Finite Group Databasebeta

← #27193641

Subgroups — #27193641

Order 13184.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#20268343C211yesmaximal, characteristic
2#20267841C211yesmaximal, characteristic
3#20267642C211yesmaximal, characteristic
4#20267529C211yesmaximal, characteristic
5#20267528C211yesmaximal, characteristic
6#20267527C211yesmaximal, characteristic
7#328×C103C211yesmaximal, characteristic
8#15693020C411yescharacteristic, complemented
9#15693019C411yescharacteristic, complemented
10#15693011—21no—
11#15693000C2211yescharacteristic
12#15692998—21no—
13Q8×Dic103C411yescharacteristic, complemented
14#15692986—21no—
15#15692986C411yescharacteristic, complemented
16#15692977—21no—
17C2×Dic103⋊C4—21no—
18C2×C4×Dic103—21no—
19C2×C4×Dic103C2211yescharacteristic
20Dic103⋊C8—21no—
21C22⋊(C103⋊C8)C2211yescharacteristic
22C8×Dic103—21no—
23C103⋊#95C2211yescharacteristic
24C22⋊Q8×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic
26#95×C103C2211yescharacteristic
27C2×Dic206—21no—
28C2×Dic206C2×C411yescharacteristic
29C22×Dic103—21no—
30C22×Dic103D411yescharacteristic
31C22×Dic103D411yescharacteristic
32C2×C103⋊C8—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103C2×C411yescharacteristic
35Dic103⋊C4—24no—
36Dic103⋊C4—21no—
37Dic103⋊C4—21no—
38Dic103⋊C4—21no—
39Dic103⋊C4—21no—
40Dic103⋊C4—21no—
41C22⋊Dic103—21no—
42C4×Dic103—21no—
43C4×Dic103—21no—
44C4×Dic103—42no—
45C4×Dic103C2×C411yescharacteristic
46C4×Dic103C2×C411yescharacteristic
47C4×Dic103D411yescharacteristic
48C4×Dic103D411yescharacteristic
49C2×Q8×C103C2×C411yescharacteristic
50C22×C4×C103—21no—
51C22×C4×C103C2311yescharacteristic
52C2×C8×C103—21no—
53C4⋊C4×C103—21no—
54C4⋊C4×C103C2×C411yescharacteristic
55C22⋊C4×C103—21no—
56C23×C103C2×D411yescharacteristic
57Q8×C103—41no—
58C2×C4×C103—22no—
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103C22×C411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C2×Dic103—22no—
67C2×Dic103—22no—
68C2×Dic103—21no—
69C2×Dic103—21no—
70C2×Dic103—41no—
71C2×Dic103—41no—
72C2×Dic103C22⋊C411yescharacteristic
73C2×Dic103C22⋊C411yescharacteristic
74C2×Dic103C22⋊C411yescharacteristic
75C2×Dic103C22⋊C411yescharacteristic
76C2×Dic103SD1612yes—
77C2×Dic103Q1612yes—
78Dic206—42no—
79Dic206—41no—
80C8×C103—41no—
81C103⋊C8—41no—
82C22×C103—21no—
83C22×C103—21no—
84C22×C103C2×C22⋊C411yescharacteristic
85C22×C103C2×SD1611yescharacteristic
86C22×C103C2×Q1611yescharacteristic
87C4×C103—21no—
88C4×C103—21no—
89C4×C103—42no—
90C4×C103—41no—
91C4×C103—41no—
92Dic103—21no—
93Dic103—42no—
94Dic103—41no—
95Dic103—41no—
96Dic103#10312yes—
97Dic103#10312yes—
98Dic103#10412yes—
99C2×C103—21no—
100C2×C103—21no—
101C2×C103#41011yescharacteristic
102C2×C103C2×#10311yescharacteristic
103C2×C103C2×#10411yescharacteristic
104#1503—1031nomaximal, Sylow
105C103#150311yescharacteristic, complemented, Sylow
106#533—1031no—
107#431—1031no—
108C4×C4⋊C4—1031no—
109#328—1031no—
110#328—1031no—
111#328—1031no—
112#328D10311yescharacteristic
113C4⋊Q8—1031no—
114C4⋊Q8—1031no—
115#125—2061no—
116C22⋊Q8—1031no—
117C22⋊Q8—2061no—
118C22⋊Q8C2×D10311yescharacteristic
119C4×Q8—1031no—
120C4×Q8—1031no—
121C4×Q8—2061no—
122#117—2061no—
123C2×C4⋊C4—2061no—
124C2×C42—1031no—
125C2×C42—2061no—
126C4⋊C8—2061no—
127C22⋊C8—1031no—
128C22⋊C8C2×D10311yescharacteristic
129C4×C8—2061no—
130#95—1031no—
131#95C2×D10311yescharacteristic
132C2×Q8—1031no—
133C2×Q8—2061no—
134C2×Q8C4×D10311yescharacteristic
135C22×C4—21no—
136C22×C4—1031no—
137C22×C4—1031no—
138C22×C4—2061no—
139C22×C4C22×D10311yescharacteristic
140C2×C8—21no—
141C2×C8—2061no—
142C4⋊C4—21no—
143C4⋊C4—1031no—
144C4⋊C4—2061no—
145C4⋊C4—2061no—
146C4⋊C4—2061no—
147C4⋊C4—2061no—
148C4⋊C4—2061no—
149C4⋊C4—2064no—
150C4⋊C4—2061no—
151C4⋊C4C4×D10311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2061no—
154C42—1031no—
155C42—1031no—
156C42—1031no—
157C42—1031no—
158C42—4122no—
159C42—2061no—
160C42—2061no—
161C23D4×D10311yescharacteristic
162Q8—41no—
163Q8—4121no—
164Q8—4122no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—1031no—
172C2×C4—1031no—
173C2×C4—1031no—
174C2×C4—1032no—
175C2×C4—1032no—
176C2×C4—1031no—
177C2×C4—4121no—
178C2×C4—4121no—
179C2×C4—2062no—
180C2×C4—2062no—
181C2×C4—2061no—
182C2×C4—2061no—
183C2×C4C2×C4×D10311yescharacteristic
184C2×C4D4×D10311yescharacteristic
185C8—41no—
186C8—4121no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D10311yescharacteristic
190C22SD16×D10311yescharacteristic
191C22Q16×D10311yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—1032no—
198C4—1032no—
199C4—1032no—
200C4—4122no—
201C4—4121no—
202C4—4121no—
203C4—2061no—
204C2—21no—
205C2—21no—
206C2#2026776311yescharacteristic
207C2#103×D10311yescharacteristic
208C2#104×D10311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#328×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC23×C103C2×D4
cosocleC22×C4×C103C23
hypercenter#328D103
hypocenterC103#1503
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #15693020C4semidirect
9. #15693019C4semidirect
13. Q8×Dic103C4semidirect
15. #15692986C4semidirect
105. C103#1503semidirect

Maximal subgroups

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

subgroupindex
#202683432
#202678412
#202676422
#202675292
#202675282
#202675272
#328×C1032
#1503103