Finite Group Databasebeta

← #28389674

Subgroups — #28389674

Order 14464.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299263C211yesmaximal, characteristic, complemented
2#20298795C211yesmaximal, characteristic, complemented
3#20298790C211yesmaximal, characteristic
4#20298344C211yesmaximal, characteristic, complemented
5#20298330C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic, complemented
7#486×C113C211yesmaximal, characteristic, complemented
8C2×Q8×D113—21no—
9C2×#14268635—21no—
10C2×#14268632—21no—
11#16813621—21no—
12#16813600—22no—
13#16813598—21no—
14C4×Dic226C2211yescharacteristic
15C4×D452C2211yescharacteristic
16#16813584—21no—
17C4⋊#11744751C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic
19#16813543—21no—
20#16813543—21no—
21C4⋊Q8×C113C2211yescharacteristic
22#127×C113C2211yescharacteristic
23#102×C113—22no—
24C4×C8×C113C2211yescharacteristic
25C2×Dic226—22no—
26C2×Dic226D411yescharacteristic
27Q8×D113—42no—
28Q8×D113—42no—
29C2×D452D411yescharacteristic
30C2×C4×D113—22no—
31C2×C4×D113—21no—
32#14268635—42no—
33#14268632—42no—
34C2×#11744751—21no—
35C2×#11744751—21no—
36C4⋊Dic113D411yescharacteristic
37C4⋊Dic113D411yescharacteristic
38#14268626—22no—
39#14268626—21no—
40#14268624—22no—
41#14268624—21no—
42C4×Dic113—21no—
43C2×Q8×C113—21no—
44C2×D4×C113—21no—
45C2×D4×C113—21no—
46C2×D4×C113—21no—
47C2×C8×C113—21no—
48C4⋊C4×C113—21no—
49C4⋊C4×C113D412yes—
50C42×C113C2311yescharacteristic
51C23×C113—41no—
52C22×D113—21no—
53Q8×C113—41no—
54Q8×C113—41no—
55D4×C113—42no—
56D4×C113—41no—
57D4×C113—41no—
58D4×C113—41no—
59D4×C113—41no—
60C2×C4×C113—22no—
61C2×C4×C113C2×D411yescharacteristic
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113C2×D411yescharacteristic
64C2×Dic113—21no—
65C2×Dic113—21no—
66C2×Dic113—21no—
67D452—21no—
68D452SD1612yescomplemented
69C4×D113—44no—
70C4×D113—41no—
71C4×D113—41no—
72Dic226—21no—
73Dic226—44no—
74Dic226D812yescomplemented
75C8×C113—41no—
76#11744751—41no—
77#11744751—41no—
78C22×C113—81no—
79C22×C113—81no—
80C22×C113—81no—
81C22×C113#12011yescharacteristic
82C2×D113—22no—
83C2×D113—41no—
84C2×D113—41no—
85C4×C113—21no—
86C4×C113—42no—
87C4×C113C2×D811yescharacteristic
88C4×C113C2×SD1611yescharacteristic
89C4×C113AGL(1,ℤ/8)11yescharacteristic
90C4×C113#13711yescharacteristic
91Dic113—22no—
92Dic113—41no—
93Dic113—41no—
94C2×C113—161no—
95C2×C113#44711yescharacteristic
96C2×C113#44811yescharacteristic
97C2×C113#45411yescharacteristic
98D113—42no—
99#1627—1131nomaximal, Sylow
100C113#162711yescharacteristic, complemented, Sylow
101D4×Q8—1131no—
102#486D11311yescharacteristic, complemented
103#460—1131no—
104#459—1131no—
105#332—1131no—
106Q8⋊C8—1131no—
107D4⋊C8—1131no—
108C22×Q8—2261no—
109C2×SD16—2261no—
110C2×D8—2261no—
111C4⋊Q8—2261no—
112C4⋊Q8C2×D11311yescharacteristic
113#127C2×D11311yescharacteristic
114C22⋊Q8—2261no—
115C22⋊Q8—2262no—
116C4×Q8—1131no—
117C4×D4—1131no—
118C4×D4—2261no—
119C4⋊C8—1131no—
120C4⋊C8—1131no—
121#102—22no—
122#102—2261no—
123#102—2261no—
124C4×C8C2×D11311yescharacteristic
125C2×Q8—21no—
126C2×Q8—1131no—
127C2×Q8—4522no—
128C2×Q8—4522no—
129C2×Q8—2262no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—1131no—
134C22×C4—2262no—
135C22×C4—2261no—
136SD16—4522no—
137D8—4522no—
138C2×C8—21no—
139C2×C8—2261no—
140C2×C8—2261no—
141C4⋊C4—21no—
142C4⋊C4—1131no—
143C4⋊C4—1131no—
144C4⋊C4—2262no—
145C4⋊C4—2261no—
146C4⋊C4C22⋊D11312yes—
147C22⋊C4—2262no—
148C22⋊C4—2261no—
149C42—2261no—
150C42C22×D11311yescharacteristic
151C23—41no—
152C23—2261no—
153Q8—41no—
154Q8—41no—
155Q8—1132no—
156Q8—4524no—
157Q8—2261no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—1132no—
164D4—2261no—
165C2×C4—22no—
166C2×C4—4524no—
167C2×C4—4521no—
168C2×C4—4521no—
169C2×C4—2261no—
170C2×C4—2261no—
171C2×C4—2261no—
172C2×C4D4×D11311yescharacteristic
173C2×C4D4×D11311yescharacteristic
174C2×C4C2×C22⋊D11311yescharacteristic
175C8—41no—
176C8—4521no—
177C8—4521no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—4521no—
182C22—4521no—
183C22—2262no—
184C22#1681359011yescharacteristic
185C4—21no—
186C4—42no—
187C4—4521no—
188C4—4521no—
189C4—2262no—
190C4D8×D11311yescharacteristic
191C4SD16×D11311yescharacteristic
192C4#1681364611yescharacteristic
193C4#1681365111yescharacteristic
194C2—161no—
195C2—4522no—
196C2#2029873011yescharacteristic
197C2#2029873511yescharacteristic
198C2#2029877011yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#486×C113C2
socleC22×C113#120
prime radical#20298790C2
hypercenter#486D113
hypocenterC113#1627
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20299263C2semidirect
2. #20298795C2semidirect
4. #20298344C2semidirect
5. #20298330C2semidirect
6. #20298327C2semidirect
7. #486×C113C2semidirect
68. D452SD16semidirect
74. Dic226D8semidirect
100. C113#1627semidirect
102. #486D113semidirect

Maximal subgroups

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

subgroupindex
#202992632
#202987952
#202987902
#202983442
#202983302
#202983272
#486×C1132
#1627113