Finite Group Databasebeta

← #15773506

Subgroups — #15773506

Order 3328.

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

normal subgroups only

This group has 464 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
1C4×#88073C211yesmaximal, characteristic
2#13113174C211yesmaximal, characteristic
3#13112842C214yesmaximal, complemented
4C13×#2486C211yesmaximal, characteristic
5C2×C13×#123—21no—
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic
8C13×#398C2212yes—
9C13×#397C412yes—
10C13×#389—21no—
11C13×#381—21no—
12C13×#380—21no—
13C13×#380C411yescharacteristic
14C2×#88073—21no—
15#11718868—21no—
16C4×#6099—21no—
17#11718122C2212yes—
18#11718120C2212yes—
19#11718117—21no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C13×#123—44no—
25C4×D4×C13—41no—
26C4×D4×C13—41no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×#6099—22no—
40C2×#6099—41no—
41C13×#95—22no—
42C13×#95—22no—
43C13×#95C2×C412yes—
44#88073—24no—
45C22⋊#1055—22no—
46C22⋊#1055—41no—
47#88043—41no—
48C4×#1055—41no—
49#11780—131nomaximal, Sylow
50C24×C13C22⋊C411yescharacteristic
51C24×C13C22⋊C411yescharacteristic
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—44no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—44no—
81C42×C13—21no—
82C42×C13—21no—
83#6099—24no—
84#6099—42no—
85#6099—82no—
86C2×#1055—42no—
87C2×#1055—42no—
88#2486D1311yescharacteristic
89C4×#100—131no—
90#1465—131no—
91#1346—134no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13#10412yes—
102C23×C13C2×C22⋊C411yescharacteristic
103D4×C13—44no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—81no—
123C2×C4×C13—84no—
124C2×C4×C13#9911yescharacteristic
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13AGL(1,ℤ/8)12yes—
127#1055—44no—
128#1055—82no—
129C2×#123—21no—
130C2×C4×D4C2×D1311yescharacteristic
131C22×C4⋊C4Dic1311yescharacteristic
132C2×#100—261no—
133#407—261no—
134C4×M16—261no—
135#398C2×D1312yes—
136#397Dic1312yes—
137#389—21no—
138#381—21no—
139#380—21no—
140#380Dic1311yescharacteristic
141#343—132no—
142#324—132no—
143#323—261no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—22no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—42no—
150C22×C13—41no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—81no—
156C22×C13C2×#9911yescharacteristic
157C22×C13#41811yescharacteristic
158C22×C13C2×#10411yescharacteristic
159C4×C13—21no—
160C4×C13—22no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—82no—
165C4×C13—82no—
166C4×C13#35212yes—
167C22×D4C22⋊D1311yescharacteristic
168C23×C4—21no—
169C23×C4C2×Dic1311yescharacteristic
170C23×C4C22⋊D1311yescharacteristic
171C2×M16—262no—
172C2×M16—521no—
173#123—44no—
174C4×D4—41no—
175C4×D4—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4C2×Dic1312yes—
182C2×C4⋊C4C22×D1311yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4C2×Dic1311yescharacteristic
186C2×C22⋊C4C22⋊D1311yescharacteristic
187C2×C42C22⋊D1311yescharacteristic
188#100—264no—
189C22⋊C8—262no—
190C22⋊C8—521no—
191#97—521no—
192C4×C8—521no—
193#95—22no—
194#95—22no—
195#95C2×Dic1312yes—
196C2×C13—21no—
197C2×C13—21no—
198C2×C13—42no—
199C2×C13—81no—
200C2×C13#150711yescharacteristic
201C2×C13C2×#35211yescharacteristic
202C2×C13#213511yescharacteristic
203C24C22⋊Dic1311yescharacteristic
204C24C22⋊Dic1311yescharacteristic
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—41no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4C22⋊Dic1311yescharacteristic
220C22×C4C22⋊Dic1311yescharacteristic
221C22×C4C22×Dic1311yescharacteristic
222C22×C4C2×C22⋊D1311yescharacteristic
223C22×C4C2×C22⋊D1311yescharacteristic
224M16—264no—
225M16—522no—
226M16—1042no—
227C2×C8—522no—
228C2×C8—522no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—44no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—42no—
238C22⋊C4—44no—
239C42—21no—
240C42—21no—
241C13#1178011yescharacteristic, complemented, Sylow
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23#8807712yes—
252C23C2×C22⋊Dic1311yescharacteristic
253D4—44no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—81no—
273C2×C4—84no—
274C2×C4#8807411yescharacteristic
275C2×C4#8807411yescharacteristic
276C2×C4#8818612yes—
277C8—524no—
278C8—1042no—
279C22—21no—
280C22—21no—
281C22—22no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—81no—
291C22#1171887611yescharacteristic
292C22C2×#8807411yescharacteristic
293C22C2×#8807711yescharacteristic
294C4—22no—
295C4—21no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—82no—
300C4—82no—
301C4#1171813112yes—
302C2—21no—
303C2—21no—
304C2—42no—
305C2—81no—
306C2#1311335211yescharacteristic
307C2C2×#1171813111yescharacteristic
308C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2486C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C4⋊C4C23
hypercenter#2486D13
hypocenterC13#11780
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2486

Complements

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

NH ≅ G/Ntype
3. #13112842C2semidirect
241. C13#11780semidirect

Maximal subgroups

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

subgroupindex
C4×#880732
#131131742
#131128422
C13×#24862
#1178013