Finite Group Databasebeta

← #14737304

Subgroups — #14737304

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic, complemented
2#13079536C211yesmaximal, characteristic
3#13078992C211yesmaximal, characteristic, complemented
4#13077359C211yesmaximal, characteristic, complemented
5#13068180C212yesmaximal, complemented
6#13068152C212yesmaximal, complemented
7#13068056C212yesmaximal, complemented
8#13068028C212yesmaximal, complemented
9#13067369C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#1542C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66954—21no—
14#10623008C2211yescharacteristic
15C2×#66927C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18#10622723—21no—
19#10622701C2212yes—
20#10622701C2212yes—
21#10622697C2212yescomplemented
22#10622696C2212yescomplemented
23#10622680—22no—
24#10622661—22no—
25#10622640—21no—
26#10622633—21no—
27#10622614—21no—
28#10622614—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C4×#4318C2211yescharacteristic
31#10622456C2212yes—
32#10622456C2212yes—
33#10622451C2212yescomplemented
34#10622449—22no—
35#10622447C2212yescomplemented
36#10622345—22no—
37#10622308—21no—
38#10622307—21no—
39C11×#333C2211yescharacteristic, complemented
40C11×#333C2211yescharacteristic, complemented
41C11×#332C2211yescharacteristic, complemented
42C11×#332C2211yescharacteristic, complemented
43#10622123C2212yes—
44#10622123C2212yes—
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C2×#4339—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×C8×C11—21no—
52C11×C4⋊Q8C2311yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C11×#117—21no—
60C2×C42×C11C2311yescharacteristic
61C2×#4325—22no—
62#66983—21no—
63#66983D412yes—
64C2×#4318D411yescharacteristic
65C2×#4318D411yescharacteristic
66C22×C11⋊C8—21no—
67C2×D88—22no—
68C2×D88—22no—
69#66954—44no—
70C2×#4313—22no—
71C2×C8×D11—22no—
72#66928—21no—
73#66927—21no—
74#66927—21no—
75#66927—21no—
76#66927D411yescharacteristic
77#66927C2312yes—
78C4×D44—21no—
79C4×D44C2312yes—
80#66922D411yescharacteristic
81C11×C4⋊C8—21no—
82C11×C4⋊C8C2311yescharacteristic
83C11×C4⋊C8C2311yescharacteristic
84C11×C4⋊C8C2311yescharacteristic
85C11×C4⋊C8C2311yescharacteristic
86C11×C22⋊C8—21no—
87C4×C8×C11—21no—
88#66899—22no—
89#66885—22no—
90#66885—22no—
91(C2×D11)⋊C8—22no—
92(C2×D11)⋊C8—22no—
93#66873—22no—
94#66873—22no—
95#66873—22no—
96#66873—22no—
97#66873—22no—
98#66872—22no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101#66867D412yes—
102C4×C11⋊C8C2312yes—
103#19234—111nomaximal, Sylow
104C23×D11—41no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×C22⋊D11—22no—
111#4339—42no—
112#4339—42no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—41no—
119C2×D44—41no—
120C2×D44—41no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44—81no—
124C2×D44—81no—
125C2×D44—82no—
126C2×D44C2×D412yes—
127C2×C4×D11—22no—
128C2×Dic22—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—42no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C22⋊C4—41no—
141C42×C11—41no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146#4325—82no—
147(C2×D11)⋊C4—22no—
148(C2×D11)⋊C4—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11C2×D412yes—
151#4318—22no—
152#4318—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—81no—
155C2×C11⋊C8C2×D412yes—
156C2×C11⋊C8C2×D412yes—
