Finite Group Databasebeta

← #15751762

Subgroups — #15751762

Order 3328.

424 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 87 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#13116169C212yesmaximal
2#13115935C211yesmaximal, characteristic
3#13112662C211yesmaximal, characteristic
4#13112659C212yesmaximal
5C13×#2809C211yesmaximal, characteristic
6C22×#6107—21no—
7C2×#88123C2211yescharacteristic
8C13×#400—21no—
9C13×#398—22no—
10C13×#391—21no—
11C13×#391C2211yescharacteristic
12C13×#389C2212yes—
13C13×#387—22no—
14C2×#88050—21no—
15C2×#88048—22no—
16#11718121—22no—
17#11718116C2212yes—
18#11718116C2211yescharacteristic
19C22×Q8×C13D411yescharacteristic
20C22×Dic26—21no—
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4D412yes—
25C2×C13×C4⋊C4D412yes—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C42×C13—21no—
28C2×C42×C13C2311yescharacteristic
29C2×#6107—42no—
30C2×#6107—42no—
31C2×#6107—42no—
32C2×C4⋊Dic13—22no—
33C22×#1055—21no—
34C22×#1055—22no—
35#88123—42no—
36C13×#95—21no—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95—22no—
40C13×#95—22no—
41#88050—42no—
42#88048—44no—
43#7760—131nomaximal, Sylow
44C2×Q8×C13—21no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13SD1612yes—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13C2×D411yescharacteristic
53C22×C4×C13C2×D412yes—
54C22×Dic13—41no—
55C2×Dic26—22no—
56C2×Dic26—41no—
57C2×Dic26—41no—
58C2×Dic26—41no—
59C2×Dic26—41no—
60C2×Dic26—41no—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—22no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—81no—
68C13×C4⋊C4—81no—
69C42×C13—41no—
70C42×C13—81no—
71#6107—48no—
72C4⋊Dic13—24no—
73C4⋊Dic13—42no—
74C2×#1055—24no—
75C2×#1055—22no—
76C2×#1055—41no—
77C2×#1055—42no—
78C2×#1055—41no—
79C2×#1055—42no—
80#2809D1311yescharacteristic
81#2058—132no—
82#2016—131no—
83#1272—131no—
84#1271—132no—
85C23×C13#12011yescharacteristic
86Q8×C13—42no—
87Q8×C13—81no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13C2×SD1611yescharacteristic
104C2×C4×C13#13512yes—
105C2×C4×C13#13711yescharacteristic
106C2×C4×C13#13712yes—
107C2×Dic13—42no—
108C2×Dic13—81no—
109C2×Dic13—81no—
110Dic26—42no—
111Dic26—42no—
112Dic26—81no—
113Dic26—81no—
114#1055—44no—
115#1055—42no—
116C22×Q16—261no—
117C2×C4⋊Q8—131no—
118C2×#106—262no—
119C2×#103—261no—
120#400—21no—
121#398—22no—
122#391—21no—
123#391C2×D1311yescharacteristic
124#389C2×D1312yes—
125#387—22no—
126#340—262no—
127#336—132no—
128#336—131no—
129C22×C13#44811yescharacteristic
130C22×C13#45212yes—
131C22×C13#45311yescharacteristic
132C22×C13#45612yes—
133C22×C13B(4,𝔽2)11yescharacteristic
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—22no—
137C4×C13—22no—
138C4×C13—42no—
139C4×C13—82no—
140C4×C13—82no—
141C4×C13—81no—
142Dic13—82no—
143C22×Q8—261no—
144C22×Q8C22⋊D1311yescharacteristic
145C2×Q16—522no—
146C2×Q16—522no—
147C2×Q16—522no—
148C22×C8—261no—
149C22×C8—262no—
150C4⋊Q8—522no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—262no—
155C2×C4⋊C4C22⋊D1312yes—
156C2×C4⋊C4C22⋊D1312yes—
157C2×C4⋊C4C22⋊D1311yescharacteristic
158C2×C42—21no—
159C2×C42C22×D1311yescharacteristic
160#106—524no—
161#103—522no—
162#95—21no—
163#95—22no—
164#95—22no—
165#95—22no—
166#95—22no—
167C2×C13#159611yescharacteristic
168C2×C13#160312yes—
169C2×C13#163411yescharacteristic
170C2×C13#165312yes—
171C2×C13#166011yescharacteristic
172C2×Q8—21no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—262no—
176C2×Q8—521no—
177C2×Q8—521no—
178C2×Q8—521no—
179C2×Q8—521no—
180C2×Q8—521no—
181C2×Q8#610612yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—521no—
187C22×C4C2×C22⋊D1311yescharacteristic
188C22×C4C2×C22⋊D1312yes—
189Q16—528no—
190C2×C8—262no—
191C2×C8—264no—
192C2×C8—522no—
193C2×C8—521no—
194C2×C8—521no—
195C2×C8—522no—
196C4⋊C4—22no—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C4⋊C4—264no—
205C4⋊C4—522no—
206C42—41no—
207C42—81no—
208C13#776011yescharacteristic, complemented, Sylow
209C23#8820711yescharacteristic
210Q8—42no—
211Q8—81no—
212Q8—522no—
213Q8—522no—
214Q8—1041no—
215Q8—1041no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—522no—
232C2×C4—1041no—
233C2×C4—1041no—
234C2×C4C2×#610611yescharacteristic
235C2×C4#8819611yescharacteristic
236C2×C4#8820412yes—
237C2×C4#8820512yes—
238C8—524no—
239C8—522no—
240C22#1171888811yescharacteristic
241C22#1171890012yes—
242C22#1171890211yescharacteristic
243C22#1171890511yescharacteristic
244C22#1171890712yes—
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—42no—
250C4—81no—
251C4—82no—
252C4—82no—
253C4—1042no—
254C2#1311375911yescharacteristic
255C2#1311379912yes—
256C2#1311398111yescharacteristic
257C2#1311411312yes—
258C2#1311414711yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2809C2
socle, prime radicalC23×C13#120
hypercenter#2809D13
hypocenterC13#7760
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

Complements

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

NH ≅ G/Ntype
208. C13#7760semidirect

Maximal subgroups

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

subgroupindex
#131161692
#131159352
#131126622
#131126592
C13×#28092
#776013