Finite Group Databasebeta

← #13118173

Subgroups — #13118173

Order 1664.

864 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 169 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×#6127C211yesmaximal, characteristic
2C22×#6101C211yesmaximal, characteristic, complemented
3C2×#88140C212yesmaximal, complemented
4C13×#381C211yesmaximal, characteristic, complemented
5#11718619C212yesmaximal, complemented
6#11718333C212yesmaximal, complemented
7#11718329C214yesmaximal, complemented
8#11718317C212yesmaximal, complemented
9C23×C4×C13C2211yescharacteristic
10C22×C22⋊D13C2212yes—
11C23×Dic13C2211yescharacteristic
12C23×Dic13C2211yescharacteristic
13C2×#6127—24no—
14C2×#6127—28no—
15C22×D52C2211yescharacteristic
16C22×C4×D13C2212yes—
17C22×Dic26C2211yescharacteristic
18C2×C13×C22⋊C4C2212yes—
19C2×#6103C2214yes—
20C2×#6103C2214yes—
21C2×C4⋊Dic13C2214yes—
22C2×#6101—24no—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25#88140—28no—
26C13×#95C2212yes—
27C13×#95C2212yes—
28#88071C2214yes—
29C24×C13C2311yescharacteristic
30C23×D13C2312yes—
31C22×C4×C13—24no—
32C22×C4×C13D414yes—
33C22×C4×C13C2314yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C2×C22⋊D13—24no—
37C2×C22⋊D13—24no—
38C2×C22⋊D13D418yes—
39C22×Dic13—22no—
40C22×Dic13—24no—
41C22×Dic13—24no—
42C22×Dic13—22no—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46#6127—232no—
47C2×D52—24no—
48C2×D52—22no—
49C2×C4×D13—24no—
50C2×C4×D13—24no—
51C2×C4×D13—24no—
52C2×Dic26—22no—
53C2×Dic26—24no—
54C13×C22⋊C4—24no—
55#6103—28no—
56#6103—28no—
57C4⋊Dic13—28no—
58#6101—24no—
59#6101—24no—
60#2406—131nomaximal, Sylow
61C23×C13—22no—
62C23×C13—22no—
63C23×C13C2×D412yes—
64C23×C13C2×D414yes—
65C23×C13C2411yescharacteristic
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—24no—
69C22×D13—24no—
70C22×D13C2×D414yes—
71C2×C4×C13—28no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—24no—
75C2×C4×C13—24no—
76C2×C4×C13—24no—
77C2×C4×C13C2×D412yes—
78C2×C4×C13C2×D412yes—
79C22⋊D13—216no—
80C2×Dic13—28no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—24no—
87C2×Dic13—44no—
88C2×Dic13C2×D414yes—
89C2×Dic13#4114yescomplemented
90D52—28no—
91C4×D13—216no—
92Dic26—28no—
93C22×#41—131no—
94C2×#123—132no—
95C22×C4⋊C4—131no—
96#395—132no—
97#394—132no—
98#386—132no—
99#385—134no—
100#381D1311yescharacteristic, complemented
101C22×C13—22no—
102C22×C13—22no—
103C22×C13—28no—
104C22×C13#12014yes—
105C22×C13C22×D411yescharacteristic
106C22×C13C22×D412yes—
107C22×C13C2×#4112yes—
108C22×C132−1+412yes—
109C2×D13—24no—
110C2×D13—28no—
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—44no—
114C4×C13—22no—
115C4×C13—22no—
116C4×C13—44no—
117Dic13—24no—
118Dic13—24no—
119Dic13—42no—
120C2×#41—268no—
121C2×#41—264no—
122C22×Q8—131no—
123C22×D4—132no—
124C22×D4—131no—
125C23×C4—131no—
126C23×C4—131no—
127C23×C4—132no—
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—134no—
135C2×C22⋊C4—134no—
136C2×C22⋊C4C2×D1312yes—
137#95—134no—
138#95C2×D1312yes—
139#95C2×D1312yes—
140C2×C13—24no—
141C2×C13C2×#12011yescharacteristic
142C2×C13#52511yescharacteristic
143C2×C13#53611yescharacteristic
144C2×C13#54714yes—
145D13—44no—
146C24—132no—
147C24C22×D1311yescharacteristic
148#41—2632no—
149C2×Q8—264no—
150C2×Q8—262no—
151C2×D4—138no—
152C2×D4—264no—
153C2×D4—264no—
154C2×D4—264no—
155C2×D4—262no—
156C22×C4—24no—
157C22×C4—132no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4—264no—
161C22×C4—264no—
162C22×C4—264no—
163C22×C4—262no—
164C22×C4—264no—
165C22×C4—262no—
166C22×C4—264no—
167C22×C4D5214yes—
168C22×C4C22×D1314yes—
169C22×C4C22×D1311yescharacteristic
170C22×C4C22×D1311yescharacteristic
171C4⋊C4—268no—
172C4⋊C4—264no—
173C4⋊C4—264no—
174C22⋊C4—24no—
175C22⋊C4—268no—
176C22⋊C4—268no—
177C13#240611yescharacteristic, complemented, Sylow
178C23—22no—
179C23—22no—
180C23—134no—
181C23—262no—
182C23—262no—
183C23—264no—
184C23—264no—
185C23C2×D5212yes—
186C23D4×D1314yes—
187C23C23×D1311yescharacteristic
188Q8—268no—
189D4—268no—
190D4—2616no—
191C2×C4—28no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—134no—
198C2×C4—134no—
199C2×C4—2616no—
200C2×C4—268no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—264no—
207C2×C4—524no—
208C2×C4C2×D5212yes—
209C2×C4C2×D5212yes—
210C22—22no—
211C22—22no—
212C22—28no—
213C22—264no—
214C22—268no—
215C22—522no—
216C22—522no—
217C22—524no—
218C22#8813614yes—
219C22C22×D5211yescharacteristic
220C22C2×D4×D1312yes—
221C22#41×D1312yes—
222C22#8825712yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—264no—
227C4—264no—
228C4—522no—
229C2—24no—
230C2—524no—
231C2C2×#8813611yescharacteristic
232C2#1171922911yescharacteristic
233C2#1171923111yescharacteristic
234C2#1171936014yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radicalC22×#6127C2
hypercenter#381D13
hypocenterC13#2406
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×#6101C2semidirect
3. C2×#88140C2semidirect
4. C13×#381C2semidirect
5. #11718619C2semidirect
6. #11718333C2semidirect
7. #11718329C2semidirect
8. #11718317C2semidirect
89. C2×Dic13#41semidirect
100. #381D13semidirect
177. C13#2406semidirect

Maximal subgroups

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

subgroupindex
C22×#61272
C22×#61012
C2×#881402
C13×#3812
#117186192
#117183332
#117183292
#117183172
#240613