Finite Group Databasebeta

← #13119147

Subgroups — #13119147

Order 1664.

584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D13C211yesmaximal, characteristic
3#11718874C212yesmaximal
4#11718873C211yesmaximal, characteristic, complemented
5#11718871C212yesmaximal, complemented
6#11718653C212yesmaximal, complemented
7#11718648C212yesmaximal, complemented
8#11718643C212yesmaximal, complemented
9#11718634C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C23×C4×C13C2212yes—
12C22×C22⋊D13C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C2×C13×C4⋊C4—24no—
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C4⋊C4C2212yes—
17C2×C22⋊Dic13C2211yescharacteristic
18C2×C22⋊Dic13C2212yes—
19C4×C22⋊D13—24no—
20C2×#6103C2211yescharacteristic
21C2×#6103C2214yes—
22C2×C4⋊Dic13C2212yes—
23C2×#6101C2211yescharacteristic
24C2×#6101C2214yes—
25C2×C4×Dic13C2211yescharacteristic
26#88071C2214yes—
27#88071C2212yes—
28#88071C2214yes—
29C24×C13C2311yescharacteristic
30C23×D13C2311yescharacteristic
31C22×C4×C13—24no—
32C22×C4×C13—24no—
33C22×C4×C13—44no—
34C22×C4×C13D414yes—
35C22×C4×C13C2314yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—22no—
39C2×C22⋊D13—22no—
40C2×C22⋊D13Q814yes—
41C22×Dic13C2311yescharacteristic
42C22×Dic13C2314yes—
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C2×C4×D13—22no—
46C2×C4×D13—24no—
47C13×C4⋊C4—24no—
48C13×C4⋊C4—24no—
49C22⋊Dic13—22no—
50C22⋊Dic13—24no—
51#6103—22no—
52#6103—44no—
53C4⋊Dic13—24no—
54#6101—22no—
55#6101—44no—
56C4×Dic13—22no—
57#2487—131nomaximal, Sylow
58C23×C13—22no—
59C23×C13—22no—
60C23×C13C2×D412yes—
61C23×C13C2×Q812yes—
62C23×C13#4112yes—
63C23×C13C2411yescharacteristic
64C22×D13—21no—
65C22×D13—22no—
66C22×D13—21no—
67C22×D13—22no—
68C22×D13C2×Q812yes—
69C2×C4×C13—22no—
70C2×C4×C13—28no—
71C2×C4×C13—24no—
72C2×C4×C13—24no—
73C2×C4×C13—24no—
74C2×C4×C13—48no—
75C2×C4×C13C2×D412yes—
76C2×C4×C13C2×D412yes—
77C2×C4×C13#4114yes—
78C22⋊D13—28no—
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13—21no—
82C2×Dic13—21no—
83C2×Dic13—24no—
84C2×Dic13—24no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—24no—
88C2×Dic13C2×Q812yes—
89C4×D13—44no—
90C2×C4×D4—131no—
91C22×C4⋊C4D1311yescharacteristic, complemented
92#400—132no—
93#399—132no—
94#389—132no—
95#386—132no—
96#385—132no—
97#380—131no—
98#380—132no—
99C22×C13—22no—
100C22×C13—22no—
101C22×C13—24no—
102C22×C13—24no—
103C22×C13C22⋊Q814yes—
104C22×C13C22×D411yescharacteristic
105C22×C13C22×Q811yescharacteristic
106C22×C13C2×#4112yes—
107C22×C13C2×#4111yescharacteristic
108C22×C13H(5,𝔽2)12yes—
109C2×D13—22no—
110C2×D13—24no—
111C2×D13—41no—
112C2×D13—41no—
113C2×D13—42no—
114C4×C13—22no—
115C4×C13—44no—
116C4×C13#12314yes—
117Dic13—22no—
118Dic13—41no—
119Dic13—41no—
120Dic13—44no—
121C22×D4—131no—
