Finite Group Databasebeta

← #46781854

Subgroups — #46781854

Order 33664.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682662C211yesmaximal, characteristic, complemented
2#30682135C211yesmaximal, characteristic, complemented
3#30682130C211yesmaximal, characteristic
4#30681684C211yesmaximal, characteristic, complemented
5#30681670C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic, complemented
7#486×C263C211yesmaximal, characteristic, complemented
8C2×#16862364—21no—
9C2×#16862361—21no—
10#22554465—22no—
11#22554459—21no—
12#22554450—21no—
13Q8×Dic263—21no—
14C4×Dic526C2211yescharacteristic
15C4×D1052C2211yescharacteristic
16#22554428—21no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554391—21no—
20#22554391—21no—
21C4⋊Q8×C263C2211yescharacteristic
22#127×C263C2211yescharacteristic
23#102×C263—22no—
24C4×C8×C263C2211yescharacteristic
25C2×Dic526D411yescharacteristic
26C2×D1052D411yescharacteristic
27C2×C4×D263—21no—
28#16862364—42no—
29#16862361—42no—
30C2×C263⋊C8—21no—
31C2×C263⋊C8—21no—
32C4⋊Dic263—22no—
33C4⋊Dic263D411yescharacteristic
34C4⋊Dic263D411yescharacteristic
35Dic263⋊C4—21no—
36(C2×D263)⋊C4—22no—
37(C2×D263)⋊C4—22no—
38(C2×D263)⋊C4—21no—
39C4×Dic263—22no—
40C4×Dic263—21no—
41C2×Q8×C263—21no—
42C2×D4×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263—21no—
45C2×C8×C263—21no—
46C4⋊C4×C263—21no—
47C4⋊C4×C263D412yes—
48C42×C263C2311yescharacteristic
49C22×D263—21no—
50Dic526—21no—
51Dic526—21no—
52D1052—21no—
53D1052—21no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C4×D263—41no—
58C4×D263—41no—
59C263⋊C8—41no—
60C263⋊C8—41no—
61C23×C263—41no—
62Q8×C263—41no—
63Q8×C263—41no—
64D4×C263—42no—
65D4×C263—41no—
66D4×C263—41no—
67D4×C263—41no—
68D4×C263—41no—
69C2×C4×C263—22no—
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C8×C263—41no—
74C22×C263—81no—
75C22×C263—81no—
76C22×C263—81no—
77C22×C263#12011yescharacteristic
78C2×D263—41no—
79C2×D263—41no—
80C2×D263—41no—
81C4×C263—21no—
82C4×C263—42no—
83C4×C263#13511yescharacteristic
84C4×C263#13511yescharacteristic
85C4×C263AGL(1,ℤ/8)11yescharacteristic
86C4×C263AGL(1,ℤ/8)11yescharacteristic
87Dic263—41no—
88Dic263—41no—
89Dic263—41no—
90C2×C263—161no—
91C2×C263#44911yescharacteristic
92C2×C263#44911yescharacteristic
93C2×C263#45411yescharacteristic
94D263—81no—
95C263#162811yescharacteristic, complemented, Sylow
96#1628—2631nomaximal, Sylow
97#556—2631no—
98#486D26311yescharacteristic, complemented
99#460—2631no—
100#459—2631no—
101#332—2631no—
102Q8⋊C8—2631no—
103D4⋊C8—2631no—
104C2×SD16—5261no—
105C2×D8—5261no—
106C4⋊Q8C2×D26311yescharacteristic
107#127C2×D26311yescharacteristic
108#126—5262no—
109#124—5261no—
110C22⋊Q8—5261no—
111C4×Q8—2631no—
112C4×Q8—5261no—
113C4×D4—2631no—
114#117—5261no—
115C4⋊C8—2631no—
116C4⋊C8—2631no—
117#102—22no—
118#102—5261no—
119#102—5261no—
120C4×C8C2×D26311yescharacteristic
121C2×Q8—21no—
122C2×Q8—2631no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—2631no—
127C22×C4—5261no—
128SD16—10522no—
129D8—10522no—
130C2×C8—21no—
131C2×C8—5261no—
132C2×C8—5261no—
133C4⋊C4—21no—
134C4⋊C4—2631no—
135C4⋊C4—2631no—
136C4⋊C4—5262no—
137C4⋊C4—5261no—
138C4⋊C4C22⋊D26312yes—
139C22⋊C4—5262no—
140C22⋊C4—5262no—
141C22⋊C4—5261no—
142C42—5262no—
143C42—5261no—
144C42C22×D26311yescharacteristic
145C23—41no—
146C23—5261no—
147Q8—41no—
148Q8—41no—
149Q8—5261no—
150Q8—5261no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—5261no—
157D4—5261no—
158C2×C4—22no—
159C2×C4—5261no—
160C2×C4—5261no—
161C2×C4—5261no—
162C2×C4—10521no—
163C2×C4—10521no—
164C2×C4D4×D26311yescharacteristic
165C2×C4D4×D26311yescharacteristic
166C2×C4C2×C22⋊D26311yescharacteristic
167C8—41no—
168C8—10521no—
169C8—10521no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—10521no—
174C22—10521no—
175C22—10521no—
176C22#2255443811yescharacteristic
177C4—21no—
178C4—42no—
179C4—10521no—
180C4—10521no—
181C4—10521no—
182C4#2255448911yescharacteristic
183C4#2255449111yescharacteristic
184C4#2255449411yescharacteristic
185C4#2255449711yescharacteristic
186C2—161no—
187C2—21041no—
188C2#3068208011yescharacteristic
189C2#3068208211yescharacteristic
190C2#3068211011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#486×C263C2
socleC22×C263#120
prime radical#30682130C2
hypercenter#486D263
hypocenterC263#1628
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #30682662C2semidirect
2. #30682135C2semidirect
4. #30681684C2semidirect
5. #30681670C2semidirect
6. #30681667C2semidirect
7. #486×C263C2semidirect
95. C263#1628semidirect
98. #486D263semidirect

Maximal subgroups

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

subgroupindex
#306826622
#306821352
#306821302
#306816842
#306816702
#306816672
#486×C2632
#1628263