Finite Group Databasebeta

← #13131004

Subgroups — #13131004

Order 1664.

344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 78 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
1D13×#124C211yesmaximal, characteristic
2C2×#88117C212yesmaximal, complemented
3C2×#88115C212yesmaximal
4C4×C4⋊#261C211yesmaximal, characteristic, complemented
5D13⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
6C2×Q8×D13C2211yescharacteristic
7C2×D4×D13C2211yescharacteristic
8C2×C4⋊#261C2212yes—
9C2×C4×#261—21no—
10C2×D13⋊C8C2212yes—
11C13×#124C411yescharacteristic, complemented
12#88201C411yescharacteristic, complemented
13#88190C411yescharacteristic, complemented
14#88139—21no—
15#88139—21no—
16C22⋊C4×D13—21no—
17C22⋊C4×D13—21no—
18#88129C411yescharacteristic, complemented
19C42×D13C2211yescharacteristic
20#88117—24no—
21#88115—24no—
22(C2×#261)⋊C4—21no—
23#88112—21no—
24C4⋊#1057—21no—
25C23×D13—21no—
26C22×#261—22no—
27C2×Q8×C13C2×C411yescharacteristic
28C2×D4×C13C2×C411yescharacteristic
29C2×C22⋊D13—21no—
30Q8×D13—22no—
31Q8×D13—22no—
32D4×D13—22no—
33D4×D13—22no—
34C2×D52C2×C411yescharacteristic
35C2×C4×D13—21no—
36C2×C4×D13D411yescharacteristic
37C2×C4×D13D411yescharacteristic
38C2×C4×D13C2311yescharacteristic
39C2×Dic26—21no—
40C2×Dic26C2×C411yescharacteristic
41C2×#1057—22no—
42C4⋊#261—22no—
43C4⋊#261D414yes—
44C4×#261—42no—
45D13⋊C8—22no—
46D13⋊C8—22no—
47C13×C22⋊C4—21no—
48C13×C22⋊C4—21no—
49C42×C13C2×C411yescharacteristic
50C22⋊Dic13—21no—
51C22⋊Dic13—21no—
52#6103—21no—
53#6103—21no—
54#6103—21no—
55#6103—21no—
56C4×Dic13C2×C411yescharacteristic
57C4×Dic13D411yescharacteristic
58C4×Dic13D411yescharacteristic
59#1983—131nomaximal, Sylow
60C23×C13—21no—
61C22×D13—21no—
62C22×D13—42no—
63C22×D13—42no—
64C22×D13—41no—
65C22×D13—41no—
66C22×D13C2×D411yescharacteristic
67C2×#261—24no—
68C2×#261—42no—
69C2×#261—42no—
70Q8×C13—22no—
71D4×C13—22no—
72C2×C4×C13—21no—
73C2×C4×C13C22⋊C411yescharacteristic
74C2×C4×C13C22⋊C411yescharacteristic
75C2×C4×C13C22×C411yescharacteristic
76C22⋊D13—41no—
77C22⋊D13—41no—
78C2×Dic13—21no—
79C2×Dic13C22⋊C411yescharacteristic
80C2×Dic13C22⋊C411yescharacteristic
81C2×Dic13C2×D411yescharacteristic
82D52—22no—
83C4×D13—22no—
84C4×D13—21no—
85C4×D13—21no—
86C4×D13—42no—
87C4×D13C2×D412yes—
88C4×D13#4112yes—
89Dic26—22no—
90Dic26—41no—
91Dic26—41no—
92#1057—42no—
93C2×#124—131no—
94C2×C4⋊C8—131no—
95C2×#103—132no—
96C2×#102—132no—
97C4×C4⋊C4—131no—
98C22×C13—41no—
99C22×C13—41no—
100C22×C13—41no—
101C22×C13C2×C22⋊C411yescharacteristic
102C2×D13—41no—
103C2×D13—41no—
104C2×D13—41no—
105C2×D13—82no—
106C2×D13—82no—
107C2×D13#12112yes—
108C2×D13#13512yes—
109C2×D13AGL(1,ℤ/8)11yescharacteristic
110C2×D13#13711yescharacteristic
111#261—44no—
112C4×C13—21no—
113C4×C13—21no—
114C4×C13—41no—
115C4×C13C4×D412yes—
116Dic13—21no—
117Dic13—21no—
118Dic13—41no—
