Finite Group Databasebeta

← #15770785

Subgroups — #15770785

Order 3328.

1042 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 1042 conjugacy classes of subgroups — too many to draw. Only its 227 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×#11718868C212yesmaximal
2C2×#11718122C214yesmaximal, complemented
3C2×C13×#380C211yesmaximal, characteristic
4C24×C4×C13C2211yescharacteristic
5C22×C13×C4⋊C4C2212yes—
6C22×C13×C22⋊C4C412yes—
7C22×#6099C2214yes—
8C13×#380—22no—
9C13×#380—22no—
10C2×C13×#95C412yes—
11#11718868—28no—
12C2×C22⋊#1055—22no—
13C2×C22⋊#1055—22no—
14#11718122—28no—
15C25×C13C2×C411yescharacteristic
16C23×C4×C13—24no—
17C23×C4×C13—24no—
18C23×C4×C13—24no—
19C23×C4×C13C2×C411yescharacteristic
20C23×C4×C13C2×C414yes—
21C23×C4×C13D412yes—
22C23×C4×C13D412yes—
23C23×C4×C13C2311yescharacteristic
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—24no—
27C2×C13×C4⋊C4—24no—
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—44no—
31C2×#6099—24no—
32C2×#6099—24no—
33C2×#6099—24no—
34C2×#6099—24no—
35C2×#6099—24no—
36C2×#6099D418yes—
37C22×#1055—24no—
38C13×#95—24no—
39C22⋊#1055—28no—
40C22⋊#1055—28no—
41#11198—131nomaximal, Sylow
42C24×C13—22no—
43C24×C13—22no—
44C24×C13—22no—
45C24×C13—24no—
46C24×C13—42no—
47C24×C13C22⋊C411yescharacteristic
48C24×C13C22⋊C411yescharacteristic
49C24×C13C22×C411yescharacteristic
50C22×C4×C13—22no—
51C22×C4×C13—24no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—24no—
55C22×C4×C13—24no—
56C22×C4×C13—24no—
57C22×C4×C13—24no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—24no—
61C22×C4×C13—28no—
62C22×C4×C13—44no—
63C22×C4×C13—44no—
64C22×C4×C13—44no—
65C22×C4×C13—44no—
66C22×C4×C13—44no—
67C22×C4×C13—44no—
68C22×C4×C13C22⋊C412yes—
69C22×C4×C13C2×D414yes—
70C22×C4×C13C2×D412yes—
71C22×C4×C13#4114yes—
72C22×C4×C13#4114yes—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—44no—
75C13×C4⋊C4—42no—
76C13×C22⋊C4—44no—
77C13×C22⋊C4—44no—
78#6099—28no—
79#6099—28no—
80#6099—44no—
81#6099—44no—
82C2×#1055—28no—
83C2×#1055—44no—
84C2×#1055—44no—
85C2×#407—132no—
86C2×#380D1311yescharacteristic
87C2×#343—134no—
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—22no—
91C23×C13—28no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—22no—
95C23×C13—22no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—48no—
101C23×C13—48no—
102C23×C13—44no—
103C23×C13—44no—
104C23×C13#10012yes—
105C23×C13#10112yes—
106C23×C13C2×C22⋊C411yescharacteristic
107C23×C13#11712yes—
108C23×C13C4×D414yes—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—44no—
113C2×C4×C13—44no—
114C2×C4×C13—44no—
115C2×C4×C13—44no—
116C2×C4×C13—44no—
117C2×C4×C13—44no—
118C2×C4×C13—44no—
119C2×C4×C13—44no—
120C2×C4×C13—88no—
121C2×C4×C13#12012yes—
122C2×C4×C13#12114yes—
123C2×C4×C13#12114yes—
124C2×C4×C13#12314yes—
125C2×C4×C13#12314yes—
126C2×C4×C13#12312yes—
127C2×C4×C13#12414yes—
128C2×C4×C13#12614yes—
129#1055—48no—
130C24×C4C2×D1311yescharacteristic
131C22×M16—134no—
132C22×C4⋊C4C2×D1312yes—
133C22×C22⋊C4Dic1312yes—
134#407—268no—
135C2×C22⋊C8—262no—
136C2×C22⋊C8—262no—
137#380—22no—
138#380—22no—
139C2×#95Dic1312yes—
140#343—268no—
141C22×C13—22no—
142C22×C13—22no—
143C22×C13—24no—
144C22×C13—24no—
145C22×C13—22no—
146C22×C13—22no—
147C22×C13—24no—
148C22×C13—24no—
149C22×C13—416no—
