Finite Group Databasebeta

← #27206039

Subgroups — #27206039

Order 13184.

378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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#20268362C212yesmaximal
2#20268133C214yesmaximal, complemented
3#20268049C212yesmaximal, complemented
4#20268032C212yesmaximal, complemented
5#20267949C214yesmaximal, complemented
6#408×C103C211yesmaximal, characteristic
7C22×Dic206C2212yes—
8C2×Dic412C2212yes—
9C2×Dic412C2212yes—
10#15693019—22no—
11#15693008—22no—
12#15693002—22no—
13#15693002—22no—
14#15693000C2214yes—
15#15693000C2214yes—
16#15692980C2212yes—
17#15692955C2212yes—
18#15692953C2212yes—
19#15692946C2214yes—
20#15692946C2214yes—
21C2×#41×C103C2211yescharacteristic
22C2×M16×C103C2211yescharacteristic
23C22×C8×C103C2211yescharacteristic
24C22⋊C8×C103C2214yes—
25C2×Dic206—22no—
26C2×Dic206—42no—
27C2×Dic206—42no—
28C2×Dic206C2314yes—
29C22×Dic103—22no—
30Dic412—42no—
31Dic412—42no—
32C4⋊Dic103C2314yes—
33Dic103⋊C4—24no—
34Dic103⋊C4—24no—
35C22⋊Dic103—22no—
36C22⋊Dic103—24no—
37C22⋊Dic103—24no—
38C4×Dic103—22no—
39#41×C103—41no—
40#41×C103—41no—
41C2×Q8×C103D411yescharacteristic
42C2×D4×C103D411yescharacteristic
43C2×D4×C103D412yes—
44C22×C4×C103C2312yes—
45C22×C4×C103C2311yescharacteristic
46M16×C103—41no—
47C2×C8×C103—41no—
48C2×C8×C103C2312yes—
49C2×C8×C103C2312yes—
50C23×C103C2×D411yescharacteristic
51C23×C103C2×D412yes—
52Q8×C103—41no—
53D4×C103—42no—
54D4×C103—41no—
55C2×C4×C103—21no—
56C2×C4×C103—21no—
57C2×C4×C103—22no—
58C2×C4×C103—22no—
59C2×C4×C103C2×D412yes—
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103C2411yescharacteristic
62C2×Dic103—24no—
63C2×Dic103—24no—
64C2×Dic103—44no—
65Dic206—24no—
66Dic206—24no—
67Dic206—44no—
68C8×C103—22no—
69C8×C103—22no—
70C22×C103—22no—
71C22×C103—21no—
72C22×C103—22no—
73C22×C103—24no—
74C22×C103C22×D411yescharacteristic
75C4×C103—22no—
76C4×C103—21no—
77C4×C103H(5,𝔽2)11yescharacteristic
78C4×C103H(5,𝔽2)11yescharacteristic
79Dic103—44no—
80Dic103—44no—
81C2×C103—42no—
82C2×C103—41no—
83C2×C103#53411yescharacteristic
84C2×C103#57812yes—
85#3202—1031nomaximal, Sylow
86C103#320211yescharacteristic, complemented, Sylow
87#536—1032no—
88#485—1034no—
89#470—1032no—
90#467—1032no—
91#451—1034no—
92#408D10311yescharacteristic
93C2×#41C2×D10311yescharacteristic
94C22×Q8—1032no—
95C2×Q16—1032no—
96C2×Q16—1032no—
97C2×M16C2×D10311yescharacteristic
98C22×C8C2×D10311yescharacteristic
99C4⋊Q8—2062no—
100#124—2062no—
101#123—2062no—
102#123—2062no—
103C22⋊Q8—1034no—
104C22⋊Q8—1034no—
105#117—1032no—
106#107—1032no—
107#106—1032no—
108#103—1034no—
109#103—1034no—
110C22⋊C8C2×D10314yes—
111#41—41no—
112#41—41no—
113C2×Q8—1034no—
114C2×Q8—4122no—
115C2×Q8—4122no—
116C2×Q8—2062no—
117C2×Q8D41211yescharacteristic
118C2×D4D41211yescharacteristic
119C2×D4D41212yes—
120C22×C4—2062no—
121C22×C4C22×D10312yes—
122C22×C4C22×D10311yescharacteristic
123Q16—4122no—
124Q16—4122no—
125M16—41no—
126C2×C8—41no—
127C2×C8C22×D10312yes—
128C2×C8C22×D10312yes—
129C4⋊C4—1034no—
130C4⋊C4—2064no—
131C4⋊C4—2064no—
132C22⋊C4—2062no—
133C22⋊C4—2064no—
134C22⋊C4—2064no—
135C42—2062no—
136C23C2×D41211yescharacteristic
137C23C2×D41212yes—
138Q8—41no—
139Q8—4124no—
140Q8—2064no—
141Q8—2064no—
142D4—42no—
143D4—41no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—4124no—
149C2×C4—2064no—
150C2×C4—2064no—
151C2×C4C2×D41212yes—
152C2×C4C2×D41211yescharacteristic
153C2×C4C23×D10311yescharacteristic
154C8—22no—
155C8—22no—
156C22—22no—
157C22—24no—
158C22—22no—
159C22—21no—
160C22C22×D41211yescharacteristic
161C4—22no—
162C4—21no—
163C4—4124no—
164C4—4124no—
165C4#1569306611yescharacteristic
166C4#1569306611yescharacteristic
167C2—42no—
168C2—41no—
169C2#2026835311yescharacteristic
170C2#2026860812yes—
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#408×C103C2
socleC22×C103C22×D4
prime radicalC2×#41×C103C22
hypercenter#408D103
hypocenterC103#3202
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #20268133C2semidirect
3. #20268049C2semidirect
4. #20268032C2semidirect
5. #20267949C2semidirect
86. C103#3202semidirect

Maximal subgroups

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

subgroupindex
#202683622
#202681332
#202680492
#202680322
#202679492
#408×C1032
#3202103