Finite Group Databasebeta

← #14723482

Subgroups — #14723482

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077729C211yesmaximal, characteristic, complemented
2C4×#67003C211yesmaximal, characteristic
3#13067494C212yesmaximal, complemented
4#13067473C212yesmaximal, complemented
5#13067466C212yesmaximal, complemented
6#13067445C212yesmaximal, complemented
7C2×#10622117C211yesmaximal, characteristic, complemented
8#13067003C211yesmaximal, characteristic, complemented
9#13067001C211yesmaximal, characteristic, complemented
10#13066909C211yesmaximal, characteristic, complemented
11C11×#2988C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003C411yescharacteristic
14C4×#4339C2211yescharacteristic
15C8×Q8×C11C2212yes—
16C8×D4×C11—22no—
17C8×D4×C11C2212yes—
18C11×#431—21no—
19C11×#431C2211yescharacteristic
20C2×C11×C4⋊C8—21no—
21C2×C11×C4⋊C8C2211yescharacteristic
22#10622846C411yescharacteristic
23C4×#4326C411yescharacteristic
24C4×#4326C2211yescharacteristic
25C4×#4325C411yescharacteristic
26C4×#4325C2211yescharacteristic
27C4×#4324C411yescharacteristic
28C4×#4324C2211yescharacteristic
29C4×#4323C411yescharacteristic
30C4×#4323C2211yescharacteristic
31#10622615C411yescharacteristic
32#10622611C411yescharacteristic
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622450—21no—
37#10622448—21no—
38#10622343—22no—
39#10622301C2212yes—
40#10622292C2212yes—
41Q8⋊(C11⋊C8)C2212yes—
42D4⋊(C11⋊C8)C2212yes—
43#10622122C2212yes—
44#10622121C2212yes—
45#10622117C2212yes—
46#10622117C2212yes—
47#10622093C2212yes—
48#10622092C2212yes—
49C2×C11×#41C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C22×C8×C11—21no—
52C22×C8×C11—22no—
53C4×Q8×C11C2×C411yescharacteristic
54C4×Q8×C11C2311yescharacteristic
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11C2×C411yescharacteristic
58C4×D4×C11C2311yescharacteristic
59C11×#117—21no—
60C11×#117C2×C411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63#67003—24no—
64C2×#4326C2×C411yescharacteristic
65C2×#4325C2×C411yescharacteristic
66C2×#4324C2×C411yescharacteristic
67C2×#4323C2×C411yescharacteristic
68C4×C22⋊D11—21no—
69C4×C22⋊D11—21no—
70#66979C2×C411yescharacteristic
71C22×C11⋊C8—21no—
72C22×C11⋊C8C2×C411yescharacteristic
73C22×C11⋊C8C2×C411yescharacteristic
74C2×#4313—22no—
75C4×D44C2×C411yescharacteristic
76C4×D44C2311yescharacteristic
77#66925—21no—
78C42×D11—21no—
79C4×Dic22C2×C411yescharacteristic
80C4×Dic22C2311yescharacteristic
81C11×C4⋊C8—22no—
82C11×C4⋊C8—21no—
83C11×C4⋊C8D411yescharacteristic
84C11×C4⋊C8D411yescharacteristic
85C11×C4⋊C8C2312yes—
86C11×C22⋊C8—22no—
87C11×C22⋊C8D412yes—
88C4×C8×C11—22no—
89C4×C8×C11C2312yes—
90#66899C2×C411yescharacteristic
91#66899C2×C411yescharacteristic
92#66896C2×C411yescharacteristic
93#66896C2×C411yescharacteristic
94C22⋊(C11⋊C8)—21no—
95(C2×D11)⋊C8—22no—
96#66879—22no—
97Dic11⋊C8—22no—
98#66874C2×C411yescharacteristic
99#66874C2×C411yescharacteristic
100#66873C2×C411yescharacteristic
101#66873C2×C411yescharacteristic
102#66872C2×C411yescharacteristic
103#66872C2×C411yescharacteristic
104#66871C2×C411yescharacteristic
105#66871C2×C411yescharacteristic
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2312yes—
109C4×C11⋊C8C2×C411yescharacteristic
110C4×C11⋊C8C2×C411yescharacteristic
111C4×C11⋊C8C2312yes—
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2311yescharacteristic
114#17881—111nomaximal, Sylow
115C11×#41—22no—
116C11×#41M1614yescomplemented
117C2×Q8×C11C22×C411yescharacteristic
118C2×D4×C11—21no—
119C2×D4×C11C22×C411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C22⋊D11—21no—
127#4339—22no—
128#4339—22no—
129C2×D44C22×C411yescharacteristic
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×Dic22C22×C411yescharacteristic
134C2×C8×C11—22no—
135C2×C8×C11—81no—
136C2×C8×C11—82no—
137C2×C8×C11C2×D412yes—
