Finite Group Databasebeta

← #27203998

Subgroups — #27203998

Order 13184.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D103C211yesmaximal, characteristic
2#20268267C211yesmaximal, characteristic, complemented
3#20268263C211yesmaximal, characteristic
4#20267894C211yesmaximal, characteristic, complemented
5#20267891C211yesmaximal, characteristic, complemented
6#20267889C211yesmaximal, characteristic, complemented
7#20267888C211yesmaximal, characteristic, complemented
8C4×#13110094C211yesmaximal, characteristic, complemented
9SD16×Dic103C211yesmaximal, characteristic, complemented
10#20267878C211yesmaximal, characteristic, complemented
11#20267826C211yesmaximal, characteristic, complemented
12#20267798C211yesmaximal, characteristic, complemented
13#20267794C211yesmaximal, characteristic
14#20267745C211yesmaximal, characteristic, complemented
15C4×SD16×C103C211yesmaximal, characteristic, complemented
16C2×Q8×D103C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18C2×#13110094C2211yescharacteristic
19C2×#13110093C2211yescharacteristic
20C2×#13110092C2211yescharacteristic
21SD16×D103C418yescomplemented
22C2×#13110088C2211yescharacteristic
23C2×C8×D103C2211yescharacteristic
24Q8×Dic103C2211yescharacteristic, complemented
25C4×Dic206—21no—
26C4×Dic206C2211yescharacteristic, complemented
27#15692986—21no—
28#15692986C2211yescharacteristic, complemented
29C4×D412C2211yescharacteristic
30D4×Dic103C2211yescharacteristic
31#15692983C2211yescharacteristic
32C4×C22⋊D103—21no—
33(C22⋊D103)⋊C4—21no—
34#15692979—21no—
35#15692979C2211yescharacteristic
36#15692979C2211yescharacteristic
37#15692978—21no—
38#15692978C2211yescharacteristic
39C2×(C2×D103)⋊C4—21no—
40C22⋊C4×D103—21no—
41#15692954C2211yescharacteristic, complemented
42#15692954C2211yescharacteristic, complemented
43#15692953C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692945C2211yescharacteristic, complemented
46#15692944C2211yescharacteristic, complemented
47#15692943C2211yescharacteristic
48#15692942C2211yescharacteristic
49#15692941C2211yescharacteristic
50#15692932C2211yescharacteristic, complemented
51#15692931C2211yescharacteristic, complemented
52C8×Dic103C2211yescharacteristic, complemented
53C2×SD16×C103C2211yescharacteristic
54C4×Q8×C103C2211yescharacteristic, complemented
55C4×D4×C103C2211yescharacteristic
56#106×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic
59C4×C8×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×D103C2311yescharacteristic
74#13110094C2×C414yescomplemented
75#13110093C2×C414yescomplemented
76#13110092C2×C414yescomplemented
77#13110088—22no—
78C2×C103⋊C8C2311yescharacteristic
79C2×C103⋊C8C2311yescharacteristic
80C8×D103C2×C414yescomplemented
81C4⋊Dic103—21no—
82C4⋊Dic103C2311yescharacteristic
83C4⋊Dic103C2311yescharacteristic
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4D411yescharacteristic
87Dic103⋊C4D411yescharacteristic
88C22⋊Dic103—21no—
89(C2×D103)⋊C4—21no—
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4D411yescharacteristic
94(C2×D103)⋊C4D411yescharacteristic
95C4×Dic103—21no—
96C4×Dic103—21no—
97C4×Dic103—21no—
98C4×Dic103—21no—
99C4×Dic103—21no—
100C4×Dic103C2311yescharacteristic
101C2×Q8×C103C2311yescharacteristic
102C2×D4×C103C2311yescharacteristic
103C22×C4×C103—21no—
104SD16×C103C2×C414yescomplemented
105C2×C8×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C4⋊C4×C103—21no—
