Finite Group Databasebeta

← #46783151

Subgroups — #46783151

Order 33664.

344 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 97 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#30682416C211yesmaximal, characteristic, complemented
2#30681943C212yesmaximal
3C2×#22554389C211yesmaximal, characteristic, complemented
4#30681698C212yesmaximal, complemented
5C2×#124×C263C211yesmaximal, characteristic
6C2×#16862360C2212yes—
7Q8×Dic263—24no—
8#22554429—22no—
9#22554429C2212yes—
10#22554391—24no—
11#22554389—22no—
12C22×Q8×C263C2211yescharacteristic
13C22×D4×C263C2211yescharacteristic
14#124×C263—22no—
15#124×C263C414yescomplemented
16C2×C22⋊C4×C263—22no—
17C2×C42×C263C2211yescharacteristic
18#16862360—22no—
19#16862360—22no—
20C2×C263⋊C8—22no—
21C4⋊Dic263—24no—
22C4⋊Dic263D414yes—
23C22⋊Dic263—22no—
24C4×Dic263—24no—
25C4×Dic263—22no—
26C24×C263—21no—
27C2×Q8×C263—22no—
28C2×Q8×C263—22no—
29C2×Q8×C263C2×C412yes—
30C2×Q8×C263D412yes—
31C2×D4×C263—22no—
32C2×D4×C263—21no—
33C2×D4×C263—22no—
34C2×D4×C263C2×C412yes—
35C22×C4×C263—21no—
36C22×C4×C263D412yes—
37C22×C4×C263C2311yescharacteristic
38C22⋊C4×C263—28no—
39C42×C263—21no—
40C42×C263C2×C412yes—
41C2×Dic263—24no—
42C263⋊C8—42no—
43C23×C263—22no—
44C23×C263—44no—
45C23×C263—41no—
46C23×C263—41no—
47C23×C263C2×D411yescharacteristic
48Q8×C263—24no—
49Q8×C263—24no—
50D4×C263—24no—
51D4×C263—42no—
52C2×C4×C263—22no—
53C2×C4×C263—22no—
54C2×C4×C263—22no—
55C2×C4×C263—42no—
56C2×C4×C263C22⋊C414yes—
57C2×C4×C263C22×C411yescharacteristic
58C2×C4×C263C2×D412yes—
59C2×C4×C263C2×D411yescharacteristic
60C2×C4×C263#4112yes—
61C22×C263—22no—
62C22×C263—44no—
63C22×C263—42no—
64C22×C263—82no—
65C22×C263—82no—
66C22×C263C2×C22⋊C411yescharacteristic
67C22×C263#12011yescharacteristic
68C22×C263#12311yescharacteristic
69C4×C263—24no—
70C4×C263—42no—
71C4×C263C4×D412yes—
72C4×C263#12112yes—
73Dic263—44no—
74C2×C263—21no—
75C2×C263—21no—
76C2×C263—82no—
77C2×C263#38611yescharacteristic
78C2×C263#45412yes—
79C263#188811yescharacteristic, complemented, Sylow
80#1888—2631nomaximal, Sylow
81C2×#124D26311yescharacteristic
82#519—2631no—
83#418—2632no—
84C2×#101—2631no—
85#339—2632no—
86C22×Q8C2×D26311yescharacteristic
87C22×D4C2×D26311yescharacteristic
88C2×M16—2632no—
89#124—22no—
90#124Dic26314yescomplemented
91C4×Q8—5264no—
92#117—2632no—
93#117—5262no—
94C2×C22⋊C4—22no—
95C2×C42C2×D26311yescharacteristic
96#102—5264no—
97#101—5262no—
98C24—21no—
99C2×Q8—22no—
100C2×Q8—22no—
101C2×Q8C2×Dic26312yes—
102C2×Q8C22⋊D26312yes—
103C2×D4—22no—
104C2×D4—21no—
105C2×D4—22no—
106C2×D4C2×Dic26312yes—
107C22×C4—21no—
108C22×C4C22⋊D26312yes—
109C22×C4C22×D26311yescharacteristic
110M16—5262no—
111M16—5262no—
112C2×C8—5262no—
113C4⋊C4—2634no—
114C4⋊C4—5264no—
115C22⋊C4—28no—
116C22⋊C4—5262no—
117C42—21no—
118C42—5264no—
119C42—5262no—
120C42C2×Dic26312yes—
121C23—22no—
122C23—44no—
123C23—41no—
124C23—41no—
125C23C2×C22⋊D26311yescharacteristic
126Q8—24no—
127Q8—24no—
128D4—24no—
129D4—42no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—42no—
134C2×C4—5264no—
135C2×C4C22⋊Dic26314yes—
136C2×C4C22×Dic26311yescharacteristic
137C2×C4D4×D26312yes—
138C2×C4C2×C22⋊D26311yescharacteristic
139C2×C4#1686237512yes—
140C8—10522no—
141C22—22no—
142C22—44no—
143C22—42no—
144C22—82no—
145C22—82no—
146C22C2×C22⋊Dic26311yescharacteristic
147C22#2255443811yescharacteristic
148C22#2255445111yescharacteristic
149C4—24no—
150C4—42no—
151C4—10524no—
152C4D4×Dic26312yes—
153C4#2255444212yes—
154C2—21no—
155C2—21no—
156C2—82no—
157C2#3068181811yescharacteristic
158C2#3068211012yes—
subgroupG/H
centerC22#22554438
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#124×C263C2
socleC22×C263#120
prime radicalC22×D4×C263C22
cosocleC22×C4×C263C23
hypercenterC2×#124D263
hypocenterC263#1888
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #30682416C2semidirect
3. C2×#22554389C2semidirect
4. #30681698C2semidirect
15. #124×C263C4semidirect
79. C263#1888semidirect
90. #124Dic263semidirect

Maximal subgroups

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

subgroupindex
#306824162
#306819432
C2×#225543892
#306816982
C2×#124×C2632
#1888263