Finite Group Databasebeta

← #14724740

Subgroups — #14724740

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#13077359C211yesmaximal, characteristic, complemented
3D4×#4318C211yesmaximal, characteristic, complemented
4#13067527C212yesmaximal, complemented
5#13067483C212yesmaximal, complemented
6#13067477C212yesmaximal, complemented
7#13067437C212yesmaximal, complemented
8#13067386C211yesmaximal, characteristic, complemented
9#13067068C211yesmaximal, characteristic, complemented
10#13066905C211yesmaximal, characteristic, complemented
11C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4318—21no—
14C2×#66954—21no—
15#10623008C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18#10622830C412yes—
19#10622820—21no—
20#10622723—21no—
21#10622628C411yescharacteristic
22#10622628C411yescharacteristic
23C4×#4323C2212yes—
24C4×#4323C2212yes—
25#10622625C2212yes—
26#10622624—22no—
27D4×C11⋊C8C2212yes—
28#10622620C411yescharacteristic
29#10622620C411yescharacteristic
30#10622580C412yes—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33C4×#4318C2211yescharacteristic
34#10622451C2212yescomplemented
35#10622449—22no—
36#10622447C2212yescomplemented
37C11×D4⋊C8C2211yescharacteristic
38C11×D4⋊C8C2211yescharacteristic
39C11×D4⋊C8C2211yescharacteristic
40C11×D4⋊C8C2211yescharacteristic
41#10622118C2212yescomplemented
42#10622118C2212yescomplemented
43#10622097C2212yescomplemented
44#10622097C2212yescomplemented
45#10622093C2212yescomplemented
46#10622092C2212yescomplemented
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11—21no—
49C2×#4339—21no—
50C22×C8×C11—21no—
51C22×C8×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11C2×C411yescharacteristic
55C4×D4×C11C2×C411yescharacteristic
56C4×D4×C11C2311yescharacteristic
57C4×D4×C11C2311yescharacteristic
58C2×C11×C4⋊C4C2×C411yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C2×#4323C2×C412yes—
62C2×#4323C2×C412yes—
63#66983—21no—
64#66983C2×C412yes—
65C2×#4318—21no—
66C2×#4318—22no—
67C2×#4318—44no—
68C2×#4318D411yescharacteristic
69C2×#4318D411yescharacteristic
70C22×C11⋊C8—22no—
71#66954—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⋊C8C2311yescharacteristic
81C11×C4⋊C8C2311yescharacteristic
82C4×C8×C11—21no—
83C4×C8×C11C2311yescharacteristic
84C4×C8×C11C2311yescharacteristic
85#66896C2×C412yes—
86#66896C2×C412yes—
87C22⋊(C11⋊C8)—22no—
88C22⋊(C11⋊C8)—22no—
89C22⋊(C11⋊C8)C2×C412yes—
90(C2×D11)⋊C8—22no—
91(C2×D11)⋊C8—22no—
92#66873C2×C412yes—
93#66873C2×C412yes—
94#66871C2×C412yes—
95#66871C2×C412yes—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2×C411yescharacteristic
98C4⋊(C11⋊C8)C2×C411yescharacteristic
99C4⋊(C11⋊C8)C2312yes—
100#66867D412yes—
101C4×C11⋊C8C2312yes—
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—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—42no—
133C2×C8×C11—42no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4C22×C411yescharacteristic
136C11×C4⋊C4C22×C411yescharacteristic
137C11×C22⋊C4—21no—
138C11×C22⋊C4—21no—
139C11×C22⋊C4—21no—
140C11×C22⋊C4—21no—
141C42×C11C22×C411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11#4111yescharacteristic
144C42×C11C2411yescharacteristic
145#4323—24no—
146#4323—42no—
147(C2×D11)⋊C4—22no—
148(C2×D11)⋊C4—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11C22×C412yes—
151#4318—22no—
152#4318—22no—
153#4318—44no—
154#4318—42no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—44no—
157C2×C11⋊C8C22×C412yes—
158C2×C11⋊C8C22×C412yes—
159C2×C11⋊C8C2×D412yes—
160C2×C11⋊C8C2×D412yes—
161#4313—44no—
162C8×D11—44no—
163#3100—111no—
164#2935—111no—
165D4×M16—111no—
166#1594—112no—
167#1586—112no—
168#1586—112no—
169#1580—112no—
170#1570—111no—
171#1492—111no—
172C2×D4⋊C8D1111yescharacteristic, complemented
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—41no—
217C8×C11—41no—
218C8×C11—41no—
219C11⋊C8—22no—
220C11⋊C8—22no—
221C11⋊C8—22no—
222C11⋊C8—22no—
223C11⋊C8—42no—
