Finite Group Databasebeta

← #15872394

Subgroups — #15872394

Order 3328.

914 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 235 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×#11719205C211yesmaximal, characteristic
2#13123471C212yesmaximal
3#13115827C214yesmaximal, complemented
4#13115823C214yesmaximal, complemented
5#13114917C212yesmaximal
6#13114916C211yesmaximal, characteristic
7C13×#1821C211yesmaximal, characteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C2×#88180C2211yescharacteristic
10C2×#88180C2211yescharacteristic
11C2×#88178C414yes—
12#11719205—28no—
13C2×#88144C412yes—
14C2×#88144C2212yes—
15C2×#88142C412yes—
16C2×#88142C2212yes—
17C13×#407C2212yes—
18#11718868C2212yes—
19#11718779C2214yes—
20M16×Dic13C2214yes—
21#11718381—28no—
22C13×#343C2214yes—
23#11718146C2214yes—
24#11718146C2214yes—
25#11718122C2214yes—
26C23×C4×C13C2×C412yes—
27C23×C4×C13C2311yescharacteristic
28C22×Dic26C2×C414yes—
29C2×C13×M16C2314yes—
30C2×C13×C4⋊C4—24no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4C2312yes—
33C2×C22⋊Dic13C2×C412yes—
34C2×C22⋊Dic13C2×C412yes—
35#88180—24no—
36#88180D418yes—
37C2×C4⋊Dic13C2×C414yes—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2311yescharacteristic
41C2×C4⋊Dic13C2311yescharacteristic
42#88178—216no—
43C2×#6101C2×C414yes—
44C2×#6101C2×C414yes—
45C2×C4×Dic13C2×C412yes—
46C2×C4×Dic13C2312yes—
47C2×#6099C2314yes—
48#88144—28no—
49#88144—24no—
50#88144—24no—
51#88142—28no—
52#88142—24no—
53#88142—24no—
54C13×C22⋊C8—24no—
55C22⋊#1055—24no—
56#88055—24no—
57#88054—28no—
58C8×Dic13—24no—
59#21832—131nomaximal, Sylow
60C24×C13C22×C411yescharacteristic
61C22×C4×C13—24no—
62C22×C4×C13—24no—
63C22×C4×C13—82no—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C22×C414yes—
66C22×C4×C13C2×D414yes—
67C22×C4×C13C2411yescharacteristic
68C22×Dic13C22×C412yes—
69C22×Dic13C22×C412yes—
70C22×Dic13C22×C412yes—
71C22×Dic13C22×C412yes—
72C2×Dic26—28no—
73C2×Dic26—84no—
74C13×M16—28no—
75C2×C8×C13—24no—
76C13×C4⋊C4—24no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C22⋊Dic13—24no—
80C22⋊Dic13C22⋊C418yes—
81C4⋊Dic13—22no—
82C4⋊Dic13—22no—
83C4⋊Dic13—28no—
84C4⋊Dic13C22⋊C414yes—
85C4⋊Dic13C22⋊C414yes—
86#6101—28no—
87#6101—28no—
88C4×Dic13—24no—
89C4×Dic13C2×D414yes—
90C4×Dic13C2×D414yes—
91#6099—28no—
92C2×#1055—24no—
93C2×#544—131no—
94#2921—132no—
95#1998—134no—
96#1997—134no—
97#1822—132no—
98#1821—131no—
99#1821D1311yescharacteristic
100C23×C13—22no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13C2×C22⋊C412yes—
104C23×C13C23×C411yescharacteristic
105C2×C4×C13—22no—
106C2×C4×C13—28no—
107C2×C4×C13—24no—
108C2×C4×C13—44no—
109C2×C4×C13—84no—
110C2×C4×C13C2×C22⋊C412yes—
111C2×C4×C13C22×D412yes—
112C2×C4×C132−1+414yes—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13C2×C22⋊C414yes—
120C2×Dic13C2×C22⋊C414yes—
121Dic26—88no—
122C8×C13—44no—
123#1055—44no—
124#544—268no—
125C2×C4⋊Q8—132no—
126C2×C4⋊Q8—132no—
127C2×#125—132no—
128C2×#125—132no—
129C2×C22⋊Q8—134no—
130C2×#117—131no—
131C2×#117—131no—
132C22×C4⋊C4C2×D1311yescharacteristic
