Finite Group Databasebeta

← #46810182

Subgroups — #46810182

Order 34432.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#31771359C211yesmaximal, characteristic, complemented
2#31770992C211yesmaximal, characteristic
3#31770969C211yesmaximal, characteristic, complemented
4#31770347C211yesmaximal, characteristic, complemented
5#31770346C211yesmaximal, characteristic, complemented
6#31770344C211yesmaximal, characteristic, complemented
7#490×C269C211yesmaximal, characteristic, complemented
8C2×#16864390—21no—
9C2×#16864387—21no—
10#22575452—21no—
11#22575448—21no—
12#22575448—21no—
13#22575445C2211yescharacteristic
14#22575441C2211yescharacteristic
15#22575438—21no—
16#22575433—21no—
17#22575431—21no—
18#22575374—21no—
19#22575374—21no—
20#22575364C2211yescharacteristic
21#22575364C2211yescharacteristic
22#127×C269C2211yescharacteristic
23#125×C269C2211yescharacteristic
24#102×C269—21no—
25#102×C269—21no—
26#97×C269C2211yescharacteristic
27C2×Dic538—21no—
28C2×Dic538D411yescharacteristic
29C2×D1076D411yescharacteristic
30C2×C4×D269—21no—
31#16864390—42no—
32#16864387—42no—
33C2×#14524130—21no—
34C2×#14524130—21no—
35C4⋊Dic269—21no—
36C4⋊Dic269D411yescharacteristic
37C4⋊Dic269D411yescharacteristic
38#16864381—21no—
39#16864381—21no—
40#16864381—21no—
41#16864379—21no—
42#16864379—21no—
43#16864379—21no—
44#16864379—21no—
45#16864379—21no—
46C4×Dic269—21no—
47C2×D4×C269—21no—
48C2×D4×C269—21no—
49C2×D4×C269—21no—
50C2×C8×C269—21no—
51C4⋊C4×C269—21no—
52C4⋊C4×C269—21no—
53C4⋊C4×C269D411yescharacteristic
54C4⋊C4×C269D411yescharacteristic
55C42×C269C2311yescharacteristic
56C22×D269—21no—
57Dic538—41no—
58Dic538—81no—
59D1076—41no—
60C2×Dic269—21no—
61C2×Dic269—21no—
62C2×Dic269—21no—
63C4×D269—81no—
64#14524130—22no—
65#14524130—41no—
66C23×C269—41no—
67D4×C269—42no—
68D4×C269—42no—
69D4×C269—41no—
70D4×C269—41no—
71C2×C4×C269—21no—
72C2×C4×C269—21no—
73C2×C4×C269C2×D411yescharacteristic
74C2×C4×C269C2×D411yescharacteristic
75C2×C4×C269C2×D411yescharacteristic
76C8×C269—41no—
77C22×C269—81no—
78C22×C269—81no—
79C22×C269—81no—
80C22×C269#12011yescharacteristic
81C2×D269—41no—
82C2×D269—41no—
83C2×D269—41no—
84C4×C269—21no—
85C4×C269—21no—
86C4×C269—21no—
87C4×C269—41no—
88C4×C269—41no—
89Dic269—41no—
90Dic269—41no—
91Dic269—41no—
92C2×C269—161no—
93C2×C269#45311yescharacteristic
94C2×C269#45411yescharacteristic
95C2×C269#45411yescharacteristic
96D269—81no—
97C269#165711yescharacteristic, complemented, Sylow
98#1657—2691nomaximal, Sylow
99#563—2691no—
100#496—2691no—
101#490—2691no—
102#490D26911yescharacteristic, complemented
103#330—2691no—
104#330—2691no—
105#329—2691no—
106C2×SD16—5381no—
107C2×D8—5381no—
108C4⋊Q8—5381no—
109#127C2×D26911yescharacteristic
110#126—5381no—
111#126—5381no—
112#125—2691no—
113#125C2×D26911yescharacteristic
114#124—2691no—
115#123—5381no—
116C22⋊Q8—5381no—
117C22⋊Q8—5381no—
118#102—21no—
119#102—21no—
120#102—5381no—
121#102—5381no—
122#97—2691no—
123#97—2691no—
124#97C2×D26911yescharacteristic
125C2×Q8—2691no—
126C2×Q8—5381no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—2691no—
131C22×C4—5381no—
132SD16—10762no—
133D8—10762no—
134C2×C8—21no—
135C2×C8—5381no—
136C2×C8—5381no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—2691no—
140C4⋊C4—2691no—
141C4⋊C4—5381no—
142C4⋊C4—5381no—
143C4⋊C4—5381no—
144C4⋊C4—5381no—
145C4⋊C4C22⋊D26911yescharacteristic
146C4⋊C4C22⋊D26911yescharacteristic
147C22⋊C4—5381no—
148C22⋊C4—5381no—
149C22⋊C4—5381no—
150C22⋊C4—5381no—
151C22⋊C4—5381no—
152C42—5381no—
153C42C22×D26911yescharacteristic
154C23—41no—
155C23—5381no—
156Q8—10761no—
157Q8—21521no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—10761no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—5381no—
166C2×C4—5381no—
167C2×C4—5381no—
168C2×C4—21521no—
169C2×C4D4×D26911yescharacteristic
170C2×C4D4×D26911yescharacteristic
171C2×C4C2×C22⋊D26911yescharacteristic
172C8—41no—
173C8—5382no—
174C8—10761no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—10761no—
179C22—10761no—
180C22—10761no—
181C22#2257542111yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—10761no—
188C4—10761no—
189C4—10761no—
190C2—161no—
191C2—21521no—
192C2#3177077111yescharacteristic
193C2#3177077611yescharacteristic
194C2#3177077711yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#490×C269C2
socleC22×C269#120
prime radical#31770992C2
hypercenter#490D269
hypocenterC269#1657
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #31771359C2semidirect
3. #31770969C2semidirect
4. #31770347C2semidirect
5. #31770346C2semidirect
6. #31770344C2semidirect
7. #490×C269C2semidirect
97. C269#1657semidirect
102. #490D269semidirect

Maximal subgroups

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

subgroupindex
#317713592
#317709922
#317709692
#317703472
#317703462
#317703442
#490×C2692
#1657269