Finite Group Databasebeta

← #13121216

Subgroups — #13121216

Order 1664.

688 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88207C211yesmaximal, characteristic
2C2×#88139C211yesmaximal, characteristic, complemented
3C13×#379C211yesmaximal, characteristic, complemented
4#11718908C211yesmaximal, characteristic, complemented
5#11718622C211yesmaximal, characteristic, complemented
6#11718620C211yesmaximal, characteristic, complemented
7#11718617C211yesmaximal, characteristic, complemented
8#11718617C211yesmaximal, characteristic, complemented
9#11718617C211yesmaximal, characteristic, complemented
10#11718614C211yesmaximal, characteristic, complemented
11#11718613C211yesmaximal, characteristic, complemented
12#11718612C211yesmaximal, characteristic, complemented
13#11718608C211yesmaximal, characteristic, complemented
14#11718608C211yesmaximal, characteristic, complemented
15#11718606C211yesmaximal, characteristic, complemented
16C25×C13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic, complemented
21C22×Dic26C2211yescharacteristic, complemented
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C13×C22⋊C4C2211yescharacteristic
28#88207—24no—
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic
33C2×C22⋊Dic13C2211yescharacteristic
34C2×C22⋊Dic13C2211yescharacteristic
35C2×C22⋊Dic13C2211yescharacteristic
36C2×C22⋊Dic13C2211yescharacteristic
37C2×C22⋊Dic13C2211yescharacteristic
38C2×#6103C2211yescharacteristic, complemented
39C2×#6103C2211yescharacteristic, complemented
40C2×#6103C2211yescharacteristic, complemented
41C2×C4⋊Dic13C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43C2×C4×Dic13C2211yescharacteristic, complemented
44#88139—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—41no—
57C24×C13—41no—
58C24×C13—41no—
59C24×C13—41no—
60C24×C13C2311yescharacteristic
61C24×C13C2311yescharacteristic
62C24×C13C2311yescharacteristic
63C23×D13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—22no—
69C2×C22⋊D13—22no—
70C2×C22⋊D13—22no—
71C2×C22⋊D13—22no—
72C2×C22⋊D13—41no—
73C2×C22⋊D13—41no—
74C2×C22⋊D13—41no—
75C2×C22⋊D13—41no—
76C2×C22⋊D13D414yes—
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×Dic26—22no—
88C2×Dic26—41no—
89C2×Dic26—41no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—22no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C22⋊Dic13—22no—
97C22⋊Dic13—22no—
98C22⋊Dic13—22no—
99C22⋊Dic13—22no—
100C22⋊Dic13—22no—
101C22⋊Dic13—41no—
102C22⋊Dic13—41no—
103C22⋊Dic13—41no—
104C22⋊Dic13—41no—
105#6103—22no—
106#6103—22no—
107#6103—41no—
108C4⋊Dic13—41no—
109#6101—41no—
110C4×Dic13—22no—
111#2684—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×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—44no—
131C23×C13—44no—
132C23×C13—44no—
133C23×C13—44no—
134C23×C13—44no—
135C23×C13—44no—
136C23×C13—44no—
137C23×C13C2×D412yes—
138C23×C13#4112yes—
139C23×C13#4112yes—
140C23×C13C2411yescharacteristic
141C22×D13—21no—
142C22×D13—21no—
143C22×D13—21no—
144C22×D13—21no—
145C22×D13—21no—
146C22×D13—21no—
147C22×D13C2×D412yes—
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—
160C22⋊D13—44no—
161C22⋊D13—44no—
162C22⋊D13—44no—
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—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×Dic13—21no—
183C2×Dic13C2×D412yes—
184C4×D13—44no—
185Dic26—44no—
186C2×#124—131no—
187C2×#120—131no—
188#397—131no—
189#397—131no—
190#394—131no—
191#394—131no—
192#393—131no—
193#393—131no—
194#388—131no—
195#388—131no—
196#386—131no—
197#386—131no—
198#386—131no—
199#379—131no—
200#379D1311yescharacteristic, complemented
201C22×C13—22no—
202C22×C13—22no—
203C22×C13—22no—
204C22×C13—22no—
205C22×C13—22no—
206C22×C13—22no—
207C22×C13—22no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13—416no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13C22×D411yescharacteristic
224C22×C13C2×#4111yescharacteristic
225C22×C13C2×#4111yescharacteristic
226C22×C13H(5,𝔽2)11yescharacteristic
227C22×C13H(5,𝔽2)11yescharacteristic
228C22×C13H(5,𝔽2)11yescharacteristic
229C22×C13H(5,𝔽2)11yescharacteristic
230C2×D13—22no—
231C2×D13—22no—
232C2×D13—22no—
233C2×D13—41no—
234C2×D13—41no—
235C2×D13—41no—
236C2×D13—41no—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—41no—
240C4×C13—41no—
241Dic13—22no—
242Dic13—41no—
243Dic13—41no—
244Dic13—41no—
245Dic13—41no—
246Dic13—41no—
247Dic13—41no—
