Finite Group Databasebeta

← #46812549

Subgroups — #46812549

Order 34432.

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

normal subgroups only

This group has 258 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#31771154C211yesmaximal, characteristic
2#31770577C212yesmaximal, complemented
3#31770400C211yesmaximal, characteristic, complemented
4#31770397C212yesmaximal, complemented
5#354×C269C211yesmaximal, characteristic, complemented
6C2×#16864403C411yescharacteristic, complemented
7C2×#16864401C2211yescharacteristic
8#22575451C411yescharacteristic, complemented
9#22575449C2211yescharacteristic
10#22575441C411yescharacteristic, complemented
11#22575426—22no—
12#22575413—22no—
13#22575409—22no—
14C42×D269C411yescharacteristic, complemented
15#22575368C2212yes—
16#22575367—22no—
17#124×C269C2211yescharacteristic
18#99×C269C2212yes—
19#16864403—41no—
20#16864403—41no—
21#16864401—41no—
22#16864401—41no—
23C2×Dic538C2×C411yescharacteristic
24C2×D1076—21no—
25C2×D1076C2×C411yescharacteristic
26C2×C22⋊D269—22no—
27C2×C22⋊D269D412yes—
28C22×Dic269D412yes—
29C2×C4×D269—21no—
30C2×C4×D269—21no—
31C2×C4×D269C2×C411yescharacteristic
32#16864381—22no—
33#16864381—42no—
34C22⋊Dic269—22no—
35#16864379—22no—
36C4×Dic269—21no—
37C4×Dic269—42no—
38C4×Dic269C2×C411yescharacteristic
39C2×Q8×C269C2×C411yescharacteristic
40C2×D4×C269C2311yescharacteristic
41C22⋊C4×C269—22no—
42C22⋊C4×C269—22no—
43C42×C269C2×C411yescharacteristic
44C22×D269—21no—
45C22×D269C22⋊C411yescharacteristic
46Dic538—41no—
47D1076—41no—
48D1076—42no—
49C22⋊D269—42no—
50C22⋊D269—44no—
51C2×Dic269—21no—
52C2×Dic269—22no—
53C2×Dic269—22no—
54C2×Dic269—42no—
55C2×Dic269C22⋊C412yes—
56C2×Dic269C22⋊C411yescharacteristic
57C4×D269—21no—
58C4×D269—21no—
59C4×D269—42no—
60C4×D269—41no—
61C4×D269—41no—
62C23×C269C2×D412yes—
63Q8×C269—41no—
64D4×C269—41no—
65C2×C4×C269—21no—
66C2×C4×C269—21no—
67C2×C4×C269—42no—
68C2×C4×C269C22×C411yescharacteristic
69C22×C269—22no—
70C22×C269—42no—
71C22×C269C2×C22⋊C411yescharacteristic
72C2×D269—21no—
73C2×D269—41no—
74C2×D269—42no—
75C2×D269—41no—
76C4×C269—21no—
77C4×C269—41no—
78C4×C269—41no—
79C4×C269—82no—
80Dic269—22no—
81Dic269—22no—
82Dic269—82no—
83Dic269#9911yescharacteristic
84Dic269#9911yescharacteristic
85C2×C269—21no—
86C2×C269—42no—
87C2×C269C2×#9911yescharacteristic
88D269—41no—
89D269—81no—
90C269#212611yescharacteristic, complemented, Sylow
91#2126—2691nomaximal, Sylow
92#532—2691no—
93#410—2692no—
94#354—2691no—
95#354D26911yescharacteristic, complemented
96#353—2692no—
97C2×#41—2691no—
98C2×#41—2691no—
99C4⋊Q8—2691no—
100#127—2691no—
101#124—2691no—
102#124C2×D26911yescharacteristic
103#121—5382no—
104C4×D4—5382no—
105#117—5382no—
106C2×C42—2691no—
107#99—2692no—
108#99—5382no—
109#99C2×D26912yes—
110#41—10761no—
111#41—10761no—
112#41—10761no—
113#41—10761no—
114C2×Q8—2691no—
115C2×Q8C4×D26911yescharacteristic
116C2×D4—2692no—
117C2×D4—2691no—
118C2×D4—5381no—
119C2×D4—5382no—
120C2×D4C22×D26911yescharacteristic
121C22×C4—2692no—
122C22×C4—2691no—
123C22×C4—5381no—
124C22×C4—5381no—
125C4⋊C4—5382no—
126C4⋊C4—10762no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—5382no—
130C22⋊C4—5382no—
131C42—2691no—
132C42—5381no—
133C42—10762no—
134C42C4×D26911yescharacteristic
135C23—2691no—
136C23—5381no—
137C23D4×D26912yes—
138Q8—41no—
139Q8—10761no—
140D4—41no—
141D4—10761no—
142D4—10762no—
143D4—10762no—
144D4—10764no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—2691no—
149C2×C4—2692no—
150C2×C4—5381no—
151C2×C4—5381no—
152C2×C4—5382no—
153C2×C4—5382no—
154C2×C4—5381no—
155C2×C4—10761no—
156C2×C4—10761no—
157C2×C4—10762no—
158C2×C4—10762no—
159C2×C4C2×C4×D26911yescharacteristic
160C22—22no—
161C22—42no—
162C22—5381no—
163C22—10761no—
164C22—10762no—
165C22—10761no—
166C22C22⋊C4×D26911yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—2691no—
172C4—2691no—
173C4—5382no—
174C4—5382no—
175C4—21522no—
176C2—21no—
177C2—42no—
178C2—10761no—
179C2—21521no—
180C2#99×D26911yescharacteristic
subgroupG/H
centerC2#99×D269
commutatorC2×C4×C269C22×C4
FrattiniC2×D4C22×D269
Fitting#354×C269C2
socleC2×C269C2×#99
prime radical#31771154C2
cosocleC2×D4×C269C23
hypercenter#354D269
hypocenterC269#2126
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. #31770577C2semidirect
3. #31770400C2semidirect
4. #31770397C2semidirect
5. #354×C269C2semidirect
6. C2×#16864403C4semidirect
8. #22575451C4semidirect
10. #22575441C4semidirect
14. C42×D269C4semidirect
90. C269#2126semidirect
95. #354D269semidirect

Maximal subgroups

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

subgroupindex
#317711542
#317705772
#317704002
#317703972
#354×C2692
#2126269