Finite Group Databasebeta

← #27205954

Subgroups — #27205954

Order 13184.

466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692995C211yesmaximal, characteristic, complemented
2#20268119C211yesmaximal, characteristic, complemented
3#20268115C212yesmaximal, complemented
4#20268102C211yesmaximal, characteristic, complemented
5#20268042C212yesmaximal, complemented
6#20268039C212yesmaximal, complemented
7#20267941C211yesmaximal, characteristic, complemented
8#20267936C212yesmaximal, complemented
9#20267924C211yesmaximal, characteristic, complemented
10#20267755C211yesmaximal, characteristic, complemented
11#525×C103C211yesmaximal, characteristic, complemented
12C22×D412C2211yescharacteristic
13C22×C22⋊D103—21no—
14C2×#13110092C2212yescomplemented
15C2×#13110090C2212yescomplemented
16C2×#13110089C2212yescomplemented
17#15692995—21no—
18#15692995—21no—
19#15692995C2212yes—
20#15692995C2212yes—
21C2×C4⋊Dic103C2211yescharacteristic
22C2×(C2×D103)⋊C4—21no—
23#15692954C2212yescomplemented
24#15692952C2212yescomplemented
25#15692945C2212yescomplemented
26#15692942C2212yescomplemented
27#15692941C2212yescomplemented
28#15692941C2212yescomplemented
29C22⋊(C103⋊C8)C2211yescharacteristic
30C22⋊(C103⋊C8)C2211yescharacteristic
31C22⋊(C103⋊C8)C2212yescomplemented
32C2×#41×C103C2211yescharacteristic, complemented
33C23×C4×C103C2211yescharacteristic
34#123×C103—21no—
35C22⋊Q8×C103C2211yescharacteristic
36C22⋊Q8×C103C2211yescharacteristic, complemented
37#121×C103C2211yescharacteristic
38#121×C103C2211yescharacteristic, complemented
39#120×C103—21no—
40C4×D4×C103—21no—
41C4×D4×C103—21no—
42#117×C103C2211yescharacteristic, complemented
43C23×D103—21no—
44C2×D412—21no—
45C2×D412—42no—
46C2×D412C2312yes—
47C2×C22⋊D103—22no—
48C2×C22⋊D103—22no—
49C2×C22⋊D103—44no—
50C22×Dic103—21no—
51#13110092—42no—
52#13110090—42no—
53#13110089—42no—
54C2×C103⋊C8C2312yes—
55C2×C103⋊C8C2312yes—
56C4⋊Dic103—21no—
57C4⋊Dic103C2312yes—
58(C2×D103)⋊C4—22no—
59(C2×D103)⋊C4—22no—
60C24×C103D411yescharacteristic
61#41×C103—42no—
62C2×Q8×C103C2311yescharacteristic
63C2×D4×C103—21no—
64C2×D4×C103—21no—
65C2×D4×C103—21no—
66C2×D4×C103C2311yescharacteristic
67C22×C4×C103—21no—
68C22×C4×C103—42no—
69C22×C4×C103D411yescharacteristic
70C22×C4×C103D411yescharacteristic
71C22×C4×C103D411yescharacteristic
72C22×C4×C103C2311yescharacteristic
73C22×C4×C103C2311yescharacteristic
74C22×C4×C103C2311yescharacteristic
75C4⋊C4×C103—21no—
76C4⋊C4×C103—21no—
77C4⋊C4×C103C2311yescharacteristic
78C4⋊C4×C103C2311yescharacteristic
79C22⋊C4×C103—21no—
80C22⋊C4×C103—21no—
81C22⋊C4×C103—21no—
82C22⋊C4×C103—21no—
83C22⋊C4×C103—21no—
84C42×C103—21no—
85C23×C103—22no—
86C23×C103—21no—
87C23×C103—41no—
88C23×C103—41no—
89C23×C103C2×D411yescharacteristic
90C23×C103C2×D411yescharacteristic
91C23×C103C2×D411yescharacteristic
92C22×D103—22no—
93C22×D103—42no—
94C22×D103—42no—
95C22×D103—42no—
96Q8×C103—22no—
97D4×C103—22no—
98D4×C103—42no—
99D4×C103—42no—
100D4×C103—42no—
101C2×C4×C103—22no—
102C2×C4×C103—22no—
103C2×C4×C103—22no—
104C2×C4×C103—21no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—41no—
108C2×C4×C103—41no—
109C2×C4×C103—41no—
110C2×C4×C103—42no—
111C2×C4×C103C2×D411yescharacteristic
112C2×C4×C103C2×D411yescharacteristic
113C2×C4×C103C2×D411yescharacteristic
114C2×C4×C103C2411yescharacteristic
115C22⋊D103—44no—
116C22⋊D103—44no—
117C2×Dic103—22no—
118C2×Dic103—42no—
119D412—22no—
120D412—22no—
121D412—42no—
122C103⋊C8—22no—
123C103⋊C8—22no—
124C22×C103—21no—
125C22×C103—21no—
126C22×C103—21no—
127C22×C103—21no—
128C22×C103—21no—
129C22×C103—21no—
130C22×C103—21no—
131C22×C103—21no—
132C22×C103—44no—
133C22×C103—41no—
134C22×C103—41no—
135C22×C103—41no—
136C22×C103AGL(1,ℤ/8)12yes—
137C22×C103C22×D411yescharacteristic
138C2×D103—42no—
139C2×D103—42no—
140C2×D103—42no—
141C2×D103—84no—
142C4×C103—21no—
143C4×C103—21no—
144C4×C103—21no—
145C4×C103—41no—
146C4×C103—41no—
147C4×C103—41no—
148C4×C103H(5,𝔽2)12yes—
149Dic103—42no—
150C2×C103—22no—
151C2×C103—41no—
152C2×C103—41no—
153C2×C103—81no—
154C2×C103#53411yescharacteristic
155C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C103#57511yescharacteristic
