Finite Group Databasebeta

← #440×D103 #27203919

Subgroups — #440×D103 #27203919

Order 13184.

544 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D103C211yesmaximal, characteristic
2C4×Q8×D103C211yesmaximal, characteristic, complemented
3C4×D4×D103C211yesmaximal, characteristic
4#20267894C211yesmaximal, characteristic, complemented
5#20267893C211yesmaximal, characteristic, complemented
6#20267892C211yesmaximal, characteristic, complemented
7#20267891C211yesmaximal, characteristic, complemented
8#20267890C211yesmaximal, characteristic, complemented
9#20267889C211yesmaximal, characteristic, complemented
10#20267888C211yesmaximal, characteristic, complemented
11#107×D103C211yesmaximal, characteristic, complemented
12#103×D103C211yesmaximal, characteristic, complemented
13#102×D103C211yesmaximal, characteristic
14#97×D103C211yesmaximal, characteristic, complemented
15#440×C103C211yesmaximal, characteristic, complemented
16C2×Q8×D103C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18C22×C4×D103—21no—
19C2×#13110094C2211yescharacteristic
20C2×#13110093C2211yescharacteristic
21C2×#13110092C2211yescharacteristic
22SD16×D103C418yescomplemented
23C2×C8×D103C2211yescharacteristic
24C2×C8×D103C2211yescharacteristic
25Q8×Dic103C2211yescharacteristic, complemented
26C4×Dic206—21no—
27C4×Dic206C2211yescharacteristic, complemented
28#15692986—21no—
29#15692986C2211yescharacteristic, complemented
30C4×D412C2211yescharacteristic
31D4×Dic103C2211yescharacteristic
32#15692983C2211yescharacteristic
33C4×C22⋊D103—21no—
34(C22⋊D103)⋊C4—21no—
35C4⋊C4×D103—21no—
36C4⋊C4×D103C2211yescharacteristic
37C4⋊C4×D103C2211yescharacteristic
38C22⋊C4×D103—21no—
39C42×D103—21no—
40C42×D103C2211yescharacteristic
41#15692955C2211yescharacteristic, complemented
42#15692954C2211yescharacteristic, complemented
43#15692954C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692945C2211yescharacteristic, complemented
46#15692944C2211yescharacteristic, complemented
47#15692943C2211yescharacteristic
48#15692942C2211yescharacteristic
49#15692941C2211yescharacteristic
50#15692932C2211yescharacteristic, complemented
51#15692931C2211yescharacteristic, complemented
52#15692931C2211yescharacteristic, complemented
53C2×SD16×C103C2211yescharacteristic
54C4×Q8×C103C2211yescharacteristic, complemented
55C4×D4×C103C2211yescharacteristic
56#107×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic
59#97×C103C2211yescharacteristic, complemented
60C23×D103—21no—
61C2×Dic206—21no—
62C2×Dic206C2311yescharacteristic
63Q8×D103—22no—
64Q8×D103C2×C414yescomplemented
65C2×D412C2311yescharacteristic
66C2×C22⋊D103—21no—
67D4×D103—22no—
68D4×D103C2×C414yes—
69C22×Dic103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74C2×C4×D103—21no—
75C2×C4×D103—44no—
76C2×C4×D103D411yescharacteristic
77C2×C4×D103D411yescharacteristic
78C2×C4×D103C2311yescharacteristic
79#13110094C2×C414yescomplemented
80#13110093C2×C414yescomplemented
81#13110092C2×C414yescomplemented
82C2×C103⋊C8C2311yescharacteristic
83C2×C103⋊C8C2311yescharacteristic
84C8×D103—22no—
85C8×D103C2×C414yescomplemented
86C4⋊Dic103—21no—
87C4⋊Dic103C2311yescharacteristic
88C4⋊Dic103C2311yescharacteristic
89Dic103⋊C4—21no—
90Dic103⋊C4—21no—
91Dic103⋊C4—21no—
92Dic103⋊C4—21no—
93C22⋊Dic103—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96C4×Dic103—21no—
97C4×Dic103—21no—
98C4×Dic103—21no—
99C4×Dic103D411yescharacteristic
100C4×Dic103D411yescharacteristic
101C4×Dic103C2311yescharacteristic
102C2×Q8×C103C2311yescharacteristic
103C2×D4×C103C2311yescharacteristic
104C22×C4×C103—21no—
105SD16×C103C2×C414yescomplemented
