Finite Group Databasebeta

← #28389545

Subgroups — #28389545

Order 14464.

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

normal subgroups only

This group has 282 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#20299179C211yesmaximal, characteristic
2#20298739C212yesmaximal, complemented
3#20298518C211yesmaximal, characteristic, complemented
4#20298333C212yesmaximal, complemented
5#324×C113C211yesmaximal, characteristic, complemented
6C2×#14268647—21no—
7C22×Dic226C2211yescharacteristic
8C2×#14268636—22no—
9#16813602—22no—
10#16813597—22no—
11#16813596—21no—
12#16813596C2212yes—
13C2×#14268626—21no—
14#16813547—22no—
15#16813529—21no—
16#16813529C2211yescharacteristic
17C2×C4⋊C4×C113C2211yescharacteristic
18C22⋊C8×C113C2212yes—
19#14268647—42no—
20#14268647—42no—
21C2×Dic226—22no—
22C2×Dic226—21no—
23C2×Dic226—42no—
24C2×D452—21no—
25C2×D452—21no—
26C2×D452D412yes—
27C2×C22⋊D113—22no—
28C22×Dic113—21no—
29C22×Dic113—21no—
30C2×C4×D113—22no—
31#14268636—44no—
32C4⋊Dic113—21no—
33C4⋊Dic113D412yes—
34#14268626—42no—
35#14268624—22no—
36#14268624—22no—
37C22×C4×C113D411yescharacteristic
38C22×C4×C113D411yescharacteristic
39C22×C4×C113C2311yescharacteristic
40C2×C8×C113—22no—
41C4⋊C4×C113—22no—
42C23×C113C2×D411yescharacteristic
43C22×D113—22no—
44C2×C4×C113—21no—
45C2×C4×C113—21no—
46C2×C4×C113—21no—
47C2×C4×C113—41no—
48C2×C4×C113—41no—
49C2×C4×C113SD1612yescomplemented
50C2×C4×C113C2×D412yes—
51C22⋊D113—42no—
52C22⋊D113—42no—
53C2×Dic113—22no—
54C2×Dic113—22no—
55C2×Dic113—22no—
56C2×Dic113—41no—
57C2×Dic113—41no—
58C2×Dic113—41no—
59C2×Dic113—41no—
60D452—42no—
61D452—42no—
62D452—81no—
63C4×D113—44no—
64Dic226—24no—
65Dic226—42no—
66Dic226—42no—
67C8×C113—42no—
68C22×C113—21no—
69C22×C113—21no—
70C22×C113#12011yescharacteristic
71C22×C113C2×SD1611yescharacteristic
72C22×C113AGL(1,ℤ/8)11yescharacteristic
73C2×D113—42no—
74C2×D113—42no—
75C2×D113—42no—
76C4×C113—22no—
77C4×C113—22no—
78C4×C113—41no—
79Dic113—42no—
80Dic113—42no—
81Dic113—42no—
82C2×C113—21no—
83C2×C113—21no—
84C2×C113#45011yescharacteristic
85C2×C113#45611yescharacteristic
86C2×C113B(4,𝔽2)11yescharacteristic
87D113—82no—
88#1604—1131nomaximal, Sylow
89C113#160411yescharacteristic, complemented, Sylow
90#537—1131no—
91#448—1132no—
92#395—1131no—
93#327—1132no—
94#324D11311yescharacteristic, complemented
95C2×#41—2261no—
96C22×Q8—1131no—
97C2×SD16—2262no—
98C22⋊Q8—2262no—
99#121—1132no—
100#121—2262no—
101#121—2261no—
102C2×C4⋊C4—2261no—
103C2×C4⋊C4C2×D11311yescharacteristic
104#103—2262no—
105C22⋊C8C2×D11312yes—
106#95—1131no—
107#95—2261no—
108#41—4522no—
109#41—4522no—
110C2×Q8—4522no—
111C2×Q8—2261no—
112C2×Q8—2262no—
113C2×D4—1132no—
114C2×D4—2261no—
115C2×D4—2261no—
116C2×D4—2262no—
117C22×C4—2262no—
118C22×C4—2261no—
119C22×C4—2261no—
120C22×C4D45211yescharacteristic
121C22×C4D45211yescharacteristic
122C22×C4C22×D11311yescharacteristic
123SD16—4524no—
124C2×C8—22no—
125C4⋊C4—22no—
126C4⋊C4—1132no—
127C4⋊C4—4522no—
128C4⋊C4—2261no—
129C22⋊C4—2262no—
130C22⋊C4—2262no—
131C23—2262no—
132C23C2×D45211yescharacteristic
133Q8—4522no—
134Q8—4522no—
135Q8—2264no—
136D4—9041no—
137D4—4522no—
138D4—4522no—
139D4—4522no—
140D4—4522no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—4524no—
147C2×C4—4521no—
148C2×C4—4521no—
149C2×C4—4521no—
150C2×C4—4521no—
151C2×C4—2262no—
152C2×C4—2262no—
153C2×C4—2262no—
154C2×C4#1426863612yescomplemented
155C2×C4D4×D11312yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—4522no—
160C22—4522no—
161C22—4522no—
162C22#1681359211yescharacteristic
163C22C2×#1426863611yescharacteristic
164C22#1681365011yescharacteristic
165C4—22no—
166C4—22no—
167C4—41no—
168C4—4522no—
169C4—4522no—
170C4—4522no—
171C2—21no—
172C2—21no—
173C2—9042no—
174C2#2029875111yescharacteristic
175C2#2029878311yescharacteristic
176C2#2029878611yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#324×C113C2
socleC22×C113#120
prime radical#20299179C2
hypercenter#324D113
hypocenterC113#1604
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20298739C2semidirect
3. #20298518C2semidirect
4. #20298333C2semidirect
5. #324×C113C2semidirect
49. C2×C4×C113SD16semidirect
89. C113#1604semidirect
94. #324D113semidirect
154. C2×C4#14268636semidirect

Maximal subgroups

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

subgroupindex
#202991792
#202987392
#202985182
#202983332
#324×C1132
#1604113