Finite Group Databasebeta

← #27206070

Subgroups — #27206070

Order 13184.

428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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#20268342C211yesmaximal, characteristic
2C4⋊Q8×D103C211yesmaximal, characteristic, complemented
3#20268165C211yesmaximal, characteristic, complemented
4#20268164C211yesmaximal, characteristic, complemented
5#20268143C211yesmaximal, characteristic, complemented
6#20267995C214yesmaximal, complemented
7#20267931C214yesmaximal, complemented
8#20267842C211yesmaximal, characteristic, complemented
9#487×C103C211yesmaximal, characteristic, complemented
10C2×#13110106—21no—
11C2×Q8×D103C2212yes—
12C2×#13110094C2214yes—
13C2×#13110092C2214yes—
14#15693021C2211yescharacteristic
15#15693020—21no—
16#15693020—21no—
17#15693019C2212yes—
18#15693018C2211yescharacteristic
19#15693010—21no—
20#15692996—21no—
21#15692996C2212yes—
22#15692983—21no—
23#15692983C2212yes—
24C4⋊C4×D103—21no—
25C4⋊C4×D103—21no—
26C42×D103C2211yescharacteristic
27Dic103⋊C8C2212yes—
28#15692944C2214yes—
29(C2×D103)⋊C8C2212yes—
30C4×C103⋊C8C2211yescharacteristic
31C4⋊Q8×C103C2211yescharacteristic
32C4⋊Q8×C103C2211yescharacteristic
33#103×C103C2214yes—
34C4×C8×C103C2211yescharacteristic
35#13110106—44no—
36C2×Dic206—22no—
37C2×Dic206C2312yes—
38Q8×D103—44no—
39C2×D412—22no—
40C2×D412—21no—
41C2×D412—21no—
42C2×D412C2312yes—
43C2×C4×D103—22no—
44C2×C4×D103—22no—
45C2×C4×D103D411yescharacteristic
46C2×C4×D103D411yescharacteristic
47C2×C4×D103C2311yescharacteristic
48#13110094—44no—
49#13110092—44no—
50C2×C103⋊C8C2312yes—
51C4⋊Dic103—21no—
52C4⋊Dic103—21no—
53Dic103⋊C4—22no—
54Dic103⋊C4—22no—
55(C2×D103)⋊C4—22no—
56(C2×D103)⋊C4—22no—
57C4×Dic103D411yescharacteristic
58C4×Dic103D411yescharacteristic
59C4×Dic103C2311yescharacteristic
60C2×Q8×C103—21no—
61C2×Q8×C103C2312yes—
62C2×C8×C103C2312yes—
63C4⋊C4×C103—21no—
64C4⋊C4×C103—21no—
65C4⋊C4×C103—21no—
66C4⋊C4×C103C2312yes—
67C42×C103C2311yescharacteristic
68C22×D103—22no—
69C22×D103C2×D411yescharacteristic
70Q8×C103—24no—
71Q8×C103—42no—
72C2×C4×C103—22no—
73C2×C4×C103—22no—
74C2×C4×C103C2×D411yescharacteristic
75C2×C4×C103C2×D411yescharacteristic
76C2×C4×C103C2411yescharacteristic
77C2×Dic103—22no—
78C2×Dic103C2×D411yescharacteristic
79C2×Dic103C2×D411yescharacteristic
80C2×Dic103C2×D411yescharacteristic
81D412—24no—
82D412—44no—
83D412—42no—
84D412—42no—
85C4×D103—22no—
86C4×D103—22no—
87C4×D103—44no—
88C4×D103—44no—
89C4×D103SD1614yescomplemented
90Dic206—24no—
91Dic206—44no—
92C8×C103—22no—
93C103⋊C8—22no—
94C22×C103C22×D411yescharacteristic
95C2×D103—21no—
96C2×D103—21no—
97C2×D103—42no—
98C2×D103—42no—
99C2×D103—42no—
100C2×D103C2×SD1612yes—
101C4×C103—42no—
102C4×C103—42no—
103C4×C103C2×SD1612yes—
104C4×C103#13712yes—
105C4×C103H(5,𝔽2)12yes—
106Dic103—21no—
107Dic103—21no—
108Dic103—42no—
109Dic103C2×SD1612yes—
110C2×C103#53511yescharacteristic
111C2×C103C22×SD1611yescharacteristic
