Finite Group Databasebeta

← #13127547

Subgroups — #13127547

Order 1664.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719423C211yesmaximal, characteristic, complemented
2#11719248C211yesmaximal, characteristic, complemented
3C13×#459C211yesmaximal, characteristic, complemented
4#11718813C212yesmaximal, complemented
5#11718811C212yesmaximal, complemented
6#11718731C211yesmaximal, characteristic, complemented
7C4×#6104C211yesmaximal, characteristic, complemented
8#11718503C211yesmaximal, characteristic, complemented
9#11718492C211yesmaximal, characteristic, complemented
10#11718425C212yesmaximal, complemented
11#11718424C212yesmaximal, complemented
12C2×#6129—21no—
13C2×C13×D8C2212yes—
14C13×#127C2211yescharacteristic
15C4×D4×C13C2211yescharacteristic
16#88194C2212yes—
17#88193—22no—
18#88192—21no—
19D4×Dic13C2212yes—
20D4×Dic13C2212yes—
21C2×#6104C2211yescharacteristic
22C2×C4⋊Dic13—21no—
23#88178—21no—
24#88144C2212yes—
25#88132—22no—
26C4×D52C2211yescharacteristic
27#88123C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×C4⋊C8C2211yescharacteristic
30C13×#102C2212yes—
31#88072C2211yescharacteristic
32#88072C2212yes—
33#88072C2212yes—
34#88061C2212yes—
35#88057C2212yes—
36#88055C2212yes—
37#88054C2212yes—
38#88049C2211yescharacteristic
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×D4×C13—21no—
42C2×D4×C13—21no—
43C2×D4×C13C2312yes—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48C22×Dic13—22no—
49C22×Dic13—22no—
50#6129—44no—
51C2×D52C2311yescharacteristic
52C2×C4×D13—21no—
53C2×Dic26—21no—
54C2×Dic26D411yescharacteristic
55C13×D8—24no—
56C2×C8×C13C2312yes—
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C42×C13C2311yescharacteristic
60C22⋊Dic13—22no—
61C22⋊Dic13—22no—
62#6104—22no—
63#6103—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—22no—
66C4⋊Dic13D411yescharacteristic
67C4⋊Dic13C2312yes—
68C4⋊Dic13C2311yescharacteristic
69#6101—22no—
70#6101D412yes—
71C4×Dic13C2312yes—
72C2×#1055C2311yescharacteristic
73C2×#1055C2311yescharacteristic
74#3366—131nomaximal, Sylow
75C23×C13—21no—
76C23×C13—22no—
77C22×D13—21no—
78D4×C13—22no—
79D4×C13—21no—
80D4×C13—22no—
81D4×C13—42no—
82D4×C13—81no—
83D4×C13#4112yescomplemented
84C2×C4×C13—21no—
85C2×C4×C13—42no—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C22⋊D13—44no—
90C22⋊D13—82no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93C2×Dic13—44no—
94C2×Dic13—82no—
95C2×Dic13C2×D412yes—
96C2×Dic13C2×D412yes—
97D52—21no—
98D52—21no—
99C4×D13—42no—
100Dic26—22no—
101Dic26—81no—
102C8×C13—22no—
103#1055—21no—
104#1055—21no—
105#554—131no—
106#550—131no—
107#490—132no—
108#486—131no—
109#478—132no—
110#476—131no—
111#459—132no—
112#459D1311yescharacteristic, complemented
113#446—131no—
114#442—132no—
115C4×D8—131no—
116C22×C13—22no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13—42no—
120C22×C13—42no—
121C22×C13—42no—
122C22×C13C22×D411yescharacteristic
123C2×D13—41no—
124C2×D13—41no—
125C2×D13—41no—
126C4×C13—21no—
127C4×C13—41no—
128C4×C13AGL(1,ℤ/8)12yes—
129C4×C13C2×#4111yescharacteristic
130C4×C132−1+411yescharacteristic
