Finite Group Databasebeta

← #28389686

Subgroups — #28389686

Order 14464.

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

normal subgroups only

This group has 216 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#20299318C211yesmaximal, characteristic, complemented
2#20298945C211yesmaximal, characteristic, complemented
3#20298799C211yesmaximal, characteristic, complemented
4#20298793C211yesmaximal, characteristic
5#20298343C211yesmaximal, characteristic, complemented
6#20298330C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic, complemented
8C2×#14268636—21no—
9C2×#14268632—21no—
10#16813622C2211yescharacteristic
11#16813619C2211yescharacteristic
12#16813615—22no—
13#16813609—21no—
14#16813601—21no—
15C4×Dic226C2211yescharacteristic
16#16813587—21no—
17#16813581—21no—
18C4⋊#11744751C2211yescharacteristic
19#16813544—21no—
20#16813544—22no—
21#16813542—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226—21no—
26C2×Dic226D411yescharacteristic
27C2×D452—21no—
28C2×D452—21no—
29C2×D452—21no—
30#14268636—42no—
31#14268632—42no—
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113D411yescharacteristic
35C4⋊Dic113D412yes—
36#14268626—22no—
37#14268626—21no—
38C22⋊Dic113—22no—
39C22⋊Dic113—22no—
40C4×Dic113—22no—
41C4×Dic113—21no—
42C2×D4×C113D411yescharacteristic
43C22×C4×C113—21no—
44C2×C8×C113—21no—
45C2×C8×C113—21no—
46C4⋊C4×C113D411yescharacteristic
47C22⋊C4×C113—21no—
48C42×C113C2311yescharacteristic
49C23×C113—21no—
50C22×D113—41no—
51D4×C113—21no—
52D4×C113—21no—
53C2×C4×C113—21no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113C2×D411yescharacteristic
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×Dic113—21no—
60C2×Dic113—21no—
61C2×Dic113—22no—
62D452—42no—
63D452—41no—
64D452—41no—
65D452—41no—
66D452—41no—
67Dic226—21no—
68Dic226—21no—
69Dic226—41no—
70Dic226—41no—
71C8×C113—41no—
72C8×C113—41no—
73#11744751—41no—
74C22×C113—41no—
75C22×C113—41no—
76C22×C113—41no—
77C22×C113#12011yescharacteristic
78C2×D113—81no—
79C2×D113—81no—
80C2×D113—81no—
81C4×C113—21no—
82C4×C113—41no—
83C4×C113#13511yescharacteristic
84C4×C113#13511yescharacteristic
85C4×C113AGL(1,ℤ/8)11yescharacteristic
86C4×C113AGL(1,ℤ/8)11yescharacteristic
87Dic113—41no—
88Dic113—42no—
89Dic113—41no—
90C2×C113—81no—
91C2×C113#44911yescharacteristic
92C2×C113#44911yescharacteristic
93C2×C113#45411yescharacteristic
94D113—161no—
95#1628—1131nomaximal, Sylow
96C113#162811yescharacteristic, complemented, Sylow
97#556—1131no—
98#486—1131no—
99#460—1131no—
100#459—1131no—
101#332—1131no—
102Q8⋊C8—1131no—
103D4⋊C8D11311yescharacteristic, complemented
104C2×SD16—2261no—
105C2×D8—2261no—
106C4⋊Q8—1131no—
107#127—1131no—
108#126—2262no—
109#124—2261no—
110C22⋊Q8—2261no—
111C4×Q8—1131no—
112C4×Q8—2261no—
113C4×D4C2×D11311yescharacteristic
114#117—2261no—
115C4⋊C8—1131no—
116C4⋊C8C2×D11311yescharacteristic
117#102—2261no—
118#102—2262no—
119#102—2261no—
120C4×C8C2×D11311yescharacteristic
121C2×Q8—1131no—
122C2×Q8—2261no—
123C2×D4—2261no—
124C2×D4—2261no—
125C2×D4—2261no—
126C2×D4D45211yescharacteristic
127C22×C4—21no—
128SD16—4522no—
129D8—4522no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—2261no—
133C4⋊C4—1131no—
134C4⋊C4—1132no—
135C4⋊C4—2262no—
136C4⋊C4—2261no—
137C4⋊C4—2261no—
138C4⋊C4D45211yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—2262no—
141C22⋊C4—2262no—
142C42—2262no—
143C42—2261no—
144C42C22×D11311yescharacteristic
145C23—21no—
146C23—4521no—
147Q8—4521no—
148Q8—4521no—
149Q8—2261no—
150Q8—2261no—
151D4—21no—
152D4—21no—
153D4—4522no—
154D4—4521no—
155D4—4521no—
156D4—4521no—
157D4—4521no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—2261no—
162C2×C4—2262no—
163C2×C4—2261no—
164C2×C4D4×D11311yescharacteristic
165C2×C4D4×D11311yescharacteristic
166C2×C4C2×D45211yescharacteristic
167C8—41no—
168C8—41no—
169C8—4521no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—9041no—
174C22—9041no—
175C22—9041no—
176C22#1681359211yescharacteristic
177C4—21no—
178C4—41no—
179C4—4521no—
180C4—4521no—
181C4—4522no—
182C4#1681364311yescharacteristic
183C4#1681364411yescharacteristic
184C4#1681364611yescharacteristic
185C4#1681365011yescharacteristic
186C2—81no—
187C2—18081no—
188C2#2029874411yescharacteristic
189C2#2029874511yescharacteristic
190C2#2029877211yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
prime radical#20298793C2
hypercenterD4⋊C8D113
hypocenterC113#1628
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
1. #20299318C2semidirect
2. #20298945C2semidirect
3. #20298799C2semidirect
5. #20298343C2semidirect
6. #20298330C2semidirect
7. D4⋊C8×C113C2semidirect
96. C113#1628semidirect
103. D4⋊C8D113semidirect

Maximal subgroups

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

subgroupindex
#202993182
#202989452
#202987992
#202987932
#202983432
#202983302
D4⋊C8×C1132
#1628113