Finite Group Databasebeta

← #14736360

Subgroups — #14736360

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078941C211yesmaximal, characteristic, complemented
2#13078620C211yesmaximal, characteristic, complemented
3#13078617C211yesmaximal, characteristic
4C2×#10622451C211yesmaximal, characteristic, complemented
5#13068194C212yesmaximal, complemented
6#13068180C212yesmaximal, complemented
7#13068166C212yesmaximal, complemented
8#13068152C212yesmaximal, complemented
9#13067362C211yesmaximal, characteristic, complemented
10#13067266C211yesmaximal, characteristic, complemented
11C11×#1542C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C22×#4313—21no—
14#10623008C2211yescharacteristic
15C2×C4×D44C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×(C2×D11)⋊C8—21no—
19#10622706C2211yescharacteristic, complemented
20#10622706C2211yescharacteristic, complemented
21#10622701C2211yescharacteristic, complemented
22#10622701C2211yescharacteristic, complemented
23#10622697C2212yes—
24#10622696C2212yes—
25#10622681—21no—
26#10622681—21no—
27#10622659—21no—
28#10622656—21no—
29C4×#4325—22no—
30#10622615—21no—
31#10622615—21no—
32#10622538C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622459C2212yes—
35#10622456C2212yes—
36#10622451—21no—
37#10622451—21no—
38#10622451C2212yes—
39#10622451C2212yes—
40#10622349—21no—
41#10622345—21no—
42C4×D88—22no—
43C11×#333C2212yescomplemented
44C11×#332C2212yescomplemented
45#10622123C2212yescomplemented
46#10622120C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C2×#4339—21no—
50C22×D44D411yescharacteristic
51C22×C4×D11—21no—
52C22×C8×C11—21no—
53C11×C4⋊Q8C2311yescharacteristic
54C11×C4⋊Q8C2311yescharacteristic
55C11×#125—21no—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4325—22no—
63#66983—21no—
64#66983—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×C4⋊Dic11D411yescharacteristic
67C22×C11⋊C8D411yescharacteristic
68C22×C11⋊C8D411yescharacteristic
69C2×D88—22no—
70C2×#4313—22no—
71C2×#4313—22no—
72C2×#4313—44no—
73#66928—21no—
74#66927C2311yescharacteristic
75C4×D44—21no—
76C4×D44—21no—
77C4×D44—21no—
78C4×D44—21no—
79C4×D44D412yes—
80C4×D44C2312yes—
81#66922C2311yescharacteristic
82C11×C4⋊C8—21no—
83C11×C4⋊C8C2312yes—
84C11×C4⋊C8C2312yes—
85C11×C22⋊C8—21no—
86C4×C8×C11—21no—
87#66899—22no—
88C22⋊(C11⋊C8)—21no—
89#66885—22no—
90#66885—22no—
91(C2×D11)⋊C8—22no—
92(C2×D11)⋊C8—22no—
93#66882—22no—
94#66874—21no—
95#66874—21no—
96#66874—21no—
97#66874—21no—
98#66873—22no—
99#66873—21no—
100#66873—21no—
101#66873—21no—
102#66873—21no—
103#66872—22no—
104C4⋊(C11⋊C8)C2312yes—
105C4×C11⋊C8—21no—
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110#19142—111nomaximal, Sylow
111C23×D11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C2×C22⋊D11—41no—
118C22×Dic11—21no—
119#4339—42no—
120#4339—42no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—42no—
126C2×D44C2×D412yes—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—41no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C2×Dic22—21no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—42no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11—41no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148#4325—44no—
149(C2×D11)⋊C4—22no—
150(C2×D11)⋊C4—22no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11C2×D412yes—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164D88—44no—
165#4313—44no—
166#4313—44no—
167#3131—111no—
168#3101—111no—
169#3100—111no—
170C2×#436—111no—
171#1703—112no—
172#1701—112no—
173#1699—112no—
174#1697—112no—
175#1564—111no—
176#1542D1111yescharacteristic, complemented
177#1540—111no—
178C23×C11#12111yescharacteristic
179C22×D11—22no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—41no—
184Q8×C11—42no—
185Q8×C11—81no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#13512yes—
194C2×C4×C11AGL(1,ℤ/8)12yes—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C22⋊D11—82no—
199C2×Dic11—22no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202D44—22no—
203D44—22no—
204D44—42no—
205D44—41no—
206D44—41no—
207D44—42no—
208D44—81no—
209C4×D11—42no—
210C4×D11—42no—
211C4×D11—44no—
212C4×D11—82no—
213Dic22—41no—
214Dic22—41no—
215C8×C11—42no—
216C8×C11—42no—
217C11⋊C8—21no—
218C11⋊C8—21no—
219C11⋊C8—21no—
220C11⋊C8—21no—
221C11⋊C8—42no—
222C22×M16—221no—
223#533C2×D1111yescharacteristic
224#532—111no—
225C2×C4×D4—111no—
226#488—221no—
227#488—221no—
228#487—111no—
229#487—111no—
230#486—111no—
231#486—111no—
232#483—221no—
233#480—221no—
234#476—112no—
235#474—112no—
236#461—112no—
237#459—112no—
238#450—221no—
239#447—221no—
240C4×SD16—222no—
241C4×D8—222no—
242#436—112no—
243#436—112no—
244#436—221no—
245#436—221no—
246#431—111no—
247#431C2×D1111yescharacteristic
248C2×C4⋊C8C2×D1111yescharacteristic
249#416—221no—
250#416—221no—
251C2×C22⋊C8—221no—
252C2×C4×C8—111no—
253#335—112no—
254#334—112no—
255#333C2×D1112yescomplemented
256#332—112no—
257#332C2×D1112yescomplemented
