Finite Group Databasebeta

← #13126765

Subgroups — #13126765

Order 1664.

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

normal subgroups only

This group has 398 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
1#11719268C211yesmaximal, characteristic, complemented
2#11719256C211yesmaximal, characteristic, complemented
3C8×D4×C13C211yesmaximal, characteristic, complemented
4#11718775C212yesmaximal, complemented
5#11718774C212yesmaximal, complemented
6#11718503C211yesmaximal, characteristic, complemented
7#11718502C211yesmaximal, characteristic, complemented
8#11718395C212yesmaximal, complemented
9#11718384C212yesmaximal, complemented
10C4×D104C211yesmaximal, characteristic, complemented
11#11718342C211yesmaximal, characteristic, complemented
12C2×#6127C2212yes—
13C22×C8×C13C2212yes—
14C4×D4×C13C2211yescharacteristic
15#88192—21no—
16#88192—21no—
17#88184C2212yes—
18#88180C2212yes—
19#88178C2212yes—
20C2×D104C2211yescharacteristic
21C2×#6095C2212yes—
22#88146—21no—
23C4⋊C4×D13—21no—
24#88139—22no—
25#88137—22no—
26C4×D52C2211yescharacteristic
27C4×D52C2211yescharacteristic
28#88123C2211yescharacteristic
29#88123C2211yescharacteristic
30C13×C4⋊C8C2211yescharacteristic
31C13×C22⋊C8C2212yes—
32C4×C8×C13C2211yescharacteristic
33#88061C2212yes—
34#88061C2211yescharacteristic
35#88061C2211yescharacteristic
36#88058C2211yescharacteristic
37#88057C2212yes—
38#88056C2212yes—
39#88056C2212yes—
40#88056C2212yes—
41C2×D4×C13D411yescharacteristic
42C22×C4×C13C2312yes—
43C2×C22⋊D13—22no—
44C2×C22⋊D13—22no—
45#6127—24no—
46#6127—42no—
47C2×D52C2311yescharacteristic
48C2×D52C2311yescharacteristic
49C2×C4×D13—21no—
50C2×C4×D13—21no—
51C2×C4×D13—22no—
52C2×Dic26—21no—
53C2×Dic26C2312yes—
54C2×C8×C13—42no—
55C2×C8×C13C2311yescharacteristic
56C2×C8×C13C2311yescharacteristic
57C2×C8×C13C2312yes—
58C13×C4⋊C4D411yescharacteristic
59C13×C22⋊C4D412yes—
60C42×C13C2311yescharacteristic
61C22⋊Dic13—22no—
62C22⋊Dic13—22no—
63#6103—21no—
64#6103—21no—
65#6103—22no—
66C4⋊Dic13—21no—
67C4⋊Dic13—21no—
68C4⋊Dic13—21no—
69C4⋊Dic13C2312yes—
70C4⋊Dic13C2311yescharacteristic
71C4⋊Dic13C2311yescharacteristic
72#6101—22no—
73C4×Dic13—22no—
74D104—22no—
75#6095—42no—
76#3303—131nomaximal, Sylow
77C23×C13C2×D412yes—
78C22×D13—21no—
79C22×D13—21no—
80D4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13C2×D412yes—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C22⋊D13—44no—
88C22⋊D13—82no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93D52—21no—
94D52—21no—
95D52—21no—
96D52#4112yes—
97C4×D13—44no—
98C4×D13—42no—
99C4×D13—42no—
100Dic26—22no—
101Dic26—22no—
102Dic26—81no—
103C8×C13—21no—
104C8×C13—22no—
105C8×C13—21no—
106#555—131no—
107#547—131no—
108#487—131no—
109#485—132no—
110#476—131no—
111#465—132no—
112#461—131no—
113#449—132no—
114C4×D8—131no—
115C8×D4D1311yescharacteristic, complemented
116#416—132no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13C22×D411yescharacteristic
121C2×D13—22no—
122C2×D13—41no—
123C2×D13—41no—
124C2×D13—41no—
125C2×D13—41no—
126C2×D13—41no—
127C4×C13—22no—
128C4×C13—21no—
129C4×C13#13512yes—
130C4×C13C2×#4111yescharacteristic
