Finite Group Databasebeta

← #14725260

Subgroups — #14725260

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077633C211yesmaximal, characteristic, complemented
2#13077628C211yesmaximal, characteristic, complemented
3C4×#66957C211yesmaximal, characteristic
4#13067517C212yesmaximal, complemented
5#13067486C212yesmaximal, complemented
6#13067479C212yesmaximal, complemented
7#13067427C212yesmaximal, complemented
8#13067048C211yesmaximal, characteristic, complemented
9#13067048C211yesmaximal, characteristic, complemented
10#13066905C211yesmaximal, characteristic, complemented
11C11×#1568C211yesmaximal, characteristic, complemented
12C2×#66957C411yescharacteristic
13C4×#4339C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#432C2211yescharacteristic
16C11×#432C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18#10622726C411yescharacteristic
19#10622726C411yescharacteristic
20#10622719C411yescharacteristic
21#10622538C2211yescharacteristic
22C4×#4318C2211yescharacteristic
23#10622451C2212yes—
24#10622447C2212yes—
25#10622444C2212yes—
26#10622443C2212yes—
27#10622342—22no—
28#10622341—22no—
29#10622320—21no—
30#10622318—21no—
31#10622318—21no—
32D11×#97—21no—
33C4×Dic44C411yescharacteristic
34C4×Dic44C2211yescharacteristic
35C4×D88C411yescharacteristic
36C4×D88C2211yescharacteristic
37C4×#4314C411yescharacteristic
38C4×#4314C411yescharacteristic
39C4×#4314C2211yescharacteristic
40C4×#4314C2211yescharacteristic
41C11×#335C2212yes—
42C11×#334C2212yes—
43#10622122C2212yes—
44#10622122C2212yes—
45#10622121C2212yes—
46#10622121C2212yes—
47#10622093C2212yes—
48#10622092C2212yes—
49C2×#4339C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C22×C8×C11C2×C411yescharacteristic
52C22×C8×C11C2×C411yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C4×C22⋊D11—21no—
55C4×C22⋊D11—21no—
56C4×C22⋊D11—21no—
57C4×C22⋊D11—21no—
58#66979C2×C411yescharacteristic
59#66979C2×C411yescharacteristic
60C2×#4318D412yes—
61C2×Dic44C2×C411yescharacteristic
62#66957—24no—
63C2×D88C2×C411yescharacteristic
64C2×#4314C2×C411yescharacteristic
65C2×#4314C2×C411yescharacteristic
66C2×#4313—22no—
67C2×C8×D11—22no—
68C4×D44C2×C411yescharacteristic
69C4×D44C2×C411yescharacteristic
70C4×D44C2311yescharacteristic
71C4×D44C2311yescharacteristic
72#66925—21no—
73#66925—21no—
74C42×D11—21no—
75C42×D11—21no—
76C4×Dic22C2×C411yescharacteristic
77C4×Dic22C2×C411yescharacteristic
78C4×Dic22C2311yescharacteristic
79C4×Dic22C2311yescharacteristic
80C11×C4⋊C8C2312yes—
81C11×C4⋊C8C2312yes—
82C11×C22⋊C8—21no—
83C11×C22⋊C8—21no—
84C11×#97—21no—
85C11×#97—21no—
86C4×C8×C11C2×C411yescharacteristic
87C4×C8×C11C2×C411yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2311yescharacteristic
90C22⋊(C11⋊C8)—21no—
91#66885C2×C411yescharacteristic
92#66885C2×C411yescharacteristic
93#66885C2×C411yescharacteristic
94#66885C2×C411yescharacteristic
95(C2×D11)⋊C8—22no—
96(C2×D11)⋊C8—22no—
97#66882C2×C411yescharacteristic
98#66882C2×C411yescharacteristic
99#66881C2×C411yescharacteristic
100#66881C2×C411yescharacteristic
101#66880C2×C411yescharacteristic
102#66880C2×C411yescharacteristic
103#66880C2×C411yescharacteristic
104#66880C2×C411yescharacteristic
105#66879—22no—
106Dic11⋊C8—22no—
107Dic11⋊C8—22no—
108C8×Dic11—22no—
109C4⋊(C11⋊C8)—21no—
110#66867D411yescharacteristic
111#66867D411yescharacteristic
112C4×C11⋊C8C2312yes—
113C4×C11⋊C8C2312yes—
114#18041—111nomaximal, Sylow
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C2×C22⋊D11—21no—
119C2×C22⋊D11—21no—
120#4339—22no—
121#4339—22no—
122#4339—41no—
123#4339—41no—
124C2×D44C22×C411yescharacteristic
125C2×D44C22×C411yescharacteristic
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×Dic22C22×C411yescharacteristic
