Finite Group Databasebeta

← #13121233

Subgroups — #13121233

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×#88191C211yesmaximal, characteristic
2C2×#88133C211yesmaximal, characteristic, complemented
3C13×#394C211yesmaximal, characteristic, complemented
4#11718883C211yesmaximal, characteristic, complemented
5#11718655C211yesmaximal, characteristic, complemented
6#11718653C211yesmaximal, characteristic, complemented
7#11718622C211yesmaximal, characteristic, complemented
8#11718620C211yesmaximal, characteristic, complemented
9#11718618C211yesmaximal, characteristic, complemented
10#11718618C211yesmaximal, characteristic, complemented
11#11718616C211yesmaximal, characteristic, complemented
12#11718616C211yesmaximal, characteristic, complemented
13#11718605C211yesmaximal, characteristic, complemented
14#11718330C211yesmaximal, characteristic, complemented
15#11718330C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic, complemented
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic, complemented
24C2×C13×C22⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic, complemented
29C2×C22⋊Dic13C2211yescharacteristic, complemented
30#88191—24no—
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×C4⋊Dic13C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45C2×#6101C2211yescharacteristic, complemented
46C2×C4×Dic13C2211yescharacteristic, complemented
47C2×C4×Dic13C2211yescharacteristic, complemented
48#88133—24no—
49C13×#95C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53C24×C13C2311yescharacteristic
54C24×C13C2311yescharacteristic
55C23×D13—22no—
56C23×D13—22no—
57C23×D13—22no—
58C23×D13—41no—
59C23×D13—41no—
60C23×D13—41no—
61C23×D13—41no—
62C23×D13C2311yescharacteristic
63C23×D13C2311yescharacteristic
64C2×D4×C13—22no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C2×C22⋊D13—22no—
73C2×C22⋊D13—22no—
74C2×C22⋊D13—22no—
75C2×C22⋊D13—22no—
76C2×C22⋊D13—41no—
77C2×C22⋊D13—41no—
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C13×C4⋊C4—41no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C22⋊Dic13—22no—
90C22⋊Dic13—41no—
91C22⋊Dic13—41no—
92C22⋊Dic13—41no—
93C22⋊Dic13D414yes—
94#6103—22no—
95#6103—22no—
96#6103—22no—
97#6103—22no—
98#6103—41no—
99#6103—41no—
100#6103—41no—
101#6103—41no—
102#6103—41no—
103#6103—41no—
104C4⋊Dic13—22no—
105#6101—22no—
106#6101—22no—
107#6101—41no—
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—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13C2×D412yes—
126C23×C13C2411yescharacteristic
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×D13#4112yes—
147C22×D13#4112yes—
148D4×C13—44no—
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—
164C22⋊D13—44no—
165C22⋊D13—44no—
166C2×Dic13—21no—
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×Dic13—21no—
182C2×Dic13C2×D412yes—
183C2×Dic13C2×D412yes—
184C2×#126—131no—
185C2×#120—131no—
186#399—131no—
187#396—131no—
188#394—131no—
189#394—131no—
190#394—131no—
191#394D1311yescharacteristic, complemented
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×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13C22×D411yescharacteristic
214C22×C13C2×#4111yescharacteristic
215C22×C13C2×#4111yescharacteristic
216C22×C13H(5,𝔽2)11yescharacteristic
217C22×C13H(5,𝔽2)11yescharacteristic
218C22×C13H(5,𝔽2)11yescharacteristic
219C22×C13H(5,𝔽2)11yescharacteristic
220C2×D13—22no—
221C2×D13—22no—
222C2×D13—22no—
223C2×D13—22no—
224C2×D13—22no—
225C2×D13—22no—
226C2×D13—416no—
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—41no—
236C4×C13—41no—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—41no—
240Dic13—22no—
241Dic13—22no—
242Dic13—41no—
243Dic13—41no—
244Dic13—41no—
245Dic13—41no—
246C25—131no—
247C22×D4—131no—
248C22×D4—131no—
249C22×D4C2×D1311yescharacteristic
250#126—264no—
251#120—264no—
252C2×C4⋊C4—131no—
253C2×C4⋊C4—131no—
254C2×C4⋊C4—131no—
255C2×C4⋊C4—131no—
256C2×C4⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
