Finite Group Databasebeta

← #13119079

Subgroups — #13119079

Order 1664.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Dic13C211yesmaximal, characteristic
2C2×#88133C211yesmaximal, characteristic, complemented
3C13×#379C211yesmaximal, characteristic
4#11718908C211yesmaximal, characteristic
5#11718614C211yesmaximal, characteristic, complemented
6#11718613C211yesmaximal, characteristic, complemented
7#11718613C211yesmaximal, characteristic, complemented
8#11718612C211yesmaximal, characteristic, complemented
9#11718611C211yesmaximal, characteristic, complemented
10#11718609C211yesmaximal, characteristic, complemented
11#11718607C211yesmaximal, characteristic, complemented
12#11718606C211yesmaximal, characteristic, complemented
13#11718605C211yesmaximal, characteristic, complemented
14#11718603C211yesmaximal, characteristic, complemented
15C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C25×C13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C23×Dic13C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C22⋊Dic13—24no—
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic
33C2×C22⋊Dic13C2211yescharacteristic
34C2×C22⋊Dic13C2211yescharacteristic
35C2×C22⋊Dic13C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic, complemented
37C2×C4⋊Dic13C2211yescharacteristic, complemented
38C2×#6101C2211yescharacteristic, complemented
39C2×#6101C2211yescharacteristic, complemented
40C2×#6101C2211yescharacteristic, complemented
41C2×#6101C2211yescharacteristic, complemented
42C2×C4×Dic13C2211yescharacteristic, complemented
43C2×C4×Dic13C2211yescharacteristic, complemented
44#88133—24no—
45#88071C2211yescharacteristic, complemented
46#88071C2211yescharacteristic, complemented
47#88071C2211yescharacteristic, complemented
48#88071C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53C24×C13—22no—
54C24×C13—22no—
55C24×C13—22no—
56C24×C13—22no—
57C24×C13—22no—
58C24×C13—41no—
59C24×C13—41no—
60C24×C13C2311yescharacteristic
61C24×C13C2311yescharacteristic
62C24×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—41no—
72C22×Dic13—41no—
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C13×C22⋊C4—22no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C22⋊Dic13—22no—
88C22⋊Dic13—22no—
89C22⋊Dic13—22no—
90C22⋊Dic13—22no—
91C22⋊Dic13—22no—
92C22⋊Dic13—22no—
93C22⋊Dic13—22no—
94C22⋊Dic13—41no—
95C22⋊Dic13—41no—
96C22⋊Dic13D414yes—
97C4⋊Dic13—22no—
98C4⋊Dic13—41no—
99#6101—22no—
100#6101—22no—
101#6101—41no—
102#6101—41no—
103C4×Dic13—22no—
104C4×Dic13—41no—
105#2480—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—28no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—44no—
124C23×C13—44no—
125C23×C13—44no—
126C23×C13—44no—
127C23×C13—44no—
128C23×C13—44no—
129C23×C13C2×D412yes—
130C23×C13#4112yes—
131C23×C13#4112yes—
132C23×C13#4112yes—
133C23×C13#4112yes—
134C23×C13C2411yescharacteristic
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
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×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
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—44no—
170C2×Dic13—44no—
171C2×Dic13C2×D412yes—
172C2×Dic13C2×D412yes—
173C2×#126—131no—
174C22×C22⋊C4—131no—
175#397—131no—
176#397—131no—
177#397—131no—
178#396—131no—
179#388—131no—
180#388—131no—
181#388—131no—
182#385—131no—
183#385—131no—
184#380—131no—
185#379—131no—
186#379D1311yescharacteristic
187C4×C22⋊C4—131no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13—22no—
195C22×C13—22no—
196C22×C13—22no—
197C22×C13—22no—
198C22×C13—22no—
199C22×C13—22no—
200C22×C13—416no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13#12614yescomplemented
210C22×C13C22×D411yescharacteristic
211C22×C13C2×#4111yescharacteristic
212C22×C13C2×#4111yescharacteristic
213C22×C13C2×#4111yescharacteristic
214C22×C13C2×#4111yescharacteristic
215C22×C13H(5,𝔽2)11yescharacteristic
216C22×C13H(5,𝔽2)11yescharacteristic
217C4×C13—41no—
218C4×C13—41no—
219C4×C13—41no—
220C4×C13—41no—
221Dic13—22no—
222Dic13—22no—
223Dic13—41no—
224Dic13—41no—
225Dic13—41no—
226Dic13—41no—
227Dic13—41no—
228Dic13—41no—
229C25C2×D1311yescharacteristic
230C23×C4—131no—
231C23×C4—131no—
232#126—264no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—131no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4—131no—
239C2×C22⋊C4—131no—
240C2×C22⋊C4—131no—
241C2×C22⋊C4—131no—
242C2×C22⋊C4—131no—
