Finite Group Databasebeta

← #13117684

Subgroups — #13117684

Order 1664.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88146C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D13C211yesmaximal, characteristic
3C2×C22⋊C4×D13C211yesmaximal, characteristic
4C13×#388C211yesmaximal, characteristic, complemented
5#11718650C211yesmaximal, characteristic, complemented
6#11718616C211yesmaximal, characteristic
7#11718612C211yesmaximal, characteristic, complemented
8#11718606C211yesmaximal, characteristic, complemented
9#11718605C211yesmaximal, characteristic, complemented
10C4×#6103C211yesmaximal, characteristic, complemented
11C4×#6103C211yesmaximal, characteristic, complemented
12#11718329C211yesmaximal, characteristic, complemented
13#11718328C211yesmaximal, characteristic, complemented
14#11718327C211yesmaximal, characteristic, complemented
15#11718325C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic, complemented
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C42×C13C2211yescharacteristic, complemented
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×C4⋊Dic13C2211yescharacteristic, complemented
38C2×#6101C2211yescharacteristic, complemented
39C2×#6101C2211yescharacteristic, complemented
40C2×C4×Dic13C2211yescharacteristic, complemented
41C2×C4×Dic13C2211yescharacteristic, complemented
42C2×C4×Dic13C2211yescharacteristic, complemented
43#88146—24no—
44C22⋊C4×D13—24no—
45C22⋊C4×D13C418yescomplemented
46C13×#95C2211yescharacteristic, complemented
47C13×#95C2211yescharacteristic, complemented
48#88071C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54C24×C13C2311yescharacteristic
55C23×D13—22no—
56C23×D13—22no—
57C23×D13—22no—
58C23×D13—22no—
59C23×D13—41no—
60C23×D13—41no—
61C23×D13C2×C414yes—
62C23×D13C2311yescharacteristic
63C23×D13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C2×C4×D13—22no—
77C2×C4×D13—22no—
78C2×C4×D13—22no—
79C2×C4×D13—22no—
80C2×C4×D13—22no—
81C2×C4×D13—22no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13C2×C414yescomplemented
87C2×C4×D13C2×C414yescomplemented
88C13×C4⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4C2×C414yescomplemented
92C42×C13—41no—
93C22⋊Dic13—22no—
94C22⋊Dic13—41no—
95C22⋊Dic13C2×C414yescomplemented
96#6103—22no—
97#6103—22no—
98#6103—22no—
99#6103—22no—
100#6103—22no—
101#6103C2×C414yes—
102#6103C2×C414yes—
103#6103D414yes—
104C4⋊Dic13—22no—
105#6101—41no—
106#6101—41no—
107C4×Dic13—22no—
108C4×Dic13—22no—
109C4×Dic13—41no—
110#2342—131nomaximal, Sylow
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C22×C412yes—
118C23×C13C2411yescharacteristic
119C22×D13—21no—
120C22×D13—21no—
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13—28no—
128C22×D13—28no—
129C22×D13—44no—
130C22×D13—44no—
131C22×D13—44no—
132C22×D13—44no—
133C22×D13—44no—
134C22×D13C22×C412yes—
135C22×D13C22×C412yes—
136C22×D13C2×D412yes—
137C22×D13#4112yes—
138C22×D13#4112yes—
139C22×D13#4112yes—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13C22×C412yes—
156C2×C4×C13C22×C412yes—
157C2×C4×C13C2×D412yes—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165C2×Dic13—21no—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13—21no—
169C2×Dic13—21no—
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13—21no—
173C2×Dic13C22×C412yes—