108C4⋊C4×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C22⋊C4×C103—21no—
111C42×C103—21no—
112C42×C103C2311yescharacteristic
113C23×C103—21no—
114C22×D103—21no—
115C22×D103—24no—
116C22×D103—81no—
117C22×D103—81no—
118C22×D103C2×D411yescharacteristic
119Q8×C103—21no—
120Q8×C103C22×C412yes—
121D4×C103—21no—
122D4×C103C22×C412yes—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—81no—
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2411yescharacteristic
130C22⋊D103—24no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—81no—
135C2×Dic103C2×D411yescharacteristic
136C2×Dic103C2×D411yescharacteristic
137C2×Dic103C2×D411yescharacteristic
138D412—21no—
139D412C22×C412yes—
140C4×D103—24no—
141C4×D103—81no—
142C4×D103—81no—
143C4×D103C22×C412yes—
144C4×D103#4112yes—
145Dic206—21no—
146Dic206—24no—
147Dic206C22×C412yes—
148C8×C103—21no—
149C8×C103C22×C412yes—
150C103⋊C8—21no—
151C103⋊C8C22×C412yes—
152C22×C103—22no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103C22×D411yescharacteristic
156C2×D103—21no—
157C2×D103—21no—
158C2×D103—22no—
159C2×D103—41no—
160C2×D103—41no—
161C2×D103—84no—
162C2×D103C4×D412yes—
163C4×C103—22no—
164C4×C103—21no—
165C4×C103—21no—
166C4×C103—41no—
167C4×C103—41no—
168C4×C103C23×C411yescharacteristic
169C4×C103C2×#4111yescharacteristic
170Dic103—22no—
171Dic103—21no—
172Dic103—21no—
173Dic103—41no—
174Dic103—41no—
175Dic103C4×D412yes—
176C2×C103—42no—
177C2×C103C2×C4×D411yescharacteristic
178C2×C103#57711yescharacteristic
179C2×C103#57711yescharacteristic
180D103—22no—
181D103—42no—
182#2949—1031nomaximal, Sylow
183C103#294911yescharacteristic, complemented, Sylow
184C22×SD16—1031no—
185#519—1031no—
186#518—1031no—
187#440—1031no—
188#440—1031no—
189#440—1031no—
190#440—1031no—
191C4×SD16—1031no—
192C4×SD16—1031no—
193C4×SD16—1031no—
194C4×SD16D10311yescharacteristic, complemented
195#427—1031no—
196#419—1031no—
197#418—1031no—
198#405—1031no—
199C22×Q8—1031no—
200C22×D4—1031no—
201C2×SD16—1031no—
202C2×SD16—1031no—
203C2×SD16—1038no—
204C2×SD16—1031no—
205C2×SD16C2×D10311yescharacteristic
206C2×M16—1031no—
207C22×C8—1031no—
208C4×Q8—1031no—
209C4×Q8—1031no—
210C4×Q8—1031no—
211C4×Q8—2061no—
212C4×Q8—2061no—
213C4×Q8C2×D10311yescharacteristic, complemented
214C4×D4—1031no—
215C4×D4—1031no—
216C4×D4—1031no—
217C4×D4—2061no—
218C4×D4—2061no—
219C4×D4C2×D10311yescharacteristic
220#117—1031no—
221#117—1031no—
222#117—1031no—
223#117—2061no—
224#117—2061no—
225C2×C22⋊C4—2061no—
226C2×C22⋊C4—2061no—
227#107—1031no—
228#107—1031no—
229#106—1031no—
230#106C2×D10311yescharacteristic, complemented
231#103—1031no—
232#103—1031no—
233#103—1031no—
234#103C2×D10311yescharacteristic, complemented
235#102—1031no—
236#102—1031no—
237#102—1031no—
238#102C2×D10311yescharacteristic
239#97—1031no—
240#97—1031no—
241C4×C8—1031no—
242C4×C8C2×D10311yescharacteristic, complemented
243C24—2061no—
244C2×Q8—1034no—
245C2×Q8—1031no—
246C2×Q8—2061no—
247C2×Q8—2062no—
248C2×Q8C22×D10311yescharacteristic
249C2×D4—1034no—
250C2×D4—1031no—
251C2×D4—2062no—
252C2×D4—2061no—
253C2×D4C22×D10311yescharacteristic
254C22×C4—21no—
255C22×C4—1031no—
256C22×C4—2061no—
257C22×C4—2061no—
258C22×C4—2061no—
259C22×C4—2061no—
260SD16—1034no—
261SD16—1034no—
262SD16—1034no—
263SD16C4×D10314yescomplemented
264M16—2062no—
265C2×C8—1031no—
266C2×C8—1034no—
