Finite Group Databasebeta

← #27193476

Subgroups — #27193476

Order 13184.

252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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×#15692978C211yesmaximal, characteristic
2#20267848C211yesmaximal, characteristic, complemented
3#20267516C212yesmaximal, complemented
4#20267514C212yesmaximal
5#432×C103C211yesmaximal, characteristic, complemented
6C22×C4×D103C411yescharacteristic
7#15692978—21no—
8#15692978—21no—
9#15692978—21no—
10#15692978—21no—
11C2×Dic103⋊C4C411yescharacteristic
12C2×Dic103⋊C4C2211yescharacteristic
13C2×(C2×D103)⋊C4C411yescharacteristic
14C2×(C2×D103)⋊C4C2211yescharacteristic
15C2×C4×Dic103C411yescharacteristic
16C4⋊(C103⋊C8)—21no—
17C22⋊(C103⋊C8)C2212yes—
18#15692932—21no—
19C2×C42×C103C2211yescharacteristic
20C4⋊C8×C103—21no—
21C22⋊C8×C103C2212yes—
22#97×C103—21no—
23C23×D103C2×C411yescharacteristic
24C22×Dic103C2×C411yescharacteristic
25C22×Dic103C2×C411yescharacteristic
26C22×Dic103C2×C411yescharacteristic
27C2×C4×D103—22no—
28C2×C4×D103—21no—
29C2×C4×D103—21no—
30C2×C4×D103—22no—
31C2×C103⋊C8—22no—
32Dic103⋊C4—21no—
33Dic103⋊C4—21no—
34Dic103⋊C4—21no—
35Dic103⋊C4—21no—
36(C2×D103)⋊C4—21no—
37(C2×D103)⋊C4—21no—
38(C2×D103)⋊C4—21no—
39(C2×D103)⋊C4—21no—
40C4×Dic103—21no—
41C4×Dic103—21no—
42C22×C4×C103C2×C411yescharacteristic
43C22×C4×C103C2×C411yescharacteristic
44C22×C4×C103C2311yescharacteristic
45C2×C8×C103—22no—
46C42×C103D411yescharacteristic
47C42×C103D411yescharacteristic
48C42×C103D411yescharacteristic
49C42×C103D411yescharacteristic
50C23×C103C22×C411yescharacteristic
51C22×D103—21no—
52C22×D103—21no—
53C22×D103—41no—
54C22×D103—41no—
55C22×D103M1612yes—
56C2×C4×C103—21no—
57C2×C4×C103—21no—
58C2×C4×C103—41no—
59C2×C4×C103—41no—
60C2×C4×C103C22⋊C411yescharacteristic
61C2×C4×C103C22⋊C411yescharacteristic
62C2×C4×C103C22⋊C411yescharacteristic
63C2×C4×C103C22⋊C411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C2×Dic103—21no—
67C2×Dic103—21no—
68C2×Dic103—21no—
69C2×Dic103—21no—
70C2×Dic103—41no—
71C2×Dic103—41no—
72C2×Dic103M1612yes—
73C4×D103—24no—
74C4×D103—24no—
75C8×C103—42no—
76C103⋊C8—42no—
77C22×C103—21no—
78C22×C103—21no—
79C22×C103C2×C22⋊C411yescharacteristic
80C22×C103C2×M1611yescharacteristic
81C22×C103C2×M1611yescharacteristic
82C2×D103—22no—
83C2×D103—42no—
84C2×D103—41no—
85C2×D103—41no—
86C2×D103—42no—
87C4×C103—21no—
88C4×C103—21no—
89C4×C103—21no—
90C4×C103—21no—
91C4×C103—21no—
92C4×C103—21no—
93Dic103—22no—
94Dic103—41no—
95Dic103—41no—
96C2×C103—21no—
97C2×C103—21no—
98C2×C103#40711yescharacteristic
99C2×C103#41011yescharacteristic
100C2×C103#41311yescharacteristic
101D103—42no—
102#1464—1031nomaximal, Sylow
103C103#146411yescharacteristic, complemented, Sylow
104C2×#117—1031no—
105#432—1031no—
106#432D10311yescharacteristic, complemented
107#324—1032no—
108#323—1032no—
109C23×C4—1031no—
110#117—2061no—
111#117—2061no—
112#117—2061no—
113#117—2061no—
114C2×C4⋊C4—1031no—
115C2×C4⋊C4—1031no—
116C2×C22⋊C4—1031no—
117C2×C22⋊C4—1031no—
118C2×C42—1031no—
119C2×C42C2×D10311yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—2061no—
122C22⋊C8—1032no—
123C22⋊C8C2×D10312yes—
124#97—21no—
125#97—2061no—
126C24—1031no—
127C22×C4—1031no—
128C22×C4—1031no—
129C22×C4—1031no—
130C22×C4—2062no—
131C22×C4—2062no—
132C22×C4—2061no—
133C22×C4—2061no—
134C22×C4C4×D10311yescharacteristic
135C22×C4C4×D10311yescharacteristic
136C22×C4C22×D10311yescharacteristic
137C2×C8—22no—
138C2×C8—2062no—
139C4⋊C4—2061no—
140C4⋊C4—2061no—
141C4⋊C4—2061no—
142C4⋊C4—2061no—
143C22⋊C4—2061no—
144C22⋊C4—2061no—
145C22⋊C4—2061no—
146C22⋊C4—2061no—
147C42—2061no—
148C42—2061no—
149C42D41211yescharacteristic
150C42D41211yescharacteristic
151C42C22⋊D10311yescharacteristic
152C42C22⋊D10311yescharacteristic
153C23—1032no—
154C23—4121no—
155C23—4121no—
156C23—2061no—
157C23—2061no—
158C23C2×C4×D10311yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—1032no—
164C2×C4—4121no—
165C2×C4—4121no—
166C2×C4—2064no—
167C2×C4—2064no—
168C2×C4—2061no—
169C2×C4—2061no—
170C2×C4—2061no—
171C2×C4—2061no—
172C2×C4(C2×D103)⋊C411yescharacteristic
173C2×C4(C2×D103)⋊C411yescharacteristic
174C2×C4(C2×D103)⋊C411yescharacteristic
175C2×C4(C2×D103)⋊C411yescharacteristic
176C2×C4C2×C22⋊D10311yescharacteristic
177C2×C4C2×D41211yescharacteristic
178C8—42no—
179C8—4122no—
180C22—21no—
181C22—21no—
182C22—4122no—
183C22—4122no—
184C22—4121no—
185C22—4121no—
186C22—2062no—
187C22C2×(C2×D103)⋊C411yescharacteristic
188C22M16×D10311yescharacteristic
189C22M16×D10311yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—4121no—
197C4—4121no—
198C4—2062no—
199C2—21no—
200C2—21no—
201C2—4122no—
202C2#2026775411yescharacteristic
203C2#2026776411yescharacteristic
204C2#2026777311yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC23×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#432×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC23×D103C2×C4
cosocleC22×C4×C103C23
hypercenter#432D103
hypocenterC103#1464
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #20267848C2semidirect
3. #20267516C2semidirect
5. #432×C103C2semidirect
103. C103#1464semidirect
106. #432D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929782
#202678482
#202675162
#202675142
#432×C1032
#1464103