Finite Group Databasebeta

← #46821015

Subgroups — #46821015

Order 34432.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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#31771162C211yesmaximal, characteristic
2#31770935C212yesmaximal
3#31770890C212yesmaximal, complemented
4#31770815C212yesmaximal, complemented
5#31770761C212yesmaximal
6#31770710C214yesmaximal, complemented
7#31770662C211yesmaximal, characteristic
8C2×C4×Q8×C269C211yesmaximal, characteristic
9C2×#16864392C2214yes—
10#22575453C2211yescharacteristic
11#22575453C2211yescharacteristic
12#22575445—21no—
13#22575432—21no—
14#22575432C2212yes—
15C4×Dic538—21no—
16C4×Dic538C2212yes—
17#22575412—21no—
18#22575384C2214yes—
19C4⋊#14524130C2212yes—
20#22575377C2214yes—
21#22575376C2214yes—
22C22⋊#14524130C2212yes—
23#22575364C2212yes—
24C22×Q8×C269C2211yescharacteristic
25C4×Q8×C269—21no—
26C4×Q8×C269—21no—
27C4×Q8×C269C2212yes—
28C4×Q8×C269C2212yes—
29C2×C4⋊C4×C269—21no—
30C2×C4⋊C4×C269C2211yescharacteristic
31C2×C42×C269—21no—
32C2×C42×C269C2211yescharacteristic
33C2×Dic538—21no—
34C2×Dic538C2312yes—
35#16864392—28no—
36C2×#14524130C2314yes—
37C4⋊Dic269—21no—
38C4⋊Dic269—21no—
39C4⋊Dic269—21no—
40C4⋊Dic269C2312yes—
41#16864381—22no—
42#16864381—22no—
43C22⋊Dic269—22no—
44C4×Dic269—22no—
45C2×Q8×C269—24no—
46C2×Q8×C269—21no—
47C2×Q8×C269C2312yes—
48C22×C4×C269—21no—
49C22×C4×C269—21no—
50C22×C4×C269D411yescharacteristic
51C22×C4×C269D411yescharacteristic
52C22×C4×C269C2311yescharacteristic
53C4⋊C4×C269—22no—
54C4⋊C4×C269—22no—
55C4⋊C4×C269—21no—
56C4⋊C4×C269C2312yes—
57C42×C269—22no—
58C42×C269—22no—
59C42×C269D411yescharacteristic
60C42×C269D411yescharacteristic
61C42×C269C2311yescharacteristic
62C42×C269C2311yescharacteristic
63Dic538—24no—
64Dic538—42no—
65C2×Dic269—22no—
66C2×Dic269—22no—
67#14524130—24no—
68C23×C269C2×D411yescharacteristic
69Q8×C269—24no—
70Q8×C269—22no—
71Q8×C269#4114yes—
72C2×C4×C269—24no—
73C2×C4×C269—22no—
74C2×C4×C269—22no—
75C2×C4×C269—22no—
76C2×C4×C269—22no—
77C2×C4×C269—22no—
78C2×C4×C269—42no—
79C2×C4×C269C2×D411yescharacteristic
80C2×C4×C269C2×D411yescharacteristic
81C2×C4×C269C2×D411yescharacteristic
82C2×C4×C269C2×D411yescharacteristic
83C2×C4×C269C2×D411yescharacteristic
84C2×C4×C269C2411yescharacteristic
85C22×C269—21no—
86C22×C269—21no—
87C22×C269#13712yes—
88C22×C269C22×D411yescharacteristic
89C4×C269—24no—
90C4×C269—21no—
91C4×C269—21no—
92C4×C269—21no—
93C4×C269—21no—
94C4×C269—42no—
95C4×C269#13712yes—
96C4×C269C2×#4112yes—
97Dic269—42no—
98Dic269—42no—
99C2×C269—22no—
100C2×C269#52511yescharacteristic
101C2×C269C2×#13711yescharacteristic
102C2×C269C2×#13711yescharacteristic
103C269#311311yescharacteristic, complemented, Sylow
104#3113—2691nomaximal, Sylow
105#533—2691no—
106C2×C4×Q8D26911yescharacteristic
107#483—2692no—
108#475—2692no—
109#462—2692no—
110#451—2692no—
111#441—2694no—
112#432—2691no—
113C22×Q8C2×D26911yescharacteristic
114C2×Q16—2694no—
115C4⋊Q8—2691no—
116C4⋊Q8—2691no—
117#125—5381no—
118C22⋊Q8—2692no—
119C22⋊Q8—5381no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—2692no—
123C4×Q8—5381no—
124C4×Q8C2×D26912yes—
125C4×Q8C2×D26912yes—
126#117—5381no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D26911yescharacteristic
129C2×C42—21no—
130C2×C42C2×D26911yescharacteristic
131#106—2694no—
132C4⋊C8—2692no—
133#103—2694no—
134#103—2694no—
135C22⋊C8—2692no—
136#97—2692no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—2692no—
140C2×Q8—5381no—
141C2×Q8C22×D26912yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D26911yescharacteristic
145C22×C4C22⋊D26911yescharacteristic
146C22×C4C22×D26911yescharacteristic
147Q16—5388no—
148C2×C8—2694no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—2692no—
153C4⋊C4—5381no—
154C4⋊C4—5381no—
155C4⋊C4—5382no—
156C4⋊C4—5382no—
157C4⋊C4—5381no—
158C4⋊C4C22×D26912yes—
159C22⋊C4—5382no—
160C42—22no—
161C42—22no—
162C42—5382no—
163C42C22⋊D26911yescharacteristic
164C42C22⋊D26911yescharacteristic
165C42C22×D26911yescharacteristic
166C42C22×D26911yescharacteristic
167C23C2×C22⋊D26911yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—5384no—
171Q8—10762no—
172Q8#1686440214yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—5382no—
181C2×C4—5382no—
182C2×C4C2×C22⋊D26911yescharacteristic
183C2×C4C2×C22⋊D26911yescharacteristic
184C2×C4C2×C22⋊D26911yescharacteristic
185C2×C4C2×C22⋊D26911yescharacteristic
186C2×C4C2×C22⋊D26911yescharacteristic
187C2×C4C23×D26911yescharacteristic
188C8—5384no—
189C22—21no—
190C22—21no—
191C22#2257548312yes—
192C22C22×C22⋊D26911yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—24no—
197C4—21no—
198C4—42no—
199C4—10762no—
200C4—10762no—
201C4#2257548412yes—
202C4C2×#1686440212yes—
203C2—22no—
204C2#3177111611yescharacteristic
205C2C2×#2257548311yescharacteristic
206C2C2×#2257548411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC2×C4×Q8×C269C2
socleC22×C269C22×D4
prime radicalC23×C269C2×D4
hypercenterC2×C4×Q8D269
hypocenterC269#3113
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #31770890C2semidirect
4. #31770815C2semidirect
6. #31770710C2semidirect
103. C269#3113semidirect

Maximal subgroups

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

subgroupindex
#317711622
#317709352
#317708902
#317708152
#317707612
#317707102
#317706622
C2×C4×Q8×C2692
#3113269