Finite Group Databasebeta

← #13127869

Subgroups — #13127869

Order 1664.

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

normal subgroups only

This group has 350 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#11719289C211yesmaximal, characteristic
2#11719275C211yesmaximal, characteristic, complemented
3C13×#446C211yesmaximal, characteristic, complemented
4#11718510C211yesmaximal, characteristic, complemented
5#11718510C212yesmaximal, complemented
6#11718506C212yesmaximal
7#11718502C211yesmaximal, characteristic
8#11718377C212yesmaximal, complemented
9#11718376C212yesmaximal
10#11718360C211yesmaximal, characteristic, complemented
11C4×#6095C211yesmaximal, characteristic
12C4×Q8×C13C2211yescharacteristic
13#88200—21no—
14Q8×Dic13—21no—
15C2×Dic52C2212yes—
16C2×Dic52C2212yes—
17C2×Dic52C2212yes—
18C2×#6095C2211yescharacteristic
19C2×#6095C2212yes—
20#88152—22no—
21#88146—21no—
22#88144—21no—
23#88144—22no—
24#88129C2212yes—
25C4×D52C2211yescharacteristic
26#88123C2211yescharacteristic
27#88123C2212yes—
28#88123C2211yescharacteristic
29C4×Dic26C2212yes—
30C4×Dic26C2211yescharacteristic
31C4×Dic26C2212yes—
32C13×C4⋊C8C2211yescharacteristic
33C13×C4⋊C8C2212yes—
34C13×#97C2212yes—
35C4×C8×C13C2211yescharacteristic
36#88061C2211yescharacteristic
37#88057C2211yescharacteristic
38#88056C2212yes—
39#88056C2212yes—
40#88056C2211yescharacteristic
41C2×Q8×C13D411yescharacteristic
42C2×D52C2311yescharacteristic
43C2×C4×D13—21no—
44C2×Dic26C2311yescharacteristic
45C2×Dic26C2312yes—
46C2×Dic26C2312yes—
47C2×C8×C13C2311yescharacteristic
48C2×C8×C13C2312yes—
49C2×C8×C13C2311yescharacteristic
50C13×C4⋊C4D411yescharacteristic
51C13×C4⋊C4D412yes—
52C42×C13C2311yescharacteristic
53C42×C13C2312yes—
54#6103—21no—
55#6103—22no—
56#6103—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13—21no—
59C4⋊Dic13—22no—
60C4⋊Dic13—21no—
61C4⋊Dic13—21no—
62C4⋊Dic13—21no—
63C4⋊Dic13C2311yescharacteristic
64C4⋊Dic13C2311yescharacteristic
65#6101—22no—
66#6101—21no—
67#6101—22no—
68C4×Dic13—22no—
69C4×Dic13—21no—
70C4×Dic13—22no—
71Dic52—24no—
72Dic52—42no—
73Dic52—42no—
74#6095—22no—
75#6095—42no—
76#3398—131nomaximal, Sylow
77C22×D13—21no—
78Q8×C13—22no—
79C2×C4×C13C2×D412yes—
80C2×C4×C13C2×D412yes—
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2411yescharacteristic
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89D52—21no—
90D52—21no—
91C4×D13—42no—
92Dic26—21no—
93Dic26—22no—
94Dic26—22no—
95Dic26—22no—
96Dic26—21no—
97Dic26—22no—
98C8×C13—22no—
99C8×C13—21no—
100C8×C13#4112yes—
101#557—131no—
102#556—131no—
103#497—132no—
104#494—131no—
105#464—132no—
106#462—132no—
107#462—131no—
108#461—131no—
109#446D1311yescharacteristic, complemented
110#441—132no—
111C4×SD16—131no—
112C22×C13C22×D411yescharacteristic
113C2×D13—41no—
114C2×D13—41no—
115C2×D13—41no—
116C4×C13—22no—
117C4×C13—22no—
118C4×C13—21no—
119C4×C13#13712yes—
