Finite Group Databasebeta

← #15767418

Subgroups — #15767418

Order 3328.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#13115005C211yesmaximal, characteristic
2#13114969C212yesmaximal
3#13112717C212yesmaximal
4#13112717C211yesmaximal, characteristic
5C13×#2844C211yesmaximal, characteristic
6C13×#400—21no—
7C13×#400—22no—
8C13×#395—21no—
9C13×#395—22no—
10C13×#382C2212yes—
11C13×#382C2211yescharacteristic
12C2×#88048—21no—
13C2×#88047—21no—
14#11718596C2211yescharacteristic
15C2×#88043C2212yes—
16C2×#88043C2211yescharacteristic
17#11718121—22no—
18#11718121—22no—
19C22×Q8×C13—21no—
20C2×C13×C4⋊C4—21no—
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4D411yescharacteristic
23C2×C13×C4⋊C4D412yes—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C4⋊C4D412yes—
26C2×C42×C13C2311yescharacteristic
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13—22no—
29C22×#1055—21no—
30C22×#1055—22no—
31C13×#95—22no—
32C13×#95—21no—
33C13×#95—21no—
34C13×#95—22no—
35C13×#95—22no—
36C13×#95—22no—
37#88048—42no—
38#88047—42no—
39#88043—21no—
40#88043—22no—
41#88043Q812yescomplemented
42#88043Q814yescomplemented
43#10584—131nomaximal, Sylow
44C2×Q8×C13—81no—
45C2×Q8×C13—82no—
46C22×C4×C13—21no—
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13—22no—
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13C2×D412yes—
52C22×Dic13—41no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C13×C4⋊C4—41no—
56C13×C4⋊C4—41no—
57C13×C4⋊C4—81no—
58C13×C4⋊C4—82no—
59C42×C13C2×Q811yescharacteristic
60C42×C13C2×Q812yes—
61C42×C13#4111yescharacteristic
62C4⋊Dic13—44no—
63C4⋊Dic13—41no—
64C4⋊Dic13—41no—
65C2×#1055—22no—
66C2×#1055—22no—
67C2×#1055—22no—
68C2×#1055—24no—
69C2×#1055—42no—
70C2×#1055—42no—
71#2844D1311yescharacteristic
72#1847—131no—
73#1836—132no—
74#1295—132no—
75#1295—131no—
76C23×C13#12011yescharacteristic
77Q8×C13—84no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—41no—
83C2×C4×C13—41no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13C22⋊Q811yescharacteristic
93C2×C4×C13C22⋊Q812yes—
94C2×C4×C13C4⋊Q811yescharacteristic
95C2×C4×C13C4⋊Q812yes—
96C2×Dic13—81no—
97C2×Dic13—82no—
98#1055—24no—
99#1055—44no—
100C2×#107—261no—
101C2×#106—261no—
102C2×#97—132no—
103C2×#97—131no—
104#400—22no—
105#400—21no—
106#395—22no—
107#395—21no—
108#384—131no—
109#382C2×D1312yes—
110#382C2×D1311yescharacteristic
111#340—262no—
112#340—262no—
113C22×C13#39511yescharacteristic
114C22×C13#45311yescharacteristic
115C22×C13#45412yes—
116C22×C13#45512yes—
117C22×C13#45611yescharacteristic
118C4×C13—21no—
119C4×C13—21no—
120C4×C13—22no—
121C4×C13—22no—
122C4×C13—81no—
123C4×C13—81no—
124C4×C13—82no—
125C4×C13—82no—
126Dic13—161no—
127C22×Q8—21no—
128C22×C8—261no—
129C22×C8—262no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—262no—
133C2×C4⋊C4—261no—
134C2×C4⋊C4C22⋊D1312yes—
135C2×C4⋊C4C22⋊D1312yes—
136C2×C4⋊C4C22⋊D1311yescharacteristic
137C2×C4⋊C4C22⋊D1311yescharacteristic
138C2×C42C22×D1311yescharacteristic
139#107—522no—
140#106—522no—
141#97—132no—
142#97—134no—
143#97—261no—
144#97—262no—
145#95—22no—
146#95—21no—
147#95—21no—
148#95—22no—
149#95—22no—
150#95—22no—
151C2×C13#165711yescharacteristic
152C2×C13#165911yescharacteristic
153C2×C13#166412yes—
154C2×C13#206011yescharacteristic
155C2×C13#206112yes—
156C2×Q8—81no—
157C2×Q8—82no—
158C22×C4—21no—
159C22×C4—22no—
160C22×C4—21no—
161C22×C4—22no—
162C22×C4—521no—
163C22×C4C2×C22⋊D1311yescharacteristic
164C22×C4C2×C22⋊D1312yes—
165C2×C8—262no—
166C2×C8—262no—
167C2×C8—262no—
168C2×C8—264no—
169C2×C8—522no—
170C2×C8—522no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—81no—
176C4⋊C4—82no—
177C4⋊C4—521no—
178C4⋊C4—521no—
179C4⋊C4—524no—
180C42Q8×D1312yes—
181C42Q8×D1311yescharacteristic
182C42#613111yescharacteristic
183C13#1058411yescharacteristic, complemented, Sylow
184C23#8820711yescharacteristic
185Q8—84no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—1041no—
201C2×C4—1042no—
202C2×C4#8819811yescharacteristic
203C2×C4#8819812yes—
204C2×C4#8820011yescharacteristic
205C2×C4#8820012yes—
206C8—264no—
207C8—524no—
208C22#1171889011yescharacteristic
209C22#1171890211yescharacteristic
210C22#1171890312yes—
211C22#1171890612yes—
212C22#1171890711yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—82no—
220C4—82no—
221C4—2081no—
222C2#1311413411yescharacteristic
223C2#1311414211yescharacteristic
224C2#1311417012yes—
225C2#1311617811yescharacteristic
226C2#1311618312yes—
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2844C2
socle, prime radicalC23×C13#120
hypercenter#2844D13
hypocenterC13#10584
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2844

Complements

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

NH ≅ G/Ntype
41. #88043Q8semidirect
42. #88043Q8semidirect
183. C13#10584semidirect

Maximal subgroups

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

subgroupindex
#131150052
#131149692
#131127172
C13×#28442
#1058413