Finite Group Databasebeta

← #15752219

Subgroups — #15752219

Order 3328.

394 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 95 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#13116399C212yesmaximal
2#13116374C211yesmaximal, characteristic
3#13112662C211yesmaximal, characteristic
4#13112659C212yesmaximal
5C13×#2734C211yesmaximal, characteristic
6C2×C13×C4⋊Q8—21no—
7C13×#398—21no—
8C13×#395—22no—
9C13×#391C2211yescharacteristic
10C13×#389C2212yes—
11C13×#387—22no—
12C2×#88075—21no—
13C2×#88047—21no—
14#11718596C2211yescharacteristic
15#11718121—22no—
16#11718121—22no—
17#11718116C2211yescharacteristic
18#11718116C2212yes—
19C22×Q8×C13—21no—
20C22×Q8×C13D411yescharacteristic
21C13×C4⋊Q8—42no—
22C13×C4⋊Q8—42no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4D412yes—
27C2×C13×C4⋊C4D412yes—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C42×C13—21no—
30C2×C42×C13C2311yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—22no—
33C22×#1055—21no—
34C22×#1055—22no—
35C13×#95—21no—
36C13×#95—22no—
37C13×#95—22no—
38C13×#95—22no—
39#88075—42no—
40#88047—42no—
41#7829—131nomaximal, Sylow
42C2×Q8×C13—21no—
43C2×Q8×C13—42no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C2×Q8×C13—81no—
47C2×Q8×C13—81no—
48C2×Q8×C13SD1612yes—
49C22×C4×C13—22no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—22no—
53C22×C4×C13C2×D411yescharacteristic
54C22×C4×C13C2×D412yes—
55C22×Dic13—41no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—42no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—44no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—81no—
63C13×C4⋊C4Q1614yes—
64C42×C13—41no—
65C42×C13—42no—
66C4⋊Dic13—41no—
67C4⋊Dic13—44no—
68C4⋊Dic13—41no—
69C2×#1055—22no—
70C2×#1055—41no—
71C2×#1055—41no—
72C2×#1055—42no—
73C2×#1055—42no—
74C2×#1055—42no—
75#2734D1311yescharacteristic
76#2100—132no—
77#2095—131no—
78#1272—131no—
79#1271—132no—
80C23×C13#12011yescharacteristic
81Q8×C13—42no—
82Q8×C13—81no—
83Q8×C13—84no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—24no—
90C2×C4×C13—42no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13C2×SD1611yescharacteristic
100C2×C4×C13C2×Q1612yes—
101C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C13#13712yes—
103C2×Dic13—81no—
104C2×Dic13—82no—
105#1055—42no—
106#1055—82no—
107C2×C4⋊Q8—21no—
108C2×#107—261no—
109C2×#103—261no—
110#398—21no—
111#395—22no—
112#391C2×D1311yescharacteristic
113#389C2×D1312yes—
114#387—22no—
115#384—131no—
116#340—262no—
117#340—262no—
118#336—131no—
119#336—132no—
120C22×C13#45011yescharacteristic
121C22×C13#45112yes—
122C22×C13#45311yescharacteristic
123C22×C13#45412yes—
124C22×C13#45811yescharacteristic
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—22no—
128C4×C13—22no—
129C4×C13—42no—
130C4×C13—44no—
131C4×C13—82no—
132C4×C13—81no—
133Dic13—161no—
134C22×Q8—21no—
135C22×Q8C22⋊D1311yescharacteristic
136C22×C8—261no—
137C22×C8—262no—
138C4⋊Q8—42no—
139C4⋊Q8—42no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—262no—
144C2×C4⋊C4—261no—
145C2×C4⋊C4C22⋊D1312yes—
146C2×C4⋊C4C22⋊D1312yes—
147C2×C4⋊C4C22⋊D1311yescharacteristic
148C2×C42—21no—
149C2×C42C22×D1311yescharacteristic
150#107—522no—
151#103—522no—
152#95—21no—
153#95—22no—
154#95—22no—
155#95—22no—
156C2×C13#161311yescharacteristic
157C2×C13#161712yes—
158C2×C13#163311yescharacteristic
159C2×C13#163712yes—
160C2×C13#165711yescharacteristic
161C2×Q8—21no—
162C2×Q8—42no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—81no—
166C2×Q8—81no—
167C2×Q8#610512yes—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—521no—
173C22×C4C2×C22⋊D1311yescharacteristic
174C22×C4C2×C22⋊D1312yes—
175C2×C8—262no—
176C2×C8—521no—
177C2×C8—521no—
178C2×C8—522no—
179C2×C8—522no—
180C2×C8—522no—
181C4⋊C4—22no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C4⋊C4—44no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—81no—
188C4⋊C4—521no—
189C4⋊C4—521no—
190C4⋊C4—524no—
191C4⋊C4#610714yes—
192C42—41no—
193C42—42no—
194C13#782911yescharacteristic, complemented, Sylow
195C23#8820711yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—84no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—1041no—
215C2×C4—1042no—
216C2×C4#8818611yescharacteristic
217C2×C4C2×#610511yescharacteristic
218C2×C4#8819612yes—
219C2×C4C2×#610712yes—
220C8—522no—
221C8—1042no—
222C22#1171887911yescharacteristic
223C22#1171888912yes—
224C22#1171890211yescharacteristic
225C22#1171890411yescharacteristic
226C22#1171890612yes—
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—44no—
233C4—82no—
234C4—81no—
235C4—2081no—
236C2#1311385611yescharacteristic
237C2#1311387812yes—
238C2#1311397611yescharacteristic
239C2#1311400112yes—
240C2#1311413411yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2734C2
socle, prime radicalC23×C13#120
hypercenter#2734D13
hypocenterC13#7829
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2734

Complements

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

NH ≅ G/Ntype
194. C13#7829semidirect

Maximal subgroups

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

subgroupindex
#131163992
#131163742
#131126622
#131126592
C13×#27342
#782913