243C2×C22⋊C4—131no—
244C2×C22⋊C4—131no—
245C2×C22⋊C4—131no—
246C2×C22⋊C4—131no—
247C2×C22⋊C4—131no—
248C2×C22⋊C4—131no—
249C2×C22⋊C4—264no—
250C2×C22⋊C4C2×D1311yescharacteristic
251C2×C22⋊C4C2×D1311yescharacteristic
252C2×C22⋊C4C2×D1311yescharacteristic
253C2×C22⋊C4C2×D1311yescharacteristic
254C2×C22⋊C4C2×D1311yescharacteristic
255C2×C22⋊C4C2×D1311yescharacteristic
256C2×C42—131no—
257C2×C42—131no—
258#95—131no—
259#95—131no—
260#95—131no—
261#95—131no—
262#95—131no—
263#95—131no—
264#95—131no—
265#95—131no—
266C2×C13—24no—
267C2×C13—42no—
268C2×C13—42no—
269C2×C13#52511yescharacteristic
270C2×C13C2×#12611yescharacteristic
271C2×C13#53811yescharacteristic
272C2×C13#54611yescharacteristic
273C2×C13#54611yescharacteristic
274C2×C13#55111yescharacteristic
275C2×C13#55111yescharacteristic
276C24—22no—
277C24—22no—
278C24—22no—
279C24—22no—
280C24—22no—
281C24—41no—
282C24—41no—
283C24C22×D1311yescharacteristic
284C24C22×D1311yescharacteristic
285C24C22×D1311yescharacteristic
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—131no—
292C22×C4—131no—
293C22×C4—131no—
294C22×C4—262no—
295C22×C4—262no—
296C22×C4—262no—
297C22×C4—262no—
298C22×C4—521no—
299C22×C4—521no—
300C22×C4C22×D1311yescharacteristic
301C22×C4C22×D1311yescharacteristic
302C22×C4C22×D1311yescharacteristic
303C22×C4C22×D1311yescharacteristic
304C4⋊C4—262no—
305C4⋊C4—262no—
306C4⋊C4—262no—
307C4⋊C4—521no—
308C4⋊C4—521no—
309C4⋊C4—521no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—134no—
317C22⋊C4—262no—
318C22⋊C4—262no—
319C22⋊C4—262no—
320C22⋊C4—262no—
321C22⋊C4—262no—
322C22⋊C4—262no—
323C22⋊C4—262no—
324C22⋊C4—521no—
325C22⋊C4—521no—
326C42—262no—
327C42—521no—
328C13#248011yescharacteristic, complemented, Sylow
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—28no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—44no—
347C23—44no—
348C23—44no—
349C23—44no—
350C23—44no—
351C23—44no—
352C23#612712yes—
353C23D4×D1312yes—
354C23#612912yes—
355C23#612912yes—
356C23#612912yes—
357C23C23×D1311yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—132no—
371C2×C4—132no—
372C2×C4—261no—
373C2×C4—261no—
374C2×C4—261no—
375C2×C4—261no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—261no—
380C2×C4—261no—
381C2×C4—261no—
382C2×C4—261no—
383C2×C4—261no—
384C2×C4—261no—
385C2×C4—261no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—261no—
389C2×C4—261no—
390C2×C4—261no—
391C2×C4—261no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—524no—
395C2×C4—524no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—416no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22#8813314yescomplemented
418C22C2×#612711yescharacteristic
419C22C2×D4×D1311yescharacteristic
420C22C2×#612911yescharacteristic
421C22C2×#612911yescharacteristic
422C22C2×#612911yescharacteristic
423C22#8825111yescharacteristic
424C22#8825111yescharacteristic
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—262no—
430C4—262no—
431C4—521no—
432C4—521no—
433C4—521no—
434C4—521no—
435C4—521no—
436C4—521no—
437C2—24no—
438C2—42no—
439C2—42no—
440C2C2×#8813311yescharacteristic
441C2#1171919511yescharacteristic
442C2#1171920011yescharacteristic
443C2#1171929111yescharacteristic
444C2#1171929211yescharacteristic
445C2#1171929611yescharacteristic
446C2#1171929811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#379C2
prime radicalC25×C13C22
hypercenter#379D13
hypocenterC13#2480
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#88133C2semidirect
5. #11718614C2semidirect
6. #11718613C2semidirect
7. #11718613C2semidirect
8. #11718612C2semidirect
9. #11718611C2semidirect
10. #11718609C2semidirect
11. #11718607C2semidirect
12. #11718606C2semidirect
13. #11718605C2semidirect
14. #11718603C2semidirect
15. C22⋊C4×Dic13C2semidirect
36. C2×C4⋊Dic13C22semidirect
37. C2×C4⋊Dic13C22semidirect
38. C2×#6101C22semidirect
39. C2×#6101C22semidirect
40. C2×#6101C22semidirect
41. C2×#6101C22semidirect
42. C2×C4×Dic13C22semidirect
43. C2×C4×Dic13C22semidirect
45. #88071C22semidirect
46. #88071C22semidirect
47. #88071C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
209. C22×C13#126semidirect
328. C13#2480semidirect
417. C22#88133semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Dic132
C2×#881332
C13×#3792
#117189082
#117186142
#117186132
#117186122
#117186112
#117186092
#117186072
#117186062
#117186052
#117186032
C22⋊C4×Dic132
#248013