Finite Group Databasebeta

← #46783274

Subgroups — #46783274

Order 33664.

344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 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#30682502C211yesmaximal, characteristic
2#30681944C212yesmaximal, complemented
3#30681912C211yesmaximal, characteristic, complemented
4#30681695C212yesmaximal, complemented
5#568×C263C211yesmaximal, characteristic, complemented
6C22×D1052C2211yescharacteristic
7#22554466C412yescomplemented
8#22554459C412yescomplemented
9#22554444—22no—
10#22554438—22no—
11#22554429C2212yes—
12#22554429C2211yescharacteristic
13#22554392—24no—
14#22554385—22no—
15C2×#41×C263C2211yescharacteristic
16#131×C263—24no—
17C2×M16×C263—22no—
18C2×M16×C263C2212yes—
19C23×D263—21no—
20C2×D1052—22no—
21C2×D1052—21no—
22C2×D1052—22no—
23C2×D1052C2×C412yes—
24C2×C22⋊D263—24no—
25C4⋊Dic263—21no—
26C4⋊Dic263—22no—
27C22⋊Dic263—21no—
28C22⋊Dic263—22no—
29(C2×D263)⋊C4—24no—
30C4×Dic263—22no—
31C4×Dic263C2×C412yes—
32#41×C263—22no—
33#41×C263—22no—
34C2×Q8×C263C2×C411yescharacteristic
35C2×D4×C263C2×C411yescharacteristic
36C2×D4×C263D412yes—
37C22×C4×C263D412yes—
38C22×C4×C263C2311yescharacteristic
39M16×C263—24no—
40M16×C263—22no—
41M16×C263—22no—
42C2×C8×C263—24no—
43C2×C8×C263D414yescomplemented
44C22×D263—22no—
45C22×D263—42no—
46C22×D263—82no—
47D1052—24no—
48D1052—41no—
49D1052—41no—
50C22⋊D263—84no—
51C2×Dic263—22no—
52C2×Dic263—42no—
53C23×C263C22⋊C412yes—
54C23×C263C2×D411yescharacteristic
55Q8×C263—22no—
56D4×C263—24no—
57D4×C263—22no—
58C2×C4×C263—22no—
59C2×C4×C263—22no—
60C2×C4×C263C22⋊C412yes—
61C2×C4×C263C22×C411yescharacteristic
62C2×C4×C263C2×D412yes—
63C2×C4×C263C2×D411yescharacteristic
64C2×C4×C263#4112yes—
65C8×C263—24no—
66C22×C263—22no—
67C22×C263—41no—
68C22×C263—42no—
69C22×C263C2×C22⋊C411yescharacteristic
70C22×C263#12112yes—
71C2×D263—44no—
72C2×D263—42no—
73C2×D263—84no—
74C4×C263—22no—
75C4×C263C4×D412yes—
76C4×C263#12011yescharacteristic
77C4×C263#12311yescharacteristic
78Dic263—42no—
79Dic263—82no—
80C2×C263—21no—
81C2×C263—22no—
82C2×C263—42no—
83C2×C263#38611yescharacteristic
84D263—82no—
85C263#191011yescharacteristic, complemented, Sylow
86#1910—2631nomaximal, Sylow
87#568D26311yescharacteristic, complemented
88#535—2631no—
89#418—2632no—
90#410—2631no—
91H(3,ℤ/4)—2632no—
92C2×#41C2×D26311yescharacteristic
93C22×D4—2631no—
94#131—24no—
95C2×M16—22no—
96C2×M16C2×D26312yes—
97#127—2632no—
98#124—2632no—
99#121—5262no—
100#120—5262no—
101#117—2631no—
102#117—2632no—
103#102—5264no—
104#99—5262no—
105C24—5261no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D26311yescharacteristic
109C2×D4—2632no—
110C2×D4—5264no—
111C2×D4—5262no—
112C2×D4—5261no—
113C2×D4—5262no—
114C2×D4C4×D26311yescharacteristic
115C2×D4D105212yes—
116C22×C4C22⋊D26312yes—
117C22×C4C22×D26311yescharacteristic
118M16—24no—
119M16—22no—
120M16—22no—
121C2×C8—24no—
122C2×C8C22⋊D26314yescomplemented
123C4⋊C4—5261no—
124C4⋊C4—5262no—
125C22⋊C4—5261no—
126C22⋊C4—5264no—
127C22⋊C4—5262no—
128C42—2632no—
129C42—5262no—
130C23—5262no—
131C23—10522no—
132C23—21042no—
133C23(C2×D263)⋊C412yes—
134C23C2×D105211yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—5264no—
139D4—10521no—
140D4—10521no—
141D4—21044no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—5262no—
145C2×C4—10522no—
146C2×C4(C2×D263)⋊C412yes—
147C2×C4C2×C4×D26311yescharacteristic
148C2×C4C2×C22⋊D26312yes—
149C2×C4C2×C22⋊D26311yescharacteristic
150C2×C4#1686237612yes—
151C8—24no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—10524no—
156C22—10522no—
157C22—21044no—
158C22C2×(C2×D263)⋊C411yescharacteristic
159C22#2255444412yes—
160C4—22no—
161C4—10522no—
162C4—21042no—
163C4C4×C22⋊D26312yes—
164C4#2255443911yescharacteristic
165C4#2255445311yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—21042no—
170C2#3068181711yescharacteristic
subgroupG/H
centerC2#30681817
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#568×C263C2
socleC2×C263#386
prime radical#30682502C2
cosocleC22×C4×C263C23
hypercenter#568D263
hypocenterC263#1910
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #30681944C2semidirect
3. #30681912C2semidirect
4. #30681695C2semidirect
5. #568×C263C2semidirect
7. #22554466C4semidirect
8. #22554459C4semidirect
43. C2×C8×C263D4semidirect
85. C263#1910semidirect
87. #568D263semidirect
122. C2×C8C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306825022
#306819442
#306819122
#306816952
#568×C2632
#1910263