Finite Group Databasebeta

← #16778536

Subgroups — #16778536

Order 3328.

630 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130727C212yesmaximal, complemented
2#13129656C212yesmaximal, complemented
3#13129652C212yesmaximal, complemented
4#13117327C211yesmaximal, characteristic
5C22×C13×#41C411yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9#11718891C411yescharacteristic
10#11718891C2211yescharacteristic
11#11718882C411yescharacteristic
12#11718882C2211yescharacteristic
13#11718881—22no—
14C4×C22⋊Dic13—22no—
15#11718290—22no—
16#11718290C2214yes—
17C2×C13×#41—22no—
18C2×C13×#41—22no—
19C2×C13×#41—42no—
20C2×C13×#41—42no—
21C22×Q8×C13C2×C411yescharacteristic
22C22×D4×C13—21no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13C2×C411yescharacteristic
26C23×Dic13D412yes—
27C22×#1057—24no—
28C2×C22⋊Dic13—21no—
29C2×C22⋊Dic13—22no—
30C2×C22⋊Dic13—22no—
31#88180—42no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4×Dic13—21no—
35C2×C4×Dic13—42no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D412yes—
38C2×C4×Dic13C2311yescharacteristic
39C22⋊#1057—44no—
40#88071—22no—
41#88071—22no—
42#7645—131nomaximal, Sylow
43C24×C13—21no—
44C24×C13C22⋊C411yescharacteristic
45C13×#41—48no—
46C13×#41—48no—
47C2×Q8×C13—21no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13M1612yes—
51C2×D4×C13—24no—
52C2×D4×C13—21no—
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13—42no—
56C2×D4×C13—42no—
57C2×D4×C13M1612yes—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—24no—
63C22×C4×C13—21no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×Dic13—24no—
69C22×Dic13—24no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—42no—
73C22×Dic13C22⋊C412yes—
74C22×Dic13C2×D412yes—
75C2×#1057—44no—
76C2×#1057—44no—
77C2×#1057—44no—
78C22⋊Dic13—44no—
79C22⋊Dic13—42no—
80C22⋊Dic13—44no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4×Dic13—41no—
84C4×Dic13—42no—
85C4×Dic13—41no—
86C4×Dic13—42no—
87#2297—131no—
88#1817—132no—
89#1272—132no—
90#1270—132no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—22no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—42no—
99C23×C13—42no—
100C23×C13#9912yes—
101C23×C13C2×C22⋊C411yescharacteristic
102Q8×C13—42no—
103Q8×C13—42no—
104D4×C13—42no—
105D4×C13—42no—
106D4×C13—48no—
107C2×C4×C13—24no—
108C2×C4×C13—24no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—22no—
114C2×C4×C13—48no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13#10012yes—
118C2×C4×C13C2×M1611yescharacteristic
119C2×C4×C13C2×M1611yescharacteristic
120C2×Dic13—22no—
121C2×Dic13—22no—
122C2×Dic13—22no—
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—48no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13#13514yes—
131#1057—84no—
132C22×#41#26111yescharacteristic
133C2×#117—131no—
134C22×C42—131no—
135C2×C22⋊C8—262no—
136#391—131no—
137#391—131no—
138#390—131no—
139#390—131no—
140#386—262no—
141C4×C22⋊C4—262no—
142#336—134no—
143#336—262no—
144C22×C13—22no—
145C22×C13—24no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13—42no—
149C22×C13—42no—
150C22×C13—44no—
151C22×C13—81no—
152C22×C13—81no—
153C22×C13—82no—
154C22×C13#40711yescharacteristic
155C22×C13C2×#9911yescharacteristic
156C22×C13C2×#10011yescharacteristic
157C22×C13#41612yes—
158C22×C13#42112yes—
159C4×C13—22no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—42no—
163Dic13—24no—
164Dic13—42no—
165Dic13—81no—
166Dic13—81no—
167C2×#41—22no—
168C2×#41—22no—
169C2×#41—42no—
170C2×#41—42no—
171C22×Q8C2×#26111yescharacteristic
172C22×D4—21no—
173C22×D4C2×#26111yescharacteristic
174C23×C4—21no—
175C23×C4—132no—
176C23×C4C2×#26111yescharacteristic
177C22×C8—264no—
178#117—522no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—131no—
181C2×C22⋊C4—262no—
182C2×C22⋊C4—262no—
183C2×C22⋊C4—261no—
184C2×C42—132no—
185C2×C42—131no—
186C2×C42—131no—
187C2×C42—261no—
188C2×C42—522no—
189C22⋊C8—524no—
190#95—262no—
191#95—262no—
192C2×C13—42no—
193C2×C13—82no—
194C2×C13#146211yescharacteristic
195C2×C13#148812yes—
196C2×C13#151612yes—
197C2×C13#153611yescharacteristic
198C2×C13#154311yescharacteristic
199C24—21no—
200C24C22⋊#26111yescharacteristic
201#41—48no—
202#41—48no—
203C2×Q8—21no—
204C2×Q8—41no—
205C2×Q8—41no—
206C2×Q8#612212yes—
207C2×D4—24no—
208C2×D4—21no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4#612212yes—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—24no—
219C22×C4—21no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—132no—
223C22×C4—132no—
224C22×C4—264no—
225C22×C4—264no—
226C22×C4—261no—
227C22×C4—261no—
228C22×C4—522no—
229C22×C4C22⋊#26111yescharacteristic
230C22×C4C22×#26111yescharacteristic
231C2×C8—524no—
232C2×C8—524no—
233C2×C8—524no—
234C4⋊C4—521no—
235C4⋊C4—521no—
236C22⋊C4—524no—
237C22⋊C4—524no—
238C22⋊C4—522no—
239C42—522no—
240C42—521no—
241C42—521no—
242C42—522no—
243C13#764511yescharacteristic, complemented, Sylow
244C23—21no—
245C23—21no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—41no—
250C23—42no—
251C23—42no—
252C23—41no—
253C23#8811912yes—
254C23C2×C22⋊#26111yescharacteristic
255Q8—42no—
256Q8—42no—
257D4—42no—
258D4—42no—
259D4—48no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—48no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—134no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—262no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4—528no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4#8812112yes—
282C2×C4C2×#612211yescharacteristic
283C2×C4C2×#612211yescharacteristic
284C8—1044no—
285C22—24no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—44no—
292C22—82no—
293C22—81no—
294C22—81no—
295C22#1171916512yes—
296C22#1171916612yes—
297C22C2×#8811911yescharacteristic
298C22#1171916911yescharacteristic
299C22C2×#8812111yescharacteristic
300C4—22no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—264no—
305C4—522no—
306C4—1041no—
307C4—1041no—
308C2—42no—
309C2—82no—
310C2#1313008111yescharacteristic
311C2#1313016712yes—
312C2#1313026212yes—
313C2#1313032411yescharacteristic
314C2#1313033911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
Fitting, prime radicalC22×C13×#41C4
socleC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC22×#41#261
hypocenterC13#7645
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #13130727C2semidirect
2. #13129656C2semidirect
3. #13129652C2semidirect
243. C13#7645semidirect

Maximal subgroups

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

subgroupindex
#131307272
#131296562
#131296522
#131173272
#764513