Finite Group Databasebeta

← #15773536

Subgroups — #15773536

Order 3328.

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

normal subgroups only

This group has 460 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#13113174C211yesmaximal, characteristic
3#13112857C214yesmaximal, complemented
4C13×#2563C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C4×D4×C13C2211yescharacteristic
7C13×#393C412yescomplemented
8C13×#393C2212yes—
9C13×#390—21no—
10C13×#382—21no—
11C13×#380—21no—
12C13×#380—21no—
13C4×C13×C4⋊C4C411yescharacteristic, complemented
14C2×#88074—21no—
15C4×C22⋊Dic13—21no—
16#11718868—21no—
17#11718120—21no—
18#11718118C2212yes—
19#11718117C2212yes—
20C22×Q8×C13C2×C412yes—
21C22×D4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C13×C4⋊Q8—41no—
25C13×C4⋊Q8—41no—
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4C2311yescharacteristic
36C2×C42×C13—21no—
37C2×C42×C13C2×C411yescharacteristic
38C2×C22⋊Dic13—22no—
39C2×C4×Dic13—41no—
40C2×#6099—41no—
41C13×#95—22no—
42C13×#95—22no—
43C13×#95C2×C412yes—
44#88074—24no—
45#88071—41no—
46C22⋊#1055—22no—
47C22⋊#1055—41no—
48#11787—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C24×C13C2×D411yescharacteristic
51C2×Q8×C13—42no—
52C2×Q8×C13—82no—
53C2×D4×C13—22no—
54C2×D4×C13—22no—
55C2×D4×C13—41no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
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×C22⋊C4—41no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—82no—
78C13×C22⋊C4—82no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—42no—
82C22⋊Dic13—24no—
83C22⋊Dic13—42no—
84C4×Dic13—82no—
85#6099—82no—
86C2×#1055—42no—
87#2563D1311yescharacteristic
88C4×#99—131no—
89#1465—131no—
90#1351—134no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13C2×C22⋊C411yescharacteristic
101C23×C13#13712yes—
102Q8×C13—84no—
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—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—81no—
123C2×C4×C13#9911yescharacteristic
124C2×C4×C13#9911yescharacteristic
125C2×C4×C13#10412yes—
126C2×Dic13—44no—
127C2×Dic13—82no—
128C2×Dic13—82no—
129#1055—82no—
130C2×C4⋊Q8Dic1311yescharacteristic, complemented
131C2×C4×D4C2×D1311yescharacteristic
132C2×#99—261no—
133#407—261no—
134#393Dic1312yescomplemented
135#393C2×D1312yes—
136#390—21no—
137#382—21no—
138#380—21no—
139#380—21no—
140C4×C4⋊C4Dic1311yescharacteristic, complemented
141C4×C22⋊C4—261no—
142#342—132no—
143#324—261no—
144#323—132no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—22no—
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×C13—81no—
157C22×C13C2×#9911yescharacteristic
158C22×C13#41911yescharacteristic
159C22×C13C2×#10411yescharacteristic
160C4×C13—21no—
161C4×C13—22no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—82no—
166C4×C13—82no—
167C4×C13#35412yes—
168Dic13—84no—
169C22×Q8C2×Dic1312yes—
170C22×D4C22⋊D1311yescharacteristic
171C23×C4C22⋊D1311yescharacteristic
172C23×C4C22⋊D1311yescharacteristic
173C2×M16—521no—
174C4⋊Q8—41no—
175C4⋊Q8—41no—
176C4×D4—41no—
177C4×D4—41no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4C22⋊D1311yescharacteristic
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—262no—
185C2×C22⋊C4C2×Dic1311yescharacteristic
186C2×C22⋊C4C22×D1311yescharacteristic
187C2×C42—21no—
188C2×C42—521no—
189C2×C42C2×Dic1311yescharacteristic
190#99—264no—
191C22⋊C8—262no—
192C22⋊C8—521no—
193#95—22no—
194#95—22no—
195#95—521no—
196#95C2×Dic1312yes—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13—42no—
200C2×C13—81no—
201C2×C13#150811yescharacteristic
202C2×C13#212211yescharacteristic
203C2×C13C2×#35411yescharacteristic
204C24C22⋊Dic1311yescharacteristic
205C24C2×C22⋊D1311yescharacteristic
206C2×Q8—42no—
207C2×Q8—82no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—41no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—522no—
220C22×C4C22⋊Dic1311yescharacteristic
221C22×C4C22⋊Dic1311yescharacteristic
222C22×C4C22⋊Dic1311yescharacteristic
223C22×C4C22×Dic1311yescharacteristic
224C22×C4C2×C22⋊D1311yescharacteristic
225M16—1042no—
226C2×C8—522no—
227C4⋊C4—41no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—82no—
235C22⋊C4—82no—
236C22⋊C4—264no—
237C22⋊C4—522no—
238C42—21no—
239C42—21no—
240C42—42no—
241C42—1042no—
242C13#1178711yescharacteristic, complemented, Sylow
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23#8819612yes—
253C23C2×C22⋊Dic1311yescharacteristic
254Q8—84no—
255D4—44no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—524no—
276C2×C4—1042no—
277C2×C4—1042no—
278C2×C4#8807411yescharacteristic
279C2×C4#8807411yescharacteristic
280C2×C4#8807712yes—
281C8—1042no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22—81no—
294C22C2×#8807411yescharacteristic
295C22#1171888611yescharacteristic
296C22C2×#8807711yescharacteristic
297C4—22no—
298C4—21no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—82no—
303C4—82no—
304C4—1044no—
305C4#1171813312yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2#1311335611yescharacteristic
311C2#1311648611yescharacteristic
312C2C2×#1171813311yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2563C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2563D13
hypocenterC13#11787
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2563

Complements

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

NH ≅ G/Ntype
3. #13112857C2semidirect
5. C2×C13×C4⋊Q8C4semidirect
7. C13×#393C4semidirect
13. C4×C13×C4⋊C4C4semidirect
130. C2×C4⋊Q8Dic13semidirect
134. #393Dic13semidirect
140. C4×C4⋊C4Dic13semidirect
242. C13#11787semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131742
#131128572
C13×#25632
#1178713