Finite Group Databasebeta

← #13124368

Subgroups — #13124368

Order 1664.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×#137C211yesmaximal, characteristic
2#11719530C211yesmaximal, characteristic
3#11719517C211yesmaximal, characteristic, complemented
4C22×#6107C211yesmaximal, characteristic, complemented
5#11718894C211yesmaximal, characteristic
6#11718843C214yesmaximal, complemented
7#11718827C214yesmaximal, complemented
8#11718781C211yesmaximal, characteristic, complemented
9#11718780C211yesmaximal, characteristic, complemented
10C2×C13×#41C2211yescharacteristic
11C22×Q8×C13C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C13×#137—24no—
14C2×C13×Q16C2212yes—
15C2×C13×SD16C2212yes—
16C2×C13×M16C2211yescharacteristic
17Q8×Dic13—22no—
18Q8×Dic13C2214yes—
19#88198C2212yes—
20C2×#6107—24no—
21C2×#6107C2214yes—
22#88190C2212yes—
23#88189—22no—
24#88180—22no—
25#88180C2211yescharacteristic
26#88180C2211yescharacteristic
27#88178—22no—
28C22×#1055C2211yescharacteristic
29#88075C2212yes—
30#88072C2212yes—
31#88056C2214yes—
32#88054C2214yes—
33C13×#41—22no—
34C13×#41—22no—
35C2×Q8×C13—21no—
36C2×Q8×C13—22no—
37C2×Q8×C13D414yes—
38C2×Q8×C13C2311yescharacteristic
39C2×Q8×C13C2312yes—
40C2×D4×C13—21no—
41C2×D4×C13C2311yescharacteristic
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13C2311yescharacteristic
45C22×Dic13—21no—
46C2×Dic26—22no—
47C2×Dic26—22no—
48C2×Dic26—21no—
49C2×Dic26C2312yes—
50C13×Q16—24no—
51C13×SD16—24no—
52C13×M16—22no—
53C2×C8×C13C2312yes—
54C22⋊Dic13—21no—
55C22⋊Dic13—24no—
56C22⋊Dic13D412yes—
57#6107—28no—
58C4⋊Dic13—24no—
59C4⋊Dic13D412yes—
60C4⋊Dic13C2312yes—
61#6101—24no—
62C4×Dic13—21no—
63C4×Dic13—24no—
64C4×Dic13C2312yes—
65C2×#1055—22no—
66C2×#1055C2312yes—
67#3044—131nomaximal, Sylow
68C23×C13—21no—
69C23×C13C2×D411yescharacteristic
70Q8×C13—24no—
71Q8×C13—22no—
72Q8×C13—21no—
73Q8×C13—21no—
74Q8×C13C2×D414yes—
75D4×C13—21no—
76D4×C13—21no—
77D4×C13—42no—
78C2×C4×C13—24no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13—42no—
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2×D412yes—
84C2×C4×C13#4112yes—
85C2×C4×C13C2411yescharacteristic
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—42no—
89C2×Dic13C2×D414yes—
90Dic26—22no—
91Dic26—22no—
92Dic26—42no—
93C8×C13—22no—
94#1055—22no—
95C2×#137D1311yescharacteristic
96C22×Q16—131no—
97#536—131no—
98#519—131no—
99#464—134no—
100#462—134no—
101#424—131no—
102#419—131no—
103#416—131no—
104C22×C13—22no—
105C22×C13—41no—
106C22×C13—42no—
107C22×C13#12112yes—
108C22×C13C22×D411yescharacteristic
109C4×C13—24no—
110C4×C13—41no—
111C4×C13#12112yes—
112C4×C13C22×D411yescharacteristic
113C4×C13C2×#4111yescharacteristic
114Dic13—24no—
115Dic13—42no—
116Dic13—42no—
117C2×#41C2×D1311yescharacteristic
118C22×Q8—131no—
119C22×Q8C2×D1311yescharacteristic
120#137—24no—
121C2×Q16—134no—
122C2×Q16—264no—
123C2×Q16C2×D1312yes—
124C2×SD16C2×D1312yes—
125C2×M16C2×D1311yescharacteristic
126C22×C8—131no—
127C4⋊Q8—132no—
128#124—132no—
129#123—262no—
130C22⋊Q8—262no—
131C4×Q8—134no—
132C4×Q8—262no—
133#117—131no—
134#117—131no—
135#117—262no—
136C4⋊C8—134no—
137#103—132no—
138#103—134no—
139#102—132no—
140C2×C13—22no—
141C2×C13—81no—
142C2×C13C2×#12111yescharacteristic
143C2×C13#57812yes—
144#41—22no—
145#41—22no—
146C2×Q8—21no—
147C2×Q8—22no—
148C2×Q8—132no—
149C2×Q8—261no—
150C2×Q8—262no—
151C2×Q8—262no—
152C2×Q8C22⋊D1314yes—
153C2×Q8C22×D1311yescharacteristic
154C2×Q8C22×D1312yes—
155C2×D4—21no—
156C2×D4C22×D1311yescharacteristic
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—261no—
160C22×C4C22×D1311yescharacteristic
161Q16—24no—
162Q16—268no—
163SD16—24no—
164M16—22no—
165C2×C8—132no—
166C2×C8—262no—
167C2×C8C22×D1312yes—
168C4⋊C4—132no—
169C4⋊C4—132no—
170C4⋊C4—264no—
171C4⋊C4—264no—
172C22⋊C4—132no—
173C22⋊C4—264no—
174C22⋊C4—261no—
175C42—132no—
176C42—264no—
177C42—261no—
178C13#304411yescharacteristic, complemented, Sylow
179C23—21no—
180C23D4×D1311yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—21no—
184Q8—21no—
185Q8—262no—
186Q8—262no—
187Q8—522no—
188Q8C2×C22⋊D1314yes—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—42no—
196C2×C4—134no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—522no—
200C2×C4D4×D1311yescharacteristic
201C2×C4#612912yes—
202C2×C4C2×C22⋊D1312yes—
203C2×C4C23×D1311yescharacteristic
204C8—22no—
205C8—262no—
206C22—22no—
207C22—42no—
208C22—41no—
209C22#8819312yes—
210C22C2×D4×D1311yescharacteristic
211C4—24no—
212C4—41no—
213C4—264no—
214C4—522no—
215C4—522no—
216C4#8819312yes—
217C4C2×#612911yescharacteristic
218C4C22×C22⋊D1311yescharacteristic
219C2—22no—
220C2—81no—
221C2#1171948412yes—
222C2C2×#8819311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#137C2
socleC22×C13C22×D4
prime radicalC2×C13×#41C22
hypercenterC2×#137D13
hypocenterC13#3044
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
3. #11719517C2semidirect
4. C22×#6107C2semidirect
6. #11718843C2semidirect
7. #11718827C2semidirect
8. #11718781C2semidirect
9. #11718780C2semidirect
178. C13#3044semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1372
#117195302
#117195172
C22×#61072
#117188942
#117188432
#117188272
#117187812
#117187802
#304413