Finite Group Databasebeta

← #13127863

Subgroups — #13127863

Order 1664.

350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C13×#557C211yesmaximal, characteristic, complemented
2#11719289C211yesmaximal, characteristic
3#11718753C211yesmaximal, characteristic, complemented
4#11718751C212yesmaximal, complemented
5#11718747C212yesmaximal
6#11718744C211yesmaximal, characteristic
7#11718692C211yesmaximal, characteristic, complemented
8#11718691C212yesmaximal, complemented
9#11718689C212yesmaximal
10C4×#6106C211yesmaximal, characteristic
11#11718685C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×C4⋊Q8C2212yes—
14C13×#125—21no—
15C13×#125—22no—
16C4×Q8×C13—21no—
17C4×Q8×C13C2211yescharacteristic
18C4×Q8×C13C2212yes—
19C4×Q8×C13C2211yescharacteristic
20#88200—21no—
21C2×#6107C2212yes—
22C2×#6107C2212yes—
23C2×#6107C2212yes—
24C2×#6106C2211yescharacteristic
25C2×#6106C2212yes—
26#88152—22no—
27#88146—21no—
28#88129C2212yes—
29C4×D52C2211yescharacteristic
30#88123C2211yescharacteristic
31C4×Dic26C2212yes—
32#88075C2211yescharacteristic
33#88075C2212yes—
34#88050C2212yes—
35#88049C2211yescharacteristic
36#88048C2211yescharacteristic
37C4⋊#1055C2212yes—
38C4⋊#1055C2211yescharacteristic
39#88043C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13D411yescharacteristic
42C2×Q8×C13C2311yescharacteristic
43C2×Q8×C13C2312yes—
44C2×D52C2311yescharacteristic
45C2×C4×D13—21no—
46C2×Dic26C2312yes—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4D411yescharacteristic
54C13×C4⋊C4D412yes—
55C13×C4⋊C4C2311yescharacteristic
56C42×C13—22no—
57C42×C13—21no—
58C42×C13C2312yes—
59C42×C13C2311yescharacteristic
60#6107—24no—
61#6107—42no—
62#6107—42no—
63#6106—22no—
64#6106—42no—
65#6103—21no—
66#6103—22no—
67#6103—22no—
68C4⋊Dic13—21no—
69C4⋊Dic13—21no—
70C4⋊Dic13C2311yescharacteristic
71#6101—22no—
72C4×Dic13—22no—
73C2×#1055C2312yes—
74C2×#1055C2311yescharacteristic
75C2×#1055C2311yescharacteristic
76#3398—131nomaximal, Sylow
77C22×D13—21no—
78Q8×C13—22no—
79Q8×C13—21no—
80Q8×C13—22no—
81Q8×C13—22no—
82Q8×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13C2×D412yes—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2411yescharacteristic
91C2×Dic13—21no—
92C2×Dic13—22no—
93D52—21no—
94D52—21no—
95C4×D13—42no—
96Dic26—22no—
97Dic26—22no—
98#1055—22no—
99#1055—21no—
100#1055#4112yes—
101#557D1311yescharacteristic, complemented
102#556—131no—
103#497—132no—
104#494—131no—
105#464—132no—
106#462—132no—
107#462—131no—
108#461—131no—
109#446—131no—
110#441—132no—
111C4×SD16—131no—
112C22×C13C22×D411yescharacteristic
113C2×D13—41no—
114C2×D13—41no—
115C2×D13—41no—
116C4×C13—22no—
117C4×C13—22no—
118C4×C13—21no—
119C4×C13—41no—
120C4×C13—42no—
121C4×C13—41no—
122C4×C13#13712yes—
123C4×C13C2×#4111yescharacteristic
124C4×C13H(5,𝔽2)11yescharacteristic
125Dic13—42no—
126Dic13—41no—
127C2×Q16—132no—
128C2×Q16—132no—
129C2×Q16—132no—
130C2×SD16—131no—
131C2×SD16—132no—
132C4⋊Q8—131no—
133C4⋊Q8C2×D1311yescharacteristic
134C4⋊Q8C2×D1312yes—
135#126—262no—
136#125—21no—
137#125—22no—
138#124—132no—
139C22⋊Q8—261no—
140C4×Q8—21no—
141C4×Q8—132no—
142C4×Q8C2×D1311yescharacteristic
143C4×Q8C2×D1312yes—
144C4×Q8C2×D1311yescharacteristic
145C4×D4—131no—
146#117—261no—
147#106—131no—
148C4⋊C8—131no—
149C4⋊C8—132no—
150#103—131no—
151#103—132no—
152#103—132no—
153#102—131no—
154#97—132no—
155C4×C8—131no—
156C2×C13#55011yescharacteristic
157C2×C13C2×#13711yescharacteristic
158C2×C13#57811yescharacteristic
159D13—81no—
160C2×Q8—132no—
161C2×Q8C22⋊D1311yescharacteristic
162C2×Q8C22×D1311yescharacteristic
163C2×Q8C22×D1312yes—
164C2×D4—131no—
165C22×C4—261no—
166Q16—264no—
167Q16—522no—
168Q16—522no—
169SD16—262no—
170SD16—522no—
171C2×C8—131no—
172C2×C8—131no—
173C2×C8—132no—
174C4⋊C4—22no—
175C4⋊C4—21no—
176C4⋊C4—22no—
177C4⋊C4—21no—
178C4⋊C4—22no—
179C4⋊C4—21no—
180C4⋊C4—131no—
181C4⋊C4—261no—
182C4⋊C4—262no—
183C4⋊C4—261no—
184C4⋊C4C22⋊D1311yescharacteristic
185C4⋊C4C22⋊D1312yes—
186C4⋊C4C22×D1311yescharacteristic
187C22⋊C4—262no—
188C22⋊C4—261no—
189C22⋊C4—262no—
190C42—22no—
191C42—21no—
192C42—262no—
193C42C22×D1311yescharacteristic
194C42C22×D1312yes—
195C13#339811yescharacteristic, complemented, Sylow
196C23—261no—
197Q8—22no—
198Q8—21no—
199Q8—22no—
200Q8—22no—
201Q8—21no—
202Q8—262no—
203Q8—262no—
204D4—261no—
205D4—261no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—261no—
210C2×C4—262no—
211C2×C4—522no—
212C2×C4C2×C22⋊D1312yes—
213C2×C4C2×C22⋊D1312yes—
214C2×C4C2×C22⋊D1311yescharacteristic
215C2×C4C2×C22⋊D1311yescharacteristic
216C2×C4C23×D1311yescharacteristic
217C8—132no—
218C8—262no—
219C8—261no—
220C22—521no—
221C22—521no—
222C22—521no—
223C22C22×C22⋊D1311yescharacteristic
224C4—22no—
225C4—22no—
226C4—21no—
227C4—41no—
228C4—42no—
229C4—41no—
230C4—521no—
231C4—522no—
232C4#8819612yes—
233C4#41×D1311yescharacteristic
234C4#8825611yescharacteristic
235C2—1041no—
236C2C2×#8819611yescharacteristic
237C2#1171953911yescharacteristic
238C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#557C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#557D13
hypocenterC13#3398
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C13×#557C2semidirect
3. #11718753C2semidirect
4. #11718751C2semidirect
7. #11718692C2semidirect
8. #11718691C2semidirect
11. #11718685C2semidirect
101. #557D13semidirect
195. C13#3398semidirect

Maximal subgroups

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

subgroupindex
C13×#5572
#117192892
#117187532
#117187512
#117187472
#117187442
#117186922
#117186912
#117186892
C4×#61062
#117186852
#339813