Finite Group Databasebeta

← #15763106

Subgroups — #15763106

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114816C211yesmaximal, 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×C4⋊#1055—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—42no—
27C13×C22⋊Q8—42no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C22⋊C4—22no—
35C2×C42×C13—42no—
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C22×#1055—22no—
41C13×#95—22no—
42C13×#95—22no—
43#88071—22no—
44#88071—42no—
45#88071—42no—
46#88071Q814yescomplemented
47C22⋊#1055—24no—
48C4⋊#1055—42no—
49#9912—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C2×Q8×C13—42no—
52C2×Q8×C13—42no—
53C2×Q8×C13—42no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—41no—
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×C13D812yes—
68C22×C4×C13SD1612yes—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×Q812yes—
72C22×C4×C13#4112yes—
73C22×Dic13—24no—
74C22×Dic13—42no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C22×Dic13—42no—
78C22×Dic13—42no—
79C22×Dic13—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—44no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C42×C13—22no—
89C42×C13—22no—
90C42×C13—41no—
91C42×C13—41no—
92C2×#1055—42no—
93C2×#1055—42no—
94C2×#1055—42no—
95#2857D1311yescharacteristic
96#1797—131no—
97#1434—131no—
98#1294—134no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13C22⋊Q812yes—
105C23×C13C2×D811yescharacteristic
106C23×C13C2×SD1611yescharacteristic
107C23×C13#13712yes—
108Q8×C13—84no—
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—21no—
121C2×C4×C13—21no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—44no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13#9912yes—
134C2×C4×C13#10212yes—
135C2×C4×C13#10212yes—
136C2×C4×C13C4×Q812yes—
137C2×C4×C13#12411yescharacteristic
138C2×C4×C13C4⋊Q811yescharacteristic
139C2×Dic13—44no—
140C2×Dic13—44no—
141C2×Dic13—44no—
142C2×Dic13—82no—
143C2×Dic13—82no—
144C2×Dic13—82no—
145C2×Dic13—82no—
146#1055—82no—
147C2×C4⋊Q8Dic1311yescharacteristic, complemented
148C2×C22⋊Q8—21no—
149C22×C42C2×D1311yescharacteristic
150C2×C4⋊C8—261no—
151C2×C22⋊C8—132no—
152#391—21no—
153#389—21no—
154#389Dic1312yescomplemented
155#384Dic1311yescharacteristic, complemented
156#380—21no—
157#380C2×D1312yes—
158C2×#95—132no—
159C2×#95—261no—
160C2×#95—261no—
161#336—261no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—22no—
165C22×C13—22no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13#39111yescharacteristic
171C22×C13C2×#9911yescharacteristic
172C22×C13#41011yescharacteristic
173C22×C13C2×#10211yescharacteristic
174C22×C13#41911yescharacteristic
175C22×C13#42111yescharacteristic
176C22×C13#42111yescharacteristic
177C22×C13#47412yes—
178C22×C13#47512yes—
179C4×C13—21no—
180C4×C13—22no—
181C4×C13—21no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—22no—
185C4×C13—41no—
186C4×C13—82no—
187C4×C13—82no—
188Dic13—84no—
189C22×Q8—21no—
190C23×C4—262no—
191C23×C4C22⋊D1311yescharacteristic
192C23×C4C22⋊D1311yescharacteristic
193C23×C4C22×D1311yescharacteristic
194C22×C8—262no—
195C4⋊Q8—42no—
196C22⋊Q8—42no—
197C22⋊Q8—42no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4C2×Dic1312yes—
203C2×C4⋊C4C2×Dic1312yes—
204C2×C22⋊C4—22no—
205C2×C42—42no—
206C2×C42C2×Dic1311yescharacteristic
207C2×C42C2×Dic1311yescharacteristic
208C2×C42C22⋊D1311yescharacteristic
209C2×C42C22⋊D1311yescharacteristic
210C4⋊C8—522no—
211C22⋊C8—264no—
212#95—22no—
213#95—22no—
214#95—134no—
215#95—262no—
216#95—522no—
217#95—522no—
218C2×C13—22no—
219C2×C13—22no—
220C2×C13#151111yescharacteristic
221C2×C13#151511yescharacteristic
222C2×C13#151711yescharacteristic
223C2×C13#151911yescharacteristic
224C2×C13#198811yescharacteristic
225C2×C13#199511yescharacteristic
226C2×C13#199611yescharacteristic
227C24C2×C22⋊D1311yescharacteristic
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—42no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—264no—
241C22×C4—522no—
242C22×C4—522no—
243C22×C4—522no—
244C22×C4—522no—
245C22×C4—522no—
246C22×C4—522no—
247C22×C4#610412yes—
248C22×C4#610512yes—
249C22×C4C22⋊Dic1311yescharacteristic
250C22×C4C22⋊Dic1311yescharacteristic
251C22×C4C22⋊Dic1311yescharacteristic
252C22×C4C22⋊Dic1311yescharacteristic
253C22×C4Q8×D1312yes—
254C22×C4#613112yes—
255C22×C4C22×Dic1311yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257C2×C8—522no—
258C2×C8—522no—
259C2×C8—522no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—44no—
265C4⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C42—22no—
269C42—22no—
270C42—41no—
271C42—41no—
272C13#991211yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23C2×#610411yescharacteristic
278C23C2×#610511yescharacteristic
279C23#8819612yes—
280C23#8820012yes—
281C23C2×C22⋊Dic1311yescharacteristic
282Q8—84no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
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—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—524no—
308C2×C4—524no—
309C2×C4—524no—
310C2×C4—1042no—
311C2×C4—1042no—
312C2×C4—1042no—
313C2×C4—1042no—
314C2×C4#8807212yes—
315C2×C4#8807212yes—
316C2×C4#8807412yes—
317C2×C4#8819811yescharacteristic
318C2×C4Q8×Dic1312yes—
319C2×C4#8820111yescharacteristic
320C8—1042no—
321C22—22no—
322C22—22no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—22no—
328C22—22no—
329C22#1171874812yes—
330C22#1171875512yes—
331C22C2×#8807211yescharacteristic
332C22C2×#8807411yescharacteristic
333C22#1171888611yescharacteristic
334C22#1171889111yescharacteristic
335C22#1171889711yescharacteristic
336C22#1171889711yescharacteristic
337C22#1171890111yescharacteristic
338C4—22no—
339C4—22no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—22no—
344C4—41no—
345C4—82no—
346C4—82no—
347C4—1044no—
348C2—22no—
349C2—22no—
350C2#1311336911yescharacteristic
351C2#1311338711yescharacteristic
352C2#1311339611yescharacteristic
353C2#1311340411yescharacteristic
354C2#1311578911yescharacteristic
355C2#1311581811yescharacteristic
356C2#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#9912
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. #88071Q8semidirect
147. C2×C4⋊Q8Dic13semidirect
154. #389Dic13semidirect
155. #384Dic13semidirect
272. C13#9912semidirect

Maximal subgroups

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

subgroupindex
#131148162
#131130632
#131127142
C13×#28572
#991213