Finite Group Databasebeta

← #27193542

Subgroups — #27193542

Order 13184.

260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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#20268341C211yesmaximal, characteristic
2#20267844C211yesmaximal, characteristic, complemented
3#20267518C214yesmaximal, complemented
4C2×C4⋊C8×C103C211yesmaximal, characteristic, complemented
5C2×#13110105—21no—
6#15693021C411yescharacteristic
7#15693018C411yescharacteristic
8#15693009—21no—
9#15692995—21no—
10#15692995C412yes—
11C4×D412—21no—
12C4×D412C2212yes—
13C4⋊(C103⋊C8)—21no—
14C22⋊(C103⋊C8)—21no—
15C4×C103⋊C8C2212yes—
16C22×C8×C103—21no—
17C2×C42×C103C2211yescharacteristic
18C4⋊C8×C103—21no—
19C4⋊C8×C103C2212yes—
20#13110105—42no—
21#13110105—42no—
22C2×Dic206—21no—
23C2×D412—21no—
24C2×D412—21no—
25C2×D412C2×C412yes—
26C2×C22⋊D103—22no—
27C2×C4×D103—22no—
28C2×C103⋊C8—22no—
29C4⋊Dic103—21no—
30C4⋊Dic103C2×C412yes—
31(C2×D103)⋊C4—22no—
32(C2×D103)⋊C4—22no—
33C22×C4×C103C2×C411yescharacteristic
34C22×C4×C103D411yescharacteristic
35C22×C4×C103D411yescharacteristic
36C2×C8×C103—22no—
37C2×C8×C103—42no—
38C42×C103C2×C411yescharacteristic
39C42×C103D411yescharacteristic
40C42×C103D411yescharacteristic
41C42×C103C2311yescharacteristic
42C23×C103C22⋊C411yescharacteristic
43C22×D103—22no—
44C2×C4×C103—22no—
45C2×C4×C103—41no—
46C2×C4×C103C22⋊C411yescharacteristic
47C2×C4×C103C22⋊C411yescharacteristic
48C2×C4×C103C22⋊C411yescharacteristic
49C2×C4×C103D812yes—
50C2×C4×C103SD1612yes—
51C2×C4×C103C22×C411yescharacteristic
52C2×C4×C103C2×D411yescharacteristic
53C2×C4×C103C2×D411yescharacteristic
54C22⋊D103—44no—
55C2×Dic103—22no—
56D412—24no—
57D412—42no—
58D412—42no—
59C4×D103—42no—
60C4×D103—42no—
61Dic206—42no—
62C8×C103—42no—
63C103⋊C8—42no—
64C22×C103—21no—
65C22×C103—21no—
66C22×C103#10212yes—
67C22×C103C2×C22⋊C411yescharacteristic
68C2×D103—42no—
69C2×D103—42no—
70C2×D103—42no—
71C4×C103—21no—
72C4×C103—21no—
73C4×C103—21no—
74C4×C103#10212yes—
75C4×C103#13112yes—
76C4×C103C2×D811yescharacteristic
77C4×C103C2×SD1611yescharacteristic
78Dic103—42no—
79C2×C103—22no—
80C2×C103#40811yescharacteristic
81C2×C103C2×#10211yescharacteristic
82C2×C103#42111yescharacteristic
83D103—82no—
84#1480—1031nomaximal, Sylow
85C103#148011yescharacteristic, complemented, Sylow
86#532—1031no—
87#431—1031no—
88C2×C4⋊C8D10311yescharacteristic, complemented
89D4⋊C8—1034no—
90C2×#41—2061no—
91C22×C8—21no—
92C4⋊Q8—1031no—
93#127—1031no—
94#124—2061no—
95#121—1032no—
96#121—2061no—
97C4×D4—1032no—
98C4×D4—2061no—
99C2×C42C2×D10311yescharacteristic
100C4⋊C8—21no—
101C4⋊C8—2061no—
102C4⋊C8C2×D10312yes—
103C22⋊C8—2061no—
104C4×C8—1032no—
105#41—4122no—
106#41—4122no—
107C2×Q8—2061no—
108C2×D4—1032no—
109C2×D4—2062no—
110C2×D4—2061no—
111C2×D4—2061no—
112C22×C4—2062no—
113C22×C4C4×D10311yescharacteristic
114C22×C4D41211yescharacteristic
115C22×C4C22⋊D10311yescharacteristic
116C2×C8—22no—
117C2×C8—42no—
118C2×C8—2062no—
119C4⋊C4—1032no—
120C4⋊C4—2061no—
121C22⋊C4—2062no—
122C22⋊C4—2062no—
123C42C4×D10311yescharacteristic
124C42D41211yescharacteristic
125C42C22⋊D10311yescharacteristic
126C42C22×D10311yescharacteristic
127C23—2062no—
128C23(C2×D103)⋊C411yescharacteristic
129Q8—4122no—
130D4—4122no—
131D4—4124no—
132D4—4122no—
133D4—2064no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—4122no—
137C2×C4—4122no—
138C2×C4—2062no—
139C2×C4(C2×D103)⋊C411yescharacteristic
140C2×C4(C2×D103)⋊C411yescharacteristic
141C2×C4(C2×D103)⋊C411yescharacteristic
142C2×C4#1311009012yes—
143C2×C4#1311009212yes—
144C2×C4C2×C4×D10311yescharacteristic
145C2×C4C2×C22⋊D10311yescharacteristic
146C2×C4C2×D41211yescharacteristic
147C8—42no—
148C8—4122no—
149C22—21no—
150C22—21no—
151C22—4122no—
152C22—4122no—
153C22—4122no—
154C22#1569294112yes—
155C22C2×(C2×D103)⋊C411yescharacteristic
156C4—21no—
157C4—21no—
158C4—21no—
159C4—4122no—
160C4#1569294112yes—
161C4#1569302712yes—
162C4C2×#1311009011yescharacteristic
163C4C2×#1311009211yescharacteristic
164C2—22no—
165C2—8242no—
166C2#2026775711yescharacteristic
167C2C2×#1569294111yescharacteristic
168C2#2026780711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
FittingC2×C4⋊C8×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268341C2
cosocleC42×C103C23
hypercenterC2×C4⋊C8D103
hypocenterC103#1480
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20267844C2semidirect
3. #20267518C2semidirect
4. C2×C4⋊C8×C103C2semidirect
85. C103#1480semidirect
88. C2×C4⋊C8D103semidirect

Maximal subgroups

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

subgroupindex
#202683412
#202678442
#202675182
C2×C4⋊C8×C1032
#1480103