Finite Group Databasebeta

← #15763007

Subgroups — #15763007

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114598C211yesmaximal, characteristic
2#13113063C211yesmaximal, characteristic
3#13112714C214yesmaximal
4C13×#2857C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C13×C22⋊Q8—21no—
7C22×C42×C13C2211yescharacteristic
8C13×#391—21no—
9C13×#389—21no—
10C13×#389C412yescomplemented
11C13×#384C411yescharacteristic, complemented
12C13×#380—21no—
13C13×#380C2212yes—
14C2×#88071—21no—
15C2×#88071—21no—
16C2×#88071C2212yes—
17C2×C22⋊#1055C2212yes—
18C2×#88043—21no—
19#11718116—21no—
20C22×Q8×C13—21no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C23×Dic13—22no—
25C13×C4⋊Q8—42no—
26C13×C22⋊Q8—44no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C22⋊C4—22no—
34C2×C42×C13—42no—
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C22×#1055—22no—
40C13×#95—22no—
41C13×#95—22no—
42#88071—24no—
43#88071—24no—
44#88071—42no—
45C22⋊#1055—22no—
46C22⋊#1055Q814yescomplemented
47#88043—42no—
48#9889—131nomaximal, Sylow
49C24×C13C2×D411yescharacteristic
50C2×Q8×C13—42no—
51C2×Q8×C13—42no—
52C2×Q8×C13—42no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×Q812yes—
70C22×C4×C13#4112yes—
71C22×Dic13—24no—
72C22×Dic13—42no—
73C22×Dic13—42no—
74C22×Dic13—42no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C22×Dic13—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—44no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—44no—
85C42×C13—22no—
86C42×C13—22no—
87C42×C13—41no—
88C42×C13—41no—
89C2×#1055—24no—
90C2×#1055—42no—
91C2×#1055—42no—
92#2857D1311yescharacteristic
93#1749—131no—
94#1434—131no—
95#1294—134no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13C2×C22⋊C411yescharacteristic
101C23×C13#12411yescharacteristic
102C23×C13C4⋊Q811yescharacteristic
103C23×C13AGL(1,ℤ/8)12yes—
104C23×C13#13712yes—
105Q8×C13—84no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—44no—
123C2×C4×C13—44no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13#9912yes—
131C2×C4×C13#10412yes—
132C2×C4×C13C4×Q812yes—
133C2×C4×C13C22⋊Q812yes—
134C2×Dic13—44no—
135C2×Dic13—44no—
136C2×Dic13—44no—
137C2×Dic13—82no—
138C2×Dic13—82no—
139C2×Dic13—82no—
140C2×Dic13—82no—
141#1055—44no—
142C2×C4⋊Q8Dic1311yescharacteristic, complemented
143C2×C22⋊Q8—21no—
144C22×C42C2×D1311yescharacteristic
145C2×C22⋊C8—132no—
146C2×#97—261no—
147#391—21no—
148#389—21no—
149#389Dic1312yescomplemented
150#384Dic1311yescharacteristic, complemented
151#380—21no—
152#380C2×D1312yes—
153C2×#95—132no—
154C2×#95—261no—
155C2×#95—261no—
156#336—261no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—22no—
165C22×C13#39111yescharacteristic
166C22×C13C2×#9911yescharacteristic
167C22×C13#41011yescharacteristic
168C22×C13#41811yescharacteristic
169C22×C13#41911yescharacteristic
170C22×C13C2×#10411yescharacteristic
171C22×C13#42111yescharacteristic
172C22×C13#48912yes—
173C22×C13#50112yes—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—22no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—82no—
181C4×C13—82no—
182Dic13—84no—
183C22×Q8—21no—
184C23×C4—262no—
185C23×C4C22⋊D1311yescharacteristic
186C23×C4C22⋊D1311yescharacteristic
187C23×C4C22×D1311yescharacteristic
188C22×C8—262no—
189C4⋊Q8—42no—
190C22⋊Q8—44no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4C2×Dic1312yes—
196C2×C4⋊C4C2×Dic1312yes—
197C2×C22⋊C4—22no—
198C2×C42—42no—
199C2×C42C2×Dic1311yescharacteristic
200C2×C42C2×Dic1311yescharacteristic
201C2×C42C22⋊D1311yescharacteristic
202C2×C42C22⋊D1311yescharacteristic
203C22⋊C8—134no—
204C22⋊C8—262no—
205#97—522no—
206#95—22no—
207#95—22no—
208#95—264no—
209#95—264no—
210#95—522no—
211C2×C13—22no—
212C2×C13—22no—
213C2×C13#150511yescharacteristic
214C2×C13#150811yescharacteristic
215C2×C13#151011yescharacteristic
216C2×C13#151511yescharacteristic
217C2×C13#198611yescharacteristic
218C2×C13#199311yescharacteristic
219C2×C13#199611yescharacteristic
220C24C2×C22⋊D1311yescharacteristic
221C2×Q8—42no—
222C2×Q8—42no—
223C2×Q8—42no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—264no—
235C22×C4—522no—
236C22×C4—522no—
237C22×C4—522no—
238C22×C4—522no—
239C22×C4—522no—
240C22×C4—522no—
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22⋊Dic1311yescharacteristic
244C22×C4C22⋊Dic1311yescharacteristic
245C22×C4Q8×D1312yes—
246C22×C4#613112yes—
247C22×C4C22×Dic1311yescharacteristic
248C22×C4C2×C22⋊D1311yescharacteristic
249C2×C8—264no—
250C2×C8—522no—
251C2×C8—522no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—44no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C22⋊C4—44no—
259C42—22no—
260C42—22no—
261C42—41no—
262C42—41no—
263C13#988911yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#8818612yes—
269C23#8819612yes—
270C23#8819811yescharacteristic
271C23#8820111yescharacteristic
272C23C2×C22⋊Dic1311yescharacteristic
273Q8—84no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—524no—
299C2×C4—524no—
300C2×C4—524no—
301C2×C4—1042no—
302C2×C4—1042no—
303C2×C4—1042no—
304C2×C4—1042no—
305C2×C4#8807412yes—
306C2×C4#8807712yes—
307C2×C4Q8×Dic1312yes—
308C2×C4#8820012yes—
309C8—524no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22#1171874112yes—
319C22#1171875012yes—
320C22#1171887611yescharacteristic
321C22C2×#8807411yescharacteristic
322C22#1171888611yescharacteristic
323C22#1171889111yescharacteristic
324C22C2×#8807711yescharacteristic
325C22#1171889711yescharacteristic
326C22#1171890111yescharacteristic
327C4—22no—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—82no—
334C4—82no—
335C4—1044no—
336C2—22no—
337C2—22no—
338C2#1311334411yescharacteristic
339C2#1311335611yescharacteristic
340C2#1311336511yescharacteristic
341C2#1311338711yescharacteristic
342C2#1311578111yescharacteristic
343C2#1311581011yescharacteristic
344C2#1311582211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2857C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2857D13
hypocenterC13#9889
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
5. C2×C13×C4⋊Q8C4semidirect
10. C13×#389C4semidirect
11. C13×#384C4semidirect
46. C22⋊#1055Q8semidirect
142. C2×C4⋊Q8Dic13semidirect
149. #389Dic13semidirect
150. #384Dic13semidirect
263. C13#9889semidirect

Maximal subgroups

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

subgroupindex
#131145982
#131130632
#131127142
C13×#28572
#988913