Finite Group Databasebeta

← #15760879

Subgroups — #15760879

Order 3328.

544 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 111 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#13123865C211yesmaximal, characteristic
2#13114916C212yesmaximal, complemented
3#13113174C211yesmaximal, characteristic
4#13112742C212yesmaximal, complemented
5C13×#2486C211yesmaximal, characteristic
6C2×C13×#123C412yes—
7C2×C4×D4×C13C2211yescharacteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C13×#398—21no—
10C13×#397—21no—
11C13×#389—21no—
12C13×#381C412yes—
13C13×#380—21no—
14C13×#380C2211yescharacteristic
15#11718868C2212yes—
16#11718868C2212yes—
17C2×C22⋊#1055—21no—
18#11718672—24no—
19#11718587—21no—
20#11718122—24no—
21#11718120—21no—
22#11718117—21no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C412yes—
25C23×C4×C13D411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C13×#123—44no—
28C4×D4×C13—22no—
29C4×D4×C13—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4C2×C412yes—
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×#6099—22no—
43C2×#6099D414yes—
44C22×#1055—22no—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95—21no—
48C22⋊#1055—22no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53C4⋊#1055—22no—
54#88043—22no—
55#9507—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C22×C411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—41no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—24no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C2×D412yes—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4112yes—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—44no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—41no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—44no—
86C13×C22⋊C4—42no—
87C42×C13—21no—
88C42×C13—21no—
89#6099—44no—
90#6099—44no—
91C2×#1055—24no—
92C2×#1055—42no—
93C2×#1055—82no—
94#2973—131no—
95#2486D1311yescharacteristic
96#1821—132no—
97#1465—131no—
98#1305—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13#10012yes—
108C23×C13C2×C22⋊C411yescharacteristic
109C23×C13C4×D412yes—
110D4×C13—44no—
111C2×C4×C13—24no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—81no—
130C2×C4×C13—84no—
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12112yes—
133C2×C4×C13#12311yescharacteristic
134#1055—44no—
135#1055—82no—
136C2×#123Dic1312yes—
137C2×C4×D4C2×D1311yescharacteristic
138C22×C4⋊C4C2×D1311yescharacteristic
139#435—264no—
140#432—261no—
141#407—132no—
142#407—132no—
143C2×C22⋊C8—261no—
144#398—21no—
145#397—21no—
146#389—21no—
147#381Dic1312yes—
148#380—21no—
149#380C2×D1311yescharacteristic
150#343—264no—
151#324—261no—
152#323—261no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—42no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—81no—
165C22×C13#38611yescharacteristic
166C22×C13C2×#10011yescharacteristic
167C22×C13#41311yescharacteristic
168C4×C13—22no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—82no—
174C4×C13—82no—
175C4×C13#45812yes—
176C22×D4C2×Dic1311yescharacteristic
177C23×C4C2×Dic1312yes—
178C23×C4C22⋊D1311yescharacteristic
179C23×C4C22×D1311yescharacteristic
180C2×M16—134no—
181C2×M16—262no—
182C22×C8—262no—
183#123—44no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C22⋊D1311yescharacteristic
193C2×C22⋊C4—22no—
194C2×C22⋊C4C2×Dic1311yescharacteristic
195C2×C22⋊C4C2×Dic1312yes—
196C2×C22⋊C4C22⋊D1311yescharacteristic
197C2×C42C22⋊D1311yescharacteristic
198C4⋊C8—262no—
199C22⋊C8—262no—
200C22⋊C8—262no—
201C22⋊C8—262no—
202C22⋊C8—262no—
203C22⋊C8—262no—
204#97—262no—
205#95—22no—
206#95—22no—
207#95—21no—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—42no—
211C2×C13—42no—
212C2×C13#189011yescharacteristic
213C2×C13#190011yescharacteristic
214C2×C13#191511yescharacteristic
215C24C22⋊Dic1311yescharacteristic
216C24C22×Dic1311yescharacteristic
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—41no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4C22⋊Dic1311yescharacteristic
230C22×C4C22⋊Dic1311yescharacteristic
231C22×C4C22⋊Dic1311yescharacteristic
232C22×C4D4×D1312yes—
233C22×C4#612912yes—
234C22×C4C2×C22⋊D1311yescharacteristic
235C22×C4C2×C22⋊D1311yescharacteristic
236M16—524no—
237M16—524no—
238C2×C8—264no—
239C2×C8—522no—
240C2×C8—1042no—
241C4⋊C4—22no—
242C4⋊C4—44no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—44no—
250C22⋊C4—42no—
251C42—21no—
252C42—21no—
253C13#950711yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23#8807312yes—
263C23D4×Dic1312yes—
264C23C2×C22⋊Dic1311yescharacteristic
265D4—44no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—84no—
286C2×C4#8818911yescharacteristic
287C2×C4#8819111yescharacteristic
288C2×C4#8819312yes—
289C8—524no—
290C8—1042no—
291C22—21no—
292C22—21no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#8807311yescharacteristic
304C22#1171888111yescharacteristic
305C22#1171889811yescharacteristic
306C4—22no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4#1171871412yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—42no—
318C2#1311525011yescharacteristic
319C2#1311530011yescharacteristic
320C2#1311538911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2486C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#2486D13
hypocenterC13#9507
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. #13114916C2semidirect
4. #13112742C2semidirect
253. C13#9507semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131149162
#131131742
#131127422
C13×#24862
#950713