Finite Group Databasebeta

← #13121234

Subgroups — #13121234

Order 1664.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88152C211yesmaximal, characteristic, complemented
2C2×#88136C211yesmaximal, characteristic
3C13×#396C211yesmaximal, characteristic, complemented
4#11718653C211yesmaximal, characteristic, complemented
5#11718652C211yesmaximal, characteristic, complemented
6#11718652C211yesmaximal, characteristic, complemented
7#11718651C211yesmaximal, characteristic, complemented
8#11718649C211yesmaximal, characteristic, complemented
9#11718622C211yesmaximal, characteristic, complemented
10#11718618C211yesmaximal, characteristic, complemented
11#11718616C211yesmaximal, characteristic, complemented
12#11718616C211yesmaximal, characteristic, complemented
13#11718605C211yesmaximal, characteristic, complemented
14#11718333C211yesmaximal, characteristic, complemented
15#11718331C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C22×D52C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic, complemented
21C2×C13×C4⋊C4C2211yescharacteristic, complemented
22C2×C13×C4⋊C4C2211yescharacteristic, complemented
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic, complemented
39C2×#6103C2211yescharacteristic, complemented
40C2×#6103C2211yescharacteristic, complemented
41C2×#6103C2211yescharacteristic, complemented
42C2×C4⋊Dic13C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45C2×C4×Dic13C2211yescharacteristic, complemented
46C2×C4×Dic13C2211yescharacteristic, complemented
47#88152—24no—
48#88136—24no—
49C13×#95C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53C24×C13C2311yescharacteristic
54C23×D13—22no—
55C23×D13—22no—
56C23×D13—22no—
57C23×D13—41no—
58C23×D13—41no—
59C23×D13—41no—
60C23×D13—41no—
61C23×D13C2311yescharacteristic
62C23×D13C2311yescharacteristic
63C23×D13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C2×C22⋊D13—22no—
71C2×C22⋊D13—22no—
72C2×C22⋊D13—41no—
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C2×D52—22no—
79C2×D52—22no—
80C2×D52—22no—
81C2×D52—41no—
82C2×D52—41no—
83C2×D52—41no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C22⋊C4—22no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C22⋊Dic13—22no—
91C22⋊Dic13—41no—
92#6103—22no—
93#6103—22no—
94#6103—22no—
95#6103—22no—
96#6103—41no—
97#6103—41no—
98#6103—41no—
99#6103—41no—
100#6103—41no—
101#6103—41no—
102#6103—41no—
103#6103—41no—
104#6103—41no—
105#6103D414yes—
106C4⋊Dic13—22no—
107#6101—22no—
108#6101—41no—
109C4×Dic13—22no—
110C4×Dic13—41no—
111#2685—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13#4112yes—
119C23×C13C2411yescharacteristic
120C22×D13—21no—
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—21no—
136C22×D13—21no—
137C22×D13—21no—
138C22×D13—21no—
139C22×D13—44no—
140C22×D13—44no—
141C22×D13—44no—
142C22×D13—44no—
143C22×D13—44no—
144C22×D13—44no—
145C22×D13—44no—
146C22×D13C2×D412yes—
147C22×D13#4112yes—
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×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13C2×D412yes—
166C22⋊D13—44no—
167C2×Dic13—21no—
168C2×Dic13—21no—
169C2×Dic13—21no—
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13—21no—
173C2×Dic13—21no—
174C2×Dic13—21no—
175C2×Dic13—21no—
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13C2×D412yes—
