Finite Group Databasebeta

← #13119082

Subgroups — #13119082

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×#6103C211yesmaximal, characteristic
2C2×#88130C211yesmaximal, characteristic, complemented
3C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
4#11718871C211yesmaximal, characteristic, complemented
5#11718616C211yesmaximal, characteristic
6#11718616C211yesmaximal, characteristic
7#11718607C211yesmaximal, characteristic, complemented
8#11718603C211yesmaximal, characteristic, complemented
9#11718601C211yesmaximal, characteristic, complemented
10#11718601C211yesmaximal, characteristic, complemented
11#11718601C211yesmaximal, characteristic, complemented
12#11718337C211yesmaximal, characteristic, complemented
13#11718336C211yesmaximal, characteristic, complemented
14#11718336C211yesmaximal, characteristic, complemented
15#11718336C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C23×Dic13C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C42×C13C2211yescharacteristic, complemented
22C2×C42×C13C2211yescharacteristic, complemented
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×#6103—24no—
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6101C2211yescharacteristic, complemented
39C2×#6101C2211yescharacteristic, complemented
40C2×#6101C2211yescharacteristic, complemented
41C2×#6101C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44#88130—24no—
45C13×#95C2211yescharacteristic, complemented
46C13×#95C2211yescharacteristic, complemented
47#88071C2211yescharacteristic, complemented
48#88071C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53C24×C13C2311yescharacteristic
54C23×D13—22no—
55C23×D13—22no—
56C23×D13—22no—
57C23×D13—22no—
58C23×D13—22no—
59C23×D13—41no—
60C23×D13—41no—
61C23×D13C2311yescharacteristic
62C23×D13C2311yescharacteristic
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—41no—
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—41no—
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C13×C22⋊C4—22no—
82C13×C22⋊C4—22no—
83C42×C13—22no—
84C42×C13—41no—
85C22⋊Dic13—22no—
86C22⋊Dic13—22no—
87#6103—22no—
88#6103—22no—
89#6103—22no—
90#6103—22no—
91#6103—22no—
92#6103—22no—
93#6103—22no—
94#6103—41no—
95#6103—41no—
96#6103—41no—
97#6103—41no—
98#6103D414yes—
99#6101—22no—
100#6101—22no—
101#6101—22no—
102#6101—41no—
103#6101—41no—
104#6101—41no—
105#2480—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13#4112yes—
111C23×C13#4112yes—
112C23×C13#4112yes—
113C23×C13C2411yescharacteristic
114C22×D13—28no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—21no—
118C22×D13—21no—
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—44no—
128C22×D13—44no—
129C22×D13—44no—
130C22×D13—44no—
131C22×D13—44no—
132C22×D13—44no—
133C22×D13C2×D412yes—
134C22×D13#4112yes—
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×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—44no—
153C2×C4×C13C2×D412yes—
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—21no—
170C2×Dic13—21no—
171C2×Dic13—44no—
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#379—131no—
187C4×C22⋊C4D1311yescharacteristic, complemented
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13#12614yescomplemented
195C22×C13C22×D411yescharacteristic
196C22×C13C2×#4111yescharacteristic
197C22×C13C2×#4111yescharacteristic
198C22×C13C2×#4111yescharacteristic
199C22×C13C2×#4111yescharacteristic
200C22×C13H(5,𝔽2)11yescharacteristic
201C22×C13H(5,𝔽2)11yescharacteristic
202C2×D13—22no—
203C2×D13—22no—
204C2×D13—22no—
205C2×D13—22no—
206C2×D13—22no—
207C2×D13—22no—
208C2×D13—416no—
209C2×D13—41no—
210C2×D13—41no—
211C2×D13—41no—
212C2×D13—41no—
213C2×D13—41no—
214C2×D13—41no—
215C2×D13—41no—
216C2×D13—41no—
217C4×C13—22no—
218C4×C13—41no—
219C4×C13—41no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223Dic13—22no—
224Dic13—41no—
225Dic13—41no—
226Dic13—41no—
227Dic13—41no—
228Dic13—41no—
229C25—131no—
230C23×C4—131no—
231C23×C4C2×D1311yescharacteristic
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—131no—
250C2×C22⋊C4—131no—
251C2×C22⋊C4—131no—
252C2×C22⋊C4—131no—
253C2×C22⋊C4—264no—