122C23×C4—131no—
123C23×C4C2×D1311yescharacteristic
124C23×C4C2×D1312yes—
125C4×D4—264no—
126C2×C4⋊C4—24no—
127C2×C4⋊C4—131no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4—134no—
130C2×C4⋊C4C2×D1312yes—
131C2×C4⋊C4C2×D1312yes—
132C2×C22⋊C4—131no—
133C2×C22⋊C4—132no—
134C2×C22⋊C4—131no—
135C2×C22⋊C4—134no—
136C2×C42—131no—
137#95—134no—
138#95—132no—
139#95—134no—
140C2×C13—24no—
141C2×C13C2×C22⋊Q811yescharacteristic
142C2×C13C2×#12311yescharacteristic
143C2×C13#53511yescharacteristic
144C2×C13#55312yes—
145C2×C13#55412yes—
146D13—42no—
147C24—131no—
148C24C22×D1311yescharacteristic
149C2×D4—134no—
150C2×D4—262no—
151C2×D4—262no—
152C22×C4—24no—
153C22×C4—24no—
154C22×C4—44no—
155C22×C4—131no—
156C22×C4—131no—
157C22×C4—134no—
158C22×C4—131no—
159C22×C4—264no—
160C22×C4—262no—
161C22×C4C22⋊D1314yes—
162C22×C4C22×D1314yes—
163C22×C4C22×D1311yescharacteristic
164C22×C4C22×D1311yescharacteristic
165C4⋊C4—24no—
166C4⋊C4—24no—
167C4⋊C4—264no—
168C4⋊C4—262no—
169C4⋊C4—524no—
170C22⋊C4—264no—
171C22⋊C4—262no—
172C22⋊C4—262no—
173C22⋊C4—524no—
174C42—262no—
175C13#248711yescharacteristic, complemented, Sylow
176C23—22no—
177C23—22no—
178C23—132no—
179C23—262no—
180C23—262no—
181C23—261no—
182C23—261no—
183C23Q8×D1312yes—
184C23#613112yes—
185C23C2×C22⋊D1312yes—
186C23C23×D1311yescharacteristic
187D4—268no—
188C2×C4—22no—
189C2×C4—28no—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—48no—
194C2×C4—132no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—264no—
198C2×C4—262no—
199C2×C4—264no—
200C2×C4—262no—
201C2×C4—264no—
202C2×C4—261no—
203C2×C4—261no—
204C2×C4—524no—
205C2×C4#612714yes—
206C2×C4C2×C22⋊D1312yes—
207C2×C4C2×C22⋊D1312yes—
208C22—24no—
209C22—24no—
210C22—22no—
211C22—22no—
212C22—264no—
213C22—262no—
214C22—522no—
215C22—521no—
216C22—521no—
217C22#8820014yes—
218C22C2×#612712yes—
219C22#8825112yes—
220C22C2×Q8×D1311yescharacteristic
221C22C2×#613111yescharacteristic
222C22C22×C22⋊D1311yescharacteristic
223C4—22no—
224C4—44no—
225C4—262no—
226C4—524no—
227C4—521no—
228C4—521no—
229C4#8818314yes—
230C2—24no—
231C2—522no—
232C2#1171921612yes—
233C2#1171921912yes—
234C2C2×#8818311yescharacteristic
235C2#1171951011yescharacteristic
236C2C2×#8820011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC22×C13×C4⋊C4C2
prime radicalC22×C22⋊D13C22
hypercenterC22×C4⋊C4D13
hypocenterC13#2487
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C13×C4⋊C4C2semidirect
4. #11718873C2semidirect
5. #11718871C2semidirect
6. #11718653C2semidirect
7. #11718648C2semidirect
8. #11718643C2semidirect
9. #11718634C2semidirect
91. C22×C4⋊C4D13semidirect
175. C13#2487semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C4⋊C42
C2×C4×C22⋊D132
#117188742
#117188732
#117188712
#117186532
#117186482
#117186432
#117186342
#248713