Finite Group Databasebeta

← #13115283

Subgroups — #13115283

Order 1664.

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

normal subgroups only

This group has 358 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#11719229C211yesmaximal, characteristic
2C2×#88126C211yesmaximal, characteristic, complemented
3C2×#88065C211yesmaximal, characteristic, complemented
4#11718787C211yesmaximal, characteristic, complemented
5C2×#88045C211yesmaximal, characteristic, complemented
6C13×#339C211yesmaximal, characteristic, complemented
7#11718124C211yesmaximal, characteristic, complemented
8C2×#6127C2211yescharacteristic
9C22×C4×D13C2211yescharacteristic
10C2×C13×M16C2211yescharacteristic
11C13×#117C2211yescharacteristic
12C2×C42×C13C2211yescharacteristic
13C2×#6103—21no—
14C2×#6101—21no—
15C2×C4×Dic13C2211yescharacteristic
16C2×#6099C2211yescharacteristic
17#88151C412yescomplemented
18#88149C412yescomplemented
19#88140—21no—
20#88136—21no—
21C4×D52—22no—
22#88126—22no—
23#88126—22no—
24#88065—22no—
25#88060—22no—
26#88045—22no—
27C23×D13D411yescharacteristic
28C22×C4×C13—21no—
29C22×C4×C13C2311yescharacteristic
30C2×C22⋊D13—21no—
31C22×Dic13—21no—
32C22×Dic13D411yescharacteristic
33#6127—21no—
34#6127—21no—
35#6127—21no—
36#6127—21no—
37C2×D52—22no—
38C2×D52C2×C411yescharacteristic
39C2×C4×D13—21no—
40C2×C4×D13—21no—
41C2×C4×D13—21no—
42C2×C4×D13—21no—
43C2×C4×D13—21no—
44C2×C4×D13C2×C412yes—
45C2×C4×D13D412yes—
46C2×Dic26C2×C411yescharacteristic
47C13×M16—21no—
48C13×M16—21no—
49C2×C8×C13—21no—
50C13×C4⋊C4C2×C412yes—
51C13×C22⋊C4—21no—
52C42×C13—21no—
53C42×C13—21no—
54C42×C13D412yescomplemented
55#6103—24no—
56#6103—22no—
57#6103—22no—
58C4⋊Dic13—22no—
59#6101—24no—
60C4×Dic13—21no—
61C4×Dic13D412yescomplemented
62#6099—21no—
63#6099—21no—
64C2×#1055—21no—
65#1897—131nomaximal, Sylow
66C23×C13C2×D411yescharacteristic
67C22×D13—21no—
68C22×D13—21no—
69C22×D13—21no—
70C22×D13—42no—
71C22×D13C22⋊C412yes—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—42no—
75C2×C4×C13C22×C411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13#4111yescharacteristic
80C2×C4×C13#4111yescharacteristic
81C22⋊D13—41no—
82C22⋊D13—41no—
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—22no—
87C2×Dic13—42no—
88C2×Dic13C22⋊C412yes—
89D52—21no—
90D52—21no—
91D52—44no—
92C4×D13—22no—
93C4×D13—22no—
94C4×D13—22no—
95C4×D13—22no—
96C4×D13—41no—
97C4×D13—41no—
98Dic26—21no—
99Dic26—21no—
100C8×C13—41no—
101#1055—41no—
102#525—131no—
103C2×#117—131no—
104C2×#104—131no—
105C2×#104—131no—
106#407—131no—
107#339—131no—
108#339D1311yescharacteristic, complemented
109C22×C13—22no—
110C22×C13C2×C22⋊C411yescharacteristic
111C22×C13#12011yescharacteristic
112C22×C13#12311yescharacteristic
113C2×D13—22no—
114C2×D13—22no—
115C2×D13—22no—
116C2×D13—42no—
117C2×D13—42no—
118C2×D13—41no—
119C2×D13—42no—
120C4×C13—42no—
121C4×C13—42no—
122C4×C13C4×D411yescharacteristic
123C4×C13C4×D411yescharacteristic
124C4×C13#12111yescharacteristic
125C4×C13#12111yescharacteristic
126Dic13—22no—
127Dic13—42no—
