Finite Group Databasebeta

← #13126361

Subgroups — #13126361

Order 1664.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#135C211yesmaximal, characteristic, complemented
2#11719534C211yesmaximal, characteristic, complemented
3#11719529C211yesmaximal, characteristic, complemented
4C2×#88165C211yesmaximal, characteristic, complemented
5#11718900C211yesmaximal, characteristic, complemented
6#11718899C211yesmaximal, characteristic, complemented
7#11718851C211yesmaximal, characteristic, complemented
8#11718850C211yesmaximal, characteristic, complemented
9#11718834C211yesmaximal, characteristic, complemented
10#11718830C211yesmaximal, characteristic, complemented
11#11718826C211yesmaximal, characteristic, complemented
12#11718823C211yesmaximal, characteristic, complemented
13#11718813C211yesmaximal, characteristic, complemented
14#11718775C211yesmaximal, characteristic, complemented
15#11718772C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×C13×#41C2211yescharacteristic, complemented
18C2×#6129C2211yescharacteristic
19C2×D4×D13C2211yescharacteristic
20C13×#135—24no—
21C2×C13×Q16C2211yescharacteristic, complemented
22C2×C13×SD16C2211yescharacteristic
23C2×C13×SD16C2211yescharacteristic, complemented
24C2×C13×D8C2211yescharacteristic
25C22×C8×C13C2211yescharacteristic, complemented
26#88201C2211yescharacteristic
27#88200C2211yescharacteristic
28#88200C2211yescharacteristic
29#88198C2211yescharacteristic, complemented
30C2×#6107C2211yescharacteristic, complemented
31C2×#6106C2211yescharacteristic
32#88193—21no—
33#88193—21no—
34#88191—21no—
35#88189—21no—
36D4×Dic13C2211yescharacteristic
37D4×Dic13C2211yescharacteristic, complemented
38C2×#6105C2211yescharacteristic
39C2×#6104C2211yescharacteristic
40#88184C2211yescharacteristic
41#88183—21no—
42#88183—21no—
43C4×C22⋊D13C2211yescharacteristic
44C2×#6103—21no—
45#88178C2211yescharacteristic, complemented
46C2×#6101—21no—
47#88165—24no—
48C2×#6095C2211yescharacteristic
49C2×#6094C2211yescharacteristic
50#88075C2211yescharacteristic, complemented
51#88075C2211yescharacteristic, complemented
52#88072C2211yescharacteristic
53#88072C2211yescharacteristic, complemented
54C22⋊#1055C2211yescharacteristic, complemented
55#88061C2211yescharacteristic
56#88060C2211yescharacteristic
57#88057C2211yescharacteristic, complemented
58#88056C2211yescharacteristic, complemented
59#88055C2211yescharacteristic, complemented
60#88054C2211yescharacteristic, complemented
61C23×D13—21no—
62C13×#41—22no—
63C13×#41—22no—
64C13×#41—41no—
65C13×#41—41no—
66C2×Q8×C13C2311yescharacteristic
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13C2311yescharacteristic
71C2×D4×C13C2311yescharacteristic
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13C2311yescharacteristic
75C2×C22⋊D13—21no—
76C2×C22⋊D13—21no—
77C2×C22⋊D13—21no—
78C2×C22⋊D13D411yescharacteristic
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82#6129—22no—
83#6129—41no—
84D4×D13—22no—
85D4×D13—41no—
86C2×D52C2311yescharacteristic
87C2×C4×D13C2311yescharacteristic
88C2×Dic26C2311yescharacteristic
89C13×Q16—22no—
90C13×SD16—22no—
91C13×SD16—22no—
92C13×D8D414yescomplemented
93C2×C8×C13—22no—
94C2×C8×C13C2311yescharacteristic
95C2×C8×C13C2311yescharacteristic
96C22⋊Dic13—21no—
97C22⋊Dic13—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13D411yescharacteristic
100#6107—41no—
101#6106—41no—
102#6105—22no—
103#6104—22no—
104#6103—21no—