120C4×C13C2×#4111yescharacteristic
121C4×C13H(5,𝔽2)11yescharacteristic
122Dic13—41no—
123Dic13—42no—
124Dic13—42no—
125Dic13—41no—
126Dic13—41no—
127C2×Q16—132no—
128C2×Q16—132no—
129C2×Q16—132no—
130C2×SD16—131no—
131C2×SD16—132no—
132C4⋊Q8—131no—
133C4⋊Q8—131no—
134C4⋊Q8—132no—
135#126—262no—
136#125—261no—
137#125—262no—
138#124—132no—
139C22⋊Q8—261no—
140C4×Q8—132no—
141C4×Q8—131no—
142C4×Q8—132no—
143C4×Q8—261no—
144C4×Q8C2×D1311yescharacteristic
145C4×D4—131no—
146#117—261no—
147#106—131no—
148C4⋊C8C2×D1311yescharacteristic
149C4⋊C8C2×D1312yes—
150#103—131no—
151#103—132no—
152#103—132no—
153#102—131no—
154#97C2×D1312yes—
155C4×C8C2×D1311yescharacteristic
156C2×C13#55011yescharacteristic
157C2×C13C2×#13711yescharacteristic
158C2×C13#57811yescharacteristic
159D13—81no—
160C2×Q8—132no—
161C2×Q8—131no—
162C2×Q8—132no—
163C2×Q8D5211yescharacteristic
164C2×D4—131no—
165C22×C4—261no—
166Q16—264no—
167Q16—522no—
168Q16—522no—
169SD16—262no—
170SD16—522no—
171C2×C8C22×D1311yescharacteristic
172C2×C8C22×D1312yes—
173C2×C8C22×D1311yescharacteristic
174C4⋊C4—131no—
175C4⋊C4—131no—
176C4⋊C4—261no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—261no—
180C4⋊C4—262no—
181C4⋊C4—261no—
182C4⋊C4—262no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4D5211yescharacteristic
186C4⋊C4D5212yes—
187C22⋊C4—262no—
188C22⋊C4—261no—
189C22⋊C4—262no—
190C42—262no—
191C42—262no—
192C42—261no—
193C42C22×D1311yescharacteristic
194C42C22×D1312yes—
195C13#339811yescharacteristic, complemented, Sylow
196C23—261no—
197Q8—22no—
198Q8—261no—
199Q8—262no—
200Q8—262no—
201Q8—262no—
202Q8—262no—
203Q8—261no—
204D4—261no—
205D4—261no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—262no—
209C2×C4—261no—
210C2×C4—262no—
211C2×C4—522no—
212C2×C4C2×D5212yes—
213C2×C4C2×D5212yes—
214C2×C4C2×D5211yescharacteristic
215C2×C4C2×D5211yescharacteristic
216C2×C4C23×D1311yescharacteristic
217C8—22no—
218C8—21no—
219C8#613112yes—
220C22—521no—
221C22—521no—
222C22—521no—
223C22C22×D5211yescharacteristic
224C4—22no—
225C4—22no—
226C4—21no—
227C4—521no—
228C4—521no—
229C4—522no—
230C4—521no—
231C4—522no—
232C4#8816312yes—
233C4C2×#613111yescharacteristic
234C4#8825611yescharacteristic
235C2—1041no—
236C2#1171928211yescharacteristic
237C2C2×#8816311yescharacteristic
238C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#446C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#446D13
hypocenterC13#3398
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #11719275C2semidirect
3. C13×#446C2semidirect
4. #11718510C2semidirect
5. #11718510C2semidirect
8. #11718377C2semidirect
10. #11718360C2semidirect
109. #446D13semidirect
195. C13#3398semidirect

Maximal subgroups

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

subgroupindex
#117192892
#117192752
C13×#4462
#117185102
#117185062
#117185022
#117183772
#117183762
#117183602
C4×#60952
#339813