Finite Group Databasebeta

← #46814070

Subgroups — #46814070

Order 34432.

408 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#22575445C211yesmaximal, characteristic
2#31770502C212yesmaximal
3#31770500C212yesmaximal
4#31770492C212yesmaximal
5#31770490C212yesmaximal
6#31770488C212yesmaximal
7#31770486C212yesmaximal
8#31770471C211yesmaximal, characteristic
9#382×C269C211yesmaximal, characteristic
10#22575445C418yescomplemented
11C2×C4⋊Dic269C2211yescharacteristic
12C2×C4⋊Dic269C2211yescharacteristic
13C2×C4⋊Dic269C2211yescharacteristic
14C2×C4⋊Dic269C2211yescharacteristic
15C2×#16864381C2212yes—
16C2×#16864381C2212yes—
17C2×#16864381C2212yes—
18C2×#16864381C2212yes—
19C2×C4×Dic269C2212yes—
20C2×C4×Dic269C2212yes—
21#22575360C2212yes—
22#22575360C2212yes—
23#22575360C2212yes—
24#22575360C2212yes—
25#22575360C2212yes—
26#22575360C2212yes—
27C2×C4⋊C4×C269C2211yescharacteristic
28C2×C4⋊C4×C269C2211yescharacteristic
29C2×C42×C269C2211yescharacteristic
30#95×C269C2212yes—
31#95×C269C2212yes—
32C22×Dic269C2312yes—
33C22×Dic269C2312yes—
34C22×Dic269C2312yes—
35C22×Dic269C2312yes—
36C4⋊Dic269—41no—
37C4⋊Dic269—41no—
38C4⋊Dic269C2×C414yes—
39C4⋊Dic269C2×C414yes—
40#16864381—42no—
41#16864381—42no—
42#16864381C2×C418yes—
43#16864381C2×C418yes—
44C4×Dic269—42no—
45C4×Dic269—42no—
46C22×C4×C269C2312yes—
47C22×C4×C269C2312yes—
48C22×C4×C269C2311yescharacteristic
49C22×C4×C269C2311yescharacteristic
50C22×C4×C269C2311yescharacteristic
51C4⋊C4×C269—41no—
52C4⋊C4×C269—41no—
53C42×C269C2×C414yes—
54C2×Dic269—22no—
55C2×Dic269—22no—
56C2×Dic269—22no—
57C2×Dic269—22no—
58C2×Dic269—22no—
59C2×Dic269—22no—
60C2×Dic269—22no—
61C2×Dic269—22no—
62C2×Dic269—22no—
63C2×Dic269—22no—
64C2×Dic269C22×C414yes—
65C2×Dic269C22×C414yes—
66C23×C269C2411yescharacteristic
67C2×C4×C269—21no—
68C2×C4×C269—21no—
69C2×C4×C269—21no—
70C2×C4×C269—21no—
71C2×C4×C269—21no—
72C2×C4×C269—21no—
73C2×C4×C269—22no—
74C2×C4×C269—22no—
75C2×C4×C269—22no—
76C2×C4×C269—22no—
77C2×C4×C269—22no—
78C2×C4×C269—22no—
79C2×C4×C269C22×C412yes—
80C2×C4×C269C22×C412yes—
81C2×C4×C269C22×C412yes—
82C22×C269C23×C411yescharacteristic
83C22×C269H(5,𝔽2)11yescharacteristic
84C22×C269H(5,𝔽2)11yescharacteristic
85C22×C2692−1+411yescharacteristic
86C22×C2692−1+411yescharacteristic
87C22×C2692−1+411yescharacteristic
88C22×C2692−1+411yescharacteristic
89C4×C269—22no—
90C4×C269—22no—
91C4×C269—22no—
92C4×C269—42no—
93C4×C269—42no—
94Dic269—24no—
95Dic269—24no—
96Dic269—42no—
97Dic269—42no—
98C2×C269#51911yescharacteristic
99C2×C269#52011yescharacteristic
100C2×C269#52011yescharacteristic
101C2×C269#56211yescharacteristic
102C2×C269#56311yescharacteristic
103C2×C269#56311yescharacteristic
104C2×C269#56411yescharacteristic
105C269#238211yescharacteristic, complemented, Sylow
106#2382—2691nomaximal, Sylow
107C2×#125—2691no—
108#389—2692no—
109#389—2692no—
110#387—2692no—
111#387—2692no—
112#387—2692no—
113#387—2692no—
114#382—2691no—
115#382D26911yescharacteristic
116#125—2698no—
117C2×C4⋊C4—2692no—
118C2×C4⋊C4—2692no—
119C2×C4⋊C4—2691no—
120C2×C4⋊C4—2691no—
121C2×C4⋊C4—2692no—
122C2×C4⋊C4—2692no—
123C2×C4⋊C4—2691no—
124C2×C4⋊C4—2691no—
125C2×C4⋊C4C2×D26911yescharacteristic
126C2×C4⋊C4C2×D26911yescharacteristic
127C2×C42—2692no—
128C2×C42—2692no—
129C2×C42C2×D26911yescharacteristic
130#95—2692no—
131#95—2692no—
132#95—2692no—
133#95—2692no—
134#95—2692no—
135#95—2692no—
136#95C2×D26912yes—
137#95C2×D26912yes—
138C22×C4—2692no—
139C22×C4—2692no—
140C22×C4—2692no—
141C22×C4—2692no—
142C22×C4C22×D26912yes—
143C22×C4C22×D26912yes—
144C22×C4C22×D26911yescharacteristic
145C22×C4C22×D26911yescharacteristic
146C22×C4C22×D26911yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—2698no—
150C4⋊C4—2698no—
151C4⋊C4—2694no—
152C4⋊C4—2694no—
153C4⋊C4—10762no—
154C4⋊C4—10762no—
155C4⋊C4—10761no—
156C4⋊C4—10761no—
157C42—10762no—
158C42—10762no—
159C42C4×D26914yes—
160C23C23×D26911yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—2694no—
174C2×C4—2694no—
175C2×C4—5382no—
176C2×C4—5382no—
177C2×C4—5382no—
178C2×C4—5382no—
179C2×C4—5382no—
180C2×C4—5382no—
181C2×C4—5382no—
182C2×C4—5382no—
183C2×C4—5382no—
184C2×C4—5382no—
185C2×C4C2×C4×D26912yes—
186C2×C4C2×C4×D26912yes—
187C2×C4C2×C4×D26912yes—
188C22C22×C4×D26911yescharacteristic
189C22#2257549811yescharacteristic
190C22#2257549911yescharacteristic
191C22#2257550011yescharacteristic
192C22#2257550011yescharacteristic
193C22#2257550011yescharacteristic
194C22#2257550111yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—5384no—
201C4—5384no—
202C4—10762no—
203C4—10762no—
204C2#3177108211yescharacteristic
205C2#3177108511yescharacteristic
206C2#3177108611yescharacteristic
207C2#3177134911yescharacteristic
208C2#3177135511yescharacteristic
209C2#3177135911yescharacteristic
210C2C269⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#382×C269C2
socle, prime radical, cosocleC23×C269C24
hypercenter#382D269
hypocenterC269#2382
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #22575445C4semidirect
105. C269#2382semidirect

Maximal subgroups

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

subgroupindex
C2×#225754452
#317705022
#317705002
#317704922
#317704902
#317704882
#317704862
#317704712
#382×C2692
#2382269