Finite Group Databasebeta

← #46781855

Subgroups — #46781855

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#30682658C211yesmaximal, characteristic, complemented
2#30682284C211yesmaximal, characteristic, complemented
3#30682135C211yesmaximal, characteristic, complemented
4#30681685C211yesmaximal, characteristic, complemented
5#30681668C211yesmaximal, characteristic, complemented
6D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
7#459×C263C211yesmaximal, characteristic
8C2×#16862364—21no—
9#22554470C2211yescharacteristic
10#22554463—22no—
11#22554457—21no—
12#22554449—21no—
13C4×Dic526C2211yescharacteristic
14#22554435—21no—
15#22554429—21no—
16C4⋊(C263⋊C8)C2211yescharacteristic
17#22554391—21no—
18#22554391—22no—
19C4×C263⋊C8C2211yescharacteristic
20C2×D8×C263—21no—
21#127×C263C2211yescharacteristic
22C4×D4×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24#102×C263—21no—
25C2×Dic526—21no—
26C2×Dic526D411yescharacteristic
27#16862364—42no—
28C2×C263⋊C8—21no—
29C2×C263⋊C8—21no—
30C4⋊Dic263—21no—
31C4⋊Dic263D411yescharacteristic
32C4⋊Dic263D412yes—
33Dic263⋊C4—22no—
34Dic263⋊C4—21no—
35C22⋊Dic263—22no—
36C22⋊Dic263—22no—
37C4×Dic263—22no—
38C4×Dic263—21no—
39C2×D4×C263—21no—
40C2×D4×C263—21no—
41C2×D4×C263—21no—
42C2×D4×C263D411yescharacteristic
43C22×C4×C263—21no—
44D8×C263—42no—
45C2×C8×C263—21no—
46C4⋊C4×C263D411yescharacteristic
47C22⋊C4×C263—21no—
48C42×C263C2311yescharacteristic
49Dic526—21no—
50Dic526—21no—
51Dic526—41no—
52Dic526—41no—
53C2×Dic263—21no—
54C2×Dic263—21no—
55C2×Dic263—22no—
56C263⋊C8—41no—
57C263⋊C8—41no—
58C23×C263—21no—
59C23×C263—41no—
60D4×C263—21no—
61D4×C263—21no—
62D4×C263—42no—
63D4×C263—41no—
64D4×C263—41no—
65D4×C263—41no—
66D4×C263—41no—
67C2×C4×C263—21no—
68C2×C4×C263—41no—
69C2×C4×C263—41no—
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C8×C263—41no—
74C22×C263—41no—
75C22×C263—41no—
76C22×C263—41no—
77C22×C263—81no—
78C22×C263—81no—
79C22×C263—81no—
80C22×C263#12011yescharacteristic
81C4×C263—21no—
82C4×C263—41no—
83C4×C263#13511yescharacteristic
84C4×C263#13511yescharacteristic
85C4×C263AGL(1,ℤ/8)11yescharacteristic
86C4×C263AGL(1,ℤ/8)11yescharacteristic
87Dic263—41no—
88Dic263—42no—
89Dic263—41no—
90C2×C263—81no—
91C2×C263—161no—
92C2×C263#44911yescharacteristic
93C2×C263#44911yescharacteristic
94C2×C263#45411yescharacteristic
95C263#162811yescharacteristic, complemented, Sylow
96#1628—2631nomaximal, Sylow
97#556—2631no—
98#486—2631no—
99#460—2631no—
100#459D26311yescharacteristic
101#332—2631no—
102Q8⋊C8—2631no—
103D4⋊C8—2631no—
104C2×SD16—5261no—
105C2×D8—21no—
106C4⋊Q8—2631no—
107#127C2×D26311yescharacteristic
108#126—5262no—
109#124—5261no—
110C22⋊Q8—5261no—
111C4×Q8—2631no—
112C4×Q8—5261no—
113C4×D4C2×D26311yescharacteristic
114#117—5261no—
115C4⋊C8—2631no—
116C4⋊C8C2×D26311yescharacteristic
117#102—21no—
118#102—5261no—
119#102—5262no—
120C4×C8—2631no—
121C2×Q8—2631no—
122C2×Q8—5261no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D26311yescharacteristic
127C22×C4—21no—
128SD16—10522no—
129D8—42no—
130C2×C8—21no—
131C2×C8—5261no—
132C2×C8—5261no—
133C4⋊C4—2631no—
134C4⋊C4—2632no—
135C4⋊C4—5262no—
136C4⋊C4—5261no—
137C4⋊C4—5261no—
138C4⋊C4C22⋊D26311yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5262no—
141C22⋊C4—5262no—
142C42—5262no—
143C42—5261no—
144C42C22×D26311yescharacteristic
145C23—21no—
146C23—41no—
147Q8—5261no—
148Q8—5261no—
149Q8—10521no—
150Q8—10521no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—5261no—
162C2×C4—5262no—
163C2×C4—5261no—
164C2×C4D4×D26311yescharacteristic
165C2×C4D4×D26311yescharacteristic
166C2×C4C2×C22⋊D26311yescharacteristic
167C8—41no—
168C8—10521no—
169C8—10521no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#2255443811yescharacteristic
177C4—21no—
178C4—41no—
179C4—10521no—
180C4—10522no—
181C4—10521no—
182C4#2255448911yescharacteristic
183C4#2255449011yescharacteristic
184C4#2255449411yescharacteristic
185C4#2255449611yescharacteristic
186C2—81no—
187C2—161no—
188C2#3068208011yescharacteristic
189C2#3068208111yescharacteristic
190C2#3068210911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting, prime radical#459×C263C2
socleC22×C263#120
hypercenter#459D263
hypocenterC263#1628
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #30682658C2semidirect
2. #30682284C2semidirect
3. #30682135C2semidirect
4. #30681685C2semidirect
5. #30681668C2semidirect
6. D4⋊(C263⋊C8)C2semidirect
95. C263#1628semidirect

Maximal subgroups

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

subgroupindex
#306826582
#306822842
#306821352
#306816852
#306816682
D4⋊(C263⋊C8)2
#459×C2632
#1628263