267C2×C8—1031no—
268C2×C8C22×D10311yescharacteristic
269C2×C8C22×D10311yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—1031no—
272C4⋊C4—1031no—
273C4⋊C4—1031no—
274C4⋊C4—1031no—
275C4⋊C4—2061no—
276C4⋊C4—2061no—
277C4⋊C4—2061no—
278C4⋊C4C22×D10311yescharacteristic
279C4⋊C4C22×D10311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1031no—
282C22⋊C4—1031no—
283C22⋊C4—2061no—
284C22⋊C4—2061no—
285C22⋊C4—2061no—
286C22⋊C4—2061no—
287C22⋊C4—2061no—
288C42—21no—
289C42—1031no—
290C42—2061no—
291C42—2061no—
292C42—2061no—
293C42—2061no—
294C42—2061no—
295C42C22×D10311yescharacteristic
296C23—21no—
297C23—8241no—
298C23—8241no—
299C23—1031no—
300C23—2064no—
301C23—2061no—
302Q8—21no—
303Q8—1032no—
304Q8—2064no—
305Q8—2061no—
306Q8C2×C4×D10312yes—
307D4—21no—
308D4—1032no—
309D4—2064no—
310D4—2061no—
311D4C2×C4×D10312yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—8241no—
317C2×C4—8241no—
318C2×C4—8241no—
319C2×C4—1031no—
320C2×C4—1032no—
321C2×C4—1032no—
322C2×C4—1031no—
323C2×C4—1031no—
324C2×C4—2064no—
325C2×C4—2061no—
326C2×C4—2061no—
327C2×C4—2061no—
328C2×C4D4×D10311yescharacteristic
329C2×C4D4×D10311yescharacteristic
330C2×C4C23×D10311yescharacteristic
331C8—21no—
332C8—1032no—
333C8—2061no—
334C8C2×C4×D10312yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—8244no—
339C22—1032no—
340C22—4121no—
341C22—4121no—
342C22—2062no—
343C22—2061no—
344C22—2061no—
345C22C2×D4×D10311yescharacteristic
346C4—21no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—1032no—
352C4—4121no—
353C4—4121no—
354C4—2061no—
355C4—2061no—
356C4—2062no—
357C4C22×C4×D10311yescharacteristic
358C4#41×D10311yescharacteristic
359C2—42no—
360C2—4122no—
361C2—2062no—
362C2C4×D4×D10311yescharacteristic
363C2#2026859711yescharacteristic
364C2#2026859811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
FittingC4×SD16×C103C2
socleC22×C103C22×D4
prime radicalC2×D4×D103C22
cosocleC2×C4×C103C24
hypercenterC4×SD16D103
hypocenterC103#2949
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #20268267C2semidirect
4. #20267894C2semidirect
5. #20267891C2semidirect
6. #20267889C2semidirect
7. #20267888C2semidirect
8. C4×#13110094C2semidirect
9. SD16×Dic103C2semidirect
10. #20267878C2semidirect
11. #20267826C2semidirect
12. #20267798C2semidirect
14. #20267745C2semidirect
15. C4×SD16×C103C2semidirect
21. SD16×D103C4semidirect
24. Q8×Dic103C22semidirect
26. C4×Dic206C22semidirect
28. #15692986C22semidirect
41. #15692954C22semidirect
42. #15692954C22semidirect
43. #15692953C22semidirect
44. #15692946C22semidirect
45. #15692945C22semidirect
46. #15692944C22semidirect
50. #15692932C22semidirect
51. #15692931C22semidirect
52. C8×Dic103C22semidirect
54. C4×Q8×C103C22semidirect
56. #106×C103C22semidirect
57. #103×C103C22semidirect
59. C4×C8×C103C22semidirect
64. Q8×D103C2×C4semidirect
74. #13110094C2×C4semidirect
75. #13110093C2×C4semidirect
76. #13110092C2×C4semidirect
80. C8×D103C2×C4semidirect
104. SD16×C103C2×C4semidirect
183. C103#2949semidirect
194. C4×SD16D103semidirect
213. C4×Q8C2×D103semidirect
230. #106C2×D103semidirect
234. #103C2×D103semidirect
242. C4×C8C2×D103semidirect
263. SD16C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1032
#202682672
#202682632
#202678942
#202678912
#202678892
#202678882
C4×#131100942
SD16×Dic1032
#202678782
#202678262
#202677982
#202677942
#202677452
C4×SD16×C1032
#2949103