105#6103—21no—
106#6103—21no—
107#6103—21no—
108#6103—21no—
109#6103D411yescharacteristic
110C4⋊Dic13C2311yescharacteristic
111C4⋊Dic13C2311yescharacteristic
112#6101—21no—
113#6101—21no—
114#6101—21no—
115#6101—21no—
116#6101—21no—
117#6101D411yescharacteristic
118C4×Dic13C2311yescharacteristic
119C2×#1055C2311yescharacteristic
120C2×#1055C2311yescharacteristic
121#6095—22no—
122#6094—22no—
123#3267—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13—21no—
126C23×C13C2×D411yescharacteristic
127C22×D13—21no—
128C22×D13—42no—
129C22×D13—42no—
130C22×D13—81no—
131C22×D13C2×D411yescharacteristic
132Q8×C13—21no—
133Q8×C13—21no—
134Q8×C13—21no—
135Q8×C13—21no—
136D4×C13—21no—
137D4×C13—21no—
138D4×C13—42no—
139D4×C13—42no—
140D4×C13C2×D412yes—
141D4×C13C2×D412yes—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13C2×D411yescharacteristic
149C2×C4×C13C2411yescharacteristic
150C22⋊D13—41no—
151C22⋊D13—42no—
152C22⋊D13—42no—
153C22⋊D13—81no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—81no—
160C2×Dic13C2×D411yescharacteristic
161C2×Dic13C2×D411yescharacteristic
162C2×Dic13C2×D411yescharacteristic
163D52—21no—
164D52—21no—
165C4×D13—21no—
166C4×D13—21no—
167Dic26—21no—
168Dic26—21no—
169C8×C13—21no—
170C8×C13C2×D412yes—
171#1055—21no—
172#1055—21no—
173C2×AGL(1,ℤ/8)—131no—
174C2×#135D1311yescharacteristic, complemented
175#547—131no—
176#546—131no—
177#497—131no—
178#470—131no—
179#465—131no—
180#463—131no—
181#461—131no—
182#452—131no—
183#452—131no—
184#450—131no—
185#449—131no—
186#442—131no—
187#435—131no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13C22×D411yescharacteristic
198C2×D13—21no—
199C2×D13—21no—
200C2×D13—21no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C2×D13—84no—
205C4×C13—21no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13C22×D411yescharacteristic
209C4×C13H(5,𝔽2)11yescharacteristic
210Dic13—21no—
211Dic13—21no—
212Dic13—21no—
213Dic13—41no—
214Dic13—41no—
215Dic13—41no—
216C2×#41—131no—
217C2×#41C2×D1311yescharacteristic
218C2×#41C2×D1311yescharacteristic, complemented
219C22×D4—131no—
220AGL(1,ℤ/8)—264no—
221#135—24no—
222C2×Q16—131no—
223C2×Q16C2×D1311yescharacteristic, complemented
224C2×SD16—131no—
225C2×SD16—131no—
226C2×SD16—131no—
227C2×SD16C2×D1311yescharacteristic
228C2×SD16C2×D1311yescharacteristic, complemented
229C2×D8—131no—
230C2×D8C2×D1311yescharacteristic
231C2×M16—131no—
232C22×C8C2×D1311yescharacteristic, complemented
233C4⋊Q8—131no—
234#124—131no—
235#123—261no—
236#123—261no—
237#123—261no—
238C22⋊Q8—131no—
239C22⋊Q8—131no—
240C22⋊Q8—131no—
241#121—131no—
242#121—261no—
243#121—261no—
244#120—261no—
245C4×D4—131no—
246C4×D4—131no—
247C4×D4—131no—
248C2×C4⋊C4—261no—
249C2×C22⋊C4—261no—
250#106—131no—
251C4⋊C8—131no—
252#103—131no—
253#103—131no—
254#103—131no—
255#102—131no—
256#102—131no—
257#102—131no—
258C22⋊C8—131no—
259C22⋊C8—131no—
260#97—131no—
261C2×C13—42no—
262C2×C13—41no—
263C2×C13—42no—
264C2×C13D4211yescharacteristic
265C2×C13#57511yescharacteristic
266C2×C13#57711yescharacteristic
267D13—41no—
268D13—81no—
269C24—261no—
270#41—22no—
271#41—22no—
272#41—41no—
273#41—41no—
274#41—262no—
275#41—521no—
276C2×Q8—131no—
277C2×Q8C22×D1311yescharacteristic
278C2×Q8C22×D1311yescharacteristic
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—131no—
282C2×D4—131no—
283C2×D4—261no—
284C2×D4—262no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—521no—
