Finite Group Databasebeta

← #46810053

Subgroups — #46810053

Order 34432.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic538C211yesmaximal, characteristic
2#31770956C211yesmaximal, characteristic, complemented
3#31770901C211yesmaximal, characteristic, complemented
4#31770895C211yesmaximal, characteristic
5#31770352C211yesmaximal, characteristic, complemented
6#31770337C211yesmaximal, characteristic, complemented
7D4⋊C8×C269C211yesmaximal, characteristic
8C22×Dic538—21no—
9#22575453C2211yescharacteristic
10#22575453C2211yescharacteristic
11#22575452—21no—
12#22575432—21no—
13#22575430—22no—
14C4×Dic538C2211yescharacteristic
15D4×Dic269—21no—
16#22575387—21no—
17#22575384—21no—
18C4⋊#14524130C2211yescharacteristic
19#22575378—21no—
20#22575378—22no—
21#22575374—21no—
22C4×D4×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24C4×C8×C269C2211yescharacteristic
25C2×Dic538—22no—
26C2×Dic538—21no—
27C2×Dic538—21no—
28C2×Dic538—42no—
29C2×Dic538—42no—
30C2×Dic538D411yescharacteristic
31C22×Dic269—22no—
32C2×#14524130—21no—
33C4⋊Dic269—21no—
34C4⋊Dic269—21no—
35C4⋊Dic269—21no—
36C4⋊Dic269D412yes—
37C4⋊Dic269D411yescharacteristic
38#16864381—22no—
39#16864381—21no—
40C22⋊Dic269—22no—
41C4×Dic269—21no—
42C2×D4×C269D411yescharacteristic
43C22×C4×C269—21no—
44C2×C8×C269—21no—
45C2×C8×C269—21no—
46C4⋊C4×C269D411yescharacteristic
47C22⋊C4×C269—21no—
48C42×C269C2311yescharacteristic
49Dic538—21no—
50Dic538—44no—
51Dic538—41no—
52Dic538—41no—
53Dic538—42no—
54Dic538SD1612yes—
55C2×Dic269—21no—
56C2×Dic269—21no—
57C2×Dic269—22no—
58C2×Dic269—44no—
59C2×Dic269—41no—
60#14524130—41no—
61C23×C269—21no—
62D4×C269—21no—
63D4×C269Q1612yes—
64C2×C4×C269—21no—
65C2×C4×C269—41no—
66C2×C4×C269—41no—
67C2×C4×C269C2×D411yescharacteristic
68C2×C4×C269C2×D411yescharacteristic
69C2×C4×C269C2×D411yescharacteristic
70C8×C269—41no—
71C8×C269—41no—
72C22×C269—22no—
73C22×C269—41no—
74C22×C269—41no—
75C22×C269#12011yescharacteristic
76C4×C269—21no—
77C4×C269—41no—
78C4×C269C2×SD1611yescharacteristic
79C4×C269C2×Q1611yescharacteristic
80C4×C269AGL(1,ℤ/8)11yescharacteristic
81C4×C269#13711yescharacteristic
82Dic269—22no—
83Dic269—42no—
84Dic269—41no—
85Dic269—81no—
86C2×C269—42no—
87C2×C269#45011yescharacteristic
88C2×C269#45111yescharacteristic
89C2×C269#45411yescharacteristic
90C269#163711yescharacteristic, complemented, Sylow
91#1637—2691nomaximal, Sylow
92D4×Q8—2691no—
93#487—2691no—
94#477—2691no—
95#476—2691no—
96#332—2691no—
97Q8⋊C8—2691no—
98D4⋊C8D26911yescharacteristic
99C22×Q8—5381no—
100C4⋊Q8—2691no—
101C4⋊Q8—2691no—
102C4⋊Q8—5381no—
103C22⋊Q8—5382no—
104C22⋊Q8—5381no—
105C4×Q8—2691no—
106C4×D4—5381no—
107C4×D4C2×D26911yescharacteristic
108#107—5381no—
109#106—5381no—
110C4⋊C8—2691no—
111C4⋊C8C2×D26911yescharacteristic
112#103—5382no—
113#103—5381no—
114#102—5381no—
115C4×C8C2×D26911yescharacteristic
116C2×Q8—2691no—
117C2×Q8—5382no—
118C2×Q8—5381no—
119C2×Q8—5381no—
120C2×Q8—10762no—
121C2×Q8—10762no—
122C2×D4D107611yescharacteristic
123C22×C4—21no—
124C22×C4—5382no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5381no—
128C4⋊C4—2692no—
129C4⋊C4—2691no—
130C4⋊C4—5382no—
131C4⋊C4—5381no—
132C4⋊C4—5381no—
133C4⋊C4—5381no—
134C4⋊C4—5381no—
135C4⋊C4D107611yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5382no—
138C42—5381no—
139C42C22×D26911yescharacteristic
140C23—21no—
141Q8—2692no—
142Q8—5381no—
143Q8—10762no—
144Q8—10764no—
145Q8—10761no—
146Q8—10761no—
147D4—21no—
148D4Dic107612yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—5381no—
153C2×C4—5381no—
154C2×C4—5382no—
155C2×C4—10764no—
156C2×C4—10761no—
157C2×C4D4×D26911yescharacteristic
158C2×C4D4×D26911yescharacteristic
159C2×C4C2×D107611yescharacteristic
160C8—41no—
161C8—41no—
162C8—10761no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#2257542311yescharacteristic
167C4—21no—
168C4—41no—
169C4—5382no—
170C4—10762no—
171C4—10761no—
172C4—21521no—
173C4SD16×D26911yescharacteristic
174C4C2×Dic107611yescharacteristic
175C4#2257547711yescharacteristic
176C4#2257548611yescharacteristic
177C2—42no—
178C2#3177075711yescharacteristic
179C2#3177076311yescharacteristic
180C2#3177077911yescharacteristic
subgroupG/H
centerC22#22575423
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
FittingD4⋊C8×C269C2
socleC22×C269#120
prime radicalC2×D4×C269D4
hypercenterD4⋊C8D269
hypocenterC269#1637
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
3. #31770901C2semidirect
5. #31770352C2semidirect
6. #31770337C2semidirect
90. C269#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5382
#317709562
#317709012
#317708952
#317703522
#317703372
D4⋊C8×C2692
#1637269