Finite Group Databasebeta

← #13120597

Subgroups — #13120597

Order 1664.

612 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 157 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×#88190C211yesmaximal, characteristic, complemented
3C2×#88180C211yesmaximal, characteristic, complemented
4C2×#88178C211yesmaximal, characteristic, complemented
5#11718883C214yesmaximal, complemented
6#11718882C211yesmaximal, characteristic, complemented
7#11718637C211yesmaximal, characteristic, complemented
8#11718635C211yesmaximal, characteristic, complemented
9#11718609C214yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C22×D4×C13C2212yes—
12C23×C4×C13C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C13×#121—24no—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2214yes—
20C2×C22⋊Dic13C2214yes—
21#88190—24no—
22#88180—24no—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊Dic13C2212yes—
25#88178—24no—
26C2×#6101C2212yes—
27C2×#6101C2214yes—
28C2×C4×Dic13C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30#88071C2214yes—
31C24×C13C2312yes—
32C24×C13C2311yescharacteristic
33C2×D4×C13—24no—
34C2×D4×C13—22no—
35C2×D4×C13—22no—
36C2×D4×C13—22no—
37C2×D4×C13—44no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13D414yes—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C22×Dic13C2312yes—
48C2×Dic26—22no—
49C2×Dic26—22no—
50C2×Dic26—22no—
51C13×C4⋊C4—22no—
52C13×C22⋊C4—24no—
53C22⋊Dic13—24no—
54C22⋊Dic13—24no—
55C22⋊Dic13—28no—
56C22⋊Dic13—44no—
57C4⋊Dic13—22no—
58C4⋊Dic13—24no—
59#6101—24no—
60#6101—44no—
61C4×Dic13—22no—
62C4×Dic13D414yescomplemented
63#2620—131nomaximal, Sylow
64C23×C13—21no—
65C23×C13—21no—
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13—22no—
70C23×C13—22no—
71C23×C13—24no—
72C23×C13—24no—
73C23×C13C2×D412yes—
74C23×C13C2411yescharacteristic
75D4×C13—48no—
76D4×C13—44no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—28no—
80C2×C4×C13—22no—
81C2×C4×C13—24no—
82C2×C4×C13C2×D412yes—
83C2×C4×C13C2×D412yes—
84C2×C4×C13C2×D412yes—
85C2×C4×C13#4112yes—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—24no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13C2×D414yes—
97Dic26—44no—
98C2×#124—131no—
99C2×C22⋊Q8—131no—
100C2×#121D1311yescharacteristic
101C2×#117—131no—
102#396—134no—
103#394—134no—
104#391—131no—
105#390—131no—
106#384—131no—
107C22×C13—22no—
108C22×C13—22no—
109C22×C13—22no—
110C22×C13—42no—
111C22×C13—42no—
112C22×C13—42no—
113C22×C13—42no—
114C22×C13—42no—
115C22×C13—44no—
116C22×C13—44no—
117C22×C13C22×D411yescharacteristic
118C22×C13C22×D411yescharacteristic
119C22×C13C2×#4111yescharacteristic
120C22×C13H(5,𝔽2)12yes—
121C22×C132−1+412yes—
122C4×C13—22no—
123C4×C13—42no—
124C4×C13#12114yes—
125Dic13—24no—
126Dic13—42no—
127Dic13—42no—
128Dic13—42no—
129C22×Q8—131no—
130C22×D4C2×D1311yescharacteristic
131C22×D4C2×D1312yes—
132C23×C4C2×D1311yescharacteristic
133#124—264no—
134C22⋊Q8—264no—
135#121—24no—
136#117—264no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4—131no—
140C2×C4⋊C4—134no—
141C2×C4⋊C4C2×D1311yescharacteristic
142C2×C22⋊C4—132no—
143C2×C22⋊C4—132no—
144C2×C22⋊C4—134no—
145C2×C22⋊C4—134no—
146C2×C22⋊C4C2×D1312yes—
147C2×C42—131no—
148C2×C42—131no—
149#95—134no—
150C2×C13—42no—
151C2×C13—82no—
152C2×C13C2×#12111yescharacteristic
153C2×C13#53511yescharacteristic
154C2×C13#53611yescharacteristic
155C2×C13#53712yes—
156C2×C13#54212yes—
157C24C22×D1312yes—
158C24C22×D1311yescharacteristic
159C2×Q8—262no—
160C2×Q8—262no—
161C2×Q8—262no—
162C2×D4—24no—
163C2×D4—22no—
164C2×D4—22no—
165C2×D4—22no—
166C2×D4—44no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—132no—
170C22×C4—132no—
171C22×C4—132no—
172C22×C4—132no—
173C22×C4C22⋊D1314yes—
174C22×C4C22×D1312yes—
175C22×C4C22×D1311yescharacteristic
176C22×C4C22×D1311yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—264no—
179C4⋊C4—264no—
180C4⋊C4—262no—
181C4⋊C4—524no—
182C22⋊C4—24no—
183C22⋊C4—264no—
184C22⋊C4—268no—
185C22⋊C4—264no—
186C22⋊C4—524no—
187C42—134no—
188C42—262no—
189C13#262011yescharacteristic, complemented, Sylow
190C23—21no—
191C23—21no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—24no—
197C23—24no—
198C23—22no—
199C23C2×C22⋊D1312yes—
200C23C23×D1311yescharacteristic
201Q8—524no—
202D4—48no—
203D4—44no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—28no—
207C2×C4—24no—
208C2×C4—22no—
209C2×C4—134no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—264no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4D4×D1312yes—
221C2×C4#612912yes—
222C2×C4C2×C22⋊D1312yes—
223C2×C4C2×C22⋊D1312yes—
224C22—22no—
225C22—22no—
226C22—22no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—44no—
233C22—44no—
234C22C2×D4×D1311yescharacteristic
235C22C2×#612911yescharacteristic
236C22#8825112yes—
237C22#8825712yes—
238C22C22×C22⋊D1311yescharacteristic
239C4—22no—
240C4—42no—
241C4—264no—
242C4—522no—
243C4—522no—
244C4—522no—
245C4#8819314yes—
246C2—42no—
247C2—82no—
248C2#1171930812yes—
249C2#1171931312yes—
250C2C2×#8819311yescharacteristic
251C2#1171951011yescharacteristic
252C2#1171953011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2620
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#88190C2semidirect
3. C2×#88180C2semidirect
4. C2×#88178C2semidirect
5. #11718883C2semidirect
6. #11718882C2semidirect
7. #11718637C2semidirect
8. #11718635C2semidirect
9. #11718609C2semidirect
62. C4×Dic13D4semidirect
189. C13#2620semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C2×#881902
C2×#881802
C2×#881782
#117188832
#117188822
#117186372
#117186352
#117186092
#262013