Finite Group Databasebeta

← #15752200

Subgroups — #15752200

Order 3328.

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

normal subgroups only

This group has 462 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, complemented
2#13116369C211yesmaximal, characteristic
3#13112659C212yesmaximal, complemented
4#13112657C211yesmaximal, characteristic
5C13×#2683C211yesmaximal, characteristic
6C2×C13×C22⋊Q8—22no—
7C13×#396—22no—
8C13×#395—21no—
9C13×#390C2211yescharacteristic
10C13×#389C2212yes—
11C13×#386—21no—
12C2×#88072—21no—
13C2×#88048—21no—
14#11718596C2211yescharacteristic
15#11718121—22no—
16#11718121—22no—
17#11718116C2212yes—
18#11718116C2211yescharacteristic
19C22×Q8×C13—21no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13—21no—
22C13×C22⋊Q8—44no—
23C13×C22⋊Q8—44no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4D412yes—
27C2×C13×C4⋊C4D412yes—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—21no—
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—22no—
35C22×#1055—21no—
36C22×#1055—22no—
37C13×#95—21no—
38C13×#95—22no—
39#88072—42no—
40#88048—42no—
41#7826—131nomaximal, Sylow
42C24×C13—21no—
43C2×Q8×C13—44no—
44C2×Q8×C13—81no—
45C2×D4×C13—21no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13Q1612yes—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—21no—
52C22×C4×C13—44no—
53C22×C4×C13—81no—
54C22×C4×C13C2×D412yes—
55C22×C4×C13C2×D411yescharacteristic
56C22×Dic13—41no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—44no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4SD1614yes—
64C13×C22⋊C4—44no—
65C13×C22⋊C4—42no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—81no—
68C42×C13—41no—
69C4⋊Dic13—41no—
70C4⋊Dic13—44no—
71C4⋊Dic13—41no—
72C2×#1055—22no—
73C2×#1055—41no—
74C2×#1055—41no—
75C2×#1055—42no—
76C2×#1055—42no—
77C2×#1055—42no—
78#2683D1311yescharacteristic
79#2100—132no—
80#2094—131no—
81#1271—132no—
82#1270—131no—
83C23×C13—22no—
84C23×C13—42no—
85C23×C13—41no—
86C23×C13—42no—
87C23×C13—41no—
88C23×C13#12011yescharacteristic
89Q8×C13—84no—
90D4×C13—42no—
91D4×C13—81no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—24no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—84no—
105C2×C4×C13C2×SD1612yes—
106C2×C4×C13C2×Q1611yescharacteristic
107C2×C4×C13AGL(1,ℤ/8)12yes—
108C2×C4×C13#13711yescharacteristic
109C2×Dic13—81no—
110C2×Dic13—82no—
111#1055—42no—
112#1055—82no—
113C2×C22⋊Q8—22no—
114C2×#106—261no—
115C2×#102—261no—
116#396—22no—
117#395—21no—
118#390C2×D1311yescharacteristic
119#389C2×D1312yes—
120#386—21no—
121#384—131no—
122#340—262no—
123#340—262no—
124#336—131no—
125#336—132no—
126C22×C13—42no—
127C22×C13—44no—
128C22×C13—82no—
129C22×C13—81no—
130C22×C13—81no—
131C22×C13#45012yes—
132C22×C13#45111yescharacteristic
133C22×C13#45311yescharacteristic
134C22×C13#45412yes—
135C22×C13#45811yescharacteristic
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—22no—
139C4×C13—22no—
140C4×C13—44no—
141C4×C13—82no—
142C4×C13—81no—
143Dic13—161no—
144C22×Q8—21no—
145C22×D4C22⋊D1311yescharacteristic
146C23×C4—21no—
147C22×C8—261no—
148C22×C8—262no—
149C22⋊Q8—44no—
150C22⋊Q8—44no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—262no—
154C2×C4⋊C4—261no—
155C2×C4⋊C4C22⋊D1312yes—
156C2×C4⋊C4C22⋊D1312yes—
157C2×C4⋊C4C22⋊D1311yescharacteristic
158C2×C22⋊C4—22no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—21no—
161C2×C42C22×D1311yescharacteristic
162#106—522no—
163#102—522no—
164#95—21no—
165#95—22no—
166C2×C13—82no—
167C2×C13#161411yescharacteristic
168C2×C13#161612yes—
169C2×C13#162911yescharacteristic
170C2×C13#163712yes—
171C2×C13#165711yescharacteristic
172C24—21no—
173C2×Q8—44no—
174C2×Q8—81no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4#610712yes—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—44no—
183C22×C4—81no—
184C22×C4—521no—
185C22×C4C2×C22⋊D1312yes—
186C22×C4C2×C22⋊D1311yescharacteristic
187C2×C8—262no—
188C2×C8—521no—
189C2×C8—521no—
190C2×C8—522no—
191C2×C8—522no—
192C2×C8—522no—
193C4⋊C4—22no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—44no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—521no—
200C4⋊C4—521no—
201C4⋊C4—524no—
202C4⋊C4#610514yes—
203C22⋊C4—44no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C22⋊C4—81no—
207C42—41no—
208C13#782611yescharacteristic, complemented, Sylow
209C23—22no—
210C23—42no—
211C23—41no—
212C23—41no—
213C23—42no—
214C23#8820711yescharacteristic
215Q8—84no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—1041no—
232C2×C4—1042no—
233C2×C4#8818612yes—
234C2×C4C2×#610512yes—
235C2×C4#8819611yescharacteristic
236C2×C4C2×#610711yescharacteristic
237C8—522no—
238C8—1042no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#1171887912yes—
245C22#1171888911yescharacteristic
246C22#1171890211yescharacteristic
247C22#1171890411yescharacteristic
248C22#1171890612yes—
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—44no—
254C4—82no—
255C4—81no—
256C4—2081no—
257C2—82no—
258C2#1311386111yescharacteristic
259C2#1311387312yes—
260C2#1311395211yescharacteristic
261C2#1311400112yes—
262C2#1311413411yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2683C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2683D13
hypocenterC13#7826
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2683

Complements

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

NH ≅ G/Ntype
1. #13116399C2semidirect
3. #13112659C2semidirect
208. C13#7826semidirect

Maximal subgroups

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

subgroupindex
#131163992
#131163692
#131126592
#131126572
C13×#26832
#782613