Finite Group Databasebeta

← #27204723

Subgroups — #27204723

Order 13184.

520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15693040C211yesmaximal, characteristic, complemented
2C22×C8×D103C211yesmaximal, characteristic, complemented
3#20268301C212yesmaximal, complemented
4#20268033C211yesmaximal, characteristic, complemented
5#20268032C211yesmaximal, characteristic, complemented
6#20268024C211yesmaximal, characteristic, complemented
7#20268019C212yesmaximal, complemented
8#20268018C212yesmaximal, complemented
9#20267828C211yesmaximal, characteristic, complemented
10#20267784C212yesmaximal, complemented
11#466×C103C211yesmaximal, characteristic, complemented
12C2×#13110104C2212yes—
13C22×C4×D103C2211yescharacteristic
14#15693040—24no—
15C2×Dic412C2211yescharacteristic, complemented
16C2×#13110093C2212yescomplemented
17C22×C103⋊C8C2211yescharacteristic
18C2×C8×D103—24no—
19C2×C8×D103C2211yescharacteristic
20C2×C8×D103C2211yescharacteristic
21C2×C8×D103C2211yescharacteristic
22C2×C8×D103C2211yescharacteristic
23#15693003—22no—
24#15693001C2212yes—
25#15693000C2212yes—
26#15692992C2212yes—
27#15692989—22no—
28D4×Dic103—22no—
29(C22⋊D103)⋊C4—22no—
30#15692979C2212yes—
31#15692955C2211yescharacteristic, complemented
32#15692952C2212yescomplemented
33#15692946C2212yescomplemented
34#15692944C2212yescomplemented
35#15692942C2212yescomplemented
36C2×D8×C103C2211yescharacteristic, complemented
37C22×C8×C103C2211yescharacteristic
38#121×C103C2212yes—
39#107×C103C2211yescharacteristic, complemented
40#102×C103C2212yescomplemented
41C23×D103D411yescharacteristic
42#13110104—24no—
43#13110104—24no—
44C2×Dic206C2312yes—
45C2×C22⋊D103—22no—
46C2×C22⋊D103—22no—
47C22×Dic103—22no—
48C22×Dic103D411yescharacteristic
49C2×C4×D103—22no—
50C2×C4×D103—22no—
51C2×C4×D103D411yescharacteristic
52C2×C4×D103D411yescharacteristic
53C2×C4×D103C2311yescharacteristic
54C2×C4×D103C2311yescharacteristic
55Dic412—22no—
56#13110093—24no—
57C2×C103⋊C8—22no—
58C2×C103⋊C8C2311yescharacteristic
59C2×C103⋊C8C2311yescharacteristic
60C8×D103—22no—
61C8×D103—22no—
62C8×D103—22no—
63C8×D103D414yescomplemented
64C4⋊Dic103—22no—
65C4⋊Dic103C2312yes—
66Dic103⋊C4—22no—
67C22⋊Dic103—22no—
68C22⋊Dic103—22no—
69(C2×D103)⋊C4—22no—
70(C2×D103)⋊C4—22no—
71C4×Dic103—22no—
72C2×D4×C103—22no—
73C2×D4×C103C2312yes—
74C22×C4×C103C2311yescharacteristic
75D8×C103—22no—
76C2×C8×C103—22no—
77C2×C8×C103C2311yescharacteristic
78C2×C8×C103C2311yescharacteristic
79C4⋊C4×C103C2312yes—
80C22⋊C4×C103—22no—
81C23×C103—22no—
82C23×C103C2×D411yescharacteristic
83C22×D103—22no—
84C22×D103—22no—
85C22×D103—22no—
86C22×D103C2×D411yescharacteristic
87C22×D103C2×D411yescharacteristic
88D4×C103—22no—
89D4×C103—22no—
90D4×C103—44no—
91C2×C4×C103—21no—
92C2×C4×C103—21no—
93C2×C4×C103—22no—
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2411yescharacteristic
96C22⋊D103—44no—
97C22⋊D103—44no—
98C2×Dic103—22no—
99C2×Dic103—22no—
100C2×Dic103—22no—
101C2×Dic103—44no—
102C2×Dic103C2×D411yescharacteristic
103C2×Dic103C2×D411yescharacteristic
104C4×D103—22no—
105C4×D103—21no—
106C4×D103—21no—
107C4×D103—22no—
108C4×D103C2×D412yes—
109C4×D103#4112yes—
110Dic206—22no—
111Dic206—22no—
112C8×C103—21no—
113C8×C103C2×D412yes—
114C103⋊C8—21no—
115C103⋊C8C2×D412yes—
116C22×C103—21no—
117C22×C103—21no—
118C22×C103—42no—
119C22×C103—42no—
120C22×C103—42no—
121C22×C103#13512yescomplemented
122C22×C103C22×D411yescharacteristic
123C2×D103—28no—
124C2×D103—21no—
125C2×D103—21no—
126C2×D103—21no—
127C2×D103—21no—
128C2×D103#12112yes—
129C2×D103#13512yescomplemented
130C4×C103—21no—
131C4×C103—42no—
132C4×C103C22×D411yescharacteristic
133C4×C103C2×#4111yescharacteristic
134Dic103—21no—
135Dic103—42no—
136Dic103—42no—
137Dic103#12112yes—
138C2×C103—22no—
139C2×C103—82no—
140C2×C103C2×#12111yescharacteristic
141C2×C103C2×#13511yescharacteristic
142C2×C103C2×#13511yescharacteristic
143D103—22no—
144D103—22no—
