Finite Group Databasebeta

← #46809572

Subgroups — #46809572

Order 34432.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#31771160C211yesmaximal, characteristic
2#31770627C211yesmaximal, characteristic
3C4⋊C8×D269C211yesmaximal, characteristic
4#31770354C211yesmaximal, characteristic, complemented
5#31770352C211yesmaximal, characteristic, complemented
6#31770350C211yesmaximal, characteristic, complemented
7#333×C269C211yesmaximal, characteristic, complemented
8C2×#16864385—21no—
9C2×C8×D269—21no—
10#22575453C2211yescharacteristic
11#22575444—21no—
12#22575433—21no—
13#22575429C412yes—
14Q8×Dic269C412yes—
15#22575418—21no—
16#22575411—21no—
17C42×D269C2211yescharacteristic
18C4⋊#14524130C2211yescharacteristic
19C4⋊#14524130C2211yescharacteristic
20#22575382—21no—
21#22575382—21no—
22C4⋊Q8×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24C4⋊C8×C269C2211yescharacteristic
25C2×Dic538—21no—
26C2×C4×D269C2×C411yescharacteristic
27C2×C4×D269D411yescharacteristic
28C2×C4×D269D411yescharacteristic
29#16864385—42no—
30C2×#14524130—21no—
31C2×#14524130—21no—
32C8×D269—42no—
33C4⋊Dic269—22no—
34C4⋊Dic269—21no—
35C4⋊Dic269C2×C412yes—
36#16864381—22no—
37#16864379—22no—
38C4×Dic269—22no—
39C4×Dic269C2×C411yescharacteristic
40C4×Dic269D411yescharacteristic
41C4×Dic269D411yescharacteristic
42C2×Q8×C269C2×C412yes—
43C2×C8×C269—21no—
44C2×C8×C269—21no—
45C4⋊C4×C269—21no—
46C4⋊C4×C269—21no—
47C42×C269C2311yescharacteristic
48C22×D269C22⋊C411yescharacteristic
49Dic538—41no—
50Dic538—41no—
51C2×Dic269—22no—
52C2×Dic269C22⋊C411yescharacteristic
53C2×Dic269C22⋊C411yescharacteristic
54C2×Dic269C22⋊C411yescharacteristic
55C4×D269—21no—
56C4×D269—21no—
57C4×D269—41no—
58C4×D269SD1612yes—
59C4×D269Q1612yes—
60#14524130—41no—
61#14524130—41no—
62Q8×C269—42no—
63C2×C4×C269—22no—
64C2×C4×C269C22×C411yescharacteristic
65C2×C4×C269C2×D411yescharacteristic
66C2×C4×C269C2×D411yescharacteristic
67C8×C269—41no—
68C8×C269—41no—
69C22×C269C2×C22⋊C411yescharacteristic
70C2×D269—21no—
71C2×D269—21no—
72C2×D269#10312yes—
73C4×C269—21no—
74C4×C269—42no—
75C4×C269C2×SD1611yescharacteristic
76C4×C269C2×Q1611yescharacteristic
77C4×C269AGL(1,ℤ/8)11yescharacteristic
78C4×C269#13711yescharacteristic
79Dic269—21no—
80Dic269—21no—
81Dic269—42no—
82Dic269#10312yes—
83C2×C269#41311yescharacteristic
84C2×C269C2×#10311yescharacteristic
85C2×C269#41711yescharacteristic
86D269—22no—
87C269#155011yescharacteristic, complemented, Sylow
88#1550—2691nomaximal, Sylow
89#533—2691no—
90#423—2691no—
91C2×C4⋊C8—2691no—
92#333—2691no—
93#333D26911yescharacteristic, complemented
94#332—2691no—
95#332—2691no—
96C2×M16—5381no—
97C22×C8—5381no—
98C4⋊Q8—2691no—
99C4⋊Q8C2×D26911yescharacteristic
100#125—5381no—
101C22⋊Q8—2692no—
102C22⋊Q8—5381no—
103C4×Q8—2692no—
104C4×Q8—5381no—
105#117—5381no—
106C2×C42—2691no—
107C4⋊C8—2691no—
108C4⋊C8—2691no—
109C4⋊C8—5381no—
110C4⋊C8—5381no—
111C4⋊C8C2×D26911yescharacteristic
112C4⋊C8C2×D26911yescharacteristic
113C2×Q8—5381no—
114C2×Q8C4×D26912yes—
115C22×C4—2691no—
116C22×C4—2691no—
117C22×C4—2691no—
118M16—10762no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—5381no—
122C2×C8—5381no—
123C2×C8—10762no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—2692no—
127C4⋊C4—5382no—
128C4⋊C4—5382no—
129C4⋊C4—5381no—
130C22⋊C4—5382no—
131C42—2691no—
132C42—2691no—
133C42—2691no—
134C42—5382no—
135C42C22×D26911yescharacteristic
136C23—2691no—
137Q8—42no—
138Q8—10761no—
139Q8—10761no—
140C2×C4—22no—
141C2×C4—2691no—
142C2×C4—2692no—
143C2×C4—2692no—
144C2×C4—2691no—
145C2×C4—2691no—
146C2×C4—5381no—
147C2×C4—5381no—
148C2×C4—5382no—
149C2×C4—10761no—
150C2×C4C2×C4×D26911yescharacteristic
151C2×C4D4×D26911yescharacteristic
152C2×C4D4×D26911yescharacteristic
153C8—41no—
154C8—41no—
155C8—10761no—
156C8—10761no—
157C22—2692no—
158C22—5381no—
159C22—5381no—
160C22C22⋊C4×D26911yescharacteristic
161C4—21no—
162C4—42no—
163C4—2692no—
164C4—5381no—
165C4—5381no—
166C4—10762no—
167C4SD16×D26911yescharacteristic
168C4Q16×D26911yescharacteristic
169C4#2257548011yescharacteristic
170C4#2257548511yescharacteristic
171C2—5382no—
172C2#3177058611yescharacteristic
173C2#103×D26911yescharacteristic
174C2#3177060511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC42C22×D269
Fitting#333×C269C2
socleC22×C269C2×C22⋊C4
prime radicalC22×D269C22⋊C4
cosocleC42×C269C23
hypercenter#333D269
hypocenterC269#1550
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #31770354C2semidirect
5. #31770352C2semidirect
6. #31770350C2semidirect
7. #333×C269C2semidirect
87. C269#1550semidirect
93. #333D269semidirect

Maximal subgroups

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

subgroupindex
#317711602
#317706272
C4⋊C8×D2692
#317703542
#317703522
#317703502
#333×C2692
#1550269