Finite Group Databasebeta

← #13125794

Subgroups — #13125794

Order 1664.

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

normal subgroups only

This group has 394 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
1#11719182C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3C13×#431C211yesmaximal, characteristic, complemented
4#11718506C214yesmaximal, complemented
5#11718394C214yesmaximal, complemented
6#11718360C211yesmaximal, characteristic, complemented
7#11718355C211yesmaximal, characteristic, complemented
8#11718354C211yesmaximal, characteristic, complemented
9#11718342C211yesmaximal, characteristic, complemented
10C2×#6127C2212yes—
11C2×C42×C13C2211yescharacteristic
12#88184—21no—
13#88184—21no—
14#88180—21no—
15#88178—21no—
16#88178C2212yes—
17C2×Dic52C2214yes—
18C2×#6095C2214yes—
19#88129C2212yes—
20#88128C2211yescharacteristic
21C4×D52—21no—
22C4×D52—21no—
23#88124—21no—
24#88123C2211yescharacteristic
25#88123C2211yescharacteristic
26#88123C2211yescharacteristic
27C4×Dic26—21no—
28C4×Dic26C2212yes—
29C13×C4⋊C8C2212yes—
30C13×C22⋊C8C2212yes—
31C4×C8×C13C2211yescharacteristic
32C4×C8×C13C2211yescharacteristic
33#88061C2214yes—
34#88056C2214yes—
35C22×C4×C13D411yescharacteristic
36C22×C4×C13D411yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—22no—
39#6127—44no—
40C2×D52—21no—
41C2×D52—21no—
42C2×D52C2312yes—
43C2×C4×D13—22no—
44C2×Dic26—21no—
45C2×Dic26C2312yes—
46C2×Dic26C2312yes—
47C2×C8×C13C2312yes—
48C2×C8×C13C2312yes—
49C42×C13D411yescharacteristic
50C42×C13D411yescharacteristic
51C42×C13C2311yescharacteristic
52C42×C13C2311yescharacteristic
53C22⋊Dic13—22no—
54#6103—22no—
55#6103—22no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C4⋊Dic13—21no—
59C4⋊Dic13—21no—
60C4⋊Dic13—21no—
61C4⋊Dic13C2312yes—
62#6101—22no—
63#6101—22no—
64C4×Dic13—22no—
65Dic52—44no—
66#6095—44no—
67#3210—131nomaximal, Sylow
68C23×C13C2×D411yescharacteristic
69C22×D13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2411yescharacteristic
79C22⋊D13—44no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83D52—24no—
84D52—42no—
85D52—42no—
86C4×D13—44no—
87Dic26—24no—
88Dic26—24no—
89Dic26—42no—
90C8×C13—22no—
91C8×C13—22no—
92#533—131no—
93#532—131no—
94#494—131no—
95#492—131no—
96#487—131no—
97#486—131no—
98#464—134no—
99#452—134no—
100#431D1311yescharacteristic, complemented
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13C22×D411yescharacteristic
105C2×D13—42no—
106C2×D13—42no—
107C2×D13—42no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—21no—
111C4×C13#13512yes—
112C4×C13#13712yes—
113C4×C13H(5,𝔽2)12yes—
114Dic13—42no—
115Dic13—42no—
116Dic13—42no—
117C2×#41—132no—
118C2×Q16—134no—
119C2×SD16—134no—
120C4⋊Q8—131no—
121C4⋊Q8—131no—
122C4⋊Q8—131no—
123#127—131no—
124#125—261no—
125#124—132no—
126C22⋊Q8—132no—
127C22⋊Q8—261no—
128#121—261no—
129#121—261no—
130C4×Q8—132no—
131C4×Q8—261no—
132C4×D4—261no—
133C4×D4—261no—
134#117—261no—
135C2×C42C2×D1311yescharacteristic
136C4⋊C8C2×D1312yes—
137#103—134no—
138#102—134no—
139C22⋊C8C2×D1312yes—
140C4×C8C2×D1311yescharacteristic
141C4×C8C2×D1311yescharacteristic
142C2×C13—41no—
143C2×C13#53511yescharacteristic
144C2×C13C2×#13511yescharacteristic
145C2×C13C2×#13711yescharacteristic
146D13—82no—
147#41—524no—
148C2×Q8—132no—
149C2×Q8—132no—
150C2×Q8—261no—
151C2×D4—132no—
152C2×D4—262no—
153C2×D4—261no—
154C2×D4—261no—
155C22×C4—262no—
156C22×C4D5211yescharacteristic
157C22×C4D5211yescharacteristic
158C22×C4C22×D1311yescharacteristic
159Q16—524no—
160SD16—524no—
161C2×C8C22×D1312yes—
162C2×C8C22×D1312yes—
163C4⋊C4—132no—
164C4⋊C4—261no—
165C4⋊C4—261no—
166C4⋊C4—261no—
167C4⋊C4—261no—
168C4⋊C4—262no—
169C4⋊C4—262no—
170C4⋊C4—261no—
171C22⋊C4—262no—
172C22⋊C4—262no—
173C22⋊C4—262no—
174C42—262no—
175C42D5211yescharacteristic
176C42D5211yescharacteristic
177C42C22×D1311yescharacteristic
178C42C22×D1311yescharacteristic
179C13#321011yescharacteristic, complemented, Sylow
180C23—262no—
181C23C2×D5211yescharacteristic
182Q8—264no—
183Q8—264no—
184Q8—522no—
185D4—264no—
186D4—524no—
187D4—522no—
188D4—522no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—262no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—524no—
196C2×C4C2×D5211yescharacteristic
197C2×C4C2×D5211yescharacteristic
198C2×C4C2×D5211yescharacteristic
199C2×C4C2×D5211yescharacteristic
200C2×C4C2×D5211yescharacteristic
201C2×C4C23×D1311yescharacteristic
202C8—22no—
203C8—22no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—522no—
208C22—522no—
209C22—522no—
210C22C22×D5211yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—522no—
215C4—522no—
216C4—522no—
217C4#8815812yes—
218C4#8816312yes—
219C4#8825612yes—
220C2—41no—
221C2—1042no—
222C2#1171923011yescharacteristic
223C2C2×#8815811yescharacteristic
224C2C2×#8816311yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#431C2
socleC22×C13C22×D4
prime radical#11719182C2
hypercenter#431D13
hypocenterC13#3210
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #11719175C2semidirect
3. C13×#431C2semidirect
4. #11718506C2semidirect
5. #11718394C2semidirect
6. #11718360C2semidirect
7. #11718355C2semidirect
8. #11718354C2semidirect
9. #11718342C2semidirect
100. #431D13semidirect
179. C13#3210semidirect

Maximal subgroups

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

subgroupindex
#117191822
#117191752
C13×#4312
#117185062
#117183942
#117183602
#117183552
#117183542
#117183422
#321013