Finite Group Databasebeta

← #28389776

Subgroups — #28389776

Order 14464.

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

normal subgroups only

This group has 250 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#20299269C211yesmaximal, characteristic
2#20298945C211yesmaximal, characteristic, complemented
3#20298884C211yesmaximal, characteristic, complemented
4#20298803C211yesmaximal, characteristic, complemented
5#20298341C211yesmaximal, characteristic, complemented
6#20298330C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic, complemented
8C2×#14268647—21no—
9C2×#14268635—21no—
10#16813622C2211yescharacteristic
11#16813619C2211yescharacteristic
12#16813618—21no—
13#16813596—21no—
14#16813595—22no—
15C4×Dic226C2211yescharacteristic
16#16813584—21no—
17#16813554—21no—
18C4⋊#11744751C2211yescharacteristic
19#16813547—21no—
20#16813545—21no—
21#16813544—22no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25#14268647—42no—
26#14268647—42no—
27C2×Dic226—21no—
28C2×Dic226D411yescharacteristic
29C2×D452—21no—
30C2×D452—21no—
31C2×D452D412yes—
32C2×C22⋊D113—22no—
33C2×C22⋊D113—22no—
34C2×C4×D113—22no—
35#14268635—42no—
36C2×#11744751—21no—
37C4⋊Dic113—21no—
38C4⋊Dic113—21no—
39C4⋊Dic113D411yescharacteristic
40#14268626—21no—
41#14268624—22no—
42C4×Dic113—21no—
43C2×D4×C113D411yescharacteristic
44C22×C4×C113—21no—
45C2×C8×C113—21no—
46C2×C8×C113—21no—
47C4⋊C4×C113D411yescharacteristic
48C22⋊C4×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—21no—
51C22×D113—22no—
52D4×C113—21no—
53D4×C113—21no—
54C2×C4×C113—21no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113C2×D411yescharacteristic
60C22⋊D113—44no—
61C22⋊D113—82no—
62C2×Dic113—21no—
63C2×Dic113—21no—
64C2×Dic113—41no—
65D452—42no—
66D452—41no—
67D452—41no—
68D452—41no—
69D452—41no—
70C4×D113—44no—
71Dic226—21no—
72Dic226—41no—
73Dic226—41no—
74Dic226SD1612yescomplemented
75C8×C113—41no—
76C8×C113—41no—
77#11744751—41no—
78C22×C113—41no—
79C22×C113—41no—
80C22×C113—41no—
81C22×C113#12011yescharacteristic
82C2×D113—42no—
83C2×D113—42no—
84C2×D113—42no—
85C4×C113—21no—
86C4×C113—41no—
87C4×C113C2×SD1611yescharacteristic
88C4×C113#13511yescharacteristic
89C4×C113AGL(1,ℤ/8)11yescharacteristic
90C4×C113AGL(1,ℤ/8)11yescharacteristic
91Dic113—22no—
92Dic113—41no—
93Dic113—81no—
94C2×C113—81no—
95C2×C113#44911yescharacteristic
96C2×C113#45011yescharacteristic
97C2×C113#45511yescharacteristic
98D113—82no—
99#1642—1131nomaximal, Sylow
100C113#164211yescharacteristic, complemented, Sylow
101#550—1131no—
102#486—1131no—
103#475—1131no—
104#461—1131no—
105#331—1131no—
106Q8⋊C8—1131no—
107D4⋊C8D11311yescharacteristic, complemented
108C2×#41—2261no—
109C2×SD16—2261no—
110C4⋊Q8—1131no—
111#127—1131no—
112#127—2261no—
113#121—2262no—
114#121—2261no—
115C4×Q8—1131no—
116C4×D4—2261no—
117C4×D4C2×D11311yescharacteristic
118#106—2261no—
119C4⋊C8—1131no—
120C4⋊C8C2×D11311yescharacteristic
121#103—2261no—
122#103—2261no—
123#102—2262no—
124C4×C8C2×D11311yescharacteristic
125#41—4522no—
126#41—4522no—
127C2×Q8—1131no—
128C2×Q8—2261no—
129C2×D4—1132no—
130C2×D4—2262no—
131C2×D4—2262no—
132C2×D4—2261no—
133C2×D4—2261no—
134C2×D4D45211yescharacteristic
135C22×C4—21no—
136C22×C4—2262no—
137SD16—4522no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—2261no—
141C4⋊C4—1131no—
142C4⋊C4—2261no—
143C4⋊C4—2261no—
144C4⋊C4—2261no—
145C4⋊C4D45211yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—2262no—
148C42—2261no—
149C42C22×D11311yescharacteristic
150C23—21no—
151C23—2262no—
152Q8—1132no—
153Q8—4521no—
154Q8—4521no—
155Q8—2261no—
156D4—21no—
157D4—21no—
158D4—9042no—
159D4—4522no—
160D4—4524no—
161D4—4521no—
162D4—4521no—
163D4—4521no—
164D4—4521no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—4524no—
169C2×C4—4521no—
170C2×C4—2261no—
171C2×C4—2261no—
172C2×C4D4×D11311yescharacteristic
173C2×C4D4×D11311yescharacteristic
174C2×C4C2×D45211yescharacteristic
175C8—41no—
176C8—41no—
177C8—4521no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—4522no—
182C22—4522no—
183C22—4522no—
184C22#1681359211yescharacteristic
185C4—21no—
186C4—41no—
187C4—9041no—
188C4—4521no—
189C4—2262no—
190C4SD16×D11311yescharacteristic
191C4#1681364411yescharacteristic
192C4#1681364611yescharacteristic
193C4#1681365011yescharacteristic
194C2—81no—
195C2—9042no—
196C2#2029874511yescharacteristic
197C2#2029875011yescharacteristic
198C2#2029877711yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
prime radical#20299269C2
hypercenterD4⋊C8D113
hypocenterC113#1642
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. #20298945C2semidirect
3. #20298884C2semidirect
4. #20298803C2semidirect
5. #20298341C2semidirect
6. #20298330C2semidirect
7. D4⋊C8×C113C2semidirect
74. Dic226SD16semidirect
100. C113#1642semidirect
107. D4⋊C8D113semidirect

Maximal subgroups

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

subgroupindex
#202992692
#202989452
#202988842
#202988032
#202983412
#202983302
D4⋊C8×C1132
#1642113