128Dic13—41no—
129C2×#41—131no—
130C23×C4—131no—
131C2×M16—131no—
132C2×M16C2×D1311yescharacteristic
133#123—261no—
134C22⋊Q8—132no—
135#121—132no—
136#120—261no—
137C4×D4—262no—
138#117—262no—
139#117—262no—
140#117C2×D1311yescharacteristic
141C2×C4⋊C4—261no—
142C2×C22⋊C4—261no—
143C2×C42—131no—
144C2×C42C2×D1311yescharacteristic
145#104—262no—
146#104—262no—
147C22⋊C8—262no—
148C2×C13—21no—
149C2×C13—21no—
150C2×C13#38611yescharacteristic
151C2×C13#42112yes—
152D13—42no—
153D13—81no—
154C24—131no—
155#41—261no—
156#41—261no—
157#41—261no—
158#41—261no—
159C2×Q8—131no—
160C2×D4—131no—
161C2×D4—262no—
162C2×D4—261no—
163C22×C4—21no—
164C22×C4—131no—
165C22×C4—132no—
166C22×C4—132no—
167C22×C4—261no—
168C22×C4—261no—
169C22×C4—261no—
170C22×C4—261no—
171C22×C4—261no—
172C22×C4—261no—
173C22×C4C22×D1311yescharacteristic
174M16—21no—
175M16—21no—
176M16—261no—
177M16—261no—
178C2×C8—21no—
179C2×C8—261no—
180C4⋊C4—262no—
181C4⋊C4—264no—
182C4⋊C4C4×D1312yes—
183C22⋊C4—21no—
184C22⋊C4—262no—
185C22⋊C4—262no—
186C22⋊C4—264no—
187C42—21no—
188C42—21no—
189C42—132no—
190C42—261no—
191C42D5212yescomplemented
192C13#189711yescharacteristic, complemented, Sylow
193C23—132no—
194C23—261no—
195C23—261no—
196C23—261no—
197C23—522no—
198C23D4×D1311yescharacteristic
199Q8—261no—
200Q8—261no—
201D4—261no—
202D4—261no—
203D4—524no—
204D4—521no—
205D4—521no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—132no—
210C2×C4—261no—
211C2×C4—261no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—261no—
217C2×C4—262no—
218C2×C4—522no—
219C2×C4—521no—
220C2×C4—521no—
221C2×C4C2×C4×D1311yescharacteristic
222C2×C4C2×D5211yescharacteristic
223C2×C4#612711yescharacteristic
224C2×C4D4×D1311yescharacteristic
225C2×C4D4×D1311yescharacteristic
226C2×C4#613111yescharacteristic
227C8—41no—
228C8—521no—
229C22—22no—
230C22—262no—
231C22—262no—
232C22—262no—
233C22—522no—
234C22—522no—
235C22—522no—
236C22—521no—
237C22C22⋊C4×D1311yescharacteristic
238C22#8813611yescharacteristic
239C22#8814811yescharacteristic
240C4—42no—
241C4—42no—
242C4—262no—
243C4—522no—
244C4—521no—
245C4C4×D5211yescharacteristic
246C4#8813811yescharacteristic
247C4#8814711yescharacteristic
248C4#8814911yescharacteristic
249C2—21no—
250C2—21no—
251C2—522no—
252C2—1041no—
253C2#1171832611yescharacteristic
254C2#1171848212yes—
subgroupG/H
centerC2×C4D4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#339C2
socleC22×C13C2×C22⋊C4
prime radical#11719229C2
cosocleC22×C4×C13C23
hypercenter#339D13
hypocenterC13#1897
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×#88126C2semidirect
3. C2×#88065C2semidirect
4. #11718787C2semidirect
5. C2×#88045C2semidirect
6. C13×#339C2semidirect
7. #11718124C2semidirect
17. #88151C4semidirect
18. #88149C4semidirect
54. C42×C13D4semidirect
61. C4×Dic13D4semidirect
108. #339D13semidirect
191. C42D52semidirect
192. C13#1897semidirect

Maximal subgroups

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

subgroupindex
#117192292
C2×#881262
C2×#880652
#117187872
C2×#880452
C13×#3392
#117181242
#189713