Finite Group Databasebeta

← #46810102

Subgroups — #46810102

Order 34432.

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

normal subgroups only

This group has 208 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#31771312C211yesmaximal, characteristic
2#31770956C211yesmaximal, characteristic, complemented
3#31770885C211yesmaximal, characteristic
4#31770816C211yesmaximal, characteristic, complemented
5#31770353C211yesmaximal, characteristic, complemented
6#31770337C211yesmaximal, characteristic, complemented
7D4⋊C8×C269C211yesmaximal, characteristic
8C2×Dic1076—21no—
9#22575453C2211yescharacteristic
10#22575453C2211yescharacteristic
11#22575444—21no—
12#22575432—21no—
13#22575430—22no—
14C4×Dic538C2211yescharacteristic
15D4×Dic269—21no—
16C2×C4⋊Dic269—21no—
17#22575386—21no—
18C4⋊#14524130C2211yescharacteristic
19#22575378—22no—
20#22575378—21no—
21#22575374—21no—
22C4×D4×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24C4×C8×C269C2211yescharacteristic
25C2×Dic538—21no—
26C2×Dic538D411yescharacteristic
27C2×Dic538D412yes—
28C22×Dic269—22no—
29Dic1076—42no—
30C2×#14524130—21no—
31C4⋊Dic269—22no—
32C4⋊Dic269—21no—
33C4⋊Dic269—21no—
34C4⋊Dic269—21no—
35C4⋊Dic269—21no—
36C4⋊Dic269D411yescharacteristic
37#16864381—22no—
38#16864381—21no—
39C22⋊Dic269—22no—
40C4×Dic269—21no—
41C2×D4×C269D411yescharacteristic
42C22×C4×C269—21no—
43C2×C8×C269—21no—
44C2×C8×C269—21no—
45C4⋊C4×C269D411yescharacteristic
46C22⋊C4×C269—21no—
47C42×C269C2311yescharacteristic
48Dic538—21no—
49Dic538—21no—
50Dic538—42no—
51Dic538—41no—
52Dic538—41no—
53C2×Dic269—21no—
54C2×Dic269—21no—
55C2×Dic269—22no—
56C2×Dic269—41no—
57C2×Dic269—82no—
58#14524130—41no—
59C23×C269—21no—
60D4×C269—21no—
61D4×C269Q1612yescomplemented
62C2×C4×C269—21no—
63C2×C4×C269—41no—
64C2×C4×C269—41no—
65C2×C4×C269C2×D411yescharacteristic
66C2×C4×C269C2×D411yescharacteristic
67C2×C4×C269C2×D411yescharacteristic
68C8×C269—41no—
69C8×C269—41no—
70C22×C269—22no—
71C22×C269—41no—
72C22×C269—41no—
73C22×C269#12011yescharacteristic
74C4×C269—21no—
75C4×C269—41no—
76C4×C269C2×Q1611yescharacteristic
77C4×C269#13511yescharacteristic
78C4×C269AGL(1,ℤ/8)11yescharacteristic
79C4×C269#13711yescharacteristic
80Dic269—41no—
81Dic269—41no—
82Dic269—42no—
83Dic269—81no—
84C2×C269—42no—
85C2×C269#44911yescharacteristic
86C2×C269#45111yescharacteristic
87C2×C269#45511yescharacteristic
88C269#164411yescharacteristic, complemented, Sylow
89#1644—2691nomaximal, Sylow
90#554—2691no—
91#487—2691no—
92#474—2691no—
93#462—2691no—
94#333—2691no—
95Q8⋊C8—2691no—
96D4⋊C8D26911yescharacteristic
97C2×Q16—5381no—
98C4⋊Q8—2691no—
99C4⋊Q8—2691no—
100#125—5381no—
101C22⋊Q8—5382no—
102C22⋊Q8—5381no—
103C4×Q8—2691no—
104C4×D4—5381no—
105C4×D4C2×D26911yescharacteristic
106C2×C4⋊C4—5381no—
107#107—5381no—
108C4⋊C8—2691no—
109C4⋊C8C2×D26911yescharacteristic
110#103—5381no—
111#103—5382no—
112#102—5381no—
113C4×C8C2×D26911yescharacteristic
114C2×Q8—2691no—
115C2×Q8—2692no—
116C2×Q8—5381no—
117C2×D4D107611yescharacteristic
118C22×C4—21no—
119C22×C4—5382no—
120Q16—10762no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—5381no—
124C4⋊C4—2691no—
125C4⋊C4—5382no—
126C4⋊C4—5382no—
127C4⋊C4—5381no—
128C4⋊C4—5381no—
129C4⋊C4—5381no—
130C4⋊C4—5381no—
131C4⋊C4—5381no—
132C4⋊C4D107611yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—5382no—
135C42—5381no—
136C42C22×D26911yescharacteristic
137C23—21no—
138Q8—5381no—
139Q8—5381no—
140Q8—10762no—
141Q8—10761no—
142Q8—10761no—
143D4—21no—
144D4Dic107612yescomplemented
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—5381no—
149C2×C4—5381no—
150C2×C4—5382no—
151C2×C4—10761no—
152C2×C4—21522no—
153C2×C4D4×D26911yescharacteristic
154C2×C4D4×D26911yescharacteristic
155C2×C4C2×D107611yescharacteristic
156C8—41no—
157C8—41no—
158C8—10761no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#2257542311yescharacteristic
163C4—21no—
164C4—41no—
165C4—10761no—
166C4—10761no—
167C4—10762no—
168C4—21521no—
169C4C2×Dic107611yescharacteristic
170C4#2257547411yescharacteristic
171C4#2257547711yescharacteristic
172C4#2257548611yescharacteristic
173C2—42no—
174C2#3177075111yescharacteristic
175C2#3177076311yescharacteristic
176C2#3177078411yescharacteristic
subgroupG/H
centerC22#22575423
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
FittingD4⋊C8×C269C2
socleC22×C269#120
prime radicalC2×D4×C269D4
hypercenterD4⋊C8D269
hypocenterC269#1644
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31770956C2semidirect
4. #31770816C2semidirect
5. #31770353C2semidirect
6. #31770337C2semidirect
61. D4×C269Q16semidirect
88. C269#1644semidirect
144. D4Dic1076semidirect

Maximal subgroups

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

subgroupindex
#317713122
#317709562
#317708852
#317708162
#317703532
#317703372
D4⋊C8×C2692
#1644269