248C25C2×D1311yescharacteristic
249C22×Q8—131no—
250C22×D4—131no—
251C22×D4—131no—
252C22×D4—131no—
253C23×C4—131no—
254#124—264no—
255#120—264no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
271C2×C22⋊C4C2×D1311yescharacteristic
272C2×C22⋊C4C2×D1311yescharacteristic
273C2×C22⋊C4C2×D1311yescharacteristic
274C2×C22⋊C4C2×D1311yescharacteristic
275C2×C22⋊C4C2×D1311yescharacteristic
276C2×C42—131no—
277#95—131no—
278#95—131no—
279#95—131no—
280#95—131no—
281#95—131no—
282#95—131no—
283#95—131no—
284#95—131no—
285C2×C13—42no—
286C2×C13—42no—
287C2×C13—42no—
288C2×C13#53411yescharacteristic
289C2×C13#53811yescharacteristic
290C2×C13#53811yescharacteristic
291C2×C13#54611yescharacteristic
292C2×C13#54611yescharacteristic
293C2×C13#55111yescharacteristic
294C2×C13H(3,𝔽4)11yescharacteristic
295D13—42no—
296C24—22no—
297C24—22no—
298C24—22no—
299C24—41no—
300C24—41no—
301C24—41no—
302C24—41no—
303C24—131no—
304C24C22×D1311yescharacteristic
305C24C22×D1311yescharacteristic
306C24C22×D1311yescharacteristic
307C2×Q8—262no—
308C2×Q8—521no—
309C2×Q8—521no—
310C2×D4—134no—
311C2×D4—262no—
312C2×D4—262no—
313C2×D4—262no—
314C2×D4—262no—
315C2×D4—521no—
316C2×D4—521no—
317C2×D4—521no—
318C2×D4—521no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—131no—
322C22×C4—131no—
323C22×C4—131no—
324C22×C4—131no—
325C22×C4—131no—
326C22×C4—521no—
327C22×C4—521no—
328C22×C4—521no—
329C22×C4C22×D1311yescharacteristic
330C22×C4C22×D1311yescharacteristic
331C22×C4C22×D1311yescharacteristic
332C22×C4C22×D1311yescharacteristic
333C4⋊C4—521no—
334C4⋊C4—521no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—262no—
342C22⋊C4—262no—
343C22⋊C4—262no—
344C22⋊C4—262no—
345C22⋊C4—262no—
346C22⋊C4—262no—
347C22⋊C4—262no—
348C22⋊C4—521no—
349C22⋊C4—521no—
350C22⋊C4—521no—
351C22⋊C4—521no—
352C22⋊C4—521no—
353C42—262no—
354C13#268411yescharacteristic, complemented, Sylow
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—44no—
377C23—44no—
378C23—44no—
379C23—44no—
380C23—132no—
381C23—261no—
382C23—261no—
383C23—261no—
384C23—261no—
385C23—261no—
386C23—261no—
387C23#612712yes—
388C23D4×D1312yes—
389C23#612912yes—
390C23C23×D1311yescharacteristic
391Q8—524no—
392D4—524no—
393D4—524no—
394D4—524no—
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—261no—
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—
425C2×C4—261no—
426C2×C4—261no—
427C2×C4—261no—
428C2×C4—524no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—416no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—262no—
452C22—262no—
453C22—262no—
454C22—521no—
455C22—521no—
456C22—521no—
457C22—521no—
458C22C2×#612711yescharacteristic
459C22C2×D4×D1311yescharacteristic
460C22C2×#612911yescharacteristic
461C22#8825111yescharacteristic
462C22#8825111yescharacteristic
463C22#8825111yescharacteristic
464C22#8825111yescharacteristic
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—262no—
470C4—521no—
471C4—521no—
472C4—521no—
473C4—521no—
474C4—521no—
475C4—521no—
476C2—42no—
477C2—42no—
478C2—42no—
479C2—522no—
480C2#1171919511yescharacteristic
481C2#1171919911yescharacteristic
482C2#1171920011yescharacteristic
483C2#1171929411yescharacteristic
484C2#1171929611yescharacteristic
485C2#1171929811yescharacteristic
486C2#1171929911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#379C2
prime radicalC2×#88207C2
hypercenter#379D13
hypocenterC13#2684
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#88139C2semidirect
3. C13×#379C2semidirect
4. #11718908C2semidirect
5. #11718622C2semidirect
6. #11718620C2semidirect
7. #11718617C2semidirect
8. #11718617C2semidirect
9. #11718617C2semidirect
10. #11718614C2semidirect
11. #11718613C2semidirect
12. #11718612C2semidirect
13. #11718608C2semidirect
14. #11718608C2semidirect
15. #11718606C2semidirect
20. C22×C4×D13C22semidirect
21. C22×Dic26C22semidirect
38. C2×#6103C22semidirect
39. C2×#6103C22semidirect
40. C2×#6103C22semidirect
41. C2×C4⋊Dic13C22semidirect
42. C2×#6101C22semidirect
43. C2×C4×Dic13C22semidirect
45. #88071C22semidirect
46. #88071C22semidirect
47. #88071C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
200. #379D13semidirect
354. C13#2684semidirect

Maximal subgroups

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

subgroupindex
C2×#882072
C2×#881392
C13×#3792
#117189082
#117186222
#117186202
#117186172
#117186142
#117186132
#117186122
#117186082
#117186062
#268413