Finite Group Databasebeta

← #13119746

Subgroups — #13119746

Order 1664.

604 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 161 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
1C2×#88151C212yesmaximal, complemented
2C2×C4×D52C211yesmaximal, characteristic
3C2×C4×Dic26C211yesmaximal, characteristic, complemented
4C13×#382C211yesmaximal, characteristic, complemented
5#11718648C212yesmaximal, complemented
6#11718333C212yesmaximal
7#11718331C214yesmaximal, complemented
8#11718322C212yesmaximal, complemented
9C22×D52C2211yescharacteristic
10C22×C4×D13C2212yes—
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2212yes—
13C2×C42×C13C2211yescharacteristic
14C2×#6103C2212yes—
15C2×#6103C2214yes—
16C2×#6103C2214yes—
17C2×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊Dic13C2214yes—
20C2×#6101C2212yes—
21C2×C4×Dic13C2212yes—
22#88151—28no—
23C4×D52—24no—
24C4×Dic26—24no—
25C13×#95C2212yes—
26C13×#95C2212yes—
27#88071C2214yes—
28C23×D13C2312yes—
29C22×C4×C13C2314yes—
30C22×C4×C13C2311yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C22×Dic13C2312yes—
34C22×Dic13C2312yes—
35C22×Dic13C2312yes—
36C2×D52—24no—
37C2×D52—22no—
38C2×C4×D13—24no—
39C2×C4×D13—24no—
40C2×C4×D13—24no—
41C2×Dic26—22no—
42C2×Dic26—22no—
43C2×Dic26D414yescomplemented
44C13×C4⋊C4—24no—
45C42×C13D414yes—
46#6103—28no—
47#6103—24no—
48#6103—28no—
49C4⋊Dic13—22no—
50C4⋊Dic13—22no—
51C4⋊Dic13—28no—
52#6101—24no—
53C4×Dic13—24no—
54#2536—131nomaximal, Sylow
55C23×C13C2411yescharacteristic
56C22×D13—22no—
57C22×D13—22no—
58C22×D13—22no—
59C22×D13—22no—
60C22×D13—22no—
61C22×D13—22no—
62C22×D13#4114yes—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—24no—
66C2×C4×C13—24no—
67C2×C4×C13—24no—
68C2×C4×C13C2×D412yes—
69C2×C4×C13C2×D412yes—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×D412yes—
72C2×C4×C13#4112yes—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—24no—
79C2×Dic13—22no—
80C2×Dic13C2×D414yes—
81D52—28no—
82C4×D13—48no—
83Dic26—28no—
84C2×C22⋊Q8—132no—
85C2×C4×Q8—131no—
86C2×C4×D4—131no—
87#398—132no—
88#394—132no—
89#388—134no—
90#382D1311yescharacteristic, complemented
91#380—132no—
92C22×C13C22×D411yescharacteristic
93C22×C13C22×D411yescharacteristic
94C22×C13C2×#4111yescharacteristic
95C22×C13C2×#4112yes—
96C22×C132−1+412yes—
97C2×D13—24no—
98C2×D13—24no—
99C2×D13—24no—
100C2×D13—42no—
101C2×D13—42no—
102C2×D13—42no—
103C2×D13—42no—
104C4×C13—22no—
105C4×C13—22no—
106C4×C13—44no—
107C4×C13#12114yes—
108Dic13—24no—
109Dic13—42no—
110Dic13—42no—
111C22×Q8—131no—
112C22×D4—131no—
113C23×C4—132no—
114C22⋊Q8—268no—
115C4×Q8—264no—
116C4×D4—264no—
117C2×C4⋊C4—131no—
118C2×C4⋊C4—132no—
119C2×C4⋊C4—131no—
120C2×C4⋊C4—134no—
121C2×C4⋊C4C2×D1312yes—
122C2×C22⋊C4—132no—
123C2×C22⋊C4—134no—
124C2×C22⋊C4—134no—
125C2×C42—132no—
126C2×C42C2×D1311yescharacteristic
127#95—134no—
128#95C2×D1312yes—
129#95C2×D1312yes—
130C2×C13C2×#12111yescharacteristic
131C2×C13#52511yescharacteristic
132C2×C13#53611yescharacteristic
133C2×C13#54812yes—
134C2×C13#55212yes—
135D13—44no—
136C24—132no—
137C2×Q8—134no—
138C2×Q8—262no—
139C2×Q8—262no—
140C2×D4—264no—
141C2×D4—262no—
142C22×C4—132no—
143C22×C4—132no—
144C22×C4—132no—
145C22×C4—264no—
146C22×C4—264no—
147C22×C4—264no—
148C22×C4C22×D1314yes—
149C22×C4C22×D1311yescharacteristic
150C22×C4C22×D1311yescharacteristic
151C22×C4C22×D1311yescharacteristic
152C4⋊C4—24no—
153C4⋊C4—268no—
154C4⋊C4—262no—
155C4⋊C4—264no—
156C4⋊C4—262no—
157C22⋊C4—268no—
158C22⋊C4—268no—
159C22⋊C4—264no—
160C42—264no—
161C42D5214yes—
162C13#253611yescharacteristic, complemented, Sylow
163C23—134no—
164C23—262no—
165C23—262no—
166C23—262no—
167C23—262no—
168C23—262no—
169C23—262no—
170C23C23×D1311yescharacteristic
171Q8—268no—
172D4—268no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—134no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—264no—
186C2×C4—528no—
187C2×C4C2×D5212yes—
188C2×C4C2×D5212yes—
189C2×C4C2×D5212yes—
190C2×C4D4×D1312yes—
191C2×C4#613112yes—
192C22—264no—
193C22—264no—
194C22—264no—
195C22—522no—
196C22—522no—
197C22—522no—
198C22—522no—
199C22C22×D5211yescharacteristic
200C22C2×D4×D1311yescharacteristic
201C22C2×#613111yescharacteristic
202C22#41×D1312yes—
203C22#8825712yes—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—264no—
208C4—522no—
209C4—522no—
210C4#8814914yes—
211C2—524no—
212C2C2×#8814911yescharacteristic
213C2#1171922911yescharacteristic
214C2#1171923111yescharacteristic
215C2#1171938212yes—
216C2#1171939912yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#382C2
prime radicalC22×D52C22
hypercenter#382D13
hypocenterC13#2536
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#88151C2semidirect
3. C2×C4×Dic26C2semidirect
4. C13×#382C2semidirect
5. #11718648C2semidirect
7. #11718331C2semidirect
8. #11718322C2semidirect
43. C2×Dic26D4semidirect
90. #382D13semidirect
162. C13#2536semidirect

Maximal subgroups

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

subgroupindex
C2×#881512
C2×C4×D522
C2×C4×Dic262
C13×#3822
#117186482
#117183332
#117183312
#117183222
#253613