Finite Group Databasebeta

← #28389778

Subgroups — #28389778

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#20299309C211yesmaximal, characteristic
2#20298880C211yesmaximal, characteristic, complemented
3#20298800C211yesmaximal, characteristic
4#20298347C211yesmaximal, characteristic, complemented
5#20298330C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic
7#487×C113C211yesmaximal, characteristic, complemented
8C2×#14268634—21no—
9#16813613—21no—
10#16813602—21no—
11#16813598—22no—
12C4×Dic226C2211yescharacteristic
13C4×D452C2211yescharacteristic
14#16813584—21no—
15C4⋊C4×D113—21no—
16#16813553—21no—
17C4⋊#11744751C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic
19#16813546—21no—
20#16813545—21no—
21C4⋊Q8×C113C2211yescharacteristic
22C4⋊Q8×C113C2211yescharacteristic
23#103×C113—22no—
24C4×C8×C113C2211yescharacteristic
25C2×Dic226D411yescharacteristic
26C2×D452D411yescharacteristic
27C2×C4×D113—21no—
28C2×C4×D113—22no—
29#14268634—42no—
30C2×#11744751—21no—
31C2×#11744751—21no—
32C4⋊Dic113—22no—
33C4⋊Dic113D411yescharacteristic
34C4⋊Dic113D411yescharacteristic
35#14268626—22no—
36#14268626—21no—
37#14268624—22no—
38#14268624—21no—
39C4×Dic113—21no—
40C2×Q8×C113—21no—
41C2×Q8×C113D412yes—
42C2×C8×C113—21no—
43C4⋊C4×C113—21no—
44C4⋊C4×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113—21no—
47C42×C113C2311yescharacteristic
48C22×D113—21no—
49Q8×C113—42no—
50Q8×C113—41no—
51Q8×C113—41no—
52C2×C4×C113—22no—
53C2×C4×C113—41no—
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×C4×C113C2×D411yescharacteristic
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—21no—
60D452—21no—
61D452SD1612yes—
62C4×D113—41no—
63C4×D113—41no—
64C4×D113—82no—
65Dic226—21no—
66Dic226—21no—
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—42no—
76C4×C113—81no—
77C4×C113C2×SD1611yescharacteristic
78C4×C113#13511yescharacteristic
79C4×C113#13711yescharacteristic
80C4×C113#13711yescharacteristic
81Dic113—41no—
82Dic113—41no—
83Dic113—41no—
84C2×C113#44811yescharacteristic
85C2×C113#45211yescharacteristic
86C2×C113#45511yescharacteristic
87D113—42no—
88#1643—1131nomaximal, Sylow
89C113#164311yescharacteristic, complemented, Sylow
90#554—1131no—
91#487D11311yescharacteristic, complemented
92#475—1131no—
93#461—1131no—
94#333—1131no—
95Q8⋊C8—1131no—
96D4⋊C8—1131no—
97C2×SD16—2261no—
98C4⋊Q8C2×D11311yescharacteristic
99C4⋊Q8C2×D11311yescharacteristic
100#125—2261no—
101C22⋊Q8—2261no—
102C22⋊Q8—2262no—
103C4×Q8—1131no—
104C4×D4—1131no—
105C4×D4—2261no—
106C2×C4⋊C4—2261no—
107#106—2261no—
108C4⋊C8—1131no—
109C4⋊C8—1131no—
110#103—22no—
111#103—2261no—
112#103—2261no—
113C4×C8C2×D11311yescharacteristic
114C2×Q8—21no—
115C2×Q8—1131no—
116C2×Q8C22⋊D11312yes—
117C2×D4—1131no—
118C22×C4—2262no—
119C22×C4—2261no—
120SD16—4522no—
121C2×C8—21no—
122C2×C8—2261no—
123C2×C8—2261no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—1131no—
129C4⋊C4—1131no—
130C4⋊C4—2262no—
131C4⋊C4—2262no—
132C4⋊C4—2261no—
133C22⋊C4—2262no—
134C22⋊C4—2261no—
135C42—2261no—
136C42C22×D11311yescharacteristic
137C23—2261no—
138Q8—42no—
139Q8—41no—
140Q8—41no—
141Q8—2261no—
142Q8—2261no—
143D4—1132no—
144D4—2261no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—9042no—
148C2×C4—4521no—
149C2×C4—4521no—
150C2×C4—2261no—
151C2×C4—2261no—
152C2×C4—2261no—
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—42no—
165C4—81no—
166C4—4521no—
167C4—4521no—
168C4—4521no—
169C4SD16×D11311yescharacteristic
170C4#1681364511yescharacteristic
171C4#1681365111yescharacteristic
172C4#1681365411yescharacteristic
173C2—4522no—
174C2#2029873511yescharacteristic
175C2#2029875911yescharacteristic
176C2#2029877511yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#487×C113C2
socleC22×C113#120
prime radicalC2×D452D4
hypercenter#487D113
hypocenterC113#1643
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #20298880C2semidirect
4. #20298347C2semidirect
5. #20298330C2semidirect
7. #487×C113C2semidirect
89. C113#1643semidirect
91. #487D113semidirect

Maximal subgroups

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

subgroupindex
#202993092
#202988802
#202988002
#202983472
#202983302
#202983272
#487×C1132
#1643113