Finite Group Databasebeta

← #46810069

Subgroups — #46810069

Order 34432.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#31771340C211yesmaximal, characteristic
2#31770953C211yesmaximal, characteristic
3#31770887C211yesmaximal, characteristic, complemented
4#31770348C211yesmaximal, characteristic
5Q8⋊#14524130C211yesmaximal, characteristic, complemented
6#31770335C211yesmaximal, characteristic, complemented
7#462×C269C211yesmaximal, characteristic, complemented
8#22575450C2211yescharacteristic
9#22575442—21no—
10#22575441—21no—
11#22575438—22no—
12C4×Dic538C2211yescharacteristic
13C4×D1076—21no—
14#22575415—21no—
15#22575384—21no—
16C4⋊#14524130C2211yescharacteristic
17#22575376—21no—
18#22575373—22no—
19C4×#14524130C2211yescharacteristic
20C2×Q16×C269—21no—
21C4⋊Q8×C269C2211yescharacteristic
22C4×Q8×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24#103×C269—21no—
25C2×Dic538D411yescharacteristic
26C2×D1076—21no—
27C2×D1076—21no—
28C2×D1076D412yes—
29C2×C4×D269—22no—
30C2×#14524130—21no—
31C2×#14524130—21no—
32C4⋊Dic269D411yescharacteristic
33#16864381—21no—
34#16864379—22no—
35#16864379—22no—
36#16864379—22no—
37C4×Dic269—21no—
38C2×Q8×C269—21no—
39C2×Q8×C269D411yescharacteristic
40Q16×C269—42no—
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—22no—
49Dic538—21no—
50Dic538—21no—
51D1076—42no—
52D1076—41no—
53D1076—41no—
54D1076—41no—
55D1076—41no—
56C2×Dic269—21no—
57C2×Dic269—21no—
58C4×D269—82no—
59#14524130—41no—
60#14524130—41no—
61Q8×C269—21no—
62Q8×C269—21no—
63Q8×C269—41no—
64Q8×C269—41no—
65C2×C4×C269—21no—
66C2×C4×C269—21no—
67C2×C4×C269—41no—
68C2×C4×C269C2×D411yescharacteristic
69C2×C4×C269C2×D411yescharacteristic
70C2×C4×C269C2×D411yescharacteristic
71C8×C269—41no—
72C22×C269#12011yescharacteristic
73C2×D269—42no—
74C2×D269—42no—
75C2×D269—42no—
76C4×C269—21no—
77C4×C269—41no—
78C4×C269—41no—
79C4×C269—81no—
80C4×C269#13511yescharacteristic
81C4×C269#13511yescharacteristic
82C4×C269AGL(1,ℤ/8)11yescharacteristic
83C4×C269#13711yescharacteristic
84Dic269—41no—
85Dic269—41no—
86C2×C269#44911yescharacteristic
87C2×C269#45211yescharacteristic
88C2×C269#45511yescharacteristic
89D269—82no—
90C269#164011yescharacteristic, complemented, Sylow
91#1640—2691nomaximal, Sylow
92#559—2691no—
93#486—2691no—
94#475—2691no—
95#462D26911yescharacteristic, complemented
96#331—2691no—
97Q8⋊C8—2691no—
98Q8⋊C8—2691no—
99C2×Q16—21no—
100C4⋊Q8C2×D26911yescharacteristic
101#127—2691no—
102#124—5381no—
103#124—5381no—
104#123—5382no—
105C4×Q8—2691no—
106C4×Q8C2×D26911yescharacteristic
107C4×D4—5381no—
108C4×D4—5381no—
109#106—5381no—
110C4⋊C8—2691no—
111C4⋊C8C2×D26911yescharacteristic
112#103—21no—
113#103—5381no—
114#102—5382no—
115C4×C8—2691no—
116C2×Q8—21no—
117C2×Q8—2691no—
118C2×Q8C22⋊D26911yescharacteristic
119C2×D4—2692no—
120C2×D4—5381no—
121C2×D4—5381no—
122C22×C4—5382no—
123Q16—42no—
124C2×C8—21no—
125C2×C8—5381no—
126C2×C8—5381no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—2691no—
131C4⋊C4—5381no—
132C4⋊C4C22⋊D26911yescharacteristic
133C22⋊C4—5382no—
134C22⋊C4—5382no—
135C22⋊C4—5382no—
136C42—21no—
137C42—5381no—
138C42C22×D26911yescharacteristic
139C23—5382no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—5381no—
145Q8—5381no—
146D4—10762no—
147D4—10761no—
148D4—10761no—
149D4—10761no—
150D4—10761no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—5381no—
155C2×C4—5381no—
156C2×C4—21522no—
157C2×C4D4×D26911yescharacteristic
158C2×C4D4×D26911yescharacteristic
159C2×C4C2×C22⋊D26911yescharacteristic
160C8—41no—
161C8—10761no—
162C8—10761no—
163C22—10762no—
164C22—10762no—
165C22—10762no—
166C22#2257542111yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—10761no—
172C4—10761no—
173C4#2257547311yescharacteristic
174C4#2257547611yescharacteristic
175C4#2257547911yescharacteristic
176C4#2257548511yescharacteristic
177C2—21522no—
178C2#3177074811yescharacteristic
179C2#3177076611yescharacteristic
180C2#3177078111yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#462×C269C2
socleC22×C269#120
prime radical#22575450C22
hypercenter#462D269
hypocenterC269#1640
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #31770887C2semidirect
5. Q8⋊#14524130C2semidirect
6. #31770335C2semidirect
7. #462×C269C2semidirect
90. C269#1640semidirect
95. #462D269semidirect

Maximal subgroups

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

subgroupindex
#317713402
#317709532
#317708872
#317703482
Q8⋊#145241302
#317703352
#462×C2692
#1640269