Finite Group Databasebeta

← #13121164

Subgroups — #13121164

Order 1664.

802 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#121C211yesmaximal, characteristic, complemented
2C2×#88191C211yesmaximal, characteristic, complemented
3C2×#88191C211yesmaximal, characteristic, complemented
4C2×#88183C211yesmaximal, characteristic, complemented
5#11718884C211yesmaximal, characteristic, complemented
6#11718884C211yesmaximal, characteristic, complemented
7#11718883C211yesmaximal, characteristic, complemented
8#11718882C211yesmaximal, characteristic, complemented
9#11718874C211yesmaximal, characteristic, complemented
10#11718655C211yesmaximal, characteristic, complemented
11#11718651C211yesmaximal, characteristic, complemented
12#11718622C211yesmaximal, characteristic, complemented
13#11718618C211yesmaximal, characteristic, complemented
14#11718616C211yesmaximal, characteristic, complemented
15#11718613C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C22×D4×C13C2211yescharacteristic
19C22×D4×C13C2211yescharacteristic, complemented
20C23×C4×C13C2211yescharacteristic, complemented
21C22×C22⋊D13C2211yescharacteristic
22C22×C22⋊D13C2211yescharacteristic
23C22×C22⋊D13C2211yescharacteristic
24C22×C22⋊D13C2211yescharacteristic
25C13×#121—24no—
26C2×C13×C4⋊C4C2211yescharacteristic, complemented
27C2×C13×C22⋊C4C2211yescharacteristic
28C2×C13×C22⋊C4C2211yescharacteristic, complemented
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic, complemented
33C2×C22⋊Dic13C2211yescharacteristic, complemented
34C2×C22⋊Dic13C2211yescharacteristic, complemented
35C2×C22⋊Dic13C2211yescharacteristic, complemented
36#88191—24no—
37#88191—24no—
38#88183—24no—
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×#6103C2211yescharacteristic
42C2×#6103C2211yescharacteristic
43C2×#6103C2211yescharacteristic
44C2×#6103C2211yescharacteristic
45C2×#6103C2211yescharacteristic
46C2×#6103C2211yescharacteristic
47C2×C4⋊Dic13C2211yescharacteristic, complemented
48C2×#6101C2211yescharacteristic, complemented
49C2×#6101C2211yescharacteristic, complemented
50C2×C4×Dic13C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55C24×C13C2311yescharacteristic
56C24×C13C2311yescharacteristic
57C24×C13C2311yescharacteristic
58C23×D13—22no—
59C23×D13—22no—
60C23×D13—22no—
61C23×D13—41no—
62C23×D13—41no—
63C23×D13—41no—
64C23×D13—41no—
65C23×D13C2311yescharacteristic
66C23×D13C2311yescharacteristic
67C2×D4×C13—22no—
68C2×D4×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13D414yescomplemented
76C22×C4×C13—22no—
77C22×C4×C13—22no—
78C22×C4×C13—41no—
79C22×C4×C13C2311yescharacteristic
80C22×C4×C13C2311yescharacteristic
81C22×C4×C13C2311yescharacteristic
82C22×C4×C13C2311yescharacteristic
83C2×C22⋊D13—22no—
84C2×C22⋊D13—22no—
85C2×C22⋊D13—22no—
86C2×C22⋊D13—22no—
87C2×C22⋊D13—22no—
88C2×C22⋊D13—22no—
89C2×C22⋊D13—22no—
90C2×C22⋊D13—41no—
