Finite Group Databasebeta

← #46784092

Subgroups — #46784092

Order 33664.

246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 73 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#30682569C211yesmaximal, characteristic
2#30681978C212yesmaximal
3#30681707C211yesmaximal, characteristic
4#30681698C212yesmaximal
5#384×C263C211yesmaximal, characteristic
6C2×#16862360C2212yes—
7#22554469—22no—
8#22554461—22no—
9#22554449—22no—
10#22554429C2212yes—
11#22554403—22no—
12#22554401—22no—
13C2×C4⋊C4×C263—22no—
14C2×C4⋊C4×C263C2211yescharacteristic
15C2×C4⋊C4×C263C2211yescharacteristic
16C2×C42×C263C2211yescharacteristic
17C2×Dic526—22no—
18#16862360—22no—
19#16862360Q814yescomplemented
20C2×C263⋊C8—22no—
21C4⋊Dic263—22no—
22C4⋊Dic263D412yes—
23C4⋊Dic263D412yes—
24Dic263⋊C4—24no—
25C22⋊Dic263—22no—
26C4×Dic263—22no—
27C22×C4×C263—21no—
28C22×C4×C263—21no—
29C22×C4×C263D412yes—
30C22×C4×C263C2311yescharacteristic
31C4⋊C4×C263—22no—
32C4⋊C4×C263—22no—
33C4⋊C4×C263—44no—
34C42×C263—21no—
35C42×C263Q812yescomplemented
36Dic526—82no—
37C2×Dic263—22no—
38C2×Dic263—22no—
39C263⋊C8—24no—
40C23×C263C2×D411yescharacteristic
41C2×C4×C263—22no—
42C2×C4×C263—22no—
43C2×C4×C263—22no—
44C2×C4×C263—22no—
45C2×C4×C263—42no—
46C2×C4×C263—42no—
47C2×C4×C263—41no—
48C2×C4×C263C2×D412yes—
49C2×C4×C263C2×Q812yes—
50C2×C4×C263C2×Q811yescharacteristic
51C2×C4×C263#4111yescharacteristic
52C22×C263—21no—
53C22×C263—21no—
54C22×C263#12011yescharacteristic
55C22×C263C22⋊Q811yescharacteristic
56C22×C263C4⋊Q811yescharacteristic
57C4×C263—24no—
58C4×C263—42no—
59C4×C263—81no—
60C4×C263C22⋊Q812yes—
61C4×C263C4⋊Q812yes—
62Dic263—42no—
63Dic263—42no—
64C2×C263—21no—
65C2×C263—21no—
66C2×C263#39511yescharacteristic
67C2×C263#45311yescharacteristic
68C2×C263#45611yescharacteristic
69C263#206011yescharacteristic, complemented, Sylow
70#2060—2631nomaximal, Sylow
71#544—2631no—
72#428—2632no—
73#384D26311yescharacteristic
74#343—2631no—
75#339—2632no—
76C2×M16—2632no—
77C4⋊Q8—5262no—
78#125—5262no—
79C22⋊Q8—5262no—
80#117—2632no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4C2×D26311yescharacteristic
83C2×C4⋊C4C2×D26311yescharacteristic
84C2×C42C2×D26311yescharacteristic
85#107—5262no—
86#106—5262no—
87C2×Q8—5262no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4C22⋊D26312yes—
91C22×C4C22×D26311yescharacteristic
92M16—2634no—
93M16—5262no—
94C2×C8—5262no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—44no—
98C4⋊C4—2632no—
99C4⋊C4—2632no—
100C4⋊C4—5262no—
101C4⋊C4—5264no—
102C22⋊C4—5262no—
103C42—21no—
104C42—5262no—
105C42Dic52612yescomplemented
106C23C2×C22⋊D26311yescharacteristic
107Q8—21042no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—22no—
111C2×C4—22no—
112C2×C4—42no—
113C2×C4—42no—
114C2×C4—41no—
115C2×C4—5262no—
116C2×C4—5262no—
117C2×C4D4×D26312yes—
118C2×C4Q8×D26312yes—
119C2×C4C2×Dic52611yescharacteristic
120C2×C4#1686237611yescharacteristic
121C8—5264no—
122C22—21no—
123C22—21no—
124C22#2255443811yescharacteristic
125C22#2255444911yescharacteristic
126C22#2255446811yescharacteristic
127C4—24no—
128C4—42no—
129C4—81no—
130C4—10522no—
131C4—10522no—
132C4#2255444812yes—
133C4#2255446912yes—
134C2—21no—
135C2—21no—
136C2#3068185811yescharacteristic
137C2#3068210511yescharacteristic
138C2#3068212011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#384×C263C2
socleC22×C263#120
prime radicalC23×C263C2×D4
hypercenter#384D263
hypocenterC263#2060
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
19. #16862360Q8semidirect
35. C42×C263Q8semidirect
69. C263#2060semidirect
105. C42Dic526semidirect

Maximal subgroups

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

subgroupindex
#306825692
#306819782
#306817072
#306816982
#384×C2632
#2060263