Finite Group Databasebeta

← #27193661

Subgroups — #27193661

Order 13184.

346 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 77 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×#15692995C211yesmaximal, characteristic
2C4×C22⋊Dic103C211yesmaximal, characteristic, complemented
3#20267526C214yesmaximal, complemented
4#407×C103C211yesmaximal, characteristic, complemented
5C22×D412C411yescharacteristic, complemented
6C22×C22⋊D103—21no—
7#15692995—21no—
8#15692995—21no—
9#15692995C412yescomplemented
10#15692995C2212yes—
11C2×C4⋊Dic103C411yescharacteristic, complemented
12C2×C22⋊Dic103—21no—
13C2×(C2×D103)⋊C4—21no—
14C2×C4×Dic103—21no—
15C103⋊#95C2212yescomplemented
16C23×C4×C103C2211yescharacteristic
17C2×M16×C103—21no—
18C22⋊C8×C103—21no—
19C22⋊C8×C103C2212yescomplemented
20C23×D103—21no—
21C2×D412—21no—
22C2×D412—42no—
23C2×D412C2×C412yes—
24C2×C22⋊D103—22no—
25C2×C22⋊D103—22no—
26C2×C22⋊D103—44no—
27C22×Dic103—21no—
28C22×Dic103—22no—
29C4⋊Dic103—21no—
30C4⋊Dic103C2×C412yes—
31C22⋊Dic103—24no—
32(C2×D103)⋊C4—22no—
33(C2×D103)⋊C4—22no—
34C4×Dic103—42no—
35C24×C103D411yescharacteristic
36C22×C4×C103—42no—
37C22×C4×C103C2×C411yescharacteristic
38C22×C4×C103C2×C411yescharacteristic
39C22×C4×C103D411yescharacteristic
40C22×C4×C103D411yescharacteristic
41C22×C4×C103D411yescharacteristic
42C22×C4×C103C2311yescharacteristic
43M16×C103—42no—
44C2×C8×C103—22no—
45C23×C103—22no—
46C23×C103—22no—
47C23×C103—41no—
48C23×C103C22⋊C411yescharacteristic
49C23×C103C22⋊C411yescharacteristic
50C23×C103C2×D411yescharacteristic
51C22×D103—22no—
52C22×D103—42no—
53C22×D103—42no—
54C22×D103—42no—
55C2×C4×C103—22no—
56C2×C4×C103—22no—
57C2×C4×C103—22no—
58C2×C4×C103—41no—
59C2×C4×C103—41no—
60C2×C4×C103—41no—
61C2×C4×C103C22⋊C411yescharacteristic
62C2×C4×C103C22⋊C411yescharacteristic
63C2×C4×C103C22×C411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C22⋊D103—44no—
66C22⋊D103—44no—
67C2×Dic103—24no—
68C2×Dic103—22no—
69C2×Dic103—42no—
70C2×Dic103—42no—
71C2×Dic103—42no—
72D412—42no—
73D412—42no—
74C8×C103—42no—
75C22×C103—21no—
76C22×C103—21no—
77C22×C103—21no—
78C22×C103—21no—
79C22×C103—21no—
80C22×C103—21no—
81C22×C103—21no—
82C22×C103—44no—
83C22×C103#10412yes—
84C22×C103C2×C22⋊C411yescharacteristic
85C22×C103AGL(1,ℤ/8)12yes—
86C2×D103—42no—
87C2×D103—42no—
88C2×D103—42no—
89C2×D103—84no—
90C4×C103—21no—
91C4×C103—21no—
92C4×C103—21no—
93C4×C103#9912yes—
94Dic103—44no—
95Dic103—42no—
96C2×C103—22no—
97C2×C103—22no—
98C2×C103—41no—
99C2×C103C2×#9911yescharacteristic
100C2×C103#41811yescharacteristic
101C2×C103C2×#10411yescharacteristic
102D103—82no—
103#1507—1031nomaximal, Sylow
104C103#150711yescharacteristic, complemented, Sylow
105C2×#121—1031no—
106#407D10311yescharacteristic, complemented
107C4×C22⋊C4—1031no—
108#327—1034no—
109C22×D4—1031no—
110C22×D4—2061no—
111C23×C4C2×D10311yescharacteristic
112C2×M16—21no—
113#121—1032no—
114#121—1032no—
115#121—2061no—
116#121—2061no—
117C2×C4⋊C4—1031no—
118C2×C22⋊C4—2061no—
119C2×C22⋊C4—2061no—
120C2×C42—2061no—
121C22⋊C8—21no—
122C22⋊C8C2×D10312yescomplemented
123#95—1032no—
124C24—2061no—
125C24D41211yescharacteristic
126C2×D4—1032no—
127C2×D4—4122no—
128C2×D4—4124no—
129C2×D4—2062no—
130C2×D4—2062no—
131C2×D4—2061no—
132C22×C4—42no—
133C22×C4—2061no—
134C22×C4—2062no—
135C22×C4C4×D10311yescharacteristic
136C22×C4C4×D10311yescharacteristic
137C22×C4D41211yescharacteristic
138C22×C4C22⋊D10311yescharacteristic
139C22×C4C22⋊D10311yescharacteristic
140C22×C4C22×D10311yescharacteristic
141M16—42no—
142C2×C8—22no—
143C4⋊C4—1032no—
144C4⋊C4—2061no—
145C22⋊C4—2064no—
146C22⋊C4—2062no—
147C22⋊C4—2062no—
148C42—4122no—
149C23—22no—
150C23—22no—
151C23—41no—
152C23—4122no—
153C23—4122no—
154C23—4122no—
155C23—2062no—
156C23(C2×D103)⋊C411yescharacteristic
157C23(C2×D103)⋊C411yescharacteristic
158C23C2×D41211yescharacteristic
159D4—4122no—
160D4—4124no—
161D4—4124no—
162D4—4122no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—4122no—
170C2×C4—4122no—
171C2×C4—4122no—
172C2×C4—2064no—
173C2×C4—2062no—
174C2×C4(C2×D103)⋊C411yescharacteristic
175C2×C4(C2×D103)⋊C411yescharacteristic
176C2×C4C2×C4×D10311yescharacteristic
177C2×C4C2×C22⋊D10311yescharacteristic
178C8—42no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—44no—
187C22—8244no—
188C22—4122no—
189C22—4122no—
190C22—4122no—
191C22#1569294712yes—
192C22C2×(C2×D103)⋊C411yescharacteristic
193C22#1569304912yes—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—4124no—
198C4—4122no—
199C4#1569293512yes—
200C2—22no—
201C2—22no—
202C2—41no—
203C2—8242no—
204C2C2×#1569293511yescharacteristic
205C2#2026779711yescharacteristic
206C2C2×#1569294711yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#407×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC2×#15692995C2
cosocleC22×C4×C103C23
hypercenter#407D103
hypocenterC103#1507
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊Dic103C2semidirect
3. #20267526C2semidirect
4. #407×C103C2semidirect
5. C22×D412C4semidirect
9. #15692995C4semidirect
11. C2×C4⋊Dic103C4semidirect
15. C103⋊#95C22semidirect
19. C22⋊C8×C103C22semidirect
104. C103#1507semidirect
106. #407D103semidirect
122. C22⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929952
C4×C22⋊Dic1032
#202675262
#407×C1032
#1507103