Finite Group Databasebeta

← #27204938

Subgroups — #27204938

Order 13184.

440 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 143 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
1#20268344C211yesmaximal, characteristic, complemented
2C2×D4×Dic103C211yesmaximal, characteristic
3#20268093C212yesmaximal, complemented
4#20268089C212yesmaximal, complemented
5#20268079C212yesmaximal, complemented
6#20268069C212yesmaximal, complemented
7#20267834C211yesmaximal, characteristic, complemented
8#20267833C211yesmaximal, characteristic, complemented
9#20267814C211yesmaximal, characteristic, complemented
10#20267796C211yesmaximal, characteristic
11#418×C103C211yesmaximal, characteristic
12C23×Dic103—21no—
13C2×#13110089C2211yescharacteristic
14#15693020C2211yescharacteristic, complemented
15#15693020C2211yescharacteristic, complemented
16#15693012C2211yescharacteristic, complemented
17#15693012C2211yescharacteristic, complemented
18#15692998—21no—
19#15692998—21no—
20C4×Dic206—21no—
21C4×Dic206—21no—
22D4×Dic103—21no—
23D4×Dic103—21no—
24D4×Dic103C2212yes—
25D4×Dic103C2212yes—
26#15692980C2211yescharacteristic
27C2×C4⋊Dic103C2211yescharacteristic
28C2×C22⋊Dic103—21no—
29C2×C4×Dic103C2211yescharacteristic
30#15692955C2212yescomplemented
31#15692954C2212yescomplemented
32#15692953C2212yescomplemented
33#15692952C2212yescomplemented
34Dic103⋊C8C2212yescomplemented
35Dic103⋊C8C2212yescomplemented
36#15692942C2212yes—
37#15692942C2212yes—
38C22×D4×C103C2211yescharacteristic
39C2×M16×C103C2211yescharacteristic
40#117×C103C2211yescharacteristic
41#102×C103C2212yes—
42#102×C103C2212yes—
43C2×Dic206—21no—
44C2×Dic206—21no—
45C22×Dic103—21no—
46C22×Dic103—22no—
47C22×Dic103—22no—
48C22×Dic103—44no—
49C22×Dic103D411yescharacteristic
50C22×Dic103D411yescharacteristic
51#13110089—22no—
52C2×C103⋊C8C2312yes—
53C4⋊Dic103—21no—
54C4⋊Dic103—21no—
55C4⋊Dic103—21no—
56C4⋊Dic103C2311yescharacteristic
57C4⋊Dic103C2311yescharacteristic
58C4⋊Dic103C2312yes—
59Dic103⋊C4—21no—
60Dic103⋊C4—21no—
61Dic103⋊C4—21no—
62Dic103⋊C4—21no—
63C22⋊Dic103—21no—
64C22⋊Dic103—22no—
65C22⋊Dic103—22no—
66C4×Dic103—21no—
67C4×Dic103D411yescharacteristic
68C4×Dic103D411yescharacteristic
69C4×Dic103C2311yescharacteristic
70C4×Dic103C2311yescharacteristic
71C24×C103—21no—
72C2×D4×C103—21no—
73C2×D4×C103—22no—
74C2×D4×C103Q814yescomplemented
75C2×D4×C103C2312yes—
76C22×C4×C103C2311yescharacteristic
77M16×C103—22no—
78C2×C8×C103C2312yes—
79C4⋊C4×C103C2311yescharacteristic
80C4⋊C4×C103C2311yescharacteristic
81C22⋊C4×C103—21no—
82C42×C103—21no—
83C23×C103—24no—
84C23×C103—22no—
85C23×C103—42no—
86C23×C103—42no—
87C23×C103C2×D411yescharacteristic
88D4×C103—24no—
89D4×C103—22no—
90D4×C103C2×Q814yes—
91C2×C4×C103—21no—
92C2×C4×C103—21no—
93C2×C4×C103C2×D411yescharacteristic
94C2×C4×C103C2×Q812yes—
95C2×C4×C103#4112yes—
96C2×C4×C103C2411yescharacteristic
97C2×Dic103—22no—
98C2×Dic103—21no—
99C2×Dic103—21no—
100C2×Dic103—22no—
101C2×Dic103—41no—
102C2×Dic103—44no—
103C2×Dic103—42no—
104C2×Dic103—44no—
105C2×Dic103C2×D411yescharacteristic
106C2×Dic103C2×D411yescharacteristic
107C2×Dic103C2×D411yescharacteristic
108C2×Dic103C2×D411yescharacteristic
109Dic206—42no—
110Dic206—42no—
111C8×C103—22no—
112C103⋊C8—22no—
113C22×C103—21no—
114C22×C103—21no—
115C22×C103—24no—
116C22×C103—48no—
117C22×C103—42no—
118C22×C103—42no—
119C22×C103C22⋊Q812yes—
120C22×C103C22×D411yescharacteristic
121C4×C103—41no—
122C4×C103—41no—
123C4×C103C22⋊Q812yes—
124C4×C103C22×Q811yescharacteristic
125C4×C103C2×#4111yescharacteristic
126Dic103—21no—
127Dic103—21no—
128Dic103—21no—
129Dic103—41no—
130Dic103—42no—
131Dic103—41no—
132Dic103AGL(1,ℤ/8)12yes—
133C2×C103—22no—
134C2×C103—44no—
135C2×C103C2×C22⋊Q811yescharacteristic
