Finite Group Databasebeta

← #27193670

Subgroups — #27193670

Order 13184.

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

normal subgroups only

This group has 242 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
1#20268325C211yesmaximal, characteristic
2C4×C4⋊Dic103C211yesmaximal, characteristic, complemented
3#20267529C212yesmaximal, complemented
4#20267526C212yesmaximal
5#432×C103C211yesmaximal, characteristic, complemented
6#15693015—21no—
7#15693013C411yescharacteristic, complemented
8#15693009C411yescharacteristic, complemented
9#15693004—21no—
10#15693000C2211yescharacteristic
11#15692995C2211yescharacteristic
12C4×Dic206C411yescharacteristic, complemented
13C4×D412C411yescharacteristic, complemented
14C4×C22⋊D103—21no—
15#15692978—21no—
16C2×C4⋊Dic103—21no—
17C2×C4×Dic103—21no—
18C103⋊#95C2212yes—
19C2×C42×C103C2211yescharacteristic
20C4⋊C8×C103—21no—
21C22⋊C8×C103C2212yes—
22#97×C103—21no—
23C2×Dic206C2×C411yescharacteristic
24C2×D412C2×C411yescharacteristic
25C2×C22⋊D103—21no—
26C22×Dic103—22no—
27C2×C4×D103—21no—
28C4⋊Dic103—24no—
29C4⋊Dic103C2×C411yescharacteristic
30C4⋊Dic103C2×C411yescharacteristic
31Dic103⋊C4—21no—
32Dic103⋊C4—21no—
33Dic103⋊C4—21no—
34Dic103⋊C4—21no—
35C22⋊Dic103—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—42no—
42C22×C4×C103D411yescharacteristic
43C22×C4×C103D411yescharacteristic
44C22×C4×C103C2311yescharacteristic
45C2×C8×C103—22no—
46C42×C103C2×C411yescharacteristic
47C42×C103C2×C411yescharacteristic
48C42×C103D411yescharacteristic
49C42×C103D411yescharacteristic
50C23×C103C2×D411yescharacteristic
51C22×D103—21no—
52C2×C4×C103—21no—
53C2×C4×C103—21no—
54C2×C4×C103—22no—
55C2×C4×C103—41no—
56C2×C4×C103C22⋊C411yescharacteristic
57C2×C4×C103C22⋊C411yescharacteristic
58C2×C4×C103C22⋊C411yescharacteristic
59C2×C4×C103C22⋊C411yescharacteristic
60C2×C4×C103C22×C411yescharacteristic
61C2×C4×C103C2×D411yescharacteristic
62C22⋊D103—41no—
63C22⋊D103—41no—
64C2×Dic103—24no—
65C2×Dic103—21no—
66C2×Dic103—21no—
67C2×Dic103—21no—
68C2×Dic103—42no—
69C2×Dic103—42no—
70D412—41no—
71C4×D103—42no—
72Dic206—41no—
73C8×C103—42no—
74C22×C103—21no—
75C22×C103—21no—
76C22×C103C2×C22⋊C411yescharacteristic
77C22×C103AGL(1,ℤ/8)11yescharacteristic
78C22×C103#13711yescharacteristic
79C2×D103—41no—
80C2×D103—41no—
81C2×D103—41no—
82C4×C103—21no—
83C4×C103—21no—
84C4×C103—21no—
85C4×C103—21no—
86C4×C103—21no—
87C4×C103#10412yes—
88Dic103—44no—
89Dic103—41no—
90Dic103—41no—
91Dic103—41no—
92C2×C103—21no—
93C2×C103—21no—
94C2×C103#41011yescharacteristic
95C2×C103#41711yescharacteristic
96C2×C103C2×#10411yescharacteristic
97D103—81no—
98#1509—1031nomaximal, Sylow
99C103#150911yescharacteristic, complemented, Sylow
100#529—1031no—
101#432D10311yescharacteristic, complemented
102C4×C4⋊C4—1031no—
103#328—1032no—
104#327—1032no—
105#126—2061no—
106#125—1031no—
107#124—1031no—
108#123—2061no—
109C22⋊Q8—1031no—
110#121—1031no—
111C4×Q8—1031no—
112C4×D4—1031no—
113C4×D4—2061no—
114#117—2061no—
115C2×C4⋊C4—2061no—
116C2×C42—2061no—
117C2×C42C2×D10311yescharacteristic
118C4⋊C8—21no—
119C22⋊C8C2×D10312yes—
120#97—21no—
121#95—1032no—
122C2×Q8—1031no—
123C2×D4—1031no—
124C2×D4—2061no—
125C22×C4—2062no—
126C22×C4—2061no—
127C22×C4D41211yescharacteristic
128C22×C4D41211yescharacteristic
129C22×C4C22×D10311yescharacteristic
130C2×C8—22no—
131C4⋊C4—1031no—
132C4⋊C4—1031no—
133C4⋊C4—2064no—
134C4⋊C4—2061no—
135C4⋊C4—2061no—
136C4⋊C4—2061no—
137C4⋊C4—2061no—
138C22⋊C4—2061no—
139C22⋊C4—2061no—
140C22⋊C4—2061no—
141C22⋊C4—2061no—
142C22⋊C4—2061no—
143C42—4122no—
144C42—2061no—
145C42C4×D10311yescharacteristic
146C42C4×D10311yescharacteristic
147C42C22⋊D10311yescharacteristic
148C42C22⋊D10311yescharacteristic
149C23—2061no—
150C23C2×D41211yescharacteristic
151Q8—4121no—
152D4—4121no—
153D4—4121no—
154D4—4121no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—4122no—
160C2×C4—4122no—
161C2×C4—4122no—
162C2×C4—2064no—
163C2×C4—2061no—
164C2×C4—2061no—
165C2×C4—2061no—
166C2×C4(C2×D103)⋊C411yescharacteristic
167C2×C4(C2×D103)⋊C411yescharacteristic
168C2×C4(C2×D103)⋊C411yescharacteristic
169C2×C4(C2×D103)⋊C411yescharacteristic
170C2×C4C2×C4×D10311yescharacteristic
171C2×C4C2×C22⋊D10311yescharacteristic
172C8—42no—
173C22—21no—
174C22—21no—
175C22—4121no—
176C22—4121no—
177C22—4121no—
178C22C2×(C2×D103)⋊C411yescharacteristic
179C22#1569304911yescharacteristic
180C22#1569305411yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—4124no—
187C4—4121no—
188C4—4121no—
189C4—4121no—
190C4#1569294712yes—
191C2—21no—
192C2—21no—
193C2—8241no—
194C2#2026776411yescharacteristic
195C2#2026779311yescharacteristic
196C2C2×#1569294711yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#432×C103C2
socleC22×C103C2×C22⋊C4
prime radical#15692995C22
cosocleC22×C4×C103C23
hypercenter#432D103
hypocenterC103#1509
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Dic103C2semidirect
3. #20267529C2semidirect
5. #432×C103C2semidirect
7. #15693013C4semidirect
8. #15693009C4semidirect
12. C4×Dic206C4semidirect
13. C4×D412C4semidirect
99. C103#1509semidirect
101. #432D103semidirect

Maximal subgroups

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

subgroupindex
#202683252
C4×C4⋊Dic1032
#202675292
#202675262
#432×C1032
#1509103