Finite Group Databasebeta

← #28400671

Subgroups — #28400671

Order 14464.

444 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299152C211yesmaximal, characteristic, complemented
2C4×D4×D113C211yesmaximal, characteristic
3#20298935C211yesmaximal, characteristic, complemented
4#20298932C211yesmaximal, characteristic, complemented
5#20298877C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298802C211yesmaximal, characteristic, complemented
8#20298801C211yesmaximal, characteristic, complemented
9#20298750C211yesmaximal, characteristic
10#20298747C211yesmaximal, characteristic
11#20298700C211yesmaximal, characteristic, complemented
12#20298698C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14#20298653C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C22×C4×D113—21no—
18C2×#14268636C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21#16813621C2211yescharacteristic, complemented
22#16813620C2211yescharacteristic, complemented
23#16813612—21no—
24#16813602C2211yescharacteristic
25#16813600—21no—
26#16813598C2211yescharacteristic
27C4×Dic226—21no—
28C4×Dic226C2211yescharacteristic, complemented
29C4×D452C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31#16813584C2211yescharacteristic
32C4×C22⋊D113—21no—
33#16813582—21no—
34#16813579—21no—
35C4⋊C4×D113C2211yescharacteristic
36C22⋊C4×D113—21no—
37C42×D113C2211yescharacteristic
38#16813556C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813546C2211yescharacteristic, complemented
45#16813545C2211yescharacteristic, complemented
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic, complemented
54C4×D4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64D4×D113—22no—
65D4×D113—22no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—44no—
71C2×C4×D113D411yescharacteristic
72C2×C4×D113D411yescharacteristic
73C2×C4×D113C2311yescharacteristic
74#14268636—22no—
75#14268635—22no—
76#14268634—22no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113D411yescharacteristic
95C4×Dic113D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100SD16×C113—22no—
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113—21no—
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C42×C113C2311yescharacteristic
109C23×C113—21no—
110C22×D113—24no—
111C22×D113—21no—
112C22×D113—42no—
113C22×D113—42no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117D4×C113—21no—
118D4×C113#4112yes—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—42no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C22⋊D113—24no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—42no—
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134D452—21no—
135D452#4112yes—
136C4×D113—22no—
137C4×D113—21no—
138C4×D113—21no—
139C4×D113—22no—
140C4×D113—42no—
141C4×D113—42no—
142C4×D113—42no—
143Dic226—21no—
144Dic226—21no—
145Dic226—42no—
146C8×C113—21no—
147C8×C113—21no—
148#11744751—21no—
149#11744751—21no—
150C22×C113—22no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113C22×D411yescharacteristic
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—22no—
157C2×D113—48no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113#13712yes—
161C4×C113—21no—
162C4×C113—21no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113C2×#4111yescharacteristic
167C4×C113C2×#4111yescharacteristic
168Dic113—21no—
169Dic113—21no—
170Dic113—41no—
171Dic113—41no—
172Dic113—41no—
173Dic113AGL(1,ℤ/8)12yes—
174C2×C113—42no—
175C2×C113#52511yescharacteristic
176C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C113C2×#13711yescharacteristic
178D113—22no—
179D113—42no—
180#3110—1131nomaximal, Sylow
181C113#311011yescharacteristic, complemented, Sylow
182#533—1131no—
183C2×C4×D4—1131no—
184#484—1131no—
185#484—1131no—
186#474—1131no—
187#474—1131no—
188#461—1131no—
189#461—1131no—
190#450—1131no—
191#450—1131no—
192#440—1131no—
193#440—1131no—
194#440—1131no—
195#440D11311yescharacteristic, complemented
196#432—1131no—
197C22×D4—1131no—
198C23×C4—2261no—
