Finite Group Databasebeta

← #13123173

Subgroups — #13123173

Order 1664.

564 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C22×C4×Dic13C211yesmaximal, characteristic
2C2×#88132C211yesmaximal, characteristic
3C13×#381C211yesmaximal, characteristic
4#11718872C211yesmaximal, characteristic
5#11718611C211yesmaximal, characteristic
6#11718607C211yesmaximal, characteristic
7#11718603C211yesmaximal, characteristic
8#11718316C212yesmaximal, complemented
9#11718315C212yesmaximal, complemented
10#11718308C212yesmaximal, complemented
11#11718307C212yesmaximal, complemented
12C23×C4×C13C2211yescharacteristic
13C23×Dic13C2211yescharacteristic
14C23×Dic13C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic13C2211yescharacteristic
19C2×C22⋊Dic13C2211yescharacteristic
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2212yes—
22C2×#6101C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13—24no—
27C2×C4×Dic13C2212yes—
28C2×C4×Dic13C2212yes—
29#88132—24no—
30C13×#95C2212yes—
31C13×#95C2212yes—
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13Q814yescomplemented
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2312yes—
45C22×Dic13—22no—
46C22×Dic13—24no—
47C22×Dic13—24no—
48C22×Dic13D414yes—
49C22×Dic13C2312yes—
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2311yescharacteristic
53C22×Dic13C2312yes—
54C22×Dic13C2311yescharacteristic
55C2×Dic26—22no—
56C2×Dic26—24no—
57C13×C22⋊C4—22no—
58C13×C22⋊C4—22no—
59C22⋊Dic13—22no—
60C22⋊Dic13—22no—
61C4⋊Dic13—22no—
62C4⋊Dic13—24no—
63#6101—22no—
64#6101—22no—
65#6101—24no—
66#6101—24no—
67C4×Dic13—24no—
68C4×Dic13—24no—
69#2855—131nomaximal, Sylow
70C23×C13—22no—
71C23×C13—22no—
72C23×C13C2×D412yes—
73C23×C13C2×Q812yes—
74C23×C13#4112yes—
75C23×C13C2411yescharacteristic
76C2×C4×C13—28no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13C2×Q814yes—
87C2×Dic13—28no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—28no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13C2×D412yes—
100C2×Dic13C2×D412yes—
101C2×Dic13#4114yes—
102C2×Dic13#4114yes—
103Dic26—44no—
104C2×C22⋊Q8—131no—
105C22×C42—131no—
106#391—132no—
107#389—132no—
108#387—132no—
109#387—132no—
110#385—131no—
111#385—131no—
112#381—131no—
113#381D1311yescharacteristic
114#380—131no—
115C22×C13—22no—
116C22×C13—22no—
117C22×C13—24no—
118C22×C13—24no—
119C22×C13C22⋊Q814yes—
120C22×C13C22×D411yescharacteristic
121C22×C13C22×Q811yescharacteristic
122C22×C13C2×#4111yescharacteristic
123C22×C13C2×#4112yes—
124C22×C13C2×#4112yes—
125C4×C13—24no—
126C4×C13—41no—
127C4×C13—41no—
128C4×C13—42no—
129Dic13—22no—
130Dic13—24no—
131Dic13—41no—
132Dic13—41no—
133Dic13—42no—
134Dic13#12314yes—
135C22×Q8—131no—
136C23×C4—131no—
137C23×C4—131no—
138C23×C4C2×D1311yescharacteristic
139C22⋊Q8—264no—
140C2×C4⋊C4—131no—
141C2×C4⋊C4—131no—
142C2×C4⋊C4—131no—
143C2×C4⋊C4—132no—
144C2×C4⋊C4—132no—
145C2×C4⋊C4—132no—
146C2×C22⋊C4—131no—
147C2×C22⋊C4—131no—
148C2×C22⋊C4C2×D1311yescharacteristic
149C2×C22⋊C4C2×D1311yescharacteristic
150C2×C42—132no—
151C2×C42—132no—
152C2×C42—264no—
153#95—132no—
154#95—132no—
155#95—132no—
156#95—132no—
157#95—132no—
158#95C2×D1312yes—
159#95C2×D1312yes—
160C2×C13—24no—
161C2×C13C2×C22⋊Q811yescharacteristic
162C2×C13C2×#12311yescharacteristic
163C2×C13#52511yescharacteristic
164C2×C13#52912yes—
165C2×C13#53312yes—
166C24C22×D1311yescharacteristic
167C2×Q8—262no—
168C2×Q8—264no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—131no—
172C22×C4—134no—
173C22×C4—131no—
174C22×C4—132no—
175C22×C4—132no—
176C22×C4—131no—
177C22×C4—131no—
178C22×C4—264no—
179C22×C4—264no—
180C22×C4—262no—
181C22×C4Dic2614yescomplemented
182C22×C4C22×D1312yes—
183C22×C4C22×D1311yescharacteristic
184C22×C4C22×D1311yescharacteristic
185C22×C4C22×D1312yes—
186C4⋊C4—262no—
187C4⋊C4—262no—
188C4⋊C4—262no—
189C4⋊C4—264no—
190C4⋊C4—264no—
191C4⋊C4—264no—
192C22⋊C4—22no—
193C22⋊C4—22no—
194C22⋊C4—262no—
195C22⋊C4—262no—
196C42—264no—
197C42—264no—
198C13#285511yescharacteristic, complemented, Sylow
199C23—22no—
200C23—22no—
201C23C2×Dic2612yes—
202C23D4×D1312yes—
203C23#612912yes—
204C23C23×D1311yescharacteristic
205Q8—524no—
206C2×C4—28no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—132no—
217C2×C4—134no—
218C2×C4—132no—
219C2×C4—134no—
220C2×C4—268no—
221C2×C4—268no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4C2×Dic2614yes—
233C22—24no—
234C22—24no—
235C22—22no—
236C22—22no—
237C22#8813214yes—
238C22C22×Dic2611yescharacteristic
239C22C2×D4×D1311yescharacteristic
240C22C2×#612911yescharacteristic
241C22#41×D1312yes—
242C22#41×D1312yes—
243C4—24no—
244C4—42no—
245C4—41no—
246C4—41no—
247C4—134no—
248C4—262no—
249C4—264no—
250C4—522no—
251C4—521no—
252C4—521no—
253C2—24no—
254C2C2×#8813211yescharacteristic
255C2#1171922212yes—
256C2#1171935412yes—
257C2D13×#12311yescharacteristic
258C2#1171936111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radicalC24×C13C23
hypercenter#381D13
hypocenterC13#2855
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
8. #11718316C2semidirect
9. #11718315C2semidirect
10. #11718308C2semidirect
11. #11718307C2semidirect
40. C22×C4×C13Q8semidirect
181. C22×C4Dic26semidirect
198. C13#2855semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic132
C2×#881322
C13×#3812
#117188722
#117186112
#117186072
#117186032
#117183162
#117183152
#117183082
#117183072
#285513