138C2×C8×C11C2×D412yes—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4C22×C411yescharacteristic
142C11×C4⋊C4C22×C411yescharacteristic
143C11×C22⋊C4—21no—
144C11×C22⋊C4—21no—
145C11×C22⋊C4—21no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11C22×C411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11#4111yescharacteristic
152C42×C11C2411yescharacteristic
153C22⋊Dic11—21no—
154#4326—22no—
155#4325—22no—
156#4324—22no—
157#4323—22no—
158(C2×D11)⋊C4—21no—
159(C2×D11)⋊C4—21no—
160C4⋊Dic11C22×C411yescharacteristic
161C4⋊Dic11C22×C411yescharacteristic
162Dic11⋊C4—21no—
163Dic11⋊C4—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C4×Dic11—21no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—81no—
172C2×C11⋊C8C22×C411yescharacteristic
173C2×C11⋊C8C22×C411yescharacteristic
174C2×C11⋊C8C22×C411yescharacteristic
175C2×C11⋊C8C22×C411yescharacteristic
176#4313—82no—
177#2989—111no—
178#2988D1111yescharacteristic, complemented
179C4×#135—111no—
180#1588—112no—
181#1585—112no—
182#1584—112no—
183#1581—112no—
184C2×#335—111no—
185#1477—111no—
186#1477—111no—
187#1452—111no—
188C23×C11—21no—
189C23×C11C4×D411yescharacteristic
190C22×D11—21no—
191Q8×C11—21no—
192Q8×C11C2×M1612yes—
193D4×C11—24no—
194D4×C11—21no—
195D4×C11C2×M1612yes—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—24no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—81no—
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11C4×D411yescharacteristic
209C2×C4×C11C2×M1612yes—
210C2×C4×C11#13112yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C22⋊D11—42no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218D44—21no—
219D44—21no—
220C4×D11—41no—
221C4×D11—41no—
222C4×D11—42no—
223C4×D11—81no—
224Dic22—21no—
225Dic22—21no—
226C8×C11—22no—
227C8×C11—22no—
228C8×C11—42no—
229C11⋊C8—21no—
230C11⋊C8—21no—
231C11⋊C8—21no—
232C11⋊C8—21no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C2×#135—111no—
236C4×#41—111no—
237C4×#41C2×D1111yescharacteristic
238#446—112no—
239C8×Q8C2×D1112yes—
240C4×Q16—111no—
241C4×Q16—111no—
242C4×SD16—111no—
243C4×SD16—111no—
244C4×SD16—111no—
245C4×SD16—111no—
246C4×D8—111no—
247C4×D8—111no—
248#436—112no—
249#435—222no—
250C8×D4—22no—
251C8×D4C2×D1112yes—
252#432—221no—
253#431—21no—
254#431—111no—
255#431C2×D1111yescharacteristic
256#427—111no—
257#423—221no—
258C2×C4⋊C8—21no—
259C2×C4⋊C8—111no—
260C2×C4⋊C8C2×D1111yescharacteristic
261#416—111no—
262#416—111no—
263C2×C4×C8—111no—
264#335—112no—
265#335—112no—
266Q8⋊C8—112no—
267Q8⋊C8—112no—
268D4⋊C8—112no—
269D4⋊C8—112no—
270#322—112no—
271#322—112no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—22no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11#43512yes—
278C22×C11C2×C4×D411yescharacteristic
279C2×D11—41no—
280C2×D11—41no—
281C2×D11—41no—
282C4×C11—22no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11#43512yes—
289C4×C11C22×M1611yescharacteristic
290C4×C11C2×#13111yescharacteristic
291C4×C11#57611yescharacteristic
292C4×C11#57811yescharacteristic
293Dic11—41no—
294Dic11—41no—
295Dic11—41no—
296C2×#41—111no—
297C2×#41C4×D1111yescharacteristic
298#135—224no—
299C2×Q16—111no—
300C2×SD16—111no—
301C2×SD16—111no—
302C2×D8—111no—
303C2×M16—222no—
304C22×C8—21no—
305C22×C8—22no—
306C22×C8—111no—
307C22×C8—111no—
308C22×C8—221no—
309C4×Q8—111no—
310C4×Q8—111no—
311C4×Q8C4×D1111yescharacteristic
312C4×Q8C22×D1111yescharacteristic
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—111no—
316C4×D4—111no—
317C4×D4—221no—
318C4×D4—221no—
319C4×D4C4×D1111yescharacteristic
320C4×D4C22×D1111yescharacteristic
321#117—21no—
322#117—111no—
323#117—221no—
324#117C4×D1111yescharacteristic
325C2×C42—21no—
326C2×C42—221no—
327C2×C42C22×D1111yescharacteristic
328#107—111no—
329#107—111no—
330#106—111no—
331#106—111no—
332C4⋊C8—22no—
333C4⋊C8—21no—
334C4⋊C8—112no—