157D88—82no—
158D88—82no—
159#4313—44no—
160C8×D11—44no—
161#3246—111no—
162#3205—111no—
163#3138—111no—
164#2935—111no—
165#1701—112no—
166#1697—112no—
167#1681—112no—
168#1677—112no—
169#1565—111no—
170#1542D1111yescharacteristic, complemented
171C2×#331—111no—
172C23×C11#12111yescharacteristic
173C22×D11—22no—
174C22×D11—42no—
175C22×D11—82no—
176C22×D11—82no—
177C22×D11—82no—
178Q8×C11—41no—
179Q8×C11—41no—
180Q8×C11—81no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#13512yes—
190C2×C4×C11AGL(1,ℤ/8)12yes—
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C22⋊D11—44no—
195C2×Dic11—22no—
196D44—22no—
197D44—22no—
198D44—42no—
199D44—42no—
200D44—42no—
201D44—42no—
202D44—42no—
203D44—81no—
204D44—82no—
205D44—82no—
206D44—82no—
207D44—82no—
208C4×D11—42no—
209C4×D11—42no—
210Dic22—42no—
211C8×C11—41no—
212C8×C11—41no—
213C8×C11—41no—
214C8×C11—41no—
215C11⋊C8—22no—
216C11⋊C8—22no—
217C11⋊C8—42no—
218C2×#131—221no—
219#533C2×D1111yescharacteristic
220#532—111no—
221C2×#127—111no—
222#493—221no—
223#490—222no—
224#486—112no—
225#486—112no—
226#486—221no—
227#476—112no—
228#475—221no—
229#465—222no—
230#461—112no—
231#460—221no—
232#459—112no—
233#459—112no—
234#447—222no—
235#436—112no—
236#435—222no—
237C8×D4—112no—
238#431C2×D1111yescharacteristic
239C2×C4⋊C8—111no—
240C2×C4⋊C8C2×D1111yescharacteristic
241#418—221no—
242#418—221no—
243#408—221no—
244C4×M16—111no—
245#335—112no—
246#334—112no—
247#333C2×D1111yescharacteristic, complemented
248#333C2×D1111yescharacteristic, complemented
249#332C2×D1111yescharacteristic, complemented
250#332C2×D1111yescharacteristic, complemented
251#331—112no—
252#331—112no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11#46312yes—
256C22×C11C2×#12111yescharacteristic
257C2×D11—42no—
258C2×D11—42no—
259C2×D11—42no—
260C2×D11—82no—
261C2×D11—82no—
262C2×D11—82no—
263C2×D11—164no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—81no—
268C4×C11—81no—
269C4×C11#46312yes—
270C4×C11C2×#13511yescharacteristic
271C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C4×C11#57611yescharacteristic
273C4×C11#57711yescharacteristic
274Dic11—42no—
275C2×#41—221no—
276C22×D4—221no—
277C22×D4—221no—
278C22×D4—221no—
279C2×SD16—222no—
280C2×D8—222no—
281C2×D8—222no—
282#131—444no—
283C2×M16—111no—
284C2×M16—111no—
285C2×M16—222no—
286C22×C8—21no—
287C22×C8—222no—
288C22×C8—221no—
289C4⋊Q8—111no—
290C4⋊Q8C22×D1111yescharacteristic
291C4⋊Q8C22×D1111yescharacteristic
292#127—111no—
293#127—112no—
294#127—221no—
295#127—221no—
296#127—221no—
297#125—21no—
298#124—221no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301#121—112no—
302#121—221no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×D4—112no—
306C4×D4—221no—
307#117—21no—
308C2×C42C22×D1111yescharacteristic
309#106—222no—
310C4⋊C8—21no—
311C4⋊C8—112no—
312C4⋊C8—221no—
313C4⋊C8C22×D1111yescharacteristic
314C4⋊C8C22×D1111yescharacteristic
315C4⋊C8C22×D1111yescharacteristic
316C4⋊C8C22×D1111yescharacteristic
317#103—222no—
318#102—222no—
319#102—222no—
320#102—222no—
321#102—222no—
322#102—222no—
323#102—222no—
324#102—222no—
325C22⋊C8—21no—
326C22⋊C8—222no—
327C22⋊C8—222no—
328#97—112no—
329C4×C8—21no—
330C4×C8—112no—
331C2×C11—22no—
332C2×C11C2×#46311yescharacteristic
333C2×C11#306211yescharacteristic
334C2×C11#306811yescharacteristic
