Finite Group Databasebeta

← #15775767

Subgroups — #15775767

Order 3328.

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

normal subgroups only

This group has 336 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#13115997C211yesmaximal, characteristic
2#13113877C212yesmaximal
3#13112863C212yesmaximal
4#13112770C211yesmaximal, characteristic
5C13×#2809C211yesmaximal, characteristic
6#11719205C2211yescharacteristic
7C13×#400C2212yes—
8C13×#398—22no—
9C13×#391—21no—
10C13×#391C2211yescharacteristic
11C13×#389—21no—
12C13×#387—22no—
13#11718886—21no—
14#11718631—22no—
15#11718122C2211yescharacteristic
16#11718120C2212yes—
17#11718115—21no—
18#11718044—22no—
19C22×Q8×C13D411yescharacteristic
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4D412yes—
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C42×C13—21no—
27C2×C42×C13D411yescharacteristic
28#88180—21no—
29#88178—22no—
30C2×#6099—21no—
31#88144—41no—
32#88142—41no—
33C13×#95—22no—
34C13×#95—22no—
35C13×#95—22no—
36C13×#95—22no—
37C13×#95D412yes—
38#88075—41no—
39#88075—41no—
40C22⋊#1055—22no—
41#88050—42no—
42#88047—42no—
43#12225—131nomaximal, Sylow
44C2×Q8×C13—21no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13Q1612yes—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13C2×D411yescharacteristic
53C22×C4×C13C2×D412yes—
54C2×Dic26—22no—
55C13×C4⋊C4—41no—
56C13×C4⋊C4—42no—
57C13×C4⋊C4—44no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4—81no—
60C13×C4⋊C4—81no—
61C42×C13—41no—
62C42×C13—81no—
63C22⋊Dic13—41no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13—22no—
67#6101—42no—
68C4×Dic13—41no—
69#6099—41no—
70#6099—41no—
71C2×#1055—42no—
72C2×#1055—41no—
73#2809D1311yescharacteristic
74#2028—131no—
75#1617—132no—
76#1353—132no—
77#1319—131no—
78C23×C13#12011yescharacteristic
79Q8×C13—42no—
80Q8×C13—81no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13C2×Q1611yescharacteristic
98C2×C4×C13#13711yescharacteristic
99C2×Dic13—41no—
100C2×Dic13—41no—
101Dic26—82no—
102#1055—81no—
103#1055—82no—
104#544—131no—
105#484—262no—
106#419—261no—
107#400C2×D1312yes—
108#398—22no—
109#391—21no—
110#391C2×D1311yescharacteristic
111#389—21no—
112#387—22no—
113#343—131no—
114#339—261no—
115#328—262no—
116#324—132no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13#45111yescharacteristic
120C22×C13#45511yescharacteristic
121C22×C13B(4,𝔽2)11yescharacteristic
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—42no—
125C4×C13—42no—
126C4×C13—42no—
127C4×C13—82no—
128C4×C13—82no—
129Dic13—81no—
130Dic13—81no—
131C22×Q8C22⋊D1311yescharacteristic
132C2×M16—261no—
133C4⋊Q8—521no—
134#125—521no—
135C22⋊Q8—262no—
136#117—261no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4C22⋊D1312yes—
142C2×C4⋊C4C22×D1311yescharacteristic
143C2×C42—21no—
144C2×C42C22⋊D1311yescharacteristic
145#107—522no—
146#103—522no—
147#103—521no—
148#103—521no—
149C22⋊C8—262no—
150#95—22no—
151#95—22no—
152#95—22no—
153#95—22no—
154#95C22⋊D1312yes—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13#160211yescharacteristic
158C2×C13#220111yescharacteristic
159C2×C13#220411yescharacteristic
160C2×Q8—21no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—262no—
164C2×Q8#610712yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4C2×C22⋊D1311yescharacteristic
170C22×C4C2×C22⋊D1312yes—
171M16—521no—
172M16—521no—
173C2×C8—522no—
174C2×C8—521no—
175C4⋊C4—41no—
176C4⋊C4—42no—
177C4⋊C4—44no—
178C4⋊C4—42no—
179C4⋊C4—81no—
180C4⋊C4—81no—
181C4⋊C4—261no—
182C4⋊C4—261no—
183C4⋊C4—262no—
184C4⋊C4—522no—
185C22⋊C4—521no—
186C42—41no—
187C42—81no—
188C42—521no—
189C13#1222511yescharacteristic, complemented, Sylow
190C23#8820711yescharacteristic
191Q8—42no—
192Q8—81no—
193Q8—1042no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—521no—
211C2×C4—521no—
212C2×C4#8819611yescharacteristic
213C2×C4C2×#610711yescharacteristic
214C8—1041no—
215C8—1042no—
216C22—21no—
217C22—21no—
218C22#1171888911yescharacteristic
219C22#1171890311yescharacteristic
220C22#1171890511yescharacteristic
221C4—21no—
222C4—21no—
223C4—42no—
224C4—42no—
225C4—42no—
226C4—82no—
227C4—82no—
228C4—1041no—
229C4—1041no—
230C2—21no—
231C2—21no—
232C2#1311379311yescharacteristic
233C2#1311684911yescharacteristic
234C2#1311686211yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2809C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2809D13
hypocenterC13#12225
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2809

Complements

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

NH ≅ G/Ntype
189. C13#12225semidirect

Maximal subgroups

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

subgroupindex
#131159972
#131138772
#131128632
#131127702
C13×#28092
#1222513