136C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C103#57511yescharacteristic
138#3077—1031nomaximal, Sylow
139C103#307711yescharacteristic, complemented, Sylow
140#533—1031no—
141C2×C4×D4—1031no—
142#478—1032no—
143#478—1032no—
144#476—1032no—
145#474—1032no—
146#428—1031no—
147#428—1031no—
148#423—1031no—
149#418—1031no—
150#418D10311yescharacteristic
151C22×D4C2×D10311yescharacteristic
152C23×C4—2061no—
153C2×M16—1031no—
154C2×M16C2×D10311yescharacteristic
155C4⋊Q8—1031no—
156C4⋊Q8—1031no—
157#125—1031no—
158#125—1031no—
159C22⋊Q8—2061no—
160C22⋊Q8—2061no—
161C4×Q8—2061no—
162C4×Q8—2061no—
163C4×D4—1032no—
164C4×D4—1032no—
165C4×D4—2061no—
166C4×D4—2061no—
167#117—1031no—
168#117C2×D10311yescharacteristic
169C2×C4⋊C4—1031no—
170C2×C22⋊C4—2061no—
171C2×C42—1031no—
172#107—1032no—
173#107—1032no—
174#106—1032no—
175#106—1032no—
176C4⋊C8—1032no—
177C4⋊C8—1032no—
178#102—1032no—
179#102—1032no—
180#102C2×D10312yes—
181#102C2×D10312yes—
182C24—21no—
183C2×Q8—2061no—
184C2×Q8—2061no—
185C2×D4—21no—
186C2×D4—22no—
187C2×D4Dic20614yescomplemented
188C2×D4C22×D10312yes—
189C22×C4—1031no—
190C22×C4—1031no—
191C22×C4—4124no—
192C22×C4—2062no—
193C22×C4—2062no—
194C22×C4—2061no—
195C22×C4C22×D10311yescharacteristic
196M16—22no—
197M16—2062no—
198C2×C8—1032no—
199C2×C8C22×D10312yes—
200C4⋊C4—1031no—
201C4⋊C4—1031no—
202C4⋊C4—1032no—
203C4⋊C4—2061no—
204C4⋊C4—2061no—
205C4⋊C4—2061no—
206C4⋊C4—2061no—
207C4⋊C4—2061no—
208C4⋊C4—2061no—
209C4⋊C4—2061no—
210C4⋊C4C22×D10311yescharacteristic
211C4⋊C4C22×D10311yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—2062no—
214C22⋊C4—2062no—
215C22⋊C4—2061no—
216C42—21no—
217C42—1031no—
218C42—1031no—
219C42—1031no—
220C42—1031no—
221C42—2061no—
222C23—22no—
223C23—24no—
224C23—42no—
225C23—42no—
226C23D4×D10311yescharacteristic
227Q8—4122no—
228Q8—4122no—
229D4—22no—
230D4—24no—
231D4C2×Dic20614yes—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—1031no—
235C2×C4—1031no—
236C2×C4—1031no—
237C2×C4—1031no—
238C2×C4—4124no—
239C2×C4—4122no—
240C2×C4—4124no—
241C2×C4—4121no—
242C2×C4—2062no—
243C2×C4—2061no—
244C2×C4—2061no—
245C2×C4—2062no—
246C2×C4D4×D10311yescharacteristic
247C2×C4C2×Dic20612yes—
248C2×C4#1311010412yes—
249C2×C4C23×D10311yescharacteristic
250C8—22no—
251C8—2062no—
252C22—21no—
253C22—21no—
254C22—24no—
255C22—48no—
256C22—42no—
257C22—42no—
258C22#1569299812yes—
259C22C2×D4×D10311yescharacteristic
260C4—41no—
261C4—41no—
262C4—1032no—
263C4—4122no—
264C4—4121no—
265C4—4121no—
266C4—2061no—
267C4—2061no—
268C4—2061no—
269C4#1569299812yes—
270C4C22×Dic20611yescharacteristic
271C4C2×#1311010411yescharacteristic
272C2—22no—
273C2—44no—
274C2C2×#1569299811yescharacteristic
275C2AGL(1,ℤ/8)×D10311yescharacteristic
276C2#2026858711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#418×C103C2
socleC22×C103C22×D4
prime radicalC22×D4×C103C22
hypercenter#418D103
hypocenterC103#3077
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #20268344C2semidirect
3. #20268093C2semidirect
4. #20268089C2semidirect
5. #20268079C2semidirect
6. #20268069C2semidirect
7. #20267834C2semidirect
8. #20267833C2semidirect
9. #20267814C2semidirect
14. #15693020C22semidirect
15. #15693020C22semidirect
16. #15693012C22semidirect
17. #15693012C22semidirect
30. #15692955C22semidirect
31. #15692954C22semidirect
32. #15692953C22semidirect
33. #15692952C22semidirect
34. Dic103⋊C8C22semidirect
35. Dic103⋊C8C22semidirect
74. C2×D4×C103Q8semidirect
139. C103#3077semidirect
187. C2×D4Dic206semidirect

Maximal subgroups

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

subgroupindex
#202683442
C2×D4×Dic1032
#202680932
#202680892
#202680792
#202680692
#202678342
#202678332
#202678142
#202677962
#418×C1032
#3077103