335D11—82no—
336D11—162no—
337C24—441no—
338#41—442no—
339#41—442no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—221no—
343C2×D4—112no—
344C2×D4—222no—
345C2×D4—221no—
346C2×D4—221no—
347C2×D4—222no—
348C2×D4—222no—
349C2×D4—222no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—442no—
354C2×D4—442no—
355C2×D4—881no—
356C2×D4—881no—
357C2×D4—882no—
358C22×C4—222no—
359C22×C4#433911yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C22×C4D4×D1111yescharacteristic
362SD16—882no—
363D8—882no—
364D8—882no—
365M16—222no—
366M16—222no—
367M16—444no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—42no—
373C2×C8—112no—
374C2×C8—112no—
375C2×C8—222no—
376C2×C8—444no—
377C2×C8—881no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—112no—
385C4⋊C4—221no—
386C22⋊C4—41no—
387C22⋊C4—222no—
388C22⋊C4—222no—
389C42—41no—
390C42#433911yescharacteristic
391C42D4×D1111yescharacteristic
392C42D4×D1111yescharacteristic
393C42C23×D1111yescharacteristic
394C11#1923411yescharacteristic, complemented, Sylow
395C23—222no—
396C23—442no—
397C23—882no—
398C23—882no—
399C23—882no—
400C23#6693711yescharacteristic
401Q8—41no—
402Q8—41no—
403Q8—81no—
404Q8—442no—
405D4—222no—
406D4—222no—
407D4—444no—
408D4—442no—
409D4—442no—
410D4—442no—
411D4—442no—
412D4—442no—
413D4—881no—
414D4—882no—
415D4—882no—
416D4—882no—
417D4—882no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—222no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4#6693711yescharacteristic
427C2×C4#6693711yescharacteristic
428C2×C4#6693711yescharacteristic
429C2×C4#6696712yes—
430C2×C4#6697212yes—
431C2×C4C2×#433911yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4C2×D4×D1111yescharacteristic
434C8—41no—
435C8—41no—
436C8—41no—
437C8—41no—
438C8—222no—
439C8—222no—
440C8—442no—
441C22—21no—
442C22—21no—
443C22—442no—
444C22—442no—
445C22—442no—
446C22—882no—
447C22—882no—
448C22—882no—
449C22—1764no—
450C22#1062243212yes—
451C22C2×#6693711yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—81no—
456C4—81no—
457C4—442no—
458C4#1062243212yes—
459C4C2×#6696711yescharacteristic
460C4C2×#6697211yescharacteristic
461C4#1062330011yescharacteristic
462C4#1062330111yescharacteristic
463C2—22no—
464C2—882no—
465C2—1762no—
466C2C2×#1062243211yescharacteristic
467C2#1307829911yescharacteristic
468C2#1307834711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radical#13079536C2
hypercenter#1542D11
hypocenterC11#19234
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #13079928C2semidirect
3. #13078992C2semidirect
4. #13077359C2semidirect
5. #13068180C2semidirect
6. #13068152C2semidirect
7. #13068056C2semidirect
8. #13068028C2semidirect
9. #13067369C2semidirect
10. C2×#10622123C2semidirect
11. C11×#1542C2semidirect
21. #10622697C22semidirect
22. #10622696C22semidirect
33. #10622451C22semidirect
35. #10622447C22semidirect
39. C11×#333C22semidirect
40. C11×#333C22semidirect
41. C11×#332C22semidirect
42. C11×#332C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
170. #1542D11semidirect
247. #333C2×D11semidirect
248. #333C2×D11semidirect
249. #332C2×D11semidirect
250. #332C2×D11semidirect
394. C11#19234semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130795362
#130789922
#130773592
#130681802
#130681522
#130680562
#130680282
#130673692
C2×#106221232
C11×#15422
#1923411