Finite Group Databasebeta

← #27195552

Subgroups — #27195552

Order 13184.

578 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 93 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×#15692989C211yesmaximal, characteristic
2C2×#15692936C211yesmaximal, characteristic, complemented
3#20267646C212yesmaximal, complemented
4#20267558C212yesmaximal, complemented
5#518×C103C211yesmaximal, characteristic, complemented
6C24×D103C2211yescharacteristic
7C22×C22⋊D103—21no—
8#15692989—22no—
9#15692989C414yescomplemented
10C2×C22⋊Dic103C2212yes—
11C2×C22⋊Dic103C2211yescharacteristic
12C2×(C2×D103)⋊C4—21no—
13C2×(C2×D103)⋊C4—24no—
14#15692936—22no—
15C22×D4×C103C2211yescharacteristic
16C4×D4×C103—24no—
17#117×C103—21no—
18C2×C22⋊C4×C103—21no—
19C2×C22⋊C4×C103C2212yes—
20C23×D103—21no—
21C23×D103—22no—
22C23×D103—21no—
23C23×D103—22no—
24C23×D103—44no—
25C23×D103C2×C412yescomplemented
26C2×C22⋊D103—24no—
27C2×C22⋊D103—44no—
28C22×Dic103—21no—
29C22×Dic103—22no—
30C22⋊Dic103—21no—
31C22⋊Dic103—22no—
32C22⋊Dic103—22no—
33C22⋊Dic103C2×C412yescomplemented
34(C2×D103)⋊C4—24no—
35(C2×D103)⋊C4—48no—
36C24×C103D411yescharacteristic
37C24×C103C2311yescharacteristic
38C2×D4×C103—22no—
39C2×D4×C103—22no—
40C2×D4×C103C2×C412yes—
41C2×D4×C103D412yes—
42C22×C4×C103—22no—
43C22×C4×C103D411yescharacteristic
44C22×C4×C103D414yescomplemented
45C4⋊C4×C103—22no—
46C22⋊C4×C103—22no—
47C22⋊C4×C103—22no—
48C22⋊C4×C103—22no—
49C42×C103—22no—
50C23×C103—21no—
51C23×C103—21no—
52C23×C103—42no—
53C23×C103—42no—
54C23×C103C22⋊C412yescomplemented
55C23×C103C22×C411yescharacteristic
56C23×C103C2×D411yescharacteristic
57C23×C103C2×D412yes—
58C23×C103C2×D411yescharacteristic
59C23×C103#4112yes—
60C22×D103—28no—
61C22×D103—24no—
62C22×D103—22no—
63C22×D103—24no—
64C22×D103—44no—
65C22×D103—44no—
66C22×D103—48no—
67C22×D103—44no—
68C22×D103—42no—
69C22×D103—41no—
70C22×D103—42no—
71C22×D103—41no—
72D4×C103—24no—
73D4×C103—24no—
74C2×C4×C103—21no—
75C2×C4×C103—21no—
76C2×C4×C103—24no—
77C2×C4×C103—44no—
78C2×C4×C103—82no—
79C2×C4×C103C22⋊C412yescomplemented
80C22⋊D103—48no—
81C2×Dic103—22no—
82C2×Dic103—42no—
83C2×Dic103—44no—
84C2×Dic103—42no—
85C22×C103—24no—
86C22×C103—22no—
87C22×C103—22no—
88C22×C103—41no—
89C22×C103—41no—
90C22×C103—42no—
91C22×C103—42no—
92C22×C103—42no—
93C22×C103—81no—
94C22×C103C2×C22⋊C411yescharacteristic
95C22×C103C4×D412yes—
96C22×C103#12011yescharacteristic
97C22×C103#12112yes—
98C22×C103#12311yescharacteristic
99C2×D103—24no—
100C2×D103—28no—
101C2×D103—42no—
102C2×D103—48no—
103C2×D103—44no—
104C2×D103—44no—
105C2×D103—42no—
106C2×D103—44no—
107C4×C103—22no—
108C4×C103—44no—
109Dic103—42no—
110Dic103—82no—
111C2×C103—21no—
112C2×C103—22no—
113C2×C103—22no—
114C2×C103—21no—
115C2×C103—42no—
116C2×C103#38611yescharacteristic
117C2×C103B(4,𝔽2)12yes—
118D103—44no—
119#1889—1031nomaximal, Sylow
120C103#188911yescharacteristic, complemented, Sylow
121C2×#120—1031no—