133#433—268no—
134#423—134no—
135#407—132no—
136#407C2×D1312yes—
137C4×M16—134no—
138#343—134no—
139#343—134no—
140#343—134no—
141#343C2×D1314yes—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—22no—
145C22×C13—22no—
146C22×C13—22no—
147C22×C13—44no—
148C22×C13C22×C22⋊C411yescharacteristic
149C22×C13#51912yes—
150C4×C13—22no—
151C4×C13—44no—
152C4×C13#53614yes—
153Dic13—24no—
154Dic13—24no—
155Dic13—42no—
156Dic13—42no—
157C22×Q8—134no—
158C23×C4C4×D1312yes—
159C23×C4C22×D1311yescharacteristic
160C2×M16—134no—
161C2×M16C22×D1314yes—
162C4⋊Q8—264no—
163C4⋊Q8—264no—
164C4⋊Q8—268no—
165#125—264no—
166#125—264no—
167#125—268no—
168C22⋊Q8—2616no—
169#117—138no—
170#117—264no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—134no—
175C2×C4⋊C4—134no—
176C2×C4⋊C4—134no—
177C2×C4⋊C4—131no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4C4×D1312yes—
180C2×C4⋊C4C22×D1312yes—
181C2×C22⋊C4—132no—
182C2×C22⋊C4—132no—
183C2×C42—132no—
184C2×C42—132no—
185C4⋊C8—268no—
186C22⋊C8—24no—
187C22⋊C8—264no—
188#97—264no—
189C4×C8—264no—
190C2×C13—22no—
191C2×C13—42no—
192C2×C13#231011yescharacteristic
193C2×C13#288811yescharacteristic
194C2×C13#288911yescharacteristic
195C24C2×C4×D1311yescharacteristic
196C2×Q8—268no—
197C2×Q8—1044no—
198C22×C4—24no—
199C22×C4—24no—
200C22×C4—82no—
201C22×C4—132no—
202C22×C4—132no—
203C22×C4—132no—
204C22×C4—132no—
205C22×C4C2×C4×D1311yescharacteristic
206C22×C4C2×C4×D1314yes—
207C22×C4D4×D1314yes—
208C22×C4C23×D1311yescharacteristic
209M16—28no—
210M16—268no—
211C2×C8—24no—
212C2×C8—264no—
213C4⋊C4—24no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—134no—
217C4⋊C4—134no—
218C4⋊C4—268no—
219C4⋊C4—268no—
220C4⋊C4—268no—
221C4⋊C4—262no—
222C4⋊C4—262no—
223C22⋊C4—138no—
224C22⋊C4—264no—
225C42—134no—
226C42—134no—
227C42—264no—
228C13#2183211yescharacteristic, complemented, Sylow
229C23—22no—
230C23—41no—
231C23—41no—
232C23C22⋊C4×D1312yes—
233C23C22×C4×D1311yescharacteristic
234Q8—1048no—
235C2×C4—22no—
236C2×C4—28no—
237C2×C4—24no—
238C2×C4—44no—
239C2×C4—84no—
240C2×C4—134no—
241C2×C4—134no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4—522no—
248C2×C4C22⋊C4×D1312yes—
249C2×C4C2×D4×D1312yes—
250C2×C4#8825714yes—
251C8—44no—
252C8—524no—
253C22—21no—
254C22—21no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—44no—
259C22C2×C22⋊C4×D1311yescharacteristic
260C22#1171922112yes—
261C4—22no—
262C4—44no—
263C4—264no—
264C4—264no—
265C4—522no—
266C4—522no—
267C4#1171935314yes—
268C2—22no—
269C2—42no—
270C2#1311742111yescharacteristic
271C2#1312331211yescharacteristic
272C2#1312331611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1821C2
socleC22×C13C22×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenter#1821D13
hypocenterC13#21832
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #13115827C2semidirect
4. #13115823C2semidirect
228. C13#21832semidirect

Maximal subgroups

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

subgroupindex
C2×#117192052
#131234712
#131158272
#131158232
#131149172
#131149162
C13×#18212
#2183213