Finite Group Databasebeta

← #13127542

Subgroups — #13127542

Order 1664.

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

normal subgroups only

This group has 396 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#11719435C211yesmaximal, characteristic, complemented
2#11719258C211yesmaximal, characteristic, complemented
3C13×#476C211yesmaximal, characteristic, complemented
4#11718749C211yesmaximal, characteristic, complemented
5C4×#6104C211yesmaximal, characteristic, complemented
6#11718532C212yesmaximal, complemented
7#11718530C212yesmaximal, complemented
8#11718504C211yesmaximal, characteristic, complemented
9#11718492C211yesmaximal, characteristic, complemented
10#11718447C212yesmaximal, complemented
11#11718425C212yesmaximal, complemented
12C2×#6127—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15#88200—22no—
16#88194C2212yes—
17C2×#6104C2211yescharacteristic
18#88184—21no—
19C2×D104C2212yes—
20#88151—21no—
21#88147C2212yes—
22#88147C2212yes—
23C4⋊C4×D13—21no—
24#88144C2212yes—
25#88138—22no—
26#88128C2211yescharacteristic
27C4×D52C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#106C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#102C2212yes—
32#88072C2211yescharacteristic
33#88061C2212yes—
34#88055C2212yes—
35#88054C2212yes—
36#88049C2211yescharacteristic
37#88049C2212yes—
38#88049C2212yes—
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C2×C22⋊D13—22no—
45C2×C22⋊D13—22no—
46#6127—44no—
47C2×D52—21no—
48C2×D52—21no—
49C2×D52C2312yes—
50C2×D52C2311yescharacteristic
51C2×C4×D13—21no—
52C2×C4×D13—22no—
53C2×C4×D13—22no—
54C2×Dic26D411yescharacteristic
55C2×C8×C13C2312yes—
56C13×C4⋊C4—21no—
57C13×C4⋊C4C2312yes—
58C13×C4⋊C4C2311yescharacteristic
59C13×C22⋊C4—21no—
60C42×C13C2311yescharacteristic
61#6104—22no—
62#6103—21no—
63#6103—22no—
64#6103—22no—
65C4⋊Dic13—22no—
66C4⋊Dic13D411yescharacteristic
67C4⋊Dic13C2311yescharacteristic
68#6101—22no—
69#6101D412yes—
70C4×Dic13C2312yes—
71C2×#1055C2311yescharacteristic
72C2×#1055C2311yescharacteristic
73D104—24no—
74#3366—131nomaximal, Sylow
75C23×C13—21no—
76C22×D13—21no—
77C22×D13—22no—
78Q8×C13—81no—
79D4×C13—21no—
80D4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—42no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C22⋊D13—44no—
88C22⋊D13—82no—
89C2×Dic13—21no—
90C2×Dic13C2×D412yes—
91C2×Dic13C2×D412yes—
92D52—22no—
93D52—21no—
94D52—22no—
95D52—42no—
96D52—81no—
97D52#4112yescomplemented
98C4×D13—44no—
99C4×D13—42no—
100C4×D13—82no—
101Dic26—22no—
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#476D1311yescharacteristic, complemented
111#459—131no—
112#459—132no—
113#446—131no—
114#442—132no—
115C4×D8—131no—
116C22×C13—41no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13C22×D411yescharacteristic
120C2×D13—22no—
121C2×D13—41no—
122C2×D13—41no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—42no—
126C4×C13—21no—
127C4×C13—41no—
128C4×C13—42no—
129C4×C13AGL(1,ℤ/8)12yes—
130C4×C13C2×#4111yescharacteristic
131C4×C132−1+411yescharacteristic
132Dic13—22no—
133Dic13—22no—
134Dic13—41no—
135C2×#41—261no—
136C2×D8—131no—
137C2×D8—132no—
138C4⋊Q8C2×D1311yescharacteristic
139#127—132no—
140#127—131no—
141#125—132no—
142C22⋊Q8—261no—
143C22⋊Q8—262no—
144#121—262no—
145#121—261no—
146C4×Q8—131no—
147C4×D4—132no—
148C4×D4—132no—
149C4×D4—131no—
150C4×D4C2×D1311yescharacteristic
151C2×C4⋊C4—261no—
152#107—131no—
153#106C2×D1312yes—
154C4⋊C8—132no—
155C4⋊C8C2×D1311yescharacteristic
156#102—131no—
157#102—132no—
158#102—131no—
159#102—132no—
160#102—132no—
161#102C2×D1312yes—
162#97—132no—
163C4×C8—131no—
164C2×C13—81no—
165C2×C13#54811yescharacteristic
166C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C13#57611yescharacteristic
168D13—42no—
169D13—82no—
170#41—524no—
171C2×Q8—21no—
172C2×Q8—131no—
173C2×D4—131no—
174C2×D4—132no—
175C2×D4—262no—
176C2×D4—262no—
177C2×D4—261no—
178C2×D4—261no—
179C2×D4C22×D1311yescharacteristic
180C22×C4—21no—
181C22×C4—262no—
182C22×C4—262no—
183C22×C4—261no—
184D8—264no—
185D8—262no—
186C2×C8—131no—
187C2×C8—131no—
188C2×C8C22×D1312yes—
189C4⋊C4—21no—
190C4⋊C4—131no—
191C4⋊C4—132no—
192C4⋊C4—131no—
193C4⋊C4—262no—
194C4⋊C4—262no—
195C4⋊C4C22×D1312yes—
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—261no—
206C23—262no—
207Q8—81no—
208Q8—262no—
209D4—21no—
210D4—21no—
211D4—132no—
212D4—261no—
213D4—262no—
214D4—262no—
215D4—524no—
216D4—522no—
217D4—1041no—
218D4—1042no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—42no—
222C2×C4—132no—
223C2×C4—132no—
224C2×C4—261no—
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—41no—
235C22—41no—
236C22—41no—
237C22—262no—
238C22—521no—
239C22—521no—
240C22—522no—
241C22—522no—
242C22—522no—
243C22C2×D4×D1311yescharacteristic
244C4—21no—
245C4—41no—
246C4—42no—
247C4—262no—
248C4—262no—
249C4—521no—
250C4#8816812yes—
251C4#8825411yescharacteristic
252C4#41×D1311yescharacteristic
253C2—81no—
254C2—522no—
255C2—1042no—
256C2#1171933811yescharacteristic
257C2C2×#8816811yescharacteristic
258C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#476C2
socleC22×C13C22×D4
hypercenter#476D13
hypocenterC13#3366
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11719435C2semidirect
2. #11719258C2semidirect
3. C13×#476C2semidirect
4. #11718749C2semidirect
5. C4×#6104C2semidirect
6. #11718532C2semidirect
7. #11718530C2semidirect
8. #11718504C2semidirect
9. #11718492C2semidirect
10. #11718447C2semidirect
11. #11718425C2semidirect
97. D52#41semidirect
110. #476D13semidirect
203. C13#3366semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117192582
C13×#4762
#117187492
C4×#61042
#117185322
#117185302
#117185042
#117184922
#117184472
#117184252
#336613