Finite Group Databasebeta

← #28392520

Subgroups — #28392520

Order 14464.

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

normal subgroups only

This group has 226 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#20299033C212yesmaximal, complemented
2#20298851C211yesmaximal, characteristic, complemented
3#20298408C212yesmaximal, complemented
4#20298380C211yesmaximal, characteristic, complemented
5#575×C113C211yesmaximal, characteristic, complemented
6C2×D904C2211yescharacteristic, complemented
7#16813596—21no—
8#16813565—22no—
9#16813563—22no—
10#16813562C2212yescomplemented
11#16813554C2211yescharacteristic, complemented
12#16813544—21no—
13C2×#41×C113—21no—
14#137×C113—22no—
15AGL(1,ℤ/8)×C113—22no—
16#135×C113—21no—
17#135×C113C2212yes—
18C2×M16×C113C2211yescharacteristic
19C2×D452—21no—
20C2×C22⋊D113—41no—
21D904—22no—
22C4⋊Dic113—21no—
23#14268624—41no—
24#14268622—22no—
25#41×C113—22no—
26#41×C113—22no—
27#41×C113—41no—
28#41×C113—41no—
29C2×Q8×C113—21no—
30C2×D4×C113—21no—
31C2×D4×C113—41no—
32C22×C4×C113—41no—
33C22×C4×C113D411yescharacteristic
34Q16×C113—21no—
35Q16×C113D412yescomplemented
36SD16×C113—22no—
37SD16×C113—22no—
38D8×C113—21no—
39D8×C113D412yescomplemented
40M16×C113—22no—
41C2×C8×C113D411yescharacteristic
42C2×C8×C113C2311yescharacteristic
43C23×C113—41no—
44C23×C113D811yescharacteristic
45C22×D113—41no—
46Q8×C113—22no—
47Q8×C113—41no—
48D4×C113—22no—
49D4×C113—41no—
50D4×C113—42no—
51D4×C113—42no—
52C2×C4×C113—21no—
53C2×C4×C113—21no—
54C2×C4×C113—42no—
55C2×C4×C113—41no—
56C2×C4×C113—42no—
57C2×C4×C113D811yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C22⋊D113—82no—
60C2×Dic113—41no—
61D452—41no—
62D452—41no—
63C8×C113—21no—
64C8×C113C2×D412yes—
65C22×C113—21no—
66C22×C113—41no—
67C22×C113—42no—
68C22×C113—82no—
69C22×C113C2×D811yescharacteristic
70C2×D113—81no—
71C2×D113—81no—
72C2×D113—81no—
73C4×C113—21no—
74C4×C113—42no—
75C4×C113#12011yescharacteristic
76C4×C113AGL(1,ℤ/8)11yescharacteristic
77Dic113—81no—
78C2×C113—21no—
79C2×C113—41no—
80C2×C113—82no—
81C2×C113#44711yescharacteristic
82D113—161no—
83#2190—1131nomaximal, Sylow
84C113#219011yescharacteristic, complemented, Sylow
85#575D11311yescharacteristic, complemented
86#509—1132no—
87#469—1131no—
88#360—1132no—
89#349—1131no—
90C2×#41—21no—
91#137—22no—
92AGL(1,ℤ/8)—22no—
93#135—21no—
94#135C2×D11312yes—
95C2×D8—1131no—
96C2×M16C2×D11311yescharacteristic
97#121—2261no—
98SD32—2262no—
99D16—2262no—
100M32—1132no—
101#106—1131no—
102#102—2261no—
103#41—22no—
104#41—22no—
105#41—41no—
106#41—41no—
107C2×Q8—21no—
108C2×D4—21no—
109C2×D4—41no—
110C2×D4—4521no—
111C2×D4—2261no—
112C22×C4—41no—
113C22×C4C22⋊D11311yescharacteristic
114Q16—21no—
115Q16C22⋊D11312yescomplemented
116SD16—22no—
117SD16—22no—
118D8—21no—
119D8—2262no—
120D8C22⋊D11312yescomplemented
121M16—22no—
122C2×C8C22⋊D11311yescharacteristic
123C2×C8C22×D11311yescharacteristic
124C4⋊C4—2261no—
125C22⋊C4—4521no—
126C16—2262no—
127C23—41no—
128C23—4521no—
129C23#1426863211yescharacteristic
130Q8—22no—
131Q8—41no—
132D4—22no—
133D4—41no—
134D4—42no—
135D4—42no—
136D4—9042no—
137D4—4521no—
138D4—4521no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—4521no—
145C2×C4#1426863211yescharacteristic
146C2×C4C2×C22⋊D11311yescharacteristic
147C8—21no—
148C8C2×C22⋊D11312yes—
149C22—21no—
150C22—41no—
151C22—42no—
152C22—82no—
153C22—9041no—
154C22—9041no—
155C22—9041no—
156C22C2×#1426863211yescharacteristic
157C4—21no—
158C4—42no—
159C4—9041no—
160C4#1681359111yescharacteristic
161C4#1681364811yescharacteristic
162C2—21no—
163C2—41no—
164C2—82no—
165C2—18081no—
166C2#2029873211yescharacteristic
subgroupG/H
centerC2#20298732
commutator, cosocleC2×C8×C113C23
FrattiniC2×C8C22×D113
Fitting#575×C113C2
socleC2×C113#447
hypercenter#575D113
hypocenterC113#2190
LCSG ▷ C2×C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #20299033C2semidirect
2. #20298851C2semidirect
3. #20298408C2semidirect
4. #20298380C2semidirect
5. #575×C113C2semidirect
6. C2×D904C22semidirect
10. #16813562C22semidirect
11. #16813554C22semidirect
35. Q16×C113D4semidirect
39. D8×C113D4semidirect
84. C113#2190semidirect
85. #575D113semidirect
115. Q16C22⋊D113semidirect
120. D8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202990332
#202988512
#202984082
#202983802
#575×C1132
#2190113