131C4×C13H(5,𝔽2)11yescharacteristic
132Dic13—42no—
133Dic13—41no—
134Dic13—41no—
135Dic13—42no—
136C2×#41—132no—
137C2×SD16—132no—
138C2×D8—131no—
139C22×C8C2×D1312yes—
140C4⋊Q8—131no—
141C4⋊Q8—131no—
142#124—262no—
143#123—262no—
144C22⋊Q8—132no—
145#121—132no—
146#121—261no—
147#121—261no—
148C4×D4—131no—
149C4×D4—131no—
150C4×D4C2×D1311yescharacteristic
151#117—132no—
152#117—261no—
153C2×C4⋊C4—261no—
154#107—131no—
155#106—132no—
156C4⋊C8C2×D1311yescharacteristic
157#103—132no—
158#103—132no—
159#103—132no—
160#102—131no—
161#102—132no—
162#102—131no—
163C22⋊C8C2×D1312yes—
164C4×C8C2×D1311yescharacteristic
165C2×C13—42no—
166C2×C13#54611yescharacteristic
167C2×C13C2×#13511yescharacteristic
168C2×C13#57711yescharacteristic
169D13—42no—
170D13—81no—
171#41—264no—
172#41—522no—
173C2×Q8—132no—
174C2×Q8—261no—
175C2×D4—131no—
176C2×D4—131no—
177C2×D4—262no—
178C2×D4—262no—
179C2×D4D5211yescharacteristic
180C22×C4—261no—
181C22×C4—262no—
182C22×C4—261no—
183C22×C4C22×D1312yes—
184SD16—522no—
185D8—262no—
186C2×C8—42no—
187C2×C8C22×D1311yescharacteristic
188C2×C8C22×D1311yescharacteristic
189C2×C8C22×D1312yes—
190C4⋊C4—132no—
191C4⋊C4—131no—
192C4⋊C4—131no—
193C4⋊C4—261no—
194C4⋊C4—262no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4D5211yescharacteristic
198C22⋊C4—262no—
199C22⋊C4—262no—
200C22⋊C4—262no—
201C22⋊C4—261no—
202C22⋊C4—261no—
203C22⋊C4D5212yes—
204C42—262no—
205C42C22×D1311yescharacteristic
206C13#330311yescharacteristic, complemented, Sylow
207C23—261no—
208C23—261no—
209C23C2×D5212yes—
210Q8—262no—
211Q8—262no—
212Q8—1041no—
213D4—22no—
214D4—132no—
215D4—261no—
216D4—261no—
217D4—261no—
218D4—524no—
219D4—1042no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—261no—
223C2×C4—262no—
224C2×C4—261no—
225C2×C4—262no—
226C2×C4—524no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4C2×D5212yes—
230C2×C4C2×D5211yescharacteristic
231C2×C4C2×D5211yescharacteristic
232C2×C4C23×D1311yescharacteristic
233C8—21no—
234C8—22no—
235C8—21no—
236C22—22no—
237C22—22no—
238C22—22no—
239C22—262no—
240C22—521no—
241C22—521no—
242C22—521no—
243C22—521no—
244C22—521no—
245C22C22×D5211yescharacteristic
246C4—21no—
247C4—22no—
248C4—521no—
249C4—521no—
250C4—522no—
251C4—522no—
252C4#8815812yes—
253C4#8825111yescharacteristic
254C4#41×D1311yescharacteristic
255C2—42no—
256C2—522no—
257C2—1041no—
258C2#1171925911yescharacteristic
259C2C2×#8815811yescharacteristic
260C2#1171945611yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC8×D4×C13C2
socleC22×C13C22×D4
hypercenterC8×D4D13
hypocenterC13#3303
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #11719268C2semidirect
2. #11719256C2semidirect
3. C8×D4×C13C2semidirect
4. #11718775C2semidirect
5. #11718774C2semidirect
6. #11718503C2semidirect
7. #11718502C2semidirect
8. #11718395C2semidirect
9. #11718384C2semidirect
10. C4×D104C2semidirect
11. #11718342C2semidirect
115. C8×D4D13semidirect
206. C13#3303semidirect

Maximal subgroups

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

subgroupindex
#117192682
#117192562
C8×D4×C132
#117187752
#117187742
#117185032
#117185022
#117183952
#117183842
C4×D1042
#117183422
#330313