Finite Group Databasebeta

← #27193846

Subgroups — #27193846

Order 13184.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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#20268339C211yesmaximal, characteristic
2#20267847C211yesmaximal, characteristic, complemented
3#20267843C211yesmaximal, characteristic, complemented
4#20267538C211yesmaximal, characteristic, complemented
5#20267536C211yesmaximal, characteristic, complemented
6#20267535C211yesmaximal, characteristic, complemented
7#331×C103C211yesmaximal, characteristic, complemented
8C2×#13110104—21no—
9#15693021C2211yescharacteristic
10#15693008—21no—
11#15692992—21no—
12#15692992C412yes—
13D4×Dic103—21no—
14D4×Dic103C412yes—
15C42×D103C2211yescharacteristic
16C4⋊(C103⋊C8)C2211yescharacteristic
17C4⋊(C103⋊C8)C2211yescharacteristic
18(C2×D103)⋊C8—21no—
19(C2×D103)⋊C8—21no—
20#15692931—21no—
21C8×Dic103—21no—
22#127×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24C4⋊C8×C103C2211yescharacteristic
25#13110104—42no—
26#13110104—42no—
27C2×Dic206—21no—
28C2×C22⋊D103—22no—
29C22×Dic103—22no—
30C2×C4×D103C2×C411yescharacteristic
31C2×C4×D103D411yescharacteristic
32C2×C4×D103D411yescharacteristic
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103C2×C412yes—
37C22⋊Dic103—22no—
38C22⋊Dic103—22no—
39C4×Dic103C2×C411yescharacteristic
40C4×Dic103D411yescharacteristic
41C4×Dic103D411yescharacteristic
42C2×D4×C103—21no—
43C2×D4×C103—21no—
44C2×D4×C103C2×C412yes—
45C2×C8×C103—21no—
46C2×C8×C103—21no—
47C42×C103C2311yescharacteristic
48C23×C103—22no—
49C22×D103C22⋊C411yescharacteristic
50D4×C103—42no—
51D4×C103—41no—
52D4×C103—41no—
53D4×C103—41no—
54D4×C103—41no—
55C2×C4×C103C22×C411yescharacteristic
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C22⋊D103—44no—
59C2×Dic103—22no—
60C2×Dic103—44no—
61C2×Dic103C22⋊C411yescharacteristic
62C2×Dic103C22⋊C411yescharacteristic
63C2×Dic103C22⋊C411yescharacteristic
64C4×D103—21no—
65C4×D103—21no—
66C4×D103—21no—
67C4×D103—21no—
68C4×D103—41no—
69Dic206—41no—
70Dic206—41no—
71C8×C103—41no—
72C8×C103—41no—
73C103⋊C8—41no—
74C103⋊C8—41no—
75C22×C103—42no—
76C22×C103—42no—
77C22×C103—42no—
78C22×C103C2×C22⋊C411yescharacteristic
79C2×D103—21no—
80C2×D103—21no—
81C2×D103—21no—
82C4×C103—21no—
83C4×C103#13511yescharacteristic
84C4×C103#13511yescharacteristic
85C4×C103AGL(1,ℤ/8)11yescharacteristic
86C4×C103AGL(1,ℤ/8)11yescharacteristic
87Dic103—21no—
88Dic103—21no—
89Dic103—21no—
90Dic103—42no—
91C2×C103—82no—
92C2×C103#41311yescharacteristic
93C2×C103#41611yescharacteristic
94C2×C103#41811yescharacteristic
95D103—41no—
96#1553—1031nomaximal, Sylow
97C103#155311yescharacteristic, complemented, Sylow
98#532—1031no—
99#432—1031no—
100#431—1031no—
101#332—1031no—
102#332—1031no—
103#331—1031no—
104#331D10311yescharacteristic, complemented
105C2×#41—2061no—
106C4⋊Q8—1031no—
107#127C2×D10311yescharacteristic
108#124—2061no—
109#121—1032no—
110#121—2061no—
111C4×D4—1032no—
112C4×D4—2061no—
113C2×C42—1031no—
114C4⋊C8—1031no—
115C4⋊C8—1031no—
116C4⋊C8C2×D10311yescharacteristic
117C4⋊C8C2×D10311yescharacteristic
118C22⋊C8—2061no—
119C22⋊C8—2061no—
120#97—2061no—
121C4×C8—2061no—
122#41—4122no—
123#41—4122no—
124C2×Q8—2061no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—2062no—
128C2×D4C4×D10312yes—
129C22×C4—1031no—
130C22×C4—1031no—
131C22×C4—1031no—
132C22×C4—2062no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2061no—
136C2×C8—2061no—
137C4⋊C4—1032no—
138C4⋊C4—2061no—
139C22⋊C4—2062no—
140C22⋊C4—2062no—
141C42—1031no—
142C42—1031no—
143C42—1031no—
144C42C22×D10311yescharacteristic
145C23—22no—
146C23—1031no—
147Q8—4121no—
148Q8—4121no—
149D4—42no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—4124no—
155C2×C4—1031no—
156C2×C4—1031no—
157C2×C4—1031no—
158C2×C4—4121no—
159C2×C4—4124no—
160C2×C4—2062no—
161C2×C4—2061no—
162C2×C4—2061no—
163C2×C4—2061no—
164C2×C4—2061no—
165C2×C4C2×C4×D10311yescharacteristic
166C2×C4D4×D10311yescharacteristic
167C2×C4D4×D10311yescharacteristic
168C8—41no—
169C8—41no—
170C8—4121no—
171C8—4121no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—2061no—
176C22—2061no—
177C22—2061no—
178C22C22⋊C4×D10311yescharacteristic
179C4—21no—
180C4—4122no—
181C4—2061no—
182C4—2061no—
183C4—2061no—
184C4#1569304011yescharacteristic
185C4#1569304211yescharacteristic
186C4#1569304511yescharacteristic
187C4#1569304811yescharacteristic
188C2—82no—
189C2—4121no—
190C2#2026777211yescharacteristic
191C2#2026778411yescharacteristic
192C2#2026779411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#331×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268339C2
cosocleC42×C103C23
hypercenter#331D103
hypocenterC103#1553
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20267847C2semidirect
3. #20267843C2semidirect
4. #20267538C2semidirect
5. #20267536C2semidirect
6. #20267535C2semidirect
7. #331×C103C2semidirect
97. C103#1553semidirect
104. #331D103semidirect

Maximal subgroups

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

subgroupindex
#202683392
#202678472
#202678432
#202675382
#202675362
#202675352
#331×C1032
#1553103