Finite Group Databasebeta

← #15765654

Subgroups — #15765654

Order 3328.

528 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 111 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#13125781C212yesmaximal
2#13123214C211yesmaximal, characteristic
3#13113518C212yesmaximal
4#13112669C211yesmaximal, characteristic
5C13×#1994C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C2×#88123C2212yes—
8C13×#423C2211yescharacteristic
9C43×C13C2211yescharacteristic
10#11718754—22no—
11#11718753—22no—
12#11718711—24no—
13#11718692—24no—
14#11718597—22no—
15#11718590—24no—
16#11718586C2212yes—
17C13×#339—22no—
18#11718073—24no—
19C22×Dic26D414yes—
20C2×C13×M16—21no—
21C13×C4⋊Q8D412yes—
22C13×#125—21no—
23C13×C22⋊Q8—22no—
24C4×Q8×C13—22no—
25C13×#117—21no—
26C2×C42×C13—22no—
27C2×C42×C13D412yes—
28C2×C42×C13C2311yescharacteristic
29C2×#6107—28no—
30C2×C4⋊Dic13—22no—
31C2×C4⋊Dic13—22no—
32#88123—22no—
33#88123—22no—
34#88123—22no—
35#88123—22no—
36C13×C4⋊C8—22no—
37#88071—28no—
38C22⋊#1055—22no—
39#88050—28no—
40C4⋊#1055D414yes—
41C4×#1055—22no—
42#10297—131nomaximal, Sylow
43C2×Q8×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13C2×D412yes—
46C22×C4×C13C2×D411yescharacteristic
47C22×Dic13—24no—
48C2×Dic26—24no—
49C2×Dic26—24no—
50C2×Dic26—48no—
51C13×M16—42no—
52C2×C8×C13—41no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—42no—
56C13×C22⋊C4—41no—
57C42×C13—22no—
58C42×C13—44no—
59C42×C13—41no—
60C42×C13Q1614yescomplemented
61C42×C13C2×D411yescharacteristic
62C42×C13C2×D412yes—
63C42×C13#4111yescharacteristic
64#6107—88no—
65C4⋊Dic13—42no—
66C4⋊Dic13—42no—
67C4⋊Dic13—42no—
68C4⋊Dic13—42no—
69C2×#1055—24no—
70#3209—132no—
71#2862—131no—
72#1994D1311yescharacteristic
73#1548—132no—
74#1276—131no—
75C23×C13#12011yescharacteristic
76Q8×C13—44no—
77C2×C4×C13—24no—
78C2×C4×C13—24no—
79C2×C4×C13—44no—
80C2×C4×C13—42no—
81C2×C4×C13#12012yes—
82C2×C4×C13#12112yes—
83C2×C4×C13#12111yescharacteristic
84C2×C4×C13#12711yescharacteristic
85C2×C4×C13C2×Q1612yes—
86C2×C4×C13#13712yes—
87C2×Dic13—48no—
88C2×Dic13—44no—
89Dic26—48no—
90Dic26—84no—
91C8×C13—81no—
92#1055—44no—
93#533C2×D1311yescharacteristic
94C2×C4⋊Q8—132no—
95#494—262no—
96#487—262no—
97#462—264no—
98#451—264no—
99#431—132no—
100#423C2×D1311yescharacteristic
101#391—264no—
102#382—262no—
103C43C2×D1311yescharacteristic
104#339—22no—
105#333—264no—
106C22×C13—22no—
107C22×C13#39211yescharacteristic
108C22×C13#45112yes—
109C4×C13—22no—
110C4×C13—44no—
111C4×C13—82no—
112C4×C13#45514yes—
113C4×C13#46212yes—
114C4×C13#49411yescharacteristic
115C4×C13#49711yescharacteristic
116Dic13—84no—
117C22×Q8—134no—
118C2×Q16—268no—
119C2×M16—21no—
120C4⋊Q8—262no—
121C4⋊Q8—262no—
122C4⋊Q8—262no—
123C4⋊Q8—262no—
124C4⋊Q8D5212yes—
125#125—21no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128#117—21no—
129C2×C4⋊C4—262no—
130C2×C4⋊C4—262no—
131C2×C42—22no—
132C2×C42C22⋊D1312yes—
133C2×C42C22×D1311yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—134no—
136#103—268no—
137C22⋊C8—262no—
138C4×C8—262no—
139#95—268no—
140C2×C13—22no—
141C2×C13#200412yes—
142C2×C13#201611yescharacteristic
143C2×Q8—22no—
144C2×Q8—264no—
145C2×Q8—264no—
146C2×Q8—528no—
147C22×C4—22no—
148C22×C4—264no—
149C22×C4D4×D1312yes—
150C22×C4C2×C22⋊D1311yescharacteristic
151Q16—1048no—
152M16—42no—
153C2×C8—41no—
154C2×C8—264no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—42no—
158C4⋊C4—522no—
159C4⋊C4—522no—
160C4⋊C4—522no—
161C4⋊C4—522no—
162C22⋊C4—41no—
163C42—22no—
164C42—44no—
165C42—41no—
166C42#610714yescomplemented
167C42C2×D5211yescharacteristic
168C42#612711yescharacteristic
169C42D4×D1312yes—
170C13#1029711yescharacteristic, complemented, Sylow
171C23#8819111yescharacteristic
172Q8—44no—
173Q8—528no—
174Q8—1044no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—42no—
179C2×C4—528no—
180C2×C4—524no—
181C2×C4#8813612yes—
182C2×C4#8813812yes—
183C2×C4#8818411yescharacteristic
184C2×C4#8819411yescharacteristic
185C2×C4C2×#610712yes—
186C2×C4#8820512yes—
187C8—81no—
188C8—524no—
189C22—22no—
190C22#1171862111yescharacteristic
191C22#1171871112yes—
192C4—22no—
193C4—44no—
194C4—82no—
195C4—1044no—
196C4#1171848614yes—
197C4#1171869212yes—
198C4#1171872111yescharacteristic
199C4#1171875311yescharacteristic
200C2—22no—
201C2#1311586412yes—
202C2#1311593511yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1994C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#1994D13
hypocenterC13#10297
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
60. C42×C13Q16semidirect
166. C42#6107semidirect
170. C13#10297semidirect

Maximal subgroups

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

subgroupindex
#131257812
#131232142
#131135182
#131126692
C13×#19942
#1029713