Finite Group Databasebeta

← #13118167

Subgroups — #13118167

Order 1664.

864 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 185 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
1C22×C13×#41C211yesmaximal, characteristic
2C2×#88189C212yesmaximal, complemented
3C22×#6101C211yesmaximal, characteristic, complemented
4#11718890C212yesmaximal, complemented
5#11718883C212yesmaximal, complemented
6#11718881C212yesmaximal, complemented
7#11718872C211yesmaximal, characteristic, complemented
8#11718871C214yesmaximal, complemented
9C2×C13×#41—28no—
10C2×C13×#41—24no—
11C22×Q8×C13C2211yescharacteristic
12C22×D4×C13C2211yescharacteristic
13C22×D4×C13C2212yes—
14C23×C4×C13C2212yes—
15C23×C4×C13C2211yescharacteristic
16C23×Dic13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C2×C22⋊Dic13C2214yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2214yes—
21#88189—28no—
22C2×#6101—24no—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2214yes—
26#88071C2212yes—
27#88071C2214yes—
28#88071C2212yes—
29C24×C13C2312yes—
30C24×C13C2311yescharacteristic
31C13×#41—232no—
32C2×Q8×C13—24no—
33C2×Q8×C13—22no—
34C2×D4×C13—24no—
35C2×D4×C13—24no—
36C2×D4×C13—24no—
37C2×D4×C13—22no—
38C2×D4×C13D418yes—
39C22×C4×C13—24no—
40C22×C4×C13—24no—
41C22×C4×C13—24no—
42C22×C4×C13—24no—
43C22×C4×C13D414yes—
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2312yes—
46C22×C4×C13C2311yescharacteristic
47C22×Dic13—22no—
48C22×Dic13—24no—
49C22×Dic13—22no—
50C22×Dic13—24no—
51C22×Dic13C2314yes—
52C22×Dic13C2312yes—
53C22×Dic13C2312yes—
54C22⋊Dic13—24no—
55C22⋊Dic13—28no—
56C22⋊Dic13—28no—
57#6101—24no—
58#6101—24no—
59#6101—28no—
60#2406—131nomaximal, Sylow
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—22no—
64C23×C13—22no—
65C23×C13—24no—
66C23×C13—24no—
67C23×C13C2×D414yes—
68C23×C13C2×D414yes—
69C23×C13C2×D412yes—
70C23×C13C2411yescharacteristic
71Q8×C13—28no—
72D4×C13—28no—
73D4×C13—216no—
74C2×C4×C13—216no—
75C2×C4×C13—28no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13C2×D412yes—
81C2×C4×C13C2×D414yes—
82C2×C4×C13C2×D412yes—
83C2×Dic13—28no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—24no—
88C2×Dic13—24no—
89C2×Dic13—24no—
90C2×Dic13—24no—
91C2×Dic13—44no—
92C2×Dic13#4114yescomplemented
93C22×#41D1311yescharacteristic
94C2×#123—132no—
95C22×C4⋊C4—131no—
96#395—132no—
97#394—132no—
98#386—132no—
99#385—134no—
100#381—131no—
101C22×C13—22no—
102C22×C13—22no—
103C22×C13—28no—
104C22×C13—24no—
105C22×C13—28no—
106C22×C13—42no—
107C22×C13—42no—
108C22×C13—44no—
109C22×C13#12014yes—
110C22×C13C22×D411yescharacteristic
111C22×C13C22×D412yes—
112C22×C13C2×#4112yes—
113C22×C132−1+412yes—
114C4×C13—22no—
115C4×C13—24no—
116C4×C13—22no—
117Dic13—24no—
118Dic13—42no—
119Dic13—44no—
120C2×#41—28no—
121C2×#41—24no—
122C22×Q8C2×D1311yescharacteristic
123C22×D4C2×D1311yescharacteristic
124C22×D4C2×D1312yes—
125C23×C4—131no—
126C23×C4—131no—
127C23×C4C2×D1312yes—
128C23×C4C2×D1311yescharacteristic
129#123—268no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4—134no—
133C2×C4⋊C4—264no—
134C2×C22⋊C4—132no—
135C2×C22⋊C4—134no—
136C2×C22⋊C4—134no—
137#95—132no—
138#95—132no—
139#95—134no—
140C2×C13—24no—
141C2×C13—44no—
142C2×C13C2×#12011yescharacteristic
143C2×C13#52511yescharacteristic
144C2×C13#53611yescharacteristic
145C2×C13#54714yes—
146C24C22×D1312yes—
147C24C22×D1311yescharacteristic
148#41—232no—
149C2×Q8—24no—
150C2×Q8—22no—
151C2×D4—24no—
152C2×D4—24no—
153C2×D4—24no—
154C2×D4—22no—
155C2×D4C22⋊D1318yes—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—24no—
160C22×C4—132no—
161C22×C4—134no—
162C22×C4—132no—
163C22×C4—264no—
164C22×C4—262no—
165C22×C4—262no—
166C22×C4—264no—
167C22×C4C22⋊D1314yes—
168C22×C4C22×D1311yescharacteristic
169C22×C4C22×D1312yes—
170C22×C4C22×D1311yescharacteristic
171C4⋊C4—264no—
172C4⋊C4—264no—
173C4⋊C4—268no—
174C22⋊C4—268no—
175C22⋊C4—264no—
176C22⋊C4—268no—
177C13#240611yescharacteristic, complemented, Sylow
178C23—22no—
179C23—22no—
180C23—24no—
181C23—24no—
182C23—22no—
183C23—22no—
184C23C2×C22⋊D1314yes—
185C23C2×C22⋊D1314yes—
186C23C2×C22⋊D1312yes—
187C23C23×D1311yescharacteristic
188Q8—28no—
189D4—28no—
190D4—216no—
191C2×C4—216no—
192C2×C4—28no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—134no—
198C2×C4—268no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—264no—
202C2×C4—264no—
203C2×C4—264no—
204C2×C4—264no—
205C2×C4—262no—
206C2×C4—524no—
207C2×C4C2×C22⋊D1312yes—
208C2×C4C2×C22⋊D1314yes—
209C2×C4C2×C22⋊D1312yes—
210C22—28no—
211C22—22no—
212C22—22no—
213C22—28no—
214C22—24no—
215C22—44no—
216C22—42no—
217C22—42no—
218C22#8820714yes—
219C22#41×D1312yes—
220C22#8825712yes—
221C22C22×C22⋊D1312yes—
222C22C22×C22⋊D1311yescharacteristic
223C4—22no—
224C4—24no—
225C4—22no—
226C4—264no—
227C4—524no—
228C4—522no—
229C2—24no—
230C2—44no—
231C2#1171952914yes—
232C2#1171953011yescharacteristic
233C2#1171953311yescharacteristic
234C2C2×#8820711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC22×C13×#41C2
hypercenterC22×#41D13
hypocenterC13#2406
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
2. C2×#88189C2semidirect
3. C22×#6101C2semidirect
4. #11718890C2semidirect
5. #11718883C2semidirect
6. #11718881C2semidirect
7. #11718872C2semidirect
8. #11718871C2semidirect
92. C2×Dic13#41semidirect
177. C13#2406semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#412
C2×#881892
C22×#61012
#117188902
#117188832
#117188812
#117188722
#117188712
#240613