Finite Group Databasebeta

← #28389648

Subgroups — #28389648

Order 14464.

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

normal subgroups only

This group has 236 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#20299305C211yesmaximal, characteristic, complemented
2#20298971C211yesmaximal, characteristic, complemented
3#20298799C211yesmaximal, characteristic, complemented
4#20298793C211yesmaximal, characteristic
5#20298346C211yesmaximal, characteristic, complemented
6#20298330C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic, complemented
8C2×#14268636—21no—
9C2×#14268636—22no—
10C2×#14268632—21no—
11#16813622C2211yescharacteristic
12#16813619C2211yescharacteristic
13#16813613—21no—
14#16813601—21no—
15#16813599—22no—
16C4×Dic226C2211yescharacteristic
17D4×Dic113—21no—
18C2×C4⋊Dic113—21no—
19C4⋊#11744751C2211yescharacteristic
20#16813544—21no—
21#16813542—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226D411yescharacteristic
26C2×Dic226D412yes—
27C2×D452—21no—
28C2×D452—21no—
29C2×D452—21no—
30C22×Dic113—22no—
31#14268636—44no—
32#14268636—42no—
33#14268632—42no—
34C2×#11744751—21no—
35C4⋊Dic113—22no—
36C4⋊Dic113—21no—
37C4⋊Dic113—21no—
38C4⋊Dic113D411yescharacteristic
39#14268626—22no—
40#14268626—21no—
41C22⋊Dic113—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—41no—
52D4×C113—21no—
53D4×C113SD1612yescomplemented
54C2×C4×C113—21no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113C2×D411yescharacteristic
60C2×Dic113—21no—
61C2×Dic113—21no—
62C2×Dic113—22no—
63C2×Dic113—82no—
64D452—42no—
65D452—41no—
66D452—41no—
67D452—41no—
68D452—41no—
69Dic226—21no—
70Dic226—21no—
71Dic226—42no—
72C8×C113—22no—
73C8×C113—41no—
74#11744751—41no—
75C22×C113—22no—
76C22×C113—41no—
77C22×C113—41no—
78C22×C113#12011yescharacteristic
79C2×D113—81no—
80C2×D113—81no—
81C2×D113—81no—
82C4×C113—21no—
83C4×C113—41no—
84C4×C113C2×SD1611yescharacteristic
85C4×C113#13511yescharacteristic
86C4×C113AGL(1,ℤ/8)11yescharacteristic
87C4×C113#13711yescharacteristic
88Dic113—41no—
89Dic113—42no—
90Dic113—41no—
91C2×C113—42no—
92C2×C113#44811yescharacteristic
93C2×C113#44911yescharacteristic
94C2×C113#45311yescharacteristic
95D113—161no—
96#1622—1131nomaximal, Sylow
97C113#162211yescharacteristic, complemented, Sylow
98#554—1131no—
99#492—1131no—
100#460—1131no—
101#459—1131no—
102#333—1131no—
103Q8⋊C8—1131no—
104D4⋊C8D11311yescharacteristic, complemented
105C2×SD16—2261no—
106C2×SD16—2262no—
107C2×D8—2261no—
108C4⋊Q8—1131no—
109#127—1131no—
110#125—2261no—
111C22⋊Q8—2262no—
112C22⋊Q8—2261no—
113C4×Q8—1131no—
114C4×D4—2261no—
115C4×D4C2×D11311yescharacteristic
116C2×C4⋊C4—2261no—
117C4⋊C8—1131no—
118C4⋊C8C2×D11311yescharacteristic
119#102—2261no—
120#102—2261no—
121C4×C8C2×D11311yescharacteristic
122C2×Q8—1132no—
123C2×Q8—1131no—
124C2×D4—2261no—
125C2×D4—2261no—
126C2×D4—2261no—
127C2×D4D45211yescharacteristic
128C22×C4—21no—
129C22×C4—2262no—
130SD16—4524no—
131SD16—4522no—
132D8—4522no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2261no—
136C4⋊C4—1131no—
137C4⋊C4—2262no—
138C4⋊C4—2262no—
139C4⋊C4—2261no—
140C4⋊C4—2261no—
141C4⋊C4—2261no—
142C4⋊C4D45211yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—2262no—
145C42—2261no—
146C42C22×D11311yescharacteristic
147C23—21no—
148C23—4521no—
149Q8—4522no—
150Q8—2261no—
151Q8—2261no—
152D4—21no—
153D4—4522no—
154D4—4521no—
155D4—4521no—
156D4—4521no—
157D4—4521no—
158D4#1426863612yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—9042no—
163C2×C4—2261no—
164C2×C4—2261no—
165C2×C4—2262no—
166C2×C4D4×D11311yescharacteristic
167C2×C4D4×D11311yescharacteristic
168C2×C4C2×D45211yescharacteristic
169C8—22no—
170C8—41no—
171C8—4521no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—9041no—
176C22—9041no—
177C22—9041no—
178C22#1681359211yescharacteristic
179C4—21no—
180C4—41no—
181C4—4521no—
182C4—4522no—
183C4—4521no—
184C4C2×#1426863611yescharacteristic
185C4#1681364311yescharacteristic
186C4#1681364611yescharacteristic
187C4#1681365511yescharacteristic
188C2—42no—
189C2—18081no—
190C2#2029873911yescharacteristic
191C2#2029874411yescharacteristic
192C2#2029876711yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
prime radical#20298793C2
hypercenterD4⋊C8D113
hypocenterC113#1622
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. #20299305C2semidirect
2. #20298971C2semidirect
3. #20298799C2semidirect
5. #20298346C2semidirect
6. #20298330C2semidirect
7. D4⋊C8×C113C2semidirect
53. D4×C113SD16semidirect
97. C113#1622semidirect
104. D4⋊C8D113semidirect
158. D4#14268636semidirect

Maximal subgroups

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

subgroupindex
#202993052
#202989712
#202987992
#202987932
#202983462
#202983302
D4⋊C8×C1132
#1622113