Finite Group Databasebeta

← #13125443

Subgroups — #13125443

Order 1664.

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

normal subgroups only

This group has 364 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
1C13×#529C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3#11718730C211yesmaximal, characteristic, complemented
4#11718726C211yesmaximal, characteristic, complemented
5#11718721C211yesmaximal, characteristic, complemented
6#11718716C211yesmaximal, characteristic, complemented
7#11718713C212yesmaximal, complemented
8#11718703C212yesmaximal
9C4×#6107C212yesmaximal, complemented
10C4×#6105C212yesmaximal, complemented
11C4×#6099C211yesmaximal, characteristic, complemented
12C13×#126—21no—
13C13×#125C2211yescharacteristic
14C13×#124C2211yescharacteristic
15C13×#123—21no—
16C13×C22⋊Q8C2211yescharacteristic
17C13×#121C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13—21no—
20C4×D4×C13C2211yescharacteristic
21C13×#117—21no—
22C2×C42×C13C2211yescharacteristic
23C2×#6107C2212yes—
24C2×#6105C2212yes—
25#88180—21no—
26#88178—21no—
27#88178C2212yes—
28C2×#6099C2212yes—
29#88124—21no—
30#88123C2211yescharacteristic
31#88123C2211yescharacteristic
32C4×Dic26—21no—
33C4×Dic26C2212yes—
34#88075C2212yes—
35#88072C2212yes—
36#88050C2212yes—
37#88050C2212yes—
38#88048C2212yes—
39#88047C2212yes—
40#88043C2211yescharacteristic
41#88043C2211yescharacteristic
42C4×#1055C2212yes—
43C2×Q8×C13C2311yescharacteristic
44C2×D4×C13—21no—
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13D411yescharacteristic
48C22×C4×C13D411yescharacteristic
49C22×C4×C13C2311yescharacteristic
50C2×Dic26—21no—
51C2×Dic26C2312yes—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2311yescharacteristic
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C13×C22⋊C4—21no—
60C13×C22⋊C4—21no—
61C13×C22⋊C4—21no—
62C13×C22⋊C4—21no—
63C42×C13—21no—
64C42×C13D411yescharacteristic
65C42×C13D411yescharacteristic
66C42×C13C2311yescharacteristic
67C42×C13C2311yescharacteristic
68C22⋊Dic13—22no—
69#6107—24no—
70#6105—24no—
71C4⋊Dic13—21no—
72C4⋊Dic13—21no—
73C4⋊Dic13—21no—
74C4⋊Dic13C2312yes—
75#6101—22no—
76#6101—22no—
77C4×Dic13—22no—
78#6099—24no—
79C2×#1055C2312yes—
80C2×#1055C2312yes—
81#3172—131nomaximal, Sylow
82C23×C13—21no—
83C23×C13C2×D411yescharacteristic
84Q8×C13—22no—
85D4×C13—22no—
86D4×C13—42no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—41no—
93C2×C4×C13—42no—
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2411yescharacteristic
100C2×Dic13—22no—
101C2×Dic13—22no—
102Dic26—22no—
103Dic26—22no—
104Dic26—42no—
105#1055—22no—
106#1055#4114yes—
107#533—131no—
108#529D1311yescharacteristic
109#501—131no—
110#497—131no—
111#491—131no—
112#489—131no—
113#470—132no—
114#468—132no—
115C4×Q16—132no—
116C4×SD16—132no—
117C4×M16—131no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13—41no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13C22×D411yescharacteristic
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13—21no—
129C4×C13—41no—
130C4×C13—41no—
131C4×C13—41no—
132C4×C13#13712yes—
133C4×C13C2×#4112yes—
134Dic13—42no—
135Dic13—42no—
136C2×Q16—132no—
137C2×SD16—132no—
138C2×M16—132no—
139C4⋊Q8—131no—
140C4⋊Q8—131no—
141#126—21no—
142#125—261no—
143#125C2×D1311yescharacteristic
144#124C2×D1311yescharacteristic
145#123—21no—
146C22⋊Q8—132no—
147C22⋊Q8—261no—
148C22⋊Q8C2×D1311yescharacteristic
149#121C2×D1311yescharacteristic
150C4×Q8—132no—
151C4×Q8—261no—
152C4×Q8C2×D1311yescharacteristic
153C4×D4—21no—
154C4×D4C2×D1311yescharacteristic
155#117—21no—
156#117—261no—
157C2×C42C2×D1311yescharacteristic
158#107—132no—
159#106—132no—
160#103—132no—
161#103—132no—
162#103—132no—
163#102—132no—
164#97—131no—
165#97—131no—
166C4×C8—132no—
167C2×C13—41no—
168C2×C13—81no—
169C2×C13#53211yescharacteristic
170C2×C13C2×#13711yescharacteristic
171C2×C13#57511yescharacteristic
172C2×Q8—132no—
173C2×Q8—261no—
174C2×Q8C22×D1311yescharacteristic
175C2×D4—21no—
176C2×D4C22×D1311yescharacteristic
177C22×C4—21no—
178C22×C4C22⋊D1311yescharacteristic
179C22×C4C22⋊D1311yescharacteristic
180C22×C4C22×D1311yescharacteristic
181Q16—264no—
182SD16—264no—
183M16—264no—
184C2×C8—132no—
185C2×C8—132no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—132no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—262no—
194C4⋊C4—262no—
195C4⋊C4—261no—
196C4⋊C4C22×D1311yescharacteristic
197C4⋊C4C22×D1311yescharacteristic
198C22⋊C4—21no—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—21no—
202C22⋊C4—21no—
203C22⋊C4—262no—
204C42—21no—
205C42—262no—
206C42C22⋊D1311yescharacteristic
207C42C22⋊D1311yescharacteristic
208C42C22×D1311yescharacteristic
209C42C22×D1311yescharacteristic
210C13#317211yescharacteristic, complemented, Sylow
211C23—21no—
212C23C2×C22⋊D1311yescharacteristic
213Q8—22no—
214Q8—262no—
215Q8—262no—
216Q8—522no—
217D4—22no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4C2×C22⋊D1311yescharacteristic
229C2×C4C2×C22⋊D1311yescharacteristic
230C2×C4C2×C22⋊D1311yescharacteristic
231C2×C4C2×C22⋊D1311yescharacteristic
232C2×C4C2×C22⋊D1311yescharacteristic
233C2×C4C23×D1311yescharacteristic
234C8—134no—
235C8—262no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22C22×C22⋊D1311yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—522no—
251C4—522no—
252C4#8820512yes—
253C4#41×D1312yes—
254C2—41no—
255C2—81no—
256C2#1171952711yescharacteristic
257C2C2×#8820511yescharacteristic
258C2#1171953711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#529C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#529D13
hypocenterC13#3172
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. #11719175C2semidirect
3. #11718730C2semidirect
4. #11718726C2semidirect
5. #11718721C2semidirect
6. #11718716C2semidirect
7. #11718713C2semidirect
9. C4×#6107C2semidirect
10. C4×#6105C2semidirect
11. C4×#6099C2semidirect
210. C13#3172semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
#117191752
#117187302
#117187262
#117187212
#117187162
#117187132
#117187032
C4×#61072
C4×#61052
C4×#60992
#317213