Finite Group Databasebeta

← #13127138

Subgroups — #13127138

Order 1664.

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

normal subgroups only

This group has 420 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#11719431C211yesmaximal, characteristic, complemented
2#11719260C211yesmaximal, characteristic, complemented
3C13×#474C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5C4×#6104C211yesmaximal, characteristic, complemented
6#11718547C212yesmaximal, complemented
7#11718545C212yesmaximal, complemented
8#11718502C211yesmaximal, characteristic, complemented
9#11718499C211yesmaximal, characteristic, complemented
10#11718442C212yesmaximal, complemented
11#11718432C212yesmaximal, complemented
12C2×#6131—21no—
13C2×#6129C2212yes—
14C13×C4⋊Q8C2211yescharacteristic
15C4×D4×C13C2211yescharacteristic
16#88200—21no—
17C2×#6104C2211yescharacteristic
18#88184—21no—
19C2×C4⋊Dic13—21no—
20C2×#6095C2212yes—
21C2×#6094C2212yes—
22#88151C2212yes—
23#88149C2212yes—
24#88148—22no—
25C4⋊C4×D13C2212yes—
26#88140—22no—
27C4×D52C2211yescharacteristic
28C4×D52C2211yescharacteristic
29#88123C2211yescharacteristic
30C13×#107C2212yes—
31C13×C4⋊C8C2211yescharacteristic
32C13×#102C2212yes—
33#88072C2211yescharacteristic
34#88060C2212yes—
35#88056C2212yes—
36#88050C2212yes—
37#88050C2212yes—
38#88049C2211yescharacteristic
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C2×C22⋊D13—22no—
45C22×Dic13—22no—
46#6131—44no—
47#6129—24no—
48#6129—42no—
49C2×D52—22no—
50C2×D52D411yescharacteristic
51C2×D52C2311yescharacteristic
52C2×C4×D13—22no—
53C2×C4×D13—21no—
54C2×C4×D13C2312yes—
55C2×Dic26C2312yes—
56C2×C8×C13C2312yes—
57C13×C4⋊C4—21no—
58C13×C4⋊C4C2312yes—
59C13×C4⋊C4C2311yescharacteristic
60C13×C22⋊C4—21no—
61C42×C13C2311yescharacteristic
62#6104—22no—
63#6103—22no—
64#6103—21no—
65#6103—22no—
66#6103D412yes—
67C4⋊Dic13—21no—
68C4⋊Dic13—21no—
69C4⋊Dic13—22no—
70C4⋊Dic13D411yescharacteristic
71C4⋊Dic13C2311yescharacteristic
72#6101—22no—
73C2×#1055C2311yescharacteristic
74C2×#1055C2311yescharacteristic
75#6095—42no—
76#6094—42no—
77#3330—131nomaximal, Sylow
78C23×C13—21no—
79C22×D13—21no—
80C22×D13C2×D412yes—
81Q8×C13—42no—
82D4×C13—21no—
83D4×C13#4112yescomplemented
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—42no—
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2411yescharacteristic
90C22⋊D13—44no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—44no—
94C2×Dic13C2×D412yes—
95D52—22no—
96D52—21no—
97D52—21no—
98D52—44no—
99C4×D13—22no—
100C4×D13—22no—
101C4×D13—44no—
102C4×D13—42no—
103Dic26—22no—
104Dic26—22no—
105C8×C13—22no—
106#1055—21no—
107#1055—21no—
108#547—131no—
109#547—131no—
110#487—131no—
111#484—132no—
112#474D1311yescharacteristic, complemented
113#468—132no—
114#461—131no—
115#449—132no—
116C4×D8—131no—
117#436—131no—
118#417—132no—
119C22×C13—22no—
120C22×C13—41no—
121C22×C13—41no—
122C22×C13C22×D411yescharacteristic
123C2×D13—22no—
124C2×D13—22no—
125C2×D13—22no—
126C2×D13—41no—
127C2×D13—41no—
128C2×D13—41no—
129C4×C13—21no—
130C4×C13—42no—
131C4×C13—41no—
132C4×C13AGL(1,ℤ/8)12yes—