145#3050—1031nomaximal, Sylow
146C103#305011yescharacteristic, complemented, Sylow
147C2×#135—1031no—
148C23×C8—1031no—
149#525—1032no—
150#467—1031no—
151#467—1031no—
152#466—1031no—
153#466D10311yescharacteristic, complemented
154#465—1032no—
155#465—1032no—
156#427—1031no—
157#416—1032no—
158C2×#41—1032no—
159C23×C4—1031no—
160#135—2064no—
161C2×Q16—1031no—
162C2×SD16—1032no—
163C2×D8C2×D10311yescharacteristic, complemented
164C22×C8—1031no—
165C22×C8—1031no—
166C22×C8—1031no—
167C22×C8—1031no—
168C22×C8—1031no—
169C22×C8—2064no—
170C22×C8C2×D10311yescharacteristic
171#123—2062no—
172C22⋊Q8—1032no—
173C22⋊Q8—1032no—
174#121—1032no—
175#121C2×D10312yes—
176#120—2062no—
177C4×D4—2062no—
178C4×D4—2062no—
179#117—1032no—
180#107—1031no—
181#107C2×D10311yescharacteristic, complemented
182#106—1032no—
183#103—1032no—
184#103—1032no—
185#102—1032no—
186#102C2×D10312yescomplemented
187C24—1031no—
188#41—2064no—
189#41—2064no—
190C2×Q8—1032no—
191C2×D4—22no—
192C2×D4—2062no—
193C2×D4—2062no—
194C2×D4C22×D10312yes—
195C22×C4—1031no—
196C22×C4—1031no—
197C22×C4—1031no—
198C22×C4—1031no—
199C22×C4—1031no—
200C22×C4—2062no—
201C22×C4—2062no—
202C22×C4—2062no—
203C22×C4C22×D10311yescharacteristic
204Q16—2062no—
205SD16—2064no—
206D8—22no—
207C2×C8—22no—
208C2×C8—1031no—
209C2×C8—1034no—
210C2×C8—1031no—
211C2×C8—2062no—
212C2×C8—2062no—
213C2×C8—2062no—
214C2×C8—2062no—
215C2×C8C22×D10311yescharacteristic
216C2×C8C22×D10311yescharacteristic
217C4⋊C4—1032no—
218C4⋊C4—2062no—
219C4⋊C4—2062no—
220C4⋊C4C22×D10312yes—
221C22⋊C4—22no—
222C22⋊C4—2062no—
223C22⋊C4—2062no—
224C22⋊C4—2062no—
225C22⋊C4—2062no—
226C42—2062no—
227C23—22no—
228C23—1031no—
229C23—1031no—
230C23—2062no—
231C23—2062no—
232C23—2062no—
233C23D4×D10311yescharacteristic
234Q8—2062no—
235Q8—2062no—
236D4—22no—
237D4—22no—
238D4—44no—
239D4—4124no—
240D4—4124no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—1031no—
245C2×C4—1032no—
246C2×C4—1032no—
247C2×C4—1031no—
248C2×C4—4124no—
249C2×C4—2062no—
250C2×C4—2062no—
251C2×C4—2062no—
252C2×C4—2062no—
253C2×C4—2062no—
254C2×C4—2061no—
255C2×C4—2061no—
256C2×C4D4×D10311yescharacteristic
257C2×C4C23×D10311yescharacteristic
258C8—21no—
259C8—1032no—
260C8—2061no—
261C8D4×D10312yes—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—1032no—
268C22—1032no—
269C22—2068no—
270C22—2061no—
271C22—2061no—
272C22—2061no—
273C22—2061no—
274C22#1569304012yescomplemented
275C22C2×D4×D10311yescharacteristic
276C4—21no—
277C4—42no—
278C4—1032no—
279C4—4122no—
280C4—4122no—
281C4—2061no—
282C4C2×D4×D10311yescharacteristic
283C4#41×D10311yescharacteristic
284C2—22no—
285C2—82no—
286C2—2062no—
287C2—2062no—
288C2#121×D10311yescharacteristic
289C2#135×D10311yescharacteristic
290C2C2×#1569304011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#466×C103C2
socleC22×C103C22×D4
hypercenter#466D103
hypocenterC103#3050
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#15693040C2semidirect
2. C22×C8×D103C2semidirect
3. #20268301C2semidirect
4. #20268033C2semidirect
5. #20268032C2semidirect
6. #20268024C2semidirect
7. #20268019C2semidirect
8. #20268018C2semidirect
9. #20267828C2semidirect
10. #20267784C2semidirect
11. #466×C103C2semidirect
15. C2×Dic412C22semidirect
16. C2×#13110093C22semidirect
31. #15692955C22semidirect
32. #15692952C22semidirect
33. #15692946C22semidirect
34. #15692944C22semidirect
35. #15692942C22semidirect
36. C2×D8×C103C22semidirect
39. #107×C103C22semidirect
40. #102×C103C22semidirect
63. C8×D103D4semidirect
121. C22×C103#135semidirect
129. C2×D103#135semidirect
146. C103#3050semidirect
153. #466D103semidirect
163. C2×D8C2×D103semidirect
181. #107C2×D103semidirect
186. #102C2×D103semidirect
274. C22#15693040semidirect

Maximal subgroups

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

subgroupindex
C2×#156930402
C22×C8×D1032
#202683012
#202680332
#202680322
#202680242
#202680192
#202680182
#202678282
#202677842
#466×C1032
#3050103