Finite Group Databasebeta

← #13124961

Subgroups — #13124961

Order 1664.

380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 123 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×Q8×Dic13C211yesmaximal, characteristic
2#11719327C211yesmaximal, characteristic
3C13×#451C211yesmaximal, characteristic
4#11718889C211yesmaximal, characteristic
5#11718845C212yesmaximal, complemented
6#11718843C212yesmaximal, complemented
7#11718704C211yesmaximal, characteristic
8#11718452C212yesmaximal, complemented
9#11718450C212yesmaximal, complemented
10#11718382C211yesmaximal, characteristic
11#11718380C211yesmaximal, characteristic
12C22×Q8×C13C2211yescharacteristic
13C2×C13×Q16C2212yes—
14C13×C22⋊Q8C2211yescharacteristic
15Q8×Dic13—21no—
16Q8×Dic13—21no—
17Q8×Dic13C2212yes—
18Q8×Dic13C2212yes—
19Q8×Dic13C2211yescharacteristic
20#88198C2211yescharacteristic
21C2×#6107C2212yes—
22C2×C4⋊Dic13—21no—
23C2×C4⋊Dic13C2211yescharacteristic
24#88178C2211yescharacteristic
25C2×C4×Dic13—21no—
26C2×C4×Dic13C2211yescharacteristic
27#88143—21no—
28#88142C2211yescharacteristic
29#88141—21no—
30#88141C2211yescharacteristic
31#88132—21no—
32#88131—21no—
33C13×#103C2212yes—
34C13×C22⋊C8C2211yescharacteristic
35#88075C2212yes—
36#88075C2212yes—
37C22⋊#1055C2211yescharacteristic
38#88057C2212yes—
39#88056C2212yes—
40#88055C2212yes—
41#88054C2212yes—
42#88048C2212yes—
43C2×Q8×C13—24no—
44C2×Q8×C13—21no—
45C2×Q8×C13C2311yescharacteristic
46C2×Q8×C13C2312yes—
47C22×C4×C13—21no—
48C22×C4×C13C2311yescharacteristic
49C22×Dic13—21no—
50C22×Dic13D411yescharacteristic
51C22×Dic13D411yescharacteristic
52C2×Dic26—21no—
53C2×Dic26C2311yescharacteristic
54C13×Q16—24no—
55C2×C8×C13C2312yes—
56C13×C4⋊C4—21no—
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C22⋊Dic13—21no—
60#6107—24no—
61C4⋊Dic13—21no—
62C4⋊Dic13—21no—
63C4⋊Dic13—22no—
64C4⋊Dic13—22no—
65C4⋊Dic13C2311yescharacteristic
66C4⋊Dic13C2312yes—
67#6101—21no—
68#6101—21no—
69#6101—21no—
70#6101—21no—
71#6101—21no—
72C4×Dic13—21no—
73C4×Dic13—21no—
74C4×Dic13—22no—
75C4×Dic13—22no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C4×Dic13C2311yescharacteristic
80C2×#1055C2312yes—
81#3113—131nomaximal, Sylow
82C23×C13C2×D411yescharacteristic
83Q8×C13—24no—
84Q8×C13—22no—
85Q8×C13—22no—
86Q8×C13#4114yes—
87C2×C4×C13—24no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2411yescharacteristic
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—42no—
100C2×Dic13C2×D411yescharacteristic
101C2×Dic13C2×D411yescharacteristic
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104Dic26—22no—
105Dic26—42no—
106C8×C13—22no—
107#1055—22no—
108#533—131no—
109C2×C4×Q8—131no—
110#483—131no—
111#483—131no—
112#475—132no—
113#462—132no—
114#451—131no—
115#451D1311yescharacteristic
116#441—132no—
117#441—132no—
118#432—131no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13#13712yes—
122C22×C13C22×D411yescharacteristic
123C4×C13—24no—
124C4×C13—21no—
125C4×C13—41no—
126C4×C13—41no—
127C4×C13C2×#4112yes—
128Dic13—21no—
129Dic13—21no—
130Dic13—21no—
131Dic13—41no—
132Dic13—41no—
133Dic13—42no—
134Dic13#13712yes—
135C22×Q8C2×D1311yescharacteristic
136C2×Q16—132no—
137C2×Q16C2×D1312yes—
138C4⋊Q8—131no—
139C4⋊Q8—131no—
140#125—261no—
141C22⋊Q8—131no—
142C22⋊Q8—261no—
143C22⋊Q8C2×D1311yescharacteristic
144C4×Q8—132no—
145C4×Q8—132no—
146C4×Q8—131no—
147C4×Q8—131no—
148C4×Q8—261no—
149C4×Q8—261no—
150C4×Q8—261no—
151#117—261no—
152C2×C4⋊C4—131no—
153C2×C4⋊C4—261no—
154C2×C42—131no—
155C2×C42—261no—
156#106—132no—
157#106—132no—
158C4⋊C8—132no—
159#103—132no—
160#103—132no—
161#103—132no—
162#103C2×D1312yes—
163C22⋊C8—131no—
164C22⋊C8C2×D1311yescharacteristic
165#97—132no—
166C2×C13—22no—
167C2×C13#52511yescharacteristic
168C2×C13C2×#13711yescharacteristic
169C2×C13C2×#13711yescharacteristic
170C2×Q8—24no—
171C2×Q8—21no—
172C2×Q8—131no—
173C2×Q8—261no—
174C2×Q8C22×D1311yescharacteristic
175C2×Q8C22×D1312yes—
176C22×C4—21no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—261no—
180C22×C4C22×D1311yescharacteristic
181Q16—24no—
182Q16—264no—
183C2×C8—132no—
184C2×C8C22×D1312yes—
185C4⋊C4—21no—
186C4⋊C4—132no—
187C4⋊C4—131no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4—261no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4C22×D1311yescharacteristic
198C22⋊C4—21no—
199C22⋊C4—261no—
200C42—131no—
201C42—131no—
202C42—131no—
203C42—131no—
204C42—262no—
205C42—262no—
206C42—261no—
207C42—261no—
208C13#311311yescharacteristic, complemented, Sylow
209C23D4×D1311yescharacteristic
210Q8—24no—
211Q8—22no—
212Q8—22no—
213Q8—262no—
214Q8—522no—
215Q8#612914yes—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—131no—
222C2×C4—131no—
223C2×C4—131no—
224C2×C4—131no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—522no—
231C2×C4D4×D1311yescharacteristic
232C2×C4C23×D1311yescharacteristic
233C8—22no—
234C8—262no—
235C22—21no—
236C22—21no—
237C22#8817212yes—
238C22C2×D4×D1311yescharacteristic
239C4—24no—
240C4—21no—
241C4—41no—
242C4—41no—
243C4—132no—
244C4—261no—
245C4—261no—
246C4—261no—
247C4—522no—
248C4—521no—
249C4—521no—
250C4C2×#612912yes—
251C2—22no—
252C2#1171929111yescharacteristic
253C2C2×#8817211yescharacteristic
254C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#451C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#451D13
hypocenterC13#3113
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
5. #11718845C2semidirect
6. #11718843C2semidirect
8. #11718452C2semidirect
9. #11718450C2semidirect
208. C13#3113semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic132
#117193272
C13×#4512
#117188892
#117188452
#117188432
#117187042
#117184522
#117184502
#117183822
#117183802
#311313