133C4×C13C2×#4111yescharacteristic
134C4×C13H(5,𝔽2)11yescharacteristic
135Dic13—22no—
136Dic13—42no—
137Dic13—41no—
138C2×#41—132no—
139C2×#41—261no—
140C2×SD16—132no—
141C2×D8—131no—
142C2×M16—132no—
143C4⋊Q8—131no—
144C4⋊Q8C2×D1311yescharacteristic
145#123—262no—
146#123—262no—
147C22⋊Q8—132no—
148C22⋊Q8—261no—
149#121—132no—
150#121—261no—
151C4×D4—131no—
152C4×D4—131no—
153C4×D4C2×D1311yescharacteristic
154C2×C4⋊C4—132no—
155C2×C4⋊C4—261no—
156#107—131no—
157#107C2×D1312yes—
158C4⋊C8C2×D1311yescharacteristic
159#103—132no—
160#103—132no—
161#103—132no—
162#102—131no—
163#102—131no—
164#102C2×D1312yes—
165C22⋊C8—132no—
166C4×C8—131no—
167C2×C13—42no—
168C2×C13#54611yescharacteristic
169C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C13#57811yescharacteristic
171D13—42no—
172D13—81no—
173#41—264no—
174#41—522no—
175#41—524no—
176C2×Q8—21no—
177C2×Q8—132no—
178C2×D4—131no—
179C2×D4—131no—
180C2×D4—262no—
181C2×D4—262no—
182C2×D4C22×D1311yescharacteristic
183C22×C4—21no—
184C22×C4—132no—
185C22×C4—262no—
186C22×C4—262no—
187C22×C4—261no—
188SD16—522no—
189D8—262no—
190M16—522no—
191C2×C8—131no—
192C2×C8—131no—
193C2×C8C22×D1312yes—
194C4⋊C4—21no—
195C4⋊C4—131no—
196C4⋊C4—131no—
197C4⋊C4—262no—
198C4⋊C4—262no—
199C4⋊C4—261no—
200C4⋊C4—261no—
201C4⋊C4C22×D1311yescharacteristic
202C4⋊C4C22×D1312yes—
203C22⋊C4—21no—
204C22⋊C4—132no—
205C22⋊C4—262no—
206C22⋊C4—262no—
207C22⋊C4—261no—
208C42C22×D1311yescharacteristic
209C13#333011yescharacteristic, complemented, Sylow
210C23—21no—
211C23—132no—
212C23—261no—
213Q8—42no—
214Q8—262no—
215Q8—262no—
216D4—21no—
217D4—262no—
218D4—261no—
219D4—261no—
220D4—524no—
221D4—524no—
222D4#613112yescomplemented
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—132no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—261no—
230C2×C4—262no—
231C2×C4—524no—
232C2×C4—524no—
233C2×C4—522no—
234C2×C4D4×D1311yescharacteristic
235C2×C4D4×D1311yescharacteristic
236C2×C4C23×D1311yescharacteristic
237C8—22no—
238C8—261no—
239C8—261no—
240C22—22no—
241C22—41no—
242C22—41no—
243C22—262no—
244C22—262no—
245C22—262no—
246C22—521no—
247C22—521no—
248C22—521no—
249C22C2×D4×D1311yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—262no—
254C4—521no—
255C4—522no—
256C4#8816512yes—
257C4C2×#613111yescharacteristic
258C4#8825611yescharacteristic
259C2—42no—
260C2—522no—
261C2—1041no—
262C2#1171933511yescharacteristic
263C2C2×#8816511yescharacteristic
264C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
hypercenter#474D13
hypocenterC13#3330
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719431C2semidirect
2. #11719260C2semidirect
3. C13×#474C2semidirect
4. #11718754C2semidirect
5. C4×#6104C2semidirect
6. #11718547C2semidirect
7. #11718545C2semidirect
8. #11718502C2semidirect
9. #11718499C2semidirect
10. #11718442C2semidirect
11. #11718432C2semidirect
83. D4×C13#41semidirect
112. #474D13semidirect
209. C13#3330semidirect
222. D4#6131semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117192602
C13×#4742
#117187542
C4×#61042
#117185472
#117185452
#117185022
#117184992
#117184422
#117184322
#333013