Finite Group Databasebeta

← #15751018

Subgroups — #15751018

Order 3328.

514 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117317C211yesmaximal, characteristic
2#13114815C211yesmaximal, characteristic
3#13114815C211yesmaximal, characteristic
4#13112660C211yesmaximal, characteristic, complemented
5#13112659C211yesmaximal, characteristic, complemented
6#13112658C211yesmaximal, characteristic, complemented
7C13×#1271C211yesmaximal, characteristic, complemented
8C2×#88146C411yescharacteristic
9C2×#88146C411yescharacteristic
10C2×C42×D13C2211yescharacteristic
11C13×#389C2211yescharacteristic
12C2×#88060—21no—
13C2×#88060—21no—
14C2×#88054—21no—
15C2×#88054—21no—
16#11718650—21no—
17#11718646C411yescharacteristic
18C4⋊C4×Dic13—21no—
19#11718634C411yescharacteristic
20#11718589C2211yescharacteristic
21#11718329—21no—
22#11718310—21no—
23C13×#336C2211yescharacteristic
24C13×#336C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×C4×D13C2×C411yescharacteristic
28C22×C4×D13D411yescharacteristic
29C22×C4×D13D411yescharacteristic
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×#6103—21no—
37C2×#6103—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C22×#1055—21no—
49C22×#1055—21no—
50#88146—22no—
51#88146—42no—
52#88146C814yescomplemented
53C42×D13—42no—
54C13×#95—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88060—42no—
59#88060—42no—
60#88054—42no—
61#88054—42no—
62#7598—131nomaximal, Sylow
63C23×D13C22⋊C411yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C2×C4×D13—22no—
75C2×C4×D13—22no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13C2×C812yes—
85C2×C4×D13M1612yes—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C2×C8×C13—41no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4C2×C812yes—
97C42×C13—41no—
98#6103—24no—
99#6103—42no—
100C4⋊Dic13—21no—
101C4⋊Dic13—42no—
102C4⋊Dic13—41no—
103C4⋊Dic13C2×C812yes—
104#6101—42no—
105#6101—41no—
106#6101—41no—
107C4×Dic13—24no—
108C4×Dic13—22no—
109C4×Dic13—22no—
110C4×Dic13—41no—
111C4×Dic13—42no—
112C2×#1055—41no—
113C2×#1055—41no—
114C2×#1055—41no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118#2296—131no—
119#1797—131no—
120#1797—131no—
121#1271—131no—
122#1271—131no—
123#1271—131no—
124#1271D1311yescharacteristic, complemented
125C23×C13C2×C22⋊C411yescharacteristic
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—21no—
132C22×D13C22⋊C812yes—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—22no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13C22×C811yescharacteristic
146C2×C4×C13C2×M1611yescharacteristic
147C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C13#13711yescharacteristic
150C2×C4×C13#13711yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13C22⋊C812yes—
164C2×Dic13#9912yes—
165C2×Dic13#10112yes—
166C4×D13—24no—
167C4×D13—24no—
168C4×D13—42no—
169C4×D13—42no—
170C4×D13—42no—
171C4×D13—42no—
172C8×C13—81no—
173C8×C13—81no—
174#1055—81no—
175#1055—81no—
176C2×#117—131no—
177C2×#117—131no—
178C22×C42—131no—
179C2×C4⋊C8—261no—
180C2×C4⋊C8—261no—
181C2×C22⋊C8—261no—
182C2×C22⋊C8—261no—
183#389—131no—
184#389—131no—
185#389—131no—
186#389C2×D1311yescharacteristic
187#385—261no—
188#385—261no—
189C4×C4⋊C4—261no—
190C4×C4⋊C4—261no—
191#336—131no—
192#336—131no—
193#336C2×D1311yescharacteristic
194#336C2×D1311yescharacteristic
195C22×C13C2×C22⋊C811yescharacteristic
196C22×C13C2×#9911yescharacteristic
197C22×C13C2×#10111yescharacteristic
198C22×C13#41711yescharacteristic
199C22×C13#41711yescharacteristic
200C22×C13#42111yescharacteristic
201C22×C13#42111yescharacteristic
202C2×D13—22no—
203C2×D13—22no—
204C2×D13—22no—
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—41no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—42no—
