Finite Group Databasebeta

← #13126756

Subgroups — #13126756

Order 1664.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#11719431C211yesmaximal, characteristic
2#11719289C211yesmaximal, characteristic, complemented
3C13×#462C211yesmaximal, characteristic, complemented
4#11718849C212yesmaximal, complemented
5#11718848C212yesmaximal, complemented
6#11718742C211yesmaximal, characteristic, complemented
7C4×#6106C211yesmaximal, characteristic, complemented
8#11718507C211yesmaximal, characteristic, complemented
9#11718495C211yesmaximal, characteristic, complemented
10#11718475C212yesmaximal, complemented
11#11718465C212yesmaximal, complemented
12C2×#6131C2212yes—
13C2×C13×Q16C2212yes—
14C13×C4⋊Q8C2211yescharacteristic
15C4×Q8×C13C2211yescharacteristic
16#88200C2212yes—
17#88200C2212yes—
18C2×#6106C2211yescharacteristic
19C2×C8×D13C2212yes—
20#88152—22no—
21#88149—21no—
22#88148—22no—
23#88146C2212yes—
24C4⋊C4×D13—21no—
25#88129—21no—
26C4×D52C2211yescharacteristic
27C4×D52C2211yescharacteristic
28#88123C2211yescharacteristic
29C4×Dic26—21no—
30C13×C4⋊C8C2211yescharacteristic
31C13×#103C2212yes—
32#88075C2211yescharacteristic
33#88075C2212yes—
34#88075C2212yes—
35#88061C2212yes—
36#88060C2212yes—
37#88058C2212yes—
38#88049C2211yescharacteristic
39#88048C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13C2312yes—
42C2×Q8×C13C2311yescharacteristic
43#6131—24no—
44#6131—42no—
45C2×D52—22no—
46C2×D52D411yescharacteristic
47C2×D52C2311yescharacteristic
48C2×C4×D13—21no—
49C2×C4×D13—22no—
50C2×C4×D13C2312yes—
51C2×Dic26—21no—
52C13×Q16—42no—
53C2×C8×C13C2312yes—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4C2311yescharacteristic
58C42×C13—21no—
59C42×C13C2311yescharacteristic
60#6106—22no—
61#6103—22no—
62#6103—22no—
63#6103—22no—
64#6103—21no—
65#6103D412yes—
66C4⋊Dic13—21no—
67C4⋊Dic13D411yescharacteristic
68C4⋊Dic13C2312yes—
69C4⋊Dic13C2311yescharacteristic
70#6101—22no—
71#6101—22no—
72C4×Dic13—22no—
73C2×#1055C2311yescharacteristic
74C2×#1055C2311yescharacteristic
75C8×D13—42no—
76#3302—131nomaximal, Sylow
77C22×D13—21no—
78C22×D13C2×D412yes—
79Q8×C13—21no—
80Q8×C13—22no—
81Q8×C13—21no—
82Q8×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C2×Dic13—22no—
90C2×Dic13—21no—
91C2×Dic13C2×D412yes—
92D52—22no—
93D52—21no—
94D52—44no—
95D52#4112yes—
96C4×D13—22no—
97C4×D13—22no—
98C4×D13—44no—
99C4×D13—42no—
100Dic26—42no—
101C8×C13—22no—
102#1055—21no—
103#1055—21no—
104#556—131no—
105#547—131no—
106#487—131no—
107#485—132no—
108#474—131no—
109#467—132no—
110#462D1311yescharacteristic, complemented
111#452—132no—
112C4×SD16—131no—
113C8×D4—131no—
114#416—132no—
115C22×C13C22×D411yescharacteristic
116C2×D13—22no—
117C2×D13—22no—
118C2×D13—22no—
119C2×D13—22no—
120C2×D13—41no—
121C2×D13—41no—
122C4×C13—21no—
123C4×C13—42no—
124C4×C13—41no—
125C4×C13—41no—
126C4×C13#13512yes—
127C4×C13C2×#4111yescharacteristic
128C4×C13H(5,𝔽2)11yescharacteristic
129Dic13—22no—
130Dic13—42no—
131Dic13—41no—
132C2×#41—132no—
133C2×Q16C2×D1312yes—
134C2×SD16—131no—
135C22×C8—132no—
136C4⋊Q8—131no—
137C4⋊Q8C2×D1311yescharacteristic
138#126—262no—
139#124—261no—
140#123—262no—
141C22⋊Q8—132no—
142C22⋊Q8—132no—
143#121—261no—
144C4×Q8—261no—
145C4×Q8C2×D1311yescharacteristic
146C4×D4—131no—
147C4×D4—131no—
148#117—132no—
149C2×C4⋊C4—261no—
150#107—132no—
151#106—131no—
152C4⋊C8C2×D1311yescharacteristic
153#103—132no—
154#103—131no—
155#103—132no—
156#103C2×D1312yes—
157#102—132no—
158#102—131no—
159C22⋊C8—132no—
160C4×C8—131no—
161C2×C13#54611yescharacteristic
162C2×C13C2×#13511yescharacteristic
163C2×C13#57811yescharacteristic
164D13—42no—
165D13—42no—
166#41—264no—
167#41—522no—
168C2×Q8—261no—
169C2×Q8C22×D1312yes—
170C2×Q8C22×D1311yescharacteristic
171C2×D4—131no—
172C2×D4—131no—
173C2×D4—262no—
174C22×C4—132no—
175C22×C4—262no—
176C22×C4—261no—
177Q16—42no—
178SD16—262no—
179C2×C8—131no—
180C2×C8—131no—
181C2×C8—522no—
182C2×C8C22×D1312yes—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—131no—
187C4⋊C4—132no—
188C4⋊C4—131no—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C4⋊C4—261no—
192C4⋊C4C22×D1311yescharacteristic
193C22⋊C4—132no—
194C22⋊C4—262no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C22⋊C4—261no—
198C42—21no—
199C42—262no—
200C42C22×D1311yescharacteristic
201C13#330211yescharacteristic, complemented, Sylow
202C23—132no—
203C23—261no—
204Q8—21no—
205Q8—22no—
206Q8—21no—
207Q8—22no—
208Q8—522no—
209D4—132no—
210D4—262no—
211D4—261no—
212D4—524no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—132no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—261no—
221C2×C4—524no—
222C2×C4—522no—
223C2×C4D4×D1311yescharacteristic
224C2×C4D4×D1311yescharacteristic
225C2×C4C23×D1311yescharacteristic
226C8—22no—
227C8—261no—
228C8—261no—
229C22—262no—
230C22—262no—
231C22—262no—
232C22—262no—
233C22—521no—
234C22—521no—
235C22C2×D4×D1311yescharacteristic
236C4—21no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—262no—
241C4—521no—
242C4—522no—
243C4#8817312yes—
244C4#8825111yescharacteristic
245C4#41×D1311yescharacteristic
246C2—522no—
247C2—522no—
248C2#1171931711yescharacteristic
249C2C2×#8817311yescharacteristic
250C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#462C2
socleC22×C13C22×D4
prime radical#11719431C2
hypercenter#462D13
hypocenterC13#3302
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #11719289C2semidirect
3. C13×#462C2semidirect
4. #11718849C2semidirect
5. #11718848C2semidirect
6. #11718742C2semidirect
7. C4×#6106C2semidirect
8. #11718507C2semidirect
9. #11718495C2semidirect
10. #11718475C2semidirect
11. #11718465C2semidirect
110. #462D13semidirect
201. C13#3302semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117192892
C13×#4622
#117188492
#117188482
#117187422
C4×#61062
#117185072
#117184952
#117184752
#117184652
#330213