Finite Group Databasebeta

← #46809954

Subgroups — #46809954

Order 34432.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#31771316C211yesmaximal, characteristic, complemented
2#31770802C211yesmaximal, characteristic, complemented
3#31770797C211yesmaximal, characteristic
4#31770354C211yesmaximal, characteristic, complemented
5#31770337C211yesmaximal, characteristic, complemented
6#31770334C211yesmaximal, characteristic, complemented
7#492×C269C211yesmaximal, characteristic, complemented
8C2×#16864390—21no—
9C2×#16864387—21no—
10#22575444—21no—
11#22575433—21no—
12#22575429—22no—
13C4×Dic538C2211yescharacteristic
14C4×D1076C2211yescharacteristic
15#22575415—21no—
16C4⋊C4×D269—21no—
17C4⋊#14524130C2211yescharacteristic
18C4⋊#14524130C2211yescharacteristic
19#22575374—21no—
20#22575374—21no—
21C2×SD16×C269—22no—
22C4⋊Q8×C269C2211yescharacteristic
23#127×C269C2211yescharacteristic
24C4×C8×C269C2211yescharacteristic
25C2×Dic538D411yescharacteristic
26C2×D1076D411yescharacteristic
27C2×C4×D269—22no—
28C2×C4×D269—21no—
29#16864390—42no—
30#16864387—42no—
31C2×#14524130—21no—
32C2×#14524130—21no—
33C4⋊Dic269—22no—
34C4⋊Dic269D411yescharacteristic
35C4⋊Dic269D411yescharacteristic
36#16864381—22no—
37#16864381—21no—
38#16864379—22no—
39#16864379—21no—
40C4×Dic269—21no—
41C2×Q8×C269D412yes—
42C2×D4×C269—21no—
43C2×D4×C269—21no—
44C2×D4×C269—21no—
45SD16×C269—44no—
46C2×C8×C269—21no—
47C4⋊C4×C269—21no—
48C4⋊C4×C269—21no—
49C42×C269C2311yescharacteristic
50C22×D269—21no—
51Dic538—21no—
52Dic538—21no—
53D1076—21no—
54D1076SD1612yescomplemented
55C2×Dic269—21no—
56C2×Dic269—21no—
57C2×Dic269—21no—
58C4×D269—41no—
59C4×D269—41no—
60C4×D269—82no—
61#14524130—41no—
62#14524130—41no—
63C23×C269—41no—
64Q8×C269—42no—
65D4×C269—42no—
66D4×C269—41no—
67D4×C269—41no—
68D4×C269—41no—
69D4×C269—41no—
70C2×C4×C269—22no—
71C2×C4×C269C2×D411yescharacteristic
72C2×C4×C269C2×D411yescharacteristic
73C2×C4×C269C2×D411yescharacteristic
74C8×C269—22no—
75C22×C269—81no—
76C22×C269—81no—
77C22×C269—81no—
78C22×C269#12011yescharacteristic
79C2×D269—22no—
80C2×D269—41no—
81C2×D269—41no—
82C4×C269—21no—
83C4×C269—42no—
84C4×C269C2×SD1611yescharacteristic
85C4×C269#13511yescharacteristic
86C4×C269AGL(1,ℤ/8)11yescharacteristic
87C4×C269#13711yescharacteristic
88Dic269—41no—
89Dic269—41no—
90Dic269—41no—
91C2×C269—161no—
92C2×C269#44811yescharacteristic
93C2×C269#44911yescharacteristic
94C2×C269#45311yescharacteristic
95D269—42no—
96C269#162211yescharacteristic, complemented, Sylow
97#1622—2691nomaximal, Sylow
98#554—2691no—
99#492D26911yescharacteristic, complemented
100#460—2691no—
101#459—2691no—
102#333—2691no—
103Q8⋊C8—2691no—
104D4⋊C8—2691no—
105C2×SD16—22no—
106C2×SD16—5381no—
107C2×D8—5381no—
108C4⋊Q8C2×D26911yescharacteristic
109#127C2×D26911yescharacteristic
110#125—5381no—
111C22⋊Q8—5381no—
112C22⋊Q8—5382no—
113C4×Q8—2691no—
114C4×D4—2691no—
115C4×D4—5381no—
116C2×C4⋊C4—5381no—
117C4⋊C8—2691no—
118C4⋊C8—2691no—
119#102—5381no—
120#102—5381no—
121C4×C8C2×D26911yescharacteristic
122C2×Q8—2691no—
123C2×Q8C22⋊D26912yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—2691no—
128C22×C4—5382no—
129C22×C4—5381no—
130SD16—44no—
131SD16—10762no—
132D8—10762no—
133C2×C8—21no—
134C2×C8—5381no—
135C2×C8—5381no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2691no—
139C4⋊C4—2691no—
140C4⋊C4—5382no—
141C4⋊C4—5382no—
142C4⋊C4—5381no—
143C22⋊C4—5382no—
144C22⋊C4—5381no—
145C42—5381no—
146C42C22×D26911yescharacteristic
147C23—41no—
148C23—5381no—
149Q8—42no—
150Q8—5381no—
151Q8—5381no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—2692no—
158D4—5381no—
159C2×C4—22no—
160C2×C4—5381no—
161C2×C4—5381no—
162C2×C4—5381no—
163C2×C4—10761no—
164C2×C4—10761no—
165C2×C4—21522no—
166C2×C4D4×D26911yescharacteristic
167C2×C4D4×D26911yescharacteristic
168C2×C4C2×C22⋊D26911yescharacteristic
169C8—22no—
170C8—10761no—
171C8—10761no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—5382no—
176C22—10761no—
177C22—10761no—
178C22#2257542111yescharacteristic
179C4—21no—
180C4—42no—
181C4—10761no—
182C4—10761no—
183C4—10761no—
184C4SD16×D26911yescharacteristic
185C4#2257547411yescharacteristic
186C4#2257548011yescharacteristic
187C4#2257548211yescharacteristic
188C2—161no—
189C2—10762no—
190C2#3177074211yescharacteristic
191C2#3177074911yescharacteristic
192C2#3177077211yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#492×C269C2
socleC22×C269#120
prime radical#31770797C2
hypercenter#492D269
hypocenterC269#1622
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #31771316C2semidirect
2. #31770802C2semidirect
4. #31770354C2semidirect
5. #31770337C2semidirect
6. #31770334C2semidirect
7. #492×C269C2semidirect
54. D1076SD16semidirect
96. C269#1622semidirect
99. #492D269semidirect

Maximal subgroups

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

subgroupindex
#317713162
#317708022
#317707972
#317703542
#317703372
#317703342
#492×C2692
#1622269