Finite Group Databasebeta

← #27195339

Subgroups — #27195339

Order 13184.

360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C22×C4⋊Dic103C211yesmaximal, characteristic
2C2×#15692953C212yesmaximal, complemented
3#20267651C211yesmaximal, characteristic
4#20267554C212yesmaximal, complemented
5C2×C22⋊C8×C103C211yesmaximal, characteristic
6C23×Dic103—21no—
7C2×C4⋊Dic103—24no—
8C2×C4⋊Dic103—21no—
9C2×C4⋊Dic103C2211yescharacteristic
10C2×C4⋊Dic103C2211yescharacteristic
11C2×C4⋊Dic103C2212yes—
12C2×C22⋊Dic103—21no—
13#15692953—24no—
14C103⋊#95—21no—
15C23×C4×C103C2211yescharacteristic
16C22×C8×C103C2212yes—
17C22⋊C8×C103C414yescomplemented
18C22×Dic103—24no—
19C22×Dic103—22no—
20C22×Dic103—21no—
21C22×Dic103—21no—
22C22×Dic103—42no—
23C22×Dic103—42no—
24C4⋊Dic103—24no—
25C4⋊Dic103—22no—
26C4⋊Dic103—22no—
27C4⋊Dic103—22no—
28C4⋊Dic103D414yes—
29C22⋊Dic103—42no—
30C24×C103D411yescharacteristic
31C22×C4×C103—22no—
32C22×C4×C103—22no—
33C22×C4×C103C2×C412yes—
34C22×C4×C103D411yescharacteristic
35C22×C4×C103Q812yes—
36C22×C4×C103C2311yescharacteristic
37C2×C8×C103—22no—
38C2×C8×C103—22no—
39C2×C8×C103C2×C414yescomplemented
40C23×C103—21no—
41C23×C103—21no—
42C23×C103—21no—
43C23×C103—21no—
44C23×C103C4⋊C412yes—
45C23×C103SD1612yes—
46C23×C103SD1612yes—
47C23×C103C2×D411yescharacteristic
48C2×C4×C103—21no—
49C2×C4×C103—21no—
50C2×C4×C103—24no—
51C2×C4×C103—24no—
52C2×C4×C103C4⋊C412yes—
53C2×C4×C103C22×C411yescharacteristic
54C2×C4×C103C2×D412yes—
55C2×C4×C103C2×Q811yescharacteristic
56C2×C4×C103#4112yes—
57C2×Dic103—24no—
58C2×Dic103—48no—
59C2×Dic103—42no—
60C2×Dic103—42no—
61C2×Dic103—41no—
62C2×Dic103—41no—
63C2×Dic103—41no—
64C2×Dic103—41no—
65C2×Dic103—41no—
66C2×Dic103—41no—
67C8×C103—24no—
68C22×C103—22no—
69C22×C103—22no—
70C22×C103—22no—
71C22×C103—22no—
72C22×C103—22no—
73C22×C103—22no—
74C22×C103#10614yescomplemented
75C22×C103C2×C4⋊C411yescharacteristic
76C22×C103#12011yescharacteristic
77C22×C103#12311yescharacteristic
78C22×C103C2×SD1611yescharacteristic
79C22×C103C2×SD1611yescharacteristic
80C22×C103AGL(1,ℤ/8)11yescharacteristic
81C22×C103#13711yescharacteristic
82C4×C103—22no—
83C4×C103C4×D412yes—
84C4×C103C22⋊Q812yes—
85Dic103—44no—
86Dic103—81no—
87Dic103—81no—
88C2×C103—24no—
89C2×C103#38511yescharacteristic
90C2×C103C2×#10611yescharacteristic
91C2×C103#42811yescharacteristic
92C2×C103#44811yescharacteristic
93C2×C103#45011yescharacteristic
94C2×C103#48111yescharacteristic
95C2×C103#48311yescharacteristic
96#1853—1031nomaximal, Sylow
97C103#185311yescharacteristic, complemented, Sylow
98C22×C4⋊C4—1031no—
99C2×#106—1032no—
100C2×C22⋊C8D10311yescharacteristic
101#380—1031no—
102#340—1032no—
103C23×C4—2061no—
104C23×C4C2×D10311yescharacteristic
105C22×C8C2×D10312yes—
106C2×C4⋊C4—1032no—
107C2×C4⋊C4—1031no—
108C2×C4⋊C4—1031no—
109C2×C4⋊C4—2064no—
110C2×C4⋊C4—2061no—
111C2×C22⋊C4—2061no—
112#106—2064no—
113C22⋊C8Dic10314yescomplemented
114#95—2061no—
115C24D41211yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—4122no—
119C22×C4—4122no—
120C22×C4—2061no—
121C22×C4—2061no—
122C22×C4—2064no—
123C22×C4—2062no—
124C22×C4Dic20612yes—
125C22×C4D41211yescharacteristic
126C22×C4C2×Dic10312yes—
127C22×C4C22×D10311yescharacteristic
128C2×C8—22no—
129C2×C8—22no—
130C2×C8C2×Dic10314yescomplemented
131C4⋊C4—1034no—
132C4⋊C4—2064no—
133C4⋊C4—2062no—
134C4⋊C4—2062no—
135C4⋊C4—2062no—
136C22⋊C4—4122no—
137C23—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23C4⋊Dic10312yes—
142C23#1311009412yes—
143C23#1311009412yes—
144C23C2×D41211yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—4121no—
150C2×C4—4121no—
151C2×C4—4121no—
152C2×C4—4121no—
153C2×C4—4121no—
154C2×C4—4121no—
155C2×C4—4128no—
156C2×C4—4122no—
157C2×C4—4122no—
158C2×C4—2064no—
159C2×C4C4⋊Dic10312yes—
160C2×C4C22×Dic10311yescharacteristic
161C2×C4D4×D10312yes—
162C2×C4C2×Dic20611yescharacteristic
163C2×C4#1311010412yes—
164C8—24no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22#1569295314yescomplemented
172C22C2×C4⋊Dic10311yescharacteristic
173C22#1569299111yescharacteristic
174C22#1569300511yescharacteristic
175C22C2×#1311009411yescharacteristic
176C22C2×#1311009411yescharacteristic
177C22#1569304911yescharacteristic
178C22#1569305411yescharacteristic
179C4—22no—
180C4—8241no—
181C4—8241no—
182C4—4124no—
183C4D4×Dic10312yes—
184C4#1569299812yes—
185C2—24no—
186C2#2026766611yescharacteristic
187C2C2×#1569295311yescharacteristic
188C2#2026783311yescharacteristic
189C2#2026793211yescharacteristic
190C2#2026794411yescharacteristic
191C2#2026811011yescharacteristic
192C2#2026812211yescharacteristic
subgroupG/H
centerC23C2×D412
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×C22⋊C8×C103C2
socleC23×C103C2×D4
prime radicalC24×C103D4
cosocleC22×C4×C103C23
hypercenterC2×C22⋊C8D103
hypocenterC103#1853
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#15692953C2semidirect
4. #20267554C2semidirect
17. C22⋊C8×C103C4semidirect
39. C2×C8×C103C2×C4semidirect
74. C22×C103#106semidirect
97. C103#1853semidirect
113. C22⋊C8Dic103semidirect
130. C2×C8C2×Dic103semidirect
171. C22#15692953semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic1032
C2×#156929532
#202676512
#202675542
C2×C22⋊C8×C1032
#1853103