Finite Group Databasebeta

← #482×D103 #27205024

Subgroups — #482×D103 #27205024

Order 13184.

468 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D103C211yesmaximal, characteristic
2#117×D103C211yesmaximal, characteristic, complemented
3#20268118C211yesmaximal, characteristic, complemented
4#20268117C211yesmaximal, characteristic, complemented
5#20268116C211yesmaximal, characteristic, complemented
6#20268115C211yesmaximal, characteristic, complemented
7#20268114C211yesmaximal, characteristic, complemented
8#20268113C211yesmaximal, characteristic, complemented
9#20268112C211yesmaximal, characteristic, complemented
10#107×D103C211yesmaximal, characteristic, complemented
11#106×D103C211yesmaximal, characteristic, complemented
12#102×D103C211yesmaximal, characteristic, complemented
13#102×D103C211yesmaximal, characteristic, complemented
14C22⋊C8×D103C211yesmaximal, characteristic, complemented
15#482×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103—21no—
17C2×D4×D103C2211yescharacteristic
18C22×C4×D103C2211yescharacteristic
19C2×C8×D103C2211yescharacteristic
20C2×C8×D103C2211yescharacteristic
21#15692996C2211yescharacteristic
22#15692995C2211yescharacteristic
23#15692994—21no—
24#15692993—21no—
25#15692992C2211yescharacteristic
26#15692980C2211yescharacteristic, complemented
27#15692979C2211yescharacteristic, complemented
28#15692979C2211yescharacteristic, complemented
29#15692978—21no—
30#15692977—21no—
31C4⋊C4×D103C2211yescharacteristic
32C4⋊C4×D103C2211yescharacteristic
33C4⋊C4×D103C2211yescharacteristic
34C22⋊C4×D103—21no—
35C22⋊C4×D103—21no—
36C42×D103—21no—
37#15692955C2211yescharacteristic, complemented
38#15692954C2211yescharacteristic, complemented
39#15692954C2211yescharacteristic, complemented
40#15692953C2211yescharacteristic, complemented
41#15692952C2211yescharacteristic, complemented
42#15692952C2211yescharacteristic, complemented
43#15692943C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic, complemented
45#15692942C2211yescharacteristic, complemented
46#15692942C2211yescharacteristic, complemented
47#15692941C2211yescharacteristic, complemented
48#15692941C2211yescharacteristic, complemented
49C22⋊(C103⋊C8)C2211yescharacteristic, complemented
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51(C2×D103)⋊C8C2211yescharacteristic, complemented
52#121×C103C2211yescharacteristic
53#117×C103C2211yescharacteristic, complemented
54#107×C103C2211yescharacteristic, complemented
55#106×C103C2211yescharacteristic, complemented
56#102×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C23×D103D411yescharacteristic
61C2×D412—21no—
62C2×D412C2311yescharacteristic
63C2×C22⋊D103—21no—
64C2×C22⋊D103—21no—
65C2×C22⋊D103—21no—
66D4×D103—22no—
67D4×D103—22no—
68D4×D103—44no—
69C22×Dic103D411yescharacteristic
70C2×C4×D103—22no—
71C2×C4×D103—22no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74C2×C4×D103—21no—
75C2×C4×D103D411yescharacteristic
76C2×C4×D103D411yescharacteristic
77C2×C4×D103C2311yescharacteristic
78C2×C4×D103C2311yescharacteristic
79C2×C103⋊C8C2311yescharacteristic
80C2×C103⋊C8C2311yescharacteristic
81C8×D103—22no—
82C8×D103—22no—
83C4⋊Dic103C2311yescharacteristic
84C4⋊Dic103C2311yescharacteristic
85C4⋊Dic103C2311yescharacteristic
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88Dic103⋊C4—21no—
89C22⋊Dic103—21no—
90C22⋊Dic103—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95C4×Dic103—21no—
96C4×Dic103—21no—
97C4×Dic103—21no—
98C2×D4×C103—21no—
99C2×D4×C103C2311yescharacteristic
100C22×C4×C103C2311yescharacteristic
101C2×C8×C103C2311yescharacteristic
