Finite Group Databasebeta

← #15783241

Subgroups — #15783241

Order 3328.

406 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 79 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#13116501C212yesmaximal
2#13113001C214yesmaximal, complemented
3C13×#3152C211yesmaximal, characteristic
4C2×C13×#137—22no—
5C13×#532C2211yescharacteristic
6C2×C13×C4⋊Q8C411yescharacteristic, complemented
7C13×#497—22no—
8C13×#494C412yescomplemented
9C13×#492C2212yes—
10C4×C13×M16C411yescharacteristic, complemented
11#11718901—22no—
12#11718137C2214yes—
13#11718133—22no—
14C2×C13×#41D412yes—
15C22×Q8×C13—21no—
16C13×#137—44no—
17C13×#137—44no—
18C2×C13×Q16—24no—
19C2×C13×SD16—24no—
20C2×C13×M16—21no—
21C13×C4⋊Q8—21no—
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8C2×C412yes—
24C13×C4⋊Q8C2×C411yescharacteristic
25C13×#127C2311yescharacteristic
26C13×#124D412yes—
27C13×#121—41no—
28C4×D4×C13—41no—
29C2×C13×C4⋊C4—41no—
30C2×C42×C13C2×C411yescharacteristic
31#88180—42no—
32C13×#97—21no—
33C4×C8×C13C2×C412yes—
34#88074—24no—
35#88074—42no—
36#13586—131nomaximal, Sylow
37C13×#41—42no—
38C13×#41—42no—
39C2×Q8×C13—22no—
40C2×Q8×C13—42no—
41C2×Q8×C13—42no—
42C2×Q8×C13—41no—
43C2×Q8×C13C22⋊C412yes—
44C2×D4×C13—22no—
45C2×D4×C13—41no—
46C2×D4×C13C2×D412yes—
47C22×C4×C13—21no—
48C22×C4×C13—22no—
49C22×C4×C13—41no—
50C22×C4×C13C22⋊C411yescharacteristic
51C13×Q16—48no—
52C13×SD16—48no—
53C13×M16—24no—
54C2×C8×C13—22no—
55C13×C4⋊C4—41no—
56C13×C4⋊C4—42no—
57C13×C4⋊C4—42no—
58C13×C22⋊C4—42no—
59C42×C13—21no—
60C42×C13C22⋊C411yescharacteristic
61C42×C13C22×C411yescharacteristic
62C22⋊Dic13—44no—
63C4⋊Dic13—82no—
64C4×Dic13—82no—
65#3152D1311yescharacteristic
66#2126—132no—
67#1409—134no—
68C23×C13—22no—
69C23×C13#9911yescharacteristic
70Q8×C13—42no—
71Q8×C13—44no—
72Q8×C13—82no—
73D4×C13—42no—
74D4×C13—82no—
75D4×C13—82no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—42no—
84C2×C4×C13—81no—
85C2×C4×C13—81no—
86C2×C4×C13#9911yescharacteristic
87C2×C4×C13C2×C22⋊C411yescharacteristic
88C2×Dic13—84no—
89C8×C13—24no—
90C2×#137—22no—
91#532C2×D1311yescharacteristic
92C2×C4⋊Q8Dic1311yescharacteristic, complemented
93#497—22no—
94#494Dic1312yescomplemented
95#492C2×D1312yes—
96#410—262no—
97C4×M16Dic1311yescharacteristic, complemented
98#354—262no—
99#353—134no—
100C22×C13—21no—
101C22×C13—41no—
102C22×C13—42no—
103C22×C13—82no—
104C22×C13C2×#9911yescharacteristic
105C4×C13—22no—
106C4×C13—21no—
107C4×C13—41no—
108C4×C13—42no—
109C4×C13—82no—
110C4×C13#35312yes—
111Dic13—164no—
112C2×#41C22⋊D1312yes—
113C22×Q8—21no—
114#137—44no—
115#137—44no—
116C2×Q16—24no—
117C2×SD16—24no—
118C2×M16—21no—
119C4⋊Q8—21no—
120C4⋊Q8—41no—
121C4⋊Q8C2×Dic1312yes—
122C4⋊Q8C2×Dic1311yescharacteristic
123#127C22×D1311yescharacteristic
124#124C22⋊D1312yes—
125#121—41no—
126C4×D4—41no—
127#117—522no—
128C2×C4⋊C4—41no—
129C2×C42C2×Dic1311yescharacteristic
130#99—264no—
131#99—522no—
132#97—21no—
133C4×C8C2×Dic1312yes—
134C2×C13—21no—
135C2×C13—41no—
136C2×C13—82no—
137C2×C13C2×#35311yescharacteristic
138#41—42no—
139#41—42no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—41no—
144C2×Q8C22⋊Dic1312yes—
145C2×D4—22no—
146C2×D4—41no—
147C2×D4C2×C22⋊D1312yes—
148C22×C4—21no—
149C22×C4—22no—
150C22×C4—41no—
151C22×C4C22⋊Dic1311yescharacteristic
152Q16—48no—
153SD16—48no—
154M16—24no—
155C2×C8—22no—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—1042no—
160C22⋊C4—42no—
161C22⋊C4—524no—
162C42—21no—
163C42—1042no—
164C42C22⋊Dic1311yescharacteristic
165C42C22×Dic1311yescharacteristic
166C13#1358611yescharacteristic, complemented, Sylow
167C23—22no—
168C23#8807411yescharacteristic
169Q8—42no—
170Q8—44no—
171Q8—82no—
172D4—42no—
173D4—82no—
174D4—82no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4—1044no—
186C2×C4#8807411yescharacteristic
187C2×C4C2×C22⋊Dic1311yescharacteristic
188C8—24no—
189C22—21no—
190C22—41no—
191C22—42no—
192C22—82no—
193C22C2×#8807411yescharacteristic
194C4—22no—
195C4—21no—
196C4—41no—
197C4—42no—
198C4—82no—
199C4—2084no—
200C4#1171813712yes—
201C2—21no—
202C2—41no—
203C2—82no—
204C2C2×#1171813711yescharacteristic
subgroupG/H
centerC2C2×#11718137
commutatorC42×C13C22×C4
Frattini#127C22×D13
FittingC13×#3152C2
socleC2×C13C2×#353
prime radicalC13×#532C22
cosocleC13×#127C23
hypercenter#3152D13
hypocenterC13#13586
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3152

Complements

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

NH ≅ G/Ntype
2. #13113001C2semidirect
6. C2×C13×C4⋊Q8C4semidirect
8. C13×#494C4semidirect
10. C4×C13×M16C4semidirect
92. C2×C4⋊Q8Dic13semidirect
94. #494Dic13semidirect
97. C4×M16Dic13semidirect
166. C13#13586semidirect

Maximal subgroups

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

subgroupindex
#131165012
#131130012
C13×#31522
#1358613