Finite Group Databasebeta

← #27194100

Subgroups — #27194100

Order 13184.

256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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#20268417C211yesmaximal, characteristic
2#20267947C212yesmaximal, complemented
3#20267527C212yesmaximal, complemented
4#20267515C211yesmaximal, characteristic
5#393×C103C211yesmaximal, characteristic
6C2×#13110095—22no—
7#15693000—21no—
8#15693000C2212yes—
9#15692998—22no—
10#15692998—22no—
11C2×C22⋊Dic103—21no—
12#15692945—22no—
13C22⋊(C103⋊C8)C2212yes—
14C22×Q8×C103C2211yescharacteristic
15C2×C22⋊C4×C103—21no—
16C2×C22⋊C4×C103C2211yescharacteristic
17#95×C103—21no—
18#95×C103C2211yescharacteristic
19C2×Dic206—21no—
20C2×Dic206D412yes—
21C22×Dic103—21no—
22C22×Dic103—21no—
23#13110095—44no—
24C2×C103⋊C8—22no—
25C4⋊Dic103—21no—
26C4⋊Dic103D412yes—
27Dic103⋊C4—22no—
28Dic103⋊C4—22no—
29C22⋊Dic103—22no—
30C22⋊Dic103—22no—
31C24×C103D411yescharacteristic
32C2×Q8×C103—22no—
33C2×Q8×C103—42no—
34C22×C4×C103—21no—
35C22×C4×C103—21no—
36C22×C4×C103D411yescharacteristic
37C22×C4×C103C2311yescharacteristic
38C22⋊C4×C103—22no—
39C22⋊C4×C103—42no—
40C23×C103—21no—
41C23×C103—21no—
42C23×C103—41no—
43C23×C103—41no—
44C23×C103Q1612yescomplemented
45C23×C103C2×D411yescharacteristic
46Q8×C103—24no—
47Q8×C103—42no—
48C2×C4×C103—22no—
49C2×C4×C103—21no—
50C2×C4×C103—41no—
51C2×C4×C103—41no—
52C2×C4×C103—41no—
53C2×C4×C103—41no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103C2×D412yes—
58C2×Dic103—22no—
59C2×Dic103—22no—
60C2×Dic103—81no—
61C2×Dic103—81no—
62Dic206—42no—
63Dic206—81no—
64C103⋊C8—42no—
65C22×C103—21no—
66C22×C103—21no—
67C22×C103—22no—
68C22×C103—42no—
69C22×C103—41no—
70C22×C103—41no—
71C22×C103—81no—
72C22×C103#12011yescharacteristic
73C22×C103C2×Q1611yescharacteristic
74C22×C103#13711yescharacteristic
75C4×C103—22no—
76C4×C103—41no—
77C4×C103—42no—
78C4×C103—81no—
79Dic103—42no—
80Dic103—42no—
81C2×C103—21no—
82C2×C103—21no—
83C2×C103—42no—
84C2×C103#45111yescharacteristic
85C2×C103#45511yescharacteristic
86C2×C103B(4,𝔽2)11yescharacteristic
87#1602—1031nomaximal, Sylow
88C103#160211yescharacteristic, complemented, Sylow
89#543—1031no—
90#451—1032no—
91#393D10311yescharacteristic
92#328—1032no—
93#323—1031no—
94C22×Q8C2×D10311yescharacteristic
95C2×Q16—2062no—
96C22⋊Q8—1032no—
97C22⋊Q8—2062no—
98C22⋊Q8—2062no—
99C22⋊Q8—2061no—
100C2×C22⋊C4—21no—
101C2×C22⋊C4—2061no—
102C2×C22⋊C4C2×D10311yescharacteristic
103#103—2062no—
104C22⋊C8—1032no—
105#95—21no—
106#95C2×D10311yescharacteristic
107C24C22⋊D10311yescharacteristic
108C2×Q8—22no—
109C2×Q8—42no—
110C2×Q8—1032no—
111C2×Q8—2061no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—2061no—
115C22×C4—2061no—
116C22×C4C22⋊D10311yescharacteristic
117C22×C4C22×D10311yescharacteristic
118Q16—4124no—
119C2×C8—2062no—
120C4⋊C4—1032no—
121C4⋊C4—2062no—
122C4⋊C4—2061no—
123C4⋊C4—2062no—
124C22⋊C4—22no—
125C22⋊C4—42no—
126C22⋊C4—2062no—
127C22⋊C4—2062no—
128C23—21no—
129C23—21no—
130C23—41no—
131C23—41no—
132C23#1311009512yescomplemented
133C23C2×C22⋊D10311yescharacteristic
134Q8—24no—
135Q8—42no—
136Q8—8241no—
137Q8—4122no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—8241no—
148C2×C4—8241no—
149C2×C4—2062no—
150C2×C4—2062no—
151C2×C4D4×D10312yes—
152C8—4122no—
153C22—21no—
154C22—21no—
155C22—22no—
156C22—42no—
157C22—41no—
158C22—41no—
159C22—81no—
160C22#1569298911yescharacteristic
161C22C2×#1311009511yescharacteristic
162C22#1569305111yescharacteristic
163C4—22no—
164C4—41no—
165C4—42no—
166C4—81no—
167C4—4122no—
168C4—4122no—
169C2—21no—
170C2—21no—
171C2—42no—
172C2#2026794611yescharacteristic
173C2#2026796811yescharacteristic
174C2#2026797711yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#393×C103C2
socleC22×C103#120
prime radicalC24×C103D4
hypercenter#393D103
hypocenterC103#1602
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #20267947C2semidirect
3. #20267527C2semidirect
44. C23×C103Q16semidirect
88. C103#1602semidirect
132. C23#13110095semidirect

Maximal subgroups

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

subgroupindex
#202684172
#202679472
#202675272
#202675152
#393×C1032
#1602103