Finite Group Databasebeta

← #46782211

Subgroups — #46782211

Order 33664.

182 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 51 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#30682310C211yesmaximal, characteristic, complemented
2#30682219C211yesmaximal, characteristic, complemented
3#30682130C211yesmaximal, characteristic
4#30682015C211yesmaximal, characteristic, complemented
5#30681690C211yesmaximal, characteristic, complemented
6#30681685C211yesmaximal, characteristic, complemented
7#331×C263C211yesmaximal, characteristic, complemented
8C2×#16862364—21no—
9C2×#16862364—21no—
10C2×#16862361—21no—
11C2×#16862359—21no—
12#22554470C2211yescharacteristic
13C4×D1052C2211yescharacteristic
14#22554404—21no—
15C4⋊(C263⋊C8)C2211yescharacteristic
16#22554392—21no—
17#22554391—21no—
18(C2×D263)⋊C8—21no—
19C4×C263⋊C8C2211yescharacteristic
20#127×C263C2211yescharacteristic
21C4⋊C8×C263C2211yescharacteristic
22C4⋊C8×C263C2211yescharacteristic
23C2×Dic526—21no—
24C2×D1052D411yescharacteristic
25C2×C4×D263—21no—
26#16862364—42no—
27#16862364—42no—
28#16862361—42no—
29#16862359—42no—
30C2×C263⋊C8—21no—
31C2×C263⋊C8D411yescharacteristic
32C2×C263⋊C8D411yescharacteristic
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263D411yescharacteristic
36(C2×D263)⋊C4—21no—
37C2×D4×C263—21no—
38C2×D4×C263—21no—
39C2×D4×C263—21no—
40C2×C8×C263—21no—
41C2×C8×C263—21no—
42C42×C263C2311yescharacteristic
43C22×D263—21no—
44Dic526—41no—
45Dic526—41no—
46D1052—21no—
47D1052—21no—
48C2×Dic263—21no—
49C2×Dic263—41no—
50C4×D263—41no—
51C4×D263—41no—
52C263⋊C8—21no—
53C263⋊C8—41no—
54C263⋊C8D812yescomplemented
55C23×C263—41no—
56D4×C263—41no—
57D4×C263—41no—
58D4×C263—41no—
59D4×C263—41no—
60D4×C263—81no—
61C2×C4×C263C2×D411yescharacteristic
62C2×C4×C263C2×D411yescharacteristic
63C2×C4×C263#4111yescharacteristic
64C8×C263—41no—
65C8×C263—41no—
66C22×C263—81no—
67C22×C263—81no—
68C22×C263—81no—
69C22×C263#12111yescharacteristic
70C2×D263—41no—
71C2×D263—41no—
72C2×D263—41no—
73C4×C263—21no—
74C4×C263C2×D811yescharacteristic
75C4×C263AGL(1,ℤ/8)11yescharacteristic
76C4×C263AGL(1,ℤ/8)11yescharacteristic
77C4×C263#13711yescharacteristic
78Dic263—41no—
79Dic263—81no—
80C2×C263—161no—
81C2×C263#45911yescharacteristic
82C2×C263#46811yescharacteristic
83C2×C263#47111yescharacteristic
84D263—81no—
85C263#168511yescharacteristic, complemented, Sylow
86#1685—2631nomaximal, Sylow
87#492—2631no—
88#474—2631no—
89#459—2631no—
90#436—2631no—
91#335—2631no—
92#332—2631no—
93#331D26311yescharacteristic, complemented
94C2×SD16—5261no—
95C2×SD16—5261no—
96C2×D8—5261no—
97C2×M16—5261no—
98C4⋊Q8—2631no—
99#127C2×D26311yescharacteristic
100C4×D4—2631no—
101#107—5261no—
102C4⋊C8—2631no—
103C4⋊C8C2×D26311yescharacteristic
104C4⋊C8C2×D26311yescharacteristic
105#102—5261no—
106#102—5261no—
107C22⋊C8—5261no—
108C4×C8—2631no—
109C2×Q8—5261no—
110C2×D4—21no—
111C2×D4—21no—
112C2×D4—21no—
113C2×D4—2631no—
114C22×C4—5261no—
115SD16—10522no—
116SD16—10522no—
117D8—10522no—
118M16—10522no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—2631no—
122C2×C8—2631no—
123C2×C8—5261no—
124C4⋊C4—2631no—
125C4⋊C4—5261no—
126C4⋊C4—5261no—
127C22⋊C4—5261no—
128C42C22×D26311yescharacteristic
129C23—41no—
130C23—5261no—
131Q8—10521no—
132Q8—10521no—
133D4—41no—
134D4—41no—
135D4—41no—
136D4—41no—
137D4—81no—
138D4—5261no—
139D4—5261no—
140C2×C4—5261no—
141C2×C4—10521no—
142C2×C4—10521no—
143C2×C4—10521no—
144C2×C4D4×D26311yescharacteristic
145C2×C4D4×D26311yescharacteristic
146C2×C4#1686237611yescharacteristic
147C8—41no—
148C8—41no—
149C8—2632no—
150C8—5261no—
151C8—10521no—
152C22—81no—
153C22—81no—
154C22—81no—
155C22—10521no—
156C22—10521no—
157C22—10521no—
158C22#2255444311yescharacteristic
159C4—21no—
160C4—10521no—
161C4—21041no—
162C4D8×D26311yescharacteristic
163C4#2255449411yescharacteristic
164C4#2255449711yescharacteristic
165C4#2255449911yescharacteristic
166C2—161no—
167C2—21041no—
168C2#3068213211yescharacteristic
169C2#3068218311yescharacteristic
170C2#3068220011yescharacteristic
subgroupG/H
centerC22#22554443
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#331×C263C2
socleC22×C263#121
prime radical#30682130C2
hypercenter#331D263
hypocenterC263#1685
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #30682310C2semidirect
2. #30682219C2semidirect
4. #30682015C2semidirect
5. #30681690C2semidirect
6. #30681685C2semidirect
7. #331×C263C2semidirect
54. C263⋊C8D8semidirect
85. C263#1685semidirect
93. #331D263semidirect

Maximal subgroups

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

subgroupindex
#306823102
#306822192
#306821302
#306820152
#306816902
#306816852
#331×C2632
#1685263