Finite Group Databasebeta

← #13127119

Subgroups — #13127119

Order 1664.

374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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
1D4×Q8×C13C211yesmaximal, characteristic
2#11719247C211yesmaximal, characteristic
3#11718889C212yesmaximal, complemented
4#11718886C212yesmaximal, complemented
5#11718751C211yesmaximal, characteristic, complemented
6#11718742C211yesmaximal, characteristic, complemented
7#11718713C212yesmaximal, complemented
8#11718706C212yesmaximal, complemented
9C4×#6107C211yesmaximal, characteristic, complemented
10#11718681C211yesmaximal, characteristic, complemented
11#11718673C211yesmaximal, characteristic
12C22×Q8×C13C2212yes—
13C13×C4⋊Q8—21no—
14C13×C4⋊Q8C2211yescharacteristic
15C13×C22⋊Q8—22no—
16C13×C22⋊Q8C2212yes—
17C4×Q8×C13C2211yescharacteristic
18C4×D4×C13—21no—
19C4×D4×C13C2211yescharacteristic
20C2×#6107C2211yescharacteristic
21C2×#6107C2212yes—
22#88190—21no—
23#88180C2212yes—
24#88178C2212yes—
25C2×#6099C2212yes—
26#88141—21no—
27#88133—22no—
28#88123C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30#88075C2212yes—
31#88075C2211yescharacteristic
32#88075C2212yes—
33#88075C2212yes—
34#88075C2212yes—
35C22⋊#1055C2212yes—
36#88050C2211yescharacteristic
37#88048C2212yes—
38#88047C2211yescharacteristic
39C4⋊#1055C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—22no—
42C2×Q8×C13—24no—
43C2×Q8×C13—42no—
44C2×Q8×C13C2312yes—
45C2×Q8×C13C2311yescharacteristic
46C2×D4×C13D411yescharacteristic
47C22×C4×C13—22no—
48C22×C4×C13C2312yes—
49C2×Dic26—21no—
50C2×Dic26C2311yescharacteristic
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4D411yescharacteristic
56C13×C4⋊C4C2311yescharacteristic
57C13×C22⋊C4—22no—
58C13×C22⋊C4D412yes—
59C42×C13—21no—
60C42×C13C2311yescharacteristic
61C22⋊Dic13—22no—
62C22⋊Dic13—22no—
63#6107—22no—
64#6107—42no—
65C4⋊Dic13—21no—
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2312yes—
68#6101—21no—
69#6101—22no—
70C4×Dic13—21no—
71C4×Dic13—22no—
72#6099—42no—
73C2×#1055C2311yescharacteristic
74C2×#1055C2312yes—
75C2×#1055C2311yescharacteristic
76#3328—131nomaximal, Sylow
77C23×C13C2×D412yes—
78Q8×C13—21no—
79Q8×C13—22no—
80Q8×C13—22no—
81Q8×C13—44no—
82Q8×C13#4112yes—
83D4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—44no—
90C2×C4×C13C2×D412yes—
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2411yescharacteristic
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97Dic26—21no—
98Dic26—21no—
99Dic26—42no—
100#1055—21no—
101#1055—21no—
102#1055—22no—
103#556—131no—
104D4×Q8D1311yescharacteristic
105#487—131no—
106#485—132no—
107#475—131no—
108#470—132no—
109#462—131no—
110#451—132no—
111C4×Q16—131no—
112#436—131no—
113#419—132no—
114C22×C13—22no—
115C22×C13—22no—
116C22×C13—22no—
117C22×C13C22×D411yescharacteristic
118C4×C13—22no—
119C4×C13—22no—
120C4×C13—21no—
121C4×C13—42no—
