Finite Group Databasebeta

← #13119997

Subgroups — #13119997

Order 1664.

532 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 153 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×C4×D52C211yesmaximal, characteristic
2C2×#88124C211yesmaximal, characteristic, complemented
3C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
4#11718648C212yesmaximal, complemented
5#11718648C212yesmaximal, complemented
6#11718601C214yesmaximal, complemented
7#11718333C212yesmaximal
8#11718320C212yesmaximal, complemented
9C22×D52C2211yescharacteristic
10C22×C4×D13C2212yes—
11C2×C13×C4⋊C4C2212yes—
12C2×C42×C13C2212yes—
13C2×C42×C13C2211yescharacteristic
14C2×#6103C2212yes—
15C2×#6103C2214yes—
16C2×#6103C2214yes—
17C2×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊Dic13C2211yescharacteristic
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C4×D52—24no—
23#88124—24no—
24C13×#95C2212yes—
25#88071C2214yes—
26#88071C2214yes—
27C23×D13C2312yes—
28C22×C4×C13C2314yes—
29C22×C4×C13C2311yescharacteristic
30C22×C4×C13C2311yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C22×Dic13C2312yes—
33C22×Dic13C2312yes—
34C22×Dic13C2312yes—
35C2×D52—24no—
36C2×D52—22no—
37C2×C4×D13—24no—
38C2×C4×D13—24no—
39C2×C4×D13—24no—
40C13×C4⋊C4—24no—
41C42×C13—42no—
42C42×C13D414yes—
43#6103—28no—
44#6103—24no—
45#6103—44no—
46C4⋊Dic13—22no—
47C4⋊Dic13—22no—
48C4⋊Dic13—22no—
49#6101—24no—
50#6101—24no—
51#2562—131nomaximal, Sylow
52C23×C13C2411yescharacteristic
53C22×D13—22no—
54C22×D13—22no—
55C22×D13—22no—
56C22×D13—22no—
57C22×D13—22no—
58C22×D13—22no—
59C22×D13#4114yes—
60C2×C4×C13—22no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—24no—
64C2×C4×C13—24no—
65C2×C4×C13—24no—
66C2×C4×C13C2×D412yes—
67C2×C4×C13C2×D412yes—
68C2×C4×C13C2×D412yes—
69C2×C4×C13#4114yes—
70C2×Dic13—22no—
71C2×Dic13—22no—
72C2×Dic13—22no—
73C2×Dic13—24no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78D52—28no—
79C4×D13—48no—
80C2×#125—131no—
81C2×C4×D4—131no—
82#400—132no—
83#394—132no—
84#388—134no—
85#380—132no—
86#380—132no—
87C4×C4⋊C4D1311yescharacteristic, complemented
88C22×C13C22×D411yescharacteristic
89C22×C13C2×#4112yes—
90C22×C13C2×#4112yes—
91C22×C13H(5,𝔽2)11yescharacteristic
92C22×C132−1+411yescharacteristic
93C2×D13—24no—
94C2×D13—24no—
95C2×D13—24no—
96C2×D13—42no—
97C2×D13—42no—
98C2×D13—42no—
99C2×D13—42no—
100C4×C13—22no—
101C4×C13—22no—
102C4×C13—44no—
103C4×C13#12414yes—
104Dic13—42no—
105Dic13—42no—
106Dic13—42no—
107C22×D4—131no—
108C23×C4—132no—
109#125—264no—
110C4×D4—264no—
111C2×C4⋊C4—131no—
112C2×C4⋊C4—132no—
113C2×C4⋊C4—132no—
114C2×C4⋊C4—131no—
115C2×C4⋊C4—131no—
116C2×C4⋊C4C2×D1312yes—
117C2×C22⋊C4—132no—
118C2×C22⋊C4—134no—
119C2×C22⋊C4—134no—
120C2×C42C2×D1312yes—
121C2×C42C2×D1311yescharacteristic
122#95—134no—
123#95—134no—
124#95C2×D1312yes—
125C2×C13#52511yescharacteristic
126C2×C13C2×#12411yescharacteristic
127C2×C13#53711yescharacteristic
128C2×C13#55212yes—
129C2×C13#55312yes—
130D13—44no—
131C24—132no—
132C2×D4—264no—
133C2×D4—262no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4—132no—
137C22×C4—264no—
138C22×C4—264no—
139C22×C4—264no—
140C22×C4C22×D1314yes—
141C22×C4C22×D1311yescharacteristic
142C22×C4C22×D1311yescharacteristic
143C22×C4C22×D1311yescharacteristic
144C4⋊C4—24no—
145C4⋊C4—262no—
146C4⋊C4—264no—
147C4⋊C4—264no—
148C4⋊C4—262no—
149C4⋊C4—262no—
150C22⋊C4—268no—
151C22⋊C4—264no—
152C22⋊C4—524no—
153C42—42no—
154C42D5214yes—
155C13#256211yescharacteristic, complemented, Sylow
156C23—134no—
157C23—262no—
158C23—262no—
159C23—262no—
160C23—262no—
161C23—262no—
162C23—262no—
163C23C23×D1311yescharacteristic
164D4—268no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—24no—
169C2×C4—24no—
170C2×C4—24no—
171C2×C4—262no—
172C2×C4—262no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—264no—
179C2×C4—528no—
180C2×C4C2×D5212yes—
181C2×C4C2×D5212yes—
182C2×C4C2×D5212yes—
183C2×C4#612714yes—
184C22—264no—
185C22—264no—
186C22—264no—
187C22—522no—
188C22—522no—
189C22—522no—
190C22—522no—
191C22C22×D5211yescharacteristic
192C22C2×#612712yes—
193C22#8825111yescharacteristic
194C22#8825411yescharacteristic
195C22#41×D1312yes—
196C4—22no—
197C4—22no—
198C4—44no—
199C4—522no—
200C4—522no—
201C4—522no—
202C4#8812914yes—
203C2—524no—
204C2C2×#8812911yescharacteristic
205C2#1171921511yescharacteristic
206C2#1171922911yescharacteristic
207C2#1171926312yes—
208C2#1171928612yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC4×C13×C4⋊C4C2
prime radicalC22×D52C22
hypercenterC4×C4⋊C4D13
hypocenterC13#2562
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#88124C2semidirect
3. C4×C13×C4⋊C4C2semidirect
4. #11718648C2semidirect
5. #11718648C2semidirect
6. #11718601C2semidirect
8. #11718320C2semidirect
87. C4×C4⋊C4D13semidirect
155. C13#2562semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D522
C2×#881242
C4×C13×C4⋊C42
#117186482
#117186012
#117183332
#117183202
#256213