174C2×Dic13C22×C412yes—
175C2×Dic13C2×D412yes—
176C4×D13—28no—
177C4×D13—44no—
178C4×D13—44no—
179C4×D13—44no—
180C2×#117—131no—
181C22×C22⋊C4—131no—
182C22×C22⋊C4—131no—
183#388—131no—
184#388—131no—
185#388—131no—
186#388D1311yescharacteristic, complemented
187#385—131no—
188#385—131no—
189#381—131no—
190#380—131no—
191#379—131no—
192C4×C22⋊C4—131no—
193C4×C22⋊C4—131no—
194C4×C22⋊C4—131no—
195C22×C13—22no—
196C22×C13—22no—
197C22×C13—22no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13C23×C411yescharacteristic
203C22×C13C22×D411yescharacteristic
204C22×C13C2×#4111yescharacteristic
205C22×C13C2×#4111yescharacteristic
206C22×C13C2×#4111yescharacteristic
207C22×C13H(5,𝔽2)11yescharacteristic
208C22×C13H(5,𝔽2)11yescharacteristic
209C2×D13—22no—
210C2×D13—22no—
211C2×D13—22no—
212C2×D13—22no—
213C2×D13—22no—
214C2×D13—22no—
215C2×D13—22no—
216C2×D13—22no—
217C2×D13—22no—
218C2×D13—22no—
219C2×D13—22no—
220C2×D13—22no—
221C2×D13—416no—
222C2×D13#11714yescomplemented
223C2×D13C4×D414yes—
224C4×C13—22no—
225C4×C13—22no—
226C4×C13—22no—
227C4×C13—41no—
228C4×C13—41no—
229C4×C13—41no—
230Dic13—22no—
231Dic13—22no—
232Dic13—22no—
233Dic13—41no—
234Dic13—41no—
235Dic13—41no—
236C25—131no—
237C23×C4—131no—
238C23×C4—131no—
239C23×C4—131no—
240C23×C4—131no—
241#117—264no—
242C2×C4⋊C4—131no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4—131no—
245C2×C4⋊C4C2×D1311yescharacteristic, complemented
246C2×C22⋊C4—131no—
247C2×C22⋊C4—131no—
248C2×C22⋊C4—131no—
249C2×C22⋊C4—131no—
250C2×C22⋊C4—138no—
251C2×C22⋊C4—131no—
252C2×C22⋊C4—131no—
253C2×C22⋊C4—131no—
254C2×C22⋊C4—131no—
255C2×C22⋊C4—131no—
256C2×C22⋊C4—131no—
257C2×C22⋊C4—131no—
258C2×C22⋊C4—264no—
259C2×C22⋊C4C2×D1311yescharacteristic
260C2×C22⋊C4C2×D1311yescharacteristic
261C2×C22⋊C4C2×D1311yescharacteristic
262C2×C42—131no—
263C2×C42—131no—
264C2×C42—131no—
265C2×C42C2×D1311yescharacteristic, complemented
266#95—131no—
267#95—131no—
268#95—131no—
269#95—131no—
270#95—131no—
271#95—131no—
272#95C2×D1311yescharacteristic, complemented
273#95C2×D1311yescharacteristic, complemented
274C2×C13—42no—
275C2×C13C2×#11711yescharacteristic
276C2×C13C2×C4×D411yescharacteristic
277C2×C13#51811yescharacteristic
278C2×C13#54611yescharacteristic
279C2×C13#54611yescharacteristic
280C2×C13#55111yescharacteristic
281C2×C13#55111yescharacteristic
282D13—24no—
283D13—24no—
284C24—131no—
285C24—131no—
286C24—134no—
287C24—262no—
288C24—262no—
289C24—262no—
290C24—262no—
291C24—521no—
292C24—521no—
293C24C22×D1311yescharacteristic
294C22×C4—131no—
295C22×C4—131no—
296C22×C4—131no—
297C22×C4—134no—
298C22×C4—134no—
299C22×C4—131no—
300C22×C4—131no—
301C22×C4—131no—
302C22×C4—262no—
303C22×C4—262no—
304C22×C4—262no—
305C22×C4—262no—
306C22×C4—262no—
307C22×C4—262no—
308C22×C4—521no—
309C22×C4—521no—
310C22×C4—521no—
311C22×C4—521no—
312C22×C4C22×D1311yescharacteristic
313C22×C4C22×D1311yescharacteristic
314C22×C4C22×D1311yescharacteristic
315C22×C4C22×D1311yescharacteristic
316C22×C4C22×D1311yescharacteristic
317C22×C4C22×D1311yescharacteristic
318C4⋊C4—22no—
319C4⋊C4—262no—
320C4⋊C4—521no—
321C4⋊C4—521no—
322C22⋊C4—22no—
323C22⋊C4—41no—
324C22⋊C4—134no—
325C22⋊C4—134no—
326C22⋊C4—134no—
327C22⋊C4—134no—
328C22⋊C4—262no—
329C22⋊C4—262no—
330C22⋊C4—262no—
331C22⋊C4—262no—
332C22⋊C4—262no—
333C22⋊C4—262no—
