Finite Group Databasebeta

← #15757973

Subgroups — #15757973

Order 3328.

616 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#11718644C211yesmaximal, characteristic
2#13114920C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic
4#13112714C212yesmaximal
5C13×#2313C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8C22×#6101—21no—
9C13×#387—24no—
10C13×#381—21no—
11C13×#380C2212yes—
12C4×C13×C22⋊C4—21no—
13C2×#88071—21no—
14C2×#88071C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16#11718644—22no—
17#11718644C414yescomplemented
18#11718121—24no—
19#11718120—22no—
20C23×C4×C13D411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4C2×C412yes—
28C2×C13×C4⋊C4D412yes—
29C2×C13×C4⋊C4D414yes—
30C2×C13×C22⋊C4—22no—
31C2×C42×C13—22no—
32C2×C4⋊Dic13—22no—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C412yes—
36C2×#6101—24no—
37C2×#6101—44no—
38C22×#1055—22no—
39C13×#95—22no—
40C13×#95—24no—
41C13×#95—22no—
42#88071—24no—
43#88071—21no—
44#88071C2×C412yes—
45C22⋊#1055—22no—
46C22⋊#1055—22no—
47#9026—131nomaximal, Sylow
48C24×C13C2×D411yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—21no—
55C22×C4×C13—24no—
56C22×C4×C13—42no—
57C22×C4×C13—42no—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D412yes—
63C22×C4×C13#4112yes—
64C22×Dic13—24no—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—42no—
68C22×Dic13—42no—
69C22×Dic13—41no—
70C22×Dic13—41no—
71C22×Dic13—42no—
72C22×Dic13—42no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—44no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—42no—
78C42×C13—82no—
79C4⋊Dic13—24no—
80C4⋊Dic13—42no—
81#6101—48no—
82C2×#1055—44no—
83C2×#1055—42no—
84C2×#398—131no—
85#2313D1311yescharacteristic
86#1823—132no—
87C2×#324—131no—
88#1294—132no—
89C23×C13—22no—
90C23×C13—22no—
91C23×C13C2×C22⋊C411yescharacteristic
92C23×C13#12011yescharacteristic
93C23×C13#12311yescharacteristic
94C23×C13#13512yes—
95C23×C13AGL(1,ℤ/8)12yes—
96C2×C4×C13—24no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—44no—
109C2×C4×C13—44no—
110C2×C4×C13—44no—
111C2×C4×C13—81no—
112C2×C4×C13C4×D412yes—
113C2×C4×C13#12112yes—
114C2×Dic13—24no—
115C2×Dic13—48no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—82no—
122C2×Dic13—82no—
123#1055—82no—
124C22×C4⋊C4—131no—
125C22×C4⋊C4—261no—
126C22×C4⋊C4C2×D1311yescharacteristic
127C2×C22⋊C8—132no—
128#398—134no—
129#398—262no—
130#387—24no—
131#381—21no—
132#380C2×D1312yes—
133C4×C22⋊C4—21no—
134C2×#95—131no—
135C2×#95—261no—
136#340—264no—
137#324—262no—
138C22×C13—24no—
139C22×C13—24no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13#38611yescharacteristic
145C22×C13#41611yescharacteristic
146C22×C13#41811yescharacteristic
147C22×C13#44912yes—
148C22×C13#45612yes—
149C22×C13#45812yes—
150C22×C13#48212yes—
151C4×C13—22no—
152C4×C13—22no—
153C4×C13—42no—
154C4×C13—42no—
155C4×C13—84no—
156Dic13—44no—
157Dic13—82no—
158C23×C4—261no—
159C23×C4—261no—
160C23×C4C22⋊D1311yescharacteristic
161C23×C4C22⋊D1311yescharacteristic
162C23×C4C22×D1311yescharacteristic
163C22×C8—262no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—132no—
167C2×C4⋊C4—262no—
168C2×C4⋊C4—262no—
169C2×C4⋊C4—264no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4—524no—
172C2×C4⋊C4C4×D1312yes—
173C2×C4⋊C4D5212yes—
174C2×C4⋊C4C22⋊D1314yes—
175C2×C22⋊C4—22no—
176C2×C42—22no—
177C22⋊C8—262no—
178C22⋊C8—262no—
179#95—22no—
180#95—24no—
181#95—22no—
182#95—132no—
183#95—264no—
184#95—261no—
185C2×C13—21no—
186C2×C13—21no—
187C2×C13—22no—
188C2×C13#160914yes—
189C2×C13#187511yescharacteristic
190C2×C13#188611yescharacteristic
191C2×C13#189011yescharacteristic
192C24C2×C22⋊D1311yescharacteristic
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—24no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—264no—
203C22×C4—262no—
204C22×C4—262no—
205C22×C4—522no—
206C22×C4—522no—
207C22×C4—521no—
208C22×C4—522no—
209C22×C4—522no—
210C22×C4—521no—
211C22×C4#610312yes—
212C22×C4#610312yes—
213C22×C4C2×C4×D1311yescharacteristic
214C22×C4C2×D5211yescharacteristic
215C22×C4#612712yes—
216C22×C4C2×C22⋊D1312yes—
217C2×C8—524no—
218C2×C8—522no—
219C4⋊C4—24no—
220C4⋊C4—24no—
221C4⋊C4—44no—
222C4⋊C4—264no—
223C4⋊C4—528no—
224C4⋊C4—522no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C42—82no—
228C13#902611yescharacteristic, complemented, Sylow
229C23—22no—
230C23—22no—
231C23C2×#610311yescharacteristic
232C23#8818311yescharacteristic
233C23#8820312yes—
234C23#8820412yes—
235C23#8820711yescharacteristic
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—44no—
249C2×C4—44no—
250C2×C4—44no—
251C2×C4—81no—
252C2×C4—264no—
253C2×C4—522no—
254C2×C4—528no—
255C2×C4—522no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—522no—
259C2×C4—1042no—
260C2×C4—1042no—
261C2×C4C4×C22⋊D1312yes—
262C2×C4#8818412yes—
263C8—1042no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—24no—
269C22—24no—
270C22#1171866211yescharacteristic
271C22#1171866311yescharacteristic
272C22#1171866412yes—
273C22#1171887411yescharacteristic
274C22#1171889912yes—
275C22#1171890412yes—
276C22#1171890712yes—
277C4—22no—
278C4—22no—
279C4—42no—
280C4—42no—
281C4—84no—
282C4—524no—
283C4—1042no—
284C2—21no—
285C2—21no—
286C2—22no—
287C2#1311383314yes—
288C2#1311515811yescharacteristic
289C2#1311522911yescharacteristic
290C2#1311524911yescharacteristic
subgroupG/H
centerC23#88207
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2313C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2313D13
hypocenterC13#9026
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
17. #11718644C4semidirect
228. C13#9026semidirect

Maximal subgroups

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

subgroupindex
C2×#117186442
#131149202
C2×#117181202
#131127142
C13×#23132
#902613