Finite Group Databasebeta

← #14759234

Subgroups — #14759234

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66925C211yesmaximal, characteristic
2#13069230C212yesmaximal
3#13069221C212yesmaximal
4#13069177C212yesmaximal, complemented
5#13069176C212yesmaximal, complemented
6#13068469C211yesmaximal, characteristic, complemented
7#13068379C211yesmaximal, characteristic
8#13068379C211yesmaximal, characteristic
9#13068364C211yesmaximal, characteristic, complemented
10#97×Dic11C211yesmaximal, characteristic, complemented
11C11×#1767C211yesmaximal, characteristic, complemented
12C2×#66925C411yescharacteristic
13C2×#66925C411yescharacteristic
14C2×C42×D11C2211yescharacteristic
15C2×C11×C4⋊C8C2212yes—
16C2×C11×#97C2211yescharacteristic
17C2×C11×#97C2211yescharacteristic
18C43×C11C2211yescharacteristic
19C2×(C2×D11)⋊C8C2212yes—
20C2×(C2×D11)⋊C8C2212yes—
21C2×#66879C2212yes—
22C2×C8×Dic11C2212yes—
23C4×(C2×D11)⋊C4C411yescharacteristic
24C4×(C2×D11)⋊C4C411yescharacteristic
25C4×(C2×D11)⋊C4C2211yescharacteristic
26C4×(C2×D11)⋊C4C2211yescharacteristic
27#10622545C411yescharacteristic
28#10622545C411yescharacteristic
29C4×Dic11⋊C4C411yescharacteristic
30C4×Dic11⋊C4C411yescharacteristic
31C4×Dic11⋊C4C2211yescharacteristic
32C4×Dic11⋊C4C2211yescharacteristic
33C42×Dic11C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2212yes—
35C2×#66867C2211yescharacteristic
36C2×#66867C2211yescharacteristic
37C11×#336C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40#10622188C2212yes—
41#10622188C2212yes—
42#10622162C2212yes—
43C22×C4×D11C2×C411yescharacteristic
44C22×C4×D11C2×C411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C22×C8×C11C2312yes—
47C22×C8×C11C2312yes—
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11C2×C411yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4C2×C411yescharacteristic
56C2×(C2×D11)⋊C4C2×C411yescharacteristic
57C2×(C2×D11)⋊C4C2×C411yescharacteristic
58C2×(C2×D11)⋊C4C2×C411yescharacteristic
59C2×Dic11⋊C4C2×C411yescharacteristic
60C2×Dic11⋊C4C2×C411yescharacteristic
61C2×Dic11⋊C4C2×C411yescharacteristic
62C2×Dic11⋊C4C2×C411yescharacteristic
63C2×C4×Dic11C2×C411yescharacteristic
64C2×C4×Dic11C2×C411yescharacteristic
65C2×C4×Dic11C2×C411yescharacteristic
66C2×C4×Dic11C2×C411yescharacteristic
67C2×C4×Dic11C2×C411yescharacteristic
68C2×C4×Dic11C2×C411yescharacteristic
69C2×C4×Dic11C2311yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73C22×C11⋊C8C2312yes—
74#66925—24no—
75#66925—24no—
76C42×D11—22no—
77C42×D11—22no—
78C11×C4⋊C8—24no—
79C11×#97—22no—
80C11×#97—22no—
81C11⋊#95C2×C411yescharacteristic
82C11⋊#95C2×C411yescharacteristic
83C11⋊#95C2×C411yescharacteristic
84C11⋊#95C2×C411yescharacteristic
85C11⋊#95C2×C411yescharacteristic
86C11⋊#95C2×C411yescharacteristic
87C11⋊#95C2×C411yescharacteristic
88C11⋊#95C2×C411yescharacteristic
89(C2×D11)⋊C8—24no—
90(C2×D11)⋊C8—24no—
91#66879—24no—
92C8×Dic11—24no—
93C4⋊(C11⋊C8)—24no—
94#66867—22no—
95#66867—22no—
96#21435—111nomaximal, Sylow
97C23×D11C22×C411yescharacteristic
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11C22×C411yescharacteristic
106C22×Dic11C22×C411yescharacteristic
107C22×Dic11C22×C411yescharacteristic
108C22×Dic11C22×C411yescharacteristic
109C22×Dic11C22×C411yescharacteristic
110C22×Dic11C22×C411yescharacteristic
111C22×Dic11C22×C411yescharacteristic
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11#4114yes—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11—22no—
