Finite Group Databasebeta

← #13116087

Subgroups — #13116087

Order 1664.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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#11719198C211yesmaximal, characteristic
2C13×#385C211yesmaximal, characteristic, complemented
3#11718874C212yesmaximal, complemented
4C2×#88046C212yesmaximal, complemented
5#11718118C211yesmaximal, characteristic, complemented
6C23×C4×C13C2211yescharacteristic
7C22×C22⋊D13C2212yes—
8C2×C13×C4⋊C4—21no—
9C2×C13×C22⋊C4C2211yescharacteristic
10C2×C13×C22⋊C4C2211yescharacteristic
11C2×C22⋊Dic13C2212yes—
12#88184—21no—
13#88184—21no—
14C2×#6103—22no—
15#88140—22no—
16#88136—22no—
17C13×#95—21no—
18#88071—22no—
19#88046—24no—
20C24×C13C2311yescharacteristic
21C23×D13D412yes—
22C22×C4×C13—22no—
23C22×C4×C13—21no—
24C22×C4×C13—21no—
25C22×C4×C13—42no—
26C22×C4×C13D411yescharacteristic
27C22×C4×C13D411yescharacteristic
28C2×C22⋊D13—22no—
29C2×C22⋊D13—22no—
30C2×C22⋊D13—22no—
31C2×C22⋊D13—22no—
32C2×C22⋊D13—22no—
33C2×C22⋊D13—22no—
34C22×Dic13—22no—
35C22×Dic13D412yes—
36C2×D52—21no—
37C2×D52—21no—
38C13×C4⋊C4—42no—
39C13×C22⋊C4—22no—
40C13×C22⋊C4—21no—
41C13×C22⋊C4D412yescomplemented
42C22⋊Dic13—22no—
43C22⋊Dic13—22no—
44#6103—22no—
45#6103—22no—
46#6103—44no—
47C4⋊Dic13—21no—
48C4⋊Dic13—21no—
49#2044—131nomaximal, Sylow
50C23×C13—41no—
51C23×C13—41no—
52C23×C13C2×D412yes—
53C23×C13C2×D411yescharacteristic
54C23×C13C2×D411yescharacteristic
55C23×C13#4111yescharacteristic
56C23×C13#4112yes—
57C22×D13—22no—
58C22×D13—22no—
59C22×D13—22no—
60C22×D13—42no—
61C22×D13—42no—
62C2×C4×C13—24no—
63C2×C4×C13—22no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13—22no—
67C2×C4×C13—41no—
68C2×C4×C13—41no—
69C2×C4×C13—42no—
70C2×C4×C13—41no—
71C2×C4×C13—41no—
72C2×C4×C13—41no—
73C2×C4×C13—41no—
74C22⋊D13—42no—
75C22⋊D13—42no—
76C22⋊D13—42no—
77C22⋊D13—42no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—42no—
82C2×Dic13—42no—
83C2×Dic13—42no—
84D52—81no—
85D52—81no—
86#534—131no—
87C2×#99—132no—
88#386—132no—
89#385D1311yescharacteristic, complemented
90#342—131no—
91C22×C13—22no—
92C22×C13—21no—
93C22×C13—22no—
94C22×C13—21no—
95C22×C13—41no—
96C22×C13—41no—
97C22×C13—42no—
98C22×C13#12011yescharacteristic
99C22×C13#12112yes—
100C22×C13#12111yescharacteristic
101C22×C13#12312yes—
102C22×C13#12411yescharacteristic
103C2×D13—44no—
104C2×D13—42no—
105C2×D13—42no—
106C2×D13—42no—
107C2×D13—82no—
108C4×C13—42no—
109C4×C13—41no—
110C4×C13—42no—
111C4×C13—41no—
112Dic13—42no—
113Dic13—82no—
114C22×D4—132no—
115C23×C4C2×D1311yescharacteristic
116#123—262no—
117#121—261no—
118#121—261no—
119#120—262no—
120C2×C4⋊C4—21no—
121C2×C22⋊C4—132no—
122C2×C22⋊C4—262no—
123C2×C22⋊C4C2×D1311yescharacteristic
124C2×C22⋊C4C2×D1311yescharacteristic
125#99—264no—
126#95—21no—
127#95—262no—
128C2×C13—22no—
129C2×C13—21no—
130C2×C13—22no—
131C2×C13—21no—
132C2×C13#39411yescharacteristic
133C2×C13B(4,𝔽2)11yescharacteristic
134C2×C13#45811yescharacteristic
135D13—82no—
136C24—132no—
137C24C22×D1311yescharacteristic
138C2×D4—261no—
139C2×D4—261no—
140C2×D4—262no—
141C2×D4—262no—
142C2×D4—262no—
143C2×D4—262no—
144C2×D4—262no—
145C2×D4—262no—
146C22×C4—22no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—42no—
150C22×C4—132no—
151C22×C4—262no—
152C22×C4C22⋊D1311yescharacteristic
153C22×C4C22⋊D1311yescharacteristic
154C4⋊C4—42no—
155C4⋊C4—261no—
156C4⋊C4—261no—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—262no—
160C22⋊C4—262no—
161C22⋊C4—262no—
162C22⋊C4—262no—
163C22⋊C4—524no—
164C22⋊C4D5212yescomplemented
165C13#204411yescharacteristic, complemented, Sylow
166C23—41no—
167C23—41no—
168C23—262no—
169C23—262no—
170C23—262no—
171C23—522no—
172C23—522no—
173C23C2×D5211yescharacteristic
174C23#612711yescharacteristic
175C23D4×D1312yes—
176C23#613112yes—
177C23C2×C22⋊D1311yescharacteristic
178D4—522no—
179D4—522no—
180D4—522no—
181D4—522no—
182D4—1041no—
183D4—1041no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—522no—
200C2×C4—522no—
201C2×C4—522no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—524no—
210C22—522no—
211C22—522no—
212C22—522no—
213C22—1042no—
214C22#8814812yes—
215C22#8814912yes—
216C22#8818411yescharacteristic
217C22#8819111yescharacteristic
218C22#8820111yescharacteristic
219C4—42no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—522no—
224C4—1042no—
225C2—21no—
226C2—22no—
227C2—22no—
228C2—21no—
229C2—1042no—
230C2#1171865211yescharacteristic
231C2#1171869311yescharacteristic
232C2#1171871411yescharacteristic
subgroupG/H
centerC22#88191
commutator, cosocleC24×C13C23
FrattiniC24C22×D13
FittingC13×#385C2
socleC22×C13#120
prime radical#11719198C2
hypercenter#385D13
hypocenterC13#2044
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C13×#385C2semidirect
3. #11718874C2semidirect
4. C2×#88046C2semidirect
5. #11718118C2semidirect
41. C13×C22⋊C4D4semidirect
89. #385D13semidirect
164. C22⋊C4D52semidirect
165. C13#2044semidirect

Maximal subgroups

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

subgroupindex
#117191982
C13×#3852
#117188742
C2×#880462
#117181182
#204413