Finite Group Databasebeta

← #46809913

Subgroups — #46809913

Order 34432.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#31771200C211yesmaximal, characteristic
2#31770940C211yesmaximal, characteristic, complemented
3#31770543C211yesmaximal, characteristic, complemented
4#31770343C211yesmaximal, characteristic, complemented
5#31770339C211yesmaximal, characteristic
6#31770330C211yesmaximal, characteristic, complemented
7#481×C269C211yesmaximal, characteristic
8#22575446—21no—
9#22575443—21no—
10#22575434—21no—
11#22575434—21no—
12#22575432C2211yescharacteristic
13#22575430—21no—
14D4×Dic269—21no—
15C2×#16864381C2211yescharacteristic
16#22575386—21no—
17#22575376—21no—
18C22⋊#14524130C2211yescharacteristic
19#22575360—21no—
20#22575360—21no—
21#22575360C2211yescharacteristic
22#121×C269C2211yescharacteristic
23C2×C4⋊C4×C269C2211yescharacteristic
24#106×C269—21no—
25#102×C269—21no—
26C22⋊C8×C269C2211yescharacteristic
27C2×Dic538D411yescharacteristic
28C22×Dic269—21no—
29C22×Dic269—21no—
30C22×Dic269D411yescharacteristic
31C22×Dic269D411yescharacteristic
32C2×#14524130—21no—
33C4⋊Dic269—21no—
34C4⋊Dic269D411yescharacteristic
35#16864381—21no—
36#16864381—21no—
37#16864381—21no—
38#16864381—21no—
39#16864381—21no—
40C22⋊Dic269—21no—
41C22⋊Dic269—21no—
42C22⋊Dic269—21no—
43C22⋊Dic269—21no—
44C4×Dic269—21no—
45C2×D4×C269—21no—
46C2×D4×C269D411yescharacteristic
47C22×C4×C269—21no—
48C22×C4×C269C2311yescharacteristic
49C2×C8×C269—21no—
50C4⋊C4×C269—21no—
51C4⋊C4×C269—21no—
52C4⋊C4×C269D411yescharacteristic
53C22⋊C4×C269—21no—
54Dic538—41no—
55C2×Dic269—21no—
56C2×Dic269—21no—
57C2×Dic269—21no—
58C2×Dic269—21no—
59C2×Dic269—21no—
60C2×Dic269—21no—
61C2×Dic269—41no—
62C2×Dic269—41no—
63C2×Dic269—41no—
64C2×Dic269—41no—
65C2×Dic269—81no—
66#14524130—41no—
67C23×C269—21no—
68C23×C269C2×D411yescharacteristic
69D4×C269—41no—
70D4×C269—41no—
71D4×C269—41no—
72C2×C4×C269—21no—
73C2×C4×C269—41no—
74C2×C4×C269—42no—
75C2×C4×C269—41no—
76C2×C4×C269C2×D411yescharacteristic
77C2×C4×C269C2×D411yescharacteristic
78C8×C269—41no—
79C22×C269—21no—
80C22×C269—21no—
81C22×C269—41no—
82C22×C269—41no—
83C22×C269—41no—
84C22×C269#12011yescharacteristic
85C22×C269#13511yescharacteristic
86C22×C269#13711yescharacteristic
87C4×C269—21no—
88C4×C269—21no—
89C4×C269—41no—
90C4×C269—81no—
91Dic269—41no—
92Dic269—41no—
93Dic269—41no—
94Dic269—41no—
95Dic269—81no—
96C2×C269—21no—
97C2×C269—21no—
98C2×C269—81no—
99C2×C269#45211yescharacteristic
100C2×C269#45411yescharacteristic
101C2×C269#45811yescharacteristic
102C269#161511yescharacteristic, complemented, Sylow
103#1615—2691nomaximal, Sylow
104#539—2691no—
105#484—2691no—
106#481D26911yescharacteristic
107#400—2691no—
108#328—2691no—
109#327—2691no—
110#324—2691no—
111#126—5381no—
112#125—5381no—
113#123—5381no—
114#123—5381no—
115C22⋊Q8—2691no—
116C22⋊Q8—5381no—
117#121C2×D26911yescharacteristic
118C4×D4—5381no—
119C2×C4⋊C4—2691no—
120C2×C4⋊C4C2×D26911yescharacteristic
121#107—5381no—
122#106—21no—
123#103—5381no—
124#102—21no—
125C22⋊C8—2691no—
126C22⋊C8C2×D26911yescharacteristic
127#95—2691no—
128#95—5381no—
129#95—5381no—
130C2×Q8—2691no—
131C2×D4—21no—
132C2×D4C22⋊D26911yescharacteristic
133C22×C4—21no—
134C22×C4—2691no—
135C22×C4—2691no—
136C22×C4—5381no—
137C22×C4—5381no—
138C22×C4C22×D26911yescharacteristic
139C2×C8—21no—
140C2×C8—5381no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2691no—
144C4⋊C4—5381no—
145C4⋊C4—5381no—
146C4⋊C4—5381no—
147C4⋊C4—5381no—
148C4⋊C4—5381no—
149C4⋊C4—5381no—
150C4⋊C4C22⋊D26911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5381no—
153C22⋊C4—5381no—
154C22⋊C4—5381no—
155C22⋊C4—5381no—
156C42—5381no—
157C23—21no—
158C23D4×D26911yescharacteristic
159Q8—10761no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—5381no—
168C2×C4—5381no—
169C2×C4—5381no—
170C2×C4—5381no—
171C2×C4—5381no—
172C2×C4—5381no—
173C2×C4—10761no—
174C2×C4—10761no—
175C2×C4—10761no—
176C2×C4—10761no—
177C2×C4—21521no—
178C2×C4D4×D26911yescharacteristic
179C2×C4C2×C22⋊D26911yescharacteristic
180C8—41no—
181C8—10761no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#2257542111yescharacteristic
188C22#2257547411yescharacteristic
189C22#2257548211yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—81no—
194C4—10761no—
195C4—10761no—
196C4—10761no—
197C4—10761no—
198C4—21521no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#3177076411yescharacteristic
203C2#3177077611yescharacteristic
204C2#3177079411yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC22×C4×C269C23
FrattiniC22×C4C22×D269
Fitting#481×C269C2
socleC22×C269#120
prime radical#121×C269C22
hypercenter#481D269
hypocenterC269#1615
LCSG ▷ C22×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #31770940C2semidirect
3. #31770543C2semidirect
4. #31770343C2semidirect
6. #31770330C2semidirect
102. C269#1615semidirect

Maximal subgroups

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

subgroupindex
#317712002
#317709402
#317705432
#317703432
#317703392
#317703302
#481×C2692
#1615269