133C2×Dic22C22×C411yescharacteristic
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—41no—
138C2×C8×C11C22×C411yescharacteristic
139C2×C8×C11C22×C411yescharacteristic
140C2×C8×C11C22×C411yescharacteristic
141C2×C8×C11C22×C411yescharacteristic
142C42×C11C22×C411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146C22⋊Dic11—21no—
147C22⋊Dic11—21no—
148(C2×D11)⋊C4—21no—
149(C2×D11)⋊C4—21no—
150(C2×D11)⋊C4—21no—
151(C2×D11)⋊C4—21no—
152C4⋊Dic11C22×C411yescharacteristic
153C4⋊Dic11C22×C411yescharacteristic
154C4⋊Dic11C22×C411yescharacteristic
155C4⋊Dic11C22×C411yescharacteristic
156Dic11⋊C4—21no—
157Dic11⋊C4—21no—
158Dic11⋊C4—21no—
159Dic11⋊C4—21no—
160C4×Dic11—21no—
161C4×Dic11—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166#4318—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8C2×D412yes—
169C2×C11⋊C8C2×D412yes—
170Dic44—22no—
171D88—22no—
172#4314—22no—
173#4314M1614yescomplemented
174#4313—44no—
175C8×D11—44no—
176#2971—111no—
177#2970—111no—
178C4×#135—111no—
179#1592—112no—
180#1587—112no—
181#1586—112no—
182SD16⋊C8—112no—
183#1568D1111yescharacteristic, complemented
184#1488—111no—
185#1488—111no—
186#1451—111no—
187C23×C11C4×D411yescharacteristic
188C22×D11—21no—
189C22×D11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11C4×D411yescharacteristic
195C2×C4×C11C4×D411yescharacteristic
196C2×C4×C11C4×D411yescharacteristic
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C22⋊D11—42no—
201C22⋊D11—42no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208D44—21no—
209D44—21no—
210D44—21no—
211D44C2×M1612yes—
212C4×D11—42no—
213C4×D11—42no—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11—81no—
217C4×D11—81no—
218Dic22—21no—
219Dic22—21no—
220Dic22—21no—
221Dic22C2×M1612yes—
222C8×C11—21no—
223C8×C11—21no—
224C8×C11—21no—
225C8×C11—42no—
226C8×C11—42no—
227C8×C11C2×M1612yes—
228C11⋊C8—22no—
229C11⋊C8—22no—
230C11⋊C8—42no—
231C2×#135—111no—
232C4×#41—111no—
233C4×#41—111no—
234#446—112no—
235C8×Q8—112no—
236C4×Q16—111no—
237C4×Q16—111no—
238C4×SD16—111no—
239C4×SD16—111no—
240C4×SD16—111no—
241C4×SD16—111no—
242C4×D8—111no—
243C4×D8—111no—
244#436—112no—
245#436—222no—
246#435—222no—
247C8×D4—112no—
248#432—221no—
249#432—221no—
250#432C2×D1111yescharacteristic
251#432C2×D1111yescharacteristic
252#431—111no—
253#427—111no—
254#416—111no—
255#416—111no—
256C4×M16—111no—
257C4×M16—221no—
258C2×#97—221no—
259C2×C4×C8C2×D1111yescharacteristic
260#335C2×D1112yes—
261#334C2×D1112yes—
262Q8⋊C8—112no—
263Q8⋊C8—112no—
264D4⋊C8—112no—
265D4⋊C8—112no—
266#322—112no—
267#322—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11C2×C4×D411yescharacteristic
272C2×D11—22no—
273C2×D11—41no—
274C2×D11—41no—
275C2×D11—41no—
276C2×D11—41no—
277C2×D11—41no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11C22×M1611yescharacteristic
283C4×C11#56811yescharacteristic
284C4×C11#57512yes—
285Dic11—22no—
286Dic11—41no—
287Dic11—41no—
288Dic11—41no—
289Dic11—41no—
290Dic11—41no—
291C2×#41—111no—
292C2×#41—111no—
293#135—224no—
294C2×Q16—111no—
295C2×SD16—111no—
296C2×SD16—111no—
297C2×D8—111no—
298C2×M16—112no—
299C2×M16—222no—
300C22×C8—222no—
301C22×C8C4×D1111yescharacteristic
302C22×C8C4×D1111yescharacteristic
303C4×Q8—111no—
304C4×Q8—111no—
305C4×Q8—111no—
306C4×Q8—111no—
307C4×D4—111no—
308C4×D4—111no—
309C4×D4—111no—
310C4×D4—111no—
311C4×D4—221no—
312C4×D4—221no—
313C4×D4—221no—
314C4×D4—221no—
315#117—111no—
316#117—111no—
317#117—221no—
318#117—221no—
319C2×C42—221no—
320C2×C42—221no—
321C2×C42C22×D1111yescharacteristic
322#107—111no—
323#107—111no—
324#106—111no—
325#106—111no—
326C4⋊C8—222no—
327C4⋊C8—222no—
