Finite Group Databasebeta

← #15776003

Subgroups — #15776003

Order 3328.

330 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 63 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#13116186C211yesmaximal, characteristic
2#13113877C212yesmaximal
3#13112863C212yesmaximal
4#13112780C211yesmaximal, characteristic
5C13×#2844C211yesmaximal, characteristic
6#11719205C2211yescharacteristic
7C13×#400—22no—
8C13×#400C2212yes—
9C13×#395—22no—
10C13×#395—21no—
11C13×#382—21no—
12C13×#382C2211yescharacteristic
13#11718631—22no—
14#11718625—21no—
15#11718122C2211yescharacteristic
16#11718120C2212yes—
17#11718115—21no—
18#11718044—22no—
19C22×Q8×C13—21no—
20C2×C13×C4⋊C4—21no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4D411yescharacteristic
24C2×C13×C4⋊C4D412yes—
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C42×C13D411yescharacteristic
27#88180—21no—
28#88178—22no—
29C2×#6099—21no—
30#88144—41no—
31#88142—41no—
32C13×#95—22no—
33C13×#95—21no—
34C13×#95—22no—
35C13×#95—22no—
36C13×#95—22no—
37C13×#95D412yes—
38C22⋊#1055—22no—
39#88050—42no—
40#88048—41no—
41#88047—41no—
42#88047—42no—
43#12261—131nomaximal, Sylow
44C2×Q8×C13—82no—
45C2×Q8×C13—81no—
46C22×C4×C13—21no—
47C22×C4×C13—22no—
48C22×C4×C13—22no—
49C22×C4×C13—21no—
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13C2×D412yes—
52C2×Dic26—22no—
53C13×C4⋊C4—41no—
54C13×C4⋊C4—41no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4—81no—
57C13×C4⋊C4—81no—
58C13×C4⋊C4—82no—
59C42×C13—21no—
60C42×C13Q1612yes—
61C22⋊Dic13—41no—
62C4⋊Dic13—21no—
63C4⋊Dic13—22no—
64C4⋊Dic13—21no—
65#6101—42no—
66C4×Dic13—41no—
67#6099—22no—
68#6099—41no—
69C2×#1055—41no—
70C2×#1055—42no—
71#2844D1311yescharacteristic
72#2061—131no—
73#1617—132no—
74#1353—132no—
75#1324—131no—
76C23×C13#12011yescharacteristic
77Q8×C13—84no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
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—41no—
92C2×C4×C13—42no—
93C2×C4×C13C2×Q1611yescharacteristic
94C2×C4×C13#13711yescharacteristic
95C2×Dic13—41no—
96C2×Dic13—41no—
97Dic26—82no—
98#1055—42no—
99#1055—82no—
100#544—131no—
101#484—262no—
102#428—261no—
103#400—22no—
104#400C2×D1312yes—
105#395—22no—
106#395—21no—
107#382—21no—
108#382C2×D1311yescharacteristic
109#343—131no—
110#339—261no—
111#328—262no—
112#324—132no—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13#45111yescharacteristic
116C22×C13#45611yescharacteristic
117C22×C13B(4,𝔽2)11yescharacteristic
118C4×C13—21no—
119C4×C13—21no—
120C4×C13—42no—
121C4×C13—42no—
122C4×C13—82no—
123C4×C13—81no—
124C4×C13—82no—
125Dic13—81no—
126Dic13—81no—
127C22×Q8—21no—
128C2×M16—261no—
129C4⋊Q8—521no—
130#125—521no—
131C22⋊Q8—262no—
132#117—261no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4C22⋊D1311yescharacteristic
137C2×C4⋊C4C22⋊D1312yes—
138C2×C4⋊C4C22×D1311yescharacteristic
139C2×C42C22⋊D1311yescharacteristic
140#107—521no—
141#107—522no—
142#106—521no—
143#103—522no—
144C22⋊C8—262no—
145#95—22no—
146#95—21no—
147#95—22no—
148#95—22no—
149#95—22no—
150#95C22⋊D1312yes—
151C2×C13—21no—
152C2×C13—21no—
153C2×C13#160511yescharacteristic
154C2×C13#220111yescharacteristic
155C2×C13#220211yescharacteristic
156C2×Q8—82no—
157C2×Q8—81no—
158C2×Q8—262no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—21no—
163C22×C4C2×C22⋊D1311yescharacteristic
164C22×C4C2×C22⋊D1312yes—
165M16—262no—
166M16—521no—
167C2×C8—521no—
168C2×C8—522no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C4⋊C4—41no—
172C4⋊C4—81no—
173C4⋊C4—81no—
174C4⋊C4—82no—
175C4⋊C4—261no—
176C4⋊C4—261no—
177C4⋊C4—262no—
178C4⋊C4—522no—
179C22⋊C4—521no—
180C42—21no—
181C42—521no—
182C42#610712yes—
183C13#1226111yescharacteristic, complemented, Sylow
184C23#8820711yescharacteristic
185Q8—84no—
186Q8—1042no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—42no—
202C2×C4—521no—
203C2×C4—521no—
204C2×C4#8819611yescharacteristic
205C2×C4C2×#610711yescharacteristic
206C8—522no—
207C8—1042no—
208C22—21no—
209C22—21no—
210C22#1171888911yescharacteristic
211C22#1171890511yescharacteristic
212C22#1171890711yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—82no—
218C4—82no—
219C4—81no—
220C4—1041no—
221C4—1041no—
222C2—21no—
223C2—21no—
224C2#1311381011yescharacteristic
225C2#1311684911yescharacteristic
226C2#1311685311yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2844C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2844D13
hypocenterC13#12261
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2844

Complements

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

NH ≅ G/Ntype
183. C13#12261semidirect

Maximal subgroups

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

subgroupindex
#131161862
#131138772
#131128632
#131127802
C13×#28442
#1226113