106C2×C8×C103C2311yescharacteristic
107C2×C8×C103C2311yescharacteristic
108C4⋊C4×C103—21no—
109C4⋊C4×C103C2311yescharacteristic
110C4⋊C4×C103C2311yescharacteristic
111C22⋊C4×C103—21no—
112C42×C103—21no—
113C42×C103C2311yescharacteristic
114C23×C103—21no—
115C22×D103—21no—
116C22×D103—24no—
117C22×D103—42no—
118C22×D103—42no—
119C22×D103C2×D411yescharacteristic
120Q8×C103—21no—
121Q8×C103C22×C412yescomplemented
122D4×C103—21no—
123D4×C103C22×C412yes—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—42no—
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2411yescharacteristic
131C22⋊D103—24no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—42no—
136C2×Dic103C2×D411yescharacteristic
137C2×Dic103C2×D411yescharacteristic
138C2×Dic103C2×D411yescharacteristic
139D412—21no—
140D412C22×C412yes—
141C4×D103—24no—
142C4×D103—22no—
143C4×D103—22no—
144C4×D103—42no—
145C4×D103—42no—
146C4×D103—42no—
147C4×D103—42no—
148C4×D103C22×C412yes—
149C4×D103#4112yes—
150Dic206—21no—
151Dic206—24no—
152Dic206C22×C412yescomplemented
153C8×C103—21no—
154C8×C103C22×C412yescomplemented
155C103⋊C8—21no—
156C103⋊C8C22×C412yescomplemented
157C22×C103—22no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103C22×D411yescharacteristic
161C2×D103—22no—
162C2×D103—41no—
163C2×D103—41no—
164C2×D103—48no—
165C2×D103C4×D412yes—
166C2×D103AGL(1,ℤ/8)12yes—
167C2×D103#13712yes—
168C4×C103—22no—
169C4×C103—21no—
170C4×C103—21no—
171C4×C103—41no—
172C4×C103—41no—
173C4×C103C23×C411yescharacteristic
174C4×C103C2×#4111yescharacteristic
175Dic103—22no—
176Dic103—21no—
177Dic103—21no—
178Dic103—41no—
179Dic103—41no—
180Dic103C4×D412yes—
181C2×C103—42no—
182C2×C103C2×C4×D411yescharacteristic
183C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C103C2×#13711yescharacteristic
185D103—42no—
186D103#44014yesdirect product factor
187C2×#440—1031nomaximal, Sylow
188C103C2×#44011yescharacteristic, complemented, Sylow
189C22×SD16—1031no—
190C2×C4×Q8—1031no—
191C2×C4×D4—1031no—
192#440—1031no—
193#440—1031no—
194#440—1031no—
195#440—1031no—
196#440—1031no—
197#440—1031no—
198#440—1031no—
199#440D10311yescharacteristic, direct product factor
200C2×#107—1031no—
201C2×#103—1031no—
202C2×#102—1031no—
203C2×#97—1031no—
204C22×Q8—1031no—
205C22×D4—1031no—
206C23×C4—2061no—
207C2×SD16—1031no—
208C2×SD16—1031no—
209C2×SD16—1038no—
210C2×SD16—1031no—
211C2×SD16C2×D10311yescharacteristic
212C22×C8—1031no—
213C22×C8—1031no—
214C4×Q8—1031no—
215C4×Q8—1031no—
216C4×Q8—1031no—
217C4×Q8—2061no—
218C4×Q8—2061no—
219C4×Q8C2×D10311yescharacteristic, complemented
220C4×D4—1031no—
221C4×D4—1031no—
222C4×D4—1031no—
223C4×D4—2061no—
224C4×D4—2061no—
225C4×D4C2×D10311yescharacteristic
226C2×C4⋊C4—1031no—
227C2×C4⋊C4—1031no—
228C2×C4⋊C4—2061no—
229C2×C22⋊C4—2061no—
230C2×C42—1031no—
231C2×C42—2061no—
232#107—1031no—
233#107—1031no—
234#107—1031no—
235#107C2×D10311yescharacteristic, complemented
236#103—1031no—
237#103—1031no—
238#103—1031no—
239#103C2×D10311yescharacteristic, complemented
240#102—1031no—
241#102—1031no—
242#102—1031no—
243#102C2×D10311yescharacteristic
244#97—1031no—
245#97—1031no—
246#97—1031no—
247#97C2×D10311yescharacteristic, complemented
248C24—2061no—
249C2×Q8—1034no—
250C2×Q8—1031no—
251C2×Q8—2061no—
252C2×Q8—2062no—
253C2×Q8C22×D10311yescharacteristic
254C2×D4—1034no—
255C2×D4—1031no—
256C2×D4—2062no—
257C2×D4—2061no—
258C2×D4C22×D10311yescharacteristic
259C22×C4—21no—
260C22×C4—1031no—
261C22×C4—1031no—
262C22×C4—1031no—
263C22×C4—4124no—
264C22×C4—2061no—
265C22×C4—2061no—
266C22×C4—2061no—
267C22×C4—2061no—
268C22×C4—2061no—
269C22×C4—2061no—
270SD16—1034no—
271SD16—1034no—
