Finite Group Databasebeta

← #15773969

Subgroups — #15773969

Order 3328.

460 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114828C211yesmaximal, characteristic
2#13113154C211yesmaximal, 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—
15C2×C22⋊#1055—21no—
16#11718585—21no—
17#11718122C2212yes—
18#11718120C2212yes—
19#11718117—21no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C13×#123—42no—
25C13×#123—42no—
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4—41no—
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×#6099—22no—
41C22×#1055—41no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95C2×C412yes—
45#88073—42no—
46C22⋊#1055—22no—
47C22⋊#1055—41no—
48C4⋊#1055—41no—
49C4⋊#1055—41no—
50#11881—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C22⋊C411yescharacteristic
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13D812yes—
56C2×D4×C13SD1612yes—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C13×C4⋊C4—41no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—44no—
84C42×C13—21no—
85C42×C13—21no—
86#6099—42no—
87#6099—42no—
88C2×#1055—42no—
89C2×#1055—42no—
90C2×#1055—82no—
91#2486D1311yescharacteristic
92#1800—131no—
93#1459—131no—
94#1346—134no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13#10212yes—
104C23×C13#10212yes—
105C23×C13C2×C22⋊C411yescharacteristic
106D4×C13—42no—
107D4×C13—42no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
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—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—81no—
127C2×C4×C13—84no—
128C2×C4×C13#9911yescharacteristic
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13C2×D811yescharacteristic
131C2×C4×C13C2×SD1611yescharacteristic
132#1055—82no—
133#1055—82no—
134C2×#123—21no—
135C2×C4×D4C2×D1311yescharacteristic
136C22×C4⋊C4Dic1311yescharacteristic
137#423—261no—
138C2×#100—261no—
139C2×C22⋊C8—261no—
140#398C2×D1312yes—
141#397Dic1312yes—
142#389—21no—
143#381—21no—
144#380—21no—
145#380Dic1311yescharacteristic
146#343—132no—
147#324—132no—
148#323—261no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—22no—
152C22×C13—22no—
153C22×C13—42no—
154C22×C13—42no—
155C22×C13—42no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—81no—
161C22×C13C2×#9911yescharacteristic
162C22×C13C2×#10211yescharacteristic
163C22×C13#42111yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—82no—
171C4×C13—82no—
172C4×C13#35212yes—
173C22×D4C22⋊D1311yescharacteristic
174C23×C4—21no—
175C23×C4C2×Dic1311yescharacteristic
176C23×C4C22⋊D1311yescharacteristic
177C2×M16—262no—
178C22×C8—521no—
179#123—42no—
180#123—42no—
181C4×D4—41no—
182C4×D4—41no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4C2×Dic1312yes—
189C2×C4⋊C4C22×D1311yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4C2×Dic1311yescharacteristic
193C2×C22⋊C4C22⋊D1311yescharacteristic
194C2×C42C22⋊D1311yescharacteristic
195C4⋊C8—521no—
196C4⋊C8—521no—
197#100—522no—
198C22⋊C8—262no—
199C22⋊C8—521no—
200#95—22no—
201#95—22no—
202#95C2×Dic1312yes—
203C2×C13—21no—
204C2×C13—21no—
205C2×C13—42no—
206C2×C13—42no—
207C2×C13#151911yescharacteristic
208C2×C13C2×#35211yescharacteristic
209C2×C13#213511yescharacteristic
210C24C22⋊Dic1311yescharacteristic
211C24C22⋊Dic1311yescharacteristic
212C2×D4—41no—
213C2×D4—41no—
214C2×D4#610412yes—
215C2×D4#610512yes—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4C22⋊Dic1311yescharacteristic
228C22×C4C22⋊Dic1311yescharacteristic
229C22×C4C22×Dic1311yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232M16—522no—
233M16—522no—
234C2×C8—522no—
235C2×C8—522no—
236C2×C8—1042no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—42no—
247C22⋊C4—44no—
248C42—21no—
249C42—21no—
250C13#1188111yescharacteristic, complemented, Sylow
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23#8807212yes—
260C23#8807212yes—
261C23C2×C22⋊Dic1311yescharacteristic
262D4—42no—
263D4—42no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—81no—
283C2×C4—84no—
284C2×C4#8807411yescharacteristic
285C2×C4#8807411yescharacteristic
286C2×C4C2×#610411yescharacteristic
287C2×C4C2×#610511yescharacteristic
288C8—1042no—
289C8—1042no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—22no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—81no—
302C22C2×#8807211yescharacteristic
303C22C2×#8807411yescharacteristic
304C22#1171889711yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4#1171813112yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—42no—
318C2#1311340411yescharacteristic
319C2C2×#1171813111yescharacteristic
320C2#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#11881
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
250. C13#11881semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131131542
#131128422
C13×#24862
#1188113