Finite Group Databasebeta

← #15772571

Subgroups — #15772571

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#13119789C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112781C214yesmaximal, complemented
4C13×#1465C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C2×#88178—21no—
7C2×#88178—21no—
8C2×#88123C411yescharacteristic
9C13×#407—21no—
10#11718882C412yes—
11C2×C22⋊#1055—21no—
12#11718637C2212yes—
13#11718610—21no—
14#11718610—21no—
15C4×C4⋊Dic13C411yescharacteristic
16C13×#324C2212yes—
17C13×#323—21no—
18#11718120C2212yes—
19#11718117—21no—
20C22×D4×C13C2×C411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C22×Dic26—21no—
24C2×C13×M16—41no—
25C4×D4×C13—41no—
26C4×D4×C13—41no—
27C2×C13×C4⋊C4C2311yescharacteristic
28C2×C13×C22⋊C4D411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C22⋊Dic13—22no—
32C2×C22⋊Dic13—22no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C412yes—
36#88178—44no—
37#88178—44no—
38C2×#6101—22no—
39C2×#6101—22no—
40C2×C4×Dic13C2×C412yes—
41C22×#1055—41no—
42#88123—41no—
43#88123—41no—
44C13×C22⋊C8—22no—
45C13×C22⋊C8—41no—
46#88071—21no—
47C22⋊#1055—22no—
48C22⋊#1055—41no—
49#11570—131nomaximal, Sylow
50C24×C13C22⋊C411yescharacteristic
51C24×C13C22⋊C411yescharacteristic
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×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—22no—
67C22×Dic13—22no—
68C2×Dic26—42no—
69C2×Dic26—42no—
70C2×Dic26—41no—
71C2×Dic26—41no—
72C13×M16—82no—
73C2×C8×C13—42no—
74C13×C4⋊C4—41no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—41no—
77C42×C13—21no—
78C42×C13—21no—
79C22⋊Dic13—44no—
80C22⋊Dic13—44no—
81C4⋊Dic13—24no—
82C4⋊Dic13—42no—
83C4⋊Dic13—42no—
84#6101—44no—
85#6101—44no—
86C4×Dic13—24no—
87C2×#1055—42no—
88C2×#1055—82no—
89#2542—131no—
90#1465D1311yescharacteristic
91#1459—131no—
92#1325—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×C13#10112yes—
103C23×C13C2×C22⋊C411yescharacteristic
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—81no—
117C2×C4×C13—81no—
118C2×C4×C13#9911yescharacteristic
119C2×C4×C13#9911yescharacteristic
120C2×C4×C13#13112yes—
121C2×Dic13—24no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127Dic26—82no—
128Dic26—82no—
129C8×C13—82no—
130#1055—82no—
131C2×C4⋊Q8—131no—
132C2×C22⋊Q8—261no—
133C2×C22⋊Q8—261no—
134C2×C4×D4C2×D1311yescharacteristic
135#407—21no—
136C2×C22⋊C8—261no—
137#399—261no—
138#399—261no—
139#390—132no—
140#384—132no—
141C4×C4⋊C4—131no—
142#324—132no—
143#324C2×D1312yes—
144#323—21no—
145#323—261no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—22no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—81no—
157C22×C13—81no—
158C22×C13#40811yescharacteristic
159C22×C13C2×#9911yescharacteristic
160C22×C13C2×#10111yescharacteristic
161C4×C13—21no—
162C4×C13—22no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13#35312yes—
167Dic13—44no—
168Dic13—82no—
169C22×Q8—261no—
170C22×D4C4×D1311yescharacteristic
171C23×C4D5211yescharacteristic
172C23×C4C22⋊D1311yescharacteristic
173C2×M16—41no—
174C22×C8—521no—
175C4⋊Q8—521no—
176C4⋊Q8—521no—
177C22⋊Q8—524no—
178C22⋊Q8—524no—
179C4×D4—41no—
180C4×D4—41no—
181C2×C4⋊C4—132no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—262no—
185C2×C4⋊C4—262no—
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C22⋊C4—262no—
188C2×C22⋊C4—262no—
189C2×C22⋊C4D5211yescharacteristic
190C2×C22⋊C4C22⋊D1311yescharacteristic
191C2×C42—132no—
192C2×C42C4×D1311yescharacteristic
193C22⋊C8—22no—
194C22⋊C8—41no—
195C22⋊C8—262no—
196C22⋊C8—521no—
197#95—261no—
198C2×C13—21no—
199C2×C13—21no—
200C2×C13—42no—
201C2×C13—81no—
202C2×C13#147211yescharacteristic
203C2×C13C2×#35311yescharacteristic
204C2×C13#213511yescharacteristic
205C24#610311yescharacteristic
206C24#610311yescharacteristic
207C2×Q8—522no—
208C2×Q8—522no—
209C2×Q8—521no—
210C2×Q8—521no—
211C2×D4—22no—
212C2×D4—22no—
213C2×D4—41no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—262no—
221C22×C4—262no—
222C22×C4#610311yescharacteristic
223C22×C4#610311yescharacteristic
224C22×C4C2×C4×D1311yescharacteristic
225C22×C4C2×D5211yescharacteristic
226C22×C4C2×C22⋊D1311yescharacteristic
227M16—82no—
228C2×C8—42no—
229C2×C8—522no—
230C2×C8—1042no—
231C4⋊C4—41no—
232C4⋊C4—264no—
233C4⋊C4—522no—
234C4⋊C4—522no—
235C4⋊C4—524no—
236C4⋊C4—524no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—524no—
240C22⋊C4—524no—
241C42—21no—
242C42—21no—
243C42—264no—
244C13#1157011yescharacteristic, complemented, Sylow
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23#8806412yes—
255C23C2×#610311yescharacteristic
256Q8—1042no—
257Q8—1042no—
258D4—44no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—264no—
273C2×C4—522no—
274C2×C4—522no—
275C2×C4—522no—
276C2×C4—522no—
277C2×C4—522no—
278C2×C4#8804611yescharacteristic
279C2×C4#8804611yescharacteristic
280C2×C4#8816112yes—
281C8—82no—
282C8—1042no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22—81no—
295C22C2×#8804611yescharacteristic
296C22#1171879011yescharacteristic
297C22C2×#8806411yescharacteristic
298C4—21no—
299C4—22no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—524no—
304C4—1042no—
305C4#1171806612yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2#1311320111yescharacteristic
311C2C2×#1171806611yescharacteristic
312C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1465C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1465D13
hypocenterC13#11570
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #13112781C2semidirect
244. C13#11570semidirect

Maximal subgroups

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

subgroupindex
#131197892
#131131542
#131127812
C13×#14652
#1157013