131C42×C11—22no—
132C42×C11—41no—
133C42×C11—41no—
134C42×C11#4112yes—
135C42×C11#4112yes—
136(C2×D11)⋊C4—22no—
137(C2×D11)⋊C4—22no—
138(C2×D11)⋊C4—22no—
139(C2×D11)⋊C4M1614yes—
140Dic11⋊C4—22no—
141Dic11⋊C4—22no—
142Dic11⋊C4—22no—
143Dic11⋊C4M1614yes—
144C4×Dic11—22no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11—21no—
151C4×Dic11—21no—
152C4×Dic11—41no—
153C4×Dic11—41no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8#4114yes—
160C4×#117—111no—
161#1924—112no—
162#1923—112no—
163#1917—112no—
164#1916—112no—
165#1767—111no—
166#1767D1111yescharacteristic, complemented
167#1749—111no—
168#1749—111no—
169#1745—111no—
170C4×#97—111no—
171C23×C11C23×C411yescharacteristic
172C22×D11—21no—
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11C2×M1612yes—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11#11712yes—
194C2×C4×C11#11712yes—
195C2×C4×C11C2×M1612yes—
196C2×C4×C11C2×M1612yes—
197C2×C4×C11C2×#4112yes—
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4112yes—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11C2×M1612yes—
220C2×Dic11C2×M1612yes—
221C2×Dic11C2×M1612yes—
222C4×D11—28no—
223C4×D11—44no—
224C4×D11—42no—
225C4×D11—42no—
226C8×C11—24no—
227C8×C11—42no—
228C11⋊C8—24no—
229C11⋊C8—42no—
230C2×#117—111no—
231C2×#117—111no—
232C22×C42—111no—
233C2×C4⋊C8—112no—
234C2×C4⋊C8C2×D1112yes—
235C2×C22⋊C8—112no—
236C2×C22⋊C8—112no—
237C2×#97—112no—
238C2×#97—111no—
239C2×#97—111no—
240C2×#97C2×D1111yescharacteristic
241C2×#97C2×D1111yescharacteristic
242C2×C4×C8—112no—
243C4×C4⋊C4—111no—
244C4×C4⋊C4—111no—
245C4×C4⋊C4—111no—
246C4×C4⋊C4—111no—
247C4×C22⋊C4—111no—
248C4×C22⋊C4—111no—
249C4×C22⋊C4—111no—
250C4×C22⋊C4—111no—
251#376—111no—
252#376—111no—
253C43—111no—
254C43C2×D1111yescharacteristic
255#336—112no—
256#336—112no—
257#336—112no—
258#336—112no—
259#336—112no—
260#336C2×D1112yes—
261C22×C11C2×#11711yescharacteristic
262C22×C11C4×#4111yescharacteristic
263C22×C11C4×#4111yescharacteristic
264C22×C11C22×M1611yescharacteristic
265C22×C11C22×M1611yescharacteristic
266C22×C11#56811yescharacteristic
267C22×C11#56811yescharacteristic
268C2×D11—22no—
269C2×D11—22no—
270C2×D11—22no—
271C2×D11—41no—
272C2×D11—41no—
273C2×D11—41no—
274C2×D11—41no—
275C4×C11—22no—
276C4×C11—22no—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—41no—
280C4×C11—41no—
281C4×C11#52912yes—
282C4×C11#52912yes—
283Dic11—22no—
284Dic11—22no—
285Dic11—22no—
286Dic11—41no—
287Dic11—41no—
288Dic11—41no—
289Dic11—41no—
290C23×C4—111no—
291C23×C4—111no—
292C23×C4—111no—
293C22×C8—112no—
294C22×C8—112no—
295C22×C8C22×D1112yes—
296C22×C8C22×D1112yes—
297#117—224no—
298#117—224no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—111no—
303C2×C22⋊C4—111no—
304C2×C22⋊C4—111no—
305C2×C22⋊C4—111no—
306C2×C22⋊C4—111no—
307C2×C42—111no—
308C2×C42—111no—
309C2×C42—111no—
310C2×C42—111no—
311C2×C42—111no—
312C2×C42—111no—
313C2×C42—111no—
314C2×C42—111no—
315C2×C42—111no—
316C2×C42—222no—
317C2×C42—222no—
318C2×C42C4×D1111yescharacteristic
319C2×C42C4×D1111yescharacteristic
320C2×C42C4×D1111yescharacteristic
321C2×C42C4×D1111yescharacteristic
322C2×C42C22×D1111yescharacteristic
323C2×C42C22×D1111yescharacteristic
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—24no—
326C4⋊C8—224no—
327C22⋊C8—224no—
328C22⋊C8—224no—
329#97—22no—
330#97—22no—
331#97—224no—
332#97—222no—
333#97—222no—
334C4×C8—224no—
335#95—111no—
