Finite Group Databasebeta

← #13126068

Subgroups — #13126068

Order 1664.

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

normal subgroups only

This group has 362 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
1#11719184C211yesmaximal, characteristic
2C2×#88123C211yesmaximal, characteristic, complemented
3C13×#432C211yesmaximal, characteristic, complemented
4#11718512C212yesmaximal, complemented
5#11718507C212yesmaximal, complemented
6#11718396C212yesmaximal
7#11718383C212yesmaximal, complemented
8#11718375C212yesmaximal, complemented
9#11718363C212yesmaximal, complemented
10C22×Dic26—21no—
11C2×C42×C13C2211yescharacteristic
12#88184C2211yescharacteristic
13#88183—21no—
14C4×C22⋊D13—21no—
15C2×C4⋊Dic13—21no—
16C2×C4⋊Dic13C2212yes—
17#88178C2211yescharacteristic
18#88130—21no—
19#88129C2211yescharacteristic
20C4×D52C2211yescharacteristic
21#88126—21no—
22#88124C2211yescharacteristic
23#88123—21no—
24#88123—21no—
25#88123C2212yes—
26#88123C2212yes—
27C4×Dic26C2211yescharacteristic
28C13×C4⋊C8C2212yes—
29C13×C22⋊C8C2212yes—
30C13×#97C2212yes—
31#88061C2214yes—
32#88058C2214yes—
33#88057C2214yes—
34#88056C2214yes—
35C22×C4×C13D411yescharacteristic
36C22×C4×C13D411yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—21no—
39C22×Dic13—22no—
40C2×D52C2311yescharacteristic
41C2×C4×D13—21no—
42C2×Dic26—22no—
43C2×Dic26—22no—
44C2×Dic26—44no—
45C2×Dic26C2311yescharacteristic
46C2×C8×C13C2314yes—
47C42×C13D411yescharacteristic
48C42×C13D411yescharacteristic
49C42×C13C2311yescharacteristic
50C42×C13C2311yescharacteristic
51C22⋊Dic13—21no—
52#6103—21no—
53#6103—21no—
54#6103—21no—
55#6103—21no—
56C4⋊Dic13—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13C2311yescharacteristic
60C4⋊Dic13C2314yes—
61C4⋊Dic13C2311yescharacteristic
62#6101—21no—
63#6101—21no—
64#6101—21no—
65#6101—21no—
66C4×Dic13—21no—
67#3239—131nomaximal, Sylow
68C23×C13C2×D411yescharacteristic
69C22×D13—21no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2411yescharacteristic
79C22⋊D13—42no—
80C2×Dic13—21no—
81C2×Dic13—21no—
82C2×Dic13—21no—
83C2×Dic13—24no—
84C2×Dic13—44no—
85D52—22no—
86C4×D13—42no—
87Dic26—22no—
88Dic26—44no—
89Dic26—44no—
90C8×C13—24no—
91C2×C4⋊Q8—131no—
92#529—131no—
93#501—132no—
94#489—132no—
95#484—132no—
96#481—132no—
97#475—132no—
98#474—132no—
99#432D1311yescharacteristic, complemented
100C22×C13—21no—
101C22×C13—21no—
102C22×C13#13712yes—
103C22×C13C22×D411yescharacteristic
104C2×D13—41no—
105C2×D13—41no—
106C2×D13—41no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—21no—
111C4×C13AGL(1,ℤ/8)12yes—
112C4×C132−1+412yes—
113Dic13—41no—
114Dic13—44no—
115Dic13—41no—
116Dic13—41no—
117C22×Q8—261no—
118C4⋊Q8—132no—
119C4⋊Q8—132no—
120C4⋊Q8—261no—
121C4⋊Q8—261no—
122#126—261no—
123#125—131no—
124#124—131no—
125#123—261no—
126C22⋊Q8—131no—
127#121—131no—
128C4×Q8—131no—
129C4×D4—131no—
130C4×D4—261no—
131#117—261no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4—261no—
134C2×C42C2×D1311yescharacteristic
135#107—134no—
136#106—134no—
137C4⋊C8C2×D1312yes—
138#103—134no—
139#102—134no—
140C22⋊C8C2×D1312yes—
141#97C2×D1312yes—
142C2×C13—22no—
143C2×C13#53611yescharacteristic
144C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C13C2×#13711yescharacteristic
146D13—81no—
147C2×Q8—131no—
148C2×Q8—262no—
149C2×Q8—262no—
150C2×Q8—524no—
151C2×D4—131no—
152C2×D4—261no—
153C22×C4—262no—
154C22×C4—261no—
155C22×C4D5211yescharacteristic
156C22×C4D5211yescharacteristic
157C22×C4C22×D1311yescharacteristic
158C2×C8C22×D1314yes—
159C4⋊C4—134no—
160C4⋊C4—131no—
161C4⋊C4—131no—
162C4⋊C4—262no—
163C4⋊C4—262no—
164C4⋊C4—262no—
165C4⋊C4—261no—
166C4⋊C4—261no—
167C4⋊C4—261no—
168C4⋊C4—261no—
169C22⋊C4—261no—
170C22⋊C4—261no—
171C22⋊C4—261no—
172C22⋊C4—261no—
173C22⋊C4—261no—
174C42—261no—
175C42D5211yescharacteristic
176C42D5211yescharacteristic
177C42C22×D1311yescharacteristic
178C42C22×D1311yescharacteristic
179C13#323911yescharacteristic, complemented, Sylow
180C23—261no—
181C23C2×D5211yescharacteristic
182Q8—262no—
183Q8—524no—
184Q8—524no—
185D4—262no—
186D4—522no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—261no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—264no—
194C2×C4—524no—
195C2×C4—522no—
196C2×C4C2×D5211yescharacteristic
197C2×C4C2×D5211yescharacteristic
198C2×C4C2×D5211yescharacteristic
199C2×C4C2×D5211yescharacteristic
200C2×C4C2×D5211yescharacteristic
201C2×C4C23×D1311yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—521no—
206C22—521no—
207C22—521no—
208C22#8816312yes—
209C22C22×D5211yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—521no—
215C4—524no—
216C4—521no—
217C4—521no—
218C4#8816212yes—
219C4#8825712yes—
220C2—22no—
221C2—1041no—
222C2#1171923111yescharacteristic
223C2C2×#8816211yescharacteristic
224C2C2×#8816311yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#432C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#432D13
hypocenterC13#3239
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×#88123C2semidirect
3. C13×#432C2semidirect
4. #11718512C2semidirect
5. #11718507C2semidirect
7. #11718383C2semidirect
8. #11718375C2semidirect
9. #11718363C2semidirect
99. #432D13semidirect
179. C13#3239semidirect

Maximal subgroups

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

subgroupindex
#117191842
C2×#881232
C13×#4322
#117185122
#117185072
#117183962
#117183832
#117183752
#117183632
#323913