Finite Group Databasebeta

← #28389671

Subgroups — #28389671

Order 14464.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299323C211yesmaximal, characteristic, complemented
2#20298946C211yesmaximal, characteristic
3#20298799C211yesmaximal, characteristic
4#20298799C211yesmaximal, characteristic
5#20298328C211yesmaximal, characteristic, complemented
6#20298328C211yesmaximal, characteristic, complemented
7#332×C113C211yesmaximal, characteristic, complemented
8C2×#14268636—21no—
9C2×#14268636—21no—
10#16813620—21no—
11#16813619C2211yescharacteristic
12#16813613—21no—
13#16813612—22no—
14Q8×Dic113—21no—
15C4×Dic226C2211yescharacteristic
16C4×Dic226C2211yescharacteristic
17#16813587—21no—
18#16813544—21no—
19#16813544—21no—
20#16813542—22no—
21C4×#11744751C2211yescharacteristic
22C4⋊Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25C2×Dic226D411yescharacteristic
26C2×Dic226D411yescharacteristic
27C2×D452—21no—
28C2×D452—21no—
29C2×D452—21no—
30#14268636—42no—
31#14268636—42no—
32C2×#11744751—21no—
33C4⋊Dic113—22no—
34C4⋊Dic113D411yescharacteristic
35C4⋊Dic113D411yescharacteristic
36#14268626—22no—
37#14268626—22no—
38#14268626—21no—
39#14268626—21no—
40C4×Dic113—22no—
41C4×Dic113—21no—
42C4×Dic113—21no—
43C2×Q8×C113—21no—
44C2×C8×C113—21no—
45C2×C8×C113—21no—
46C4⋊C4×C113—21no—
47C4⋊C4×C113D412yes—
48C42×C113C2311yescharacteristic
49C22×D113—41no—
50Q8×C113—41no—
51Q8×C113—41no—
52C2×C4×C113—22no—
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×Dic113—21no—
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—21no—
60D452—42no—
61D452—41no—
62D452—41no—
63D452—41no—
64D452—41no—
65Dic226—21no—
66Dic226—21no—
67Dic226—21no—
68Dic226SD1612yescomplemented
69C8×C113—41no—
70C8×C113—41no—
71#11744751—41no—
72C22×C113#12011yescharacteristic
73C2×D113—81no—
74C2×D113—81no—
75C2×D113—81no—
76C4×C113—21no—
77C4×C113—42no—
78C4×C113C2×SD1611yescharacteristic
79C4×C113#13511yescharacteristic
80C4×C113AGL(1,ℤ/8)11yescharacteristic
81C4×C113#13711yescharacteristic
82Dic113—22no—
83Dic113—41no—
84Dic113—41no—
85Dic113—41no—
86C2×C113#44811yescharacteristic
87C2×C113#44911yescharacteristic
88C2×C113#45411yescharacteristic
89D113—161no—
90#1626—1131nomaximal, Sylow
91C113#162611yescharacteristic, complemented, Sylow
92#557—1131no—
93#486—1131no—
94#460—1131no—
95#460—1131no—
96#332D11311yescharacteristic, complemented
97Q8⋊C8—1131no—
98Q8⋊C8—1131no—
99C2×SD16—2261no—
100C2×SD16—2261no—
101C4⋊Q8—2261no—
102C4⋊Q8C2×D11311yescharacteristic
103#127—1131no—
104#125—2261no—
105#125—2262no—
106C4×Q8—1131no—
107C4×Q8—1131no—
108C4×Q8—2261no—
109C4×Q8—2261no—
110C4⋊C8C2×D11311yescharacteristic
111C4⋊C8C2×D11311yescharacteristic
112#102—2261no—
113#102—2261no—
114#102—2262no—
115C4×C8—1131no—
116C2×Q8—21no—
117C2×Q8—1131no—
118C2×Q8—1131no—
119C2×D4—2261no—
120C2×D4—2261no—
121C2×D4—2261no—
122SD16—4522no—
123SD16—4522no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—2261no—
127C4⋊C4—21no—
128C4⋊C4—1131no—
129C4⋊C4—1131no—
130C4⋊C4—2262no—
131C4⋊C4—2262no—
132C4⋊C4—2262no—
133C4⋊C4—2261no—
134C4⋊C4—2261no—
135C4⋊C4D45212yes—
136C42—2262no—
137C42—2261no—
138C42—2261no—
139C42C22×D11311yescharacteristic
140C23—4521no—
141Q8—41no—
142Q8—41no—
143Q8—1132no—
144Q8—2261no—
145Q8—2261no—
146Q8—2261no—
147D4—4522no—
148D4—4521no—
149D4—4521no—
150D4—4521no—
151D4—4521no—
152C2×C4—22no—
153C2×C4—2261no—
154C2×C4—2261no—
155C2×C4—2261no—
156C2×C4—2261no—
157C2×C4D4×D11311yescharacteristic
158C2×C4D4×D11311yescharacteristic
159C2×C4C2×D45211yescharacteristic
160C8—41no—
161C8—41no—
162C8—4521no—
163C22—9041no—
164C22—9041no—
165C22—9041no—
166C22#1681359211yescharacteristic
167C4—21no—
168C4—42no—
169C4—4521no—
170C4—4521no—
171C4—4521no—
172C4—2262no—
173C4SD16×D11311yescharacteristic
174C4#1681364311yescharacteristic
175C4#1681364611yescharacteristic
176C4#1681365411yescharacteristic
177C2—18081no—
178C2#2029873811yescharacteristic
179C2#2029874411yescharacteristic
180C2#2029877311yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#332×C113C2
socleC22×C113#120
prime radical#16813619C22
hypercenter#332D113
hypocenterC113#1626
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #20299323C2semidirect
5. #20298328C2semidirect
6. #20298328C2semidirect
7. #332×C113C2semidirect
68. Dic226SD16semidirect
91. C113#1626semidirect
96. #332D113semidirect

Maximal subgroups

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

subgroupindex
#202993232
#202989462
#202987992
#202983282
#332×C1132
#1626113