Finite Group Databasebeta

← #15773605

Subgroups — #15773605

Order 3328.

478 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 95 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#13114916C211yesmaximal, characteristic
2#13113166C211yesmaximal, characteristic
3#13112842C214yesmaximal, complemented
4C2×C13×#398C211yesmaximal, characteristic
5C22×C13×C4⋊C4—21no—
6C22×C13×C4⋊C4C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#398—21no—
9C13×#398—21no—
10C13×#398C412yes—
11C13×#398C2212yes—
12C2×C13×#95—21no—
13C2×C13×#95C411yescharacteristic
14#11718868—21no—
15#11718868—21no—
16#11718122—21no—
17#11718122C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C23×C4×C13—21no—
21C23×C4×C13—21no—
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—41no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4—44no—
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4C2311yescharacteristic
38C2×#6099—22no—
39C2×#6099—41no—
40C13×#95—21no—
41C13×#95—22no—
42C13×#95—22no—
43C13×#95C2×C412yes—
44C22⋊#1055—22no—
45C22⋊#1055—41no—
46C22⋊#1055—41no—
47C22⋊#1055—41no—
48#11803—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C22×C4×C13—24no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—41no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—44no—
82C13×C4⋊C4—44no—
83#6099—42no—
84#6099—42no—
85#6099—82no—
86C2×#1055—42no—
87C2×#1055—42no—
88C2×#398D1311yescharacteristic
89#1821—131no—
90#1463—131no—
91#1346—134no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13#9911yescharacteristic
97C23×C13#9911yescharacteristic
98C23×C13C2×C22⋊C411yescharacteristic
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—24no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—48no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—81no—
125C2×C4×C13—82no—
126C2×C4×C13—82no—
127C2×C4×C13AGL(1,ℤ/8)12yes—
128#1055—82no—
129#1055—82no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4Dic1311yescharacteristic
132C22×C4⋊C4C2×D1311yescharacteristic
133#407—261no—
134#407—261no—
135#398—21no—
136#398—21no—
137#398Dic1312yes—
138#398C2×D1312yes—
139C2×#95—21no—
140C2×#95Dic1311yescharacteristic
141#343—132no—
142#343—261no—
143#324—132no—
144#324—261no—
145C22×C13—24no—
146C22×C13—24no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13#35212yes—
154C22×C13#35612yes—
155C22×C13C2×#9911yescharacteristic
156C22×C13#41811yescharacteristic
157C22×C13#42111yescharacteristic
158C4×C13—22no—
159C4×C13—44no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—82no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4C2×Dic1311yescharacteristic
169C23×C4C22⋊D1311yescharacteristic
170C23×C4C22⋊D1311yescharacteristic
171C2×M16—262no—
172C2×M16—521no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4C2×Dic1312yes—
182C2×C4⋊C4C2×Dic1311yescharacteristic
183C2×C4⋊C4C22⋊D1311yescharacteristic
184C2×C4⋊C4C22⋊D1311yescharacteristic
185C2×C4⋊C4C22×D1311yescharacteristic
186C22⋊C8—262no—
187C22⋊C8—521no—
188C22⋊C8—521no—
189C22⋊C8—521no—
190#95—22no—
191#95—21no—
192#95—22no—
193#95C2×Dic1312yes—
194C2×C13—21no—
195C2×C13—22no—
196C2×C13—22no—
197C2×C13—21no—
198C2×C13#151011yescharacteristic
199C2×C13C2×#35211yescharacteristic
200C2×C13C2×#35611yescharacteristic
201C24C22⋊Dic1311yescharacteristic
202C22×C4—24no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—41no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4C22⋊Dic1311yescharacteristic
222C22×C4C22⋊Dic1311yescharacteristic
223C22×C4C22⋊Dic1311yescharacteristic
224C22×C4C22×Dic1311yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226C22×C4C2×C22⋊D1311yescharacteristic
227M16—522no—
228M16—522no—
229M16—1042no—
230C2×C8—522no—
231C2×C8—522no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—44no—
238C4⋊C4—42no—
239C4⋊C4—44no—
240C13#1180311yescharacteristic, complemented, Sylow
241C23—21no—
242C23—21no—
243C23—22no—
244C23—22no—
245C23#8807411yescharacteristic
246C23#8807411yescharacteristic
247C23C2×C22⋊Dic1311yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—24no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—48no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4#8818612yes—
277C8—1042no—
278C8—1042no—
279C22—24no—
280C22—24no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22#1171813112yes—
288C22#1171814012yes—
289C22#1171887611yescharacteristic
290C22C2×#8807411yescharacteristic
291C22#1171889711yescharacteristic
292C4—22no—
293C4—44no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—82no—
300C2—21no—
301C2—21no—
302C2—22no—
303C2—22no—
304C2#1311336511yescharacteristic
305C2C2×#1171813111yescharacteristic
306C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#398C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#398D13
hypocenterC13#11803
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #13112842C2semidirect
240. C13#11803semidirect

Maximal subgroups

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

subgroupindex
#131149162
#131131662
#131128422
C2×C13×#3982
#1180313