no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—444no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—442no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4C4⋊C4×D1112yes—
437C2×C4C4⋊C4×D1112yes—
438C2×C4#6696512yes—
439C2×C4#6697212yes—
440C2×C4C22×C4×D1111yescharacteristic
441C2×C4#6703711yescharacteristic
442C2×C4C2×Q8×D1111yescharacteristic
443C2×C4#6704011yescharacteristic
444C2×C4#6704211yescharacteristic
445C2×C4#6704311yescharacteristic
446C8—24no—
447C8—224no—
448C22—222no—
449C22—222no—
450C22—222no—
451C22—441no—
452C22—441no—
453C22—441no—
454C22—441no—
455C22C2×C4⋊C4×D1111yescharacteristic
456C22#1062313811yescharacteristic
457C22#1062315911yescharacteristic
458C22C2×#6696511yescharacteristic
459C22C2×#6697211yescharacteristic
460C22#1062330411yescharacteristic
461C22#1062330811yescharacteristic
462C4—22no—
463C4—81no—
464C4—82no—
465C4—81no—
466C4—222no—
467C4—222no—
468C4—222no—
469C4—881no—
470C4—882no—
471C4—881no—
472C4#1062249314yes—
473C4#1062307711yescharacteristic
474C4#1062310511yescharacteristic
475C4#1062322011yescharacteristic
476C4#1062326011yescharacteristic
477C2—442no—
478C2#1307123811yescharacteristic
479C2C2×#1062249311yescharacteristic
480C2#1307720311yescharacteristic
481C2#1307959011yescharacteristic
482C2#1307959711yescharacteristic
483C2#1307979311yescharacteristic
484C2#1307980011yescharacteristic
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#21985
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. #13069379C2semidirect
5. #13069377C2semidirect
6. #13069375C2semidirect
9. #13068779C2semidirect
10. #13068745C2semidirect
11. C11×#1947C2semidirect
37. #10622446C4semidirect
157. #1947D11semidirect
392. C11#21985semidirect

Maximal subgroups

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

subgroupindex
C2×#106224462
#130710212
#130710122
#130693792
#130693772
#130693752
#130688182
#130688122
#130687792
#130687452
C11×#19472
#2198511