336#95—111no—
337#95—111no—
338#95—111no—
339#95—111no—
340#95—111no—
341#95—111no—
342#95—111no—
343C2×C11#229811yescharacteristic
344C2×C11#292011yescharacteristic
345C2×C11#292111yescharacteristic
346C2×C11#297011yescharacteristic
347C2×C11#297011yescharacteristic
348C2×C11#297011yescharacteristic
349C2×C11#297111yescharacteristic
350D11—42no—
351C24—111no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—111no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—222no—
367C22×C4—441no—
368C22×C4—441no—
369C22×C4C2×C4×D1111yescharacteristic
370C22×C4C2×C4×D1111yescharacteristic
371C22×C4C2×C4×D1111yescharacteristic
372C22×C4C2×C4×D1111yescharacteristic
373C22×C4C2×C4×D1111yescharacteristic
374C22×C4C2×C4×D1111yescharacteristic
375C22×C4C23×D1111yescharacteristic
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—114no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8#433914yes—
388C4⋊C4—114no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C22⋊C4—114no—
393C22⋊C4—222no—
394C22⋊C4—222no—
395C22⋊C4—222no—
396C42—22no—
397C42—22no—
398C42—22no—
399C42—22no—
400C42—41no—
401C42—41no—
402C42—222no—
403C42—222no—
404C42—222no—
405C42—222no—
406C42—222no—
407C42—221no—
408C42—221no—
409C42—222no—
410C42—441no—
411C42—441no—
412C42#434112yes—
413C42#434312yes—
414C11#2143511yescharacteristic, complemented, Sylow
415C23—112no—
416C23—221no—
417C23—221no—
418C23—221no—
419C23—221no—
420C23—221no—
421C23—221no—
422C23C22×C4×D1111yescharacteristic
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—112no—
438C2×C4—112no—
439C2×C4—112no—
440C2×C4—228no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—444no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4#6694512yes—
463C2×C4#6694512yes—
464C2×C4M16×D1112yes—
465C2×C4M16×D1112yes—
466C2×C4C2×#433912yes—
467C2×C4C2×#434111yescharacteristic
468C2×C4C2×#434311yescharacteristic
469C2×C4#41×D1112yes—
470C8—24no—
471C8—42no—
472C8—224no—
473C8—442no—
474C22—222no—
475C22—222no—
476C22—222no—
477C22—441no—
478C22—441no—
479C22—441no—
480C22—441no—
481C22C4×#433911yescharacteristic
482C22C2×#6694511yescharacteristic
483C22#1062305311yescharacteristic
484C22C2×M16×D1111yescharacteristic
485C22C2×M16×D1111yescharacteristic
486C22#1062327611yescharacteristic
487C22#1062327611yescharacteristic
488C4—22no—
489C4—22no—
490C4—22no—
491C4—22no—
492C4—41no—
493C4—41no—
494C4—222no—
495C4—222no—
496C4—222no—
497C4—441no—
498C4—441no—
499C4—441no—
500C4—441no—
501C4#1062306912yes—
502C4#1062311112yes—
503C2—442no—
504C2#1307110911yescharacteristic
505C2#1307724811yescharacteristic
506C2#1307725311yescharacteristic
507C2#1307762511yescharacteristic
508C2#1307762711yescharacteristic
509C2#1307762811yescharacteristic
510C2#1307763411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1767C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1767D11
hypocenterC11#21435
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1767

Complements

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

NH ≅ G/Ntype
4. #13069177C2semidirect
5. #13069176C2semidirect
6. #13068469C2semidirect
9. #13068364C2semidirect
10. #97×Dic11C2semidirect
11. C11×#1767C2semidirect
166. #1767D11semidirect
414. C11#21435semidirect

Maximal subgroups

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

subgroupindex
C4×#669252
#130692302
#130692212
#130691772
#130691762
#130684692
#130683792
#130683642
#97×Dic112
C11×#17672
#2143511