Finite Group Databasebeta

← #28389762

Subgroups — #28389762

Order 14464.

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

normal subgroups only

This group has 212 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#20299333C211yesmaximal, characteristic
2#20298945C211yesmaximal, characteristic
3#20298884C211yesmaximal, characteristic, complemented
4#20298808C211yesmaximal, characteristic, complemented
5#20298341C211yesmaximal, characteristic
6#20298330C211yesmaximal, characteristic, complemented
7Q8⋊C8×C113C211yesmaximal, characteristic, complemented
8C2×#14268637—21no—
9#16813622C2211yescharacteristic
10#16813619C2211yescharacteristic
11#16813611—21no—
12#16813610—21no—
13#16813607—22no—
14C4×Dic226C2211yescharacteristic
15C4×D452—21no—
16#16813584—21no—
17#16813554—21no—
18C4⋊#11744751C2211yescharacteristic
19#16813547—21no—
20#16813545—21no—
21#16813544—22no—
22C4×Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226—21no—
26C2×Dic226D411yescharacteristic
27C2×D452—21no—
28C2×D452—21no—
29C2×D452D412yes—
30C2×C4×D113—22no—
31#14268637—42no—
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113D411yescharacteristic
36#14268626—21no—
37#14268624—22no—
38#14268624—22no—
39#14268624—22no—
40C4×Dic113—21no—
41C2×Q8×C113D411yescharacteristic
42C2×C8×C113—21no—
43C2×C8×C113—21no—
44C4⋊C4×C113—21no—
45C4⋊C4×C113D411yescharacteristic
46C42×C113—21no—
47C42×C113C2311yescharacteristic
48C22×D113—22no—
49Q8×C113—21no—
50Q8×C113—21no—
51C2×C4×C113—21no—
52C2×C4×C113—21no—
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×Dic113—21no—
57C2×Dic113—21no—
58C2×Dic113—41no—
59D452—42no—
60D452—41no—
61D452—41no—
62D452—41no—
63D452—41no—
64C4×D113—82no—
65Dic226—21no—
66Dic226—21no—
67Dic226—41no—
68Dic226—41no—
69C8×C113—41no—
70C8×C113—41no—
71#11744751—41no—
72C22×C113#12011yescharacteristic
73C2×D113—42no—
74C2×D113—42no—
75C2×D113—42no—
76C4×C113—21no—
77C4×C113—41no—
78C4×C113—41no—
79C4×C113#13511yescharacteristic
80C4×C113#13511yescharacteristic
81C4×C113AGL(1,ℤ/8)11yescharacteristic
82C4×C113#13711yescharacteristic
83Dic113—41no—
84Dic113—41no—
85Dic113—81no—
86C2×C113#44911yescharacteristic
87C2×C113#45211yescharacteristic
88C2×C113#45511yescharacteristic
89D113—82no—
90#1640—1131nomaximal, Sylow
91C113#164011yescharacteristic, complemented, Sylow
92#559—1131no—
93#486—1131no—
94#475—1131no—
95#462—1131no—
96#331—1131no—
97Q8⋊C8—1131no—
98Q8⋊C8D11311yescharacteristic, complemented
99C2×Q16—2261no—
100C4⋊Q8—1131no—
101#127—1131no—
102#124—2261no—
103#124—2261no—
104#123—2262no—
105C4×Q8—1131no—
106C4×Q8C2×D11311yescharacteristic
107C4×D4—2261no—
108C4×D4—2261no—
109#106—2261no—
110C4⋊C8—1131no—
111C4⋊C8C2×D11311yescharacteristic
112#103—2261no—
113#103—2261no—
114#102—2262no—
115C4×C8C2×D11311yescharacteristic
116C2×Q8—1131no—
117C2×Q8—2261no—
118C2×Q8D45211yescharacteristic
119C2×D4—1132no—
120C2×D4—2261no—
121C2×D4—2261no—
122C22×C4—2262no—
123Q16—4522no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—2261no—
127C4⋊C4—21no—
128C4⋊C4—1131no—
129C4⋊C4—2261no—
130C4⋊C4—2261no—
131C4⋊C4—2261no—
132C4⋊C4D45211yescharacteristic
133C22⋊C4—2262no—
134C22⋊C4—2262no—
135C22⋊C4—2262no—
136C42—21no—
137C42—2261no—
138C42C22×D11311yescharacteristic
139C23—2262no—
140Q8—21no—
141Q8—21no—
142Q8—4521no—
143Q8—4521no—
144Q8—2261no—
145Q8—2261no—
146D4—4522no—
147D4—4521no—
148D4—4521no—
149D4—4521no—
150D4—4521no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—9042no—
154C2×C4—4521no—
155C2×C4—2261no—
156C2×C4—2261no—
157C2×C4D4×D11311yescharacteristic
158C2×C4D4×D11311yescharacteristic
159C2×C4C2×D45211yescharacteristic
160C8—41no—
161C8—41no—
162C8—4521no—
163C22—4522no—
164C22—4522no—
165C22—4522no—
166C22#1681359211yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—9041no—
171C4—4521no—
172C4—4521no—
173C4#1681364311yescharacteristic
174C4#1681364411yescharacteristic
175C4#1681365011yescharacteristic
176C4#1681365411yescharacteristic
177C2—9042no—
178C2#2029874511yescharacteristic
179C2#2029876311yescharacteristic
180C2#2029877711yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingQ8⋊C8×C113C2
socleC22×C113#120
prime radical#16813619C22
hypercenterQ8⋊C8D113
hypocenterC113#1640
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #20298884C2semidirect
4. #20298808C2semidirect
6. #20298330C2semidirect
7. Q8⋊C8×C113C2semidirect
91. C113#1640semidirect
98. Q8⋊C8D113semidirect

Maximal subgroups

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

subgroupindex
#202993332
#202989452
#202988842
#202988082
#202983412
#202983302
Q8⋊C8×C1132
#1640113