Finite Group Databasebeta

← #46822355

Subgroups — #46822355

Order 34432.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#31771222C212yesmaximal, complemented
2#31770893C212yesmaximal, complemented
3#31770889C212yesmaximal, complemented
4#31770863C211yesmaximal, characteristic, complemented
5#31770832C212yesmaximal, complemented
6#31770826C212yesmaximal, complemented
7#31770818C212yesmaximal, complemented
8#31770633C211yesmaximal, characteristic, complemented
9#469×C269C211yesmaximal, characteristic
10C2×Dic1076C2211yescharacteristic
11C2×#16864390C2212yes—
12C22×#14524130C2211yescharacteristic
13#22575452C2212yes—
14#22575446—22no—
15#22575440—22no—
16#22575440C2212yes—
17#22575434—22no—
18#22575432C2212yes—
19#22575430—22no—
20#22575418C2212yes—
21D4×Dic269C2212yes—
22#22575412C2211yescharacteristic
23#22575385C2211yescharacteristic
24#22575384C2212yes—
25#22575382C2212yes—
26#22575382C2212yes—
27#22575378C2212yes—
28#22575376C2212yes—
29#22575374C2212yes—
30C2×D8×C269C2211yescharacteristic
31C2×M16×C269C2211yescharacteristic
32#121×C269C2212yes—
33#106×C269C2211yescharacteristic
34#102×C269C2212yes—
35C2×Dic538—22no—
36C2×Dic538C2312yes—
37C22×Dic269—22no—
38Dic1076—41no—
39#16864390—42no—
40C2×#14524130—41no—
41C2×#14524130C2312yes—
42C4⋊Dic269D412yes—
43C4⋊Dic269C2312yes—
44#16864381—22no—
45#16864381—22no—
46#16864381—22no—
47C22⋊Dic269—22no—
48C22⋊Dic269—22no—
49C22⋊Dic269—22no—
50C22⋊Dic269—22no—
51C22⋊Dic269D411yescharacteristic
52C22⋊Dic269D411yescharacteristic
53C4×Dic269—22no—
54C4×Dic269C2312yes—
55C2×D4×C269—22no—
56C2×D4×C269C2312yes—
57C22×C4×C269C2311yescharacteristic
58D8×C269—41no—
59M16×C269—41no—
60C2×C8×C269C2311yescharacteristic
61C2×C8×C269C2311yescharacteristic
62C4⋊C4×C269C2312yes—
63C22⋊C4×C269—22no—
64Dic538—22no—
65Dic538—22no—
66Dic538—82no—
67C2×Dic269—22no—
68C2×Dic269—22no—
69C2×Dic269—82no—
70C2×Dic269C2×D412yes—
71C2×Dic269C2×D412yes—
72#14524130—22no—
73C23×C269—22no—
74C23×C269C2×D411yescharacteristic
75D4×C269—22no—
76D4×C269—22no—
77D4×C269—82no—
78C2×C4×C269—21no—
79C2×C4×C269—21no—
80C2×C4×C269—22no—
81C2×C4×C269C2×D411yescharacteristic
82C2×C4×C269C2411yescharacteristic
83C8×C269—21no—
84C8×C269—21no—
85C22×C269—21no—
86C22×C269—22no—
87C22×C269—42no—
88C22×C269—42no—
89C22×C269—42no—
90C22×C269C22×D411yescharacteristic
91C4×C269—21no—
92C4×C269—42no—
93C4×C269H(5,𝔽2)11yescharacteristic
94C4×C2692−1+411yescharacteristic
95Dic269—22no—
96Dic269—22no—
97Dic269—42no—
98Dic269—42no—
99C2×C269—41no—
100C2×C269—82no—
101C2×C269#53711yescharacteristic
102C2×C269#57712yes—
103C269#326311yescharacteristic, complemented, Sylow
104#3263—2691nomaximal, Sylow
105#542—2692no—
106#476—2692no—
107#475—2692no—
108#470—2691no—
109#469D26911yescharacteristic
110#465—2692no—
111#464—2692no—
112#463—2692no—
113#424—2691no—
114C2×Q16—2691no—
115C2×SD16—2692no—
116C2×D8C2×D26911yescharacteristic
117C2×M16C2×D26911yescharacteristic
118C22×C8—2691no—
119C4⋊Q8—2692no—
120#126—5382no—
121#124—2692no—
122#124—5382no—
123#123—5382no—
124C22⋊Q8—2692no—
125C22⋊Q8—5382no—
126#121C2×D26912yes—
127C4×Q8—2692no—
128C4×D4—2692no—
129#117—2691no—
130#106—2691no—
131#106—2692no—
132#106C2×D26911yescharacteristic
133C4⋊C8—2692no—
134C4⋊C8—2692no—
135#103—2692no—
136#103—2692no—
137#102—2692no—
138#102C2×D26912yes—
139C2×Q8—2692no—
140C2×Q8—5382no—
141C2×D4—22no—
142C2×D4C22×D26912yes—
143C22×C4—5382no—
144C22×C4C22×D26911yescharacteristic
145Q16—10761no—
146SD16—10762no—
147D8—41no—
148M16—41no—
149C2×C8—2692no—
150C2×C8—10761no—
151C2×C8C22×D26911yescharacteristic
152C2×C8C22×D26911yescharacteristic
153C4⋊C4—2692no—
154C4⋊C4—2692no—
155C4⋊C4—5382no—
156C4⋊C4—5382no—
157C4⋊C4—5382no—
158C4⋊C4C22×D26912yes—
159C22⋊C4—22no—
160C22⋊C4—2691no—
161C22⋊C4—2691no—
162C22⋊C4—5382no—
163C22⋊C4—5382no—
164C22⋊C4—5382no—
165C22⋊C4—5382no—
166C42—2692no—
167C42—5382no—
168C23—22no—
169C23D4×D26911yescharacteristic
170Q8—5382no—
171Q8—5382no—
172Q8—21522no—
173D4—22no—
174D4—22no—
175D4—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—2692no—
180C2×C4—2692no—
181C2×C4—5382no—
182C2×C4—5382no—
183C2×C4—21522no—
184C2×C4D4×D26911yescharacteristic
185C2×C4C23×D26911yescharacteristic
186C8—21no—
187C8—21no—
188C8—5382no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D26911yescharacteristic
195C4—21no—
196C4—42no—
197C4—5382no—
198C4—5382no—
199C4—10762no—
200C4—10762no—
201C4#2257549811yescharacteristic
202C4#2257550011yescharacteristic
203C2—41no—
204C2—82no—
205C2#3177118211yescharacteristic
206C2#3177141512yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting, prime radical#469×C269C2
socleC22×C269C22×D4
hypercenter#469D269
hypocenterC269#3263
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #31771222C2semidirect
2. #31770893C2semidirect
3. #31770889C2semidirect
4. #31770863C2semidirect
5. #31770832C2semidirect
6. #31770826C2semidirect
7. #31770818C2semidirect
8. #31770633C2semidirect
103. C269#3263semidirect

Maximal subgroups

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

subgroupindex
#317712222
#317708932
#317708892
#317708632
#317708322
#317708262
#317708182
#317706332
#469×C2692
#3263269