Finite Group Databasebeta

← #13121223

Subgroups — #13121223

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×C13×#120C211yesmaximal, characteristic
2C2×#88133C211yesmaximal, characteristic, complemented
3#11718908C211yesmaximal, characteristic, complemented
4#11718908C211yesmaximal, characteristic, complemented
5#11718883C211yesmaximal, characteristic, complemented
6#11718883C211yesmaximal, characteristic, complemented
7#11718883C211yesmaximal, characteristic, complemented
8#11718883C211yesmaximal, characteristic, complemented
9#11718882C211yesmaximal, characteristic, complemented
10#11718882C211yesmaximal, characteristic, complemented
11#11718612C211yesmaximal, characteristic, complemented
12#11718610C211yesmaximal, characteristic, complemented
13#11718609C211yesmaximal, characteristic, complemented
14#11718606C211yesmaximal, characteristic, complemented
15#11718605C211yesmaximal, characteristic, complemented
16C25×C13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C22×D4×C13C2211yescharacteristic
19C22×D4×C13C2211yescharacteristic
20C13×#120—24no—
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic
33C2×C22⋊Dic13C2211yescharacteristic
34C2×C22⋊Dic13C2211yescharacteristic
35C2×C22⋊Dic13C2211yescharacteristic
36C2×C22⋊Dic13C2211yescharacteristic, complemented
37C2×C22⋊Dic13C2211yescharacteristic, complemented
38C2×C22⋊Dic13C2211yescharacteristic, complemented
39C2×C22⋊Dic13C2211yescharacteristic, complemented
40C2×C4⋊Dic13C2211yescharacteristic, complemented
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—
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
63C24×C13C2311yescharacteristic
64C2×D4×C13—22no—
65C2×D4×C13—22no—
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—22no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C22×C4×C13C2311yescharacteristic
74C22×C4×C13C2311yescharacteristic
75C22×C4×C13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C13×C22⋊C4—22no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4D414yes—
87C22⋊Dic13—22no—
88C22⋊Dic13—22no—
89C22⋊Dic13—22no—
90C22⋊Dic13—22no—
91C22⋊Dic13—41no—
92C22⋊Dic13—41no—
93C22⋊Dic13—41no—
94C22⋊Dic13—41no—
95C22⋊Dic13—41no—
96C22⋊Dic13—41no—
97C22⋊Dic13—41no—
98C22⋊Dic13—41no—
99C22⋊Dic13—41no—
100C22⋊Dic13—41no—
101C22⋊Dic13—41no—
102C22⋊Dic13—41no—
103C4⋊Dic13—22no—
104C4⋊Dic13—41no—
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×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—44no—
138C23×C13—44no—
139C23×C13—44no—
140C23×C13—44no—
141C23×C13—44no—
142C23×C13—44no—
143C23×C13—44no—
144C23×C13C2×D412yes—
145C23×C13#4112yes—
146C23×C13#4112yes—
147C23×C13C2411yescharacteristic
148D4×C13—44no—
149D4×C13—44no—
150D4×C13—44no—
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×C13C2×D412yes—
159C2×C4×C13C2×D412yes—
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—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×Dic13—21no—
184C2×#126—131no—
185C2×#120D1311yescharacteristic
186#399—131no—
187#396—131no—
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—22no—
203C22×C13—22no—
204C22×C13—22no—
205C22×C13—22no—
206C22×C13—22no—
207C22×C13—22no—
208C22×C13—416no—
209C22×C13—41no—
210C22×C13—41no—
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×C13—41no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13—41no—
227C22×C13—41no—
228C22×C13C22×D411yescharacteristic
229C22×C13C2×#4111yescharacteristic
230C22×C13C2×#4111yescharacteristic
231C22×C13H(5,𝔽2)11yescharacteristic
232C22×C13H(5,𝔽2)11yescharacteristic
233C22×C13H(5,𝔽2)11yescharacteristic
234C22×C13H(5,𝔽2)11yescharacteristic
235C4×C13—22no—
236C4×C13—22no—
237C4×C13—41no—
238Dic13—41no—
239Dic13—41no—
240Dic13—41no—
241Dic13—41no—
242Dic13—41no—
243Dic13—41no—
244Dic13—41no—
245Dic13—41no—
246C25C2×D1311yescharacteristic
247C22×D4C2×D1311yescharacteristic