91C2×C22⋊D13—41no—
92C2×C22⋊D13—41no—
93C2×C22⋊D13—41no—
94C2×C22⋊D13—41no—
95C22×Dic13C2311yescharacteristic
96C22×Dic13C2311yescharacteristic
97C22×Dic13C2311yescharacteristic
98C22×Dic13C2311yescharacteristic
99C22×Dic13C2311yescharacteristic
100C22×Dic13C2311yescharacteristic
101C13×C4⋊C4—22no—
102C13×C22⋊C4—22no—
103C13×C22⋊C4—22no—
104C22⋊Dic13—22no—
105C22⋊Dic13—22no—
106C22⋊Dic13—22no—
107C22⋊Dic13—41no—
108C22⋊Dic13—41no—
109C22⋊Dic13—41no—
110C22⋊Dic13—41no—
111#6103—22no—
112#6103—22no—
113#6103—22no—
114#6103—22no—
115#6103—41no—
116#6103—41no—
117#6103—41no—
118#6103D414yescomplemented
119C4⋊Dic13—41no—
120#6101—22no—
121#6101—22no—
122C4×Dic13—41no—
123#2678—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13—21no—
138C23×C13—21no—
139C23×C13—21no—
140C23×C13—21no—
141C23×C13—21no—
142C23×C13—21no—
143C23×C13C2×D412yes—
144C23×C13C2×D412yes—
145C23×C13C2411yescharacteristic
146C22×D13—21no—
147C22×D13—21no—
148C22×D13—21no—
149C22×D13—21no—
150C22×D13—21no—
151C22×D13—21no—
152C22×D13—21no—
153C22×D13—21no—
154C22×D13—21no—
155C22×D13—21no—
156C22×D13—21no—
157C22×D13—21no—
158C22×D13—44no—
159C22×D13—44no—
160C22×D13—44no—
161C22×D13—44no—
162C22×D13—44no—
163C22×D13—44no—
164C22×D13—44no—
165C22×D13C2×D412yes—
166C22×D13#4112yes—
167D4×C13—44no—
168D4×C13—44no—
169D4×C13—44no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—44no—
181C2×C4×C13C2×D412yes—
182C2×C4×C13C2×D412yes—
183C22⋊D13—44no—
184C22⋊D13—44no—
185C22⋊D13—44no—
186C22⋊D13—44no—
187C2×Dic13—21no—
188C2×Dic13—21no—
189C2×Dic13—21no—
190C2×Dic13—21no—
191C2×Dic13—21no—
192C2×Dic13—21no—
193C2×Dic13—21no—
194C2×Dic13—21no—
195C2×Dic13—21no—
196C2×Dic13—21no—
197C2×Dic13—21no—
198C2×Dic13—21no—
199C2×Dic13—21no—
200C2×Dic13—21no—
201C2×Dic13—21no—
202C2×Dic13—21no—
203C2×Dic13—21no—
204C2×Dic13C2×D412yes—
205C2×#123—131no—
206C2×#121D1311yescharacteristic, complemented
207C2×#120—131no—
208C2×#120—131no—
209#397—131no—
210#396—131no—
211#394—131no—
212#394—131no—
213#392—131no—
214#392—131no—
215#390—131no—
216#390—131no—
217#388—131no—
218#386—131no—
219#379—131no—
220C22×C13—22no—
221C22×C13—22no—
222C22×C13—22no—
223C22×C13—22no—
224C22×C13—22no—
225C22×C13—22no—
226C22×C13—41no—
227C22×C13—41no—
228C22×C13—41no—
229C22×C13—41no—
230C22×C13—41no—
231C22×C13—41no—
232C22×C13—41no—
233C22×C13—41no—
234C22×C13—41no—
235C22×C13—41no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13C22×D411yescharacteristic
242C22×C13C22×D411yescharacteristic
243C22×C13C2×#4111yescharacteristic
244C22×C13H(5,𝔽2)11yescharacteristic
245C22×C13H(5,𝔽2)11yescharacteristic
246C22×C13H(5,𝔽2)11yescharacteristic
247C22×C13H(5,𝔽2)11yescharacteristic
248C2×D13—22no—
249C2×D13—22no—
250C2×D13—22no—
251C2×D13—22no—
252C2×D13—22no—
253C2×D13—22no—
254C2×D13—416no—
255C2×D13—41no—
256C2×D13—41no—
257C2×D13—41no—
258C2×D13—41no—
259C2×D13—41no—