224C2×#131—221no—
225C22×M16—221no—
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#436—112no—
238#435—222no—
239#435—222no—
240C8×D4—112no—
241C8×D4—112no—
242#431—111no—
243#423—111no—
244C2×C4⋊C8C2×D1111yescharacteristic
245#408—221no—
246#407—221no—
247C4×M16—111no—
248C2×C4×C8C2×D1111yescharacteristic
249#334—112no—
250#334—112no—
251D4⋊C8—112no—
252D4⋊C8—112no—
253D4⋊C8C2×D1111yescharacteristic
254D4⋊C8C2×D1111yescharacteristic
255D4⋊C8C2×D1111yescharacteristic
256D4⋊C8C2×D1111yescharacteristic
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—111no—
291C2×M16—111no—
292C2×M16—222no—
293C2×M16—222no—
294C2×M16—221no—
295C2×M16—444no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—222no—
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—112no—
322C4⋊C8—221no—
323C4⋊C8C22×D1111yescharacteristic
324C4⋊C8C22×D1111yescharacteristic
325#102—112no—
326#102—112no—
327#102—112no—
328#102—112no—
329C22⋊C8—112no—
330C22⋊C8—222no—
331C22⋊C8—222no—
332C22⋊C8—222no—
333C22⋊C8—222no—
334#97—112no—
335C4×C8—21no—
336C4×C8—112no—
337C4×C8—112no—
338C4×C8C22×D1111yescharacteristic
339C4×C8C22×D1111yescharacteristic
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×C4D4×D1111yescharacteristic
370C22×C4#434111yescharacteristic
371D8—224no—
372D8—442no—
373M16—222no—
374M16—222no—
375M16—444no—
376M16—444no—
377M16—442no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—42no—
383C2×C8—42no—
384C2×C8—112no—
385C2×C8—112no—
386C2×C8—112no—
387C2×C8—112no—
388C2×C8—222no—
389C2×C8—444no—
390C2×C8—444no—
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
403C42D4×D1111yescharacteristic
404C42#434111yescharacteristic
405C42C23×D1111yescharacteristic
406C11#1800111yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—42no—
410C23—42no—
411C23—81no—
412C23—222no—
413C23(C22⋊D11)⋊C411yescharacteristic
414Q8—442no—
415D4—21no—
416D4—21no—
417D4—21no—
418D4—42no—
419D4—222no—
420D4—222no—
421D4—444no—
422D4—442no—
423D4—881no—
424D4#6695412yescomplemented
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×C4(C22⋊D11)⋊C411yescharacteristic
441C2×C4(C22⋊D11)⋊C411yescharacteristic
442C2×C4(C22⋊D11)⋊C411yescharacteristic
443C2×C4#6696412yes—
444C2×C4#6696712yes—
445C2×C4C22×C4×D1111yescharacteristic
446C2×C4C2×D4×D1111yescharacteristic
447C2×C4C2×#434111yescharacteristic
448C8—22no—
449C8—41no—
450C8—41no—
451C8—41no—
452C8—222no—
453C8—222no—
454C8—222no—
455C8—222no—
456C8—442no—
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#1062239812yes—
470C22C2×(C22⋊D11)⋊C411yescharacteristic
471C4—21no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—442no—
477C4#1062239812yes—
478C4C2×#6695411yescharacteristic
479C4#1062327611yescharacteristic
480C4C2×#6696411yescharacteristic
481C4C2×#6696711yescharacteristic
482C2—22no—
483C2—42no—
484C2—81no—
485C2—882no—
486C2#1307733711yescharacteristic
487C2C2×#1062239811yescharacteristic
488C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC22×C11C2×C4×D4
prime radical#13078616C2
cosocleC42×C11C24
hypercenterC2×D4⋊C8D11
hypocenterC11#18001
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13077359C2semidirect
3. D4×#4318C2semidirect
4. #13067527C2semidirect
5. #13067483C2semidirect
6. #13067477C2semidirect
7. #13067437C2semidirect
8. #13067386C2semidirect
9. #13067068C2semidirect
10. #13066905C2semidirect
11. C2×C11×D4⋊C8C2semidirect
34. #10622451C22semidirect
36. #10622447C22semidirect
41. #10622118C22semidirect
42. #10622118C22semidirect
43. #10622097C22semidirect
44. #10622097C22semidirect
45. #10622093C22semidirect
46. #10622092C22semidirect
172. C2×D4⋊C8D11semidirect
185. D4×C11#131semidirect
406. C11#18001semidirect
424. D4#66954semidirect

Maximal subgroups

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

subgroupindex
#130786162
#130773592
D4×#43182
#130675272
#130674832
#130674772
#130674372
#130673862
#130670682
#130669052
C2×C11×D4⋊C82
#1800111