Finite Group Databasebeta

← #28389847

Subgroups — #28389847

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#20298996C211yesmaximal, characteristic, complemented
3#20298878C211yesmaximal, characteristic
4#20298809C211yesmaximal, characteristic, complemented
5#20298343C211yesmaximal, characteristic, complemented
6#20298330C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic
8C2×Dic452—21no—
9#16813622C2211yescharacteristic
10#16813622C2211yescharacteristic
11#16813615—22no—
12#16813609—21no—
13#16813601—21no—
14C4×Dic226C2211yescharacteristic
15#16813587—21no—
16#16813581—21no—
17#16813555—21no—
18#16813554—22no—
19C4⋊#11744751C2211yescharacteristic
20#16813547—21no—
21#16813543—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226—21no—
26C2×Dic226—21no—
27C2×Dic226D411yescharacteristic
28Dic452—42no—
29C2×#11744751—21no—
30C4⋊Dic113—21no—
31C4⋊Dic113—21no—
32C4⋊Dic113—21no—
33C4⋊Dic113D411yescharacteristic
34C4⋊Dic113D412yes—
35#14268626—22no—
36#14268626—21no—
37C22⋊Dic113—22no—
38C22⋊Dic113—22no—
39C4×Dic113—22no—
40C4×Dic113—21no—
41C2×D4×C113D411yescharacteristic
42C22×C4×C113—21no—
43C2×C8×C113—21no—
44C2×C8×C113—21no—
45C4⋊C4×C113D411yescharacteristic
46C22⋊C4×C113—21no—
47C42×C113C2311yescharacteristic
48C23×C113—21no—
49D4×C113—21no—
50D4×C113—21no—
51C2×C4×C113—21no—
52C2×C4×C113—41no—
53C2×C4×C113—41no—
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×C4×C113C2×D411yescharacteristic
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—22no—
60C2×Dic113—41no—
61Dic226—21no—
62Dic226—21no—
63Dic226—41no—
64Dic226—41no—
65Dic226—41no—
66Dic226—41no—
67C8×C113—22no—
68C8×C113—41no—
69#11744751—41no—
70C22×C113—41no—
71C22×C113—41no—
72C22×C113—41no—
73C22×C113#12011yescharacteristic
74C4×C113—21no—
75C4×C113—41no—
76C4×C113#13511yescharacteristic
77C4×C113#13511yescharacteristic
78C4×C113AGL(1,ℤ/8)11yescharacteristic
79C4×C113#13711yescharacteristic
80Dic113—41no—
81Dic113—42no—
82Dic113—41no—
83Dic113—81no—
84C2×C113—81no—
85C2×C113#44911yescharacteristic
86C2×C113#45211yescharacteristic
87C2×C113#45611yescharacteristic
88#1652—1131nomaximal, Sylow
89C113#165211yescharacteristic, complemented, Sylow
90#556—1131no—
91#498—1131no—
92#474—1131no—
93#462—1131no—
94#332—1131no—
95Q8⋊C8—1131no—
96D4⋊C8D11311yescharacteristic
97C2×Q16—2261no—
98C4⋊Q8—1131no—
99C4⋊Q8—1131no—
100#126—2262no—
101#124—2261no—
102C22⋊Q8—2261no—
103C4×Q8—1131no—
104C4×Q8—2261no—
105C4×D4C2×D11311yescharacteristic
106#117—2261no—
107#107—2261no—
108#106—2262no—
109C4⋊C8—1131no—
110C4⋊C8C2×D11311yescharacteristic
111#103—2261no—
112#102—2261no—
113C4×C8C2×D11311yescharacteristic
114C2×Q8—1131no—
115C2×Q8—2261no—
116C2×Q8—2261no—
117C2×D4D45211yescharacteristic
118C22×C4—21no—
119Q16—4522no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—2261no—
123C4⋊C4—1131no—
124C4⋊C4—1132no—
125C4⋊C4—2262no—
126C4⋊C4—2261no—
127C4⋊C4—2261no—
128C4⋊C4—2261no—
129C4⋊C4—2261no—
130C4⋊C4D45211yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—2262no—
133C22⋊C4—2262no—
134C42—2262no—
135C42—2261no—
136C42C22×D11311yescharacteristic
137C23—21no—
138Q8—4521no—
139Q8—4521no—
140Q8—4521no—
141Q8—4521no—
142Q8—2261no—
143Q8—2261no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—4521no—
150C2×C4—2261no—
151C2×C4—2262no—
152C2×C4—2261no—
153C2×C4D4×D11311yescharacteristic
154C2×C4D4×D11311yescharacteristic
155C2×C4C2×D45211yescharacteristic
156C8—22no—
157C8—41no—
158C8—4521no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1681359211yescharacteristic
163C4—21no—
164C4—41no—
165C4—9041no—
166C4—4522no—
167C4—4521no—
168C4—4521no—
169C4#1681364311yescharacteristic
170C4#1681364411yescharacteristic
171C4#1681364611yescharacteristic
172C4#1681365511yescharacteristic
173C2—81no—
174C2#2029874411yescharacteristic
175C2#2029876211yescharacteristic
176C2#2029878211yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
prime radicalC2×D4×C113D4
hypercenterD4⋊C8D113
hypocenterC113#1652
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20298996C2semidirect
4. #20298809C2semidirect
5. #20298343C2semidirect
6. #20298330C2semidirect
89. C113#1652semidirect

Maximal subgroups

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

subgroupindex
#202993182
#202989962
#202988782
#202988092
#202983432
#202983302
D4⋊C8×C1132
#1652113