216C4×C13—81no—
217Dic13—42no—
218Dic13—41no—
219Dic13—41no—
220Dic13—81no—
221Dic13#32414yes—
222C23×C4—131no—
223C23×C4—131no—
224C23×C4—131no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—261no—
228C22×C8—261no—
229#117—134no—
230#117—262no—
231#117—522no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4C4×D1311yescharacteristic
239C2×C4⋊C4C4×D1311yescharacteristic
240C2×C22⋊C4—261no—
241C2×C22⋊C4—261no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—261no—
246C2×C42—261no—
247C2×C42—522no—
248C2×C42C22×D1311yescharacteristic
249C4⋊C8—522no—
250C4⋊C8—522no—
251C22⋊C8—522no—
252C22⋊C8—522no—
253#95—21no—
254#95—261no—
255#95—261no—
256#95—261no—
257C2×C13C2×#32411yescharacteristic
258C2×C13#147711yescharacteristic
259C2×C13#147711yescharacteristic
260C2×C13#151311yescharacteristic
261C2×C13#151311yescharacteristic
262C2×C13#153711yescharacteristic
263C2×C13#156111yescharacteristic
264D13—42no—
265C24—131no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—131no—
269C22×C4—132no—
270C22×C4—132no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—262no—
274C22×C4—262no—
275C22×C4—261no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—521no—
282C22×C4—521no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4C2×C4×D1311yescharacteristic
286C22×C4D4×D1311yescharacteristic
287C22×C4D4×D1311yescharacteristic
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—521no—
295C2×C8—521no—
296C2×C8—521no—
297C2×C8—521no—
298C2×C8—521no—
299C2×C8—521no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—132no—
305C4⋊C4—261no—
306C4⋊C4—521no—
307C4⋊C4—522no—
308C4⋊C4—522no—
309C4⋊C4—521no—
310C4⋊C4—521no—
311C4⋊C4C8×D1312yes—
312C22⋊C4—264no—
313C22⋊C4—522no—
314C42—41no—
315C42—262no—
316C42—262no—
317C42—264no—
318C42—521no—
319C42—522no—
320C13#759811yescharacteristic, complemented, Sylow
321C23—132no—
322C23—261no—
323C23—261no—
324C23—261no—
325C23—261no—
326C23—261no—
327C23—261no—
328C23C22⋊C4×D1311yescharacteristic
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—132no—
342C2×C4—132no—
343C2×C4—132no—
344C2×C4—264no—
345C2×C4—264no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—262no—
353C2×C4—522no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4C2×C8×D1311yescharacteristic
363C2×C4M16×D1311yescharacteristic
364C2×C4#8816511yescharacteristic
365C2×C4#8816811yescharacteristic
366C2×C4#8816911yescharacteristic
367C2×C4#8817211yescharacteristic
368C8—81no—
369C8—81no—
370C8—1041no—
371C8—1041no—
372C22—262no—
373C22—262no—
374C22—262no—
375C22—521no—
376C22—521no—
377C22—521no—
378C22—521no—
379C22D13×C22⋊C811yescharacteristic
380C22D13×#9911yescharacteristic
381C22D13×#10111yescharacteristic
382C22#1171843211yescharacteristic
383C22#1171846411yescharacteristic
384C22#1171848211yescharacteristic
385C22#1171848211yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—42no—
393C4—81no—
394C4—134no—
395C4—521no—
396C4—521no—
397C4—522no—
398C4—1041no—
399C2—522no—
400C2D13×#32411yescharacteristic
401C2#1311322011yescharacteristic
402C2#1311322211yescharacteristic
403C2#1311337611yescharacteristic
404C2#1311337811yescharacteristic
405C2#1311347211yescharacteristic
406C2#1311357211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1271C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1271D13
hypocenterC13#7598
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #13112660C2semidirect
5. #13112659C2semidirect
6. #13112658C2semidirect
7. C13×#1271C2semidirect
52. #88146C8semidirect
124. #1271D13semidirect
320. C13#7598semidirect

Maximal subgroups

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

subgroupindex
#131173172
#131148152
#131126602
#131126592
#131126582
C13×#12712
#759813