328C4⋊C8—221no—
329C4⋊C8C22×D1112yes—
330C4⋊C8C22×D1112yes—
331#103—111no—
332#103—111no—
333#103—111no—
334#103—111no—
335#102—111no—
336#102—111no—
337#102—111no—
338#102—111no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—222no—
342C22⋊C8—222no—
343C22⋊C8—221no—
344#97—21no—
345#97—21no—
346#97—111no—
347#97—111no—
348#97—222no—
349C4×C8—112no—
350C4×C8—112no—
351C4×C8—222no—
352C4×C8C4×D1111yescharacteristic
353C4×C8C4×D1111yescharacteristic
354C4×C8C22×D1111yescharacteristic
355C4×C8C22×D1111yescharacteristic
356C2×C11—41no—
357C2×C11D4×M1611yescharacteristic
358C2×C11#294311yescharacteristic
359C2×C11#295711yescharacteristic
360D11—42no—
361D11—81no—
362#41—222no—
363#41—222no—
364#41—441no—
365#41—441no—
366C2×Q8—111no—
367C2×Q8—111no—
368C2×D4—111no—
369C2×D4—111no—
370C2×D4—221no—
371C2×D4—221no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4C2×C4×D1111yescharacteristic
379C22×C4D4×D1111yescharacteristic
380C22×C4#434311yescharacteristic
381Q16—222no—
382SD16—114no—
383SD16—222no—
384D8—222no—
385M16—444no—
386M16—442no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—41no—
391C2×C8—112no—
392C2×C8—112no—
393C2×C8—222no—
394C2×C8—444no—
395C2×C8C2×C4×D1111yescharacteristic
396C2×C8C2×C4×D1111yescharacteristic
397C2×C8C2×C4×D1111yescharacteristic
398C2×C8C2×C4×D1111yescharacteristic
399C4⋊C4—111no—
400C4⋊C4—111no—
401C4⋊C4—111no—
402C4⋊C4—111no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C22⋊C4—221no—
408C22⋊C4—221no—
409C22⋊C4—221no—
410C22⋊C4—221no—
411C22⋊C4—221no—
412C22⋊C4—221no—
413C42—221no—
414C42—221no—
415C42—221no—
416C42—221no—
417C42—221no—
418C42—221no—
419C42C2×C4×D1111yescharacteristic
420C42D4×D1111yescharacteristic
421C42#434311yescharacteristic
422C42C23×D1111yescharacteristic
423C11#1804111yescharacteristic, complemented, Sylow
424C23—221no—
425C23—221no—
426C23#6694611yescharacteristic
427Q8—112no—
428Q8—221no—
429Q8—221no—
430Q8—221no—
431D4—112no—
432D4—221no—
433D4—221no—
434D4—221no—
435D4—442no—
436D4—442no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—881no—
452C2×C4—881no—
453C2×C4#6694611yescharacteristic
454C2×C4#6694611yescharacteristic
455C2×C4#6694611yescharacteristic
456C2×C4C22×C4×D1111yescharacteristic
457C2×C4C2×D4×D1111yescharacteristic
458C2×C4C2×#434311yescharacteristic
459C8—21no—
460C8—21no—
461C8—21no—
462C8—42no—
463C8—42no—
464C8—222no—
465C8—222no—
466C8—442no—
467C8M16×D1112yes—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—222no—
472C22—441no—
473C22—441no—
474C22—441no—
475C22—441no—
476C22—441no—
477C22C2×#6694611yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—222no—
483C4—441no—
484C4—441no—
485C4—441no—
486C4—441no—
487C4—441no—
488C4C2×M16×D1111yescharacteristic
489C4#1062327611yescharacteristic
490C4#1062329912yes—
491C2—41no—
492C2—442no—
493C2—881no—
494C2#1307735111yescharacteristic
495C2#1307741611yescharacteristic
496C2#1307753211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1568C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C4
cosocleC42×C11C24
hypercenter#1568D11
hypocenterC11#18041
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
1. #13077633C2semidirect
2. #13077628C2semidirect
4. #13067517C2semidirect
5. #13067486C2semidirect
6. #13067479C2semidirect
7. #13067427C2semidirect
8. #13067048C2semidirect
9. #13067048C2semidirect
10. #13066905C2semidirect
11. C11×#1568C2semidirect
173. #4314M16semidirect
183. #1568D11semidirect
423. C11#18041semidirect

Maximal subgroups

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

subgroupindex
#130776332
#130776282
C4×#669572
#130675172
#130674862
#130674792
#130674272
#130670482
#130669052
C11×#15682
#1804111