Finite Group Databasebeta

← #28392530

Subgroups — #28392530

Order 14464.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#20299399C211yesmaximal, characteristic, complemented
2#20299034C211yesmaximal, characteristic, complemented
3#20298865C211yesmaximal, characteristic, complemented
4#20298411C211yesmaximal, characteristic, complemented
5#20298406C211yesmaximal, characteristic, complemented
6#20298381C211yesmaximal, characteristic, complemented
7C2×D16×C113C211yesmaximal, characteristic, complemented
8#16813667—21no—
9#16813648—21no—
10#16813648—21no—
11#16813646—22no—
12#16813644C2211yescharacteristic
13#16813641—21no—
14D8×D113—21no—
15#16813628C2211yescharacteristic
16#16813566—21no—
17#16813563—21no—
18#16813562C2211yescharacteristic, complemented
19#16813558C2211yescharacteristic, complemented
20#16813539—21no—
21C2×D8×C113C2211yescharacteristic
22C2×D8×C113C2211yescharacteristic, complemented
23D16×C113—22no—
24C2×C16×C113C2211yescharacteristic, complemented
25#14268647—21no—
26#14268647D411yescharacteristic
27#14268646—22no—
28#14268646—41no—
29C2×C22⋊D113—42no—
30D4×D113—22no—
31D4×D113—41no—
32Dic452D411yescharacteristic
33#14268636—21no—
34#14268635—22no—
35#14268635—41no—
36D904D411yescharacteristic
37#14268632—22no—
38#14268632—41no—
39#14268631—21no—
40#14268631D411yescharacteristic
41#14268630—21no—
42C8×D113—21no—
43#14268622—21no—
44C2×D4×C113—21no—
45C2×D4×C113—21no—
46D8×C113—21no—
47D8×C113—21no—
48D8×C113—21no—
49D8×C113D412yes—
50C2×C8×C113C2311yescharacteristic
51C16×C113—21no—
52C23×C113—41no—
53C23×C113—41no—
54C22×D113—42no—
55D4×C113—22no—
56D4×C113—41no—
57D4×C113—41no—
58D4×C113—41no—
59C2×C4×C113C2×D411yescharacteristic
60C22⋊D113—21no—
61C22⋊D113—42no—
62C22⋊D113—42no—
63C22⋊D113—41no—
64C2×Dic113—42no—
65D452—21no—
66D452D811yescharacteristic
67C4×D113—21no—
68C4×D113—41no—
69Dic226—21no—
70Dic226D811yescharacteristic
71C8×C113C2×D411yescharacteristic
72C8×C113C2×D411yescharacteristic
73#11744751—21no—
74#11744751—41no—
75C22×C113—42no—
76C22×C113—81no—
77C22×C113—161no—
78C22×C113—161no—
79C22×C113AGL(1,ℤ/8)11yescharacteristic
80C2×D113—21no—
81C2×D113—41no—
82C2×D113—162no—
83C4×C113#12011yescharacteristic
84C4×C113C2×D811yescharacteristic
85Dic113—21no—
86Dic113—41no—
87C2×C113—21no—
88C2×C113—82no—
89C2×C113—161no—
90C2×C113#44711yescharacteristic
91D113—41no—
92D113—81no—
93#2192—1131nomaximal, Sylow
94C113#219211yescharacteristic, complemented, Sylow
95#576—1131no—
96#509—1131no—
97C2×D16D11311yescharacteristic, complemented
98#472—1131no—
99#361—1131no—
100#359—1131no—
101#350—1131no—
102H(5,𝔽2)—2261no—
103AGL(1,ℤ/8)—2261no—
104AGL(1,ℤ/8)—2261no—
105AGL(1,ℤ/8)—2262no—
106#135—1131no—
107#135—2261no—
108C2×D8—2261no—
109C2×D8C2×D11311yescharacteristic
110C2×D8C2×D11311yescharacteristic, complemented
111#131—1131no—
112SD32—2261no—
113D16—22no—
114D16—2261no—
115M32—1131no—
116C2×C16C2×D11311yescharacteristic, complemented
117#108—1131no—
118#100—2261no—
119#41—1131no—
120#41—4521no—
121#41—2262no—
122#41—2261no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—4521no—
126C2×D4—4522no—
127C2×D4—2262no—
128Q16—1131no—
129SD16—4521no—
130SD16—2262no—
131SD16—2261no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—1131no—
136D8—4521no—
137D8—2262no—
138D8C22⋊D11312yes—
139M16—1131no—
140M16—2261no—
141M16—2261no—
142C2×C8—2261no—
143C2×C8C22×D11311yescharacteristic
144C16—21no—
145C16—2261no—
146C23—41no—
147C23—41no—
148C23—4522no—
149Q8—1131no—
150Q8—2261no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—1131no—
156D4—4522no—
157D4—4521no—
158D4—4522no—
159D4—2261no—
160D4—2261no—
161C2×C4—4522no—
162C2×C4—4521no—
163C2×C4—2261no—
164C2×C4D4×D11311yescharacteristic
165C8—4521no—
166C8—2261no—
167C8D4×D11311yescharacteristic
168C8C2×C22⋊D11311yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—18082no—
174C22—4521no—
175C22—2261no—
176C22#1681364611yescharacteristic
177C4—4521no—
178C4—2261no—
179C4#1681359011yescharacteristic
180C4D8×D11311yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—9041no—
185C2—4521no—
186C2#2029873011yescharacteristic
subgroupG/H
centerC2#20298730
commutator, cosocleC2×C8×C113C23
FrattiniC2×C8C22×D113
FittingC2×D16×C113C2
socleC2×C113#447
hypercenterC2×D16D113
hypocenterC113#2192
LCSG ▷ C2×C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #20299399C2semidirect
2. #20299034C2semidirect
3. #20298865C2semidirect
4. #20298411C2semidirect
5. #20298406C2semidirect
6. #20298381C2semidirect
7. C2×D16×C113C2semidirect
18. #16813562C22semidirect
19. #16813558C22semidirect
22. C2×D8×C113C22semidirect
24. C2×C16×C113C22semidirect
94. C113#2192semidirect
97. C2×D16D113semidirect
110. C2×D8C2×D113semidirect
116. C2×C16C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993992
#202990342
#202988652
#202984112
#202984062
#202983812
C2×D16×C1132
#2192113