Finite Group Databasebeta

← #28389786

Subgroups — #28389786

Order 14464.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299308C211yesmaximal, characteristic
2#20298950C211yesmaximal, characteristic, complemented
3#20298875C211yesmaximal, characteristic
4#20298346C211yesmaximal, characteristic, complemented
5Q8⋊#11744751C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic
7#462×C113C211yesmaximal, characteristic, complemented
8#16813622C2211yescharacteristic
9#16813614—21no—
10#16813600—22no—
11#16813598—21no—
12C4×D452—21no—
13C4×D452C2211yescharacteristic
14C4⋊C4×D113—21no—
15#16813555—21no—
16C4⋊#11744751C2211yescharacteristic
17#16813545—22no—
18#16813542—21no—
19C4×#11744751C2211yescharacteristic
20C2×Q16×C113—21no—
21C4⋊Q8×C113C2211yescharacteristic
22C4×Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24#103×C113—21no—
25C2×Dic226D412yes—
26C2×D452D411yescharacteristic
27C2×C4×D113—21no—
28C2×C4×D113—22no—
29C2×#11744751—21no—
30C2×#11744751—21no—
31C4⋊Dic113—21no—
32C4⋊Dic113—21no—
33C4⋊Dic113D411yescharacteristic
34#14268626—22no—
35#14268626—22no—
36#14268624—22no—
37#14268624—21no—
38C2×Q8×C113—21no—
39C2×Q8×C113D411yescharacteristic
40Q16×C113—42no—
41C2×C8×C113—21no—
42C4⋊C4×C113—21no—
43C4⋊C4×C113—21no—
44C4⋊C4×C113—21no—
45C4⋊C4×C113D411yescharacteristic
46C42×C113—21no—
47C42×C113C2311yescharacteristic
48C22×D113—21no—
49Q8×C113—21no—
50Q8×C113—21no—
51Q8×C113—41no—
52Q8×C113—41no—
53C2×C4×C113—21no—
54C2×C4×C113—21no—
55C2×C4×C113—41no—
56C2×C4×C113C2×D411yescharacteristic
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×Dic113—21no—
60C2×Dic113—22no—
61D452—21no—
62D452Q1612yescomplemented
63C4×D113—41no—
64C4×D113—41no—
65C4×D113—82no—
66Dic226—42no—
67C8×C113—41no—
68#11744751—41no—
69#11744751—41no—
70C22×C113#12011yescharacteristic
71C2×D113—22no—
72C2×D113—41no—
73C2×D113—41no—
74C4×C113—21no—
75C4×C113—41no—
76C4×C113—41no—
77C4×C113—81no—
78C4×C113C2×Q1611yescharacteristic
79C4×C113#13511yescharacteristic
80C4×C113AGL(1,ℤ/8)11yescharacteristic
81C4×C113#13711yescharacteristic
82Dic113—41no—
83Dic113—42no—
84C2×C113#44911yescharacteristic
85C2×C113#45111yescharacteristic
86C2×C113#45511yescharacteristic
87D113—42no—
88#1644—1131nomaximal, Sylow
89C113#164411yescharacteristic, complemented, Sylow
90#554—1131no—
91#487—1131no—
92#474—1131no—
93#462D11311yescharacteristic, complemented
94#333—1131no—
95Q8⋊C8—1131no—
96D4⋊C8—1131no—
97C2×Q16—21no—
98C4⋊Q8—1131no—
99C4⋊Q8C2×D11311yescharacteristic
100#125—2261no—
101C22⋊Q8—2262no—
102C22⋊Q8—2261no—
103C4×Q8C2×D11311yescharacteristic
104C4×D4—1131no—
105C4×D4—2261no—
106C2×C4⋊C4—2261no—
107#107—2261no—
108C4⋊C8—1131no—
109C4⋊C8C2×D11311yescharacteristic
110#103—21no—
111#103—2262no—
112#102—2261no—
113C4×C8—1131no—
114C2×Q8—21no—
115C2×Q8—1132no—
116C2×Q8C22⋊D11311yescharacteristic
117C2×D4—1131no—
118C22×C4—2262no—
119C22×C4—2261no—
120Q16—42no—
121C2×C8—21no—
122C2×C8—2261no—
123C2×C8—2261no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1131no—
128C4⋊C4—2262no—
129C4⋊C4—2262no—
130C4⋊C4—2261no—
131C4⋊C4—2261no—
132C4⋊C4C22⋊D11311yescharacteristic
133C22⋊C4—2262no—
134C22⋊C4—2261no—
135C42—21no—
136C42C22×D11311yescharacteristic
137C23—2261no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—4522no—
143D4—1132no—
144D4—2261no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—9042no—
149C2×C4—4521no—
150C2×C4—4521no—
151C2×C4—2261no—
152C2×C4—2262no—
153C2×C4D4×D11311yescharacteristic
154C2×C4D4×D11311yescharacteristic
155C2×C4C2×C22⋊D11311yescharacteristic
156C8—41no—
157C8—4521no—
158C8—4521no—
159C22—4521no—
160C22—4521no—
161C22—2262no—
162C22#1681359011yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—4522no—
168C4—4521no—
169C4Q16×D11311yescharacteristic
170C4#1681364211yescharacteristic
171C4#1681364811yescharacteristic
172C4#1681365411yescharacteristic
173C2—4522no—
174C2#2029874111yescharacteristic
175C2#2029875211yescharacteristic
176C2#2029877411yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#462×C113C2
socleC22×C113#120
prime radicalC2×D452D4
hypercenter#462D113
hypocenterC113#1644
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #20298950C2semidirect
4. #20298346C2semidirect
5. Q8⋊#11744751C2semidirect
7. #462×C113C2semidirect
62. D452Q16semidirect
89. C113#1644semidirect
93. #462D113semidirect

Maximal subgroups

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

subgroupindex
#202993082
#202989502
#202988752
#202983462
Q8⋊#117447512
#202983252
#462×C1132
#1644113