Finite Group Databasebeta

← #46822356

Subgroups — #46822356

Order 34432.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#31771226C212yesmaximal, complemented
2#31770896C212yesmaximal, complemented
3#31770891C212yesmaximal, complemented
4#31770863C211yesmaximal, characteristic, complemented
5#31770858C211yesmaximal, characteristic
6#31770834C212yesmaximal, complemented
7#31770828C212yesmaximal, complemented
8#31770821C212yesmaximal, complemented
9#424×C269C211yesmaximal, characteristic, complemented
10C2×Dic1076C2211yescharacteristic
11C2×#16864391C2212yes—
12C2×D2152C2211yescharacteristic
13#22575453C2212yes—
14#22575448—22no—
15#22575441C2212yes—
16#22575439—22no—
17#22575435—22no—
18#22575432C2212yes—
19#22575431—22no—
20#22575427C2212yes—
21C4×Dic538C2212yes—
22C4×D1076C2212yes—
23#22575385C2211yescharacteristic
24#22575385C2212yes—
25#22575385C2211yescharacteristic
26#22575378C2212yes—
27#22575378C2212yes—
28#22575375C2212yes—
29#22575375C2212yes—
30C2×M16×C269C2211yescharacteristic
31C22×C8×C269C2211yescharacteristic
32#117×C269C2211yescharacteristic
33C4⋊C8×C269C2212yes—
34C4⋊C8×C269C2212yes—
35C2×Dic538—22no—
36C2×Dic538C2312yes—
37C2×D1076C2312yes—
38C2×C22⋊D269—22no—
39C2×C4×D269—22no—
40Dic1076—41no—
41#16864391—42no—
42D2152—41no—
43C4⋊Dic269—22no—
44C4⋊Dic269C2312yes—
45C4⋊Dic269C2312yes—
46#16864381—22no—
47#16864381—22no—
48C22⋊Dic269—22no—
49#16864379—22no—
50#16864379—22no—
51#16864379—22no—
52#16864379—22no—
53C4×Dic269—22no—
54C22×C4×C269C2311yescharacteristic
55M16×C269—41no—
56C2×C8×C269—41no—
57C2×C8×C269C2311yescharacteristic
58C2×C8×C269C2312yes—
59C2×C8×C269C2311yescharacteristic
60C4⋊C4×C269D412yes—
61C22⋊C4×C269D411yescharacteristic
62C22⋊C4×C269D411yescharacteristic
63C42×C269C2312yes—
64C22×D269—22no—
65Dic538—22no—
66Dic538—22no—
67Dic538—82no—
68D1076—22no—
69D1076—22no—
70C22⋊D269—82no—
71C2×Dic269—22no—
72C2×Dic269—22no—
73C2×Dic269—22no—
74C4×D269—82no—
75C23×C269C2×D411yescharacteristic
76C2×C4×C269—21no—
77C2×C4×C269—21no—
78C2×C4×C269C2×D412yes—
79C2×C4×C269C2×D412yes—
80C2×C4×C269C2×D411yescharacteristic
81C2×C4×C269C2411yescharacteristic
82C8×C269—22no—
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—22no—
93C4×C269—22no—
94C4×C269H(5,𝔽2)11yescharacteristic
95C4×C2692−1+411yescharacteristic
96Dic269—42no—
97Dic269—42no—
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#470—2691no—
109#469—2691no—
110#465—2692no—
111#464—2692no—
112#463—2692no—
113#424D26911yescharacteristic, complemented
114C2×Q16—2691no—
115C2×SD16—2692no—
116C2×D8—2691no—
117C2×M16C2×D26911yescharacteristic
118C22×C8C2×D26911yescharacteristic
119C4⋊Q8—2692no—
120#126—5382no—
121#124—2692no—
122#124—5382no—
123#123—5382no—
124C22⋊Q8—2692no—
125C22⋊Q8—5382no—
126#121—2692no—
127C4×Q8—2692no—
128C4×D4—2692no—
129#117C2×D26911yescharacteristic
130#106—2692no—
131#106—2691no—
132#106—2691no—
133C4⋊C8C2×D26912yes—
134C4⋊C8C2×D26912yes—
135#103—2692no—
136#103—2692no—
137#102—2692no—
138#102—2692no—
139C2×Q8—2692no—
140C2×Q8—5382no—
141C2×D4—2692no—
142C2×D4—5382no—
143C22×C4—5382no—
144C22×C4C22×D26911yescharacteristic
145Q16—10761no—
146SD16—10762no—
147D8—10761no—
148M16—41no—
149C2×C8—41no—
150C2×C8C22×D26911yescharacteristic
151C2×C8C22×D26912yes—
152C2×C8C22×D26911yescharacteristic
153C4⋊C4—2692no—
154C4⋊C4—2692no—
155C4⋊C4—5382no—
156C4⋊C4—5382no—
157C4⋊C4—5382no—
158C4⋊C4D107612yes—
159C22⋊C4—5382no—
160C22⋊C4—5382no—
161C22⋊C4—5382no—
162C22⋊C4—5382no—
163C22⋊C4—5382no—
164C22⋊C4D107611yescharacteristic
165C22⋊C4D107611yescharacteristic
166C42—5382no—
167C42C22×D26912yes—
168C23—5382no—
169C23C2×D107611yescharacteristic
170Q8—5382no—
171Q8—5382no—
172Q8—21522no—
173D4—5382no—
174D4—5382no—
175D4—21522no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—5382no—
179C2×C4—5382no—
180C2×C4—5382no—
181C2×C4—21522no—
182C2×C4C2×D107612yes—
183C2×C4C2×D107612yes—
184C2×C4C2×D107611yescharacteristic
185C2×C4C23×D26911yescharacteristic
186C8—22no—
187C8—21no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—10762no—
192C22—10762no—
193C22—10762no—
194C22C22×D107611yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—10762no—
199C4—10762no—
200C4—10762no—
201C4#2257549811yescharacteristic
202C4#2257550111yescharacteristic
203C2—41no—
204C2—21522no—
205C2#3177118611yescharacteristic
206C2#3177141712yes—
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#424×C269C2
socleC22×C269C22×D4
prime radical#31770858C2
hypercenter#424D269
hypocenterC269#3263
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #31771226C2semidirect
2. #31770896C2semidirect
3. #31770891C2semidirect
4. #31770863C2semidirect
6. #31770834C2semidirect
7. #31770828C2semidirect
8. #31770821C2semidirect
9. #424×C269C2semidirect
103. C269#3263semidirect
113. #424D269semidirect

Maximal subgroups

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

subgroupindex
#317712262
#317708962
#317708912
#317708632
#317708582
#317708342
#317708282
#317708212
#424×C2692
#3263269