260C2×D13—41no—
261C2×D13—41no—
262C2×D13—41no—
263C4×C13—22no—
264C4×C13—22no—
265C4×C13—41no—
266C4×C13—41no—
267Dic13—22no—
268Dic13—41no—
269Dic13—41no—
270Dic13—41no—
271Dic13—41no—
272Dic13—41no—
273C25—131no—
274C22×D4—131no—
275C22×D4—131no—
276C22×D4—131no—
277C22×D4—131no—
278C22×D4C2×D1311yescharacteristic
279C22×D4C2×D1311yescharacteristic
280C22×D4C2×D1311yescharacteristic, complemented
281C23×C4C2×D1311yescharacteristic, complemented
282#123—264no—
283#121—24no—
284#120—264no—
285#120—264no—
286C2×C4⋊C4—131no—
287C2×C4⋊C4—131no—
288C2×C4⋊C4—131no—
289C2×C4⋊C4C2×D1311yescharacteristic, complemented
290C2×C22⋊C4—131no—
291C2×C22⋊C4—131no—
292C2×C22⋊C4—131no—
293C2×C22⋊C4—131no—
294C2×C22⋊C4—131no—
295C2×C22⋊C4—131no—
296C2×C22⋊C4—131no—
297C2×C22⋊C4—131no—
298C2×C22⋊C4—131no—
299C2×C22⋊C4—131no—
300C2×C22⋊C4—131no—
301C2×C22⋊C4—131no—
302C2×C22⋊C4—131no—
303C2×C22⋊C4—131no—
304C2×C22⋊C4—131no—
305C2×C22⋊C4C2×D1311yescharacteristic
306C2×C22⋊C4C2×D1311yescharacteristic, complemented
307C2×C42—131no—
308#95—131no—
309#95—131no—
310#95—131no—
311#95—131no—
312C2×C13—42no—
313C2×C13—42no—
314C2×C13—81no—
315C2×C13#53411yescharacteristic
316C2×C13#53511yescharacteristic
317C2×C13#53811yescharacteristic
318C2×C13D4211yescharacteristic
319C2×C13#54611yescharacteristic
320C2×C13#54611yescharacteristic
321C2×C13#56011yescharacteristic
322D13—42no—
323D13—42no—
324C24—131no—
325C24—131no—
326C24—262no—
327C24—262no—
328C24—262no—
329C24—521no—
330C24—521no—
331C24—521no—
332C24—521no—
333C24C22×D1311yescharacteristic
334C24C22×D1311yescharacteristic
335C24C22×D1311yescharacteristic
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—262no—
345C2×D4—262no—
346C2×D4—262no—
347C2×D4—262no—
348C2×D4—262no—
349C2×D4—262no—
350C2×D4—262no—
351C2×D4—521no—
352C2×D4—521no—
353C2×D4—521no—
354C2×D4—521no—
355C2×D4—521no—
356C2×D4C22⋊D1314yescomplemented
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—41no—
360C22×C4—131no—
361C22×C4—131no—
362C22×C4—131no—
363C22×C4—131no—
364C22×C4—131no—
365C22×C4—131no—
366C22×C4C22×D1311yescharacteristic
367C22×C4C22×D1311yescharacteristic
368C22×C4C22×D1311yescharacteristic
369C22×C4C22×D1311yescharacteristic
370C4⋊C4—22no—
371C4⋊C4—262no—
372C4⋊C4—262no—
373C4⋊C4—521no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—134no—
377C22⋊C4—262no—
378C22⋊C4—262no—
379C22⋊C4—262no—
380C22⋊C4—262no—
381C22⋊C4—262no—
382C22⋊C4—262no—
383C22⋊C4—262no—
384C22⋊C4—521no—
385C22⋊C4—521no—
386C22⋊C4—521no—
387C22⋊C4—521no—
388C22⋊C4—521no—
389C22⋊C4—521no—
390C22⋊C4—521no—
391C42—521no—
392C13#267811yescharacteristic, complemented, Sylow
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—132no—
413C23—132no—
414C23—261no—
415C23—261no—
416C23—261no—
417C23—261no—
418C23—261no—
419C23—261no—
420C23—261no—
421C23—261no—
422C23—261no—
423C23—261no—
424C23—261no—
425C23—261no—
