Finite Group Databasebeta

← #15767806

Subgroups — #15767806

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#13113611C211yesmaximal, characteristic
2#13113567C211yesmaximal, characteristic
3#13113537C211yesmaximal, characteristic
4#13113310C211yesmaximal, characteristic
5#13112746C211yesmaximal, characteristic
6#13112705C211yesmaximal, characteristic
7C13×#1287C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C13×#432C2211yescharacteristic
10C13×#432C2211yescharacteristic
11C13×#431C2211yescharacteristic
12#11718587C2211yescharacteristic
13#11718585C2211yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15#11718078—21no—
16#11718078—21no—
17#11718074—21no—
18#11718073—21no—
19#11718050—22no—
20#11718048—22no—
21C2×C42×C13C2311yescharacteristic
22#88180—21no—
23#88178—21no—
24#88178—21no—
25C2×#6099—21no—
26C22×#1055—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×C22⋊C8—21no—
36C13×C22⋊C8—21no—
37C13×C22⋊C8—21no—
38C13×#97—21no—
39C13×#97—21no—
40C4×C8×C13D412yes—
41C22⋊#1055—21no—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44C4⋊#1055—21no—
45C4⋊#1055—21no—
46C4⋊#1055—21no—
47#88043—21no—
48#10646—131nomaximal, Sylow
49C22×C4×C13#4111yescharacteristic
50C22×C4×C13#4111yescharacteristic
51C22×C4×C13#4111yescharacteristic
52C2×Dic26—21no—
53C2×Dic26—21no—
54C2×C8×C13—22no—
55C2×C8×C13—41no—
56C2×C8×C13—41no—
57C42×C13C2×D411yescharacteristic
58C42×C13C2×D411yescharacteristic
59C42×C13#4111yescharacteristic
60C42×C13#4111yescharacteristic
61C22⋊Dic13—41no—
62C4⋊Dic13—21no—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66#6101—41no—
67#6101—41no—
68C4×Dic13—41no—
69#6099—81no—
70C2×#1055—41no—
71C2×#1055—41no—
72C2×#1055—41no—
73C2×#1055—81no—
74#1571—131no—
75#1559—131no—
76#1552—131no—
77#1497—131no—
78#1307—131no—
79#1290—131no—
80#1287D1311yescharacteristic
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#432C2×D1311yescharacteristic
106#432C2×D1311yescharacteristic
107#431C2×D1311yescharacteristic
108#423—131no—
109C2×C4⋊C8—131no—
110#335—262no—
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#47211yescharacteristic
126C4×C13#47311yescharacteristic
127Dic13—81no—
128Dic13—81no—
129C2×M16—261no—
130C22×C8—261no—
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—261no—
144C4⋊C8—261no—
145C4⋊C8—261no—
146C4⋊C8—261no—
147C4⋊C8—261no—
148C22⋊C8—21no—
149C22⋊C8—21no—
150C22⋊C8—21no—
151C22⋊C8—261no—
152#97—21no—
153#97—21no—
154#97—261no—
155C4×C8D5212yes—
156C2×C13—41no—
157C2×C13#207811yescharacteristic
158C2×C13#208011yescharacteristic
159C2×C13#208211yescharacteristic
160C2×Q8—261no—
161C2×Q8—261no—
162C22×C4#612711yescharacteristic
163C22×C4#612911yescharacteristic
164C22×C4#613111yescharacteristic
165M16—1041no—
166C2×C8—22no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—521no—
170C2×C8—521no—
171C2×C8—521no—
172C2×C8—1041no—
173C4⋊C4—261no—
174C4⋊C4—261no—
175C4⋊C4—261no—
176C4⋊C4—261no—
177C4⋊C4—521no—
178C4⋊C4—521no—
179C22⋊C4—521no—
180C42—521no—
181C42C2×D5211yescharacteristic
182C42#612711yescharacteristic
183C42D4×D1311yescharacteristic
184C42#612911yescharacteristic
185C13#1064611yescharacteristic, 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#8812911yescharacteristic
197C2×C4#8813711yescharacteristic
198C2×C4#8813711yescharacteristic
199C2×C4#8814011yescharacteristic
200C2×C4#8814911yescharacteristic
201C2×C4#8815211yescharacteristic
202C8—42no—
203C8—81no—
204C8—81no—
205C8—1041no—
206C8—1041no—
207C8—1041no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1171833511yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—1041no—
218C4—1041no—
219C4#1171855711yescharacteristic
220C4#1171855811yescharacteristic
221C2—41no—
222C2#1311627811yescharacteristic
223C2#1311628811yescharacteristic
224C2#1311630211yescharacteristic
subgroupG/H
centerC22#11718335
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1287C2
socleC22×C13#397
prime radicalC23×C13#126
hypercenter#1287D13
hypocenterC13#10646
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1287

Complements

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

NH ≅ G/Ntype
185. C13#10646semidirect

Maximal subgroups

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

subgroupindex
#131136112
#131135672
#131135372
#131133102
#131127462
#131127052
C13×#12872
#1064613