Finite Group Databasebeta

← #46782248

Subgroups — #46782248

Order 33664.

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

normal subgroups only

This group has 160 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#30682334C211yesmaximal, characteristic, complemented
2#30682143C211yesmaximal, characteristic
3#30682016C211yesmaximal, characteristic
4#30681690C211yesmaximal, characteristic, complemented
5#30681687C211yesmaximal, characteristic, complemented
6#30681685C211yesmaximal, characteristic, complemented
7#476×C263C211yesmaximal, characteristic
8C2×#16862364—21no—
9C2×#16862360—21no—
10#22554470C2211yescharacteristic
11#22554401—21no—
12#22554401—21no—
13C4⋊(C263⋊C8)C2211yescharacteristic
14C4⋊(C263⋊C8)C2211yescharacteristic
15#22554393—21no—
16C22⋊(C263⋊C8)—21no—
17C4×C263⋊C8C2211yescharacteristic
18C4⋊Q8×C263C2211yescharacteristic
19C4×D4×C263C2211yescharacteristic
20#106×C263—21no—
21C4⋊C8×C263C2211yescharacteristic
22#102×C263—21no—
23C2×Dic526—21no—
24#16862364—42no—
25#16862360—42no—
26C2×C263⋊C8—21no—
27C2×C263⋊C8—21no—
28C2×C263⋊C8D411yescharacteristic
29C2×C263⋊C8D411yescharacteristic
30C4⋊Dic263—21no—
31C4⋊Dic263—21no—
32C2×Q8×C263—21no—
33C2×D4×C263D411yescharacteristic
34C22×C4×C263—21no—
35C2×C8×C263—21no—
36C4⋊C4×C263—21no—
37C4⋊C4×C263—21no—
38C4⋊C4×C263D411yescharacteristic
39C22⋊C4×C263—21no—
40C42×C263C2311yescharacteristic
41Dic526—41no—
42Dic526—41no—
43C2×Dic263—41no—
44C263⋊C8—21no—
45C263⋊C8—41no—
46C263⋊C8—41no—
47C263⋊C8SD1612yescomplemented
48C23×C263—21no—
49Q8×C263—81no—
50D4×C263—21no—
51D4×C263—21no—
52C2×C4×C263—21no—
53C2×C4×C263—41no—
54C2×C4×C263—41no—
55C2×C4×C263—41no—
56C2×C4×C263C2×D411yescharacteristic
57C2×C4×C263C2×D411yescharacteristic
58C2×C4×C263#4111yescharacteristic
59C8×C263—41no—
60C22×C263—41no—
61C22×C263—41no—
62C22×C263—41no—
63C22×C263#12111yescharacteristic
64C4×C263—21no—
65C4×C263—41no—
66C4×C263—81no—
67C4×C263C2×SD1611yescharacteristic
68C4×C263AGL(1,ℤ/8)11yescharacteristic
69C4×C263#13711yescharacteristic
70C4×C263#13711yescharacteristic
71Dic263—81no—
72C2×C263—81no—
73C2×C263#46111yescharacteristic
74C2×C263#46811yescharacteristic
75C2×C263#47111yescharacteristic
76C263#169111yescharacteristic, complemented, Sylow
77#1691—2631nomaximal, Sylow
78#498—2631no—
79#476D26311yescharacteristic
80#461—2631no—
81#436—2631no—
82#335—2631no—
83#333—2631no—
84#332—2631no—
85C2×SD16—5261no—
86C2×M16—5261no—
87C4⋊Q8—2631no—
88C4⋊Q8C2×D26311yescharacteristic
89C4×D4C2×D26311yescharacteristic
90#106—21no—
91#106—5261no—
92#106—5261no—
93C4⋊C8—2631no—
94C4⋊C8—2631no—
95C4⋊C8C2×D26311yescharacteristic
96#103—5261no—
97#102—21no—
98C22⋊C8—5261no—
99C4×C8—2631no—
100C2×Q8—21no—
101C2×Q8—5261no—
102C2×D4C22⋊D26311yescharacteristic
103C22×C4—21no—
104SD16—10522no—
105M16—10522no—
106C2×C8—21no—
107C2×C8—2631no—
108C2×C8—2631no—
109C2×C8—5261no—
110C2×C8—5261no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—5261no—
114C4⋊C4—5261no—
115C4⋊C4C22⋊D26311yescharacteristic
116C22⋊C4—21no—
117C42C22×D26311yescharacteristic
118C23—21no—
119Q8—81no—
120Q8—10521no—
121Q8—10521no—
122D4—21no—
123D4—21no—
124C2×C4—21no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—10521no—
129C2×C4D4×D26311yescharacteristic
130C2×C4C2×C22⋊D26311yescharacteristic
131C2×C4#1686237511yescharacteristic
132C8—41no—
133C8—2632no—
134C8—5261no—
135C8—10521no—
136C8—10521no—
137C22—41no—
138C22—41no—
139C22—41no—
140C22#2255444211yescharacteristic
141C4—21no—
142C4—41no—
143C4—81no—
144C4—21041no—
145C4SD16×D26311yescharacteristic
146C4#2255449511yescharacteristic
147C4#2255449911yescharacteristic
148C4#2255450111yescharacteristic
149C2—81no—
150C2#3068214111yescharacteristic
151C2#3068218611yescharacteristic
152C2#3068219911yescharacteristic
subgroupG/H
centerC22#22554442
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#476×C263C2
socleC22×C263#121
prime radicalC2×D4×C263D4
hypercenter#476D263
hypocenterC263#1691
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #30682334C2semidirect
4. #30681690C2semidirect
5. #30681687C2semidirect
6. #30681685C2semidirect
47. C263⋊C8SD16semidirect
76. C263#1691semidirect

Maximal subgroups

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

subgroupindex
#306823342
#306821432
#306820162
#306816902
#306816872
#306816852
#476×C2632
#1691263