Finite Group Databasebeta

← #46810091

Subgroups — #46810091

Order 34432.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#31771315C211yesmaximal, characteristic
2#31770957C211yesmaximal, characteristic, complemented
3#31770807C211yesmaximal, characteristic
4#31770353C211yesmaximal, characteristic, complemented
5Q8⋊#14524130C211yesmaximal, characteristic, complemented
6#31770332C211yesmaximal, characteristic
7#475×C269C211yesmaximal, characteristic, complemented
8C2×#16864389—21no—
9#22575453C2211yescharacteristic
10#22575445—21no—
11#22575431—22no—
12#22575429—21no—
13C4×D1076—21no—
14C4×D1076C2211yescharacteristic
15C4⋊C4×D269—21no—
16C4⋊#14524130C2211yescharacteristic
17#22575377—21no—
18#22575376—22no—
19C4×#14524130C2211yescharacteristic
20C4⋊Q8×C269C2211yescharacteristic
21C4×Q8×C269C2211yescharacteristic
22#106×C269—21no—
23C4⋊C8×C269C2211yescharacteristic
24#103×C269—21no—
25C2×Dic538D412yes—
26C2×D1076D411yescharacteristic
27C2×C4×D269—22no—
28C2×C4×D269—21no—
29#16864389—42no—
30C2×#14524130—21no—
31C2×#14524130—21no—
32C4⋊Dic269—21no—
33C4⋊Dic269—21no—
34C4⋊Dic269D411yescharacteristic
35#16864381—22no—
36#16864381—22no—
37#16864379—22no—
38#16864379—21no—
39C2×Q8×C269—21no—
40C2×Q8×C269D411yescharacteristic
41C2×C8×C269—21no—
42C4⋊C4×C269—21no—
43C4⋊C4×C269—21no—
44C4⋊C4×C269—21no—
45C4⋊C4×C269D411yescharacteristic
46C42×C269—21no—
47C42×C269C2311yescharacteristic
48C22×D269—21no—
49Dic538—42no—
50D1076—21no—
51D1076SD1612yes—
52C2×Dic269—21no—
53C2×Dic269—22no—
54C4×D269—41no—
55C4×D269—41no—
56C4×D269—82no—
57#14524130—41no—
58#14524130—41no—
59Q8×C269—21no—
60Q8×C269—21no—
61Q8×C269—41no—
62Q8×C269—41no—
63C2×C4×C269—21no—
64C2×C4×C269—21no—
65C2×C4×C269—41no—
66C2×C4×C269C2×D411yescharacteristic
67C2×C4×C269C2×D411yescharacteristic
68C2×C4×C269C2×D411yescharacteristic
69C8×C269—41no—
70C22×C269#12011yescharacteristic
71C2×D269—22no—
72C2×D269—41no—
73C2×D269—41no—
74C4×C269—21no—
75C4×C269—41no—
76C4×C269—41no—
77C4×C269—81no—
78C4×C269C2×SD1611yescharacteristic
79C4×C269#13511yescharacteristic
80C4×C269#13711yescharacteristic
81C4×C269#13711yescharacteristic
82Dic269—41no—
83Dic269—42no—
84C2×C269#44811yescharacteristic
85C2×C269#45211yescharacteristic
86C2×C269#45511yescharacteristic
87D269—42no—
88C269#164311yescharacteristic, complemented, Sylow
89#1643—2691nomaximal, Sylow
90#554—2691no—
91#487—2691no—
92#475D26911yescharacteristic, complemented
93#461—2691no—
94#333—2691no—
95Q8⋊C8—2691no—
96D4⋊C8—2691no—
97C2×SD16—5381no—
98C4⋊Q8—2691no—
99C4⋊Q8C2×D26911yescharacteristic
100#125—5381no—
101C22⋊Q8—5382no—
102C22⋊Q8—5381no—
103C4×Q8C2×D26911yescharacteristic
104C4×D4—2691no—
105C4×D4—5381no—
106C2×C4⋊C4—5381no—
107#106—21no—
108C4⋊C8—2691no—
109C4⋊C8C2×D26911yescharacteristic
110#103—21no—
111#103—5382no—
112#103—5381no—
113C4×C8—2691no—
114C2×Q8—21no—
115C2×Q8—2692no—
116C2×Q8C22⋊D26911yescharacteristic
117C2×D4—2691no—
118C22×C4—5382no—
119C22×C4—5381no—
120SD16—10762no—
121C2×C8—21no—
122C2×C8—5381no—
123C2×C8—5381no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—2691no—
128C4⋊C4—5382no—
129C4⋊C4—5382no—
130C4⋊C4—5381no—
131C4⋊C4—5381no—
132C4⋊C4C22⋊D26911yescharacteristic
133C22⋊C4—5382no—
134C22⋊C4—5381no—
135C42—21no—
136C42C22×D26911yescharacteristic
137C23—5381no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—10762no—
143D4—2692no—
144D4—5381no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—5381no—
149C2×C4—5382no—
150C2×C4—10761no—
151C2×C4—10761no—
152C2×C4—21522no—
153C2×C4D4×D26911yescharacteristic
154C2×C4D4×D26911yescharacteristic
155C2×C4C2×C22⋊D26911yescharacteristic
156C8—41no—
157C8—10761no—
158C8—10761no—
159C22—5382no—
160C22—10761no—
161C22—10761no—
162C22#2257542111yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—10761no—
168C4—10762no—
169C4SD16×D26911yescharacteristic
170C4#2257547311yescharacteristic
171C4#2257548211yescharacteristic
172C4#2257548411yescharacteristic
173C2—10762no—
174C2#3177074211yescharacteristic
175C2#3177076511yescharacteristic
176C2#3177078111yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#475×C269C2
socleC22×C269#120
prime radicalC2×D1076D4
hypercenter#475D269
hypocenterC269#1643
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #31770957C2semidirect
4. #31770353C2semidirect
5. Q8⋊#14524130C2semidirect
7. #475×C269C2semidirect
88. C269#1643semidirect
92. #475D269semidirect

Maximal subgroups

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

subgroupindex
#317713152
#317709572
#317708072
#317703532
Q8⋊#145241302
#317703322
#475×C2692
#1643269