Finite Group Databasebeta

← #15751440

Subgroups — #15751440

Order 3328.

494 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114904C211yesmaximal, characteristic
2#13114530C211yesmaximal, characteristic
3#13112662C212yesmaximal, complemented
4#13112659C212yesmaximal, complemented
5C13×#2855C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C22×C42×C13C2211yescharacteristic
8C22×#6099—21no—
9C13×#391C411yescharacteristic
10C13×#391C2211yescharacteristic
11C13×#389C411yescharacteristic
12C13×#389C2211yescharacteristic
13C13×#387—21no—
14C13×#387—21no—
15C13×#385—21no—
16C13×#381—21no—
17C13×#380C411yescharacteristic
18C2×C22⋊#1055—21no—
19#11718116—21no—
20#11718116—21no—
21#11718116C2212yes—
22#11718116C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C22⋊Q8—42no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C42×C13—42no—
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13C2311yescharacteristic
41C2×#6099—24no—
42C2×#6099—42no—
43C2×#6099—42no—
44C22×#1055—22no—
45C22×#1055—22no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C22⋊#1055—42no—
54#7695—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C2×Q8×C13—22no—
57C2×Q8×C13—41no—
58C2×Q8×C13—41no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C13×C4⋊C4—22no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C42×C13—41no—
89C42×C13—41no—
90C42×C13—41no—
91C42×C13—41no—
92#6099—48no—
93C2×#1055—24no—
94C2×#1055—42no—
95C2×#1055—42no—
96C2×#1055—42no—
97C2×#1055—42no—
98C2×#1055—42no—
99#2855D1311yescharacteristic
100#1817—131no—
101#1728—131no—
102#1272—132no—
103#1271—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13#9912yes—
111C23×C13C2×C22⋊C411yescharacteristic
112Q8×C13—82no—
113C2×C4×C13—24no—
114C2×C4×C13—24no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—44no—
130C2×C4×C13—44no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13#10412yes—
144C2×C4×C13#13112yes—
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13#13711yescharacteristic
147C2×C4×C13#13712yes—
148#1055—44no—
149#1055—82no—
150C22×M16—261no—
151C2×C22⋊Q8Dic1311yescharacteristic
152C22×C42C2×D1311yescharacteristic
153C2×C22⋊C8—261no—
154#391Dic1311yescharacteristic
155#391C2×D1311yescharacteristic
156#389Dic1311yescharacteristic
157#389C2×D1311yescharacteristic
158#387—21no—
159#387—21no—
160#385—21no—
161#381—21no—
162#380Dic1311yescharacteristic
163#336—132no—
164#336—132no—
165#336—261no—
166#336—261no—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13#40811yescharacteristic
175C22×C13C2×#9911yescharacteristic
176C22×C13#41311yescharacteristic
177C22×C13#41711yescharacteristic
178C22×C13#41911yescharacteristic
179C22×C13C2×#10411yescharacteristic
180C22×C13#42111yescharacteristic
181C4×C13—22no—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—21no—
185C4×C13—22no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13—81no—
192C22×Q8C2×Dic1311yescharacteristic
193C23×C4C2×Dic1311yescharacteristic
194C23×C4C22⋊D1311yescharacteristic
195C23×C4C22⋊D1311yescharacteristic
196C2×M16—264no—
197C2×M16—522no—
198C2×M16—522no—
199C22×C8—262no—
200C22×C8—262no—
201C22⋊Q8—42no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic1311yescharacteristic
206C2×C4⋊C4C2×Dic1311yescharacteristic
207C2×C4⋊C4C2×Dic1311yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C42—42no—
211C2×C42C2×Dic1311yescharacteristic
212C2×C42C22⋊D1311yescharacteristic
213C2×C42C22⋊D1311yescharacteristic
214C2×C42C22×D1311yescharacteristic
215C22⋊C8—522no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223C2×C13—42no—
224C2×C13#146811yescharacteristic
225C2×C13#148511yescharacteristic
226C2×C13#149511yescharacteristic
227C2×C13#150411yescharacteristic
228C2×C13#151111yescharacteristic
229C2×C13#152911yescharacteristic
230C2×C13#155911yescharacteristic
231C24C22⋊Dic1311yescharacteristic
232C2×Q8—22no—
233C2×Q8—41no—
234C2×Q8—41no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4C22⋊Dic1311yescharacteristic
250C22×C4C22⋊Dic1311yescharacteristic
251C22×C4C22⋊Dic1311yescharacteristic
252C22×C4C22×Dic1311yescharacteristic
253C22×C4C2×C22⋊D1311yescharacteristic
254C22×C4C2×C22⋊D1311yescharacteristic
255M16—528no—
256C2×C8—264no—
257C2×C8—522no—
258C2×C8—522no—
259C2×C8—522no—
260C2×C8—522no—
261C2×C8—522no—
262C4⋊C4—22no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C42—41no—
272C42—41no—
273C42—41no—
274C42—41no—
275C13#769511yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23#8807412yes—
283C23C2×C22⋊Dic1311yescharacteristic
284Q8—82no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4#8807712yes—
316C2×C4#8819612yes—
317C2×C4#8820212yes—
318C2×C4#8820311yescharacteristic
319C2×C4#8820511yescharacteristic
320C8—524no—
321C8—1042no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×#8807411yescharacteristic
330C22#1171888611yescharacteristic
331C22#1171889311yescharacteristic
332C22#1171889511yescharacteristic
333C22C2×#8807711yescharacteristic
334C22#1171889711yescharacteristic
335C22#1171889811yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—22no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C2—42no—
348C2#1311318411yescharacteristic
349C2#1311325711yescharacteristic
350C2#1311330111yescharacteristic
351C2#1311334011yescharacteristic
352C2#1311336911yescharacteristic
353C2#1311344311yescharacteristic
354C2#1311356611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2855C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2855D13
hypocenterC13#7695
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
3. #13112662C2semidirect
4. #13112659C2semidirect
275. C13#7695semidirect

Maximal subgroups

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

subgroupindex
#131149042
#131145302
#131126622
#131126592
C13×#28552
#769513