Finite Group Databasebeta

← #13126548

Subgroups — #13126548

Order 1664.

504 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×#88158C211yesmaximal, characteristic, complemented
2C22×#6095C211yesmaximal, characteristic, complemented
3#11719257C211yesmaximal, characteristic, complemented
4#11719255C211yesmaximal, characteristic, complemented
5C8×D4×C13C211yesmaximal, characteristic, complemented
6#11718775C211yesmaximal, characteristic, complemented
7#11718775C211yesmaximal, characteristic, complemented
8#11718506C211yesmaximal, characteristic, complemented
9#11718505C211yesmaximal, characteristic, complemented
10#11718400C211yesmaximal, characteristic, complemented
11#11718395C211yesmaximal, characteristic, complemented
12#11718394C211yesmaximal, characteristic, complemented
13#11718393C211yesmaximal, characteristic, complemented
14#11718357C211yesmaximal, characteristic, complemented
15C4×#6095C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C2×#6127C2211yescharacteristic, complemented
18C22×D52C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C22×C8×C13C2211yescharacteristic
21C22×C8×C13C2211yescharacteristic, complemented
22C4×D4×C13C2211yescharacteristic
23#88193—21no—
24#88191—21no—
25#88184C2211yescharacteristic
26#88184C2211yescharacteristic
27#88178C2211yescharacteristic
28#88178C2211yescharacteristic, complemented
29C2×Dic52C2211yescharacteristic, complemented
30C2×Dic52C2211yescharacteristic, complemented
31#88158—24no—
32C2×D104C2211yescharacteristic
33C2×D104C2211yescharacteristic
34C2×#6095—24no—
35C2×#6095C2211yescharacteristic
36C2×#6095C2211yescharacteristic
37C2×#6095C2211yescharacteristic
38C2×#6095C2211yescharacteristic
39C2×#6095C2211yescharacteristic, complemented
40#88150—21no—
41#88148—21no—
42#88139—21no—
43#88138—21no—
44#88135—21no—
45C22⋊C4×D13—21no—
46#88129C2211yescharacteristic
47#88129C2211yescharacteristic, complemented
48C4×D52C2211yescharacteristic
49C4×Dic26C2211yescharacteristic, complemented
50C13×C4⋊C8C2211yescharacteristic, complemented
51C13×C22⋊C8C2211yescharacteristic
52C13×C22⋊C8C2211yescharacteristic, complemented
53C4×C8×C13C2211yescharacteristic, complemented
54#88061C2211yescharacteristic
55#88061C2211yescharacteristic
56#88061C2211yescharacteristic, complemented
57#88057C2211yescharacteristic, complemented
58#88056C2211yescharacteristic, complemented
59#88056C2211yescharacteristic, complemented
60#88056C2211yescharacteristic, complemented
61C23×D13—21no—
62C2×D4×C13D411yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C22×Dic13—21no—
70#6127—22no—
71#6127—22no—
72#6127—41no—
73#6127—41no—
74C2×D52—22no—
75C2×D52—21no—
76C2×D52—41no—
77C2×D52C2311yescharacteristic
78C2×D52C2311yescharacteristic
79C2×D52C2311yescharacteristic
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13—21no—
83C2×Dic26—22no—
84C2×Dic26—21no—
85C2×Dic26—41no—
86C2×Dic26C2311yescharacteristic
87C2×Dic26C2311yescharacteristic
88C2×Dic26C2311yescharacteristic
89C2×C8×C13—22no—
90C2×C8×C13—22no—
91C2×C8×C13C2311yescharacteristic
92C2×C8×C13C2311yescharacteristic
93C2×C8×C13C2311yescharacteristic
94C2×C8×C13C2311yescharacteristic
95C13×C4⋊C4D411yescharacteristic
96C13×C22⋊C4D411yescharacteristic
97C13×C22⋊C4D411yescharacteristic
98C42×C13C2311yescharacteristic
99C22⋊Dic13—21no—
100C22⋊Dic13—21no—
101#6103—21no—
102#6103—21no—
103#6103—21no—
104#6103—21no—
105#6103—21no—
106#6103—21no—
107#6103—21no—
108C4⋊Dic13C2311yescharacteristic