122#518D10311yescharacteristic, complemented
123C2×#99—1031no—
124#379—1032no—
125#342—1032no—
126C25—1031no—
127C22×D4—2061no—
128C22×D4C2×D10311yescharacteristic
129#120—1034no—
130#120—2062no—
131C4×D4—24no—
132#117—21no—
133C2×C22⋊C4—21no—
134C2×C22⋊C4—1031no—
135C2×C22⋊C4—1032no—
136C2×C22⋊C4—2064no—
137C2×C22⋊C4—2061no—
138C2×C22⋊C4C2×D10312yes—
139#99—2062no—
140C24—1032no—
141C24—4124no—
142C24—2061no—
143C24—2062no—
144C24—2062no—
145C24—2061no—
146C24C22⋊D10311yescharacteristic
147C24C22×D10311yescharacteristic
148C2×D4—22no—
149C2×D4—22no—
150C2×D4—4124no—
151C2×D4—2064no—
152C2×D4C4×D10312yes—
153C2×D4D41212yes—
154C22×C4—22no—
155C22×C4—2062no—
156C22×C4—2061no—
157C22×C4C22⋊D10311yescharacteristic
158C22×C4C22⋊D10314yescomplemented
159C4⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—1032no—
164C22⋊C4—4128no—
165C22⋊C4—2062no—
166C22⋊C4—2062no—
167C22⋊C4—2061no—
168C22⋊C4—2064no—
169C42—22no—
170C23—21no—
171C23—21no—
172C23—42no—
173C23—42no—
174C23—4124no—
175C23—4122no—
176C23—4124no—
177C23—4128no—
178C23—4124no—
179C23—4121no—
180C23—4122no—
181C23—4121no—
182C23—2068no—
183C23—2064no—
184C23—2062no—
185C23—2064no—
186C23(C2×D103)⋊C412yescomplemented
187C23C2×C4×D10311yescharacteristic
188C23C2×C22⋊D10311yescharacteristic
189C23C2×C22⋊D10312yes—
190C23C2×D41211yescharacteristic
191C23#1311010512yes—
192D4—24no—
193D4—24no—
194D4—4128no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—24no—
198C2×C4—44no—
199C2×C4—82no—
200C2×C4—4124no—
201C2×C4—4122no—
202C2×C4—4122no—
203C2×C4—2062no—
204C2×C4(C2×D103)⋊C412yescomplemented
205C22—24no—
206C22—22no—
207C22—22no—
208C22—41no—
209C22—41no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—81no—
214C22—4128no—
215C22—4122no—
216C22—4124no—
217C22—4124no—
218C22—4122no—
219C22—4124no—
220C22—2064no—
221C22—2068no—
222C22C2×(C2×D103)⋊C411yescharacteristic
223C22C4×C22⋊D10312yes—
224C22#1569299011yescharacteristic
225C22#1569299512yes—
226C22#1569300411yescharacteristic
227C4—22no—
228C4—44no—
229C4—8242no—
230C4—4122no—
231C2—22no—
232C2—21no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2—4124no—
237C2#2026767011yescharacteristic
238C2#2026797812yes—
subgroupG/H
centerC22#15692990
commutatorC23×C103C22×C4
FrattiniC24C22×D103
Fitting#518×C103C2
socleC22×C103#120
prime radicalC2×#15692989C2
cosocleC24×C103C23
hypercenter#518D103
hypocenterC103#1889
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C2×#15692936C2semidirect
3. #20267646C2semidirect
4. #20267558C2semidirect
5. #518×C103C2semidirect
9. #15692989C4semidirect
25. C23×D103C2×C4semidirect
33. C22⋊Dic103C2×C4semidirect
44. C22×C4×C103D4semidirect
54. C23×C103C22⋊C4semidirect
79. C2×C4×C103C22⋊C4semidirect
120. C103#1889semidirect
122. #518D103semidirect
158. C22×C4C22⋊D103semidirect
186. C23(C2×D103)⋊C4semidirect
204. C2×C4(C2×D103)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156929892
C2×#156929362
#202676462
#202675582
#518×C1032
#1889103