102C2×C8×C103C2311yescharacteristic
103C4⋊C4×C103C2311yescharacteristic
104C4⋊C4×C103C2311yescharacteristic
105C4⋊C4×C103C2311yescharacteristic
106C22⋊C4×C103—21no—
107C22⋊C4×C103—21no—
108C42×C103—21no—
109C23×C103—21no—
110C23×C103C2×D411yescharacteristic
111C22×D103—22no—
112C22×D103—22no—
113C22×D103—22no—
114C22×D103—21no—
115C22×D103—42no—
116C22×D103—42no—
117C22×D103—42no—
118C22×D103C2×D411yescharacteristic
119C22×D103C2×D411yescharacteristic
120D4×C103—21no—
121D4×C103—21no—
122D4×C103—42no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2411yescharacteristic
130C22⋊D103—42no—
131C22⋊D103—42no—
132C22⋊D103—42no—
133C2×Dic103—22no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103C2×D411yescharacteristic
138C2×Dic103C2×D411yescharacteristic
139D412—21no—
140D412—21no—
141D412—42no—
142C4×D103—22no—
143C4×D103—21no—
144C4×D103—21no—
145C4×D103—22no—
146C4×D103—42no—
147C4×D103—42no—
148C4×D103—42no—
149C4×D103#4112yes—
150C4×D103#4112yes—
151C8×C103—21no—
152C8×C103—21no—
153C103⋊C8—21no—
154C103⋊C8—21no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103—21no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103—41no—
161C22×C103C22×D411yescharacteristic
162C2×D103—21no—
163C2×D103—21no—
164C2×D103—21no—
165C2×D103—44no—
166C2×D103—41no—
167C2×D103—41no—
168C2×D103—41no—
169C2×D103—84no—
170C2×D103#12312yes—
171C2×D103#13512yes—
172C2×D103AGL(1,ℤ/8)12yes—
173C4×C103—21no—
174C4×C103—41no—
175C4×C103—41no—
176C4×C103—41no—
177C4×C103C2×#4111yescharacteristic
178C4×C103C2×#4111yescharacteristic
179Dic103—21no—
180Dic103—41no—
181Dic103—41no—
182Dic103—41no—
183Dic103#12312yes—
184C2×C103—41no—
185C2×C103—81no—
186C2×C103C2×#12311yescharacteristic
187C2×C103C2×#13511yescharacteristic
188C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
189D103—41no—
190D103—81no—
191D103#48214yesdirect product factor
192C2×#482—1031nomaximal, Sylow
193C103C2×#48211yescharacteristic, complemented, Sylow
194C2×#121—1031no—
195C2×#117—1031no—
196#482—1031no—
197#482—1031no—
198#482—1031no—
199#482—1031no—
200#482—1031no—
201#482—1031no—
202#482—1031no—
203#482D10311yescharacteristic, direct product factor
204C2×#107—1031no—
205C2×#106—1031no—
206C2×#102—1031no—
207C2×#102—1031no—
208C2×C22⋊C8—1031no—
209C22×D4—1031no—
210C22×D4—2061no—
211C23×C4—1031no—
212C22×C8—1031no—
213C22×C8—1031no—
214#121—1031no—
215#121—1031no—
216#121—1031no—
217#121—2061no—
218#121—2061no—
219#121C2×D10311yescharacteristic
220#117—1031no—
221#117—1031no—
222#117—1031no—
223#117—2061no—
224#117—2061no—
225#117C2×D10311yescharacteristic, complemented
226C2×C4⋊C4—1031no—
227C2×C4⋊C4—1031no—
228C2×C4⋊C4—1031no—
229C2×C22⋊C4—2061no—
230C2×C22⋊C4—2061no—
231C2×C42—2061no—
232#107—1031no—
233#107—1031no—
234#107—1031no—
235#107C2×D10311yescharacteristic, complemented
236#106—1031no—
237#106—1031no—
238#106—1031no—
239#106C2×D10311yescharacteristic, complemented
240#102—1031no—
241#102—1031no—
242#102—1031no—
243#102—1031no—
244#102—1031no—
245#102—1031no—
246#102C2×D10311yescharacteristic, complemented
247#102C2×D10311yescharacteristic, complemented
248C22⋊C8—1031no—
249C22⋊C8—1031no—
250C22⋊C8—1031no—
251C22⋊C8C2×D10311yescharacteristic, complemented
252C24—1031no—
253C24—2061no—
254C2×D4—21no—
255C2×D4—1031no—
256C2×D4—4124no—
257C2×D4—2061no—
258C2×D4—2062no—
259C2×D4—2062no—
260C2×D4—2061no—
261C2×D4—2061no—
262C2×D4—2061no—
263C2×D4C22×D10311yescharacteristic
264C22×C4—1031no—
265C22×C4—1031no—
266C22×C4—1031no—
267C22×C4—1031no—
268C22×C4—1031no—
269C22×C4—2062no—
270C22×C4—2062no—
271C22×C4—2061no—
