Finite Group Databasebeta

← #15863079

Subgroups — #15863079

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718660C211yesmaximal, characteristic
2#117×Dic13C211yesmaximal, characteristic
3#13114955C214yesmaximal, complemented
4#13114952C214yesmaximal, complemented
5#13114534C211yesmaximal, characteristic
6#13114532C211yesmaximal, characteristic
7#13114529C211yesmaximal, characteristic
8C2×#11718142C211yesmaximal, characteristic
9C2×C13×#424C211yesmaximal, characteristic
10C22×C13×M16C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C22×C4×Dic13C2211yescharacteristic
15C22×#6099C2211yescharacteristic
16C23×#1055C2211yescharacteristic
17C13×#424—24no—
18C2×C13×C4⋊C8C2214yes—
19#11718660—24no—
20C4⋊C4×Dic13C412yes—
21C4⋊C4×Dic13C412yes—
22C22⋊C4×Dic13C414yes—
23#11718593C2212yes—
24C42×Dic13C2212yes—
25C2×C4⋊#1055C2214yes—
26#11718142C2212yes—
27#11718142C2212yes—
28#11718142C2214yes—
29#11718142C2214yes—
30#11718142C2212yes—
31#11718142C2212yes—
32C23×C4×C13C2311yescharacteristic
33C23×Dic13C2×C412yes—
34C2×C13×M16—22no—
35C2×C13×M16—22no—
36C2×C13×M16—22no—
37C22×C8×C13—22no—
38C22×C8×C13—22no—
39C22×C8×C13—22no—
40C22×C8×C13C2312yes—
41C22×C8×C13C2312yes—
42C13×#117D414yes—
43C13×#117Q814yes—
44C2×C13×C4⋊C4C2×C412yes—
45C2×C13×C22⋊C4C2×C412yes—
46C2×C42×C13C2312yes—
47C2×C22⋊Dic13C2×C412yes—
48#88180—22no—
49#88180—22no—
50C2×C4⋊Dic13C2×C411yescharacteristic
51C2×C4⋊Dic13C2×C411yescharacteristic
52C2×C4×Dic13—22no—
53C2×C4×Dic13—22no—
54C2×C4×Dic13C2×C412yes—
55C2×C4×Dic13C2×C414yes—
56C2×C4×Dic13C2×C414yes—
57C2×C4×Dic13C2311yescharacteristic
58C2×C4×Dic13C2311yescharacteristic
59C2×C4×Dic13C2312yes—
60C2×#6099—22no—
61C2×#6099—22no—
62C2×#6099—22no—
63C22×#1055—22no—
64C22×#1055—22no—
65C22×#1055—22no—
66C22×#1055C2312yes—
67C22×#1055C2312yes—
68C13×C4⋊C8—28no—
69#88071C2×C414yes—
70#88071C2×C414yes—
71C4⋊#1055—28no—
72#20754—131nomaximal, Sylow
73C24×C13C22×C411yescharacteristic
74C22×C4×C13C22×C414yes—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D412yes—
77C22×C4×C13C2×Q812yes—
78C22×C4×C13#4112yes—
79C22×C4×C13#4112yes—
80C22×C4×C13#4112yes—
81C22×C4×C13#4112yes—
82C22×C4×C13C2411yescharacteristic
83C22×Dic13—24no—
84C22×Dic13—24no—
85C22×Dic13—42no—
86C22×Dic13C22×C412yes—
87C22×Dic13C22×C412yes—
88C22×Dic13C22×C412yes—
89C22×Dic13C22×C412yes—
90C13×M16—44no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13—22no—
94C2×C8×C13—22no—
95C2×C8×C13—22no—
96C2×C8×C13—22no—
97C2×C8×C13—44no—
98C13×C4⋊C4C4⋊C418yes—
99C13×C22⋊C4C4⋊C418yes—
100C42×C13C2×D414yes—
101C42×C13C2×Q814yes—
102C22⋊Dic13—24no—
103C4⋊Dic13—22no—
104C4⋊Dic13—22no—
105C4×Dic13—24no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13—21no—
109C4×Dic13—21no—
110C4×Dic13—22no—
111C4×Dic13—22no—
112C4×Dic13—28no—
113C4×Dic13—44no—
114#6099—44no—
115C2×#1055—22no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055—22no—