182D52—44no—
183D52—44no—
184C2×#126—131no—
185C2×#120—131no—
186#399—131no—
187#396D1311yescharacteristic, complemented
188#394—131no—
189#394—131no—
190#394—131no—
191#394—131no—
192#390—131no—
193#390—131no—
194#388—131no—
195#388—131no—
196#388—131no—
197#379—131no—
198#379—131no—
199C22×C13—22no—
200C22×C13—22no—
201C22×C13—22no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13C22×D411yescharacteristic
207C22×C13C2×#4111yescharacteristic
208C22×C13C2×#4111yescharacteristic
209C22×C13H(5,𝔽2)11yescharacteristic
210C22×C13H(5,𝔽2)11yescharacteristic
211C22×C13H(5,𝔽2)11yescharacteristic
212C22×C13H(5,𝔽2)11yescharacteristic
213C2×D13—22no—
214C2×D13—22no—
215C2×D13—22no—
216C2×D13—22no—
217C2×D13—22no—
218C2×D13—22no—
219C2×D13—416no—
220C2×D13—41no—
221C2×D13—41no—
222C2×D13—41no—
223C2×D13—41no—
224C2×D13—41no—
225C2×D13—41no—
226C2×D13—41no—
227C2×D13—41no—
228C2×D13—41no—
229C2×D13—41no—
230C2×D13—41no—
231C2×D13—41no—
232C2×D13—41no—
233C2×D13—41no—
234C2×D13—41no—
235C4×C13—22no—
236C4×C13—41no—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—41no—
240C4×C13—41no—
241Dic13—22no—
242Dic13—41no—
243Dic13—41no—
244Dic13—41no—
245Dic13—41no—
246C25—131no—
247C22×D4—131no—
248C22×D4—131no—
249C22×D4—131no—
250#126—264no—
251#120—264no—
252C2×C4⋊C4—131no—
253C2×C4⋊C4—131no—
254C2×C4⋊C4—131no—
255C2×C4⋊C4C2×D1311yescharacteristic, complemented
256C2×C4⋊C4C2×D1311yescharacteristic, complemented
257C2×C4⋊C4C2×D1311yescharacteristic, complemented
258C2×C22⋊C4—131no—
259C2×C22⋊C4—131no—
260C2×C22⋊C4—131no—
261C2×C22⋊C4—131no—
262C2×C22⋊C4—131no—
263C2×C22⋊C4—131no—
264C2×C22⋊C4—131no—
265C2×C22⋊C4—131no—
266C2×C22⋊C4—131no—
267C2×C22⋊C4—131no—
268C2×C22⋊C4—131no—
269C2×C22⋊C4—131no—
270C2×C22⋊C4—131no—
271C2×C22⋊C4—131no—
272C2×C22⋊C4—131no—
273C2×C22⋊C4—131no—
274C2×C22⋊C4C2×D1311yescharacteristic
275C2×C22⋊C4C2×D1311yescharacteristic
276C2×C22⋊C4C2×D1311yescharacteristic
277C2×C42—131no—
278C2×C42—131no—
279#95—131no—
280#95—131no—
281#95—131no—
282#95C2×D1311yescharacteristic, complemented
283C2×C13—42no—
284C2×C13#53511yescharacteristic
285C2×C13#53811yescharacteristic
286C2×C13#53811yescharacteristic
287C2×C13#54611yescharacteristic
288C2×C13#54611yescharacteristic
289C2×C13#55111yescharacteristic
290C2×C13#56011yescharacteristic
291D13—42no—
292D13—42no—
293D13—81no—
294C24—131no—
295C24—131no—
296C24—131no—
297C24—262no—
298C24—262no—
299C24—262no—
300C24—521no—
301C24—521no—
302C24—521no—
303C24—521no—
304C24C22×D1311yescharacteristic
305C2×D4—262no—
306C2×D4—262no—
307C2×D4—262no—
308C2×D4—262no—
309C2×D4—262no—
310C2×D4—521no—
311C2×D4—521no—
312C2×D4—521no—
313C2×D4—521no—
314C22×C4—131no—
315C22×C4—131no—
316C22×C4—131no—
317C22×C4—131no—
318C22×C4—131no—
319C22×C4C22×D1311yescharacteristic
320C22×C4C22×D1311yescharacteristic
321C22×C4C22×D1311yescharacteristic
322C22×C4C22×D1311yescharacteristic
323C22×C4C22×D1311yescharacteristic
324C22×C4C22×D1311yescharacteristic
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—262no—
329C4⋊C4—262no—
330C4⋊C4—521no—
331C22⋊C4—22no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—134no—
335C22⋊C4—262no—
336C22⋊C4—262no—
337C22⋊C4—262no—
338C22⋊C4—262no—
339C22⋊C4—262no—
340C22⋊C4—521no—
341C22⋊C4—521no—
342C22⋊C4—521no—
343C22⋊C4—521no—
344C22⋊C4—521no—