272SD16—1034no—
273SD16C4×D10314yescomplemented
274C2×C8—1031no—
275C2×C8—1034no—
276C2×C8—1031no—
277C2×C8—2062no—
278C2×C8C22×D10311yescharacteristic
279C2×C8C22×D10311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—1031no—
282C4⋊C4—1031no—
283C4⋊C4—2061no—
284C4⋊C4—2061no—
285C4⋊C4—2061no—
286C4⋊C4—2061no—
287C4⋊C4—2061no—
288C4⋊C4C22×D10311yescharacteristic
289C4⋊C4C22×D10311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2061no—
292C22⋊C4—2061no—
293C22⋊C4—2061no—
294C42—21no—
295C42—1031no—
296C42—1031no—
297C42—1031no—
298C42—2061no—
299C42—2061no—
300C42—2061no—
301C42C22×D10311yescharacteristic
302C23—21no—
303C23—1031no—
304C23—4122no—
305C23—4122no—
306C23—2064no—
307C23—2061no—
308Q8—21no—
309Q8—1032no—
310Q8—2064no—
311Q8—2061no—
312Q8C2×C4×D10312yescomplemented
313D4—21no—
314D4—1032no—
315D4—2064no—
316D4—2061no—
317D4C2×C4×D10312yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—1031no—
323C2×C4—1032no—
324C2×C4—1032no—
325C2×C4—1031no—
326C2×C4—1031no—
327C2×C4—4122no—
328C2×C4—4122no—
329C2×C4—4122no—
330C2×C4—4122no—
331C2×C4—4122no—
332C2×C4—2062no—
333C2×C4—2062no—
334C2×C4—2064no—
335C2×C4—2061no—
336C2×C4—2061no—
337C2×C4—2061no—
338C2×C4D4×D10311yescharacteristic
339C2×C4D4×D10311yescharacteristic
340C2×C4C23×D10311yescharacteristic
341C8—21no—
342C8—1032no—
343C8—2061no—
344C8C2×C4×D10312yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—1032no—
349C22—1032no—
350C22—1032no—
351C22—4128no—
352C22—4121no—
353C22—4121no—
354C22—2062no—
355C22C2×D4×D10311yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—1032no—
362C4—4121no—
363C4—4121no—
364C4—2061no—
365C4—2061no—
366C4—2062no—
367C4C22×C4×D10311yescharacteristic
368C4#41×D10311yescharacteristic
369C2—42no—
370C2—1034no—
371C2—4122no—
372C2C4×D4×D10311yescharacteristic
373C2AGL(1,ℤ/8)×D10311yescharacteristic
374C2#137×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
Fitting#440×C103C2
socleC22×C103C22×D4
prime radicalC2×D4×D103C22
cosocleC2×C4×C103C24
hypercenter#440D103
hypocenterC103C2×#440
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D103C2semidirect
4. #20267894C2semidirect
5. #20267893C2semidirect
6. #20267892C2semidirect
7. #20267891C2semidirect
8. #20267890C2semidirect
9. #20267889C2semidirect
10. #20267888C2semidirect
11. #107×D103C2semidirect
12. #103×D103C2semidirect
14. #97×D103C2semidirect
15. #440×C103C2semidirect
22. SD16×D103C4semidirect
25. Q8×Dic103C22semidirect
27. C4×Dic206C22semidirect
29. #15692986C22semidirect
41. #15692955C22semidirect
42. #15692954C22semidirect
43. #15692954C22semidirect
44. #15692946C22semidirect
45. #15692945C22semidirect
46. #15692944C22semidirect
50. #15692932C22semidirect
51. #15692931C22semidirect
52. #15692931C22semidirect
54. C4×Q8×C103C22semidirect
56. #107×C103C22semidirect
57. #103×C103C22semidirect
59. #97×C103C22semidirect
64. Q8×D103C2×C4semidirect
79. #13110094C2×C4semidirect
80. #13110093C2×C4semidirect
81. #13110092C2×C4semidirect
85. C8×D103C2×C4semidirect
105. SD16×C103C2×C4semidirect
121. Q8×C103C22×C4semidirect
152. Dic206C22×C4semidirect
154. C8×C103C22×C4semidirect
156. C103⋊C8C22×C4semidirect
186. D103#440direct (N × H)
188. C103C2×#440semidirect
199. #440D103direct (N × H)
219. C4×Q8C2×D103semidirect
235. #107C2×D103semidirect
239. #103C2×D103semidirect
247. #97C2×D103semidirect
273. SD16C4×D103semidirect
312. Q8C2×C4×D103semidirect
344. C8C2×C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1032
C4×Q8×D1032
C4×D4×D1032
#202678942
#202678932
#202678922
#202678912
#202678902
#202678892
#202678882
#107×D1032
#103×D1032
#102×D1032
#97×D1032
#440×C1032
C2×#440103