Finite Group Databasebeta

← #13119847

Subgroups — #13119847

Order 1664.

544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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×#88178C212yesmaximal
2C2×C13×#95C211yesmaximal, characteristic
3#11718873C211yesmaximal, characteristic
4#11718871C212yesmaximal
5C4×C22⋊Dic13C211yesmaximal, characteristic
6#11718318C212yesmaximal, complemented
7#11718317C212yesmaximal, complemented
8#11718308C212yesmaximal, complemented
9#11718307C212yesmaximal, complemented
10C23×C4×C13C2212yes—
11C23×C4×C13C2211yescharacteristic
12C22×Dic26C2212yes—
13C2×C22⋊Dic13C2212yes—
14C2×C22⋊Dic13C2211yescharacteristic
15C2×C22⋊Dic13C2211yescharacteristic
16C2×C4⋊Dic13C2212yes—
17C2×C4⋊Dic13C2212yes—
18#88178—28no—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×C4×Dic13C2212yes—
24C13×#95C2212yes—
25C13×#95C2211yescharacteristic
26C13×#95C2211yescharacteristic
27#88071C2211yescharacteristic
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31#88071C2212yes—
32C24×C13C2311yescharacteristic
33C22×C4×C13—24no—
34C22×C4×C13—24no—
35C22×C4×C13—42no—
36C22×C4×C13—42no—
37C22×C4×C13Q814yescomplemented
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C2×Dic26—24no—
47C2×Dic26—24no—
48C2×Dic26—42no—
49C22⋊Dic13—24no—
50C22⋊Dic13D414yes—
51C22⋊Dic13Q814yescomplemented
52C4⋊Dic13—24no—
53C4⋊Dic13—42no—
54#6101—24no—
55#6101—24no—
56#6101—24no—
57#6101—42no—
58C4×Dic13—42no—
59#2549—131nomaximal, Sylow
60C23×C13—22no—
61C23×C13—22no—
62C23×C13C2×D412yes—
63C23×C13C2×Q812yes—
64C23×C13C2×Q812yes—
65C23×C13C2411yescharacteristic
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—44no—
74C2×C4×C13—48no—
75C2×C4×C13C2×Q812yes—
76C2×C4×C13C2×Q812yes—
77C2×C4×C13#4114yes—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13C2×D414yes—
89C2×Dic13C2×Q814yes—
90Dic26—48no—
91C2×C22⋊Q8—132no—
92#398—132no—
93#395—132no—
94#391—132no—
95#389—132no—
96#385—132no—
97#380—131no—
98C4×C22⋊C4—131no—
99C2×#95D1311yescharacteristic
100C22×C13—22no—
101C22×C13—22no—
102C22×C13—24no—
103C22×C13—24no—
104C22×C13C4⋊Q814yes—
105C22×C13C22×D411yescharacteristic
106C22×C13C22×Q811yescharacteristic
107C22×C13C22×Q811yescharacteristic
108C22×C13C2×#4112yes—
109C22×C13H(5,𝔽2)12yes—
110C4×C13—22no—
111C4×C13—22no—
112C4×C13—24no—
113C4×C13—42no—
114Dic13—24no—
115Dic13—24no—
116Dic13—42no—
117Dic13—42no—
118C22×Q8—132no—
119C23×C4C2×D1312yes—
120C23×C4C2×D1311yescharacteristic
121C22⋊Q8—268no—
122C2×C4⋊C4—132no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—132no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—132no—
128C2×C22⋊C4—131no—
129C2×C22⋊C4—131no—
130C2×C22⋊C4—132no—
131C2×C42—132no—
132#95—132no—
133#95—131no—
134#95—131no—
135#95—132no—
136#95—132no—
137#95C2×D1312yes—
138#95C2×D1311yescharacteristic
139#95C2×D1311yescharacteristic
140C2×C13—24no—
141C2×C13C2×C4⋊Q811yescharacteristic
142C2×C13#53311yescharacteristic
143C2×C13#54311yescharacteristic
144C2×C13#54612yes—
145C2×C13#55412yes—
146C24C22×D1311yescharacteristic
147C2×Q8—264no—
148C2×Q8—264no—
149C2×Q8—522no—
150C22×C4—24no—
151C22×C4—24no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—132no—
155C22×C4—132no—
156C22×C4—132no—
157C22×C4—132no—
158C22×C4Dic2614yescomplemented
159C22×C4C22×D1312yes—
160C22×C4C22×D1311yescharacteristic
161C22×C4C22×D1311yescharacteristic
162C22×C4C22×D1312yes—
163C4⋊C4—264no—
164C4⋊C4—264no—
165C4⋊C4—264no—
166C4⋊C4—264no—
167C4⋊C4—522no—
168C4⋊C4—522no—
169C22⋊C4—134no—
170C22⋊C4—134no—
171C22⋊C4—264no—
172C42—522no—
173C13#254911yescharacteristic, complemented, Sylow
174C23—22no—
175C23—22no—
176C23C2×Dic2612yes—
177C23D4×D1312yes—
178C23Q8×D1312yes—
179C23C23×D1311yescharacteristic
180Q8—528no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—44no—
189C2×C4—48no—
190C2×C4—134no—
191C2×C4—134no—
192C2×C4—262no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4C2×Dic2612yes—
203C2×C4C2×Dic2612yes—
204C2×C4#612714yes—
205C22—22no—
206C22—22no—
207C22—24no—
208C22—24no—
209C22#8814214yes—
210C22C22×Dic2611yescharacteristic
211C22C2×#612712yes—
212C22C2×D4×D1311yescharacteristic
213C22#8825112yes—
214C22C2×Q8×D1311yescharacteristic
215C4—22no—
216C4—22no—
217C4—24no—
218C4—42no—
219C4—264no—
220C4—264no—
221C4—522no—
222C4—522no—
223C2—24no—
224C2#1171917511yescharacteristic
225C2#1171918811yescharacteristic
226C2#1171919512yes—
227C2C2×#8814211yescharacteristic
228C2#1171921612yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#95C2
prime radicalC24×C13C23
hypercenterC2×#95D13
hypocenterC13#2549
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
6. #11718318C2semidirect
7. #11718317C2semidirect
8. #11718308C2semidirect
9. #11718307C2semidirect
37. C22×C4×C13Q8semidirect
51. C22⋊Dic13Q8semidirect
158. C22×C4Dic26semidirect
173. C13#2549semidirect

Maximal subgroups

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

subgroupindex
C2×#881782
C2×C13×#952
#117188732
#117188712
C4×C22⋊Dic132
#117183182
#117183172
#117183082
#117183072
#254913