Finite Group Databasebeta

← #13122880

Subgroups — #13122880

Order 1664.

580 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#88139C212yesmaximal, complemented
2C13×#394C211yesmaximal, characteristic, complemented
3#11718884C212yesmaximal, complemented
4#11718652C211yesmaximal, characteristic, complemented
5#11718638C211yesmaximal, characteristic, complemented
6#11718622C212yesmaximal, complemented
7#11718621C212yesmaximal, complemented
8#11718608C212yesmaximal, complemented
9#11718334C212yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×C22⋊D13C2212yes—
13C22×D52C2211yescharacteristic
14C22×Dic26C2212yes—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4×Dic13C2211yescharacteristic
26#88139—28no—
27C13×#95C2211yescharacteristic
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31#88071C2212yes—
32C24×C13C2312yes—
33C23×D13C2312yes—
34C2×D4×C13—42no—
35C2×D4×C13—41no—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C2×C22⋊D13—24no—
41C2×C22⋊D13—42no—
42C2×C22⋊D13—42no—
43C2×C22⋊D13—42no—
44C2×C22⋊D13—42no—
45C2×C22⋊D13—42no—
46C22×Dic13C2312yes—
47C22×Dic13C2312yes—
48C22×Dic13C2312yes—
49C2×D52—42no—
50C2×D52—41no—
51C2×Dic26—24no—
52C2×Dic26—42no—
53C2×Dic26—42no—
54C13×C4⋊C4—41no—
55C13×C22⋊C4—24no—
56C13×C22⋊C4—42no—
57C22⋊Dic13—24no—
58C22⋊Dic13—42no—
59#6103—24no—
60#6103—24no—
61#6103—42no—
62#6103—42no—
63C4⋊Dic13—41no—
64C4×Dic13D414yescomplemented
65#2819—131nomaximal, Sylow
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13—22no—
70C23×C13—22no—
71C23×C13—22no—
72C23×C13—22no—
73C23×C13C2411yescharacteristic
74C22×D13—22no—
75C22×D13—22no—
76C22×D13—22no—
77C22×D13—22no—
78C22×D13—22no—
79C22×D13—22no—
80C22×D13—22no—
81D4×C13—44no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13C2×D412yes—
92C22⋊D13—48no—
93C22⋊D13—48no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13C2×D414yes—
103D52—44no—
104Dic26—48no—
105C2×#124—132no—
106#394—131no—
107#394—132no—
108#394D1311yescharacteristic, complemented
109#393—132no—
110#393—132no—
111#392—132no—
112#392—132no—
113#382—131no—
114C22×C13—42no—
115C22×C13—42no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13—42no—
120C22×C13—42no—
121C22×C13C22×D411yescharacteristic
122C22×C13H(5,𝔽2)12yes—
123C22×C13H(5,𝔽2)11yescharacteristic
124C22×C13H(5,𝔽2)12yes—
125C22×C132−1+411yescharacteristic
126C2×D13—42no—
127C2×D13—42no—
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—42no—
131C2×D13—42no—
132C2×D13—42no—
133C4×C13—22no—
134C4×C13—42no—
135C4×C13—41no—
136C4×C13—41no—
137Dic13—24no—
138Dic13—42no—
139Dic13—42no—
140C22×Q8—132no—
141C22×D4—132no—
142C22×D4—132no—
143C22×D4—131no—
144C22×D4C2×D1311yescharacteristic
145#124—268no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4C2×D1311yescharacteristic
148C2×C22⋊C4—132no—
149C2×C22⋊C4—132no—
150C2×C22⋊C4—132no—
151C2×C22⋊C4—132no—
152C2×C22⋊C4—132no—
153C2×C22⋊C4—132no—
154C2×C22⋊C4C2×D1312yes—
155C2×C22⋊C4C2×D1312yes—
156C2×C42—131no—
157#95—132no—
158#95—132no—
159#95—132no—
160#95—131no—
161#95C2×D1311yescharacteristic
162C2×C13—82no—
163C2×C13#53512yes—
164C2×C13#53711yescharacteristic
165C2×C13H(3,𝔽4)11yescharacteristic
166C2×C13H(3,𝔽4)11yescharacteristic
167C2×C13#56212yes—
168D13—82no—
169C24—132no—
170C24C22×D1312yes—
171C2×Q8—264no—
172C2×Q8—522no—
173C2×Q8—522no—
174C2×D4—42no—
175C2×D4—41no—
176C2×D4—264no—
177C2×D4—522no—
178C2×D4—521no—
179C2×D4—522no—
180C2×D4—522no—
181C2×D4—522no—
182C2×D4—522no—
183C2×D4—522no—
184C22×C4—132no—
185C22×C4—132no—
186C22×C4—132no—
187C22×C4C22×D1311yescharacteristic
188C22×C4C22×D1311yescharacteristic
189C22×C4C22×D1312yes—
190C22×C4C22×D1311yescharacteristic
191C4⋊C4—41no—
192C4⋊C4—521no—
193C22⋊C4—24no—
194C22⋊C4—42no—
195C22⋊C4—264no—
196C22⋊C4—264no—
197C22⋊C4—264no—
198C22⋊C4—522no—
199C22⋊C4—522no—
200C22⋊C4—522no—
201C42—134no—
202C13#281911yescharacteristic, complemented, Sylow
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—262no—
211C23—262no—
212C23—262no—
213C23—262no—
214C23—262no—
215C23—262no—
216C23—262no—
217C23C23×D1311yescharacteristic
218Q8—528no—
219D4—44no—
220D4—524no—
221D4—528no—
222D4—528no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—134no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4D4×D1312yes—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—522no—
250C22—522no—
251C22—522no—
252C22—522no—
253C22—522no—
254C22—522no—
255C22—522no—
256C22C2×D4×D1311yescharacteristic
257C22#8825111yescharacteristic
258C22#8825112yes—
259C22#8825612yes—
260C22#8825711yescharacteristic
261C4—22no—
262C4—41no—
263C4—41no—
264C4—42no—
265C4—264no—
266C4—522no—
267C4—522no—
268C2—82no—
269C2—1042no—
270C2#1171929911yescharacteristic
271C2#1171930211yescharacteristic
272C2#1171931212yes—
273C2#1171937212yes—
274C2#1171938811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
hypercenter#394D13
hypocenterC13#2819
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#88139C2semidirect
2. C13×#394C2semidirect
3. #11718884C2semidirect
4. #11718652C2semidirect
5. #11718638C2semidirect
6. #11718622C2semidirect
7. #11718621C2semidirect
8. #11718608C2semidirect
9. #11718334C2semidirect
64. C4×Dic13D4semidirect
108. #394D13semidirect
202. C13#2819semidirect

Maximal subgroups

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

subgroupindex
C2×#881392
C13×#3942
#117188842
#117186522
#117186382
#117186222
#117186212
#117186082
#117183342
#281913