Finite Group Databasebeta

← #28389828

Subgroups — #28389828

Order 14464.

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

normal subgroups only

This group has 200 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#20299318C211yesmaximal, characteristic
2#20299001C211yesmaximal, characteristic, complemented
3#20298880C211yesmaximal, characteristic, complemented
4#20298345C211yesmaximal, characteristic, complemented
5#20298328C211yesmaximal, characteristic, complemented
6D4⋊#11744751C211yesmaximal, characteristic
7#461×C113C211yesmaximal, characteristic
8#16813622C2211yescharacteristic
9#16813615—22no—
10#16813609—21no—
11#16813601—21no—
12C4×Dic226C2211yescharacteristic
13#16813587—21no—
14#16813581—21no—
15#16813555—22no—
16#16813553—21no—
17C4⋊#11744751C2211yescharacteristic
18#16813545—21no—
19C4×#11744751C2211yescharacteristic
20C2×SD16×C113—21no—
21C4⋊Q8×C113C2211yescharacteristic
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24#103×C113—21no—
25C2×Dic226—21no—
26C2×Dic226D411yescharacteristic
27C2×#11744751—21no—
28C2×#11744751—21no—
29C4⋊Dic113—21no—
30C4⋊Dic113D411yescharacteristic
31C4⋊Dic113D412yes—
32#14268626—22no—
33#14268626—21no—
34C22⋊Dic113—22no—
35C22⋊Dic113—22no—
36C4×Dic113—22no—
37C4×Dic113—21no—
38C2×Q8×C113—21no—
39C2×D4×C113D411yescharacteristic
40C22×C4×C113—21no—
41SD16×C113—42no—
42C2×C8×C113—21no—
43C4⋊C4×C113—21no—
44C4⋊C4×C113—21no—
45C4⋊C4×C113D411yescharacteristic
46C22⋊C4×C113—21no—
47C42×C113C2311yescharacteristic
48C23×C113—21no—
49Q8×C113—41no—
50Q8×C113—41no—
51D4×C113—21no—
52D4×C113—21no—
53C2×C4×C113—21no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113C2×D411yescharacteristic
60C2×Dic113—21no—
61C2×Dic113—21no—
62C2×Dic113—22no—
63Dic226—21no—
64Dic226—21no—
65Dic226—41no—
66Dic226—41no—
67C8×C113—41no—
68#11744751—22no—
69#11744751—41no—
70C22×C113—41no—
71C22×C113—41no—
72C22×C113—41no—
73C22×C113#12011yescharacteristic
74C4×C113—21no—
75C4×C113—41no—
76C4×C113—81no—
77C4×C113#13511yescharacteristic
78C4×C113#13511yescharacteristic
79C4×C113AGL(1,ℤ/8)11yescharacteristic
80C4×C113#13711yescharacteristic
81Dic113—42no—
82Dic113—41no—
83Dic113—41no—
84C2×C113—81no—
85C2×C113#44911yescharacteristic
86C2×C113#45211yescharacteristic
87C2×C113#45611yescharacteristic
88#1650—1131nomaximal, Sylow
89C113#165011yescharacteristic, complemented, Sylow
90#556—1131no—
91#500—1131no—
92#475—1131no—
93#461D11311yescharacteristic
94#332—1131no—
95Q8⋊C8—1131no—
96D4⋊C8—1131no—
97C2×SD16—21no—
98C4⋊Q8—1131no—
99C4⋊Q8C2×D11311yescharacteristic
100#126—2262no—
101#124—2261no—
102C22⋊Q8—2261no—
103C4×Q8—1131no—
104C4×Q8—2261no—
105C4×D4C2×D11311yescharacteristic
106#117—2261no—
107#107—2262no—
108#106—2261no—
109C4⋊C8—1131no—
110C4⋊C8C2×D11311yescharacteristic
111#103—21no—
112#103—2261no—
113C4×C8—1131no—
114C2×Q8—21no—
115C2×Q8—1131no—
116C2×Q8—2261no—
117C2×D4C22⋊D11311yescharacteristic
118C22×C4—21no—
119SD16—42no—
120C2×C8—21no—
121C2×C8—2261no—
122C2×C8—2261no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—1131no—
126C4⋊C4—1132no—
127C4⋊C4—2262no—
128C4⋊C4—2261no—
129C4⋊C4—2261no—
130C4⋊C4C22⋊D11311yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—2262no—
133C22⋊C4—2262no—
134C42—2262no—
135C42—2261no—
136C42C22×D11311yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—4521no—
141Q8—4521no—
142Q8—2261no—
143Q8—2261no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—2261no—
151C2×C4—2262no—
152C2×C4—2261no—
153C2×C4D4×D11311yescharacteristic
154C2×C4D4×D11311yescharacteristic
155C2×C4C2×C22⋊D11311yescharacteristic
156C8—41no—
157C8—4521no—
158C8—2262no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1681359011yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—4521no—
167C4—4521no—
168C4—4522no—
169C4#1681364211yescharacteristic
170C4#1681364311yescharacteristic
171C4#1681364811yescharacteristic
172C4#1681365111yescharacteristic
173C2—81no—
174C2#2029874111yescharacteristic
175C2#2029875711yescharacteristic
176C2#2029877911yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#461×C113C2
socleC22×C113#120
prime radicalC2×D4×C113D4
hypercenter#461D113
hypocenterC113#1650
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #20299001C2semidirect
3. #20298880C2semidirect
4. #20298345C2semidirect
5. #20298328C2semidirect
89. C113#1650semidirect

Maximal subgroups

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

subgroupindex
#202993182
#202990012
#202988802
#202983452
#202983282
D4⋊#117447512
#461×C1132
#1650113