Finite Group Databasebeta

← #46822351

Subgroups — #46822351

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#31771228C212yesmaximal, complemented
2#31770894C212yesmaximal, complemented
3#31770888C212yesmaximal, complemented
4#31770858C211yesmaximal, characteristic
5#31770836C212yesmaximal, complemented
6#31770829C212yesmaximal, complemented
7#31770823C212yesmaximal, complemented
8#31770633C211yesmaximal, characteristic, complemented
9#470×C269C211yesmaximal, characteristic, complemented
10C2×#16864389C2212yes—
11C2×D2152C2211yescharacteristic
12C22×#14524130C2211yescharacteristic
13#22575452C2212yes—
14#22575448—22no—
15#22575442C2212yes—
16#22575439—22no—
17#22575435—22no—
18#22575433—22no—
19#22575427C2212yes—
20Q8×Dic269C2212yes—
21#22575415C2212yes—
22#22575412C2211yescharacteristic
23#22575385C2211yescharacteristic
24#22575384C2212yes—
25#22575382C2212yes—
26#22575382C2212yes—
27#22575377C2212yes—
28#22575375C2212yes—
29#22575373C2212yes—
30C2×Q16×C269C2211yescharacteristic
31C2×M16×C269C2211yescharacteristic
32C22⋊Q8×C269C2212yes—
33#106×C269C2211yescharacteristic
34#103×C269C2212yes—
35C2×Dic538—22no—
36C2×D1076C2312yes—
37C2×C22⋊D269—22no—
38C2×C4×D269—22no—
39#16864389—42no—
40D2152—41no—
41C2×#14524130—41no—
42C2×#14524130C2312yes—
43C4⋊Dic269—22no—
44C4⋊Dic269D412yes—
45C4⋊Dic269C2312yes—
46#16864381—22no—
47C22⋊Dic269D411yescharacteristic
48C22⋊Dic269D411yescharacteristic
49#16864379—22no—
50#16864379—22no—
51#16864379—22no—
52#16864379—22no—
53C4×Dic269—22no—
54C4×Dic269C2312yes—
55C2×Q8×C269C2312yes—
56C22×C4×C269C2311yescharacteristic
57Q16×C269—41no—
58M16×C269—41no—
59C2×C8×C269C2311yescharacteristic
60C2×C8×C269C2311yescharacteristic
61C4⋊C4×C269—22no—
62C4⋊C4×C269C2312yes—
63C22⋊C4×C269—22no—
64C22×D269—22no—
65Dic538—82no—
66D1076—22no—
67D1076—22no—
68C22⋊D269—82no—
69C2×Dic269—22no—
70C2×Dic269C2×D412yes—
71C2×Dic269C2×D412yes—
72C4×D269—82no—
73#14524130—22no—
74C23×C269C2×D411yescharacteristic
75Q8×C269—22no—
76Q8×C269—22no—
77C2×C4×C269—21no—
78C2×C4×C269—21no—
79C2×C4×C269—22no—
80C2×C4×C269—22no—
81C2×C4×C269C2×D411yescharacteristic
82C2×C4×C269C2411yescharacteristic
83C8×C269—21no—
84C8×C269—21no—
85C22×C269—21no—
86C22×C269—22no—
87C22×C269C22×D411yescharacteristic
88C2×D269—42no—
89C2×D269—42no—
90C2×D269—42no—
91C4×C269—21no—
92C4×C269—42no—
93C4×C269—42no—
94C4×C269H(5,𝔽2)11yescharacteristic
95C4×C2692−1+411yescharacteristic
96Dic269—22no—
97Dic269—22no—
98Dic269—42no—
99C2×C269—41no—
100C2×C269#53711yescharacteristic
101C2×C269#57712yes—
102D269—82no—
103C269#326311yescharacteristic, complemented, Sylow
104#3263—2691nomaximal, Sylow
105#542—2692no—
106#476—2692no—
107#475—2692no—
108#470D26911yescharacteristic, complemented
109#469—2691no—
110#465—2692no—
111#464—2692no—
112#463—2692no—
113#424—2691no—
114C2×Q16C2×D26911yescharacteristic
115C2×SD16—2692no—
116C2×D8—2691no—
117C2×M16C2×D26911yescharacteristic
118C22×C8—2691no—
119C4⋊Q8—2692no—
120#126—5382no—
121#124—2692no—
122#124—5382no—
123#123—5382no—
124C22⋊Q8—5382no—
125C22⋊Q8C2×D26912yes—
126#121—2692no—
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#103C2×D26912yes—
137#102—2692no—
138#102—2692no—
139C2×Q8—5382no—
140C2×Q8C22×D26912yes—
141C2×D4—2692no—
142C2×D4—5382no—
143C22×C4—5382no—
144C22×C4C22×D26911yescharacteristic
145Q16—41no—
146SD16—10762no—
147D8—10761no—
148M16—41no—
149C2×C8—2692no—
150C2×C8—10761no—
151C2×C8C22×D26911yescharacteristic
152C2×C8C22×D26911yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—2692no—
155C4⋊C4—2692no—
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—5382no—
169C23D4×D26911yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—21522no—
173D4—5382no—
174D4—5382no—
175D4—21522no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—2692no—
181C2×C4—2692no—
182C2×C4—5382no—
183C2×C4—21522no—
184C2×C4D4×D26911yescharacteristic
185C2×C4C23×D26911yescharacteristic
186C8—21no—
187C8—21no—
188C8—5382no—
189C22—22no—
190C22—21no—
191C22—10762no—
192C22—10762no—
193C22—10762no—
194C22C2×D4×D26911yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—5382no—
199C4—5382no—
200C4—10762no—
201C4#2257549811yescharacteristic
202C4#2257550011yescharacteristic
203C2—41no—
204C2—21522no—
205C2#3177118211yescharacteristic
206C2#3177141412yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#470×C269C2
socleC22×C269C22×D4
prime radical#31770858C2
hypercenter#470D269
hypocenterC269#3263
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #31771228C2semidirect
2. #31770894C2semidirect
3. #31770888C2semidirect
5. #31770836C2semidirect
6. #31770829C2semidirect
7. #31770823C2semidirect
8. #31770633C2semidirect
9. #470×C269C2semidirect
103. C269#3263semidirect
108. #470D269semidirect

Maximal subgroups

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

subgroupindex
#317712282
#317708942
#317708882
#317708582
#317708362
#317708292
#317708232
#317706332
#470×C2692
#3263269