272C22×C4—2061no—
273C22×C4—2061no—
274C22×C4C22×D10311yescharacteristic
275C2×C8—1031no—
276C2×C8—1031no—
277C2×C8—2062no—
278C2×C8—2062no—
279C2×C8C22×D10311yescharacteristic
280C2×C8C22×D10311yescharacteristic
281C4⋊C4—1031no—
282C4⋊C4—1031no—
283C4⋊C4—1031no—
284C4⋊C4—2061no—
285C4⋊C4—2061no—
286C4⋊C4—2061no—
287C4⋊C4C22×D10311yescharacteristic
288C4⋊C4C22×D10311yescharacteristic
289C4⋊C4C22×D10311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—2061no—
293C22⋊C4—2061no—
294C22⋊C4—2061no—
295C22⋊C4—2061no—
296C22⋊C4—2061no—
297C22⋊C4—2061no—
298C42—21no—
299C42—2061no—
300C42—2061no—
301C42—2061no—
302C23—21no—
303C23—1031no—
304C23—1031no—
305C23—4122no—
306C23—4122no—
307C23—4122no—
308C23—2062no—
309C23—2062no—
310C23—2062no—
311C23—2061no—
312C23D4×D10311yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—4122no—
317D4—4122no—
318D4—4122no—
319D4—4122no—
320D4—2061no—
321D4—2061no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—1031no—
328C2×C4—1032no—
329C2×C4—1032no—
330C2×C4—1031no—
331C2×C4—4122no—
332C2×C4—4122no—
333C2×C4—4122no—
334C2×C4—2062no—
335C2×C4—2062no—
336C2×C4—2062no—
337C2×C4—2061no—
338C2×C4—2061no—
339C2×C4—2061no—
340C2×C4—2061no—
341C2×C4—2061no—
342C2×C4D4×D10311yescharacteristic
343C2×C4C23×D10311yescharacteristic
344C8—21no—
345C8—21no—
346C8—2061no—
347C8—2061no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—8244no—
355C22—1032no—
356C22—1032no—
357C22—1032no—
358C22—4124no—
359C22—4121no—
360C22—4121no—
361C22—4121no—
362C22—2061no—
363C22—2061no—
364C22—2061no—
365C22C2×D4×D10311yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—1032no—
371C4—4121no—
372C4—4121no—
373C4—4121no—
374C4—2061no—
375C4#41×D10311yescharacteristic
376C4#41×D10311yescharacteristic
377C2—41no—
378C2—81no—
379C2—8241no—
380C2—1034no—
381C2—4121no—
382C2#123×D10311yescharacteristic
383C2#135×D10311yescharacteristic
384C2AGL(1,ℤ/8)×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#482×C103C2
socleC22×C103C22×D4
prime radical#121×D103C2
hypercenter#482D103
hypocenterC103C2×#482
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D103C2semidirect
3. #20268118C2semidirect
4. #20268117C2semidirect
5. #20268116C2semidirect
6. #20268115C2semidirect
7. #20268114C2semidirect
8. #20268113C2semidirect
9. #20268112C2semidirect
10. #107×D103C2semidirect
11. #106×D103C2semidirect
12. #102×D103C2semidirect
13. #102×D103C2semidirect
14. C22⋊C8×D103C2semidirect
15. #482×C103C2semidirect
26. #15692980C22semidirect
27. #15692979C22semidirect
28. #15692979C22semidirect
37. #15692955C22semidirect
38. #15692954C22semidirect
39. #15692954C22semidirect
40. #15692953C22semidirect
41. #15692952C22semidirect
42. #15692952C22semidirect
43. #15692943C22semidirect
44. #15692943C22semidirect
45. #15692942C22semidirect
46. #15692942C22semidirect
47. #15692941C22semidirect
48. #15692941C22semidirect
49. C22⋊(C103⋊C8)C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. (C2×D103)⋊C8C22semidirect
53. #117×C103C22semidirect
54. #107×C103C22semidirect
55. #106×C103C22semidirect
56. #102×C103C22semidirect
57. #102×C103C22semidirect
58. C22⋊C8×C103C22semidirect
191. D103#482direct (N × H)
193. C103C2×#482semidirect
203. #482D103direct (N × H)
225. #117C2×D103semidirect
235. #107C2×D103semidirect
239. #106C2×D103semidirect
246. #102C2×D103semidirect
247. #102C2×D103semidirect
251. C22⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#121×D1032
#117×D1032
#202681182
#202681172
#202681162
#202681152
#202681142
#202681132
#202681122
#107×D1032
#106×D1032
#102×D1032
C22⋊C8×D1032
#482×C1032
C2×#482103