Finite Group Databasebeta

← #13113377

Subgroups — #13113377

Order 1664.

286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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#11719496C211yesmaximal, characteristic
2C13×#380C211yesmaximal, characteristic, complemented
3#11718868C211yesmaximal, characteristic, complemented
4#11718044C212yesmaximal, complemented
5#11718043C212yesmaximal, complemented
6C23×C4×C13C2211yescharacteristic
7C2×#6127C411yescharacteristic, complemented
8C2×C13×C4⋊C4—21no—
9C2×C13×C22⋊C4—21no—
10#88207—21no—
11#88184C411yescharacteristic, complemented
12#88184C2211yescharacteristic
13#88183—21no—
14C4×C22⋊D13—21no—
15C4×C22⋊D13—21no—
16#88180C411yescharacteristic, complemented
17#88178C411yescharacteristic, complemented
18#88178C2211yescharacteristic
19C2×#6099—21no—
20C13×#95C2212yes—
21C22⋊#1055—21no—
22C22⋊#1055C2212yes—
23C24×C13D411yescharacteristic
24C22×C4×C13—22no—
25C22×C4×C13—42no—
26C22×C4×C13C2×C411yescharacteristic
27C22×C4×C13C2×C411yescharacteristic
28C22×C4×C13D411yescharacteristic
29C22×C4×C13D411yescharacteristic
30C22×C4×C13D411yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C2×C22⋊D13—21no—
33C2×C22⋊D13—21no—
34C2×C22⋊D13—21no—
35#6127—42no—
36C2×D52C2×C411yescharacteristic
37C2×C4×D13—21no—
38C2×Dic26C2×C411yescharacteristic
39C13×C4⋊C4—42no—
40C13×C22⋊C4—42no—
41C22⋊Dic13—21no—
42C22⋊Dic13—21no—
43C22⋊Dic13—21no—
44#6103—21no—
45#6103—21no—
46C4⋊Dic13C2×C411yescharacteristic
47C4⋊Dic13C2×C411yescharacteristic
48#6101—21no—
49#6101—21no—
50C4×Dic13—21no—
51#6099—42no—
52C2×#1055—22no—
53#1513—131nomaximal, Sylow
54C23×C13—21no—
55C23×C13—21no—
56C23×C13—41no—
57C23×C13—41no—
58C23×C13C22⋊C411yescharacteristic
59C23×C13C22⋊C411yescharacteristic
60C23×C13C2×D411yescharacteristic
61C22×D13—21no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13—42no—
69C2×C4×C13—42no—
70C2×C4×C13—42no—
71C2×C4×C13C22⋊C411yescharacteristic
72C2×C4×C13C22⋊C411yescharacteristic
73C2×C4×C13C22×C411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C22⋊D13—42no—
76C22⋊D13—42no—
77C22⋊D13—41no—
78C22⋊D13—41no—
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13—21no—
82D52—41no—
83C4×D13—42no—
84Dic26—41no—
85#1055—42no—
86#525—131no—
87#407—131no—
88#380D1311yescharacteristic, complemented
89#328—132no—
90#327—132no—
91C22×C13—21no—
92C22×C13—21no—
93C22×C13—21no—
94C22×C13—21no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13—21no—
98C22×C13—21no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13C2×C22⋊C411yescharacteristic
102C22×C13AGL(1,ℤ/8)11yescharacteristic
103C22×C13#13711yescharacteristic
104C2×D13—41no—
105C2×D13—41no—
106C2×D13—41no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—82no—
111C4×C13#9912yes—
112Dic13—41no—
113Dic13—41no—
114Dic13—41no—
115C2×#41—131no—
116C23×C4C2×D1311yescharacteristic
117C2×M16—261no—
118#123—261no—
119C22⋊Q8—131no—
120C22⋊Q8—131no—
121#121—131no—
122#121—131no—
123#120—261no—
124C4×D4—261no—
125C4×D4—261no—
126#117—131no—
127C2×C4⋊C4—21no—
128C2×C22⋊C4—21no—
129C22⋊C8—132no—
130C22⋊C8—261no—
131#95C2×D1312yes—
132C2×C13—21no—
133C2×C13—21no—
134C2×C13—41no—
135C2×C13—41no—
136C2×C13C2×#9911yescharacteristic
137C2×C13#41711yescharacteristic
138C2×C13#42111yescharacteristic
139D13—81no—
140C24C22⋊D1311yescharacteristic
141#41—522no—
142C2×Q8—131no—
143C2×D4—131no—
144C2×D4—261no—
145C2×D4—261no—
146C2×D4—261no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—261no—
150C22×C4C4×D1311yescharacteristic
151C22×C4C4×D1311yescharacteristic
152C22×C4D5211yescharacteristic
153C22×C4D5211yescharacteristic
154C22×C4C22⋊D1311yescharacteristic
155C22×C4C22×D1311yescharacteristic
156M16—522no—
157C2×C8—262no—
158C4⋊C4—42no—
159C4⋊C4—131no—
160C4⋊C4—131no—
161C4⋊C4—261no—
162C4⋊C4—261no—
163C22⋊C4—42no—
164C22⋊C4—261no—
165C22⋊C4—261no—
166C22⋊C4—261no—
167C22⋊C4—261no—
168C22⋊C4—261no—
169C42—261no—
170C13#151311yescharacteristic, complemented, Sylow
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23—261no—
176C23#610311yescharacteristic
177C23#610311yescharacteristic
178C23C2×C22⋊D1311yescharacteristic
179Q8—521no—
180D4—521no—
181D4—522no—
182D4—522no—
183D4—521no—
184D4—521no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—522no—
198C2×C4#610311yescharacteristic
199C2×C4#610311yescharacteristic
200C2×C4C2×C4×D1311yescharacteristic
201C2×C4C2×D5211yescharacteristic
202C8—522no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—521no—
214C22—521no—
215C22—521no—
216C22C2×#610311yescharacteristic
217C22#8818611yescharacteristic
218C22#8819611yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—82no—
223C4—521no—
224C4—521no—
225C4—521no—
226C4#8804612yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—1041no—
232C2C2×#8804611yescharacteristic
233C2#1171862711yescharacteristic
234C2#1171866611yescharacteristic
subgroupG/H
centerC22C2×#6103
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#380C2
socleC22×C13C2×C22⋊C4
prime radical#11719496C2
cosocleC22×C4×C13C23
hypercenter#380D13
hypocenterC13#1513
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C13×#380C2semidirect
3. #11718868C2semidirect
4. #11718044C2semidirect
5. #11718043C2semidirect
7. C2×#6127C4semidirect
11. #88184C4semidirect
16. #88180C4semidirect
17. #88178C4semidirect
88. #380D13semidirect
170. C13#1513semidirect

Maximal subgroups

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

subgroupindex
#117194962
C13×#3802
#117188682
#117180442
#117180432
#151313