Finite Group Databasebeta

← #15758009

Subgroups — #15758009

Order 3328.

528 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#13123400C211yesmaximal, characteristic
2#13113265C212yesmaximal, complemented
3#13113150C211yesmaximal, characteristic
4#13112739C212yesmaximal, complemented
5C13×#2396C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C22×#6099—21no—
9C13×#400C411yescharacteristic
10C13×#399C411yescharacteristic
11C13×#398—21no—
12C13×#396—21no—
13C13×#395C411yescharacteristic
14C13×#393C411yescharacteristic
15C4×C13×C4⋊C4—21no—
16C4×C13×C4⋊C4C2211yescharacteristic
17C4×C13×C22⋊C4—21no—
18#11718660—24no—
19#11718586C2212yes—
20#11718585—21no—
21#11718585C2212yes—
22Q8⋊#1055—24no—
23#11718120—21no—
24#11718117—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C4×Q8×C13—22no—
28C4×Q8×C13—22no—
29C13×#117—22no—
30C13×#117—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13—21no—
44C2×C42×C13D411yescharacteristic
45C2×C42×C13C2311yescharacteristic
46C2×#6099—22no—
47C2×#6099—22no—
48C2×#6099—42no—
49C2×#6099—42no—
50C22×#1055—22no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95C2×C411yescharacteristic
56C13×#95C2×C411yescharacteristic
57C22⋊#1055—22no—
58C4⋊#1055—24no—
59C4⋊#1055—22no—
60C4⋊#1055—22no—
61C4⋊#1055D414yes—
62C4×#1055—22no—
63#9033—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C2×Q8×C13—22no—
66C2×Q8×C13—42no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13SD1612yes—
79C22×C4×C13Q1612yes—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C13×C4⋊C4—22no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—42no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—22no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—41no—
97C42×C13—41no—
98C42×C13—41no—
99C42×C13—41no—
100C42×C13C2×D412yes—
101C42×C13#4112yes—
102#6099—44no—
103#6099—42no—
104#6099—42no—
105C2×#1055—24no—
106C2×#1055—44no—
107C2×#1055—42no—
108#2905—131no—
109#2396D1311yescharacteristic
110#1487—132no—
111#1458—131no—
112#1303—132no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13#10312yes—
118C23×C13C2×C22⋊C411yescharacteristic
119Q8×C13—24no—
120Q8×C13—42no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
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—41no—
144C2×C4×C13—41no—
145C2×C4×C13#10312yes—
146C2×C4×C13C4×D412yes—
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13#12112yes—
149C2×C4×C13#12311yescharacteristic
150C2×C4×C13C2×SD1611yescharacteristic
151C2×C4×C13C2×Q1611yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13#13711yescharacteristic
154#1055—44no—
155#1055—82no—
156C22×M16—261no—
157C2×C4×Q8C2×D1311yescharacteristic
158C2×#117C2×D1311yescharacteristic
159#431—132no—
160#424—264no—
161#423—132no—
162#423—261no—
163#400Dic1311yescharacteristic
164#399Dic1311yescharacteristic
165#398—21no—
166#396—21no—
167#395Dic1311yescharacteristic
168#393Dic1311yescharacteristic
169C4×C4⋊C4—21no—
170C4×C4⋊C4C2×D1311yescharacteristic
171C4×C22⋊C4—21no—
172Q8⋊C8—264no—
173#324—261no—
174#323—261no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—22no—
178C22×C13—42no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—81no—
182C22×C13#38611yescharacteristic
183C22×C13C2×#10311yescharacteristic
184C22×C13#41711yescharacteristic
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—22no—
188C4×C13—42no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—42no—
192C4×C13—81no—
193C4×C13—81no—
194C4×C13#45011yescharacteristic
195C4×C13#45111yescharacteristic
196C4×C13#48311yescharacteristic
197C4×C13#48411yescharacteristic
198C22×Q8C2×Dic1311yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C2×M16—262no—
201C2×M16—262no—
202C2×M16—522no—
203C2×M16—522no—
204C22×C8—262no—
205C4×Q8—22no—
206C4×Q8—22no—
207#117—22no—
208#117—22no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×Dic1311yescharacteristic
214C2×C4⋊C4C2×Dic1311yescharacteristic
215C2×C4⋊C4C22⋊D1311yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4C2×Dic1311yescharacteristic
219C2×C22⋊C4C22⋊D1311yescharacteristic
220C2×C42—21no—
221C2×C42—21no—
222C2×C42C22⋊D1311yescharacteristic
223C2×C42C22×D1311yescharacteristic
224C4⋊C8—134no—
225C4⋊C8—264no—
226C4⋊C8—262no—
227C4⋊C8—262no—
228C22⋊C8—262no—
229C4×C8—262no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95C2×Dic1311yescharacteristic
235#95C2×Dic1311yescharacteristic
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—42no—
239C2×C13#187211yescharacteristic
240C2×C13#188411yescharacteristic
241C2×C13#189111yescharacteristic
242C24C22⋊Dic1311yescharacteristic
243C2×Q8—22no—
244C2×Q8—42no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4#610612yes—
254C22×C4#610712yes—
255C22×C4C22⋊Dic1311yescharacteristic
256C22×C4C22⋊Dic1311yescharacteristic
257C22×C4C22⋊Dic1311yescharacteristic
258C22×C4C22×Dic1311yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261M16—524no—
262M16—522no—
263M16—522no—
264C2×C8—264no—
265C2×C8—524no—
266C2×C8—522no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C42—21no—
279C42—21no—
280C42—41no—
281C42—41no—
282C42—41no—
283C42—41no—
284C42D4×D1312yes—
285C42#612912yes—
286C13#903311yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23#8807512yes—
292C23C2×C22⋊Dic1311yescharacteristic
293Q8—24no—
294Q8—42no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
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—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4#8807512yes—
320C2×C4D4×Dic1312yes—
321C2×C4#8818911yescharacteristic
322C2×C4#8819111yescharacteristic
323C2×C4#8819312yes—
324C2×C4C2×#610611yescharacteristic
325C2×C4C2×#610711yescharacteristic
326C2×C4#8820311yescharacteristic
327C2×C4#8820511yescharacteristic
328C8—524no—
329C8—1042no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—81no—
337C22#1171888111yescharacteristic
338C22C2×#8807511yescharacteristic
339C22#1171889311yescharacteristic
340C4—22no—
341C4—22no—
342C4—22no—
343C4—42no—
344C4—41no—
345C4—41no—
346C4—42no—
347C4—81no—
348C4—81no—
349C4#1171870411yescharacteristic
350C4#1171870511yescharacteristic
351C4#1171870711yescharacteristic
352C4#1171871111yescharacteristic
353C2—21no—
354C2—21no—
355C2—42no—
356C2#1311514411yescharacteristic
357C2#1311522011yescharacteristic
358C2#1311525511yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2396C2
socleC22×C13#386
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2396D13
hypocenterC13#9033
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2396

Complements

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

NH ≅ G/Ntype
2. #13113265C2semidirect
4. #13112739C2semidirect
286. C13#9033semidirect

Maximal subgroups

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

subgroupindex
#131234002
#131132652
#131131502
#131127392
C13×#23962
#903313