119C2×#1055—22no—
120C2×#1055—22no—
121C2×#1055—44no—
122C2×#424—131no—
123C2×#424D1311yescharacteristic
124C4×#117—131no—
125#1832—134no—
126#1831—134no—
127#1729—131no—
128#1729—131no—
129#1728—131no—
130C2×#336—131no—
131C23×C13—22no—
132C23×C13—22no—
133C23×C13C2×C4⋊C412yes—
134C23×C13#11712yes—
135C23×C13#11712yes—
136C23×C13C23×C411yescharacteristic
137C2×C4×C13—24no—
138C2×C4×C13—24no—
139C2×C4×C13C2×C4⋊C418yes—
140C2×C4×C13C2×C4⋊C412yes—
141C2×C4×C13#11712yes—
142C2×C4×C13#11712yes—
143C2×C4×C13#12414yes—
144C2×C4×C13#12414yes—
145C2×C4×C13#12514yes—
146C2×C4×C13#12514yes—
147C2×C4×C13C22×D411yescharacteristic
148C2×C4×C13C22×Q811yescharacteristic
149C2×C4×C13C2×#4111yescharacteristic
150C2×C4×C13C2×#4111yescharacteristic
151C2×C4×C13C2×#4111yescharacteristic
152C2×C4×C13C2×#4111yescharacteristic
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—22no—
157C2×Dic13—22no—
158C2×Dic13—24no—
159C2×Dic13—22no—
160C2×Dic13—24no—
161C2×Dic13—22no—
162C2×Dic13—48no—
163C2×Dic13#13114yes—
164C8×C13—42no—
165C8×C13—42no—
166#1055—42no—
167#1055—42no—
168C22×M16—131no—
169C22×M16C2×D1311yescharacteristic
170C23×C8—131no—
171C23×C8C2×D1311yescharacteristic
172C2×#117—131no—
173C2×#117C2×D1311yescharacteristic
174C22×C42—131no—
175#424—24no—
176#424—264no—
177C2×C4⋊C8—134no—
178C2×C4⋊C8C2×D1314yes—
179C4×C4⋊C4—132no—
180C4×C4⋊C4—132no—
181C4×C22⋊C4—134no—
182#376—132no—
183C43—132no—
184#336—132no—
185#336—132no—
186#336—134no—
187#336—134no—
188#336—132no—
189#336—132no—
190C22×C13—24no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—24no—
194C22×C13#38214yes—
195C22×C13C22×C4⋊C411yescharacteristic
196C22×C13C2×#11711yescharacteristic
197C22×C13C2×#11711yescharacteristic
198C22×C13C2×#13112yes—
199C22×C13#56812yes—
200C4×C13—28no—
201C4×C13#38214yes—
202C4×C13C2×#12411yescharacteristic
203C4×C13C2×#12411yescharacteristic
204C4×C13C2×#12511yescharacteristic
205C4×C13C2×#12511yescharacteristic
206Dic13—24no—
207Dic13—42no—
208Dic13—42no—
209Dic13—42no—
210C23×C4—132no—
211C23×C4C22×D1311yescharacteristic
212C2×M16—22no—
213C2×M16—22no—
214C2×M16—22no—
215C2×M16—262no—
216C2×M16—262no—
217C2×M16—262no—
218C22×C8—22no—
219C22×C8—22no—
220C22×C8—22no—
221C22×C8—132no—
222C22×C8—132no—
223C22×C8—262no—
224C22×C8—262no—
225C22×C8—262no—
226C22×C8C22×D1312yes—
227C22×C8C22×D1312yes—
228#117—262no—
229#117—262no—
230#117Dic2614yes—
231#117C22⋊D1314yes—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4C4×D1312yes—
235C2×C22⋊C4—132no—
236C2×C22⋊C4C4×D1312yes—
237C2×C42—134no—
238C2×C42—132no—
239C2×C42—132no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—134no—
243C2×C42—262no—
244C2×C42—262no—
245C2×C42C22×D1312yes—
246C4⋊C8—28no—
247C4⋊C8—268no—
248#95—134no—
249#95—134no—
250C2×C13—24no—
251C2×C13C2×#38211yescharacteristic
252C2×C13#290612yes—