258#331—112no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11#46312yes—
262C22×C11C2×#12111yescharacteristic
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—84no—
267C2×D11—81no—
268C2×D11—81no—
269C2×D11—81no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11#46312yes—
276C4×C11C2×#13511yescharacteristic
277C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
278C4×C11#57512yes—
279Dic11—42no—
280Dic11—81no—
281C2×#41—221no—
282C22×D4—111no—
283C23×C4—221no—
284C2×SD16—222no—
285C2×D8—222no—
286C2×M16—222no—
287C2×M16—222no—
288C2×M16—444no—
289C22×C8—21no—
290C22×C8—111no—
291C22×C8—111no—
292C4⋊Q8—111no—
293C4⋊Q8C22×D1111yescharacteristic
294C4⋊Q8C22×D1111yescharacteristic
295#127—111no—
296#125—21no—
297#124—221no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300#121—221no—
301#121—221no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×D4—112no—
305C4×D4—112no—
306C4×D4—221no—
307C4×D4—221no—
308C4×D4—221no—
309C4×D4—221no—
310#117—21no—
311C2×C4⋊C4—111no—
312C2×C22⋊C4—221no—
313C2×C42C22×D1111yescharacteristic
314#107—222no—
315#106—222no—
316C4⋊C8—21no—
317C4⋊C8—112no—
318C4⋊C8C22×D1112yes—
319C4⋊C8C22×D1112yes—
320#103—221no—
321#103—221no—
322#103—221no—
323#103—221no—
324#103—222no—
325#102—221no—
326#102—221no—
327#102—221no—
328#102—221no—
329#102—222no—
330#102—222no—
331#102—222no—
332C22⋊C8—21no—
333C22⋊C8—222no—
334C22⋊C8—222no—
335C22⋊C8—221no—
336C4×C8—21no—
337C4×C8—111no—
338C4×C8—111no—
339C4×C8—111no—
340C4×C8—111no—
341C4×C8—221no—
342C2×C11—22no—
343C2×C11C2×#46311yescharacteristic
344C2×C11#305411yescharacteristic
345C2×C11#306711yescharacteristic
346D11—82no—
347D11—161no—
348C24—221no—
349#41—442no—
350#41—442no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—221no—
354C2×D4—112no—
355C2×D4—221no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—442no—
360C2×D4—441no—
361C22×C4—221no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—442no—
365C22×C4—442no—
366C22×C4—441no—
367C22×C4#433911yescharacteristic
368C22×C4D4×D1111yescharacteristic
369C22×C4D4×D1111yescharacteristic
370SD16—444no—
371D8—444no—
372M16—444no—
373M16—444no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—42no—
377C2×C8—111no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—112no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C22⋊C4—41no—
395C22⋊C4—222no—
396C22⋊C4—222no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C42—41no—
400C42#433911yescharacteristic
401C42D4×D1111yescharacteristic
402C42D4×D1111yescharacteristic
403C42C23×D1111yescharacteristic
404C11#1914211yescharacteristic, complemented, Sylow
405C23—222no—
406C23—442no—
407C23—442no—
408C23—442no—
409C23—441no—
410C23#6693711yescharacteristic
411Q8—42no—
412Q8—81no—
413Q8—441no—
414Q8—441no—
415D4—222no—
416D4—222no—
417D4—442no—
418D4—441no—
419D4—441no—
420D4—442no—
421D4—881no—
422D4—882no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—222no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—444no—
432C2×C4—441no—
433C2×C4—882no—
434C2×C4#6693711yescharacteristic
435C2×C4#6693711yescharacteristic
436C2×C4#6693711yescharacteristic
437C2×C4#6696712yes—
438C2×C4#6697212yes—
439C2×C4C2×#433911yescharacteristic
440C2×C4C2×D4×D1111yescharacteristic
441C2×C4C2×D4×D1111yescharacteristic
442C8—42no—
443C8—42no—
444C8—221no—
445C8—221no—
446C8—221no—
447C8—221no—
448C8—442no—
449C22—21no—
450C22—21no—
451C22—442no—
452C22—442no—
453C22—442no—
454C22—884no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22#1062243212yes—
459C22C2×#6693711yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—81no—
464C4—81no—
465C4—442no—
466C4—881no—
467C4#1062243212yes—
468C4C2×#6696711yescharacteristic
469C4C2×#6697211yescharacteristic
470C4#1062329912yes—
471C2—22no—
472C2—882no—
473C2—1761no—
474C2C2×#1062243211yescharacteristic
475C2#1307822411yescharacteristic
476C2#1307833511yescharacteristic
subgroupG/H
centerC2×C4#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radical#13078617C2
hypercenter#1542D11
hypocenterC11#19142
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #13078941C2semidirect
2. #13078620C2semidirect
4. C2×#10622451C2semidirect
5. #13068194C2semidirect
6. #13068180C2semidirect
7. #13068166C2semidirect
8. #13068152C2semidirect
9. #13067362C2semidirect
10. #13067266C2semidirect
11. C11×#1542C2semidirect
19. #10622706C22semidirect
20. #10622706C22semidirect
21. #10622701C22semidirect
22. #10622701C22semidirect
43. C11×#333C22semidirect
44. C11×#332C22semidirect
45. #10622123C22semidirect
46. #10622120C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
176. #1542D11semidirect
255. #333C2×D11semidirect
257. #332C2×D11semidirect
404. C11#19142semidirect

Maximal subgroups

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

subgroupindex
#130789412
#130786202
#130786172
C2×#106224512
#130681942
#130681802
#130681662
#130681522
#130673622
#130672662
C11×#15422
#1914211