Finite Group Databasebeta

← #46782839

Subgroups — #46782839

Order 33664.

300 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#22554429C211yesmaximal, characteristic
2C2×C22⋊(C263⋊C8)C211yesmaximal, characteristic
3#30681700C212yesmaximal, complemented
4#30681700C212yesmaximal, complemented
5#380×C263C211yesmaximal, characteristic
6C22×C263⋊C8C2212yes—
7#22554429—22no—
8#22554429C414yescomplemented
9C2×C4⋊Dic263C2211yescharacteristic
10C2×C4⋊Dic263C2211yescharacteristic
11C2×C22⋊Dic263—21no—
12C2×C4×Dic263—21no—
13C22⋊(C263⋊C8)—22no—
14C23×C4×C263C2211yescharacteristic
15C2×C4⋊C4×C263C2212yes—
16C2×C22⋊C4×C263—21no—
17#95×C263—21no—
18C22×Dic263—21no—
19C22×Dic263—21no—
20C2×C263⋊C8—22no—
21C2×C263⋊C8—24no—
22C4⋊Dic263—21no—
23C4⋊Dic263—21no—
24C4⋊Dic263C2×C412yes—
25C4⋊Dic263C2×C412yes—
26C22⋊Dic263—24no—
27C4×Dic263—24no—
28C24×C263D411yescharacteristic
29C22×C4×C263—24no—
30C22×C4×C263—22no—
31C22×C4×C263C2×C412yes—
32C22×C4×C263D411yescharacteristic
33C22×C4×C263D412yes—
34C22×C4×C263C2311yescharacteristic
35C4⋊C4×C263—24no—
36C22⋊C4×C263—42no—
37C2×Dic263—22no—
38C2×Dic263—22no—
39C2×Dic263—42no—
40C2×Dic263—41no—
41C2×Dic263—41no—
42C263⋊C8—42no—
43C23×C263—22no—
44C23×C263—22no—
45C23×C263—21no—
46C23×C263—21no—
47C23×C263C22⋊C412yes—
48C23×C263C2×D411yescharacteristic
49C2×C4×C263—22no—
50C2×C4×C263—24no—
51C2×C4×C263—24no—
52C2×C4×C263—42no—
53C2×C4×C263—42no—
54C2×C4×C263—42no—
55C2×C4×C263C22⋊C412yes—
56C2×C4×C263C22×C411yescharacteristic
57C2×C4×C263C2×D411yescharacteristic
58C2×C4×C263#4114yes—
59C22×C263—22no—
60C22×C263—22no—
61C22×C263—22no—
62C22×C263—42no—
63C22×C263—42no—
64C22×C263C2×C22⋊C411yescharacteristic
65C22×C263#12312yes—
66C22×C263#13512yes—
67C22×C263AGL(1,ℤ/8)11yescharacteristic
68C22×C263#13711yescharacteristic
69C4×C263—22no—
70C4×C263—82no—
71C4×C263#11712yes—
72C4×C263#12312yes—
73Dic263—42no—
74Dic263—42no—
75C2×C263—42no—
76C2×C263#38111yescharacteristic
77C2×C263#41611yescharacteristic
78C2×C263#41711yescharacteristic
79C2×C263#48212yes—
80C2×C263#48512yes—
81C263#182511yescharacteristic, complemented, Sylow
82#1825—2631nomaximal, Sylow
83C2×#117—2631no—
84C2×C22⋊C8—2631no—
85#380D26311yescharacteristic
86#340—2632no—
87#340—2632no—
88C23×C4C2×D26311yescharacteristic
89C22×C8—2632no—
90#117—2634no—
91#117—5262no—
92C2×C4⋊C4—2631no—
93C2×C4⋊C4—2631no—
94C2×C4⋊C4C2×D26312yes—
95C2×C22⋊C4—21no—
96C2×C22⋊C4—5261no—
97C2×C42—5261no—
98C22⋊C8—5262no—
99#95—21no—
100C24C22⋊D26311yescharacteristic
101C22×C4—24no—
102C22×C4—22no—
103C22×C4—5261no—
104C22×C4—5261no—
105C22×C4C4×D26312yes—
106C22×C4C22⋊D26311yescharacteristic
107C22×C4D105212yes—
108C22×C4C22×D26311yescharacteristic
109C2×C8—5262no—
110C2×C8—5264no—
111C4⋊C4—24no—
112C4⋊C4—2632no—
113C4⋊C4—2632no—
114C4⋊C4—5261no—
115C4⋊C4—5261no—
116C22⋊C4—42no—
117C22⋊C4—5264no—
118C42—5264no—
119C23—22no—
120C23—22no—
121C23—21no—
122C23—21no—
123C23(C2×D263)⋊C412yes—
124C23C2×C22⋊D26311yescharacteristic
125C2×C4—22no—
126C2×C4—24no—
127C2×C4—24no—
128C2×C4—42no—
129C2×C4—42no—
130C2×C4—42no—
131C2×C4—5262no—
132C2×C4—5262no—
133C2×C4—10522no—
134C2×C4—10521no—
135C2×C4—10521no—
136C2×C4(C2×D263)⋊C412yes—
137C2×C4C2×C4×D26311yescharacteristic
138C2×C4C2×D105211yescharacteristic
139C2×C4#1686237514yes—
140C8—10522no—
141C22—22no—
142C22—22no—
143C22—22no—
144C22—42no—
145C22—42no—
146C22C2×(C2×D263)⋊C411yescharacteristic
147C22#2255445112yes—
148C22#2255449012yes—
149C22#2255449611yescharacteristic
150C22#2255450111yescharacteristic
151C4—22no—
152C4—82no—
153C4—10522no—
154C4—10522no—
155C4#2255442612yes—
156C4#2255445412yes—
157C2—42no—
158C2#3068179911yescharacteristic
159C2#3068193211yescharacteristic
160C2#3068193711yescharacteristic
161C2#3068225912yes—
162C2#3068227612yes—
subgroupG/H
centerC23C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#380×C263C2
socleC23×C263C2×D4
prime radicalC24×C263D4
cosocleC22×C4×C263C23
hypercenter#380D263
hypocenterC263#1825
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #30681700C2semidirect
4. #30681700C2semidirect
8. #22554429C4semidirect
81. C263#1825semidirect

Maximal subgroups

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

subgroupindex
C2×#225544292
C2×C22⋊(C263⋊C8)2
#306817002
#380×C2632
#1825263