Finite Group Databasebeta

← #15752052

Subgroups — #15752052

Order 3328.

366 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 83 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#13122824C211yesmaximal, characteristic
2#13116379C211yesmaximal, characteristic
3#13116309C212yesmaximal
4#13112660C212yesmaximal
5C13×#1272C211yesmaximal, characteristic
6C13×#391C2211yescharacteristic
7#11718891—21no—
8C2×#88075—21no—
9C2×#88058—22no—
10#11718647—21no—
11C2×#88048—21no—
12#11718596C2211yescharacteristic
13#11718589C2212yes—
14#11718322—22no—
15#11718316—22no—
16C13×#336C2212yes—
17#11718143—22no—
18#11718116C2211yescharacteristic
19C22×Q8×C13D411yescharacteristic
20C22×C8×C13—22no—
21C2×C13×C4⋊C4D411yescharacteristic
22C2×C42×C13C2311yescharacteristic
23C2×C4⋊Dic13—22no—
24C2×C4⋊Dic13—21no—
25C2×C4⋊Dic13—21no—
26C2×C4⋊Dic13—21no—
27C2×C4⋊Dic13D412yes—
28C2×C4⋊Dic13D412yes—
29C2×#6101—22no—
30C2×C4×Dic13—21no—
31C22×#1055—21no—
32C13×#95—22no—
33#88075—42no—
34#88071—21no—
35#88071—22no—
36#88071—22no—
37#88071—22no—
38#88058—44no—
39#88048—42no—
40#7802—131nomaximal, Sylow
41C2×Q8×C13—21no—
42C2×Q8×C13—41no—
43C2×Q8×C13—41no—
44C2×Q8×C13Q1612yes—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C2×D411yescharacteristic
48C22×C4×C13C2×D412yes—
49C22×Dic13—22no—
50C22×Dic13—22no—
51C22×Dic13—41no—
52C2×C8×C13—24no—
53C2×C8×C13—42no—
54C2×C8×C13—42no—
55C13×C4⋊C4—41no—
56C42×C13—41no—
57C4⋊Dic13—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13—42no—
60C4⋊Dic13—41no—
61C4⋊Dic13—41no—
62C4⋊Dic13—42no—
63C4⋊Dic13—42no—
64C4⋊Dic13—81no—
65C4⋊Dic13—81no—
66#6101—42no—
67#6101—42no—
68C4×Dic13—81no—
69C2×#1055—22no—
70C2×#1055—41no—
71C2×#1055—41no—
72#2809—131no—
73#2096—131no—
74#2083—132no—
75#1272D1311yescharacteristic
76#1271—132no—
77C23×C13#12011yescharacteristic
78Q8×C13—42no—
79Q8×C13—81no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13—42no—
89C2×C4×C13C2×Q1611yescharacteristic
90C2×C4×C13#13512yes—
91C2×C4×C13AGL(1,ℤ/8)12yes—
92C2×C4×C13#13711yescharacteristic
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—82no—
100C2×Dic13—81no—
101C8×C13—44no—
102#1055—42no—
103C2×#107—262no—
104C2×#106—261no—
105C2×#103—261no—
106#400—261no—
107#398—262no—
108#391—261no—
109#391C2×D1311yescharacteristic
110#389—132no—
111#387—262no—
112#384—131no—
113#340—262no—
114#336—131no—
115#336C2×D1312yes—
116C22×C13#44912yes—
117C22×C13#45111yescharacteristic
118C22×C13#45311yescharacteristic
119C22×C13#45612yes—
120C22×C13#45811yescharacteristic
121C4×C13—22no—
122C4×C13—22no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—42no—
126C4×C13—81no—
127Dic13—82no—
128Dic13—82no—
129Dic13—161no—
130C22×Q8D5211yescharacteristic
131C22×C8—22no—
132C22×C8—261no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4—262no—
136C2×C4⋊C4—261no—
137C2×C4⋊C4—262no—
138C2×C4⋊C4—261no—
139C2×C4⋊C4—261no—
140C2×C4⋊C4D5211yescharacteristic
141C2×C42—261no—
142C2×C42C22×D1311yescharacteristic
143#107—524no—
144#106—522no—
145#103—522no—
146#95—22no—
147#95—261no—
148#95—262no—
149#95—262no—
150#95—262no—
151C2×C13#160912yes—
152C2×C13#161411yescharacteristic
153C2×C13#162411yescharacteristic
154C2×C13#164812yes—
155C2×C13#166011yescharacteristic
156C2×Q8—21no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8Dic5212yes—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—262no—
163C22×C4—262no—
164C22×C4—521no—
165C22×C4C2×D5211yescharacteristic
166C22×C4D4×D1312yes—
167C2×C8—24no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—262no—
171C2×C8—521no—
172C2×C8—521no—
173C4⋊C4—41no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—522no—
177C4⋊C4—521no—
178C4⋊C4—521no—
179C4⋊C4—522no—
180C4⋊C4—522no—
181C4⋊C4—522no—
182C4⋊C4—522no—
183C4⋊C4—1041no—
184C4⋊C4—1041no—
185C42—41no—
186C42—1041no—
187C13#780211yescharacteristic, complemented, Sylow
188C23#8813611yescharacteristic
189Q8—42no—
190Q8—81no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—522no—
201C2×C4—522no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4—1041no—
207C2×C4—1042no—
208C2×C4C2×Dic5211yescharacteristic
209C2×C4#8816311yescharacteristic
210C2×C4#8816812yes—
211C2×C4#8817312yes—
212C8—44no—
213C8—522no—
214C22#1171840011yescharacteristic
215C22#1171840311yescharacteristic
216C22#1171840811yescharacteristic
217C22#1171847212yes—
218C22#1171848712yes—
219C4—21no—
220C4—21no—
221C4—22no—
222C4—22no—
223C4—42no—
224C4—81no—
225C4—1042no—
226C4—1042no—
227C4—2081no—
228C2#1311383612yes—
229C2#1311386311yescharacteristic
230C2#1311392011yescharacteristic
231C2#1311408112yes—
232C2#1311414811yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1272C2
socle, prime radicalC23×C13#120
hypercenter#1272D13
hypocenterC13#7802
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
187. C13#7802semidirect

Maximal subgroups

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

subgroupindex
#131228242
#131163792
#131163092
#131126602
C13×#12722
#780213