Finite Group Databasebeta

← #13124490

Subgroups — #13124490

Order 1664.

460 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#11719521C211yesmaximal, characteristic
2C22×#6107C211yesmaximal, characteristic, complemented
3C2×#88161C211yesmaximal, characteristic
4#11719231C211yesmaximal, characteristic
5C13×#419C211yesmaximal, characteristic, complemented
6#11718781C211yesmaximal, characteristic, complemented
7#11718659C211yesmaximal, characteristic, complemented
8#11718477C214yesmaximal, complemented
9#11718474C214yesmaximal, complemented
10C22×Q8×C13C2211yescharacteristic
11C2×#6127C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×M16C2211yescharacteristic
14C13×#117C2211yescharacteristic
15#88201—21no—
16#88200C2214yes—
17#88198—21no—
18C2×#6107—24no—
19C2×#6107C2212yes—
20C2×#6107C2212yes—
21#88183—22no—
22#88180C2211yescharacteristic
23C22×#1055C2211yescharacteristic
24#88161—24no—
25C2×#6094C2212yes—
26C2×C8×D13C2212yes—
27#88151C2214yes—
28#88140—22no—
29#88129—21no—
30#88123—21no—
31C13×#103C2214yes—
32#88056C2214yes—
33#88048C2212yes—
34#88047C2212yes—
35C2×Q8×C13—21no—
36C2×Q8×C13—22no—
37C2×Q8×C13—22no—
38C2×Q8×C13C2312yes—
39C22×C4×C13—21no—
40C22×C4×C13C2311yescharacteristic
41C2×C22⋊D13D412yes—
42C22×Dic13—21no—
43#6127—22no—
44#6127—22no—
45C2×D52D411yescharacteristic
46C2×C4×D13C2312yes—
47C2×Dic26—22no—
48C2×Dic26—22no—
49C2×Dic26—21no—
50C2×Dic26D411yescharacteristic
51C2×Dic26C2312yes—
52C13×M16—22no—
53C2×C8×C13C2312yes—
54C13×C4⋊C4C2312yes—
55C13×C22⋊C4—21no—
56C42×C13—21no—
57C22⋊Dic13—21no—
58#6107—24no—
59#6107—24no—
60#6103—24no—
61#6103—24no—
62C4⋊Dic13—24no—
63C4⋊Dic13C2312yes—
64#6101—24no—
65C4×Dic13—21no—
66C2×#1055D414yes—
67C2×#1055C2311yescharacteristic
68C2×#1055C2311yescharacteristic
69#6094—24no—
70C8×D13—24no—
71#3059—131nomaximal, Sylow
72C23×C13C2×D411yescharacteristic
73C22×D13C2×D412yes—
74Q8×C13—22no—
75Q8×C13—22no—
76Q8×C13—42no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—42no—
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2×D412yes—
82C2×C4×C13#4112yes—
83C2×C4×C13C2411yescharacteristic
84C22⋊D13—24no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—42no—
88C2×Dic13C2×D412yes—
89D52—22no—
90C4×D13—22no—
91C4×D13—22no—
92Dic26—22no—
93Dic26—22no—
94Dic26—22no—
95Dic26—42no—
96C8×C13—22no—
97#1055C2×D412yes—
98#1055C2×D412yes—
99C22×Q16—131no—
100C2×#131—131no—
101#536—131no—
102#536—131no—
103#470—134no—
104#467—134no—
105#427—131no—
106#419—131no—
107#419D1311yescharacteristic, complemented
108C22×C13—22no—
109C22×C13#12112yes—
110C22×C13C22×D411yescharacteristic
111C2×D13—22no—
112C2×D13—24no—
113C4×C13—42no—
114C4×C13—42no—
115C4×C13#12112yes—
116C4×C13C22×D411yescharacteristic
117C4×C13C2×#4111yescharacteristic
118Dic13—22no—
119Dic13—42no—
120Dic13—42no—
121C2×#41—131no—
122C22×Q8—131no—
123C22×Q8C2×D1311yescharacteristic
124C2×Q16—132no—
125C2×Q16—132no—
126C2×Q16—264no—
127#131—264no—
128C2×M16—132no—
129C2×M16C2×D1311yescharacteristic
130C22×C8—131no—
131C22×C8—132no—
132C4⋊Q8—261no—
133C4⋊Q8—261no—
134#124—261no—
135#124—261no—
136#123—262no—
137#123—262no—
138C22⋊Q8—134no—
139C22⋊Q8—134no—
140#117—131no—
141#117C2×D1311yescharacteristic
142#107—132no—
143#106—132no—
144#103—134no—
145#103C2×D1314yes—
146C2×C13—22no—
147C2×C13C2×#12111yescharacteristic
148C2×C13#57812yes—
149D13—42no—
150#41—262no—
151#41—262no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—131no—
156C2×Q8—132no—
157C2×Q8—261no—
158C2×Q8—262no—
159C2×Q8—262no—
160C2×Q8C22×D1312yes—
161C2×D4—132no—
162C2×D4—131no—
163C22×C4—21no—
164C22×C4—132no—
165C22×C4—261no—
166C22×C4C22×D1311yescharacteristic
167Q16—264no—
168Q16—264no—
169M16—22no—
170M16—264no—
171C2×C8—134no—
172C2×C8—131no—
173C2×C8—131no—
174C2×C8—264no—
175C2×C8C22×D1312yes—
176C4⋊C4—132no—
177C4⋊C4—264no—
178C4⋊C4—264no—
179C4⋊C4C22×D1312yes—
180C22⋊C4—21no—
181C22⋊C4—264no—
182C22⋊C4—264no—
183C22⋊C4—261no—
184C42—21no—
185C42—261no—
186C13#305911yescharacteristic, complemented, Sylow
187C23—132no—
188C23D4×D1311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—262no—
193Q8—262no—
194Q8—262no—
195Q8—522no—
196D4—264no—
197D4—262no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—132no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—522no—
207C2×C4#612712yes—
208C2×C4D4×D1311yescharacteristic
209C2×C4D4×D1312yes—
210C2×C4C23×D1311yescharacteristic
211C8—22no—
212C8—132no—
213C8—132no—
214C22—22no—
215C22—262no—
216C22—264no—
217C22#8813812yes—
218C22C2×D4×D1311yescharacteristic
219C4—42no—
220C4—42no—
221C4—262no—
222C4—522no—
223C4—522no—
224C4#8813812yes—
225C4C2×#612711yescharacteristic
226C4C2×D4×D1311yescharacteristic
227C2—22no—
228C2—522no—
229C2C2×#8813811yescharacteristic
230C2#1171948412yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#419C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenter#419D13
hypocenterC13#3059
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C22×#6107C2semidirect
5. C13×#419C2semidirect
6. #11718781C2semidirect
7. #11718659C2semidirect
8. #11718477C2semidirect
9. #11718474C2semidirect
107. #419D13semidirect
186. C13#3059semidirect

Maximal subgroups

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

subgroupindex
#117195212
C22×#61072
C2×#881612
#117192312
C13×#4192
#117187812
#117186592
#117184772
#117184742
#305913