Finite Group Databasebeta

← #13127872

Subgroups — #13127872

Order 1664.

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

normal subgroups only

This group has 350 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#11719437C211yesmaximal, characteristic
2#11719426C211yesmaximal, characteristic, complemented
3C13×#494C211yesmaximal, characteristic, complemented
4#11718851C212yesmaximal
5#11718846C212yesmaximal
6#11718845C212yesmaximal, complemented
7#11718843C212yesmaximal, complemented
8#11718751C211yesmaximal, characteristic, complemented
9#11718744C211yesmaximal, characteristic
10C4×#6095C211yesmaximal, characteristic
11#11718340C211yesmaximal, characteristic, complemented
12C2×C13×Q16C2212yes—
13C2×C13×Q16C2212yes—
14C13×C4⋊Q8C2211yescharacteristic
15C13×C4⋊Q8C2211yescharacteristic
16#88201C2212yes—
17Q8×Dic13C2212yes—
18Q8×Dic13C2212yes—
19#88198C2212yes—
20C2×#6107C2212yes—
21C2×#6106C2212yes—
22C2×#6095C2211yescharacteristic
23#88152—22no—
24#88151—21no—
25#88146—21no—
26#88144—21no—
27#88143—22no—
28#88141—21no—
29C4×D52C2211yescharacteristic
30C4×Dic26C2211yescharacteristic
31C4×Dic26C2211yescharacteristic
32C4×C8×C13C2211yescharacteristic
33#88075C2212yes—
34#88075C2212yes—
35#88061C2211yescharacteristic
36#88057C2211yescharacteristic
37#88056C2211yescharacteristic
38#88055C2212yes—
39#88054C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13C2312yes—
42C2×Q8×C13C2312yes—
43C2×D52C2311yescharacteristic
44C2×C4×D13—21no—
45C2×Dic26D411yescharacteristic
46C2×Dic26C2311yescharacteristic
47C13×Q16—24no—
48C13×Q16—42no—
49C2×C8×C13C2311yescharacteristic
50C2×C8×C13C2311yescharacteristic
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C42×C13C2311yescharacteristic
56#6107—42no—
57#6106—42no—
58#6103—21no—
59#6103—22no—
60#6103—22no—
61C4⋊Dic13—22no—
62C4⋊Dic13—22no—
63C4⋊Dic13D411yescharacteristic
64C4⋊Dic13C2311yescharacteristic
65C4⋊Dic13C2311yescharacteristic
66#6101—21no—
67#6101—22no—
68#6101—22no—
69#6101D412yes—
70C4×Dic13—21no—
71C4×Dic13—22no—
72C4×Dic13—22no—
73C4×Dic13C2312yes—
74C2×#1055C2312yes—
75#6095—22no—
76#3398—131nomaximal, Sylow
77C22×D13—21no—
78Q8×C13—22no—
79Q8×C13—22no—
80Q8×C13—22no—
81Q8×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13C2×D412yes—
91C2×Dic13C2×D412yes—
92D52—21no—
93D52—21no—
94C4×D13—42no—
95Dic26—22no—
96Dic26—21no—
97Dic26—21no—
98C8×C13—21no—
99C8×C13#4112yes—
100#1055—22no—
101#557—131no—
102#556—131no—
103#497—132no—
104#494D1311yescharacteristic, complemented
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—21no—
117C4×C13—42no—
118C4×C13—42no—
119C4×C13#13712yes—
120C4×C13C2×#4111yescharacteristic
121C4×C13H(5,𝔽2)11yescharacteristic
122Dic13—22no—
123Dic13—22no—
124Dic13—41no—
125Dic13—41no—
126Dic13—41no—
127C2×Q16—132no—
128C2×Q16C2×D1312yes—
129C2×Q16C2×D1312yes—
130C2×SD16—132no—
131C2×SD16—131no—
132C4⋊Q8—132no—
133C4⋊Q8C2×D1311yescharacteristic
134C4⋊Q8C2×D1311yescharacteristic
135#126—262no—
136#125—262no—
137#125—261no—
138#124—132no—
139C22⋊Q8—261no—
140C4×Q8—131no—
141C4×Q8—132no—
142C4×Q8—132no—
143C4×Q8—131no—
144C4×Q8—261no—
145C4×D4—131no—
146#117—261no—
147#106—131no—
148C4⋊C8—132no—
149C4⋊C8—131no—
150#103—132no—
151#103—132no—
152#103—131no—
153#102—131no—
154#97—132no—
155C4×C8C2×D1311yescharacteristic
156C2×C13#55011yescharacteristic
157C2×C13C2×#13711yescharacteristic
158C2×C13#57811yescharacteristic
159D13—81no—
160C2×Q8—131no—
161C2×Q8—131no—
162C2×Q8C22×D1312yes—
163C2×Q8C22×D1312yes—
164C2×D4—131no—
165C22×C4—261no—
166Q16—24no—
167Q16—42no—
168Q16—522no—
169SD16—262no—
170SD16—522no—
171C2×C8—132no—
172C2×C8C22×D1311yescharacteristic
173C2×C8C22×D1311yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—131no—
179C4⋊C4—132no—
180C4⋊C4—131no—
181C4⋊C4—131no—
182C4⋊C4—262no—
183C4⋊C4—262no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4—261no—
187C22⋊C4—262no—
188C22⋊C4—262no—
189C22⋊C4—261no—
190C42—132no—
191C42—262no—
192C42—262no—
193C42—261no—
194C42C22×D1311yescharacteristic
195C13#339811yescharacteristic, complemented, Sylow
196C23—261no—
197Q8—22no—
198Q8—22no—
199Q8—22no—
200Q8—22no—
201Q8—262no—
202Q8—261no—
203Q8—261no—
204D4—261no—
205D4—261no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—132no—
209C2×C4—132no—
210C2×C4—261no—
211C2×C4—261no—
212C2×C4—261no—
213C2×C4—522no—
214C2×C4D4×D1311yescharacteristic
215C2×C4D4×D1311yescharacteristic
216C2×C4C23×D1311yescharacteristic
217C8—21no—
218C8—262no—
219C8#612912yes—
220C22—521no—
221C22—521no—
222C22—521no—
223C22C2×D4×D1311yescharacteristic
224C4—21no—
225C4—42no—
226C4—42no—
227C4—262no—
228C4—262no—
229C4—521no—
230C4—521no—
231C4—521no—
232C4#8817212yes—
233C4C2×#612911yescharacteristic
234C4#8825111yescharacteristic
235C2—1041no—
236C2#1171942311yescharacteristic
237C2C2×#8817211yescharacteristic
238C2#1171947111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#494C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#494D13
hypocenterC13#3398
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #11719426C2semidirect
3. C13×#494C2semidirect
6. #11718845C2semidirect
7. #11718843C2semidirect
8. #11718751C2semidirect
11. #11718340C2semidirect
104. #494D13semidirect
195. C13#3398semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117194262
C13×#4942
#117188512
#117188462
#117188452
#117188432
#117187512
#117187442
C4×#60952
#117183402
#339813