Finite Group Databasebeta

← #46783294

Subgroups — #46783294

Order 33664.

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

normal subgroups only

This group has 340 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#30681922C211yesmaximal, characteristic, complemented
3C2×#22554386C212yesmaximal, complemented
4#30681710C212yesmaximal, complemented
5#568×C263C211yesmaximal, characteristic, complemented
6C22×D1052C2211yescharacteristic
7C2×#16862360C2212yes—
8#22554466—21no—
9#22554459—21no—
10#22554444—22no—
11#22554438C414yes—
12#22554429C2211yescharacteristic
13#22554389—21no—
14#22554387—21no—
15#22554386—24no—
16C2×#41×C263C2211yescharacteristic
17#131×C263—24no—
18C2×M16×C263—22no—
19C2×M16×C263C2212yes—
20C23×D263C2×C412yes—
21C2×D1052—22no—
22C2×D1052—21no—
23C2×D1052—21no—
24C2×D1052—22no—
25C2×C22⋊D263—24no—
26#16862360—22no—
27#16862360—22no—
28C2×C263⋊C8—22no—
29C4⋊Dic263—21no—
30C22⋊Dic263C2×C412yes—
31(C2×D263)⋊C4—24no—
32C4×Dic263—21no—
33#41×C263—22no—
34#41×C263—22no—
35C2×Q8×C263D411yescharacteristic
36C2×D4×C263C2×C412yes—
37C2×D4×C263D411yescharacteristic
38C22×C4×C263D412yes—
39C22×C4×C263C2311yescharacteristic
40M16×C263—24no—
41M16×C263—22no—
42M16×C263D414yescomplemented
43C2×C8×C263—24no—
44C2×C8×C263—22no—
45C22×D263—22no—
46C22×D263—24no—
47C22×D263—82no—
48D1052—41no—
49D1052—42no—
50D1052—41no—
51C22⋊D263—84no—
52C2×Dic263—22no—
53C263⋊C8—42no—
54C23×C263C22⋊C412yes—
55C23×C263C22×C411yescharacteristic
56Q8×C263—22no—
57D4×C263—24no—
58D4×C263—22no—
59C2×C4×C263—22no—
60C2×C4×C263—22no—
61C2×C4×C263C22⋊C412yes—
62C2×C4×C263C2×D412yes—
63C2×C4×C263C2×D411yescharacteristic
64C2×C4×C263C2×D411yescharacteristic
65C2×C4×C263#4112yes—
66C8×C263—24no—
67C22×C263—22no—
68C22×C263—41no—
69C22×C263—42no—
70C22×C263C2×C22⋊C411yescharacteristic
71C22×C263C4×D412yes—
72C2×D263—44no—
73C2×D263—42no—
74C2×D263—84no—
75C4×C263—22no—
76C4×C263#12011yescharacteristic
77C4×C263#12112yes—
78C4×C263#12311yescharacteristic
79Dic263—42no—
80C2×C263—21no—
81C2×C263—22no—
82C2×C263—42no—
83C2×C263#38611yescharacteristic
84D263—82no—
85C263#191411yescharacteristic, complemented, Sylow
86#1914—2631nomaximal, Sylow
87#568D26311yescharacteristic, complemented
88#535—2631no—
89#413—2631no—
90C2×#100—2632no—
91#344—2632no—
92C2×#41C2×D26311yescharacteristic
93C22×D4—2631no—
94#131—24no—
95C2×M16—22no—
96C2×M16—2632no—
97C2×M16C2×D26312yes—
98#127—5261no—
99#124—5261no—
100#121—5262no—
101#120—2634no—
102#117—2631no—
103#101—5261no—
104#100—5261no—
105#100—5264no—
106C24—2632no—
107#41—22no—
108#41—22no—
109C2×Q8D105211yescharacteristic
110C2×D4—5264no—
111C2×D4—5262no—
112C2×D4—5261no—
113C2×D4—5261no—
114C2×D4—5262no—
115C2×D4C4×D26312yes—
116C2×D4D105211yescharacteristic
117C22×C4C22⋊D26312yes—
118C22×C4C22×D26311yescharacteristic
119M16—24no—
120M16—22no—
121M16—5262no—
122M16—5262no—
123M16C22⋊D26314yescomplemented
124C2×C8—24no—
125C2×C8—22no—
126C2×C8—5262no—
127C4⋊C4—5261no—
128C22⋊C4—2632no—
129C22⋊C4—5264no—
130C42—5261no—
131C23—5262no—
132C23—5264no—
133C23—21042no—
134C23(C2×D263)⋊C412yes—
135C23C2×C4×D26311yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—10521no—
140D4—10522no—
141D4—10521no—
142D4—21044no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—5262no—
146C2×C4(C2×D263)⋊C412yes—
147C2×C4C2×C22⋊D26312yes—
148C2×C4C2×C22⋊D26311yescharacteristic
149C2×C4C2×D105211yescharacteristic
150C2×C4#1686237612yes—
151C8—24no—
152C8—10522no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—10524no—
157C22—10522no—
158C22—21044no—
159C22C2×(C2×D263)⋊C411yescharacteristic
160C22C4×C22⋊D26312yes—
161C4—22no—
162C4—10522no—
163C4#2255443911yescharacteristic
164C4#2255444412yes—
165C4#2255445311yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—21042no—
170C2#3068181711yescharacteristic
subgroupG/H
centerC2#30681817
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#568×C263C2
socleC2×C263#386
prime radical#30682502C2
cosocleC22×C4×C263C23
hypercenter#568D263
hypocenterC263#1914
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #30681922C2semidirect
3. C2×#22554386C2semidirect
4. #30681710C2semidirect
5. #568×C263C2semidirect
42. M16×C263D4semidirect
85. C263#1914semidirect
87. #568D263semidirect
123. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306825022
#306819222
C2×#225543862
#306817102
#568×C2632
#1914263