Finite Group Databasebeta

← #46812553

Subgroups — #46812553

Order 34432.

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

normal subgroups only

This group has 286 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#31771173C211yesmaximal, characteristic
2#99×D269C212yesmaximal, complemented
3#31770400C211yesmaximal, characteristic, complemented
4#31770397C212yesmaximal, complemented
5#354×C269C211yesmaximal, characteristic, complemented
6C2×#16864403C411yescharacteristic, complemented
7C2×D4×D269C2211yescharacteristic
8#22575450C411yescharacteristic, complemented
9#22575449C2211yescharacteristic
10#22575442C411yescharacteristic, complemented
11#22575426—22no—
12#22575423—22no—
13#22575410C411yescharacteristic, complemented
14C22⋊C4×D269—22no—
15#22575368C2212yes—
16#22575367—22no—
17#124×C269C2211yescharacteristic
18#99×C269C2212yes—
19C23×D269D412yes—
20#16864403—42no—
21C2×D1076—21no—
22C2×D1076—22no—
23C2×D1076C2×C411yescharacteristic
24C2×D1076C2×C411yescharacteristic, complemented
25C2×C22⋊D269—22no—
26C2×C22⋊D269D412yes—
27D4×D269—42no—
28C2×C4×D269—21no—
29C2×C4×D269—42no—
30C2×C4×D269C2×C411yescharacteristic
31#16864381—21no—
32C22⋊Dic269—22no—
33#16864379—21no—
34#16864379—22no—
35#16864379—42no—
36C4×Dic269C2×C411yescharacteristic, complemented
37C2×Q8×C269C2×C411yescharacteristic, complemented
38C2×D4×C269C2311yescharacteristic
39C22⋊C4×C269—22no—
40C22⋊C4×C269—22no—
41C42×C269C2×C411yescharacteristic, complemented
42C22×D269—22no—
43C22×D269—22no—
44C22×D269—21no—
45C22×D269—82no—
46C22×D269C22⋊C412yes—
47C22×D269C22⋊C411yescharacteristic
48D1076—41no—
49D1076—41no—
50D1076—42no—
51D1076—82no—
52C22⋊D269—42no—
53C22⋊D269—82no—
54C2×Dic269—21no—
55C2×Dic269—42no—
56C2×Dic269C22⋊C411yescharacteristic
57C4×D269—22no—
58C4×D269—42no—
59C4×D269—84no—
60C23×C269C2×D412yes—
61Q8×C269—41no—
62D4×C269—41no—
63C2×C4×C269—21no—
64C2×C4×C269—21no—
65C2×C4×C269—42no—
66C2×C4×C269C22×C411yescharacteristic
67C22×C269—22no—
68C22×C269—42no—
69C22×C269C2×C22⋊C411yescharacteristic
70C2×D269—22no—
71C2×D269—41no—
72C2×D269—44no—
73C2×D269—42no—
74C2×D269—42no—
75C2×D269—41no—
76C2×D269—82no—
77C2×D269#9912yes—
78C4×C269—21no—
79C4×C269—41no—
80C4×C269—41no—
81C4×C269—82no—
82Dic269—21no—
83Dic269—41no—
84Dic269—82no—
85C2×C269—21no—
86C2×C269—42no—
87C2×C269C2×#9911yescharacteristic
88D269—22no—
89D269—42no—
90D269—81no—
91C269#212711yescharacteristic, complemented, Sylow
92#2127—2691nomaximal, Sylow
93#535—2691no—
94C2×#99—2692no—
95#354—2691no—
96#354D26911yescharacteristic, complemented
97#353—2692no—
98C2×#41—2691no—
99C22×D4—2691no—
100#127—2691no—
101#127—2691no—
102#124—2691no—
103#124C2×D26911yescharacteristic
104#121—5382no—
105#120—5382no—
106#117—2691no—
107C2×C22⋊C4—5382no—
108#99—2692no—
109#99—5382no—
110#99C2×D26912yes—
111C24—2692no—
112#41—10762no—
113C2×Q8C4×D26911yescharacteristic, complemented
114C2×D4—2692no—
115C2×D4—2691no—
116C2×D4—2691no—
117C2×D4—5381no—
118C2×D4—5382no—
119C2×D4—5382no—
120C2×D4—10762no—
121C2×D4C22×D26911yescharacteristic
122C22×C4—2691no—
123C22×C4—5381no—
124C22×C4—10762no—
125C4⋊C4—5381no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—5381no—
129C22⋊C4—5382no—
130C22⋊C4—5382no—
131C22⋊C4—10762no—
132C42—2691no—
133C42C4×D26911yescharacteristic, complemented
134C23—2691no—
135C23—2692no—
136C23—5382no—
137C23—5382no—
138C23—5381no—
139C23—21522no—
140C23D4×D26912yes—
141Q8—41no—
142D4—41no—
143D4—10761no—
144D4—10761no—
145D4—10762no—
146D4—10762no—
147D4—21522no—
148D4—21522no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—2691no—
153C2×C4—5382no—
154C2×C4—5381no—
155C2×C4—10762no—
156C2×C4—10762no—
157C2×C4—21524no—
158C2×C4C2×C4×D26911yescharacteristic
159C22—22no—
160C22—42no—
161C22—2692no—
162C22—5382no—
163C22—10761no—
164C22—10762no—
165C22—10762no—
166C22—10764no—
167C22—10761no—
168C22—21522no—
169C22C22⋊C4×D26911yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—5381no—
175C4—10761no—
176C4—21522no—
177C2—21no—
178C2—42no—
179C2—5382no—
180C2—10762no—
181C2—21521no—
182C2#99×D26911yescharacteristic
subgroupG/H
centerC2#99×D269
commutatorC2×C4×C269C22×C4
FrattiniC2×D4C22×D269
Fitting#354×C269C2
socleC2×C269C2×#99
prime radical#31771173C2
cosocleC2×D4×C269C23
hypercenter#354D269
hypocenterC269#2127
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D269C2semidirect
3. #31770400C2semidirect
4. #31770397C2semidirect
5. #354×C269C2semidirect
6. C2×#16864403C4semidirect
8. #22575450C4semidirect
10. #22575442C4semidirect
13. #22575410C4semidirect
24. C2×D1076C2×C4semidirect
36. C4×Dic269C2×C4semidirect
37. C2×Q8×C269C2×C4semidirect
41. C42×C269C2×C4semidirect
91. C269#2127semidirect
96. #354D269semidirect
113. C2×Q8C4×D269semidirect
133. C42C4×D269semidirect

Maximal subgroups

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

subgroupindex
#317711732
#99×D2692
#317704002
#317703972
#354×C2692
#2127269