Finite Group Databasebeta

← #14737295

Subgroups — #14737295

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#13079534C211yesmaximal, characteristic
3#13077362C211yesmaximal, characteristic, complemented
4#13068174C212yesmaximal, complemented
5#13068146C212yesmaximal, complemented
6#13068050C212yesmaximal, complemented
7#13068022C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067273C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic, complemented
11C11×#3138C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×#66960—21no—
15#10623008C2211yescharacteristic
16C11×#490—22no—
17C11×#486C2212yes—
18C11×#486C2212yes—
19C11×#418—21no—
20C11×#418—21no—
21C4×C11×M16C2211yescharacteristic
22#10622830—22no—
23#10622742—21no—
24#10622697C2212yescomplemented
25#10622696C2212yescomplemented
26#10622686—21no—
27#10622685C2212yes—
28#10622685C2212yes—
29#10622683—21no—
30#10622661—22no—
31#10622640—21no—
32#10622633—21no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622319—22no—
37#10622301C2212yescomplemented
38C8×D44C2212yescomplemented
39#10622185C2211yescharacteristic, complemented
40#10622185C2211yescharacteristic, complemented
41#10622184C2211yescharacteristic, complemented
42#10622184C2211yescharacteristic, complemented
43#10622182C2212yes—
44#10622182C2212yes—
45#10622096C2212yescomplemented
46#10622095C2212yescomplemented
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C2×#4339—21no—
51C2×C11×M16D411yescharacteristic
52C2×C11×M16D411yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×C4⋊Q8C2311yescharacteristic
55C11×#127—21no—
56C11×#127—21no—
57C11×#127—21no—
58C11×#127C2312yes—
59C11×#125—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C11×#117—21no—
65C2×C42×C11C2311yescharacteristic
66C2×#4325—22no—
67C2×#4323—22no—
68C2×#4323—22no—
69#66983—21no—
70#66983D412yes—
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73#66960—44no—
74C2×#4313—22no—
75C2×C8×D11—22no—
76#66928—21no—
77#66927D411yescharacteristic
78C4×D44—21no—
79C4×D44C2312yes—
80#66922D411yescharacteristic
81C11×#102—22no—
82C11×#102—22no—
83C11×#102—22no—
84C11×#102—22no—
85C11×#97D412yes—
86C4×C8×C11C2312yes—
87#66899—22no—
88#66896—22no—
89#66896—22no—
90C22⋊(C11⋊C8)—21no—
91(C2×D11)⋊C8—22no—
92(C2×D11)⋊C8—22no—
93#66873—22no—
94#66872—22no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4×C11⋊C8—21no—
103#19234—111nomaximal, Sylow
104C24×C11—41no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—81no—
116C2×D4×C11—81no—
117C2×D4×C11—82no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C2×C22⋊D11—22no—
122#4339—42no—
123#4339—42no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44C2×D412yes—
127C2×C4×D11—22no—
128C2×Dic22—21no—
129C11×M16—22no—
130C11×M16—22no—
131C2×C8×C11C2×D412yes—
132C2×C8×C11C2×D412yes—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—41no—
140C42×C11—41no—
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11#4111yescharacteristic
144C42×C11C2411yescharacteristic
145#4325—82no—
146#4323—82no—
147#4323—82no—
148(C2×D11)⋊C4—22no—
149(C2×D11)⋊C4—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11C2×D412yes—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—42no—
158C2×C11⋊C8—81no—
159#4313—44no—
160C8×D11—44no—
161#3246—111no—
162#3205—111no—
163#3138D1111yescharacteristic, complemented
164#2935—111no—
165#1701—112no—
166#1697—112no—
167#1681—112no—
168#1677—112no—
169#1565—111no—
170#1542—111no—
171C2×#331—111no—
172C23×C11—42no—
173C23×C11—82no—
174C23×C11—82no—
175C23×C11—82no—
176C23×C11#12111yescharacteristic
177C22×D11—22no—
178Q8×C11—41no—
179Q8×C11—41no—
180Q8×C11—81no—
181D4×C11—42no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—42no—
185D4×C11—82no—
186D4×C11—82no—
187D4×C11—82no—
188D4×C11—82no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#13512yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C22⋊D11—44no—
203C2×Dic11—22no—
204D44—22no—
205D44—22no—
206D44—42no—
207D44—81no—
208C4×D11—42no—
209C4×D11—42no—
210Dic22—42no—
211C8×C11—22no—
212C8×C11—22no—
213C11⋊C8—41no—
214C11⋊C8—41no—
215C11⋊C8—42no—
216C11⋊C8—41no—
217C11⋊C8—41no—
218C2×#131—221no—
219#533C2×D1111yescharacteristic
220#532—111no—
221C2×#127C2×D1111yescharacteristic
222#493—221no—
223#490—22no—
224#486—221no—
225#486C2×D1112yes—
226#486C2×D1112yes—
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#431—111no—
239C2×C4⋊C8—111no—
240C2×C4⋊C8—111no—
241#418—21no—
242#418—21no—
243#408—221no—
