Finite Group Databasebeta

← #46809382

Subgroups — #46809382

Order 34432.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#31771157C211yesmaximal, characteristic
2#31770655C211yesmaximal, characteristic
3#31770456C211yesmaximal, characteristic
4#31770343C211yesmaximal, characteristic
5#31770342C211yesmaximal, characteristic
6#31770341C211yesmaximal, characteristic
7#328×C269C211yesmaximal, characteristic
8#22575452C411yescharacteristic, complemented
9#22575451C411yescharacteristic, complemented
10#22575443—21no—
11#22575432C2211yescharacteristic
12#22575430—21no—
13Q8×Dic269C411yescharacteristic, complemented
14#22575418—21no—
15#22575418C411yescharacteristic, complemented
16#22575409—21no—
17C2×#16864381—21no—
18C2×C4×Dic269—21no—
19C2×C4×Dic269C2211yescharacteristic
20#22575382—21no—
21C22⋊#14524130C2211yescharacteristic
22C8×Dic269—21no—
23#22575360C2211yescharacteristic
24C22⋊Q8×C269C2211yescharacteristic
25C22⋊C8×C269C2211yescharacteristic
26#95×C269C2211yescharacteristic
27C2×Dic538—21no—
28C2×Dic538C2×C411yescharacteristic
29C22×Dic269—21no—
30C22×Dic269D411yescharacteristic
31C22×Dic269D411yescharacteristic
32C2×#14524130—21no—
33C4⋊Dic269—21no—
34C4⋊Dic269C2×C411yescharacteristic
35#16864381—24no—
36#16864381—21no—
37#16864381—21no—
38#16864381—21no—
39#16864381—21no—
40#16864381—21no—
41C22⋊Dic269—21no—
42C4×Dic269—21no—
43C4×Dic269—21no—
44C4×Dic269—42no—
45C4×Dic269C2×C411yescharacteristic
46C4×Dic269C2×C411yescharacteristic
47C4×Dic269D411yescharacteristic
48C4×Dic269D411yescharacteristic
49C2×Q8×C269C2×C411yescharacteristic
50C22×C4×C269—21no—
51C22×C4×C269C2311yescharacteristic
52C2×C8×C269—21no—
53C4⋊C4×C269—21no—
54C4⋊C4×C269C2×C411yescharacteristic
55C22⋊C4×C269—21no—
56Dic538—42no—
57Dic538—41no—
58C2×Dic269—22no—
59C2×Dic269—22no—
60C2×Dic269—21no—
61C2×Dic269—21no—
62C2×Dic269—41no—
63C2×Dic269—41no—
64C2×Dic269C22⋊C411yescharacteristic
65C2×Dic269C22⋊C411yescharacteristic
66C2×Dic269C22⋊C411yescharacteristic
67C2×Dic269C22⋊C411yescharacteristic
68C2×Dic269SD1612yes—
69C2×Dic269Q1612yes—
70#14524130—41no—
71C23×C269C2×D411yescharacteristic
72Q8×C269—41no—
73C2×C4×C269—22no—
74C2×C4×C269—21no—
75C2×C4×C269—21no—
76C2×C4×C269—41no—
77C2×C4×C269—41no—
78C2×C4×C269—41no—
79C2×C4×C269C22×C411yescharacteristic
80C2×C4×C269C2×D411yescharacteristic
81C8×C269—41no—
82C22×C269—21no—
83C22×C269—21no—
84C22×C269C2×C22⋊C411yescharacteristic
85C22×C269C2×SD1611yescharacteristic
86C22×C269C2×Q1611yescharacteristic
87C4×C269—21no—
88C4×C269—21no—
89C4×C269—42no—
90C4×C269—41no—
91C4×C269—41no—
92Dic269—21no—
93Dic269—42no—
94Dic269—41no—
95Dic269—41no—
96Dic269#10312yes—
97Dic269#10312yes—
98Dic269#10412yes—
99C2×C269—21no—
100C2×C269—21no—
101C2×C269#41011yescharacteristic
102C2×C269C2×#10311yescharacteristic
103C2×C269C2×#10411yescharacteristic
104C269#150311yescharacteristic, complemented, Sylow
105#1503—2691nomaximal, Sylow
106#533—2691no—
107#431—2691no—
108C4×C4⋊C4—2691no—
109#328—2691no—
110#328—2691no—
111#328—2691no—
112#328D26911yescharacteristic
113C4⋊Q8—2691no—
114C4⋊Q8—2691no—
115#125—5381no—
116C22⋊Q8—2691no—
117C22⋊Q8—5381no—
118C22⋊Q8C2×D26911yescharacteristic
119C4×Q8—2691no—
120C4×Q8—2691no—
121C4×Q8—5381no—
122#117—5381no—
123C2×C4⋊C4—5381no—
124C2×C42—2691no—
125C2×C42—5381no—
126C4⋊C8—5381no—
127C22⋊C8—2691no—
128C22⋊C8C2×D26911yescharacteristic
129C4×C8—5381no—
130#95—2691no—
131#95C2×D26911yescharacteristic
132C2×Q8—2691no—
133C2×Q8—5381no—
134C2×Q8C4×D26911yescharacteristic
135C22×C4—21no—
136C22×C4—2691no—
137C22×C4—2691no—
138C22×C4—5381no—
139C22×C4C22×D26911yescharacteristic
140C2×C8—21no—
141C2×C8—5381no—
142C4⋊C4—21no—
143C4⋊C4—2691no—
144C4⋊C4—5381no—
145C4⋊C4—5381no—
146C4⋊C4—5381no—
147C4⋊C4—5381no—
148C4⋊C4—5381no—
149C4⋊C4—5384no—
150C4⋊C4—5381no—
151C4⋊C4C4×D26911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5381no—
154C42—2691no—
155C42—2691no—
156C42—2691no—
157C42—2691no—
158C42—5381no—
159C42—5381no—
160C42—10762no—
161C23D4×D26911yescharacteristic
162Q8—41no—
163Q8—10761no—
164Q8—10762no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—2691no—
172C2×C4—2691no—
173C2×C4—2691no—
174C2×C4—2692no—
175C2×C4—2692no—
176C2×C4—2691no—
177C2×C4—5382no—
178C2×C4—5382no—
179C2×C4—5381no—
180C2×C4—5381no—
181C2×C4—10761no—
182C2×C4—10761no—
183C2×C4C2×C4×D26911yescharacteristic
184C2×C4D4×D26911yescharacteristic
185C8—41no—
186C8—10761no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D26911yescharacteristic
190C22SD16×D26911yescharacteristic
191C22Q16×D26911yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—2692no—
198C4—2692no—
199C4—2692no—
200C4—5381no—
201C4—10762no—
202C4—10761no—
203C4—10761no—
204C2—21no—
205C2—21no—
206C2#3177057711yescharacteristic
207C2#103×D26911yescharacteristic
208C2#104×D26911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#328×C269C2
socleC22×C269C2×C22⋊C4
prime radicalC23×C269C2×D4
cosocleC22×C4×C269C23
hypercenter#328D269
hypocenterC269#1503
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #22575452C4semidirect
9. #22575451C4semidirect
13. Q8×Dic269C4semidirect
15. #22575418C4semidirect
104. C269#1503semidirect

Maximal subgroups

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

subgroupindex
#317711572
#317706552
#317704562
#317703432
#317703422
#317703412
#328×C2692
#1503269