131Dic13—22no—
132Dic13—22no—
133Dic13—41no—
134Dic13—42no—
135C2×#41—261no—
136C2×D8—131no—
137C2×D8C2×D1312yes—
138C4⋊Q8—131no—
139#127—132no—
140#127C2×D1311yescharacteristic
141#125—132no—
142C22⋊Q8—262no—
143C22⋊Q8—261no—
144#121—261no—
145#121—262no—
146C4×Q8—131no—
147C4×D4—132no—
148C4×D4—132no—
149C4×D4—131no—
150C4×D4C2×D1311yescharacteristic
151C2×C4⋊C4—261no—
152#107—131no—
153#106—132no—
154C4⋊C8—132no—
155C4⋊C8C2×D1311yescharacteristic
156#102—131no—
157#102—132no—
158#102—132no—
159#102—132no—
160#102—131no—
161#102C2×D1312yes—
162#97—132no—
163C4×C8—131no—
164C2×C13—42no—
165C2×C13—82no—
166C2×C13#54811yescharacteristic
167C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C13#57611yescharacteristic
169D13—81no—
170#41—524no—
171C2×Q8—131no—
172C2×Q8—261no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—131no—
176C2×D4—262no—
177C2×D4—262no—
178C2×D4C22×D1312yes—
179C2×D4C22×D1311yescharacteristic
180C22×C4—21no—
181C22×C4—262no—
182C22×C4—262no—
183C22×C4—261no—
184D8—24no—
185D8—262no—
186C2×C8—131no—
187C2×C8—131no—
188C2×C8C22×D1312yes—
189C4⋊C4—131no—
190C4⋊C4—132no—
191C4⋊C4—132no—
192C4⋊C4—131no—
193C4⋊C4—262no—
194C4⋊C4—262no—
195C4⋊C4—261no—
196C4⋊C4C22×D1311yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—262no—
199C22⋊C4—262no—
200C22⋊C4—261no—
201C42—132no—
202C42C22×D1311yescharacteristic
203C13#336611yescharacteristic, complemented, Sylow
204C23—21no—
205C23—22no—
206C23—261no—
207Q8—262no—
208Q8—1041no—
209D4—22no—
210D4—21no—
211D4—22no—
212D4—42no—
213D4—81no—
214D4—261no—
215D4—261no—
216D4—524no—
217D4—1042no—
218D4#612912yescomplemented
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—132no—
222C2×C4—132no—
223C2×C4—261no—
224C2×C4—262no—
225C2×C4—524no—
226C2×C4—522no—
227C2×C4—1042no—
228C2×C4D4×D1311yescharacteristic
229C2×C4D4×D1311yescharacteristic
230C2×C4C23×D1311yescharacteristic
231C8—22no—
232C8—261no—
233C8—261no—
234C22—22no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—521no—
241C22—521no—
242C22—521no—
243C22C2×D4×D1311yescharacteristic
244C4—21no—
245C4—41no—
246C4—262no—
247C4—262no—
248C4—521no—
249C4—522no—
250C4#8816512yes—
251C4C2×#612911yescharacteristic
252C4#8825711yescharacteristic
253C2—42no—
254C2—82no—
255C2—1041no—
256C2#1171930311yescharacteristic
257C2C2×#8816511yescharacteristic
258C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#459C2
socleC22×C13C22×D4
hypercenter#459D13
hypocenterC13#3366
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #11719423C2semidirect
2. #11719248C2semidirect
3. C13×#459C2semidirect
4. #11718813C2semidirect
5. #11718811C2semidirect
6. #11718731C2semidirect
7. C4×#6104C2semidirect
8. #11718503C2semidirect
9. #11718492C2semidirect
10. #11718425C2semidirect
11. #11718424C2semidirect
83. D4×C13#41semidirect
112. #459D13semidirect
203. C13#3366semidirect
218. D4#6129semidirect

Maximal subgroups

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

subgroupindex
#117194232
#117192482
C13×#4592
#117188132
#117188112
#117187312
C4×#61042
#117185032
#117184922
#117184252
#117184242
#336613