Finite Group Databasebeta

← #14773520

Subgroups — #14773520

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4323C211yesmaximal, characteristic
2#13071563C211yesmaximal, characteristic, complemented
3#13069481C212yesmaximal
4#13069236C212yesmaximal, complemented
5#13069233C212yesmaximal, complemented
6#13068775C211yesmaximal, characteristic, complemented
7#13068616C211yesmaximal, characteristic, complemented
8#13068613C211yesmaximal, characteristic, complemented
9C4×#66871C212yesmaximal, complemented
10C4⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
11C11×#2354C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×C11×#117—21no—
14C22×#4323C2211yescharacteristic
15C2×#66945—21no—
16C2×C4×D44C2211yescharacteristic
17C11×#390C2212yes—
18C11×#388—22no—
19C11×#384C2211yescharacteristic
20C11×#380—21no—
21C4×C11×C4⋊C4C2212yes—
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66896C2212yes—
24C2×#66896C2211yescharacteristic
25C4×#4323C418yescomplemented
26#10622600—21no—
27C2×#66873C2212yes—
28C2×#66873C2211yescharacteristic
29C2×#66871C2212yes—
30C2×#66871C2212yes—
31C2×#66871C2211yescharacteristic
32#10622552C2212yes—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622283—22no—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622162C2212yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C4×D4×C11—22no—
47C4×D4×C11C2×C414yes—
48C11×#117—44no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C42×C11—22no—
59C2×C42×C11C2312yes—
60C2×C42×C11C2311yescharacteristic
61C2×#4323—22no—
62C2×#4323—22no—
63C2×#4323C2×C414yes—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4×Dic11—22no—
72C22×C11⋊C8C2312yes—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75#66945—44no—
76C4×D44—22no—
77C4×D44C2×C414yes—
78C11×#95—22no—
79C11×#95D412yes—
80#66896—42no—
81#66896C2×C414yes—
82C11⋊#95—22no—
83#66873—42no—
84#66873C2×C414yes—
85#66871—24no—
86#66871—42no—
87#66871C2×C414yes—
88C4⋊(C11⋊C8)—22no—
89C4×C11⋊C8—24no—
90C4×C11⋊C8C2×C414yes—
91#22807—111nomaximal, Sylow
92C24×C11—21no—
93C23×D11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11C22×C412yes—
100C22×C4×C11—21no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—22no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44C22×C412yes—
118C2×C4×D11—24no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—81no—
127C11×C4⋊C4D814yescomplemented
128C11×C4⋊C4C22×C412yes—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—44no—
131C11×C22⋊C4—82no—
132C42×C11—22no—
133C42×C11—22no—
134C42×C11—44no—
135C42×C11C22×C412yes—
136C42×C11#4112yes—
137#4323—28no—
138(C2×D11)⋊C4—24no—
139(C2×D11)⋊C4—44no—
140(C2×D11)⋊C4—82no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—42no—
145C4⋊Dic11—81no—
146C4⋊Dic11C22×C412yes—
147C4×Dic11—44no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8C22×C412yes—
154C2×C11⋊C8C22×C412yes—
155C2×C11⋊C8#4112yes—
156C2×C11⋊C8#4112yes—
157C2×C4×D8—111no—
158#2354—111no—
159#2354D1111yescharacteristic, complemented
160#1970—112no—
161#1925—112no—
162#1925—112no—
163#1845—111no—
164#1802—111no—
165#1802—111no—
166C4×#107—112no—
167C8×C4⋊C4—111no—
168C23×C11—22no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11C22×D411yescharacteristic
176C22×D11—22no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—41no—
183D4×C11—22no—
184D4×C11—22no—
185D4×C11—41no—
186D4×C11—41no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—48no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11C4×D412yes—
202C2×C4×C11C4×D412yes—
203C2×C4×C11C2×D814yes—
204C2×C4×C11C2×D812yes—
205C2×C4×C11#13512yes—
206C2×C4×C11C23×C411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218D44—22no—
219D44—22no—
220D44—41no—
221D44—41no—
222C4×D11—48no—
223C11⋊C8—22no—
224C11⋊C8—42no—
225C11⋊C8#11714yescomplemented
226C22×D8—111no—
227C2×C4×D4—111no—
228C2×C4×D4C2×D1111yescharacteristic
229C2×#117—21no—
230C2×#117—221no—
231C4×D8—118no—
232C2×#107—111no—
233C2×#107—112no—
234C2×#107—112no—
235C2×C4⋊C8—111no—
236C2×#102—111no—
237C2×#102—111no—
238C2×#102—112no—
239C2×#102—112no—
240C2×C4×C8—111no—
241C2×C4×C8—112no—
242#390—112no—
243#390C2×D1112yes—
244#388—22no—
245#388—222no—
246#384—111no—
247#384C2×D1111yescharacteristic
248#380—21no—
249#380—221no—
250C4×C4⋊C4—112no—
251C4×C4⋊C4C2×D1112yes—
252C4×C4⋊C4C2×D1111yescharacteristic
253#340—112no—
254#340—112no—
255#336—112no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11C2×C4×D411yescharacteristic
264C22×C11#54711yescharacteristic
265C22×C11#55011yescharacteristic
266C22×C11C22×D811yescharacteristic
267C22×C11C2×#13511yescharacteristic
268C22×C11#57611yescharacteristic
269C22×C11#57811yescharacteristic
270C2×D11—42no—
271C2×D11—42no—
272C2×D11—42no—
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—24no—
278C4×C11—22no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—82no—
282C4×C11C4×D814yes—