335C4⋊C8—222no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338C4⋊C8C22⋊D1111yescharacteristic
339C4⋊C8C22⋊D1111yescharacteristic
340C4⋊C8C22×D1112yes—
341#103—111no—
342#103—111no—
343#103—111no—
344#103—111no—
345#102—111no—
346#102—111no—
347#102—111no—
348#102—111no—
349C22⋊C8—22no—
350C22⋊C8—221no—
351C22⋊C8—222no—
352C22⋊C8C22⋊D1112yes—
353#97—222no—
354C4×C8—22no—
355C4×C8—111no—
356C4×C8—111no—
357C4×C8—111no—
358C4×C8—111no—
359C4×C8—112no—
360C4×C8C22×D1112yes—
361C2×C11—22no—
362C2×C11—42no—
363C2×C11C2×#43511yescharacteristic
364C2×C11#295111yescharacteristic
365C2×C11#295711yescharacteristic
366D11—81no—
367#41—22no—
368#41—222no—
369#41—222no—
370#41#431314yescomplemented
371C2×Q8—111no—
372C2×Q8C2×C4×D1111yescharacteristic
373C2×D4—21no—
374C2×D4—111no—
375C2×D4—221no—
376C2×D4C2×C4×D1111yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4C2×C4×D1111yescharacteristic
384C22×C4#433911yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386Q16—222no—
387SD16—222no—
388SD16—222no—
389D8—222no—
390M16—882no—
391C2×C8—22no—
392C2×C8—82no—
393C2×C8—81no—
394C2×C8—111no—
395C2×C8—111no—
396C2×C8—111no—
397C2×C8—111no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8—881no—
403C2×C8C2×C22⋊D1112yes—
404C2×C8C2×C22⋊D1112yes—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—111no—
408C4⋊C4—111no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4C2×C4×D1111yescharacteristic
412C4⋊C4C2×C4×D1111yescharacteristic
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—221no—
417C22⋊C4—221no—
418C22⋊C4—221no—
419C42—21no—
420C42—21no—
421C42—21no—
422C42—221no—
423C42—221no—
424C42—221no—
425C42C2×C4×D1111yescharacteristic
426C42#433911yescharacteristic
427C42C2×C22⋊D1111yescharacteristic
428C42C23×D1111yescharacteristic
429C11#1788111yescharacteristic, complemented, Sylow
430C23—21no—
431C23—221no—
432C23C4×C22⋊D1111yescharacteristic
433Q8—21no—
434Q8—221no—
435Q8—221no—
436Q8C2×#431312yes—
437D4—24no—
438D4—21no—
439D4—221no—
440D4—221no—
441D4—442no—
442D4C2×#431312yes—
443C2×C4—21no—
444C2×C4—24no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—442no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—881no—
460C2×C4C2×#431312yes—
461C2×C4#6695412yes—
462C2×C4C4×C22⋊D1111yescharacteristic
463C2×C4C4×C22⋊D1111yescharacteristic
464C2×C4C4×C22⋊D1111yescharacteristic
465C2×C4C22×C4×D1111yescharacteristic
466C2×C4C2×#433911yescharacteristic
467C2×C4C22×C22⋊D1111yescharacteristic
468C8—22no—
469C8—22no—
470C8—42no—
471C8—221no—
472C8—221no—
473C8—221no—
474C8—221no—
475C8—442no—
476C8—442no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—41no—
481C22—41no—
482C22—441no—
483C22—441no—
484C22—441no—
485C22#1062272412yes—
486C22C2×C4×C22⋊D1111yescharacteristic
487C4—21no—
488C4—21no—
489C4—22no—
490C4—21no—
491C4—41no—
492C4—41no—
493C4—441no—
494C4—441no—
495C4—441no—
496C4#1062272412yes—
497C4C22×#431311yescharacteristic
498C4C2×#6695411yescharacteristic
499C4#1062336611yescharacteristic
500C4#1062336911yescharacteristic
501C2—22no—
502C2—42no—
503C2—881no—
504C2C2×#1062272411yescharacteristic
505C2#1307748911yescharacteristic
506C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C4
cosocleC42×C11C24
hypercenter#2988D11
hypocenterC11#17881
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13077729C2semidirect
3. #13067494C2semidirect
4. #13067473C2semidirect
5. #13067466C2semidirect
6. #13067445C2semidirect
7. C2×#10622117C2semidirect
8. #13067003C2semidirect
9. #13067001C2semidirect
10. #13066909C2semidirect
11. C11×#2988C2semidirect
116. C11×#41M16semidirect
178. #2988D11semidirect
370. #41#4313semidirect
429. C11#17881semidirect

Maximal subgroups

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

subgroupindex
#130777292
C4×#670032
#130674942
#130674732
#130674662
#130674452
C2×#106221172
#130670032
#130670012
#130669092
C11×#29882
#1788111