Finite Group Databasebeta

← #15751204

Subgroups — #15751204

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114979C211yesmaximal, characteristic, complemented
2#13114953C211yesmaximal, characteristic, complemented
3#13112659C212yesmaximal, complemented
4#13112657C212yesmaximal
5C13×#2293C211yesmaximal, characteristic
6C2×C4×D4×C13C411yescharacteristic
7C2×C13×#117—21no—
8C13×#390C411yescharacteristic
9C13×#390C2211yescharacteristic
10C13×#389C411yescharacteristic
11C13×#389C2211yescharacteristic
12C13×#388—21no—
13C13×#388—21no—
14C4×C13×C4⋊C4C411yescharacteristic
15C4×C13×C22⋊C4—21no—
16C43×C13C2211yescharacteristic
17C2×C4⋊#1055—21no—
18#11718116—21no—
19#11718116—21no—
20#11718116—21no—
21#11718116C2212yes—
22#11718116C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13—21no—
25C4×D4×C13—22no—
26C4×D4×C13—22no—
27C13×#117—42no—
28C13×#117—42no—
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×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C42×C13—21no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×C42×C13C2311yescharacteristic
47C22×#1055—22no—
48C22×#1055—22no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C4⋊#1055—42no—
53#7642—131nomaximal, Sylow
54C24×C13—21no—
55C2×D4×C13—21no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13M1612yes—
59C22×C4×C13—24no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4M1612yes—
79C13×C22⋊C4—24no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—22no—
88C42×C13—41no—
89C42×C13—41no—
90C42×C13—41no—
91C42×C13—41no—
92C42×C13—42no—
93C42×C13D812yes—
94C42×C13SD1612yes—
95C2×#1055—42no—
96C2×#1055—42no—
97C2×#1055—42no—
98C2×#1055—42no—
99C2×#1055—42no—
100C2×#1055—42no—
101#2293D1311yescharacteristic
102#1839—131no—
103#1831—131no—
104#1271—132no—
105#1270—132no—
106C23×C13—22no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13C2×C22⋊C411yescharacteristic
114D4×C13—42no—
115D4×C13—42no—
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—22no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—48no—
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#10212yes—
143C2×C4×C13#10212yes—
144C2×C4×C13C2×M1611yescharacteristic
145C2×C4×C13C2×M1611yescharacteristic
146C2×C4×C13C2×D811yescharacteristic
147C2×C4×C13C2×SD1611yescharacteristic
148C2×C4×C13#13512yes—
149#1055—82no—
150#1055—82no—
151C2×C4×D4Dic1311yescharacteristic
152C2×#117—21no—
153C2×C4⋊C8—261no—
154#390Dic1311yescharacteristic
155#390C2×D1311yescharacteristic
156#389Dic1311yescharacteristic
157#389C2×D1311yescharacteristic
158#388—21no—
159#388—21no—
160C4×C4⋊C4Dic1311yescharacteristic
161C4×C22⋊C4—21no—
162C43C2×D1311yescharacteristic
163#336—132no—
164#336—132no—
165#336—261no—
166#336—261no—
167#336—261no—
168C22×C13—42no—
169C22×C13—42no—
170C22×C13—42no—
171C22×C13—81no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13—81no—
175C22×C13#40711yescharacteristic
176C22×C13#41011yescharacteristic
177C22×C13#41311yescharacteristic
178C22×C13C2×#10211yescharacteristic
179C22×C13#41611yescharacteristic
180C22×C13#42111yescharacteristic
181C22×C13#42111yescharacteristic
182C4×C13—22no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—22no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—22no—
189C4×C13—42no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—81no—
193C4×C13—81no—
194C22×D4C2×Dic1311yescharacteristic
195C23×C4—21no—
196C22×C8—262no—
197C22×C8—262no—
198C4×D4—22no—
199C4×D4—22no—
200#117—42no—
201#117—42no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×Dic1311yescharacteristic
205C2×C4⋊C4C2×Dic1311yescharacteristic
206C2×C4⋊C4C2×Dic1311yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C42—21no—
213C2×C42C2×Dic1311yescharacteristic
214C2×C42C2×Dic1311yescharacteristic
215C2×C42C22⋊D1311yescharacteristic
216C2×C42C22⋊D1311yescharacteristic
217C2×C42C22⋊D1311yescharacteristic
218C2×C42C22⋊D1311yescharacteristic
219C2×C42C22×D1311yescharacteristic
220C4⋊C8—522no—
221#95—21no—
222#95—21no—
223#95—21no—
224C2×C13—82no—
225C2×C13#146411yescharacteristic
226C2×C13#148611yescharacteristic
227C2×C13#148811yescharacteristic
228C2×C13#151711yescharacteristic
229C2×C13#152111yescharacteristic
230C2×C13#153511yescharacteristic
231C2×C13#154011yescharacteristic
232C24—21no—
233C2×D4—21no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4#609912yes—
237C22×C4—24no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4C22⋊Dic1311yescharacteristic
244C22×C4C22⋊Dic1311yescharacteristic
245C22×C4C22⋊Dic1311yescharacteristic
246C22×C4C22⋊Dic1311yescharacteristic
247C22×C4C22×Dic1311yescharacteristic
248C22×C4C2×C22⋊D1311yescharacteristic
249C22×C4C2×C22⋊D1311yescharacteristic
250C2×C8—522no—
251C2×C8—522no—
252C2×C8—522no—
253C2×C8—522no—
254C2×C8—522no—
255C2×C8—522no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4#609912yes—
263C22⋊C4—24no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—42no—
269C42—21no—
270C42—21no—
271C42—22no—
272C42—41no—
273C42—41no—
274C42—41no—
275C42—41no—
276C42—42no—
277C42#610412yes—
278C42#610512yes—
279C13#764211yescharacteristic, complemented, Sylow
280C23—22no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23C2×C22⋊Dic1311yescharacteristic
288D4—42no—
289D4—42no—
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—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—48no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4#8807212yes—
317C2×C4#8807212yes—
318C2×C4C2×#609911yescharacteristic
319C2×C4C2×#609911yescharacteristic
320C2×C4C2×#610411yescharacteristic
321C2×C4C2×#610511yescharacteristic
322C2×C4#8820412yes—
323C8—1042no—
324C8—1042no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22#1171886811yescharacteristic
333C22C2×#8807211yescharacteristic
334C22#1171889411yescharacteristic
335C22#1171889711yescharacteristic
336C22#1171889711yescharacteristic
337C22#1171889811yescharacteristic
338C22#1171890111yescharacteristic
339C4—21no—
340C4—21no—
341C4—22no—
342C4—21no—
343C4—21no—
344C4—22no—
345C4—22no—
346C4—41no—
347C4—42no—
348C4—41no—
349C4—81no—
350C4—81no—
351C2—82no—
352C2#1311317011yescharacteristic
353C2#1311326111yescharacteristic
354C2#1311327011yescharacteristic
355C2#1311339611yescharacteristic
356C2#1311341311yescharacteristic
357C2#1311346711yescharacteristic
358C2#1311348511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2293C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2293D13
hypocenterC13#7642
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

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

NH ≅ G/Ntype
1. #13114979C2semidirect
2. #13114953C2semidirect
3. #13112659C2semidirect
279. C13#7642semidirect

Maximal subgroups

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

subgroupindex
#131149792
#131149532
#131126592
#131126572
C13×#22932
#764213