Finite Group Databasebeta

← #13130253

Subgroups — #13130253

Order 1664.

286 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 60 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
2#11719136C211yesmaximal, characteristic, complemented
3#11719127C211yesmaximal, characteristic, complemented
4#11718241C212yesmaximal, complemented
5#11718240C212yesmaximal, complemented
6C2×#6127C411yescharacteristic, complemented
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C2×C4⋊#261—21no—
10C2×#6118—21no—
11C13×#117C411yescharacteristic, complemented
12#88151C411yescharacteristic, complemented
13#88151C2211yescharacteristic
14#88149C411yescharacteristic, complemented
15#88149C2211yescharacteristic
16#88140—21no—
17#88136—21no—
18C4×D52—21no—
19C4×D52—21no—
20C22⋊#1057—21no—
21(C2×#261)⋊C4C2212yes—
22#88111C2212yes—
23C23×D13D411yescharacteristic
24C22×#261—22no—
25C22×C4×C13C2×C411yescharacteristic
26C2×C22⋊D13—21no—
27C22×Dic13D411yescharacteristic
28#6127—42no—
29C2×D52—21no—
30C2×D52—21no—
31C2×D52C2×C411yescharacteristic
32C2×C4×D13—21no—
33C2×C4×D13—42no—
34C2×C4×D13C2×C411yescharacteristic
35C2×C4×D13D411yescharacteristic
36C2×C4×D13D411yescharacteristic
37C2×C4×D13C2311yescharacteristic
38C2×Dic26C2×C411yescharacteristic
39C22⋊#261—42no—
40C2×#1057—22no—
41C4⋊#261—42no—
42#6118—42no—
43C13×C4⋊C4C2×C411yescharacteristic
44C13×C4⋊C4C2×C411yescharacteristic
45C13×C22⋊C4—21no—
46C42×C13—21no—
47#6103—21no—
48#6103—21no—
49#6103—21no—
50#6103—21no—
51C4⋊Dic13—21no—
52C4⋊Dic13—21no—
53#1513—131nomaximal, Sylow
54C23×C13C22⋊C411yescharacteristic
55C22×D13—21no—
56C22×D13—21no—
57C22×D13—21no—
58C22×D13—41no—
59C22×D13—41no—
60C22×D13C22⋊C411yescharacteristic
61C22×D13C2×D411yescharacteristic
62C2×#261—42no—
63C2×#261—42no—
64C2×#261—42no—
65C2×C4×C13—22no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13C22⋊C411yescharacteristic
69C2×C4×C13C22×C411yescharacteristic
70C22⋊D13—42no—
71C2×Dic13—21no—
72C2×Dic13—41no—
73C2×Dic13C22⋊C411yescharacteristic
74C2×Dic13C2×D411yescharacteristic
75D52—41no—
76D52—42no—
77D52—41no—
78D52—41no—
79C4×D13—22no—
80C4×D13—22no—
81C4×D13—41no—
82C4×D13—41no—
83C4×D13—42no—
84Dic26—41no—
85#1057—42no—
86#525—131no—
87#407—131no—
88#380—131no—
89#328—132no—
90#327—132no—
91C22×C13—21no—
92C22×C13—21no—
93C22×C13—21no—
94C22×C13C2×C22⋊C411yescharacteristic
95C2×D13—21no—
96C2×D13—21no—
97C2×D13—21no—
98C2×D13—21no—
99C2×D13—21no—
100C2×D13—42no—
101C2×D13—42no—
102C2×D13—41no—
103C2×D13—41no—
104C2×D13—41no—
105C2×D13AGL(1,ℤ/8)11yescharacteristic
106C2×D13#13711yescharacteristic
107#261—82no—
108C4×C13—21no—
109C4×C13—41no—
110C4×C13—41no—
111C4×C13#9912yes—
112Dic13—21no—
113Dic13—21no—
114Dic13—41no—
115C2×#41—131no—
116C23×C4—131no—
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#26111yescharacteristic, complemented
127C2×C4⋊C4—261no—
128C2×C22⋊C4—261no—
129C22⋊C8—132no—
130C22⋊C8—261no—
131#95—132no—
132C2×C13—41no—
133C2×C13C2×#9911yescharacteristic
134C2×C13#41711yescharacteristic
135C2×C13#42111yescharacteristic
136D13—21no—
137D13—21no—
138D13—41no—
139D13—81no—
140C24—131no—
141#41—522no—
142C2×Q8—131no—
143C2×D4—131no—
144C2×D4—261no—
145C2×D4—261no—
146C2×D4—261no—
147C22×C4—131no—
148C22×C4—131no—
149C22×C4—131no—
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—261no—
153C22×C4—262no—
154C22×C4—522no—
155C22×C4C2×#26111yescharacteristic
156M16—522no—
157C2×C8—262no—
158C4⋊C4—261no—
159C4⋊C4—261no—
160C4⋊C4—522no—
161C4⋊C4C2×#26111yescharacteristic
162C4⋊C4C2×#26111yescharacteristic
163C22⋊C4—21no—
164C22⋊C4—261no—
165C22⋊C4—261no—
166C22⋊C4—261no—
167C22⋊C4—261no—
168C22⋊C4—522no—
169C42—21no—
170C13#151311yescharacteristic, complemented, Sylow
171C23—131no—
172C23—131no—
173C23—261no—
174C23—261no—
175C23—261no—
176C23—521no—
177C23—521no—
178C23C22⋊#26111yescharacteristic
179Q8—521no—
180D4—521no—
181D4—521no—
182D4—521no—
183D4—522no—
184D4—522no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—261no—
193C2×C4—521no—
194C2×C4—521no—
195C2×C4—521no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4C22⋊#26111yescharacteristic
201C2×C4C22×#26111yescharacteristic
202C8—522no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—131no—
207C22—131no—
208C22—261no—
209C22—261no—
210C22—261no—
211C22—261no—
212C22—261no—
213C22—522no—
214C22—522no—
215C22—521no—
216C22—521no—
217C22—521no—
218C22C2×C22⋊#26111yescharacteristic
219C4—21no—
220C4—41no—
221C4—41no—
222C4—261no—
223C4—261no—
224C4—521no—
225C4—1042no—
226C4#8810712yes—
227C2—41no—
228C2—261no—
229C2—261no—
230C2—521no—
231C2—1041no—
232C2C2×#8810711yescharacteristic
233C2#1171916411yescharacteristic
234C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#117C4
socleC22×C13C2×C22⋊C4
prime radical#11719229C2
cosocleC2×C4×D13C23
hypercenter#117#261
hypocenterC13#1513
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11719136C2semidirect
3. #11719127C2semidirect
4. #11718241C2semidirect
5. #11718240C2semidirect
6. C2×#6127C4semidirect
11. C13×#117C4semidirect
12. #88151C4semidirect
14. #88149C4semidirect
126. #117#261semidirect
170. C13#1513semidirect

Maximal subgroups

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

subgroupindex
#117192292
#117191362
#117191272
#117182412
#117182402
#151313