Finite Group Databasebeta

← #13127558

Subgroups — #13127558

Order 1664.

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

normal subgroups only

This group has 372 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, complemented
2D4×Dic26C211yesmaximal, characteristic, complemented
3C13×#461C211yesmaximal, characteristic, complemented
4#11718826C212yesmaximal
5#11718825C212yesmaximal, complemented
6#11718742C211yesmaximal, characteristic, complemented
7C4×#6104C211yesmaximal, characteristic
8#11718507C211yesmaximal, characteristic, complemented
9#11718492C211yesmaximal, characteristic, complemented
10#11718456C212yesmaximal, complemented
11#11718455C212yesmaximal, complemented
12C22×Dic26—21no—
13C2×C13×SD16C2212yes—
14C13×C4⋊Q8C2211yescharacteristic
15C4×D4×C13C2211yescharacteristic
16#88201C2212yes—
17Q8×Dic13C2212yes—
18D4×Dic13C2212yes—
19C2×#6104C2211yescharacteristic
20#88178—21no—
21#88152—22no—
22#88151—21no—
23#88146—21no—
24#88142C2212yes—
25#88132—22no—
26C4×D52C2211yescharacteristic
27#88123C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×C4⋊C8C2211yescharacteristic
30C13×#103C2212yes—
31#88075C2212yes—
32#88075C2212yes—
33#88072C2211yescharacteristic
34#88061C2212yes—
35#88058C2212yes—
36#88055C2212yes—
37#88054C2212yes—
38#88049C2211yescharacteristic
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13C2312yes—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C22×Dic13—22no—
45C2×D52C2311yescharacteristic
46C2×C4×D13—21no—
47C2×Dic26—21no—
48C2×Dic26—22no—
49C2×Dic26—44no—
50C2×Dic26D411yescharacteristic
51C13×SD16—24no—
52C2×C8×C13C2312yes—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4C2311yescharacteristic
56C13×C22⋊C4—21no—
57C42×C13C2311yescharacteristic
58C22⋊Dic13—22no—
59#6104—22no—
60#6103—21no—
61#6103—22no—
62#6103—22no—
63C4⋊Dic13—21no—
64C4⋊Dic13—22no—
65C4⋊Dic13D411yescharacteristic
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2312yes—
68#6101—22no—
69#6101D412yes—
70C4×Dic13—22no—
71C4×Dic13C2312yes—
72C2×#1055C2311yescharacteristic
73C2×#1055C2311yescharacteristic
74#3367—131nomaximal, Sylow
75C23×C13—21no—
76C22×D13—21no—
77Q8×C13—22no—
78Q8×C13—22no—
79D4×C13—21no—
80D4×C13#4112yes—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—42no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—44no—
90C2×Dic13C2×D412yes—
91C2×Dic13C2×D412yes—
92D52—21no—
93D52—21no—
94C4×D13—42no—
95Dic26—22no—
96Dic26—44no—
97Dic26—42no—
98C8×C13—22no—
99#1055—21no—
100#1055—21no—
101#556—131no—
102D4×Q8—131no—
103#489—132no—
104#487—131no—
105#477—132no—
106#474—131no—
107#463—132no—
108#461D1311yescharacteristic, complemented
109#446—131no—
110#440—132no—
111C4×D8—131no—
112C22×C13—22no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13C22×D411yescharacteristic
116C2×D13—41no—
117C2×D13—41no—
118C2×D13—41no—
119C4×C13—21no—
120C4×C13—42no—
121C4×C13—41no—
122C4×C13AGL(1,ℤ/8)12yes—
123C4×C13C2×#4111yescharacteristic
124C4×C132−1+411yescharacteristic
125Dic13—22no—
126Dic13—22no—
127Dic13—42no—
128Dic13—41no—
129C22×Q8—261no—
130C2×SD16C2×D1312yes—
131C2×D8—131no—
132C4⋊Q8—132no—
133C4⋊Q8—131no—
134C4⋊Q8C2×D1311yescharacteristic
135#126—262no—
136#124—132no—
137C22⋊Q8—262no—
138C22⋊Q8—261no—
139C22⋊Q8—261no—
140C4×Q8—131no—
141C4×Q8—132no—
142C4×D4—132no—
143C4×D4—131no—
144C4×D4C2×D1311yescharacteristic
145#117—261no—
146#107—132no—
147#107—131no—
148C4⋊C8—132no—
149C4⋊C8C2×D1311yescharacteristic
150#103—132no—
151#103—132no—
152#103C2×D1312yes—
153#102—131no—
154#102—132no—
155#102—131no—
156#97—132no—
157C4×C8—131no—
158C2×C13—42no—
159C2×C13#54811yescharacteristic
160C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
161C2×C13#57811yescharacteristic
162D13—81no—
163C2×Q8—131no—
164C2×Q8—262no—
165C2×Q8—261no—
166C2×Q8—524no—
167C2×Q8C22×D1312yes—
168C2×D4—131no—
169C2×D4C22×D1311yescharacteristic
170C22×C4—21no—
171C22×C4—262no—
172C22×C4—261no—
173SD16—24no—
174D8—262no—
175C2×C8—131no—
176C2×C8—131no—
177C2×C8C22×D1312yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—131no—
181C4⋊C4—132no—
182C4⋊C4—132no—
183C4⋊C4—131no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4—261no—
187C4⋊C4C22×D1311yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—262no—
190C22⋊C4—262no—
191C22⋊C4—262no—
192C22⋊C4—261no—
193C42—132no—
194C42—262no—
195C42C22×D1311yescharacteristic
196C13#336711yescharacteristic, complemented, Sylow
197C23—21no—
198C23—261no—
199Q8—22no—
200Q8—22no—
201Q8—262no—
202Q8—524no—
203Q8—522no—
204D4—21no—
205D4—261no—
206D4—261no—
207D4#612912yes—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—132no—
212C2×C4—132no—
213C2×C4—261no—
214C2×C4—262no—
215C2×C4—524no—
216C2×C4—522no—
217C2×C4D4×D1311yescharacteristic
218C2×C4D4×D1311yescharacteristic
219C2×C4C23×D1311yescharacteristic
220C8—22no—
221C8—261no—
222C8—261no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—521no—
227C22—521no—
228C22—521no—
229C22C2×D4×D1311yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—262no—
234C4—262no—
235C4—521no—
236C4—522no—
237C4#8816812yes—
238C4C2×#612911yescharacteristic
239C4#8825711yescharacteristic
240C2—42no—
241C2—1041no—
242C2#1171930311yescharacteristic
243C2C2×#8816811yescharacteristic
244C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#461D13
hypocenterC13#3367
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #11719437C2semidirect
2. D4×Dic26C2semidirect
3. C13×#461C2semidirect
5. #11718825C2semidirect
6. #11718742C2semidirect
8. #11718507C2semidirect
9. #11718492C2semidirect
10. #11718456C2semidirect
11. #11718455C2semidirect
108. #461D13semidirect
196. C13#3367semidirect

Maximal subgroups

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

subgroupindex
#117194372
D4×Dic262
C13×#4612
#117188262
#117188252
#117187422
C4×#61042
#117185072
#117184922
#117184562
#117184552
#336713