288C2×D4C22×D1311yescharacteristic
289C2×D4C22×D1311yescharacteristic
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—131no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4C22×D1311yescharacteristic
297Q16—22no—
298Q16—521no—
299SD16—22no—
300SD16—22no—
301SD16—262no—
302SD16—262no—
303SD16—521no—
304D8—262no—
305D8C22⋊D1314yescomplemented
306M16—262no—
307C2×C8—22no—
308C2×C8—131no—
309C2×C8—131no—
310C2×C8C22×D1311yescharacteristic
311C2×C8C22×D1311yescharacteristic
312C4⋊C4—131no—
313C4⋊C4—131no—
314C4⋊C4—131no—
315C4⋊C4—261no—
316C4⋊C4—261no—
317C4⋊C4—261no—
318C4⋊C4—261no—
319C4⋊C4—261no—
320C22⋊C4—131no—
321C22⋊C4—131no—
322C22⋊C4—261no—
323C22⋊C4—261no—
324C22⋊C4—261no—
325C22⋊C4—261no—
326C22⋊C4—261no—
327C22⋊C4—261no—
328C22⋊C4—261no—
329C22⋊C4—261no—
330C42—131no—
331C13#326711yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—131no—
335C23—261no—
336C23—522no—
337C23—522no—
338C23—1041no—
339C23D4×D1311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—261no—
345Q8—261no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—42no—
350D4—261no—
351D4—261no—
352D4—521no—
353D4—522no—
354D4—522no—
355D4—1041no—
356D4C2×C22⋊D1312yes—
357D4C2×C22⋊D1312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—131no—
365C2×C4—131no—
366C2×C4—131no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—522no—
373C2×C4—522no—
374C2×C4—1041no—
375C2×C4D4×D1311yescharacteristic
376C2×C4C23×D1311yescharacteristic
377C8—21no—
378C8—261no—
379C8—261no—
380C8C2×C22⋊D1312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—261no—
391C22—261no—
392C22—261no—
393C22—521no—
394C22—521no—
395C22—521no—
396C22—1044no—
397C22C2×D4×D1311yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—261no—
402C4—261no—
403C4—261no—
404C4—521no—
405C4—521no—
406C4—521no—
407C4#8825111yescharacteristic
408C4C22×C22⋊D1311yescharacteristic
409C2—41no—
410C2—42no—
411C2—42no—
412C2—521no—
413C2—1041no—
414C2#1171947311yescharacteristic
415C2#1171947511yescharacteristic
416C2D4×C22⋊D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#135C2
socleC22×C13C22×D4
hypercenterC2×#135D13
hypocenterC13#3267
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C13×#135C2semidirect
2. #11719534C2semidirect
3. #11719529C2semidirect
4. C2×#88165C2semidirect
5. #11718900C2semidirect
6. #11718899C2semidirect
7. #11718851C2semidirect
8. #11718850C2semidirect
9. #11718834C2semidirect
10. #11718830C2semidirect
11. #11718826C2semidirect
12. #11718823C2semidirect
13. #11718813C2semidirect
14. #11718775C2semidirect
15. #11718772C2semidirect
17. C2×C13×#41C22semidirect
21. C2×C13×Q16C22semidirect
23. C2×C13×SD16C22semidirect
25. C22×C8×C13C22semidirect
29. #88198C22semidirect
30. C2×#6107C22semidirect
37. D4×Dic13C22semidirect
45. #88178C22semidirect
50. #88075C22semidirect
51. #88075C22semidirect
53. #88072C22semidirect
54. C22⋊#1055C22semidirect
57. #88057C22semidirect
58. #88056C22semidirect
59. #88055C22semidirect
60. #88054C22semidirect
92. C13×D8D4semidirect
174. C2×#135D13semidirect
218. C2×#41C2×D13semidirect
223. C2×Q16C2×D13semidirect
228. C2×SD16C2×D13semidirect
232. C22×C8C2×D13semidirect
305. D8C22⋊D13semidirect
331. C13#3267semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1352
#117195342
#117195292
C2×#881652
#117189002
#117188992
#117188512
#117188502
#117188342
#117188302
#117188262
#117188232
#117188132
#117187752
#117187722
#326713