Finite Group Databasebeta

← #14724744

Subgroups — #14724744

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078616C211yesmaximal, characteristic
2#13077362C211yesmaximal, characteristic, complemented
3#13067528C212yesmaximal, complemented
4#13067480C212yesmaximal, complemented
5#13067478C212yesmaximal, complemented
6#13067438C212yesmaximal, complemented
7#13067388C211yesmaximal, characteristic, complemented
8#13067066C211yesmaximal, characteristic, complemented
9C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
10#13066903C211yesmaximal, characteristic, complemented
11D4×C11×M16C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66960—21no—
15#10623008C2211yescharacteristic
16C11×#436C2212yes—
17C11×#435—22no—
18C8×D4×C11C2212yes—
19C11×#423C2211yescharacteristic
20C11×#407—21no—
21C4×C11×M16C2211yescharacteristic
22#10622830C412yes—
23#10622742—21no—
24#10622628C411yescharacteristic
25#10622628C411yescharacteristic
26C4×#4323C2212yes—
27C4×#4323C2212yes—
28#10622620C411yescharacteristic
29#10622620C411yescharacteristic
30#10622580C412yes—
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622319—22no—
35#10622301C2212yescomplemented
36C8×D44C2212yescomplemented
37D4⋊(C11⋊C8)C2211yescharacteristic
38D4⋊(C11⋊C8)C2211yescharacteristic
39D4⋊(C11⋊C8)C2211yescharacteristic
40D4⋊(C11⋊C8)C2211yescharacteristic
41#10622121C2212yescomplemented
42#10622121C2212yescomplemented
43#10622118C2212yescomplemented
44#10622118C2212yescomplemented
45#10622092C2212yescomplemented
46#10622092C2212yescomplemented
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11—21no—
49C2×#4339—21no—
50C2×C11×M16—21no—
51C2×C11×M16—22no—
52C2×C11×M16—44no—
53C2×C11×M16D411yescharacteristic
54C2×C11×M16D411yescharacteristic
55C22×C8×C11—22no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11C2×C411yescharacteristic
59C4×D4×C11C2×C411yescharacteristic
60C4×D4×C11C2311yescharacteristic
61C4×D4×C11C2311yescharacteristic
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4323C2×C412yes—
66C2×#4323C2×C412yes—
67#66983—21no—
68#66983C2×C412yes—
69C22×C11⋊C8—21no—
70C22×C11⋊C8—21no—
71#66960—44no—
72C2×#4313—22no—
73C2×C8×D11—22no—
74#66928—21no—
75#66927C2×C411yescharacteristic
76C4×D44—21no—
77C4×D44C2312yes—
78#66922C2×C411yescharacteristic
79C11×C4⋊C8—21no—
80C11×C4⋊C8C2312yes—
81C11×C22⋊C8—22no—
82C11×C22⋊C8—22no—
83C11×#97D412yes—
84C4×C8×C11C2312yes—
85#66896C2×C412yes—
86#66896C2×C412yes—
87C22⋊(C11⋊C8)C2×C412yes—
88(C2×D11)⋊C8—22no—
89(C2×D11)⋊C8—22no—
90#66873C2×C412yes—
91#66873C2×C412yes—
92#66871C2×C412yes—
93#66871C2×C412yes—
94C4⋊(C11⋊C8)—21no—
95C4⋊(C11⋊C8)C2×C411yescharacteristic
96C4⋊(C11⋊C8)C2×C411yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4×C11⋊C8—21no—
100C4×C11⋊C8C2311yescharacteristic
101C4×C11⋊C8C2311yescharacteristic
102C4×C11⋊C8C2312yes—
103#18001—111nomaximal, Sylow
104C24×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—41no—
108C2×D4×C11C22×C411yescharacteristic
109C2×D4×C11C22×C411yescharacteristic
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×C22⋊D11—22no—
121#4339—42no—
122#4339—42no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44C22×C412yes—
126C2×C4×D11—22no—
127C2×Dic22—21no—
128C11×M16—22no—
129C11×M16—22no—
130C11×M16—44no—
131C11×M16—42no—
132C2×C8×C11—22no—
133C2×C8×C11—44no—
134C2×C8×C11C2×D412yes—
135C2×C8×C11C2×D412yes—
136C11×C4⋊C4—21no—
137C11×C4⋊C4C22×C411yescharacteristic
138C11×C4⋊C4C22×C411yescharacteristic
139C11×C22⋊C4—21no—
140C11×C22⋊C4—21no—
141C11×C22⋊C4—21no—
142C11×C22⋊C4—21no—
143C42×C11C22×C411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147#4323—24no—