283C4×C11C2×#11711yescharacteristic
284C4×C11#52011yescharacteristic
285C4×C11#55511yescharacteristic
286C4×C11#55611yescharacteristic
287Dic11—42no—
288Dic11—82no—
289C22×D4—111no—
290C22×D4C22×D1111yescharacteristic
291C23×C4—21no—
292C23×C4—221no—
293C2×D8—114no—
294C2×D8—222no—
295C2×D8—222no—
296C22×C8—111no—
297C22×C8—111no—
298C22×C8—112no—
299C4×D4—22no—
300C4×D4—114no—
301C4×D4—222no—
302C4×D4C4×D1114yes—
303#117—44no—
304#117—444no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4C22⋊D1111yescharacteristic
312C2×C4⋊C4C22⋊D1111yescharacteristic
313C2×C4⋊C4C22×D1112yes—
314C2×C4⋊C4C22×D1111yescharacteristic
315C2×C22⋊C4—21no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C42—22no—
322C2×C42—222no—
323C2×C42C22×D1112yes—
324C2×C42C22×D1111yescharacteristic
325#107—114no—
326#107—224no—
327#107—442no—
328C4⋊C8—222no—
329#102—114no—
330#102—114no—
331#102—442no—
332#102—442no—
333C4×C8—114no—
334C4×C8—224no—
335#95—22no—
336#95—222no—
337#95C22⋊D1112yes—
338C2×C11—82no—
339C2×C11#235411yescharacteristic
340C2×C11C2×C4×D811yescharacteristic
341C2×C11#295111yescharacteristic
342C2×C11#333411yescharacteristic
343C2×C11#334111yescharacteristic
344C2×C11#339111yescharacteristic
345C2×C11#339311yescharacteristic
346D11—82no—
347C24—21no—
348C24—221no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—112no—
355C2×D4—221no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—221no—
360C2×D4C2×C4×D1112yes—
361C22×C4—21no—
362C22×C4—24no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—221no—
367C22×C4—224no—
368C22×C4—222no—
369C22×C4—442no—
370C22×C4—442no—
371C22×C4C2×C22⋊D1112yes—
372C22×C4C2×C22⋊D1111yescharacteristic
373C22×C4C2×C22⋊D1112yes—
374C22×C4C2×C22⋊D1111yescharacteristic
375C22×C4C23×D1111yescharacteristic
376D8—228no—
377C2×C8—112no—
378C2×C8—112no—
379C2×C8—112no—
380C2×C8—112no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—222no—
384C2×C8—222no—
385C2×C8—222no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—42no—
391C4⋊C4—81no—
392C4⋊C4—112no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4—442no—
397C4⋊C4—881no—
398C4⋊C4#432314yescomplemented
399C4⋊C4C2×C4×D1112yes—
400C22⋊C4—24no—
401C22⋊C4—44no—
402C22⋊C4—82no—
403C22⋊C4—224no—
404C22⋊C4—444no—
405C22⋊C4—882no—
406C42—22no—
407C42—22no—
408C42—44no—
409C42—444no—
410C42C2×C4×D1112yes—
411C42#433912yes—
412C11#2280711yescharacteristic, complemented, Sylow
413C23—22no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—222no—
421C23—441no—
422C23—441no—
423C23—441no—
424C23—441no—
425C23—441no—
426C23—441no—
427C23C22×C22⋊D1111yescharacteristic
428D4—22no—
429D4—22no—
430D4—41no—
431D4—41no—
432D4—222no—
433D4—222no—
434D4—441no—
435D4—441no—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—48no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—222no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—448no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4C4×C22⋊D1112yes—
458C2×C4C4×C22⋊D1112yes—
459C2×C4C2×#432314yes—
460C2×C4C2×#432312yes—
461C2×C4#6700312yes—
462C2×C4C22×C4×D1111yescharacteristic
463C2×C4C2×#433911yescharacteristic
464C2×C4#41×D1111yescharacteristic
465C2×C4#41×D1111yescharacteristic
466C2×C4#6704211yescharacteristic
467C2×C4#6704311yescharacteristic
468C8—114no—
469C8—222no—
470C8—442no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—442no—
479C22—442no—
480C22—442no—
481C22—881no—
482C22—881no—
483C22—881no—
484C22—881no—
485C22C2×C4×C22⋊D1111yescharacteristic
486C22C22×#432311yescharacteristic
487C22C2×#6700311yescharacteristic
488C22#1062335511yescharacteristic
489C22#1062336511yescharacteristic
490C22#1062336611yescharacteristic
491C22#1062336911yescharacteristic
492C4—24no—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—82no—
497C4—442no—
498C4—882no—
499C4C4×#432314yes—
500C4D11×#11711yescharacteristic
501C4#1062305411yescharacteristic
502C4#1062306311yescharacteristic
503C4#1062306411yescharacteristic
504C2—82no—
505C2—882no—
506C2#1307156611yescharacteristic
507C2C2×C4×#432311yescharacteristic
508C2#1307748911yescharacteristic
509C2#1308095911yescharacteristic
510C2#1308103411yescharacteristic
511C2#1308158811yescharacteristic
512C2#1308160011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#2354D11
hypocenterC11#22807
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #13071563C2semidirect
4. #13069236C2semidirect
5. #13069233C2semidirect
6. #13068775C2semidirect
7. #13068616C2semidirect
8. #13068613C2semidirect
9. C4×#66871C2semidirect
10. C4⋊C4×C11⋊C8C2semidirect
11. C11×#2354C2semidirect
25. C4×#4323C4semidirect
127. C11×C4⋊C4D8semidirect
159. #2354D11semidirect
225. C11⋊C8#117semidirect
398. C4⋊C4#4323semidirect
412. C11#22807semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43232
#130715632
#130694812
#130692362
#130692332
#130687752
#130686162
#130686132
C4×#668712
C4⋊C4×C11⋊C82
C11×#23542
#2280711