253C2×C13#292211yescharacteristic
254C2×C13#292311yescharacteristic
255C2×C13#292412yes—
256C24C2×C4×D1311yescharacteristic
257C22×C4—132no—
258C22×C4—132no—
259C22×C4—132no—
260C22×C4—132no—
261C22×C4—264no—
262C22×C4—264no—
263C22×C4—522no—
264C22×C4C2×Dic2612yes—
265C22×C4C2×C4×D1314yes—
266C22×C4C2×C4×D1311yescharacteristic
267C22×C4#612912yes—
268C22×C4#612912yes—
269C22×C4#613112yes—
270C22×C4#613112yes—
271C22×C4C2×C22⋊D1312yes—
272C22×C4C23×D1311yescharacteristic
273M16—44no—
274M16—524no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—44no—
282C2×C8—262no—
283C2×C8—262no—
284C2×C8—262no—
285C2×C8—262no—
286C2×C8—262no—
287C2×C8—262no—
288C2×C8—524no—
289C4⋊C4—262no—
290C4⋊C4—262no—
291C4⋊C4#610118yes—
292C22⋊C4—264no—
293C22⋊C4#610118yes—
294C42—268no—
295C42—264no—
296C42—261no—
297C42—261no—
298C42—262no—
299C42—261no—
300C42—261no—
301C42—262no—
302C42—524no—
303C42C2×Dic2614yes—
304C42C2×C22⋊D1314yes—
305C13#2075411yescharacteristic, complemented, Sylow
306C23—22no—
307C23—22no—
308C23#8814612yes—
309C23#8814612yes—
310C23C2×#610112yes—
311C23C22×C4×D1311yescharacteristic
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—134no—
315C2×C4—262no—
316C2×C4—262no—
317C2×C4—264no—
318C2×C4—262no—
319C2×C4—264no—
320C2×C4—262no—
321C2×C4—262no—
322C2×C4—262no—
323C2×C4—262no—
324C2×C4—528no—
325C2×C4#8814414yes—
326C2×C4#8814414yes—
327C2×C4#8814612yes—
328C2×C4#8814612yes—
329C2×C4C2×#610118yes—
330C2×C4C2×#610112yes—
331C2×C4#8819014yes—
332C2×C4#8820114yes—
333C2×C4C22×Dic2611yescharacteristic
334C2×C4C2×#612911yescharacteristic
335C2×C4C2×#612911yescharacteristic
336C2×C4C2×#613111yescharacteristic
337C2×C4C2×#613111yescharacteristic
338C2×C4C22×C22⋊D1311yescharacteristic
339C8—42no—
340C8—42no—
341C8—522no—
342C8—522no—
343C22—24no—
344C22—22no—
345C22—22no—
346C22—24no—
347C22#1171863814yes—
348C22C2×#8814611yescharacteristic
349C22C2×#8814611yescharacteristic
350C22D13×#13112yes—
351C22#1171945512yes—
352C22C22×#610111yescharacteristic
353C4—28no—
354C4—264no—
355C4—522no—
356C4—522no—
357C4—522no—
358C4#1171863814yes—
359C4C2×#8814411yescharacteristic
360C4C2×#8814411yescharacteristic
361C4C2×#8819011yescharacteristic
362C4C2×#8820111yescharacteristic
363C2—24no—
364C2C2×#1171863811yescharacteristic
365C2#1312340212yes—
366C2#1312347911yescharacteristic
367C2#1312348611yescharacteristic
368C2#1312349312yes—
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#424C2
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenterC2×#424D13
hypocenterC13#20754
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
3. #13114955C2semidirect
4. #13114952C2semidirect
305. C13#20754semidirect

Maximal subgroups

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

subgroupindex
C2×#117186602
#117×Dic132
#131149552
#131149522
#131145342
#131145322
#131145292
C2×#117181422
C2×C13×#4242
#2075413