Finite Group Databasebeta

← #46780875

Subgroups — #46780875

Order 33664.

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

normal subgroups only

This group has 162 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#30681922C211yesmaximal, characteristic
2#30681905C211yesmaximal, characteristic
3#410×C263C211yesmaximal, characteristic
4C2×#16862360—21no—
5C2×#16862360C411yescharacteristic, complemented
6C22×C263⋊C8C411yescharacteristic, complemented
7#22554389C412yescomplemented
8#22554387—21no—
9C22⋊(C263⋊C8)—21no—
10C22⋊(C263⋊C8)—21no—
11C2×#41×C263C2211yescharacteristic
12#117×C263—21no—
13#99×C263—21no—
14#99×C263C412yes—
15#16862360—22no—
16#16862360—41no—
17#16862360—41no—
18C2×C263⋊C8—21no—
19C2×C263⋊C8—21no—
20C2×C263⋊C8—41no—
21C2×C263⋊C8—41no—
22#41×C263—41no—
23#41×C263—41no—
24C2×Q8×C263C2×C411yescharacteristic
25C2×D4×C263C2×C411yescharacteristic
26C2×D4×C263D411yescharacteristic
27C2×D4×C263Q811yescharacteristic
28C22×C4×C263C2×C411yescharacteristic
29C22×C4×C263D411yescharacteristic
30C22×C4×C263D411yescharacteristic
31C4⋊C4×C263—41no—
32C22⋊C4×C263—22no—
33C42×C263—41no—
34C263⋊C8—42no—
35C263⋊C8—41no—
36C263⋊C8—41no—
37C23×C263C22⋊C411yescharacteristic
38C23×C263C4⋊C411yescharacteristic
39C23×C263C4⋊C411yescharacteristic
40Q8×C263—41no—
41D4×C263—41no—
42D4×C263—41no—
43D4×C263—41no—
44C2×C4×C263—21no—
45C2×C4×C263—21no—
46C2×C4×C263—21no—
47C2×C4×C263—21no—
48C2×C4×C263—21no—
49C2×C4×C263—21no—
50C2×C4×C263—42no—
51C2×C4×C263C4211yescharacteristic
52C2×C4×C263C22⋊C411yescharacteristic
53C2×C4×C263C22⋊C411yescharacteristic
54C2×C4×C263C4⋊C411yescharacteristic
55C22×C263—21no—
56C22×C263—21no—
57C22×C263—21no—
58C22×C263—41no—
59C22×C263—41no—
60C22×C263—41no—
61C22×C263#9511yescharacteristic
62C4×C263—21no—
63C4×C263—21no—
64C4×C263—21no—
65C4×C263—82no—
66C4×C263#9911yescharacteristic
67C4×C263#9911yescharacteristic
68C2×C263—21no—
69C2×C263—41no—
70C2×C263—41no—
71C2×C263—41no—
72C2×C263#34211yescharacteristic
73C263#139511yescharacteristic, complemented, Sylow
74#1395—2631nomaximal, Sylow
75#413—2631no—
76#410D26311yescharacteristic
77#408—2631no—
78C2×#41C2×D26311yescharacteristic
79C2×M16—2631no—
80C2×M16—5261no—
81C22×C8—2631no—
82#117—21no—
83#101—2632no—
84#100—5261no—
85#99—21no—
86#99Dic26312yes—
87C22⋊C8—5261no—
88C22⋊C8—5261no—
89#41—41no—
90#41—41no—
91C2×Q8C4×D26311yescharacteristic
92C2×D4C2×Dic26311yescharacteristic
93C2×D4C22⋊D26311yescharacteristic
94C2×D4Dic52611yescharacteristic
95C22×C4C4×D26311yescharacteristic
96C22×C4C22⋊D26311yescharacteristic
97C22×C4D105211yescharacteristic
98M16—5262no—
99M16—10521no—
100M16—10521no—
101C2×C8—5261no—
102C2×C8—5261no—
103C2×C8—10521no—
104C2×C8—10521no—
105C4⋊C4—41no—
106C22⋊C4—22no—
107C42—41no—
108C23C22⋊Dic26311yescharacteristic
109C23Dic263⋊C411yescharacteristic
110C23C4⋊Dic26311yescharacteristic
111Q8—41no—
112D4—41no—
113D4—41no—
114D4—41no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—42no—
122C2×C4C4×Dic26311yescharacteristic
123C2×C4(C2×D263)⋊C411yescharacteristic
124C2×C4(C2×D263)⋊C411yescharacteristic
125C2×C4Dic263⋊C411yescharacteristic
126C8—10522no—
127C8—10521no—
128C8—10521no—
129C22—21no—
130C22—21no—
131C22—21no—
132C22—41no—
133C22—41no—
134C22—41no—
135C22C263⋊#9511yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—82no—
140C4#2255438411yescharacteristic
141C4#2255438411yescharacteristic
142C2—21no—
143C2—41no—
144C2—41no—
145C2—41no—
146C2#3068170411yescharacteristic
subgroupG/H
centerC4#22554384
commutatorC2×C4×C263C42
FrattiniC2×#41C2×D263
Fitting#410×C263C2
socleC2×C263#342
prime radical, cosocleC2×#41×C263C22
hypercenter#410D263
hypocenterC263#1395
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
5. C2×#16862360C4semidirect
6. C22×C263⋊C8C4semidirect
7. #22554389C4semidirect
73. C263#1395semidirect

Maximal subgroups

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

subgroupindex
#306819222
#306819052
#410×C2632
#1395263