112C2×C103C2×#13711yescharacteristic
113D103—22no—
114D103—82no—
115#3206—1031nomaximal, Sylow
116C103#320611yescharacteristic, complemented, Sylow
117#532—1031no—
118C2×C4⋊Q8—1031no—
119#492—1031no—
120#492—1031no—
121#487—1031no—
122#487D10311yescharacteristic, complemented
123#461—1034no—
124#448—1034no—
125#431—1031no—
126C2×#41—2061no—
127C22×Q8—1032no—
128C2×SD16—1034no—
129C2×SD16—1034no—
130C4⋊Q8—1032no—
131C4⋊Q8—1031no—
132C4⋊Q8—2061no—
133C4⋊Q8—2061no—
134C4⋊Q8C2×D10311yescharacteristic
135C4⋊Q8C2×D10311yescharacteristic
136#127—1031no—
137#124—2061no—
138#121—1032no—
139#121—2061no—
140C4×D4—1032no—
141C4×D4—2061no—
142C2×C4⋊C4—2061no—
143C2×C4⋊C4—2061no—
144C2×C42—1031no—
145C4⋊C8—1032no—
146#103—1034no—
147#103C2×D10314yes—
148C22⋊C8—1032no—
149C4×C8—1031no—
150C4×C8C2×D10311yescharacteristic
151#41—4124no—
152C2×Q8—21no—
153C2×Q8—1032no—
154C2×Q8—4124no—
155C2×Q8—2062no—
156C2×Q8C22×D10312yes—
157C2×D4—1032no—
158C2×D4—2062no—
159C2×D4—2061no—
160C2×D4—2061no—
161C22×C4—1031no—
162C22×C4—1031no—
163C22×C4—1031no—
164C22×C4—2062no—
165C22×C4—2062no—
166SD16—4124no—
167SD16—4124no—
168C2×C8—1032no—
169C2×C8C22×D10312yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—2062no—
174C4⋊C4—2062no—
175C4⋊C4—2061no—
176C4⋊C4—2061no—
177C4⋊C4C22×D10312yes—
178C22⋊C4—2062no—
179C22⋊C4—2062no—
180C42—1031no—
181C42—1031no—
182C42—1031no—
183C42C22×D10311yescharacteristic
184C23—1031no—
185C23—2062no—
186Q8—24no—
187Q8—42no—
188Q8—4124no—
189Q8—2064no—
190D4—4124no—
191D4—4122no—
192D4—4122no—
193D4—2064no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—1031no—
197C2×C4—1034no—
198C2×C4—1031no—
199C2×C4—1031no—
200C2×C4—4124no—
201C2×C4—4124no—
202C2×C4—2062no—
203C2×C4—2062no—
204C2×C4—2062no—
205C2×C4D4×D10311yescharacteristic
206C2×C4D4×D10311yescharacteristic
207C2×C4C23×D10311yescharacteristic
208C8—22no—
209C8—2062no—
210C22—1032no—
211C22—4122no—
212C22—4122no—
213C22—4122no—
214C22—2061no—
215C22—2061no—
216C22C2×D4×D10311yescharacteristic
217C4—42no—
218C4—42no—
219C4—1032no—
220C4—4122no—
221C4—2061no—
222C4—2061no—
223C4SD16×D10312yes—
224C4#1569305312yes—
225C4#1569306712yes—
226C2—8242no—
227C2—2062no—
228C2#2026835911yescharacteristic
229C2C2×SD16×D10311yescharacteristic
230C2C2×#1569305311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#487×C103C2
socleC22×C103C22×D4
prime radical#20268342C2
hypercenter#487D103
hypocenterC103#3206
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D103C2semidirect
3. #20268165C2semidirect
4. #20268164C2semidirect
5. #20268143C2semidirect
6. #20267995C2semidirect
7. #20267931C2semidirect
8. #20267842C2semidirect
9. #487×C103C2semidirect
89. C4×D103SD16semidirect
116. C103#3206semidirect
122. #487D103semidirect

Maximal subgroups

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

subgroupindex
#202683422
C4⋊Q8×D1032
#202681652
#202681642
#202681432
#202679952
#202679312
#202678422
#487×C1032
#3206103