345C22⋊C4—521no—
346C22⋊C4—521no—
347C22⋊C4—521no—
348C22⋊C4—521no—
349C22⋊C4—521no—
350C42—262no—
351C42—521no—
352C13#268511yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—132no—
360C23—132no—
361C23—261no—
362C23—261no—
363C23—261no—
364C23—261no—
365C23—261no—
366C23—261no—
367C23—261no—
368C23—261no—
369C23—261no—
370C23—261no—
371C23—261no—
372C23—261no—
373C23—261no—
374C23—261no—
375C23—261no—
376C23—261no—
377C23—261no—
378C23—261no—
379C23—261no—
380C23—524no—
381C23—524no—
382C23—524no—
383C23—524no—
384C23—524no—
385C23—524no—
386C23—524no—
387C23#613112yes—
388C23C23×D1311yescharacteristic
389D4—524no—
390D4—524no—
391D4—524no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—132no—
410C2×C4—261no—
411C2×C4—261no—
412C2×C4—261no—
413C2×C4—261no—
414C2×C4—261no—
415C2×C4—261no—
416C2×C4—261no—
417C2×C4—261no—
418C2×C4—261no—
419C2×C4—261no—
420C2×C4—261no—
421C2×C4—261no—
422C2×C4—261no—
423C2×C4—261no—
424C2×C4D4×D1312yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—262no—
433C22—262no—
434C22—262no—
435C22—262no—
436C22—262no—
437C22—262no—
438C22—5216no—
439C22—521no—
440C22—521no—
441C22—521no—
442C22—521no—
443C22—521no—
444C22—521no—
445C22—521no—
446C22—521no—
447C22—521no—
448C22—521no—
449C22—521no—
450C22—521no—
451C22—521no—
452C22—521no—
453C22—521no—
454C22C2×D4×D1311yescharacteristic
455C22#8825111yescharacteristic
456C22#8825111yescharacteristic
457C22C2×#613111yescharacteristic
458C22#41×D1311yescharacteristic
459C22#8825611yescharacteristic
460C22#8825611yescharacteristic
461C4—22no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—262no—
468C4—521no—
469C4—521no—
470C4—521no—
471C4—521no—
472C2—42no—
473C2—522no—
474C2—522no—
475C2—1041no—
476C2#1171931211yescharacteristic
477C2#1171931511yescharacteristic
478C2#1171932511yescharacteristic
479C2#1171933511yescharacteristic
480C2#1171934211yescharacteristic
481C2#1171934911yescharacteristic
482C2#1171940911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#396C2
prime radicalC2×#88136C2
hypercenter#396D13
hypocenterC13#2685
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#88152C2semidirect
3. C13×#396C2semidirect
4. #11718653C2semidirect
5. #11718652C2semidirect
6. #11718652C2semidirect
7. #11718651C2semidirect
8. #11718649C2semidirect
9. #11718622C2semidirect
10. #11718618C2semidirect
11. #11718616C2semidirect
12. #11718616C2semidirect
13. #11718605C2semidirect
14. #11718333C2semidirect
15. #11718331C2semidirect
20. C2×C13×C4⋊C4C22semidirect
21. C2×C13×C4⋊C4C22semidirect
22. C2×C13×C4⋊C4C22semidirect
38. C2×#6103C22semidirect
39. C2×#6103C22semidirect
40. C2×#6103C22semidirect
41. C2×#6103C22semidirect
42. C2×C4⋊Dic13C22semidirect
43. C2×#6101C22semidirect
44. C2×#6101C22semidirect
45. C2×C4×Dic13C22semidirect
46. C2×C4×Dic13C22semidirect
49. C13×#95C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
187. #396D13semidirect
255. C2×C4⋊C4C2×D13semidirect
256. C2×C4⋊C4C2×D13semidirect
257. C2×C4⋊C4C2×D13semidirect
282. #95C2×D13semidirect
352. C13#2685semidirect

Maximal subgroups

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

subgroupindex
C2×#881522
C2×#881362
C13×#3962
#117186532
#117186522
#117186512
#117186492
#117186222
#117186182
#117186162
#117186052
#117183332
#117183312
#268513