Finite Group Databasebeta

← #15767819

Subgroups — #15767819

Order 3328.

236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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#13113564C211yesmaximal, characteristic
2#13113534C211yesmaximal, characteristic
3#13113310C211yesmaximal, characteristic
4#13112747C211yesmaximal, characteristic
5#13112706C211yesmaximal, characteristic
6#13112698C211yesmaximal, characteristic
7C13×#1570C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12#11718587C2211yescharacteristic
13#11718587C2211yescharacteristic
14#11718587C2211yescharacteristic
15C13×#334—22no—
16#11718078—21no—
17#11718074—21no—
18#11718074—21no—
19#11718073—21no—
20#11718048—22no—
21C2×C13×M16—21no—
22C22×C8×C13—21no—
23C2×C42×C13C2311yescharacteristic
24#88180—21no—
25#88178—21no—
26#88178—21no—
27#88124—21no—
28#88123D411yescharacteristic
29#88123D411yescharacteristic
30C4×Dic26—21no—
31C4×Dic26—21no—
32C13×C4⋊C8—21no—
33C13×C4⋊C8—21no—
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C4⋊C8—21no—
37C13×C22⋊C8—21no—
38C4×C8×C13D412yes—
39C22⋊#1055—21no—
40C22⋊#1055—21no—
41C22⋊#1055—21no—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44C4⋊#1055—21no—
45#88043—21no—
46#88043—21no—
47#88043—21no—
48#10648—131nomaximal, Sylow
49C22×C4×C13#4111yescharacteristic
50C22×C4×C13#4111yescharacteristic
51C22×C4×C13#4111yescharacteristic
52C2×Dic26—21no—
53C2×Dic26—21no—
54C13×M16—81no—
55C2×C8×C13—22no—
56C2×C8×C13—41no—
57C2×C8×C13—41no—
58C2×C8×C13—81no—
59C42×C13C2×D411yescharacteristic
60C42×C13C2×D411yescharacteristic
61C42×C13#4111yescharacteristic
62C42×C13#4111yescharacteristic
63C22⋊Dic13—41no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13—21no—
67C4⋊Dic13—21no—
68#6101—41no—
69#6101—41no—
70C4×Dic13—41no—
71C2×#1055—41no—
72C2×#1055—41no—
73C2×#1055—41no—
74#1570D1311yescharacteristic
75#1559—131no—
76#1552—131no—
77#1497—131no—
78#1307—131no—
79#1290—131no—
80#1287—131no—
81C23×C13#12611yescharacteristic
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13#12111yescharacteristic
87C2×C4×C13#12311yescharacteristic
88C2×C4×C13#12311yescharacteristic
89C2×C4×C13#12311yescharacteristic
90C2×C4×C13#12411yescharacteristic
91C2×C4×C13#12611yescharacteristic
92C2×Dic13—41no—
93C2×Dic13—41no—
94Dic26—41no—
95Dic26—41no—
96Dic26—81no—
97C8×C13—42no—
98C8×C13—81no—
99C8×C13—81no—
100#1055—81no—
101#1055—81no—
102#1055—81no—
103#533—131no—
104#432—131no—
105#432—131no—
106#432—131no—
107#431C2×D1311yescharacteristic
108#423C2×D1311yescharacteristic
109C2×C4⋊C8C2×D1311yescharacteristic
110#334—22no—
111#333—261no—
112#332—261no—
113#332—261no—
114#332—261no—
115Q8⋊C8—262no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13#39711yescharacteristic
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13#47111yescharacteristic
126C4×C13#47111yescharacteristic
127Dic13—81no—
128Dic13—81no—
129C2×M16—21no—
130C22×C8—21no—
131C4⋊Q8—131no—
132C4⋊Q8—131no—
133#125—261no—
134C22⋊Q8—261no—
135C22⋊Q8—261no—
136C4×Q8—261no—
137C4×Q8—261no—
138#117—261no—
139C2×C42C22×D1311yescharacteristic
140C4⋊C8—21no—
141C4⋊C8—21no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—21no—
145C4⋊C8—261no—
146C4⋊C8—261no—
147C4⋊C8—261no—
148C22⋊C8—21no—
149C22⋊C8—261no—
150C22⋊C8—261no—
151C22⋊C8—261no—
152#97—261no—
153#97—261no—
154#97—261no—
155C4×C8C22⋊D1312yes—
156C2×C13—41no—
157C2×C13#207911yescharacteristic
158C2×C13#208011yescharacteristic
159C2×C13#208211yescharacteristic
160C2×Q8—261no—
161C2×Q8—261no—
162C22×C4#612711yescharacteristic
163C22×C4#612911yescharacteristic
164C22×C4#613111yescharacteristic
165M16—81no—
166C2×C8—22no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—81no—
170C2×C8—521no—
171C2×C8—521no—
172C2×C8—521no—
173C4⋊C4—261no—
174C4⋊C4—261no—
175C4⋊C4—261no—
176C4⋊C4—261no—
177C4⋊C4—521no—
178C4⋊C4—521no—
179C22⋊C4—521no—
180C42—521no—
181C42#612711yescharacteristic
182C42D4×D1311yescharacteristic
183C42#613111yescharacteristic
184C42C2×C22⋊D1311yescharacteristic
185C13#1064811yescharacteristic, complemented, Sylow
186C23#8815211yescharacteristic
187Q8—521no—
188Q8—521no—
189Q8—1041no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—521no—
195C2×C4—521no—
196C2×C4#8814811yescharacteristic
197C2×C4#8814811yescharacteristic
198C2×C4#8815211yescharacteristic
199C2×C4#8818311yescharacteristic
200C2×C4#8819211yescharacteristic
201C2×C4#8820111yescharacteristic
202C8—42no—
203C8—81no—
204C8—81no—
205C8—1041no—
206C8—1041no—
207C8—1041no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1171865411yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—1041no—
218C4—1041no—
219C4#1171883811yescharacteristic
220C4#1171883811yescharacteristic
221C2—41no—
222C2#1311628211yescharacteristic
223C2#1311628711yescharacteristic
224C2#1311630111yescharacteristic
subgroupG/H
centerC22#11718654
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1570C2
socleC22×C13#397
prime radicalC23×C13#126
hypercenter#1570D13
hypocenterC13#10648
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
185. C13#10648semidirect

Maximal subgroups

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

subgroupindex
#131135642
#131135342
#131133102
#131127472
#131127062
#131126982
C13×#15702
#1064813