157D103—82no—
158#3194—1031nomaximal, Sylow
159C103#319411yescharacteristic, complemented, Sylow
160#525D10311yescharacteristic, complemented
161C2×#121—1031no—
162#483—1031no—
163#482—1032no—
164#480—1031no—
165#469—1032no—
166#468—1032no—
167#450—1031no—
168#449—1032no—
169#447—1031no—
170#407—1031no—
171C2×#41C2×D10311yescharacteristic, complemented
172C22×D4—1031no—
173C22×D4—2061no—
174C23×C4C2×D10311yescharacteristic
175C2×SD16—1032no—
176C2×D8—1032no—
177C2×M16—1032no—
178#123—21no—
179C22⋊Q8C2×D10311yescharacteristic
180C22⋊Q8C2×D10311yescharacteristic, complemented
181#121—1032no—
182#121—1032no—
183#121—2061no—
184#121—2061no—
185#121C2×D10311yescharacteristic
186#121C2×D10311yescharacteristic, complemented
187#120—21no—
188C4×D4—21no—
189C4×D4—21no—
190#117C2×D10311yescharacteristic, complemented
191C2×C4⋊C4—1031no—
192C2×C22⋊C4—2061no—
193#107—1032no—
194#106—1032no—
195#103—1032no—
196#102—1032no—
197#102—1032no—
198#102—1032no—
199C22⋊C8—1031no—
200C22⋊C8—1031no—
201C22⋊C8—1032no—
202C24—2061no—
203C24C22⋊D10311yescharacteristic
204#41—42no—
205C2×Q8C22×D10311yescharacteristic
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—1032no—
210C2×D4—4122no—
211C2×D4—4124no—
212C2×D4—2062no—
213C2×D4—2062no—
214C2×D4—2061no—
215C2×D4C22×D10311yescharacteristic
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—2061no—
219C22×C4C22⋊D10311yescharacteristic
220C22×C4C22⋊D10311yescharacteristic
221C22×C4C22⋊D10311yescharacteristic
222C22×C4C22×D10311yescharacteristic
223C22×C4C22×D10311yescharacteristic
224C22×C4C22×D10311yescharacteristic
225SD16—4122no—
226D8—4122no—
227M16—4122no—
228C2×C8—1032no—
229C2×C8—1032no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—1032no—
233C4⋊C4—2061no—
234C4⋊C4C22×D10311yescharacteristic
235C4⋊C4C22×D10311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—2062no—
242C22⋊C4—2062no—
243C42—21no—
244C23—22no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23—4122no—
249C23—4122no—
250C23—4122no—
251C23—2062no—
252C23C2×C22⋊D10311yescharacteristic
253C23C2×C22⋊D10311yescharacteristic
254C23C2×C22⋊D10311yescharacteristic
255Q8—22no—
256D4—22no—
257D4—42no—
258D4—42no—
259D4—42no—
260D4—4122no—
261D4—4124no—
262D4—4124no—
263D4—2062no—
264D4—2062no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—4122no—
276C2×C4—2062no—
277C2×C4C2×C22⋊D10311yescharacteristic
278C2×C4C2×C22⋊D10311yescharacteristic
279C2×C4C2×C22⋊D10311yescharacteristic
280C2×C4C23×D10311yescharacteristic
281C8—2062no—
282C8—2062no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—8244no—
296C22—4122no—
297C22—4122no—
298C22—4122no—
299C22#1569304612yes—
300C22C22×C22⋊D10311yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—4122no—
308C4#1569306612yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—81no—
313C2—8242no—
314C2#2026835011yescharacteristic
315C2C2×#1569304611yescharacteristic
316C2#2026858911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#525×C103C2
socleC22×C103C22×D4
hypercenter#525D103
hypocenterC103#3194
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#15692995C2semidirect
2. #20268119C2semidirect
3. #20268115C2semidirect
4. #20268102C2semidirect
5. #20268042C2semidirect
6. #20268039C2semidirect
7. #20267941C2semidirect
8. #20267936C2semidirect
9. #20267924C2semidirect
10. #20267755C2semidirect
11. #525×C103C2semidirect
14. C2×#13110092C22semidirect
15. C2×#13110090C22semidirect
16. C2×#13110089C22semidirect
23. #15692954C22semidirect
24. #15692952C22semidirect
25. #15692945C22semidirect
26. #15692942C22semidirect
27. #15692941C22semidirect
28. #15692941C22semidirect
31. C22⋊(C103⋊C8)C22semidirect
32. C2×#41×C103C22semidirect
36. C22⋊Q8×C103C22semidirect
38. #121×C103C22semidirect
42. #117×C103C22semidirect
159. C103#3194semidirect
160. #525D103semidirect
171. C2×#41C2×D103semidirect
180. C22⋊Q8C2×D103semidirect
186. #121C2×D103semidirect
190. #117C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929952
#202681192
#202681152
#202681022
#202680422
#202680392
#202679412
#202679362
#202679242
#202677552
#525×C1032
#3194103