Finite Group Databasebeta

← #46809891

Subgroups — #46809891

Order 34432.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#31771234C211yesmaximal, characteristic
2#31770935C211yesmaximal, characteristic
3#31770536C211yesmaximal, characteristic
4#31770343C211yesmaximal, characteristic
5#31770342C211yesmaximal, characteristic
6#31770330C211yesmaximal, characteristic
7#483×C269C211yesmaximal, characteristic
8#22575452—21no—
9#22575451—21no—
10#22575443—21no—
11#22575443—21no—
12#22575432C2211yescharacteristic
13#22575430—21no—
14#22575409—21no—
15C2×#16864381—21no—
16C2×#16864381C2211yescharacteristic
17#22575384—21no—
18#22575376—21no—
19C22⋊#14524130C2211yescharacteristic
20#22575360—21no—
21#22575360C2211yescharacteristic
22C22⋊Q8×C269C2211yescharacteristic
23C2×C4⋊C4×C269C2211yescharacteristic
24#106×C269—21no—
25#103×C269—21no—
26C22⋊C8×C269C2211yescharacteristic
27C2×Dic538—21no—
28C2×Dic538D411yescharacteristic
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—
40#16864381—21no—
41#16864381—21no—
42#16864381—42no—
43C22⋊Dic269—21no—
44C4×Dic269—21no—
45C4×Dic269—21no—
46C2×Q8×C269D411yescharacteristic
47C22×C4×C269—21no—
48C22×C4×C269C2311yescharacteristic
49C2×C8×C269—21no—
50C4⋊C4×C269—21no—
51C4⋊C4×C269—21no—
52C4⋊C4×C269—21no—
53C4⋊C4×C269D411yescharacteristic
54C22⋊C4×C269—21no—
55Dic538—41no—
56Dic538—81no—
57C2×Dic269—21no—
58C2×Dic269—21no—
59C2×Dic269—22no—
60C2×Dic269—21no—
61C2×Dic269—21no—
62C2×Dic269—21no—
63C2×Dic269—41no—
64C2×Dic269—41no—
65C2×Dic269—41no—
66C2×Dic269SD1612yes—
67#14524130—41no—
68C23×C269C2×D411yescharacteristic
69Q8×C269—41no—
70C2×C4×C269—21no—
71C2×C4×C269—21no—
72C2×C4×C269—41no—
73C2×C4×C269—41no—
74C2×C4×C269—41no—
75C2×C4×C269—41no—
76C2×C4×C269C2×D411yescharacteristic
77C2×C4×C269C2×D411yescharacteristic
78C8×C269—41no—
79C22×C269—21no—
80C22×C269—21no—
81C22×C269#12011yescharacteristic
82C22×C269C2×SD1611yescharacteristic
83C22×C269#13711yescharacteristic
84C4×C269—21no—
85C4×C269—21no—
86C4×C269—41no—
87C4×C269—41no—
88C4×C269—81no—
89Dic269—22no—
90Dic269—42no—
91Dic269—41no—
92Dic269—41no—
93Dic269—41no—
94C2×C269—21no—
95C2×C269—21no—
96C2×C269#44811yescharacteristic
97C2×C269#45611yescharacteristic
98C2×C269#45811yescharacteristic
99C269#161111yescharacteristic, complemented, Sylow
100#1611—2691nomaximal, Sylow
101#544—2691no—
102#483—2691no—
103#483D26911yescharacteristic
104#398—2691no—
105#328—2691no—
106#328—2691no—
107#324—2691no—
108C4⋊Q8—5381no—
109C4⋊Q8—5381no—
110#125—5381no—
111#125—5381no—
112C22⋊Q8—2691no—
113C22⋊Q8—5381no—
114C22⋊Q8C2×D26911yescharacteristic
115#117—5381no—
116C2×C4⋊C4—2691no—
117C2×C4⋊C4—5381no—
118C2×C4⋊C4C2×D26911yescharacteristic
119#106—21no—
120#106—5381no—
121#103—21no—
122#103—5381no—
123C22⋊C8—2691no—
124C22⋊C8C2×D26911yescharacteristic
125#95—2691no—
126#95—5381no—
127C2×Q8—2691no—
128C2×Q8—5381no—
129C2×Q8C22⋊D26911yescharacteristic
130C22×C4—21no—
131C22×C4—2691no—
132C22×C4—2691no—
133C22×C4—5381no—
134C22×C4C22×D26911yescharacteristic
135C2×C8—21no—
136C2×C8—5381no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—2691no—
141C4⋊C4—5381no—
142C4⋊C4—5381no—
143C4⋊C4—5381no—
144C4⋊C4—5381no—
145C4⋊C4—5381no—
146C4⋊C4—5381no—
147C4⋊C4—5381no—
148C4⋊C4—5381no—
149C4⋊C4—10762no—
150C4⋊C4C22⋊D26911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5381no—
153C42—5381no—
154C42—5381no—
155C23D4×D26911yescharacteristic
156Q8—41no—
157Q8—10761no—
158Q8—21521no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—2692no—
166C2×C4—5381no—
167C2×C4—5381no—
168C2×C4—5382no—
169C2×C4—5381no—
170C2×C4—5381no—
171C2×C4—5381no—
172C2×C4—10761no—
173C2×C4—10761no—
174C2×C4—10761no—
175C2×C4D4×D26911yescharacteristic
176C2×C4C2×C22⋊D26911yescharacteristic
177C8—41no—
178C8—10761no—
179C22—21no—
180C22—21no—
181C22#2257542111yescharacteristic
182C22SD16×D26911yescharacteristic
183C22#2257548211yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—81no—
189C4—5382no—
190C4—10762no—
191C4—10761no—
192C4—10761no—
193C4—10761no—
194C2—21no—
195C2—21no—
196C2#3177074211yescharacteristic
197C2#3177078611yescharacteristic
198C2#3177079411yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC22×C4×C269C23
FrattiniC22×C4C22×D269
Fitting#483×C269C2
socleC22×C269#120
prime radicalC23×C269C2×D4
hypercenter#483D269
hypocenterC269#1611
LCSG ▷ C22×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
99. C269#1611semidirect

Maximal subgroups

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

subgroupindex
#317712342
#317709352
#317705362
#317703432
#317703422
#317703302
#483×C2692
#1611269