248C22×D4C2×D1311yescharacteristic
249C22×D4C2×D1311yescharacteristic
250#126—264no—
251#120—24no—
252C2×C4⋊C4—131no—
253C2×C4⋊C4—131no—
254C2×C4⋊C4—131no—
255C2×C4⋊C4—131no—
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⋊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#95—131no—
283C2×C13—42no—
284C2×C13—42no—
285C2×C13—42no—
286C2×C13—81no—
287C2×C13#53511yescharacteristic
288C2×C13#53811yescharacteristic
289C2×C13#53811yescharacteristic
290C2×C13#54611yescharacteristic
291C2×C13#54611yescharacteristic
292C2×C13#55111yescharacteristic
293C2×C13#56011yescharacteristic
294C24—22no—
295C24—22no—
296C24—22no—
297C24—41no—
298C24—41no—
299C24—41no—
300C24—41no—
301C24C22×D1311yescharacteristic
302C24C22×D1311yescharacteristic
303C24C22×D1311yescharacteristic
304C24C22×D1311yescharacteristic
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C22×C4—131no—
315C22×C4—131no—
316C22×C4—131no—
317C22×C4—131no—
318C22×C4—131no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—131no—
322C22×C4C22×D1311yescharacteristic
323C22×C4C22×D1311yescharacteristic
324C22×C4C22×D1311yescharacteristic
325C4⋊C4—262no—
326C4⋊C4—262no—
327C4⋊C4—262no—
328C4⋊C4—521no—
329C4⋊C4—521no—
330C4⋊C4—521no—
331C22⋊C4—22no—
332C22⋊C4—22no—
333C22⋊C4—262no—
334C22⋊C4—262no—
335C22⋊C4—262no—
336C22⋊C4—262no—
337C22⋊C4—521no—
338C22⋊C4—521no—
339C22⋊C4—521no—
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⋊C4C22⋊D1314yes—
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—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—44no—
379C23—44no—
380C23—44no—
381C23—44no—
382C23—44no—
383C23—44no—
384C23—44no—
385C23#612912yes—
386C23#612912yes—
387C23C2×C22⋊D1312yes—
388C23C23×D1311yescharacteristic
389D4—44no—
390D4—44no—
391D4—44no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—261no—
400C2×C4—261no—
401C2×C4—261no—
402C2×C4—261no—
403C2×C4—261no—
404C2×C4—261no—
405C2×C4—261no—
406C2×C4—261no—
407C2×C4—261no—
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×C4C2×C22⋊D1312yes—
424C2×C4C2×C22⋊D1312yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—416no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
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—41no—
452C22—41no—
453C22—41no—
454C22C2×#612911yescharacteristic
455C22C2×#612911yescharacteristic
456C22#8825111yescharacteristic
457C22#8825111yescharacteristic
458C22#8825111yescharacteristic
459C22#8825111yescharacteristic
460C22C22×C22⋊D1311yescharacteristic
461C4—22no—
462C4—22no—
463C4—41no—
464C4—521no—
465C4—521no—
466C4—521no—
467C4—521no—
468C4—521no—
469C4—521no—
470C4—521no—
471C4—521no—
472C2—42no—
473C2—42no—
474C2—42no—
475C2—81no—
476C2#1171929211yescharacteristic
477C2#1171929811yescharacteristic
478C2#1171929811yescharacteristic
479C2#1171930011yescharacteristic
480C2#1171951011yescharacteristic
481C2#1171951111yescharacteristic
482C2#1171951111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC2×C13×#120C2
hypercenterC2×#120D13
hypocenterC13#2685
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
2. C2×#88133C2semidirect
3. #11718908C2semidirect
4. #11718908C2semidirect
5. #11718883C2semidirect
6. #11718883C2semidirect
7. #11718883C2semidirect
8. #11718883C2semidirect
9. #11718882C2semidirect
10. #11718882C2semidirect
11. #11718612C2semidirect
12. #11718610C2semidirect
13. #11718609C2semidirect
14. #11718606C2semidirect
15. #11718605C2semidirect
36. C2×C22⋊Dic13C22semidirect
37. C2×C22⋊Dic13C22semidirect
38. C2×C22⋊Dic13C22semidirect
39. C2×C22⋊Dic13C22semidirect
40. C2×C4⋊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. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
352. C13#2685semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1202
C2×#881332
#117189082
#117188832
#117188822
#117186122
#117186102
#117186092
#117186062
#117186052
#268513