Finite Group Databasebeta

← #15752186

Subgroups — #15752186

Order 3328.

418 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 83 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#13121766C211yesmaximal, characteristic
2#13116398C212yesmaximal, complemented
3#13112660C212yesmaximal, complemented
4#13112657C211yesmaximal, characteristic
5C13×#2094C211yesmaximal, characteristic
6C2×#88189—21no—
7C2×C13×#106—21no—
8C2×C13×#102—21no—
9C13×#390C2211yescharacteristic
10C13×#384C2211yescharacteristic
11#11718644—21no—
12#11718614—22no—
13#11718611—22no—
14#11718589C2212yes—
15C13×#336C2211yescharacteristic
16#11718121—22no—
17#11718121—22no—
18#11718116C2212yes—
19C22×D4×C13D411yescharacteristic
20C23×Dic13—21no—
21C22×C8×C13—21no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C22⋊C4—22no—
26C2×C42×C13C2311yescharacteristic
27C2×C22⋊Dic13—22no—
28C2×C22⋊Dic13—21no—
29#88189—42no—
30#88189—42no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13D412yes—
33C2×C4⋊Dic13D412yes—
34C2×#6101—22no—
35C22×#1055—22no—
36C13×#106—42no—
37C13×#102—42no—
38#88071—22no—
39#88071—21no—
40#88071—22no—
41#7824—131nomaximal, Sylow
42C24×C13—21no—
43C2×D4×C13—21no—
44C2×D4×C13—41no—
45C2×D4×C13—41no—
46C2×D4×C13SD1612yes—
47C22×C4×C13—21no—
48C22×C4×C13—41no—
49C22×C4×C13C2×D412yes—
50C22×C4×C13C2×D411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13—42no—
54C22×Dic13—81no—
55C22×Dic13—81no—
56C2×C8×C13—22no—
57C2×C8×C13—41no—
58C2×C8×C13—41no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—44no—
63C13×C22⋊C4—42no—
64C13×C22⋊C4—42no—
65C42×C13—41no—
66C22⋊Dic13—42no—
67C22⋊Dic13—44no—
68C4⋊Dic13—22no—
69C4⋊Dic13—22no—
70C4⋊Dic13—42no—
71C4⋊Dic13—81no—
72#6101—42no—
73#6101—42no—
74C2×#1055—42no—
75C2×#1055—42no—
76C2×#1055—42no—
77#2724—131no—
78#2100—132no—
79#2094D1311yescharacteristic
80#1271—132no—
81#1270—131no—
82C23×C13—22no—
83C23×C13—42no—
84C23×C13—41no—
85C23×C13—42no—
86C23×C13—41no—
87C23×C13#12011yescharacteristic
88D4×C13—42no—
89D4×C13—81no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13—81no—
97C2×C4×C13—82no—
98C2×C4×C13C2×SD1611yescharacteristic
99C2×C4×C13#13512yes—
100C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
101C2×C4×C13#13712yes—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—84no—
109C8×C13—42no—
110#1055—82no—
111C2×#123—261no—
112C2×#106—21no—
113C2×#102—21no—
114#398—261no—
115#397—262no—
116#390C2×D1311yescharacteristic
117#389—132no—
118#385—262no—
119#384C2×D1311yescharacteristic
120#340—262no—
121#340—262no—
122#336—132no—
123#336C2×D1311yescharacteristic
124C22×C13—42no—
125C22×C13—44no—
126C22×C13—82no—
127C22×C13—81no—
128C22×C13—81no—
129C22×C13#45011yescharacteristic
130C22×C13#45212yes—
131C22×C13#45311yescharacteristic
132C22×C13#45412yes—
133C22×C13#45811yescharacteristic
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—22no—
137C4×C13—22no—
138C4×C13—81no—
139C4×C13—161no—
140Dic13—82no—
141Dic13—82no—
142C22×D4C22⋊D1311yescharacteristic
143C23×C4—261no—
144C22×C8—21no—
145C22×C8—262no—
146#123—522no—
147#123—522no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—132no—
152C2×C4⋊C4—262no—
153C2×C4⋊C4—261no—
154C2×C4⋊C4C22⋊D1311yescharacteristic
155C2×C22⋊C4—22no—
156C2×C22⋊C4—262no—
157C2×C22⋊C4—261no—
158C2×C42C22×D1311yescharacteristic
159#106—42no—
160#102—42no—
161#95—262no—
162#95—261no—
163#95—262no—
164C2×C13—82no—
165C2×C13#161311yescharacteristic
166C2×C13#161512yes—
167C2×C13#163011yescharacteristic
168C2×C13#163512yes—
169C2×C13#165711yescharacteristic
170C24—21no—
171C2×D4—21no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4#610612yes—
175C22×C4—21no—
176C22×C4—41no—
177C22×C4—262no—
178C22×C4—262no—
179C22×C4—522no—
180C22×C4—1041no—
181C22×C4—1041no—
182C22×C4D4×D1312yes—
183C22×C4C2×C22⋊D1311yescharacteristic
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—522no—
188C2×C8—522no—
189C2×C8—522no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—44no—
194C4⋊C4—262no—
195C4⋊C4—262no—
196C4⋊C4—522no—
197C4⋊C4—522no—
198C4⋊C4—522no—
199C4⋊C4—1041no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C22⋊C4—522no—
203C22⋊C4—524no—
204C42—41no—
205C13#782411yescharacteristic, complemented, Sylow
206C23—22no—
207C23—41no—
208C23—41no—
209C23—42no—
210C23—42no—
211C23#8819111yescharacteristic
212D4—42no—
213D4—81no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—81no—
221C2×C4—82no—
222C2×C4—522no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—522no—
226C2×C4—522no—
227C2×C4—522no—
228C2×C4—1044no—
229C2×C4#8816912yes—
230C2×C4#8817012yes—
231C2×C4C2×#610611yescharacteristic
232C2×C4#8820311yescharacteristic
233C8—42no—
234C8—1042no—
235C22—44no—
236C22—42no—
237C22—82no—
238C22—81no—
239C22—81no—
240C22#1171870711yescharacteristic
241C22#1171871411yescharacteristic
242C22#1171873811yescharacteristic
243C22#1171883412yes—
244C22#1171886212yes—
245C4—22no—
246C4—22no—
247C4—21no—
248C4—21no—
249C4—81no—
250C4—161no—
251C4—1042no—
252C4—1042no—
253C2—82no—
254C2#1311385511yescharacteristic
255C2#1311386412yes—
256C2#1311395511yescharacteristic
257C2#1311398512yes—
258C2#1311413211yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2094C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2094D13
hypocenterC13#7824
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
2. #13116398C2semidirect
3. #13112660C2semidirect
205. C13#7824semidirect

Maximal subgroups

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

subgroupindex
#131217662
#131163982
#131126602
#131126572
C13×#20942
#782413