Finite Group Databasebeta

← #13119299

Subgroups — #13119299

Order 1664.

568 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 153 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×C13×#121C211yesmaximal, characteristic
2C2×#88180C211yesmaximal, characteristic, complemented
3#11718883C214yesmaximal, complemented
4#11718882C211yesmaximal, characteristic, complemented
5#11718882C211yesmaximal, characteristic, complemented
6C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
7#11718638C211yesmaximal, characteristic, complemented
8#11718637C211yesmaximal, characteristic, complemented
9#11718605C214yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C22×D4×C13C2212yes—
12C23×C4×C13C2211yescharacteristic
13C13×#121—24no—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2212yes—
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2214yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2214yes—
20#88180—24no—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2214yes—
24C2×C4×Dic13C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2211yescharacteristic
27#88071C2212yes—
28#88071C2214yes—
29C24×C13C2312yes—
30C24×C13C2311yescharacteristic
31C2×D4×C13—24no—
32C2×D4×C13—22no—
33C2×D4×C13—22no—
34C2×D4×C13—22no—
35C2×D4×C13—44no—
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13D414yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C13×C4⋊C4—22no—
47C13×C22⋊C4—24no—
48C22⋊Dic13—24no—
49C22⋊Dic13—24no—
50C22⋊Dic13—28no—
51C22⋊Dic13—44no—
52C4⋊Dic13—22no—
53C4⋊Dic13—22no—
54#6101—44no—
55C4×Dic13—24no—
56C4×Dic13—22no—
57C4×Dic13—22no—
58#2500—131nomaximal, Sylow
59C23×C13—22no—
60C23×C13—21no—
61C23×C13—21no—
62C23×C13—22no—
63C23×C13—22no—
64C23×C13—24no—
65C23×C13—22no—
66C23×C13—22no—
67C23×C13—24no—
68C23×C13C2×D412yes—
69C23×C13C2411yescharacteristic
70D4×C13—48no—
71D4×C13—44no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—28no—
75C2×C4×C13—22no—
76C2×C4×C13—24no—
77C2×C4×C13C2×D412yes—
78C2×C4×C13C2×D412yes—
79C2×C4×C13#4112yes—
80C2×C4×C13#4112yes—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—24no—
87C2×Dic13—22no—
88C2×Dic13—24no—
89C2×Dic13—22no—
90C2×Dic13#4114yes—
91C2×#121D1311yescharacteristic
92C2×#117—131no—
93#394—134no—
94#390—131no—
95#390—131no—
96#388—134no—
97#384—131no—
98#382—131no—
99C4×C22⋊C4—131no—
100C22×C13—22no—
101C22×C13—22no—
102C22×C13—22no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13—42no—
106C22×C13—42no—
107C22×C13—42no—
108C22×C13—44no—
109C22×C13—44no—
110C22×C13C22×D411yescharacteristic
111C22×C13C2×#4111yescharacteristic
112C22×C13C2×#4111yescharacteristic
113C22×C13C2×#4112yes—
114C22×C13H(5,𝔽2)12yes—
115C4×C13—22no—
116C4×C13—42no—
117C4×C13#12314yes—
118Dic13—24no—
119Dic13—42no—
120Dic13—42no—
121Dic13—42no—
122C22×D4C2×D1311yescharacteristic
123C22×D4C2×D1312yes—
124C23×C4C2×D1311yescharacteristic
125#121—24no—
126#117—264no—
127C2×C4⋊C4—131no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—134no—
130C2×C4⋊C4C2×D1311yescharacteristic
131C2×C22⋊C4—132no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—134no—
134C2×C22⋊C4—134no—
135C2×C22⋊C4C2×D1312yes—
136C2×C42—132no—
137C2×C42—131no—
138C2×C42—131no—
139#95—132no—
140#95—134no—
141C2×C13—42no—
142C2×C13—82no—
143C2×C13C2×#12311yescharacteristic
144C2×C13#53211yescharacteristic
145C2×C13#53511yescharacteristic
146C2×C13#55312yes—
147C2×C13#55512yes—
148C24C22×D1312yes—
149C24C22×D1311yescharacteristic
150C2×D4—24no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—44no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—132no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4C22⋊D1314yes—
162C22×C4C22×D1312yes—
163C22×C4C22×D1311yescharacteristic
164C22×C4C22×D1311yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C4⋊C4—524no—
169C22⋊C4—24no—
170C22⋊C4—264no—
171C22⋊C4—268no—
172C22⋊C4—264no—
173C22⋊C4—524no—
174C42—262no—
175C42—262no—
176C42—264no—
177C13#250011yescharacteristic, complemented, Sylow
178C23—21no—
179C23—21no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23—24no—
185C23—24no—
186C23—22no—
187C23C2×C22⋊D1312yes—
188C23C23×D1311yescharacteristic
189D4—48no—
190D4—44no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—28no—
194C2×C4—24no—
195C2×C4—22no—
196C2×C4—134no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—264no—
202C2×C4—264no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4#612912yes—
207C2×C4#612912yes—
208C2×C4C2×C22⋊D1312yes—
209C2×C4C2×C22⋊D1312yes—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22—44no—
219C22—44no—
220C22C2×#612911yescharacteristic
221C22C2×#612911yescharacteristic
222C22#8825112yes—
223C22#41×D1312yes—
224C22C22×C22⋊D1311yescharacteristic
225C4—22no—
226C4—42no—
227C4—264no—
228C4—522no—
229C4—522no—
230C4—522no—
231C4#8818914yes—
232C2—42no—
233C2—82no—
234C2#1171931912yes—
235C2#1171932112yes—
236C2C2×#8818911yescharacteristic
237C2#1171951011yescharacteristic
238C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2500
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#88180C2semidirect
3. #11718883C2semidirect
4. #11718882C2semidirect
5. #11718882C2semidirect
6. C4×C22⋊Dic13C2semidirect
7. #11718638C2semidirect
8. #11718637C2semidirect
9. #11718605C2semidirect
177. C13#2500semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C2×#881802
#117188832
#117188822
C4×C22⋊Dic132
#117186382
#117186372
#117186052
#250013