Finite Group Databasebeta

← #2082×C263 #46779051

Subgroups — #2082×C263 #46779051

Order 33664.

184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 72 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#430×C263C211yesmaximal, characteristic
2#419×C263C211yesmaximal, characteristic
3#419×C263C211yesmaximal, characteristic
4C2×#101×C263C211yesmaximal, characteristic
5#344×C263C211yesmaximal, characteristic
6#344×C263C211yesmaximal, characteristic
7H(3,ℤ/4)×C263C211yesmaximal, characteristic
8C22×Q8×C263C2211yescharacteristic
9C2×M16×C263C2211yescharacteristic
10C2×M16×C263C2211yescharacteristic
11C2×M16×C263C2211yescharacteristic
12C2×M16×C263C2211yescharacteristic
13#117×C263C2211yescharacteristic
14#117×C263C2211yescharacteristic
15#108×C263—22no—
16#103×C263—22no—
17#103×C263—22no—
18#101×C263—22no—
19C2×Q8×C263—21no—
20C2×Q8×C263—21no—
21C2×Q8×C263—21no—
22C2×Q8×C263—21no—
23C2×Q8×C263—21no—
24C2×Q8×C263D412yes—
25C22×C4×C263—21no—
26C22×C4×C263C2311yescharacteristic
27M16×C263—21no—
28M16×C263—21no—
29M16×C263—21no—
30M16×C263—21no—
31M16×C263—21no—
32M16×C263—21no—
33M16×C263—21no—
34M16×C263—21no—
35C2×C8×C263—21no—
36C2×C8×C263—21no—
37C2×C8×C263—21no—
38C2×C8×C263D412yes—
39C4⋊C4×C263—21no—
40C4⋊C4×C263—21no—
41C22⋊C4×C263—21no—
42C22⋊C4×C263—21no—
43C42×C263—21no—
44C42×C263—21no—
45C23×C263#4111yescharacteristic
46Q8×C263—22no—
47Q8×C263—22no—
48Q8×C263—41no—
49Q8×C263—41no—
50C2×C4×C263—22no—
51C2×C4×C263—41no—
52C2×C4×C263—41no—
53C2×C4×C263—41no—
54C2×C4×C263—41no—
55C2×C4×C263C2×D411yescharacteristic
56C2×C4×C263C2×D411yescharacteristic
57C2×C4×C263#4111yescharacteristic
58C2×C4×C263#4111yescharacteristic
59C2×C4×C263#4111yescharacteristic
60C2×C4×C263#4111yescharacteristic
61C8×C263—22no—
62C8×C263—41no—
63C8×C263—41no—
64C8×C263—41no—
65C22×C263—41no—
66C22×C263#12311yescharacteristic
67C22×C263#12411yescharacteristic
68C22×C263#12611yescharacteristic
69C4×C263—42no—
70C4×C263—81no—
71C4×C263—81no—
72C4×C263#12111yescharacteristic
73C4×C263#12311yescharacteristic
74C4×C263#12311yescharacteristic
75C4×C263#12611yescharacteristic
76C2×C263—21no—
77C2×C263—21no—
78C2×C263—21no—
79C2×C263#39711yescharacteristic
80C263#208211yescharacteristic, direct product factor, Sylow
81#2082C26311yesmaximal, characteristic, direct product factor, Sylow
82#430C2×C26311yescharacteristic
83#419C2×C26311yescharacteristic
84#419C2×C26311yescharacteristic
85C2×#101C2×C26311yescharacteristic
86#344C2×C26311yescharacteristic
87#344C2×C26311yescharacteristic
88H(3,ℤ/4)C2×C26311yescharacteristic
89C22×Q8C22×C26311yescharacteristic
90C2×M16C22×C26311yescharacteristic
91C2×M16C22×C26311yescharacteristic
92C2×M16C22×C26311yescharacteristic
93C2×M16C22×C26311yescharacteristic
94#117C22×C26311yescharacteristic
95#117C22×C26311yescharacteristic
96#108—22no—
97#103—22no—
98#103—22no—
99#101—22no—
100C2×Q8—21no—
101C2×Q8—21no—
102C2×Q8—21no—
103C2×Q8—21no—
104C2×Q8—21no—
105C2×Q8D4×C26312yes—
106C22×C4—21no—
107C22×C4C23×C26311yescharacteristic
108M16—21no—
109M16—21no—
110M16—21no—
111M16—21no—
112M16—21no—
113M16—21no—
114M16—21no—
115M16—21no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8D4×C26312yes—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C22⋊C4—21no—
123C22⋊C4—21no—
124C42—21no—
125C42—21no—
126C23#41×C26311yescharacteristic
127Q8—22no—
128Q8—22no—
129Q8—41no—
130Q8—41no—
131C2×C4—22no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4C2×D4×C26311yescharacteristic
137C2×C4C2×D4×C26311yescharacteristic
138C2×C4#41×C26311yescharacteristic
139C2×C4#41×C26311yescharacteristic
140C2×C4#41×C26311yescharacteristic
141C2×C4#41×C26311yescharacteristic
142C8—22no—
143C8—41no—
144C8—41no—
145C8—41no—
146C22—41no—
147C22#123×C26311yescharacteristic
148C22#124×C26311yescharacteristic
149C22#126×C26311yescharacteristic
150C4—42no—
151C4—81no—
152C4—81no—
153C4#121×C26311yescharacteristic
154C4#123×C26311yescharacteristic
155C4#123×C26311yescharacteristic
156C4#126×C26311yescharacteristic
157C2—21no—
158C2—21no—
159C2—21no—
160C2#397×C26311yescharacteristic
subgroupG/H
center, socleC2×C263#397
commutator, Frattini, cosocleC22×C4C23×C263
prime radicalC23×C263#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C263 ◁ C22×C4×C263 ◁ G

Complements

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

NH ≅ G/Ntype
80. C263#2082direct (N × H)
81. #2082C263direct (N × H)

Maximal subgroups

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

subgroupindex
#430×C2632
#419×C2632
C2×#101×C2632
#344×C2632
H(3,ℤ/4)×C2632
#2082263