109C4⋊Dic13C2311yescharacteristic
110#6101—21no—
111#6101—21no—
112#6101—21no—
113C4×Dic13—21no—
114Dic52—22no—
115Dic52—41no—
116D104—22no—
117D104—41no—
118#6095—22no—
119#6095—22no—
120#6095—22no—
121#6095—22no—
122#6095D414yescomplemented
123#3282—131nomaximal, Sylow
124C23×C13C2×D411yescharacteristic
125C23×C13C2×D411yescharacteristic
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—42no—
130C22×D13—42no—
131C22×D13—81no—
132D4×C13—22no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2×D411yescharacteristic
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2×D411yescharacteristic
141C2×C4×C13C2411yescharacteristic
142C22⋊D13—42no—
143C22⋊D13—42no—
144C22⋊D13—42no—
145C22⋊D13—81no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—42no—
152D52—21no—
153D52—21no—
154D52—21no—
155D52—21no—
156D52—21no—
157D52—42no—
158D52C2×D412yes—
159C4×D13—42no—
160C4×D13—42no—
161C4×D13—81no—
162Dic26—21no—
163Dic26—21no—
164Dic26—21no—
165Dic26—21no—
166Dic26—21no—
167Dic26—42no—
168Dic26C2×D412yes—
169C8×C13—21no—
170C8×C13—21no—
171C8×C13—21no—
172C8×C13C2×D412yes—
173C2×#135—131no—
174C22×SD16—131no—
175#548—131no—
176#546—131no—
177#495—131no—
178#465—131no—
179#465—131no—
180#464—131no—
181#463—131no—
182#452—131no—
183#451—131no—
184#449—131no—
185#447—131no—
186C4×SD16—131no—
187C8×D4D1311yescharacteristic, complemented
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13#13512yescomplemented
194C22×C13C22×D411yescharacteristic
195C2×D13—22no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C2×D13—41no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C2×D13—84no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13C22×D411yescharacteristic
210C4×C13H(5,𝔽2)11yescharacteristic
211Dic13—22no—
212Dic13—41no—
213Dic13—41no—
214Dic13—41no—
215Dic13—41no—
216C2×#41—131no—
217C2×#41—131no—
218C22×Q8—131no—
219C22×D4—131no—
220#135—264no—
221C2×Q16—131no—
222C2×Q16—131no—
223C2×SD16—131no—
224C2×SD16—131no—
225C2×SD16—131no—
226C2×SD16—131no—
227C2×SD16—131no—
228C2×SD16—264no—
229C2×D8—131no—
230C2×D8—131no—
231C22×C8C2×D1311yescharacteristic
232C22×C8C2×D1311yescharacteristic, complemented
233#124—131no—
234#124—131no—
235#124—261no—
236#123—261no—
237C22⋊Q8—131no—
238C22⋊Q8—131no—
239C22⋊Q8—261no—
240#121—131no—
241#121—131no—
242#121—261no—
243#121—261no—
244#120—261no—
245C4×Q8—131no—
246C4×D4—131no—
247C4×D4—261no—
248C4×D4C2×D1311yescharacteristic
249C2×C22⋊C4—261no—
250#106—131no—
251C4⋊C8C2×D1311yescharacteristic, complemented
252#103—131no—
253#103—131no—
254#103—131no—
255#102—131no—
256#102—131no—
257#102—131no—
258C22⋊C8C2×D1311yescharacteristic
259C22⋊C8C2×D1311yescharacteristic, complemented
260C4×C8C2×D1311yescharacteristic, complemented
261C2×C13—22no—
262C2×C13—41no—
263C2×C13D4211yescharacteristic
264C2×C13C2×#13511yescharacteristic
265C2×C13#57711yescharacteristic
266D13—42no—
267D13—81no—
268D13—81no—
269C24—261no—
270#41—262no—
271#41—262no—
272#41—521no—
273#41—521no—
274C2×Q8—131no—
275C2×Q8—131no—
276C2×Q8—131no—
277C2×Q8—262no—
278C2×Q8—261no—
279C2×Q8—521no—
280C2×D4—131no—
281C2×D4—131no—
282C2×D4—131no—
283C2×D4—262no—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—521no—
290C2×D4D5211yescharacteristic
291C22×C4—261no—
292C22×C4—261no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4C22×D1311yescharacteristic
296C22×C4C22×D1311yescharacteristic
297Q16—262no—
298Q16—521no—
299SD16—134no—
300SD16—262no—
301SD16—262no—