148#4323—42no—
149(C2×D11)⋊C4—22no—
150(C2×D11)⋊C4—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11C22×C412yes—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—42no—
158C2×C11⋊C8—42no—
159C2×C11⋊C8C22×C412yes—
160C2×C11⋊C8C22×C412yes—
161#4313—44no—
162C8×D11—44no—
163#3100—111no—
164#2935—111no—
165D4×M16D1111yescharacteristic, complemented
166#1594—112no—
167#1586—112no—
168#1586—112no—
169#1580—112no—
170#1570—111no—
171#1492—111no—
172C2×D4⋊C8—111no—
173#1451—111no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—81no—
179C23×C11C4×D411yescharacteristic
180C22×D11—22no—
181D4×C11—21no—
182D4×C11—21no—
183D4×C11—21no—
184D4×C11—42no—
185D4×C11#13112yescomplemented
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11C4×D411yescharacteristic
199C2×C4×C11C4×D411yescharacteristic
200C2×C4×C11C4×D411yescharacteristic
201C2×C4×C11AGL(1,ℤ/8)12yes—
202C2×C4×C11AGL(1,ℤ/8)12yes—
203C2×C4×C11C23×C411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C22⋊D11—44no—
207C2×Dic11—22no—
208D44—22no—
209D44—22no—
210D44—42no—
211D44—81no—
212C4×D11—42no—
213C4×D11—42no—
214Dic22—42no—
215C8×C11—22no—
216C8×C11—22no—
217C8×C11—42no—
218C11⋊C8—22no—
219C11⋊C8—22no—
220C11⋊C8—22no—
221C11⋊C8—41no—
222C11⋊C8—41no—
223C11⋊C8—41no—
224C2×#131—221no—
225C22×M16—21no—
226#532—111no—
227C2×C4×D4C2×D1111yescharacteristic
228#480—112no—
229#474—111no—
230#474—111no—
231#459—111no—
232#459—111no—
233#447—112no—
234C4×D8—112no—
235C4×D8—112no—
236#436—112no—
237#436C2×D1112yes—
238#435—22no—
239#435—222no—
240C8×D4—112no—
241C8×D4C2×D1112yes—
242#431—111no—
243#423C2×D1111yescharacteristic
244C2×C4⋊C8—111no—
245#408—221no—
246#407—21no—
247C4×M16C2×D1111yescharacteristic
248C2×C4×C8—111no—
249#334—112no—
250#334—112no—
251D4⋊C8—111no—
252D4⋊C8—111no—
253D4⋊C8—111no—
254D4⋊C8—111no—
255D4⋊C8—112no—
256D4⋊C8—112no—
257#322—112no—
258#322—112no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—22no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—84no—
268C22×C11#44212yes—
269C22×C11C2×C4×D411yescharacteristic
270C2×D11—42no—
271C2×D11—42no—
272C2×D11—42no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—41no—
277C4×C11—41no—
278C4×C11#44212yes—
279C4×C11C2×#13111yescharacteristic
280C4×C11#56811yescharacteristic
281C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
282C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
283Dic11—42no—
284C2×#41—221no—
285C22×D4C4×D1111yescharacteristic
286C23×C4—21no—
287C2×D8—112no—
288C2×D8—112no—
289#131—444no—
290C2×M16—21no—
291C2×M16—22no—
292C2×M16—44no—
293C2×M16—222no—
294C2×M16C22⋊D1111yescharacteristic
295C2×M16C22⋊D1111yescharacteristic
296C22×C8—22no—
297C22×C8—221no—
298C22×C8—221no—
299C22×C8—222no—
300C4⋊Q8—111no—
301#127—111no—
302#124—221no—
303#121—112no—
304#121—221no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4—112no—
308C4×D4—221no—
309C4×D4C4×D1111yescharacteristic
310C4×D4C4×D1111yescharacteristic
311C4×D4C22×D1111yescharacteristic
312C4×D4C22×D1111yescharacteristic
313C2×C4⋊C4C4×D1111yescharacteristic
314C2×C22⋊C4—21no—
315C2×C42C22×D1111yescharacteristic
316#107—112no—
317#107—112no—
318C4⋊C8—21no—
319C4⋊C8—111no—
320C4⋊C8—111no—
321C4⋊C8—111no—
322C4⋊C8—111no—
323C4⋊C8—221no—
324C4⋊C8C22×D1112yes—
325#102—112no—
326#102—112no—
327#102—112no—
328#102—112no—
329C22⋊C8—22no—
330C22⋊C8—22no—
331C22⋊C8—112no—
332C22⋊C8—222no—
333C22⋊C8—222no—
334#97C22⋊D1112yes—
335C4×C8—112no—
336C4×C8—111no—
337C4×C8—111no—
338C4×C8—221no—
339C4×C8C22×D1112yes—
340C2×C11—22no—
341C2×C11—42no—
342C2×C11—81no—
