Finite Group Databasebeta

← #15773492

Subgroups — #15773492

Order 3328.

480 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 87 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#13119828C211yesmaximal, characteristic
2#13113174C211yesmaximal, characteristic
3#13112835C214yesmaximal, complemented
4C4×C13×#99C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C2×#88190—21no—
7C2×#88123C411yescharacteristic, complemented
8C2×C13×#99—21no—
9C4×C13×C22⋊C4—21no—
10#11718873—21no—
11#11718873—21no—
12#11718868—21no—
13#11718635—21no—
14#11718614C412yescomplemented
15#11718614C2212yes—
16C4×C4⋊Dic13C411yescharacteristic, complemented
17C13×#342C2212yes—
18#11718120—21no—
19#11718117C2212yes—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C22×Dic26—21no—
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4C2×C411yescharacteristic
29C2×C13×C22⋊C4C2311yescharacteristic
30C2×C42×C13—41no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C22⋊Dic13—22no—
33C2×C22⋊Dic13—22no—
34#88190—44no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C412yes—
38C2×C4×Dic13—21no—
39C2×#6099—41no—
40#88123—41no—
41#88123—41no—
42C13×#99—24no—
43C13×#95—41no—
44#88071—22no—
45#88071—22no—
46#88071C2×C412yes—
47C22⋊#1055—22no—
48C22⋊#1055—41no—
49#11777—131nomaximal, Sylow
50C24×C13C22⋊C411yescharacteristic
51C24×C13C2×D411yescharacteristic
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—22no—
68C22×Dic13—22no—
69C2×Dic26—42no—
70C2×Dic26—42no—
71C2×Dic26—42no—
72C13×C4⋊C4—41no—
73C13×C22⋊C4—24no—
74C13×C22⋊C4—41no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—42no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—82no—
80C22⋊Dic13—44no—
81C22⋊Dic13—44no—
82C4⋊Dic13—42no—
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85C4⋊Dic13—42no—
86C4×Dic13—42no—
87#6099—82no—
88C2×#1055—42no—
89#2547—131no—
90C4×#99D1311yescharacteristic
91#1465—131no—
92#1344—134no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13C2×C22⋊C411yescharacteristic
103C23×C13AGL(1,ℤ/8)12yes—
104D4×C13—44no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—44no—
117C2×C4×C13—81no—
118C2×C4×C13—81no—
119C2×C4×C13—82no—
120C2×C4×C13—82no—
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13#10412yes—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130Dic26—84no—
131#1055—82no—
132C2×C4⋊Q8—131no—
133C2×#124—261no—
134C2×C4×D4C2×D1311yescharacteristic
135C2×#99—21no—
136#407—261no—
137#397—132no—
138#397—132no—
139#391—261no—
140#380—261no—
141#380—261no—
142C4×C4⋊C4—131no—
143C4×C22⋊C4—21no—
144#342C2×D1312yes—
145#324—261no—
146#323—132no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—22no—
150C22×C13—42no—
151C22×C13—42no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—81no—
158C22×C13—81no—
159C22×C13C2×#9911yescharacteristic
160C22×C13#41811yescharacteristic
161C22×C13C2×#10411yescharacteristic
162C4×C13—21no—
163C4×C13—22no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—84no—
168C4×C13#35412yes—
169Dic13—82no—
170Dic13—82no—
171C22×Q8—261no—
172C22×D4C22⋊D1311yescharacteristic
173C23×C4D5211yescharacteristic
174C23×C4C22⋊D1311yescharacteristic
175C2×M16—521no—
176C4⋊Q8—521no—
177C4⋊Q8—521no—
178#124—524no—
179C4×D4—41no—
180C4×D4—41no—
181C2×C4⋊C4—132no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4D5211yescharacteristic
185C2×C22⋊C4—22no—
186C2×C22⋊C4—262no—
187C2×C22⋊C4—262no—
188C2×C22⋊C4C4×D1311yescharacteristic
189C2×C22⋊C4C22×D1311yescharacteristic
190C2×C42—41no—
191C2×C42—261no—
192C2×C42C4×D1311yescharacteristic
193#99—24no—
194C22⋊C8—262no—
195C22⋊C8—521no—
196#95—41no—
197#95—132no—
198#95—262no—
199#95—262no—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13—42no—
203C2×C13—81no—
204C2×C13#150711yescharacteristic
205C2×C13#212311yescharacteristic
206C2×C13C2×#35411yescharacteristic
207C24#610311yescharacteristic
208C24C2×C22⋊D1311yescharacteristic
209C2×Q8—522no—
210C2×Q8—522no—
211C2×Q8—522no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—41no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—262no—
223C22×C4—262no—
224C22×C4#610311yescharacteristic
225C22×C4#610311yescharacteristic
226C22×C4#610311yescharacteristic
227C22×C4C2×C4×D1311yescharacteristic
228C22×C4C2×D5211yescharacteristic
229M16—1042no—
230C2×C8—522no—
231C4⋊C4—41no—
232C4⋊C4—522no—
233C4⋊C4—522no—
234C4⋊C4—521no—
235C4⋊C4—521no—
236C22⋊C4—24no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—42no—
240C22⋊C4—524no—
241C22⋊C4—524no—
242C42—21no—
243C42—21no—
244C42—82no—
245C42—522no—
246C13#1177711yescharacteristic, complemented, Sylow
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23C2×#610311yescharacteristic
257C23#8820312yes—
258Q8—1044no—
259D4—44no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—522no—
277C2×C4—522no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4#8804512yes—
283C2×C4#8804611yescharacteristic
284C2×C4#8804611yescharacteristic
285C8—1042no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—81no—
298C22C2×#8804511yescharacteristic
299C22C2×#8804611yescharacteristic
300C22#1171866211yescharacteristic
301C4—22no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—84no—
307C4—1042no—
308C4—1042no—
309C4#1171806512yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—81no—
314C2#1311335111yescharacteristic
315C2#1311648911yescharacteristic
316C2C2×#1171806511yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC4×C13×#99C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenterC4×#99D13
hypocenterC13#11777
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #13112835C2semidirect
7. C2×#88123C4semidirect
14. #11718614C4semidirect
16. C4×C4⋊Dic13C4semidirect
246. C13#11777semidirect

Maximal subgroups

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

subgroupindex
#131198282
#131131742
#131128352
C4×C13×#992
#1177713