302SD16—262no—
303SD16—262no—
304D8—262no—
305D8—521no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8C22×D1311yescharacteristic
309C2×C8C22×D1311yescharacteristic
310C2×C8C22×D1311yescharacteristic
311C2×C8C22×D1311yescharacteristic
312C4⋊C4—131no—
313C4⋊C4—131no—
314C4⋊C4—261no—
315C4⋊C4—261no—
316C4⋊C4—261no—
317C4⋊C4D5211yescharacteristic
318C22⋊C4—261no—
319C22⋊C4—261no—
320C22⋊C4—261no—
321C22⋊C4—261no—
322C22⋊C4—261no—
323C22⋊C4—261no—
324C22⋊C4—261no—
325C22⋊C4—261no—
326C22⋊C4—261no—
327C22⋊C4D5211yescharacteristic
328C22⋊C4D5211yescharacteristic
329C42—261no—
330C42C22×D1311yescharacteristic
331C13#328211yescharacteristic, complemented, Sylow
332C23—261no—
333C23—261no—
334C23—261no—
335C23—522no—
336C23—522no—
337C23—1041no—
338C23C2×D5211yescharacteristic
339C23C2×D5211yescharacteristic
340Q8—132no—
341Q8—261no—
342Q8—261no—
343Q8—261no—
344Q8—261no—
345Q8—261no—
346Q8—522no—
347D4—22no—
348D4—132no—
349D4—261no—
350D4—261no—
351D4—261no—
352D4—261no—
353D4—261no—
354D4—522no—
355D4—522no—
356D4—522no—
357D4—522no—
358D4—1041no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—261no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—522no—
369C2×C4—522no—
370C2×C4—522no—
371C2×C4—1041no—
372C2×C4C2×D5211yescharacteristic
373C2×C4C2×D5211yescharacteristic
374C2×C4C2×D5211yescharacteristic
375C2×C4C2×D5211yescharacteristic
376C2×C4C23×D1311yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D1312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—262no—
387C22—521no—
388C22—521no—
389C22—521no—
390C22—521no—
391C22—521no—
392C22—521no—
393C22—521no—
394C22—521no—
395C22—1044no—
396C22#8815812yescomplemented
397C22C22×D5211yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—262no—
403C4—521no—
404C4—521no—
405C4—521no—
406C4—521no—
407C4C2×D4×D1311yescharacteristic
408C4#8825611yescharacteristic
409C2—22no—
410C2—41no—
411C2—522no—
412C2—1041no—
413C2—1041no—
414C2D4×D5211yescharacteristic
415C2C2×#8815811yescharacteristic
416C2#1171945611yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC8×D4×C13C2
socleC22×C13C22×D4
hypercenterC8×D4D13
hypocenterC13#3282
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#88158C2semidirect
2. C22×#6095C2semidirect
3. #11719257C2semidirect
4. #11719255C2semidirect
5. C8×D4×C13C2semidirect
6. #11718775C2semidirect
7. #11718775C2semidirect
8. #11718506C2semidirect
9. #11718505C2semidirect
10. #11718400C2semidirect
11. #11718395C2semidirect
12. #11718394C2semidirect
13. #11718393C2semidirect
14. #11718357C2semidirect
15. C4×#6095C2semidirect
17. C2×#6127C22semidirect
21. C22×C8×C13C22semidirect
28. #88178C22semidirect
29. C2×Dic52C22semidirect
30. C2×Dic52C22semidirect
39. C2×#6095C22semidirect
47. #88129C22semidirect
49. C4×Dic26C22semidirect
50. C13×C4⋊C8C22semidirect
52. C13×C22⋊C8C22semidirect
53. C4×C8×C13C22semidirect
56. #88061C22semidirect
57. #88057C22semidirect
58. #88056C22semidirect
59. #88056C22semidirect
60. #88056C22semidirect
122. #6095D4semidirect
187. C8×D4D13semidirect
193. C22×C13#135semidirect
232. C22×C8C2×D13semidirect
251. C4⋊C8C2×D13semidirect
259. C22⋊C8C2×D13semidirect
260. C4×C8C2×D13semidirect
331. C13#3282semidirect
396. C22#88158semidirect

Maximal subgroups

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

subgroupindex
C2×#881582
C22×#60952
#117192572
#117192552
C8×D4×C132
#117187752
#117185062
#117185052
#117184002
#117183952
#117183942
#117183932
#117183572
C4×#60952
#328213