150C22×C13—41no—
151C22×C13—41no—
152C22×C13—42no—
153C22×C13—42no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13#38111yescharacteristic
157C22×C13#38612yes—
158C22×C13#38814yes—
159C22×C13C2×#10011yescharacteristic
160C22×C13C2×#10111yescharacteristic
161C22×C13#41312yes—
162C4×C13—42no—
163C4×C13—84no—
164C4×C13#39414yes—
165C4×C13#39714yes—
166C25C2×Dic1311yescharacteristic
167C23×C4—24no—
168C23×C4—24no—
169C23×C4—24no—
170C23×C4C2×Dic1311yescharacteristic
171C23×C4C2×Dic1314yes—
172C23×C4C22⋊D1312yes—
173C23×C4C22⋊D1312yes—
174C23×C4C22×D1311yescharacteristic
175C2×M16—138no—
176C2×M16—264no—
177C2×M16—264no—
178C2×M16—264no—
179C2×M16—264no—
180C2×M16—264no—
181C22×C8—264no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—44no—
189C22⋊C8—268no—
190C22⋊C8—268no—
191#95—24no—
192C2×C13—24no—
193C2×C13—42no—
194C2×C13—42no—
195C2×C13#144011yescharacteristic
196C2×C13#182111yescharacteristic
197C2×C13#182211yescharacteristic
198C2×C13#190012yes—
199C2×C13#190112yes—
200C24—22no—
201C24—22no—
202C24—22no—
203C24—24no—
204C24—42no—
205C24C22⋊Dic1311yescharacteristic
206C24C22⋊Dic1311yescharacteristic
207C24C22×Dic1311yescharacteristic
208C22×C4—22no—
209C22×C4—24no—
210C22×C4—24no—
211C22×C4—24no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—28no—
220C22×C4—44no—
221C22×C4—44no—
222C22×C4—44no—
223C22×C4—44no—
224C22×C4—44no—
225C22×C4—44no—
226C22×C4C22⋊Dic1312yes—
227C22×C4#612714yes—
228C22×C4D4×D1314yes—
229C22×C4#612914yes—
230C22×C4C2×C22⋊D1312yes—
231M16—268no—
232M16—268no—
233M16—524no—
234M16—524no—
235C2×C8—268no—
236C2×C8—524no—
237C2×C8—524no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—44no—
241C22⋊C4—44no—
242C22⋊C4—44no—
243C13#1119811yescharacteristic, complemented, Sylow
244C23—21no—
245C23—21no—
246C23—22no—
247C23—28no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—22no—
252C23—22no—
253C23—21no—
254C23—22no—
255C23—22no—
256C23—48no—
257C23—48no—
258C23—44no—
259C23—44no—
260C23#8807312yes—
261C23#8807612yes—
262C23#8818012yes—
263C23D4×Dic1314yes—
264C23C2×C22⋊Dic1311yescharacteristic
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—88no—
277C2×C4#8813314yes—
278C2×C4#8813714yes—
279C2×C4#8813814yes—
280C2×C4#8813914yes—
281C2×C4#8818314yes—
282C2×C4#8818912yes—
283C2×C4#8819112yes—
284C2×C4#8819314yes—
285C8—528no—
286C22—22no—
287C22—22no—
288C22—24no—
289C22—24no—
290C22—22no—
291C22—22no—
292C22—24no—
293C22—24no—
294C22—416no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#1171861214yes—
302C22#1171887211yescharacteristic
303C22C2×#8807311yescharacteristic
304C22#1171888112yes—
305C22C2×#8807611yescharacteristic
306C22#1171889812yes—
307C4—42no—
308C4—84no—
309C4#1171861314yes—
310C4#1171862014yes—
311C2—24no—
312C2—42no—
313C2—42no—
314C2#1311308511yescharacteristic
315C2#1311491611yescharacteristic
316C2#1311491911yescharacteristic
317C2#1311530012yes—
318C2#1311530512yes—
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#380C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenterC2×#380D13
hypocenterC13#11198
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#11718122C2semidirect
243. C13#11198semidirect

Maximal subgroups

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

subgroupindex
C2×#117188682
C2×#117181222
C2×C13×#3802
#1119813