Finite Group Databasebeta

← #13126072

Subgroups — #13126072

Order 1664.

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

normal subgroups only

This group has 328 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
1C13×#529C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3#11718726C211yesmaximal, characteristic, complemented
4#11718726C211yesmaximal, characteristic, complemented
5#11718716C211yesmaximal, characteristic, complemented
6#11718716C211yesmaximal, characteristic, complemented
7#11718706C212yesmaximal, complemented
8#11718696C212yesmaximal
9#11718683C212yesmaximal, complemented
10#11718670C212yesmaximal, complemented
11#11718587C211yesmaximal, characteristic, complemented
12C13×#126—21no—
13C13×#125C2211yescharacteristic
14C13×#124C2211yescharacteristic
15C13×#123—21no—
16C13×C22⋊Q8C2211yescharacteristic
17C13×#121C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13—21no—
20C4×D4×C13C2211yescharacteristic
21C13×#117—21no—
22C2×C42×C13C2211yescharacteristic
23#88180C2212yes—
24#88178—21no—
25#88178—21no—
26#88124C2212yes—
27#88123C2211yescharacteristic
28#88123C2211yescharacteristic
29C4×Dic26—21no—
30C4×Dic26—21no—
31#88075C2212yes—
32#88075C2212yes—
33#88072C2212yes—
34#88072C2212yes—
35C22⋊#1055C2212yes—
36#88048C2212yes—
37#88048C2212yes—
38#88047C2212yes—
39#88047C2212yes—
40C4⋊#1055C2212yes—
41#88043C2211yescharacteristic
42#88043C2211yescharacteristic
43C2×Q8×C13C2311yescharacteristic
44C2×D4×C13—21no—
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13D411yescharacteristic
48C22×C4×C13D411yescharacteristic
49C22×C4×C13C2311yescharacteristic
50C2×Dic26—21no—
51C2×Dic26—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2311yescharacteristic
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C13×C22⋊C4—21no—
60C13×C22⋊C4—21no—
61C13×C22⋊C4—21no—
62C13×C22⋊C4—21no—
63C42×C13—21no—
64C42×C13D411yescharacteristic
65C42×C13D411yescharacteristic
66C42×C13C2311yescharacteristic
67C42×C13C2311yescharacteristic
68C22⋊Dic13—22no—
69C4⋊Dic13—21no—
70C4⋊Dic13—21no—
71C4⋊Dic13C2312yes—
72C4⋊Dic13C2312yes—
73#6101—22no—
74#6101—22no—
75C4×Dic13—22no—
76C2×#1055C2312yes—
77C2×#1055C2312yes—
78#3240—131nomaximal, Sylow
79C23×C13—21no—
80C23×C13C2×D411yescharacteristic
81Q8×C13—22no—
82D4×C13—22no—
83D4×C13—42no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—42no—
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2411yescharacteristic
97C2×Dic13—22no—
98C2×Dic13—22no—
99Dic26—42no—
100Dic26—42no—
101#1055—22no—
102#1055—22no—
103#533—131no—
104#529D1311yescharacteristic
105#501—131no—
106#501—131no—
107#489—131no—
108#489—131no—
109#485—132no—
110#482—132no—
111#479—132no—
112#478—132no—
113#432—131no—
114C22×C13—21no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13—41no—
120C22×C13C22×D411yescharacteristic
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—41no—
127C4×C13—41no—
128C4×C13—41no—
129C4×C132−1+412yes—
130Dic13—42no—
131Dic13—42no—
132C4⋊Q8—131no—
133C4⋊Q8—131no—
134#126—21no—
135#125—132no—
136#125C2×D1311yescharacteristic
137#124C2×D1311yescharacteristic
138#123—21no—
139C22⋊Q8—261no—
140C22⋊Q8—261no—
141C22⋊Q8C2×D1311yescharacteristic
142#121C2×D1311yescharacteristic
143C4×Q8—261no—
144C4×Q8—261no—
145C4×Q8C2×D1311yescharacteristic
146C4×D4—21no—
147C4×D4C2×D1311yescharacteristic
148#117—21no—
149#117—132no—
150C2×C42C2×D1311yescharacteristic
151#107—132no—
152#107—132no—
153#106—132no—
154#106—132no—
155C4⋊C8—132no—
156#103—132no—
157#103—132no—
158#102—132no—
159#102—132no—
160C22⋊C8—132no—
161#97—131no—
162#97—131no—
163C2×C13—41no—
164C2×C13—81no—
165C2×C13#53611yescharacteristic
166C2×C13#57511yescharacteristic
167C2×C13#57511yescharacteristic
168C2×Q8—261no—
169C2×Q8—261no—
170C2×Q8C22×D1311yescharacteristic
171C2×D4—21no—
172C2×D4C22×D1311yescharacteristic
173C22×C4—21no—
174C22×C4C22⋊D1311yescharacteristic
175C22×C4C22⋊D1311yescharacteristic
176C22×C4C22×D1311yescharacteristic
177C2×C8—132no—
178C2×C8—132no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—132no—
184C4⋊C4—132no—
185C4⋊C4—262no—
186C4⋊C4—262no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4C22×D1311yescharacteristic
190C4⋊C4C22×D1311yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—21no—
196C22⋊C4—262no—
197C42—21no—
198C42—262no—
199C42C22⋊D1311yescharacteristic
200C42C22⋊D1311yescharacteristic
201C42C22×D1311yescharacteristic
202C42C22×D1311yescharacteristic
203C13#324011yescharacteristic, complemented, Sylow
204C23—21no—
205C23C2×C22⋊D1311yescharacteristic
206Q8—22no—
207Q8—522no—
208Q8—522no—
209D4—22no—
210D4—42no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4C2×C22⋊D1311yescharacteristic
221C2×C4C2×C22⋊D1311yescharacteristic
222C2×C4C2×C22⋊D1311yescharacteristic
223C2×C4C2×C22⋊D1311yescharacteristic
224C2×C4C2×C22⋊D1311yescharacteristic
225C2×C4C23×D1311yescharacteristic
226C8—262no—
227C8—262no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22C22×C22⋊D1311yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—41no—
243C4—522no—
244C4—522no—
245C4#8825712yes—
246C2—41no—
247C2—81no—
248C2#1171952711yescharacteristic
249C2#1171952711yescharacteristic
250C2#1171953011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#529C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#529D13
hypocenterC13#3240
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. #11719175C2semidirect
3. #11718726C2semidirect
4. #11718726C2semidirect
5. #11718716C2semidirect
6. #11718716C2semidirect
7. #11718706C2semidirect
9. #11718683C2semidirect
10. #11718670C2semidirect
11. #11718587C2semidirect
203. C13#3240semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
#117191752
#117187262
#117187162
#117187062
#117186962
#117186832
#117186702
#117185872
#324013