Finite Group Databasebeta

← #28392570

Subgroups — #28392570

Order 14464.

246 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 45 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#20298787C212yesmaximal, complemented
2#20298765C211yesmaximal, characteristic
3#20298391C211yesmaximal, characteristic, complemented
4#20298388C212yesmaximal, complemented
5#559×C113C211yesmaximal, characteristic, complemented
6#16813667C2211yescharacteristic
7#16813648—21no—
8#16813605—22no—
9#16813550—21no—
10#16813539C2211yescharacteristic
11#16813537C2212yes—
12#16813536—22no—
13#127×C113C2211yescharacteristic
14#124×C113—22no—
15#123×C113—21no—
16#123×C113C2212yes—
17C4×Q8×C113—21no—
18C4×D4×C113—22no—
19#14268647—21no—
20#14268646—41no—
21C2×C22⋊D113—22no—
22D4×D113—41no—
23#14268635—41no—
24#14268632—41no—
25#14268631—21no—
26#14268626—42no—
27C22⋊Dic113—22no—
28#14268624—42no—
29C2×Q8×C113—21no—
30C2×D4×C113—22no—
31C2×D4×C113D411yescharacteristic
32C2×D4×C113C2311yescharacteristic
33C22×C4×C113—21no—
34C22×C4×C113D412yes—
35C4⋊C4×C113—21no—
36C4⋊C4×C113—22no—
37C22⋊C4×C113—22no—
38C22⋊C4×C113—21no—
39C22⋊C4×C113—22no—
40C22⋊C4×C113D412yes—
41C42×C113—22no—
42C42×C113D411yescharacteristic
43C23×C113—21no—
44C23×C113C2×D412yes—
45C22×D113—22no—
46Q8×C113—42no—
47D4×C113—41no—
48D4×C113—41no—
49D4×C113—44no—
50C2×C4×C113—21no—
51C2×C4×C113—22no—
52C2×C4×C113—22no—
53C2×C4×C113—42no—
54C2×C4×C113—81no—
55C2×C4×C113C2×D411yescharacteristic
56C22⋊D113—42no—
57C22⋊D113—41no—
58C2×Dic113—22no—
59C2×Dic113—42no—
60D452—21no—
61C4×D113—41no—
62Dic226—21no—
63#11744751—41no—
64C22×C113—22no—
65C22×C113—42no—
66C22×C113—42no—
67C22×C113—41no—
68C22×C113#12011yescharacteristic
69C2×D113—41no—
70C2×D113—82no—
71C4×C113—22no—
72C4×C113—21no—
73C4×C113—42no—
74C4×C113—42no—
75Dic113—41no—
76Dic113—82no—
77C2×C113—21no—
78C2×C113—42no—
79C2×C113—81no—
80C2×C113B(4,𝔽2)11yescharacteristic
81D113—81no—
82#2198—1131nomaximal, Sylow
83C113#219811yescharacteristic, complemented, Sylow
84#559D11311yescharacteristic, complemented
85#458—1132no—
86#453—1131no—
87#353—1131no—
88#352—1132no—
89H(5,𝔽2)—1131no—
90AGL(1,ℤ/8)—2261no—
91#127C2×D11311yescharacteristic
92#124—22no—
93#123—21no—
94#123—2262no—
95#123C2×D11312yes—
96C4×Q8—21no—
97C4×D4—22no—
98#104—2261no—
99#100—1131no—
100#99—1132no—
101#99—2262no—
102#41—4521no—
103#41—2261no—
104C2×Q8—21no—
105C2×D4—22no—
106C2×D4—4521no—
107C2×D4—2262no—
108C2×D4C22⋊D11311yescharacteristic
109C2×D4C22×D11311yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D11312yes—
112SD16—4521no—
113D8—4521no—
114M16—2261no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C4⋊C4—4522no—
118C22⋊C4—22no—
119C22⋊C4—21no—
120C22⋊C4—22no—
121C22⋊C4—4522no—
122C22⋊C4—2262no—
123C22⋊C4C22⋊D11312yes—
124C42—22no—
125C42C22⋊D11311yescharacteristic
126C23—21no—
127C23—2262no—
128C23C2×C22⋊D11312yes—
129Q8—42no—
130Q8—2261no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—4522no—
135D4—4521no—
136D4—2261no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—81no—
142C2×C4—4521no—
143C2×C4—4522no—
144C2×C4—2262no—
145C2×C4C2×C22⋊D11311yescharacteristic
146C8—4521no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—9042no—
152C22—4521no—
153C22#1681359111yescharacteristic
154C4—22no—
155C4—21no—
156C4—42no—
157C4—42no—
158C4—9042no—
159C4—4521no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—9041no—
164C2#2029878511yescharacteristic
subgroupG/H
centerC2#20298785
commutator, cosocleC2×D4×C113C23
FrattiniC2×D4C22×D113
Fitting#559×C113C2
socleC2×C113B(4,𝔽2)
prime radical#20298765C2
hypercenter#559D113
hypocenterC113#2198
LCSG ▷ C2×D4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #20298787C2semidirect
3. #20298391C2semidirect
4. #20298388C2semidirect
5. #559×C113C2semidirect
83. C113#2198semidirect
84. #559D113semidirect

Maximal subgroups

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

subgroupindex
#202987872
#202987652
#202983912
#202983882
#559×C1132
#2198113