Finite Group Databasebeta

← #15773532

Subgroups — #15773532

Order 3328.

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

normal subgroups only

This group has 462 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×#88074C211yesmaximal, characteristic
2#13113177C211yesmaximal, characteristic
3#13112860C214yesmaximal, complemented
4C13×#2487C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic, complemented
7C13×#400C412yescomplemented
8C13×#399C2212yes—
9C13×#389—21no—
10C13×#386—21no—
11C13×#385—21no—
12C13×#380—21no—
13C13×#380C411yescharacteristic, complemented
14C2×#88074—21no—
15C4×C22⋊Dic13—21no—
16#11718587—21no—
17#11718118C2212yes—
18#11718117—21no—
19#11718117C2212yes—
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⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C13×C22⋊C4C2311yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C22⋊Dic13—22no—
39C2×C4×Dic13—41no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95C2×C412yes—
43#88074—24no—
44#88071—41no—
45C22⋊#1055—22no—
46C4⋊#1055—41no—
47#88043—41no—
48#11786—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C24×C13C2×D411yescharacteristic
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×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—42no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—82no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—82no—
80C42×C13—21no—
81C42×C13—21no—
82C22⋊Dic13—24no—
83C22⋊Dic13—42no—
84C4×Dic13—82no—
85C2×#1055—42no—
86#2487D1311yescharacteristic
87C4×#99—131no—
88#1466—131no—
89#1352—134no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—41no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13#10412yes—
99C23×C13C2×C22⋊C411yescharacteristic
100C23×C13#13712yes—
101D4×C13—44no—
102C2×C4×C13—22no—
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—42no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—81no—
122C2×C4×C13—84no—
123C2×C4×C13#9911yescharacteristic
124C2×C4×C13#9911yescharacteristic
125C2×Dic13—44no—
126C2×Dic13—82no—
127C2×Dic13—82no—
128#1055—82no—
129C2×C4×D4C2×D1311yescharacteristic
130C22×C4⋊C4Dic1311yescharacteristic, complemented
131#432—261no—
132C2×#99—261no—
133#400Dic1312yescomplemented
134#399C2×D1312yes—
135#389—21no—
136#386—21no—
137#385—21no—
138#380—21no—
139#380Dic1311yescharacteristic, complemented
140C4×C22⋊C4—261no—
141#342—132no—
142#323—132no—
143#323—261no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—22no—
147C22×C13—22no—
148C22×C13—42no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—81no—
156C22×C13C2×#9911yescharacteristic
157C22×C13#41911yescharacteristic
158C22×C13C2×#10411yescharacteristic
159C4×C13—21no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—82no—
165C4×C13—82no—
166C4×C13#35212yes—
167Dic13—84no—
168C22×D4C22⋊D1311yescharacteristic
169C23×C4—21no—
170C23×C4C2×Dic1311yescharacteristic
171C23×C4C22⋊D1311yescharacteristic
172C4×D4—41no—
173C4×D4—41no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4C2×Dic1312yes—
180C2×C4⋊C4C2×Dic1311yescharacteristic
181C2×C22⋊C4—21no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—262no—
184C2×C22⋊C4C22⋊D1311yescharacteristic
185C2×C22⋊C4C22×D1311yescharacteristic
186C2×C42—521no—
187C2×C42C22⋊D1311yescharacteristic
188C4⋊C8—521no—
189#99—264no—
190C22⋊C8—262no—
191#97—521no—
192#95—22no—
193#95—22no—
194#95—521no—
195#95C2×Dic1312yes—
196C2×C13—21no—
197C2×C13—21no—
198C2×C13—42no—
199C2×C13—42no—
200C2×C13#150811yescharacteristic
201C2×C13C2×#35211yescharacteristic
202C2×C13#212811yescharacteristic
203C24C22⋊Dic1311yescharacteristic
204C24C2×C22⋊D1311yescharacteristic
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—82no—
218C22×C4—522no—
219C22×C4C22⋊Dic1311yescharacteristic
220C22×C4C22⋊Dic1311yescharacteristic
221C22×C4C22⋊Dic1311yescharacteristic
222C22×C4C22×Dic1311yescharacteristic
223C22×C4C2×C22⋊D1311yescharacteristic
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—
235C22⋊C4—264no—
236C22⋊C4—522no—
237C42—21no—
238C42—21no—
239C42—1042no—
240C13#1178611yescharacteristic, complemented, Sylow
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23#8807712yes—
250C23#8819612yes—
251C23C2×C22⋊Dic1311yescharacteristic
252D4—44no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
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—524no—
275C2×C4—1042no—
276C2×C4—1042no—
277C2×C4#8807411yescharacteristic
278C2×C4#8807411yescharacteristic
279C8—1042no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—22no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—81no—
292C22C2×#8807411yescharacteristic
293C22#1171888611yescharacteristic
294C22C2×#8807711yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—82no—
301C4—82no—
302C4—1044no—
303C4#1171813112yes—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2#1311335611yescharacteristic
309C2C2×#1171813111yescharacteristic
310C2#1311650811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2487C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2487D13
hypocenterC13#11786
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. #13112860C2semidirect
6. C22×C13×C4⋊C4C4semidirect
7. C13×#400C4semidirect
13. C13×#380C4semidirect
130. C22×C4⋊C4Dic13semidirect
133. #400Dic13semidirect
139. #380Dic13semidirect
240. C13#11786semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131772
#131128602
C13×#24872
#1178613