244C4×M16C2×D1111yescharacteristic
245#335—112no—
246#334—112no—
247#333—111no—
248#333—111no—
249#332—111no—
250#332—111no—
251#331—112no—
252#331—112no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—82no—
256C22×C11—82no—
257C22×C11—82no—
258C22×C11—164no—
259C22×C11#46312yes—
260C22×C11C2×#12111yescharacteristic
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
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—21no—
277C22×D4—21no—
278C22×D4—21no—
279C2×SD16—222no—
280C2×D8—222no—
281C2×D8—222no—
282#131—444no—
283C2×M16—222no—
284C2×M16C22⋊D1111yescharacteristic
285C2×M16C22⋊D1111yescharacteristic
286C22×C8—221no—
287C22×C8—221no—
288C22×C8—222no—
289C4⋊Q8—111no—
290C4⋊Q8C22×D1111yescharacteristic
291C4⋊Q8C22×D1111yescharacteristic
292#127—21no—
293#127—21no—
294#127—21no—
295#127—111no—
296#127C22×D1112yes—
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—111no—
311C4⋊C8—111no—
312C4⋊C8—112no—
313C4⋊C8—111no—
314C4⋊C8—111no—
315C4⋊C8—221no—
316C4⋊C8—221no—
317#103—222no—
318#102—22no—
319#102—22no—
320#102—22no—
321#102—22no—
322#102—222no—
323#102—222no—
324#102—222no—
325C22⋊C8—221no—
326C22⋊C8—222no—
327C22⋊C8—222no—
328#97C22⋊D1112yes—
329C4×C8—221no—
330C4×C8C22×D1112yes—
331C2×C11—22no—
332C2×C11—162no—
333C2×C11C2×#46311yescharacteristic
334C2×C11#306211yescharacteristic
335C2×C11#306811yescharacteristic
336D11—82no—
337C24—41no—
338#41—442no—
339#41—442no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—221no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—42no—
350C2×D4—42no—
351C2×D4—81no—
352C2×D4—81no—
353C2×D4—82no—
354C2×D4—112no—
355C2×D4—222no—
356C2×D4—221no—
357C2×D4—221no—
358C22×C4—222no—
359C22×C4D4×D1111yescharacteristic
360C22×C4#434111yescharacteristic
361C22×C4C2×C22⋊D1111yescharacteristic
362SD16—882no—
363D8—882no—
364D8—882no—
365M16—22no—
366M16—22no—
367M16—444no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8—222no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—444no—
374C2×C8—442no—
375C2×C8—881no—
376C2×C8C2×C22⋊D1112yes—
377C2×C8C2×C22⋊D1112yes—
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—
390C42D4×D1111yescharacteristic
391C42#434111yescharacteristic
392C42C2×C22⋊D1111yescharacteristic
393C42C23×D1111yescharacteristic
394C11#1923411yescharacteristic, complemented, Sylow
395C23—42no—
396C23—82no—
397C23—82no—
398C23—82no—
399C23—222no—
400C23#6699111yescharacteristic
401Q8—41no—
402Q8—41no—
403Q8—81no—
404Q8—442no—
405D4—42no—
406D4—42no—
407D4—42no—
408D4—42no—
409D4—82no—
410D4—82no—
411D4—82no—
412D4—82no—
413D4—222no—
414D4—222no—
415D4—444no—
416D4—442no—
417D4—881no—
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#6699111yescharacteristic
427C2×C4#6699111yescharacteristic
428C2×C4#6699111yescharacteristic
429C2×C4#6700212yes—
430C2×C4#6700312yes—
431C2×C4C2×D4×D1111yescharacteristic
432C2×C4C2×#434111yescharacteristic
433C2×C4C22×C22⋊D1111yescharacteristic
434C8—22no—
435C8—22no—
436C8—442no—
437C8—441no—
438C8—441no—
439C8—441no—
440C8—441no—
441C22—21no—
442C22—21no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—164no—
447C22—442no—
448C22—442no—
449C22—442no—
450C22#1062267012yes—
451C22C2×#6699111yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—81no—
456C4—81no—
457C4—442no—
458C4#1062267012yes—
459C4#1062330511yescharacteristic
460C4#1062330611yescharacteristic
461C4C2×#6700211yescharacteristic
462C4C2×#6700311yescharacteristic
463C2—22no—
464C2—162no—
465C2—882no—
466C2C2×#1062267011yescharacteristic
467C2#1307829011yescharacteristic
468C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3138C2
socleC22×C11C2×#121
prime radical#13079534C2
hypercenter#3138D11
hypocenterC11#19234
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #13079928C2semidirect
3. #13077362C2semidirect
4. #13068174C2semidirect
5. #13068146C2semidirect
6. #13068050C2semidirect
7. #13068022C2semidirect
8. #13067368C2semidirect
9. #13067273C2semidirect
10. C2×#10622182C2semidirect
11. C11×#3138C2semidirect
24. #10622697C22semidirect
25. #10622696C22semidirect
37. #10622301C22semidirect
38. C8×D44C22semidirect
39. #10622185C22semidirect
40. #10622185C22semidirect
41. #10622184C22semidirect
42. #10622184C22semidirect
45. #10622096C22semidirect
46. #10622095C22semidirect
163. #3138D11semidirect
394. C11#19234semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130795342
#130773622
#130681742
#130681462
#130680502
#130680222
#130673682
#130672732
C2×#106221822
C11×#31382
#1923411