119Dic13#12411yescharacteristic
120Dic13#12711yescharacteristic
121C22×Q8—131no—
122C22×D4—131no—
123C22×C8—132no—
124#124—131no—
125#124—131no—
126#124—131no—
127#124—261no—
128#124—261no—
129#124#26111yescharacteristic, complemented
130C2×C4⋊C4—132no—
131C2×C22⋊C4—261no—
132C2×C22⋊C4—261no—
133C2×C42—131no—
134C2×C42—261no—
135C4⋊C8—261no—
136C4⋊C8—261no—
137#103—264no—
138#102—264no—
139#95—261no—
140C2×C13—81no—
141C2×C13#39011yescharacteristic
142C2×C13#41611yescharacteristic
143C2×C13#41711yescharacteristic
144D13—81no—
145D13#46312yes—
146D13#46412yes—
147C24—261no—
148C2×Q8—131no—
149C2×Q8—261no—
150C2×Q8—262no—
151C2×Q8—262no—
152C2×Q8C2×#26111yescharacteristic
153C2×D4—131no—
154C2×D4—262no—
155C2×D4—262no—
156C2×D4—261no—
157C2×D4C2×#26111yescharacteristic
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—261no—
162C22×C4—262no—
163C2×C8—262no—
164C2×C8—262no—
165C2×C8—262no—
166C4⋊C4—134no—
167C4⋊C4—262no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—261no—
171C22⋊C4—261no—
172C22⋊C4—261no—
173C22⋊C4—261no—
174C22⋊C4—261no—
175C22⋊C4—261no—
176C42—131no—
177C42—131no—
178C42—131no—
179C42—522no—
180C42C2×#26111yescharacteristic
181C13#198311yescharacteristic, complemented, Sylow
182C23—21no—
183C23—131no—
184C23—261no—
185C23—522no—
186C23—521no—
187C23—521no—
188C23—522no—
189Q8—22no—
190Q8—262no—
191Q8—521no—
192Q8—521no—
193D4—22no—
194D4—262no—
195D4—521no—
196D4—521no—
197C2×C4—21no—
198C2×C4—131no—
199C2×C4—132no—
200C2×C4—132no—
201C2×C4—131no—
202C2×C4—131no—
203C2×C4—261no—
204C2×C4—261no—
205C2×C4—262no—
206C2×C4—264no—
207C2×C4—261no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4—522no—
211C2×C4C22⋊#26111yescharacteristic
212C2×C4C22⋊#26111yescharacteristic
213C2×C4C22×#26111yescharacteristic
214C8—522no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—132no—
219C22—131no—
220C22—131no—
221C22—132no—
222C22—521no—
223C22—521no—
224C22—521no—
225C22—1042no—
226C22—1042no—
227C22C2×C22⋊#26111yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—131no—
232C4—131no—
233C4—261no—
234C4—261no—
235C4—524no—
236C4—521no—
237C4D4×#26112yes—
238C2—81no—
239C2—132no—
240C2—132no—
241C2—1041no—
242C2#1171915111yescharacteristic
243C2#1171916411yescharacteristic
244C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC22×C13C2×C22⋊C4
prime radicalC2×D4×D13C22
cosocleC2×C4×D13C23
hypercenter#124#261
hypocenterC13#1983
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C2×#88117C2semidirect
4. C4×C4⋊#261C2semidirect
5. D13⋊(C4⋊C8)C2semidirect
11. C13×#124C4semidirect
12. #88201C4semidirect
13. #88190C4semidirect
18. #88129C4semidirect
129. #124#261semidirect
181. C13#1983semidirect

Maximal subgroups

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

subgroupindex
D13×#1242
C2×#881172
C2×#881152
C4×C4⋊#2612
D13⋊(C4⋊C8)2
#198313