254C2×C22⋊C4C2×D1311yescharacteristic
255C2×C22⋊C4C2×D1311yescharacteristic
256C2×C42C2×D1311yescharacteristic, complemented
257C2×C42C2×D1311yescharacteristic, complemented
258#95—131no—
259#95—131no—
260#95—131no—
261#95—131no—
262#95—131no—
263#95—131no—
264#95C2×D1311yescharacteristic, complemented
265#95C2×D1311yescharacteristic, complemented
266C2×C13—24no—
267C2×C13#52511yescharacteristic
268C2×C13C2×#12611yescharacteristic
269C2×C13#53811yescharacteristic
270C2×C13#54611yescharacteristic
271C2×C13#54611yescharacteristic
272C2×C13#55111yescharacteristic
273C2×C13#55111yescharacteristic
274D13—42no—
275D13—42no—
276C24—131no—
277C24—131no—
278C24—262no—
279C24—262no—
280C24—262no—
281C24—262no—
282C24—262no—
283C24—521no—
284C24—521no—
285C24C22×D1311yescharacteristic
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—131no—
292C22×C4—131no—
293C22×C4—131no—
294C22×C4—131no—
295C22×C4—262no—
296C22×C4—262no—
297C22×C4—521no—
298C22×C4C22×D1311yescharacteristic
299C22×C4C22×D1311yescharacteristic
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—134no—
313C22⋊C4—262no—
314C22⋊C4—262no—
315C22⋊C4—262no—
316C22⋊C4—262no—
317C22⋊C4—262no—
318C22⋊C4—262no—
319C22⋊C4—262no—
320C22⋊C4—262no—
321C22⋊C4—262no—
322C22⋊C4—521no—
323C22⋊C4—521no—
324C22⋊C4—521no—
325C22⋊C4—521no—
326C42—22no—
327C42—41no—
328C13#248011yescharacteristic, complemented, Sylow
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—132no—
334C23—132no—
335C23—268no—
336C23—261no—
337C23—261no—
338C23—261no—
339C23—261no—
340C23—261no—
341C23—261no—
342C23—261no—
343C23—261no—
344C23—261no—
345C23—261no—
346C23—261no—
347C23—261no—
348C23—524no—
349C23—524no—
350C23—524no—
351C23—524no—
352C23—524no—
353C23—524no—
354C23#612712yes—
355C23#612712yes—
356C23#612712yes—
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—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—132no—
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×C4D4×D1312yes—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—262no—
403C22—262no—
404C22—262no—
405C22—262no—
406C22—262no—
407C22—262no—
408C22—5216no—
409C22—521no—
410C22—521no—
411C22—521no—
412C22—521no—
413C22—521no—
414C22—521no—
415C22—521no—
416C22—521no—
417C22#8813014yescomplemented
418C22C2×#612711yescharacteristic
419C22C2×#612711yescharacteristic
420C22C2×#612711yescharacteristic
421C22C2×D4×D1311yescharacteristic
422C22#8825111yescharacteristic
423C22#41×D1311yescharacteristic
424C22#8825611yescharacteristic
425C4—22no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—262no—
432C4—521no—
433C4—521no—
434C4—521no—
435C4—521no—
436C4—521no—
437C2—24no—
438C2—522no—
439C2—522no—
440C2C2×#8813011yescharacteristic
441C2#1171919511yescharacteristic
442C2#1171923211yescharacteristic
443C2#1171925211yescharacteristic
444C2#1171925511yescharacteristic
445C2#1171926111yescharacteristic
446C2#1171926511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC4×C13×C22⋊C4C2
prime radicalC24×D13C22
hypercenterC4×C22⋊C4D13
hypocenterC13#2480
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#88130C2semidirect
3. C4×C13×C22⋊C4C2semidirect
4. #11718871C2semidirect
7. #11718607C2semidirect
8. #11718603C2semidirect
9. #11718601C2semidirect
10. #11718601C2semidirect
11. #11718601C2semidirect
12. #11718337C2semidirect
13. #11718336C2semidirect
14. #11718336C2semidirect
15. #11718336C2semidirect
21. C2×C42×C13C22semidirect
22. C2×C42×C13C22semidirect
38. C2×#6101C22semidirect
39. C2×#6101C22semidirect
40. C2×#6101C22semidirect
41. C2×#6101C22semidirect
42. C2×#6101C22semidirect
43. C2×#6101C22semidirect
45. C13×#95C22semidirect
46. C13×#95C22semidirect
47. #88071C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
187. C4×C22⋊C4D13semidirect
194. C22×C13#126semidirect
256. C2×C42C2×D13semidirect
257. C2×C42C2×D13semidirect
264. #95C2×D13semidirect
265. #95C2×D13semidirect
328. C13#2480semidirect
417. C22#88130semidirect

Maximal subgroups

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

subgroupindex
C22×#61032
C2×#881302
C4×C13×C22⋊C42
#117188712
#117186162
#117186072
#117186032
#117186012
#117183372
#117183362
#248013