Finite Group Databasebeta

← #13116150

Subgroups — #13116150

Order 1664.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C22×#6106C211yesmaximal, characteristic
2C2×C13×#103C211yesmaximal, characteristic, complemented
3#11718891C211yesmaximal, characteristic, complemented
4C2×#88061C211yesmaximal, characteristic
5C2×#88054C211yesmaximal, characteristic, complemented
6#11718649C211yesmaximal, characteristic
7#11718121C211yesmaximal, characteristic, complemented
8C22×Q8×C13C2211yescharacteristic
9C22×D52C2211yescharacteristic
10C22×C8×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×#6106—22no—
13C2×#6106—22no—
14C2×#6106—22no—
15C2×#6103—21no—
16C2×#6103—21no—
17C2×C4⋊Dic13C2211yescharacteristic
18C2×C4×Dic13C2211yescharacteristic
19C22×#1055C2211yescharacteristic
20C13×#103—22no—
21#88071—21no—
22#88071—21no—
23#88061—22no—
24#88054—22no—
25C23×D13—21no—
26C2×Q8×C13—21no—
27C2×Q8×C13—21no—
28C2×Q8×C13—21no—
29C2×Q8×C13—21no—
30C2×Q8×C13—21no—
31C2×Q8×C13D412yes—
32C22×C4×C13—21no—
33C22×C4×C13—21no—
34C22×C4×C13C2311yescharacteristic
35C22×Dic13—21no—
36C22×Dic13D411yescharacteristic
37C22×Dic13D411yescharacteristic
38C2×D52—21no—
39C2×D52—21no—
40C2×D52—21no—
41C2×D52—21no—
42C2×D52—21no—
43C2×D52D412yes—
44C2×C8×C13—21no—
45C2×C8×C13—21no—
46C2×C8×C13—21no—
47C13×C4⋊C4—21no—
48C13×C4⋊C4—21no—
49#6106—28no—
50#6103—42no—
51#6103—42no—
52C4⋊Dic13—21no—
53C4⋊Dic13—21no—
54C4×Dic13—21no—
55C4×Dic13—21no—
56C2×#1055—21no—
57C2×#1055—21no—
58C2×#1055D412yes—
59#2055—131nomaximal, Sylow
60C23×C13C2×D411yescharacteristic
61C22×D13—22no—
62C22×D13—41no—
63C22×D13—41no—
64C22×D13—41no—
65C22×D13—41no—
66C22×D13—41no—
67C22×D13—41no—
68Q8×C13—22no—
69Q8×C13—22no—
70Q8×C13—41no—
71Q8×C13—41no—
72C2×C4×C13—22no—
73C2×C4×C13—41no—
74C2×C4×C13—41no—
75C2×C4×C13—41no—
76C2×C4×C13—41no—
77C2×C4×C13—41no—
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13#4111yescharacteristic
82C2×C4×C13#4111yescharacteristic
83C2×C4×C13#4111yescharacteristic
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—41no—
90C2×Dic13—41no—
91C2×Dic13—41no—
92C2×Dic13SD1612yescomplemented
93D52—22no—
94D52—22no—
95D52—41no—
96D52—41no—
97C8×C13—41no—
98#1055—22no—
99C22×SD16—131no—
100C2×C4⋊C8—131no—
101C2×#103D1311yescharacteristic, complemented
102C2×#102—131no—
103#391—131no—
104#390—131no—
105#340—131no—
106C22×C13#12111yescharacteristic
107C22×C13#12111yescharacteristic
108C22×C13#12111yescharacteristic
109C22×C13C2×SD1611yescharacteristic
110C22×C13#13511yescharacteristic
111C22×C13AGL(1,ℤ/8)11yescharacteristic
112C22×C13#13711yescharacteristic
113C2×D13—42no—
114C2×D13—42no—
115C2×D13—42no—
116C2×D13—81no—
117C2×D13—81no—
118C2×D13—81no—
119C2×D13—81no—
120C4×C13—42no—
121C4×C13—81no—
122C4×C13#12011yescharacteristic
123C4×C13#12311yescharacteristic
124C4×C13#12311yescharacteristic
125C4×C13#12411yescharacteristic
126Dic13—22no—
127Dic13—41no—
128Dic13—81no—
129C22×Q8C2×D1311yescharacteristic
130C22×D4—131no—
131C2×SD16—262no—
132C2×SD16—262no—
133C2×SD16—262no—
134C22×C8—131no—
