Finite Group Databasebeta

← #15765933

Subgroups — #15765933

Order 3328.

504 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 129 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#13119865C211yesmaximal, characteristic
2#13115783C212yesmaximal
3#13115637C211yesmaximal, characteristic
4#13112675C212yesmaximal
5C13×#1296C211yesmaximal, characteristic
6C2×#88142—22no—
7C2×#88123C2211yescharacteristic
8C2×C13×C4⋊C8C2212yes—
9C13×#384C2211yescharacteristic
10#11718640—22no—
11#11718634—22no—
12C2×#88050—22no—
13C4×C4⋊Dic13C2212yes—
14C2×C4×#1055C2211yescharacteristic
15#11718143—22no—
16#11718143—22no—
17C22×Dic26—21no—
18C22×Dic26—22no—
19C22×C8×C13—22no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4D412yes—
22C2×C42×C13C2311yescharacteristic
23C2×C4⋊Dic13—22no—
24C2×C4⋊Dic13D412yes—
25C2×C4⋊Dic13D412yes—
26C2×#6101—24no—
27C2×C4×Dic13—22no—
28C22×#1055—21no—
29#88142—44no—
30#88142—44no—
31#88123—22no—
32#88123—21no—
33#88123Q812yescomplemented
34C13×C4⋊C8—22no—
35C13×C4⋊C8—22no—
36#88071—22no—
37#88071—22no—
38#88050—44no—
39C4×#1055—22no—
40#10349—131nomaximal, Sylow
41C22×C4×C13—22no—
42C22×C4×C13C2×D411yescharacteristic
43C22×C4×C13C2×D412yes—
44C22×Dic13—22no—
45C22×Dic13—22no—
46C22×Dic13—41no—
47C2×Dic26—22no—
48C2×Dic26—42no—
49C2×Dic26—42no—
50C2×Dic26—48no—
51C2×Dic26—41no—
52C2×Dic26—82no—
53C2×C8×C13—42no—
54C2×C8×C13—42no—
55C2×C8×C13—42no—
56C13×C4⋊C4—42no—
57C13×C4⋊C4—42no—
58C13×C4⋊C4—42no—
59C42×C13C2×Q811yescharacteristic
60C42×C13#4112yes—
61C42×C13#4111yescharacteristic
62C4⋊Dic13—22no—
63C4⋊Dic13—22no—
64C4⋊Dic13—24no—
65C4⋊Dic13—42no—
66C4⋊Dic13SD1614yes—
67C4⋊Dic13Q1614yes—
68#6101—48no—
69C4×Dic13—42no—
70C4×Dic13—42no—
71C2×#1055—22no—
72C2×#1055—41no—
73C2×#1055—41no—
74#2551—131no—
75#1987—132no—
76#1956—131no—
77#1296D1311yescharacteristic
78#1279—132no—
79C23×C13#12011yescharacteristic
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—44no—
83C2×C4×C13—42no—
84C2×C4×C13C22⋊Q811yescharacteristic
85C2×C4×C13C22⋊Q812yes—
86C2×C4×C13#12411yescharacteristic
87C2×C4×C13#12412yes—
88C2×C4×C13C2×SD1612yes—
89C2×C4×C13C2×Q1612yes—
90C2×C4×C13AGL(1,ℤ/8)12yes—
91C2×C4×C13#13712yes—
92C2×Dic13—24no—
93C2×Dic13—24no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—81no—
100C2×Dic13—81no—
101Dic26—44no—
102Dic26—88no—
103Dic26—82no—
104C8×C13—82no—
105#1055—42no—
106C2×C4⋊Q8—131no—
107C2×C4⋊Q8—262no—
108C2×C4⋊C8C2×D1312yes—
109C2×#103—262no—
110C2×C4×C8—131no—
111#395—262no—
112#389—262no—
113#384C2×D1311yescharacteristic
114C4×C4⋊C4—132no—
115#340—262no—
116#340—262no—
117C22×C13#39311yescharacteristic
118C22×C13#45012yes—
119C22×C13#45112yes—
120C22×C13#45311yescharacteristic
121C22×C13#45411yescharacteristic
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—82no—
125C4×C13#47512yes—
126C4×C13#47712yes—
127C4×C13#48712yes—
128C4×C13#48912yes—
129Dic13—44no—
130Dic13—44no—
131Dic13—82no—
132C22×Q8—262no—
133C22×Q8—261no—
134C22×C8—22no—
135C22×C8—261no—
136C4⋊Q8—132no—
137C4⋊Q8—262no—
138C4⋊Q8—261no—
139C4⋊Q8—524no—
140C4⋊Q8—524no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—132no—
144C2×C4⋊C4—262no—
145C2×C4⋊C4—264no—
146C2×C4⋊C4D5212yes—
147C2×C42—262no—
148C2×C42C22×D1311yescharacteristic
149C4⋊C8—22no—
150C4⋊C8—22no—
151#103—524no—
152C4×C8—262no—
153#95—262no—
154#95—262no—
155C2×C13#162911yescharacteristic
156C2×C13#163311yescharacteristic
157C2×C13#163712yes—
158C2×C13#202412yes—
159C2×C13#202711yescharacteristic
160C2×Q8—262no—
161C2×Q8—522no—
162C2×Q8—522no—
163C2×Q8—528no—
164C2×Q8—521no—
165C2×Q8—1042no—
166C22×C4—22no—
167C22×C4—262no—
168C22×C4—262no—
169C22×C4—521no—
170C22×C4C2×D5211yescharacteristic
171C22×C4D4×D1312yes—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—262no—
176C2×C8—521no—
177C2×C8—521no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—134no—
182C4⋊C4—134no—
183C4⋊C4—262no—
184C4⋊C4—262no—
185C4⋊C4—264no—
186C4⋊C4—528no—
187C4⋊C4—522no—
188C42—522no—
189C42—522no—
190C42#612712yes—
191C42#612911yescharacteristic
192C42Q8×D1311yescharacteristic
193C13#1034911yescharacteristic, complemented, Sylow
194C23#8813611yescharacteristic
195Q8—524no—
196Q8—1042no—
197Q8—1048no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—264no—
203C2×C4—264no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4—522no—
209C2×C4—1041no—
210C2×C4—1041no—
211C2×C4#8812911yescharacteristic
212C2×C4#8813912yes—
213C2×C4#8815012yes—
214C2×C4#8815111yescharacteristic
215C2×C4#8816512yes—
216C2×C4SD16×D1312yes—
217C2×C4#8816912yes—
218C2×C4Q16×D1312yes—
219C8—82no—
220C8—522no—
221C22#1171833411yescharacteristic
222C22#1171840811yescharacteristic
223C22#1171841411yescharacteristic
224C22#1171843712yes—
225C22#1171846912yes—
226C4—21no—
227C4—21no—
228C4—82no—
229C4—524no—
230C4—524no—
231C4—1042no—
232C4#1171842612yes—
233C4#1171845312yes—
234C4#1171851512yes—
235C4#1171853612yes—
236C2#1311395311yescharacteristic
237C2#1311397711yescharacteristic
238C2#1311400212yes—
239C2#1311597612yes—
240C2#1311599311yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socle, prime radicalC23×C13#120
hypercenter#1296D13
hypocenterC13#10349
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
33. #88123Q8semidirect
193. C13#10349semidirect

Maximal subgroups

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

subgroupindex
#131198652
#131157832
#131156372
#131126752
C13×#12962
#1034913