Finite Group Databasebeta

← #15752016

Subgroups — #15752016

Order 3328.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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#13121208C211yesmaximal, characteristic
2#13116308C212yesmaximal, complemented
3#13112658C212yesmaximal, complemented
4#13112657C211yesmaximal, characteristic
5C13×#2093C211yesmaximal, characteristic
6C2×#88132—22no—
7C2×C13×#107—21no—
8C2×C13×#102—21no—
9C13×#390C2211yescharacteristic
10C13×#384C2211yescharacteristic
11#11718881—21no—
12#11718640—21no—
13C2×#88047—22no—
14#11718609—22no—
15#11718589C2212yes—
16C13×#336C2211yescharacteristic
17#11718121—22no—
18#11718116C2212yes—
19C22×D4×C13D411yescharacteristic
20C23×Dic13—21no—
21C22×Dic26—21no—
22C22×C8×C13—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C22⋊C4—22no—
27C2×C42×C13C2311yescharacteristic
28C2×C22⋊Dic13—22no—
29C2×C22⋊Dic13—21no—
30C2×C4⋊Dic13D412yes—
31C2×C4⋊Dic13D412yes—
32C2×#6101—22no—
33C2×#6101—22no—
34C22×#1055—22no—
35#88132—44no—
36#88132—44no—
37C13×#107—42no—
38C13×#102—42no—
39#88071—21no—
40#88071—22no—
41#88047—44no—
42#7797—131nomaximal, Sylow
43C24×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13—41no—
46C2×D4×C13—41no—
47C2×D4×C13Q1612yes—
48C22×C4×C13—21no—
49C22×C4×C13—41no—
50C22×C4×C13C2×D412yes—
51C22×C4×C13C2×D411yescharacteristic
52C22×Dic13—22no—
53C22×Dic13—22no—
54C22×Dic13—44no—
55C22×Dic13—81no—
56C2×Dic26—44no—
57C2×Dic26—81no—
58C2×C8×C13—22no—
59C2×C8×C13—41no—
60C2×C8×C13—41no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—42no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—42no—
68C42×C13—41no—
69C22⋊Dic13—44no—
70C22⋊Dic13—81no—
71C4⋊Dic13—22no—
72C4⋊Dic13—42no—
73C4⋊Dic13D814yes—
74#6101—44no—
75#6101—42no—
76#6101—42no—
77C2×#1055—24no—
78C2×#1055—42no—
79C2×#1055—42no—
80#2683—131no—
81#2093D1311yescharacteristic
82#2083—132no—
83#1271—132no—
84#1270—131no—
85C23×C13—22no—
86C23×C13—42no—
87C23×C13—41no—
88C23×C13—42no—
89C23×C13—41no—
90C23×C13#12011yescharacteristic
91D4×C13—42no—
92D4×C13—81no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13—82no—
100C2×C4×C13—81no—
101C2×C4×C13C2×D812yes—
102C2×C4×C13C2×Q1611yescharacteristic
103C2×C4×C13AGL(1,ℤ/8)12yes—
104C2×C4×C13#13711yescharacteristic
105C2×Dic13—24no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—84no—
112Dic26—84no—
113C8×C13—42no—
114#1055—44no—
115C2×C22⋊Q8—262no—
116C2×#107—21no—
117C2×#107—262no—
118C2×#102—21no—
119#396—262no—
120#395—261no—
121#390C2×D1311yescharacteristic
122#389—132no—
123#386—261no—
124#384C2×D1311yescharacteristic
125#340—262no—
126#336—132no—
127#336C2×D1311yescharacteristic
128C22×C13—42no—
129C22×C13—44no—
130C22×C13—82no—
131C22×C13—81no—
132C22×C13—81no—
133C22×C13#44712yes—
134C22×C13#45111yescharacteristic
135C22×C13#45311yescharacteristic
136C22×C13#45612yes—
137C22×C13#45811yescharacteristic
138C4×C13—22no—
139C4×C13—22no—
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—81no—
143C4×C13—161no—
144Dic13—44no—
145Dic13—82no—
146C22×Q8—261no—
147C22×D4C22⋊D1311yescharacteristic
148C23×C4—261no—
149C22×C8—21no—
150C22×C8—262no—
151C22⋊Q8—524no—
152C22⋊Q8—524no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—132no—
156C2×C4⋊C4—132no—
157C2×C4⋊C4—262no—
158C2×C4⋊C4—262no—
159C2×C4⋊C4C22⋊D1311yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—262no—
162C2×C22⋊C4—261no—
163C2×C42C22×D1311yescharacteristic
164#107—42no—
165#107—524no—
166#102—42no—
167#95—261no—
168#95—262no—
169C2×C13—82no—
170C2×C13#161012yes—
171C2×C13#161411yescharacteristic
172C2×C13#161911yescharacteristic
173C2×C13#164912yes—
174C2×C13#166011yescharacteristic
175C24—21no—
176C2×Q8—524no—
177C2×Q8—1041no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4#610712yes—
182C22×C4—21no—
183C22×C4—41no—
184C22×C4—262no—
185C22×C4—262no—
186C22×C4—524no—
187C22×C4—1041no—
188C22×C4D4×D1312yes—
189C22×C4C2×C22⋊D1311yescharacteristic
190C2×C8—22no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—264no—
194C2×C8—522no—
195C2×C8—522no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—134no—
202C4⋊C4—262no—
203C4⋊C4—522no—
204C4⋊C4—524no—
205C4⋊C4—522no—
206C4⋊C4—522no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C22⋊C4—524no—
210C22⋊C4—1041no—
211C42—41no—
212C13#779711yescharacteristic, complemented, Sylow
213C23—22no—
214C23—41no—
215C23—41no—
216C23—42no—
217C23—42no—
218C23#8819111yescharacteristic
219Q8—1044no—
220D4—42no—
221D4—81no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—81no—
229C2×C4—82no—
230C2×C4—264no—
231C2×C4—522no—
232C2×C4—522no—
233C2×C4—522no—
234C2×C4—522no—
235C2×C4—522no—
236C2×C4—1044no—
237C2×C4D8×D1312yes—
238C2×C4#8816512yes—
239C2×C4C2×#610711yescharacteristic
240C2×C4#8820511yescharacteristic
241C8—42no—
242C8—524no—
243C22—42no—
244C22—44no—
245C22—81no—
246C22—81no—
247C22—82no—
248C22#1171871111yescharacteristic
249C22#1171871411yescharacteristic
250C22#1171873811yescharacteristic
251C22#1171881712yes—
252C22#1171886612yes—
253C4—21no—
254C4—21no—
255C4—22no—
256C4—22no—
257C4—81no—
258C4—161no—
259C4—524no—
260C4—1042no—
261C2—82no—
262C2#1311383712yes—
263C2#1311386011yescharacteristic
264C2#1311388811yescharacteristic
265C2#1311408412yes—
266C2#1311414511yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2093C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2093D13
hypocenterC13#7797
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
2. #13116308C2semidirect
3. #13112658C2semidirect
212. C13#7797semidirect

Maximal subgroups

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

subgroupindex
#131212082
#131163082
#131126582
#131126572
C13×#20932
#779713