135C22×C8C2×D1311yescharacteristic
136C2×C4⋊C4—131no—
137C2×C4⋊C4C2×D1311yescharacteristic
138C2×C22⋊C4—261no—
139C2×C22⋊C4—261no—
140C2×C42—131no—
141C4⋊C8—262no—
142#103—22no—
143#102—262no—
144#95—261no—
145#95—261no—
146C2×C13#39411yescharacteristic
147C2×C13#46011yescharacteristic
148C2×C13#46111yescharacteristic
149C2×C13#46311yescharacteristic
150C2×C13#46411yescharacteristic
151C2×C13#46511yescharacteristic
152C2×C13#46811yescharacteristic
153D13—82no—
154C24—261no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8C22⋊D1312yes—
161C2×D4—132no—
162C2×D4—261no—
163C2×D4—261no—
164C2×D4—261no—
165C2×D4—261no—
166C2×D4—261no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—131no—
170C22×C4—131no—
171C22×C4—261no—
172C22×C4C22×D1311yescharacteristic
173SD16—268no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—132no—
178C2×C8—261no—
179C2×C8—261no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—261no—
183C4⋊C4—261no—
184C22⋊C4—522no—
185C22⋊C4—522no—
186C42—261no—
187C42—261no—
188C13#205511yescharacteristic, complemented, Sylow
189C23—262no—
190C23—521no—
191C23—521no—
192C23—521no—
193C23—521no—
194C23—521no—
195C23—521no—
196C23D4×D1311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—262no—
202D4—262no—
203D4—521no—
204D4—521no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—132no—
212C2×C4—261no—
213C2×C4—261no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4—261no—
217C2×C4—521no—
218C2×C4—521no—
219C2×C4—521no—
220C2×C4#612711yescharacteristic
221C2×C4#612711yescharacteristic
222C2×C4D4×D1311yescharacteristic
223C2×C4D4×D1311yescharacteristic
224C2×C4#612911yescharacteristic
225C2×C4C2×C22⋊D1311yescharacteristic
226C8—41no—
227C8—262no—
228C22—522no—
229C22—522no—
230C22—522no—
231C22—1041no—
232C22—1041no—
233C22—1041no—
234C22—1041no—
235C22#8813811yescharacteristic
236C22#8813811yescharacteristic
237C22SD16×D1311yescharacteristic
238C22#8816811yescharacteristic
239C22#8817211yescharacteristic
240C22#8817311yescharacteristic
241C22#8819311yescharacteristic
242C4—42no—
243C4—81no—
244C4—262no—
245C4—521no—
246C4—1041no—
247C4#8813711yescharacteristic
248C4#8813911yescharacteristic
249C4#8818311yescharacteristic
250C4#8819111yescharacteristic
251C2—1042no—
252C2#1171846811yescharacteristic
253C2#1171847311yescharacteristic
254C2#1171847911yescharacteristic
255C2#1171848011yescharacteristic
256C2#1171862011yescharacteristic
257C2#1171882411yescharacteristic
258C2#1171884611yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC2×C13×#103C2
socleC23×C13C2×D4
prime radicalC22×D52C22
hypercenterC2×#103D13
hypocenterC13#2055
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×C13×#103C2semidirect
3. #11718891C2semidirect
5. C2×#88054C2semidirect
7. #11718121C2semidirect
92. C2×Dic13SD16semidirect
101. C2×#103D13semidirect
188. C13#2055semidirect

Maximal subgroups

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

subgroupindex
C22×#61062
C2×C13×#1032
#117188912
C2×#880612
C2×#880542
#117186492
#117181212
#205513