Finite Group Databasebeta

← #15773549

Subgroups — #15773549

Order 3328.

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

normal subgroups only

This group has 444 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#13112863C214yesmaximal, complemented
4C13×#2487C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C13×#400C2212yes—
8C13×#399C412yes—
9C13×#389—21no—
10C13×#386—21no—
11C13×#385—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
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×#6099—22no—
39C2×#6099—41no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95C2×C412yes—
43#88073—24no—
44C22⋊#1055—22no—
45C22⋊#1055—41no—
46#88043—41no—
47C4×#1055—41no—
48#11790—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C24×C13C22⋊C411yescharacteristic
51C2×D4×C13—22no—
52C2×D4×C13—22no—
53C2×D4×C13—41no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—82no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—82no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—42no—
78C13×C22⋊C4—82no—
79C42×C13—21no—
80C42×C13—21no—
81#6099—24no—
82#6099—42no—
83#6099—82no—
84C2×#1055—42no—
85C2×#1055—42no—
86#2487D1311yescharacteristic
87C4×#100—131no—
88#1465—131no—
89#1353—134no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13#10412yes—
100C23×C13C2×C22⋊C411yescharacteristic
101D4×C13—44no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—81no—
121C2×C4×C13—84no—
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13#9911yescharacteristic
124C2×C4×C13#13712yes—
125#1055—44no—
126#1055—82no—
127C2×C4×D4C2×D1311yescharacteristic
128C22×C4⋊C4Dic1311yescharacteristic
129C2×#100—261no—
130#407—261no—
131C4×M16—261no—
132#400C2×D1312yes—
133#399Dic1312yes—
134#389—21no—
135#386—21no—
136#385—21no—
137#380—21no—
138#380Dic1311yescharacteristic
139#343—132no—
140#324—132no—
141#323—261no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—22no—
145C22×C13—42no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—41no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—81no—
154C22×C13C2×#9911yescharacteristic
155C22×C13#41911yescharacteristic
156C22×C13C2×#10411yescharacteristic
157C4×C13—21no—
158C4×C13—22no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—82no—
163C4×C13—82no—
164C4×C13#35212yes—
165C22×D4C22⋊D1311yescharacteristic
166C23×C4—21no—
167C23×C4C2×Dic1311yescharacteristic
168C23×C4C22⋊D1311yescharacteristic
169C2×M16—262no—
170C2×M16—521no—
171C4×D4—41no—
172C4×D4—41no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4C2×Dic1312yes—
179C2×C4⋊C4C22×D1311yescharacteristic
180C2×C22⋊C4—21no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4C2×Dic1311yescharacteristic
183C2×C22⋊C4C22⋊D1311yescharacteristic
184C2×C42C22⋊D1311yescharacteristic
185#100—264no—
186C22⋊C8—262no—
187C22⋊C8—521no—
188#97—521no—
189C4×C8—521no—
190#95—22no—
191#95—22no—
192#95C2×Dic1312yes—
193C2×C13—21no—
194C2×C13—21no—
195C2×C13—42no—
196C2×C13—81no—
197C2×C13#150811yescharacteristic
198C2×C13C2×#35211yescharacteristic
199C2×C13#213411yescharacteristic
200C24C22⋊Dic1311yescharacteristic
201C24C22⋊Dic1311yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—82no—
215C22×C4C22⋊Dic1311yescharacteristic
216C22×C4C22⋊Dic1311yescharacteristic
217C22×C4C22×Dic1311yescharacteristic
218C22×C4C2×C22⋊D1311yescharacteristic
219C22×C4C2×C22⋊D1311yescharacteristic
220M16—264no—
221M16—522no—
222M16—1042no—
223C2×C8—522no—
224C2×C8—522no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—82no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—42no—
234C22⋊C4—82no—
235C42—21no—
236C42—21no—
237C13#1179011yescharacteristic, complemented, Sylow
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23#8807712yes—
248C23C2×C22⋊Dic1311yescharacteristic
249D4—44no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—81no—
269C2×C4—84no—
270C2×C4#8807411yescharacteristic
271C2×C4#8807411yescharacteristic
272C2×C4#8819612yes—
273C8—524no—
274C8—1042no—
275C22—21no—
276C22—21no—
277C22—22no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—81no—
287C22C2×#8807411yescharacteristic
288C22#1171888611yescharacteristic
289C22C2×#8807711yescharacteristic
290C4—22no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—82no—
296C4—82no—
297C4#1171813112yes—
298C2—21no—
299C2—21no—
300C2—42no—
301C2—81no—
302C2#1311335611yescharacteristic
303C2C2×#1171813111yescharacteristic
304C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2487C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C4⋊C4C23
hypercenter#2487D13
hypocenterC13#11790
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
3. #13112863C2semidirect
237. C13#11790semidirect

Maximal subgroups

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

subgroupindex
C4×#880732
#131131742
#131128632
C13×#24872
#1179013