274C2×C22⋊C4C2×D1311yescharacteristic
275C2×C22⋊C4C2×D1311yescharacteristic, complemented
276C2×C22⋊C4C2×D1311yescharacteristic, complemented
277C2×C42—131no—
278C2×C42—131no—
279#95—131no—
280#95—131no—
281#95—131no—
282#95C2×D1311yescharacteristic, complemented
283C2×C13—42no—
284C2×C13—81no—
285C2×C13#53511yescharacteristic
286C2×C13#53811yescharacteristic
287C2×C13#53811yescharacteristic
288C2×C13#54611yescharacteristic
289C2×C13#54611yescharacteristic
290C2×C13#55111yescharacteristic
291C2×C13#56011yescharacteristic
292D13—42no—
293D13—42no—
294C24—131no—
295C24—131no—
296C24—262no—
297C24—262no—
298C24—262no—
299C24—521no—
300C24—521no—
301C24—521no—
302C24—521no—
303C24C22×D1311yescharacteristic
304C24C22×D1311yescharacteristic
305C2×D4—22no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—262no—
309C2×D4—262no—
310C2×D4—262no—
311C2×D4—262no—
312C2×D4—521no—
313C2×D4—521no—
314C22×C4—131no—
315C22×C4—131no—
316C22×C4—131no—
317C22×C4—131no—
318C22×C4—131no—
319C22×C4—131no—
320C22×C4C22×D1311yescharacteristic
321C22×C4C22×D1311yescharacteristic
322C22×C4C22×D1311yescharacteristic
323C22×C4C22×D1311yescharacteristic
324C22×C4C22×D1311yescharacteristic
325C4⋊C4—41no—
326C4⋊C4—262no—
327C4⋊C4—262no—
328C4⋊C4—262no—
329C4⋊C4—521no—
330C4⋊C4—521no—
331C22⋊C4—22no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—134no—
336C22⋊C4—262no—
337C22⋊C4—262no—
338C22⋊C4—262no—
339C22⋊C4—262no—
340C22⋊C4—262no—
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—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—132no—
367C23—132no—
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—
387C23D4×D1312yes—
388C23C23×D1311yescharacteristic
389D4—44no—
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—132no—
408C2×C4—132no—
409C2×C4—261no—
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×C4—261no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—262no—
440C22—262no—
441C22—262no—
442C22—262no—
443C22—262no—
444C22—262no—
445C22—5216no—
446C22—521no—
447C22—521no—
448C22—521no—
449C22—521no—
450C22—521no—
451C22—521no—
452C22—521no—
453C22—521no—
454C22C2×D4×D1311yescharacteristic
455C22#8825111yescharacteristic
456C22#8825111yescharacteristic
457C22#8825111yescharacteristic
458C22#41×D1311yescharacteristic
459C22#41×D1311yescharacteristic
460C22#8825611yescharacteristic
461C4—41no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—262no—
467C4—262no—
468C4—521no—
469C4—521no—
470C4—521no—
471C4—521no—
472C2—42no—
473C2—81no—
474C2—522no—
475C2—522no—
476C2#1171929711yescharacteristic
477C2#1171931511yescharacteristic
478C2#1171931811yescharacteristic
479C2#1171932511yescharacteristic
480C2#1171935911yescharacteristic
481C2#1171936211yescharacteristic
482C2#1171938411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC2×#88191C2
hypercenter#394D13
hypocenterC13#2685
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88133C2semidirect
3. C13×#394C2semidirect
4. #11718883C2semidirect
5. #11718655C2semidirect
6. #11718653C2semidirect
7. #11718622C2semidirect
8. #11718620C2semidirect
9. #11718618C2semidirect
10. #11718618C2semidirect
11. #11718616C2semidirect
12. #11718616C2semidirect
13. #11718605C2semidirect
14. #11718330C2semidirect
15. #11718330C2semidirect
20. C2×C13×C4⋊C4C22semidirect
23. C2×C13×C22⋊C4C22semidirect
24. C2×C13×C22⋊C4C22semidirect
28. C2×C22⋊Dic13C22semidirect
29. C2×C22⋊Dic13C22semidirect
41. C2×C4⋊Dic13C22semidirect
42. C2×#6101C22semidirect
43. C2×#6101C22semidirect
44. C2×#6101C22semidirect
45. C2×#6101C22semidirect
46. C2×C4×Dic13C22semidirect
47. C2×C4×Dic13C22semidirect
49. C13×#95C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
191. #394D13semidirect
257. C2×C4⋊C4C2×D13semidirect
275. C2×C22⋊C4C2×D13semidirect
276. C2×C22⋊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×#881912
C2×#881332
C13×#3942
#117188832
#117186552
#117186532
#117186222
#117186202
#117186182
#117186162
#117186052
#117183302
#268513