Finite Group Databasebeta

← #28389792

Subgroups — #28389792

Order 14464.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299328C211yesmaximal, characteristic
2#20298880C211yesmaximal, characteristic
3#20298805C211yesmaximal, characteristic
4#20298347C211yesmaximal, characteristic
5#20298330C211yesmaximal, characteristic
6#20298330C211yesmaximal, characteristic
7#487×C113C211yesmaximal, characteristic
8C2×#14268637—21no—
9#16813621—21no—
10#16813621—21no—
11#16813620—22no—
12C4×Dic226C2211yescharacteristic
13C4×Dic226C2211yescharacteristic
14#16813587—21no—
15#16813587—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×Dic226—22no—
26C2×Dic226D411yescharacteristic
27C2×Dic226D411yescharacteristic
28#14268637—42no—
29C2×#11744751—21no—
30C2×#11744751—21no—
31C4⋊Dic113D411yescharacteristic
32C4⋊Dic113D411yescharacteristic
33#14268626—22no—
34#14268626—22no—
35#14268626—21no—
36#14268626—21no—
37C4×Dic113—22no—
38C4×Dic113—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
48Q8×C113—42no—
49Q8×C113—41no—
50Q8×C113—41no—
51C2×C4×C113—22no—
52C2×C4×C113—41no—
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×Dic113—21no—
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—21no—
60Dic226—21no—
61Dic226—21no—
62Dic226—82no—
63Dic226SD1612yes—
64Dic226Q1612yescomplemented
65C8×C113—41no—
66#11744751—41no—
67#11744751—41no—
68C22×C113#12011yescharacteristic
69C4×C113—21no—
70C4×C113—42no—
71C4×C113—81no—
72C4×C113C2×SD1611yescharacteristic
73C4×C113C2×Q1611yescharacteristic
74C4×C113#13711yescharacteristic
75C4×C113#13711yescharacteristic
76Dic113—22no—
77Dic113—22no—
78Dic113—41no—
79Dic113—41no—
80C2×C113#44811yescharacteristic
81C2×C113#45111yescharacteristic
82C2×C113#45511yescharacteristic
83#1645—1131nomaximal, Sylow
84C113#164511yescharacteristic, complemented, Sylow
85Q82—1131no—
86#487D11311yescharacteristic
87#475—1131no—
88#462—1131no—
89#333—1131no—
90Q8⋊C8—1131no—
91Q8⋊C8—1131no—
92C2×Q16—2261no—
93C4⋊Q8—2261no—
94C4⋊Q8—2261no—
95C4⋊Q8—2262no—
96C4⋊Q8C2×D11311yescharacteristic
97C4⋊Q8C2×D11311yescharacteristic
98C4×Q8—1131no—
99C4×Q8—1131no—
100C4×Q8—2261no—
101C4×Q8—2261no—
102#106—2261no—
103C4⋊C8—1131no—
104C4⋊C8—1131no—
105#103—22no—
106#103—2261no—
107#103—2261no—
108C4×C8C2×D11311yescharacteristic
109C2×Q8—21no—
110C2×Q8—1131no—
111C2×Q8—1131no—
112C2×Q8—2262no—
113C2×Q8C22⋊D11312yes—
114Q16—4522no—
115C2×C8—21no—
116C2×C8—2261no—
117C2×C8—2261no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—1131no—
123C4⋊C4—1131no—
124C4⋊C4—2262no—
125C4⋊C4—2262no—
126C4⋊C4—2261no—
127C4⋊C4—2261no—
128C42—2262no—
129C42—2261no—
130C42—2261no—
131C42C22×D11311yescharacteristic
132Q8—42no—
133Q8—41no—
134Q8—41no—
135Q8—1132no—
136Q8—1132no—
137Q8—9042no—
138Q8—2261no—
139Q8—2261no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—2261no—
143C2×C4—2261no—
144C2×C4—2261no—
145C2×C4—2261no—
146C2×C4D4×D11311yescharacteristic
147C2×C4D4×D11311yescharacteristic
148C2×C4C2×C22⋊D11311yescharacteristic
149C8—41no—
150C8—4521no—
151C8—4521no—
152C22#1681359011yescharacteristic
153C4—21no—
154C4—42no—
155C4—81no—
156C4—4521no—
157C4—4521no—
158C4—2262no—
159C4—2262no—
160C4SD16×D11311yescharacteristic
161C4Q16×D11311yescharacteristic
162C4#1681365111yescharacteristic
163C4#1681365411yescharacteristic
164C2#2029873511yescharacteristic
165C2#2029875211yescharacteristic
166C2#2029877511yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#487×C113C2
socle, prime radicalC22×C113#120
hypercenter#487D113
hypocenterC113#1645
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
64. Dic226Q16semidirect
84. C113#1645semidirect

Maximal subgroups

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

subgroupindex
#202993282
#202988802
#202988052
#202983472
#202983302
#487×C1132
#1645113