Finite Group Databasebeta

← #28392544

Subgroups — #28392544

Order 14464.

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

normal subgroups only

This group has 216 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
2#20299039C211yesmaximal, characteristic, complemented
3#20298870C211yesmaximal, characteristic, complemented
4#20298411C211yesmaximal, characteristic, complemented
5#20298406C211yesmaximal, characteristic, complemented
6#20298381C211yesmaximal, characteristic, complemented
7C2×SD32×C113C211yesmaximal, characteristic, complemented
8#16813667—21no—
9#16813653—21no—
10#16813648—21no—
11#16813646—22no—
12#16813644C2211yescharacteristic
13#16813641—21no—
14D8×D113—21no—
15#16813628C2211yescharacteristic
16#16813568—21no—
17#16813565—21no—
18#16813562C2211yescharacteristic, complemented
19#16813558C2211yescharacteristic, complemented
20#16813541—21no—
21C2×Q16×C113C2211yescharacteristic, complemented
22C2×D8×C113C2211yescharacteristic
23SD32×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#14268637—41no—
34#14268636—21no—
35#14268635—22no—
36#14268634—41no—
37D904D411yescharacteristic
38#14268632—22no—
39#14268631—21no—
40#14268631D411yescharacteristic
41#14268630—21no—
42C8×D113—21no—
43#14268622—21no—
44C2×Q8×C113—21no—
45C2×D4×C113—21no—
46Q16×C113—21no—
47Q16×C113—21no—
48D8×C113—21no—
49D8×C113D412yes—
50C2×C8×C113C2311yescharacteristic
51C16×C113—21no—
52C23×C113—41no—
53C22×D113—42no—
54Q8×C113—41no—
55Q8×C113—41no—
56D4×C113—22no—
57D4×C113—41no—
58C2×C4×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—161no—
77C22×C113AGL(1,ℤ/8)11yescharacteristic
78C2×D113—21no—
79C2×D113—41no—
80C2×D113—162no—
81C4×C113—81no—
82C4×C113#12011yescharacteristic
83C4×C113C2×D811yescharacteristic
84Dic113—21no—
85Dic113—41no—
86C2×C113—21no—
87C2×C113—82no—
88C2×C113#44711yescharacteristic
89D113—41no—
90D113—81no—
91#2194—1131nomaximal, Sylow
92C113#219411yescharacteristic, complemented, Sylow
93#576—1131no—
94#510—1131no—
95C2×SD32D11311yescharacteristic, complemented
96#473—1131no—
97#361—1131no—
98#359—1131no—
99#350—1131no—
100H(5,𝔽2)—2261no—
101#137—2261no—
102AGL(1,ℤ/8)—2261no—
103AGL(1,ℤ/8)—2262no—
104#135—1131no—
105#135—2261no—
106C2×Q16C2×D11311yescharacteristic, complemented
107C2×D8—2261no—
108C2×D8C2×D11311yescharacteristic
109#131—1131no—
110Q32—2261no—
111SD32—22no—
112SD32—2261no—
113M32—1131no—
114C2×C16C2×D11311yescharacteristic, complemented
115#108—1131no—
116#101—2261no—
117#41—1131no—
118#41—4521no—
119#41—2262no—
120#41—2261no—
121C2×Q8—21no—
122C2×D4—21no—
123C2×D4—4521no—
124C2×D4—4522no—
125C2×D4—2262no—
126Q16—21no—
127Q16—21no—
128Q16—1131no—
129Q16—4521no—
130SD16—4521no—
131SD16—2262no—
132SD16—2261no—
133D8—21no—
134D8—1131no—
135D8—2262no—
136D8C22⋊D11312yes—
137M16—1131no—
138M16—2261no—
139M16—2261no—
140C2×C8—2261no—
141C2×C8C22×D11311yescharacteristic
142C16—21no—
143C16—2261no—
144C23—41no—
145C23—4522no—
146Q8—41no—
147Q8—41no—
148Q8—1131no—
149Q8—2261no—
150D4—22no—
151D4—41no—
152D4—1131no—
153D4—4522no—
154D4—4521no—
155D4—4522no—
156D4—2261no—
157D4—2261no—
158C2×C4—41no—
159C2×C4—4522no—
160C2×C4—4521no—
161C2×C4—2261no—
162C2×C4D4×D11311yescharacteristic
163C8—4521no—
164C8—2261no—
165C8D4×D11311yescharacteristic
166C8C2×C22⋊D11311yescharacteristic
167C22—42no—
168C22—161no—
169C22—18082no—
170C22—4521no—
171C22—2261no—
172C22#1681364611yescharacteristic
173C4—81no—
174C4—4521no—
175C4—2261no—
176C4#1681359011yescharacteristic
177C4D8×D11311yescharacteristic
178C2—21no—
179C2—82no—
180C2—9041no—
181C2—4521no—
182C2#2029873011yescharacteristic
subgroupG/H
centerC2#20298730
commutator, cosocleC2×C8×C113C23
FrattiniC2×C8C22×D113
FittingC2×SD32×C113C2
socleC2×C113#447
prime radical#20299399C2
hypercenterC2×SD32D113
hypocenterC113#2194
LCSG ▷ C2×C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. #20299039C2semidirect
3. #20298870C2semidirect
4. #20298411C2semidirect
5. #20298406C2semidirect
6. #20298381C2semidirect
7. C2×SD32×C113C2semidirect
18. #16813562C22semidirect
19. #16813558C22semidirect
21. C2×Q16×C113C22semidirect
24. C2×C16×C113C22semidirect
92. C113#2194semidirect
95. C2×SD32D113semidirect
106. C2×Q16C2×D113semidirect
114. C2×C16C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993992
#202990392
#202988702
#202984112
#202984062
#202983812
C2×SD32×C1132
#2194113