343C2×C11#293311yescharacteristic
344C2×C11C2×#44211yescharacteristic
345C2×C11#295611yescharacteristic
346D11—82no—
347C24—21no—
348#41—442no—
349#41—442no—
350C2×Q8—221no—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—41no—
354C2×D4—112no—
355C2×D4—222no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4C2×C4×D1111yescharacteristic
359C2×D4C2×C4×D1111yescharacteristic
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—222no—
368C22×C4C2×C4×D1111yescharacteristic
369C22×C4#433911yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371D8—224no—
372D8—442no—
373M16—22no—
374M16—22no—
375M16—44no—
376M16—42no—
377M16—444no—
378C2×C8—22no—
379C2×C8—44no—
380C2×C8—112no—
381C2×C8—112no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—221no—
385C2×C8—221no—
386C2×C8—444no—
387C2×C8—442no—
388C2×C8—442no—
389C2×C8C2×C22⋊D1112yes—
390C2×C8C2×C22⋊D1112yes—
391C4⋊C4—21no—
392C4⋊C4—112no—
393C4⋊C4—221no—
394C4⋊C4C2×C4×D1111yescharacteristic
395C4⋊C4C2×C4×D1111yescharacteristic
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—222no—
401C22⋊C4—222no—
402C42C2×C4×D1111yescharacteristic
403C42#433911yescharacteristic
404C42C2×C22⋊D1111yescharacteristic
405C42C23×D1111yescharacteristic
406C11#1800111yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—42no—
410C23—42no—
411C23—81no—
412C23—222no—
413C23C4×C22⋊D1111yescharacteristic
414Q8—442no—
415D4—21no—
416D4—21no—
417D4—21no—
418D4—42no—
419D4—222no—
420D4—222no—
421D4—444no—
422D4—442no—
423D4—881no—
424D4#6696012yescomplemented
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—222no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4C4×C22⋊D1111yescharacteristic
441C2×C4C4×C22⋊D1111yescharacteristic
442C2×C4C4×C22⋊D1111yescharacteristic
443C2×C4#6698512yes—
444C2×C4#6700212yes—
445C2×C4C22×C4×D1111yescharacteristic
446C2×C4C2×#433911yescharacteristic
447C2×C4C22×C22⋊D1111yescharacteristic
448C8—22no—
449C8—22no—
450C8—42no—
451C8—222no—
452C8—222no—
453C8—222no—
454C8—441no—
455C8—441no—
456C8—441no—
457C22—21no—
458C22—21no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—84no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22#1062262712yes—
470C22C2×C4×C22⋊D1111yescharacteristic
471C4—21no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—442no—
477C4#1062262712yes—
478C4C2×#6696011yescharacteristic
479C4#1062327611yescharacteristic
480C4C2×#6698511yescharacteristic
481C4C2×#6700211yescharacteristic
482C2—22no—
483C2—42no—
484C2—81no—
485C2—882no—
486C2#1307734111yescharacteristic
487C2C2×#1062262711yescharacteristic
488C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingD4×C11×M16C2
socleC22×C11C2×C4×D4
prime radical#13078616C2
cosocleC42×C11C24
hypercenterD4×M16D11
hypocenterC11#18001
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. #13077362C2semidirect
3. #13067528C2semidirect
4. #13067480C2semidirect
5. #13067478C2semidirect
6. #13067438C2semidirect
7. #13067388C2semidirect
8. #13067066C2semidirect
9. C2×D4⋊(C11⋊C8)C2semidirect
10. #13066903C2semidirect
11. D4×C11×M16C2semidirect
35. #10622301C22semidirect
36. C8×D44C22semidirect
41. #10622121C22semidirect
42. #10622121C22semidirect
43. #10622118C22semidirect
44. #10622118C22semidirect
45. #10622092C22semidirect
46. #10622092C22semidirect
165. D4×M16D11semidirect
185. D4×C11#131semidirect
406. C11#18001semidirect
424. D4#66960semidirect

Maximal subgroups

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

subgroupindex
#130786162
#130773622
#130675282
#130674802
#130674782
#130674382
#130673882
#130670662
C2×D4⋊(C11⋊C8)2
#130669032
D4×C11×M162
#1800111