Finite Group Databasebeta

← #15765657

Subgroups — #15765657

Order 3328.

528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 113 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#13125786C212yesmaximal
2#13123214C211yesmaximal, characteristic
3#13115813C211yesmaximal, characteristic
4#13113516C212yesmaximal
5C13×#1276C211yesmaximal, characteristic
6#11719175C2211yescharacteristic
7C2×#88123C2212yes—
8C13×#431C2212yes—
9C43×C13C2211yescharacteristic
10#11718597—22no—
11#11718590—24no—
12#11718585C2211yescharacteristic
13#11718510—24no—
14#11718400—24no—
15#11718360—22no—
16#11718342—22no—
17#11718115—22no—
18#11718073—24no—
19C22×Dic26D414yes—
20C2×C42×C13—22no—
21C2×C42×C13D412yes—
22C2×C42×C13C2311yescharacteristic
23#88180—21no—
24C2×C4⋊Dic13—22no—
25C2×C4⋊Dic13—22no—
26#88178—22no—
27C2×#6099—21no—
28C2×Dic52—28no—
29#88124—21no—
30#88123—22no—
31#88123—22no—
32#88123—22no—
33#88123—22no—
34#88123D412yes—
35C4×Dic26—22no—
36C13×C4⋊C8D414yes—
37C13×C22⋊C8—22no—
38C4×C8×C13—22no—
39#88071—28no—
40#88056—28no—
41C4⋊#1055—22no—
42#10297—131nomaximal, Sylow
43C22×C4×C13—22no—
44C22×C4×C13C2×D411yescharacteristic
45C22×C4×C13C2×D412yes—
46C22×Dic13—24no—
47C2×Dic26—22no—
48C2×Dic26—24no—
49C2×Dic26—24no—
50C2×Dic26—48no—
51C2×C8×C13—24no—
52C42×C13—22no—
53C42×C13—44no—
54C42×C13Q1614yescomplemented
55C42×C13C2×D412yes—
56C42×C13C2×D411yescharacteristic
57C42×C13#4111yescharacteristic
58C22⋊Dic13—41no—
59C4⋊Dic13—22no—
60C4⋊Dic13—22no—
61C4⋊Dic13—42no—
62C4⋊Dic13—42no—
63C4⋊Dic13—42no—
64C4⋊Dic13—42no—
65#6101—42no—
66C4×Dic13—41no—
67#6099—42no—
68C2×#1055—41no—
69Dic52—88no—
70#3209—132no—
71#2862—131no—
72#1994—131no—
73#1548—132no—
74#1276D1311yescharacteristic
75C23×C13#12011yescharacteristic
76C2×C4×C13—24no—
77C2×C4×C13—24no—
78C2×C4×C13—44no—
79C2×C4×C13#12012yes—
80C2×C4×C13#12112yes—
81C2×C4×C13#12111yescharacteristic
82C2×C4×C13#12711yescharacteristic
83C2×C4×C13C2×Q1612yes—
84C2×C4×C13#13712yes—
85C2×Dic13—48no—
86C2×Dic13—42no—
87C2×Dic13—44no—
88Dic26—44no—
89Dic26—48no—
90Dic26—84no—
91C8×C13—44no—
92#1055—81no—
93#533—131no—
94C2×C4⋊Q8—132no—
95#494—262no—
96#487—262no—
97#462—264no—
98#451—264no—
99#431C2×D1312yes—
100#423—131no—
101#391—264no—
102#382—262no—
103C43C2×D1311yescharacteristic
104#339—262no—
105#333—264no—
106C22×C13—22no—
107C22×C13#39211yescharacteristic
108C22×C13#45112yes—
109C4×C13—22no—
110C4×C13—44no—
111C4×C13#45514yes—
112C4×C13#46212yes—
113C4×C13#49411yescharacteristic
114C4×C13#49711yescharacteristic
115Dic13—84no—
116Dic13—82no—
117C22×Q8—134no—
118C2×Q16—268no—
119C2×M16—261no—
120C4⋊Q8—132no—
121C4⋊Q8—262no—
122C4⋊Q8—262no—
123C4⋊Q8—262no—
124C4⋊Q8—262no—
125#125—261no—
126C22⋊Q8—262no—
127C4×Q8—262no—
128#117—261no—
129C2×C4⋊C4—262no—
130C2×C4⋊C4—262no—
131C2×C42—22no—
132C2×C42D5212yes—
133C2×C42C22×D1311yescharacteristic
134C4⋊C8—262no—
135C4⋊C8D5214yes—
136#103—268no—
137C22⋊C8—22no—
138C4×C8—22no—
139#95—268no—
140C2×C13—22no—
141C2×C13#200412yes—
142C2×C13#201611yescharacteristic
143C2×Q8—264no—
144C2×Q8—262no—
145C2×Q8—264no—
146C2×Q8—528no—
147C22×C4—22no—
148C22×C4—264no—
149C22×C4C2×D5211yescharacteristic
150C22×C4D4×D1312yes—
151Q16—1048no—
152M16—522no—
153C2×C8—24no—
154C2×C8—521no—
155C4⋊C4—262no—
156C4⋊C4—262no—
157C4⋊C4—522no—
158C4⋊C4—522no—
159C4⋊C4—522no—
160C4⋊C4—522no—
161C4⋊C4—522no—
162C22⋊C4—521no—
163C42—22no—
164C42—44no—
165C42—521no—
166C42Dic5214yescomplemented
167C42C2×D5212yes—
168C42D4×D1311yescharacteristic
169C42#613111yescharacteristic
170C13#1029711yescharacteristic, complemented, Sylow
171C23#8813611yescharacteristic
172Q8—524no—
173Q8—528no—
174Q8—1044no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—528no—
179C2×C4—522no—
180C2×C4—524no—
181C2×C4#8812811yescharacteristic
182C2×C4#8813612yes—
183C2×C4#8814912yes—
184C2×C4#8814911yescharacteristic
185C2×C4C2×Dic5212yes—
186C2×C4#8816312yes—
187C8—44no—
188C8—1041no—
189C22—22no—
190C22#1171833211yescharacteristic
191C22#1171840012yes—
192C4—22no—
193C4—44no—
194C4—1044no—
195C4—1042no—
196C4#1171836011yescharacteristic
197C4#1171837611yescharacteristic
198C4#1171848614yes—
199C4#1171851012yes—
200C2—22no—
201C2#1311586812yes—
202C2#1311593811yescharacteristic
subgroupG/H
centerC22#11718332
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#1276D13
hypocenterC13#10297
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
54. C42×C13Q16semidirect
166. C42Dic52semidirect
170. C13#10297semidirect

Maximal subgroups

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

subgroupindex
#131257862
#131232142
#131158132
#131135162
C13×#12762
#1029713