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×SD16—1131no—
202C2×SD16C2×D11311yescharacteristic
203C4⋊Q8—1131no—
204C4⋊Q8—1131no—
205#125—2261no—
206C22⋊Q8—1131no—
207C22⋊Q8—1131no—
208C22⋊Q8—2261no—
209C4×Q8—1131no—
210C4×Q8—2261no—
211C4×Q8C2×D11311yescharacteristic, complemented
212C4×D4—1131no—
213C4×D4—1131no—
214C4×D4—1131no—
215C4×D4—2261no—
216C4×D4—2261no—
217C4×D4C2×D11311yescharacteristic
218#117—2261no—
219C2×C4⋊C4—1131no—
220C2×C22⋊C4—2261no—
221C2×C42—1131no—
222#107—1131no—
223#107—1131no—
224#107—1131no—
225#107C2×D11311yescharacteristic, complemented
226C4⋊C8—1131no—
227C4⋊C8—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103C2×D11311yescharacteristic, complemented
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102C2×D11311yescharacteristic
236C22⋊C8—1131no—
237C22⋊C8—1131no—
238#97—1131no—
239#97C2×D11311yescharacteristic, complemented
240C24—2261no—
241C2×Q8—1131no—
242C2×Q8—2261no—
243C2×Q8C22×D11311yescharacteristic
244C2×D4—1131no—
245C2×D4—2261no—
246C2×D4—2262no—
247C2×D4—2262no—
248C2×D4C22×D11311yescharacteristic
249C22×C4—21no—
250C22×C4—1131no—
251C22×C4—1131no—
252C22×C4—1131no—
253C22×C4—4524no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4—2261no—
258SD16—22no—
259SD16—2262no—
260SD16—2262no—
261SD16—2262no—
262C2×C8—1131no—
263C2×C8—1131no—
264C2×C8C22×D11311yescharacteristic
265C2×C8C22×D11311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4C22×D11311yescharacteristic
277C4⋊C4C22×D11311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C42—21no—
285C42—1131no—
286C42—1131no—
287C42—1131no—
288C42—2261no—
289C42C22×D11311yescharacteristic
290C23—21no—
291C23—1131no—
292C23—4522no—
293C23—4522no—
294C23—2264no—
295C23—2261no—
296Q8—21no—
297Q8—21no—
298Q8—4522no—
299Q8—2261no—
300Q8—2261no—
301D4—21no—
302D4—1132no—
303D4—2264no—
304D4—2261no—
305D4#1426864712yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—1131no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—4522no—
314C2×C4—4522no—
315C2×C4—4522no—
316C2×C4—4522no—
317C2×C4—2262no—
318C2×C4—2262no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4D4×D11311yescharacteristic
325C2×C4D4×D11311yescharacteristic
326C2×C4C23×D11311yescharacteristic
327C8—21no—
328C8—21no—
329C8—2261no—
330C8—2261no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—1132no—
335C22—4528no—
336C22—4521no—
337C22—4521no—
338C22—2262no—
339C22—2261no—
340C22—2261no—
341C22C2×D4×D11311yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—1132no—
348C4—4521no—
349C4—4521no—
350C4—4521no—
351C4—2261no—
352C4—2261no—
353C4#41×D11311yescharacteristic
354C4C2×#1426864711yescharacteristic
355C2—42no—
356C2—4522no—
357C2—2262no—
358C2#2029910711yescharacteristic
359C2AGL(1,ℤ/8)×D11311yescharacteristic
360C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#440D113
hypocenterC113#3110
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #20299152C2semidirect
3. #20298935C2semidirect
4. #20298932C2semidirect
5. #20298877C2semidirect
6. #20298876C2semidirect
7. #20298802C2semidirect
8. #20298801C2semidirect
11. #20298700C2semidirect
12. #20298698C2semidirect
13. #20298696C2semidirect
14. #20298653C2semidirect
15. #440×C113C2semidirect
21. #16813621C22semidirect
22. #16813620C22semidirect
28. C4×Dic226C22semidirect
38. #16813556C22semidirect
39. #16813555C22semidirect
40. #16813555C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
43. #16813547C22semidirect
44. #16813546C22semidirect
45. #16813545C22semidirect
51. #16813533C22semidirect
53. C4×Q8×C113C22semidirect
55. #107×C113C22semidirect
56. #103×C113C22semidirect
58. #97×C113C22semidirect
181. C113#3110semidirect
195. #440D113semidirect
211. C4×Q8C2×D113semidirect
225. #107C2×D113semidirect
231. #103C2×D113semidirect
239. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991522
C4×D4×D1132
#202989352
#202989322
#202988772
#202988762
#202988022
#202988012
#202987502
#202987472
#202987002
#202986982
#202986962
#202986532
#440×C1132
#3110113