122C4×C13—41no—
123C4×C13#13712yes—
124C4×C13C2×#4111yescharacteristic
125C4×C13H(5,𝔽2)11yescharacteristic
126Dic13—41no—
127Dic13—42no—
128Dic13—41no—
129C22×Q8C2×D1312yes—
130C2×Q16—131no—
131C2×Q16—132no—
132C2×M16—132no—
133C4⋊Q8—21no—
134C4⋊Q8—131no—
135C4⋊Q8C2×D1311yescharacteristic
136#126—262no—
137#124—261no—
138C22⋊Q8—22no—
139C22⋊Q8—132no—
140C22⋊Q8C2×D1312yes—
141C4×Q8—131no—
142C4×Q8—261no—
143C4×Q8C2×D1311yescharacteristic
144C4×D4—21no—
145C4×D4C2×D1311yescharacteristic
146#117—132no—
147#107—131no—
148#106—132no—
149C4⋊C8—131no—
150#103—131no—
151#103—132no—
152#103—132no—
153#103—132no—
154#103—132no—
155#103—131no—
156C22⋊C8—132no—
157C4×C8—131no—
158C2×C13—42no—
159C2×C13#54611yescharacteristic
160C2×C13C2×#13711yescharacteristic
161C2×C13#57811yescharacteristic
162C2×Q8—22no—
163C2×Q8—24no—
164C2×Q8—42no—
165C2×Q8—131no—
166C2×Q8—261no—
167C2×Q8C22×D1312yes—
168C2×Q8C22×D1311yescharacteristic
169C2×D4C22⋊D1311yescharacteristic
170C22×C4—22no—
171C22×C4C22×D1312yes—
172Q16—262no—
173Q16—522no—
174M16—522no—
175C2×C8—131no—
176C2×C8—131no—
177C2×C8—132no—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—22no—
182C4⋊C4—132no—
183C4⋊C4—131no—
184C4⋊C4—261no—
185C4⋊C4—262no—
186C4⋊C4—261no—
187C4⋊C4C22⋊D1311yescharacteristic
188C4⋊C4C22×D1311yescharacteristic
189C22⋊C4—22no—
190C22⋊C4—262no—
191C22⋊C4—262no—
192C22⋊C4C22⋊D1312yes—
193C42—21no—
194C42—262no—
195C42—261no—
196C42C22×D1311yescharacteristic
197C13#332811yescharacteristic, complemented, Sylow
198C23C2×C22⋊D1312yes—
199Q8—21no—
200Q8—22no—
201Q8—22no—
202Q8—44no—
203Q8—261no—
204Q8—261no—
205Q8—522no—
206Q8#612912yes—
207D4—22no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—44no—
214C2×C4—261no—
215C2×C4—262no—
216C2×C4—261no—
217C2×C4C2×C22⋊D1312yes—
218C2×C4C2×C22⋊D1311yescharacteristic
219C2×C4C2×C22⋊D1311yescharacteristic
220C2×C4C23×D1311yescharacteristic
221C8—261no—
222C8—261no—
223C8—262no—
224C22—22no—
225C22—22no—
226C22—22no—
227C22C22×C22⋊D1311yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—42no—
232C4—41no—
233C4—521no—
234C4—522no—
235C4—521no—
236C4#8819612yes—
237C4C2×#612911yescharacteristic
238C4#8825111yescharacteristic
239C2—42no—
240C2#1171951111yescharacteristic
241C2C2×#8819611yescharacteristic
242C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingD4×Q8×C13C2
socleC22×C13C22×D4
prime radicalC2×D4×C13D4
hypercenterD4×Q8D13
hypocenterC13#3328
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
3. #11718889C2semidirect
4. #11718886C2semidirect
5. #11718751C2semidirect
6. #11718742C2semidirect
7. #11718713C2semidirect
8. #11718706C2semidirect
9. C4×#6107C2semidirect
10. #11718681C2semidirect
197. C13#3328semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C132
#117192472
#117188892
#117188862
#117187512
#117187422
#117187132
#117187062
C4×#61072
#117186812
#117186732
#332813