426C23—524no—
427C23—524no—
428C23—524no—
429C23—524no—
430C23—524no—
431C23—524no—
432C23—524no—
433C23C2×C22⋊D1312yes—
434C23C2×C22⋊D1312yes—
435C23C23×D1311yescharacteristic
436D4—44no—
437D4—44no—
438D4—44no—
439D4—524no—
440D4—524no—
441D4—524no—
442D4—524no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—44no—
454C2×C4—132no—
455C2×C4—261no—
456C2×C4—261no—
457C2×C4—261no—
458C2×C4—261no—
459C2×C4—261no—
460C2×C4—261no—
461C2×C4—261no—
462C2×C4—261no—
463C2×C4—261no—
464C2×C4—261no—
465C2×C4—261no—
466C2×C4—261no—
467C2×C4—261no—
468C2×C4—261no—
469C2×C4—261no—
470C2×C4—261no—
471C2×C4—261no—
472C2×C4D4×D1312yes—
473C2×C4C2×C22⋊D1312yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—262no—
496C22—262no—
497C22—262no—
498C22—262no—
499C22—262no—
500C22—262no—
501C22—5216no—
502C22—521no—
503C22—521no—
504C22—521no—
505C22—521no—
506C22—521no—
507C22—521no—
508C22—521no—
509C22—521no—
510C22C2×D4×D1311yescharacteristic
511C22#8825111yescharacteristic
512C22#8825111yescharacteristic
513C22#8825111yescharacteristic
514C22#41×D1311yescharacteristic
515C22#8825611yescharacteristic
516C22C22×C22⋊D1311yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—41no—
521C4—262no—
522C4—521no—
523C4—521no—
524C4—521no—
525C4—521no—
526C4—521no—
527C2—42no—
528C2—42no—
529C2—81no—
530C2—522no—
531C2—522no—
532C2#1171931211yescharacteristic
533C2#1171931711yescharacteristic
534C2#1171931811yescharacteristic
535C2#1171932511yescharacteristic
536C2D4×C22⋊D1311yescharacteristic
537C2#1171950911yescharacteristic
538C2#1171953411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2678
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C13×#121C2semidirect
2. C2×#88191C2semidirect
3. C2×#88191C2semidirect
4. C2×#88183C2semidirect
5. #11718884C2semidirect
6. #11718884C2semidirect
7. #11718883C2semidirect
8. #11718882C2semidirect
9. #11718874C2semidirect
10. #11718655C2semidirect
11. #11718651C2semidirect
12. #11718622C2semidirect
13. #11718618C2semidirect
14. #11718616C2semidirect
15. #11718613C2semidirect
19. C22×D4×C13C22semidirect
20. C23×C4×C13C22semidirect
26. C2×C13×C4⋊C4C22semidirect
28. C2×C13×C22⋊C4C22semidirect
32. C2×C22⋊Dic13C22semidirect
33. C2×C22⋊Dic13C22semidirect
34. C2×C22⋊Dic13C22semidirect
35. C2×C22⋊Dic13C22semidirect
47. C2×C4⋊Dic13C22semidirect
48. C2×#6101C22semidirect
49. C2×#6101C22semidirect
50. C2×C4×Dic13C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
75. C2×D4×C13D4semidirect
118. #6103D4semidirect
206. C2×#121D13semidirect
280. C22×D4C2×D13semidirect
281. C23×C4C2×D13semidirect
289. C2×C4⋊C4C2×D13semidirect
306. C2×C22⋊C4C2×D13semidirect
356. C2×D4C22⋊D13semidirect
392. C13#2678semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C2×#881912
C2×#881832
#117188842
#117188832
#117188822
#117188742
#117186552
#117186512
#117186222
#117186182
#117186162
#117186132
#267813