Finite Group Databasebeta

← #28389837

Subgroups — #28389837

Order 14464.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#20298994C211yesmaximal, characteristic, complemented
2#20298883C211yesmaximal, characteristic, complemented
3#20298803C211yesmaximal, characteristic
4#20298344C211yesmaximal, characteristic, complemented
5Q8⋊#11744751C211yesmaximal, characteristic, complemented
6D4⋊#11744751C211yesmaximal, characteristic
7D4×Q8×C113C211yesmaximal, characteristic
8C2×#14268635—21no—
9#16813622C2211yescharacteristic
10#16813553—21no—
11#16813553—22no—
12C4⋊#11744751C2211yescharacteristic
13C4⋊#11744751C2211yescharacteristic
14#16813546—21no—
15#16813545—21no—
16C4×#11744751C2211yescharacteristic
17C22×Q8×C113—21no—
18C4⋊Q8×C113—21no—
19C4⋊Q8×C113C2211yescharacteristic
20C22⋊Q8×C113—21no—
21C22⋊Q8×C113—22no—
22C4×Q8×C113C2211yescharacteristic
23C4×D4×C113—21no—
24C4×D4×C113C2211yescharacteristic
25C2×Dic226—21no—
26#14268635—42no—
27C2×#11744751—21no—
28C2×#11744751—21no—
29C2×#11744751—21no—
30C4⋊Dic113—21no—
31C4⋊Dic113—21no—
32C2×Q8×C113—22no—
33C2×Q8×C113—21no—
34C2×Q8×C113—42no—
35C2×Q8×C113—42no—
36C2×Q8×C113D411yescharacteristic
37C2×D4×C113D411yescharacteristic
38C22×C4×C113—22no—
39C22×C4×C113—21no—
40C4⋊C4×C113—22no—
41C4⋊C4×C113—21no—
42C4⋊C4×C113—21no—
43C4⋊C4×C113D411yescharacteristic
44C4⋊C4×C113D411yescharacteristic
45C4⋊C4×C113D412yes—
46C22⋊C4×C113—22no—
47C22⋊C4×C113—21no—
48C42×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—21no—
51Q8×C113—21no—
52Q8×C113—44no—
53Q8×C113—41no—
54Q8×C113—41no—
55Q8×C113SD1612yescomplemented
56D4×C113—21no—
57D4×C113SD1612yes—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—22no—
61C2×C4×C113—21no—
62C2×C4×C113—44no—
63C2×C4×C113—41no—
64C2×C4×C113—41no—
65C2×C4×C113C2×D411yescharacteristic
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113C2×D411yescharacteristic
68C2×Dic113—41no—
69Dic226—41no—
70Dic226—41no—
71#11744751—22no—
72#11744751—41no—
73#11744751—41no—
74C22×C113—22no—
75C22×C113—41no—
76C22×C113—41no—
77C22×C113#12011yescharacteristic
78C4×C113—22no—
79C4×C113—21no—
80C4×C113—42no—
81C4×C113—41no—
82C4×C113—41no—
83C4×C113C2×SD1611yescharacteristic
84C4×C113C2×SD1611yescharacteristic
85C4×C113AGL(1,ℤ/8)11yescharacteristic
86C4×C113#13711yescharacteristic
87Dic113—81no—
88C2×C113—42no—
89C2×C113#44811yescharacteristic
90C2×C113#45011yescharacteristic
91C2×C113#45611yescharacteristic
92#1651—1131nomaximal, Sylow
93C113#165111yescharacteristic, complemented, Sylow
94D4×Q8D11311yescharacteristic
95#498—1131no—
96#475—1131no—
97#461—1131no—
98#332—1131no—
99Q8⋊C8—1131no—
100D4⋊C8—1131no—
101C22×Q8—21no—
102C2×SD16—2261no—
103C4⋊Q8—21no—
104C4⋊Q8—1131no—
105C4⋊Q8C2×D11311yescharacteristic
106C22⋊Q8—21no—
107C22⋊Q8—22no—
108C4×Q8C2×D11311yescharacteristic
109C4×D4—21no—
110C4×D4C2×D11311yescharacteristic
111#106—2261no—
112#106—2262no—
113C4⋊C8—1131no—
114C4⋊C8—1131no—
115#103—2261no—
116#103—2261no—
117C4×C8—1131no—
118C2×Q8—22no—
119C2×Q8—21no—
120C2×Q8—42no—
121C2×Q8—42no—
122C2×Q8—2261no—
123C2×Q8C22⋊D11311yescharacteristic
124C2×D4C22⋊D11311yescharacteristic
125C22×C4—22no—
126C22×C4—21no—
127SD16—4522no—
128C2×C8—2261no—
129C2×C8—2261no—
130C2×C8—2261no—
131C4⋊C4—22no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2261no—
135C4⋊C4—2261no—
136C4⋊C4C22⋊D11311yescharacteristic
137C4⋊C4C22⋊D11311yescharacteristic
138C4⋊C4C22⋊D11312yes—
139C22⋊C4—22no—
140C22⋊C4—21no—
141C42—21no—
142C42C22×D11311yescharacteristic
143C23—21no—
144Q8—21no—
145Q8—44no—
146Q8—41no—
147Q8—41no—
148Q8—4521no—
149Q8—4521no—
150Q8#1426863512yescomplemented
151D4—21no—
152D4#1426863412yes—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—44no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—4521no—
161C2×C4C2×C22⋊D11311yescharacteristic
162C2×C4C2×C22⋊D11311yescharacteristic
163C2×C4C2×C22⋊D11311yescharacteristic
164C8—4521no—
165C8—4521no—
166C8—2262no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1681359111yescharacteristic
171C4—21no—
172C4—22no—
173C4—41no—
174C4—42no—
175C4—41no—
176C4—9041no—
177C4C2×#1426863411yescharacteristic
178C4C2×#1426863511yescharacteristic
179C4#1681364811yescharacteristic
180C4#1681365311yescharacteristic
181C2—42no—
182C2#2029873711yescharacteristic
183C2#2029874911yescharacteristic
184C2#2029878111yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4×Q8×C113C2
socleC22×C113#120
prime radicalC2×D4×C113D4
hypercenterD4×Q8D113
hypocenterC113#1651
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #20298994C2semidirect
2. #20298883C2semidirect
4. #20298344C2semidirect
5. Q8⋊#11744751C2semidirect
55. Q8×C113SD16semidirect
93. C113#1651semidirect
150. Q8#14268635semidirect

Maximal subgroups

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

subgroupindex
#202989942
#202988832
#202988032
#202983442
Q8⋊#117447512
D4⋊#117447512
D4×Q8×C1132
#1651113