334C22⋊C4—521no—
335C22⋊C4C4×D1314yescomplemented
336C42—41no—
337C42—262no—
338C42—262no—
339C42—521no—
340C13#234211yescharacteristic, complemented, Sylow
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—132no—
348C23—132no—
349C23—132no—
350C23—132no—
351C23—132no—
352C23—132no—
353C23—268no—
354C23—268no—
355C23—261no—
356C23—261no—
357C23—261no—
358C23—261no—
359C23—261no—
360C23—261no—
361C23—261no—
362C23—261no—
363C23—524no—
364C23—524no—
365C23—524no—
366C23—524no—
367C23—524no—
368C23C2×C4×D1312yes—
369C23C23×D1311yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—132no—
386C2×C4—132no—
387C2×C4—132no—
388C2×C4—268no—
389C2×C4—261no—
390C2×C4—261no—
391C2×C4—261no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—261no—
395C2×C4—261no—
396C2×C4—261no—
397C2×C4—261no—
398C2×C4—261no—
399C2×C4—261no—
400C2×C4—261no—
401C2×C4—261no—
402C2×C4—261no—
403C2×C4—261no—
404C2×C4—524no—
405C2×C4—524no—
406C2×C4—524no—
407C2×C4C2×C4×D1312yes—
408C2×C4C2×C4×D1312yes—
409C2×C4D4×D1312yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—134no—
418C22—134no—
419C22—262no—
420C22—262no—
421C22—262no—
422C22—262no—
423C22—262no—
424C22—262no—
425C22—262no—
426C22—262no—
427C22—262no—
428C22—262no—
429C22—262no—
430C22—262no—
431C22—5216no—
432C22C22×C4×D1311yescharacteristic
433C22C2×D4×D1311yescharacteristic
434C22#8825111yescharacteristic
435C22#41×D1311yescharacteristic
436C22#41×D1311yescharacteristic
437C22#41×D1311yescharacteristic
438C22#8825611yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—262no—
446C4—262no—
447C4—262no—
448C4—521no—
449C4—521no—
450C4—521no—
451C2—42no—
452C2—264no—
453C2—264no—
454C2D13×#11711yescharacteristic
455C2C4×D4×D1311yescharacteristic
456C2#1171925011yescharacteristic
457C2#1171931511yescharacteristic
458C2#1171936411yescharacteristic
459C2#1171938111yescharacteristic
460C2#1171941011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#388C2
socle, cosocleC23×C13C24
prime radicalC24×D13C22
hypercenter#388D13
hypocenterC13#2342
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#88146C2semidirect
4. C13×#388C2semidirect
5. #11718650C2semidirect
7. #11718612C2semidirect
8. #11718606C2semidirect
9. #11718605C2semidirect
10. C4×#6103C2semidirect
11. C4×#6103C2semidirect
12. #11718329C2semidirect
13. #11718328C2semidirect
14. #11718327C2semidirect
15. #11718325C2semidirect
21. C2×C13×C4⋊C4C22semidirect
25. C2×C42×C13C22semidirect
37. C2×C4⋊Dic13C22semidirect
38. C2×#6101C22semidirect
39. C2×#6101C22semidirect
40. C2×C4×Dic13C22semidirect
41. C2×C4×Dic13C22semidirect
42. C2×C4×Dic13C22semidirect
45. C22⋊C4×D13C4semidirect
46. C13×#95C22semidirect
47. C13×#95C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
86. C2×C4×D13C2×C4semidirect
87. C2×C4×D13C2×C4semidirect
91. C13×C22⋊C4C2×C4semidirect
95. C22⋊Dic13C2×C4semidirect
186. #388D13semidirect
222. C2×D13#117semidirect
245. C2×C4⋊C4C2×D13semidirect
265. C2×C42C2×D13semidirect
272. #95C2×D13semidirect
273. #95C2×D13semidirect
335. C22⋊C4C4×D13semidirect
340. C13#2342semidirect

Maximal subgroups

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

subgroupindex
C2×#881462
C2×C22⋊C4×D132
C13×#3882
#117186502
#117186162
#117186122
#117186062
#117186052
C4×#61032
#117183292
#117183282
#117183272
#117183252
#234213