Finite Group Databasebeta

← #15757951

Subgroups — #15757951

Order 3328.

572 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 127 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×#11718647C211yesmaximal, characteristic
2#13117439C211yesmaximal, characteristic
3#13114927C212yesmaximal
4#13112716C212yesmaximal
5C2×C13×#324C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8C2×C13×C22⋊C8C2212yes—
9#11718873C2212yes—
10#11718872—21no—
11C4×C22⋊Dic13—21no—
12C2×#88071—21no—
13C2×#88071—21no—
14C2×#88071C2211yescharacteristic
15#11718647—22no—
16#11718647C414yescomplemented
17#11718642—24no—
18C13×#324—22no—
19#11718143—24no—
20C23×C4×C13D411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C22×C8×C13—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C4⋊C4D412yes—
30C2×C22⋊Dic13—22no—
31C2×C4⋊Dic13—22no—
32C2×C4⋊Dic13—22no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C412yes—
35C2×C4⋊Dic13D414yes—
36C2×C4×Dic13—22no—
37C13×C22⋊C8—22no—
38C13×C22⋊C8—22no—
39#88071—22no—
40#88071—24no—
41#88071—24no—
42#88071—24no—
43#88071—21no—
44#88071—22no—
45#88071C2×C412yes—
46#9022—131nomaximal, Sylow
47C24×C13C2×D411yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—21no—
54C22×C4×C13—42no—
55C22×C4×C13—42no—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22⋊C412yes—
58C22×C4×C13C22×C411yescharacteristic
59C22×C4×C13C2×D412yes—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13#4112yes—
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—24no—
65C22×Dic13—42no—
66C22×Dic13—42no—
67C22×Dic13—44no—
68C22×Dic13—41no—
69C22×Dic13—41no—
70C22×Dic13—42no—
71C2×C8×C13—44no—
72C2×C8×C13—42no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—24no—
75C22⋊Dic13—42no—
76C22⋊Dic13—42no—
77C4⋊Dic13—24no—
78C4⋊Dic13—42no—
79C4⋊Dic13—44no—
80C4×Dic13—82no—
81C2×#400—131no—
82#2313—131no—
83#1824—132no—
84C2×#324D1311yescharacteristic
85#1294—132no—
86C23×C13—22no—
87C23×C13—22no—
88C23×C13C2×C22⋊C411yescharacteristic
89C23×C13#12011yescharacteristic
90C23×C13#12311yescharacteristic
91C23×C13#13512yes—
92C23×C13#13712yes—
93C2×C4×C13—24no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—81no—
106C2×C4×C13C4×D412yes—
107C2×C4×C13#12112yes—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—44no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—44no—
114C2×Dic13—44no—
115C2×Dic13—44no—
116C2×Dic13—84no—
117C2×Dic13—82no—
118C2×Dic13—82no—
119C8×C13—82no—
120C22×C4⋊C4—131no—
121C22×C4⋊C4C2×D1311yescharacteristic
122C2×C22⋊C8C2×D1312yes—
123#400—134no—
124#400—262no—
125#387—264no—
126#381—261no—
127#380—132no—
128C4×C22⋊C4—261no—
129C2×#95—131no—
130C2×#95—261no—
131C2×#95—261no—
132#340—264no—
133#324—22no—
134C22×C13—24no—
135C22×C13—24no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13#38611yescharacteristic
141C22×C13#41611yescharacteristic
142C22×C13#41911yescharacteristic
143C22×C13#45212yes—
144C22×C13#45412yes—
145C22×C13#45812yes—
146C22×C13#48512yes—
147C4×C13—22no—
148C4×C13—22no—
149C4×C13—42no—
150C4×C13—42no—
151Dic13—82no—
152Dic13—84no—
153Dic13—82no—
154C23×C4—261no—
155C23×C4—261no—
156C23×C4D5211yescharacteristic
157C23×C4D5211yescharacteristic
158C23×C4C22×D1311yescharacteristic
159C22×C8—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—134no—
164C2×C4⋊C4—262no—
165C2×C4⋊C4—262no—
166C2×C4⋊C4—261no—
167C2×C4⋊C4C4×D1312yes—
168C2×C4⋊C4C22⋊D1312yes—
169C2×C22⋊C4—262no—
170C2×C42—262no—
171C22⋊C8—22no—
172C22⋊C8—22no—
173#95—132no—
174#95—262no—
175#95—264no—
176#95—264no—
177#95—264no—
178#95—262no—
179#95—261no—
180C2×C13—21no—
181C2×C13—21no—
182C2×C13—22no—
183C2×C13#161514yes—
184C2×C13#187311yescharacteristic
185C2×C13#188811yescharacteristic
186C2×C13#189011yescharacteristic
187C24C2×D5211yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—21no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—264no—
197C22×C4—262no—
198C22×C4—262no—
199C22×C4—522no—
200C22×C4—522no—
201C22×C4—524no—
202C22×C4—521no—
203C22×C4—521no—
204C22×C4—522no—
205C22×C4#610312yes—
206C22×C4#610312yes—
207C22×C4C2×C4×D1311yescharacteristic
208C22×C4D4×D1312yes—
209C22×C4#612912yes—
210C22×C4C2×C22⋊D1311yescharacteristic
211C2×C8—44no—
212C2×C8—42no—
213C4⋊C4—24no—
214C4⋊C4—24no—
215C4⋊C4—264no—
216C4⋊C4—524no—
217C4⋊C4—522no—
218C22⋊C4—522no—
219C22⋊C4—522no—
220C42—1042no—
221C13#902211yescharacteristic, complemented, Sylow
222C23—22no—
223C23—22no—
224C23#8813611yescharacteristic
225C23#8814011yescharacteristic
226C23#8815812yes—
227C23#8816312yes—
228C23C2×#610311yescharacteristic
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—81no—
242C2×C4—522no—
243C2×C4—522no—
244C2×C4—524no—
245C2×C4—524no—
246C2×C4—524no—
247C2×C4—522no—
248C2×C4—522no—
249C2×C4—524no—
250C2×C4—1044no—
251C2×C4—1042no—
252C2×C4—1042no—
253C2×C4#8813512yes—
254C2×C4#8819312yes—
255C8—82no—
256C22—24no—
257C22—24no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22#1171838412yes—
263C22#1171839412yes—
264C22#1171840312yes—
265C22#1171841412yes—
266C22#1171861911yescharacteristic
267C22#1171877411yescharacteristic
268C22#1171878111yescharacteristic
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—1042no—
274C4—1044no—
275C4—1042no—
276C2—21no—
277C2—21no—
278C2—22no—
279C2#1311386914yes—
280C2#1311514611yescharacteristic
281C2#1311523711yescharacteristic
282C2#1311524711yescharacteristic
subgroupG/H
centerC23#88136
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#324C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#324D13
hypocenterC13#9022
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
16. #11718647C4semidirect
221. C13#9022semidirect

Maximal subgroups

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

subgroupindex
C2×#117186472
#131174392
#131149272
#131127162
C2×C13×#3242
#902213