Finite Group Databasebeta

← #13126363

Subgroups — #13126363

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×#88166C211yesmaximal, characteristic, complemented
2C2×#88165C211yesmaximal, characteristic, complemented
3#11719260C211yesmaximal, characteristic, complemented
4#11719259C211yesmaximal, characteristic, complemented
5C13×#442C211yesmaximal, characteristic, complemented
6#11718680C211yesmaximal, characteristic, complemented
7#11718677C211yesmaximal, characteristic, complemented
8#11718529C211yesmaximal, characteristic, complemented
9#11718525C211yesmaximal, characteristic, complemented
10#11718444C211yesmaximal, characteristic, complemented
11#11718444C211yesmaximal, characteristic, complemented
12#11718442C211yesmaximal, characteristic, complemented
13#11718437C211yesmaximal, characteristic, complemented
14#11718376C211yesmaximal, characteristic, complemented
15#11718367C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×#6129C2211yescharacteristic, complemented
19C2×D4×D13C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic
21C4×D4×C13C2211yescharacteristic
22C4×D4×C13C2211yescharacteristic, complemented
23C2×#6105C2211yescharacteristic
24C2×#6105C2211yescharacteristic
25C2×#6105C2211yescharacteristic, complemented
26C2×#6104C2211yescharacteristic
27#88184—21no—
28#88184—21no—
29C2×#6103—21no—
30C2×C4⋊Dic13—21no—
31#88166—24no—
32#88165—24no—
33C2×Dic52C2211yescharacteristic, complemented
34C2×Dic52C2211yescharacteristic, complemented
35C2×#6095C2211yescharacteristic
36C2×#6095C2211yescharacteristic
37C2×#6094C2211yescharacteristic
38C2×C8×D13C2211yescharacteristic, complemented
39#88151C2211yescharacteristic
40#88151C2211yescharacteristic
41#88151C2211yescharacteristic, complemented
42#88149C2211yescharacteristic
43#88140—21no—
44#88140—21no—
45#88140—21no—
46#88136—21no—
47#88129C2211yescharacteristic
48C4×D52C2211yescharacteristic
49#88123C2211yescharacteristic, complemented
50C13×#106C2211yescharacteristic, complemented
51C13×#102C2211yescharacteristic
52C13×#102C2211yescharacteristic, complemented
53C13×#97C2211yescharacteristic, complemented
54#88060C2211yescharacteristic
55#88060C2211yescharacteristic, complemented
56#88050C2211yescharacteristic, complemented
57#88050C2211yescharacteristic, complemented
58#88050C2211yescharacteristic, complemented
59#88049C2211yescharacteristic
60C4⋊#1055C2211yescharacteristic, complemented
61C23×D13—21no—
62C2×D4×C13C2311yescharacteristic
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73#6129—22no—
74#6129—22no—
75#6129—22no—
76#6129—41no—
77#6129—41no—
78#6129—41no—
79D4×D13—22no—
80D4×D13—41no—
81C2×D52—21no—
82C2×D52D411yescharacteristic
83C2×D52C2311yescharacteristic
84C2×C4×D13C2311yescharacteristic
85C2×C4×D13C2311yescharacteristic
86C2×Dic26C2311yescharacteristic
87C2×Dic26C2311yescharacteristic
88C2×Dic26C2311yescharacteristic
89C13×D8D414yescomplemented
90C2×C8×C13C2311yescharacteristic
91C2×C8×C13C2311yescharacteristic
92C13×C4⋊C4C2311yescharacteristic
93C13×C4⋊C4C2311yescharacteristic
94C13×C22⋊C4—21no—
95C13×C22⋊C4—21no—
96C42×C13C2311yescharacteristic
97#6105—22no—
98#6105—22no—
99#6105—22no—
100#6104—22no—
101#6103—21no—
102#6103—21no—
103#6103—21no—
104#6103—21no—
105#6103—21no—
106#6103—21no—
107#6103D411yescharacteristic
108#6103D411yescharacteristic
109C4⋊Dic13—21no—
110C4⋊Dic13—21no—
111C4⋊Dic13—21no—
112C4⋊Dic13—21no—
113C4⋊Dic13—21no—
114C4⋊Dic13D411yescharacteristic
115C2×#1055C2311yescharacteristic
116C2×#1055C2311yescharacteristic
117Dic52—22no—
118Dic52—41no—
119#6095—22no—
120#6095—41no—
121#6094—22no—
122C8×D13—22no—
123#3267—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13—21no—
126C22×D13—21no—
127C22×D13—42no—
128C22×D13—42no—
129C22×D13—81no—
130C22×D13C2×D411yescharacteristic
131C22×D13C2×D411yescharacteristic
132D4×C13—21no—
133D4×C13—21no—
134D4×C13C2×D412yes—
135D4×C13C2×D412yes—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—42no—
139C2×C4×C13—81no—
140C2×C4×C13C2×D411yescharacteristic
141C2×C4×C13C2×D411yescharacteristic
142C2×C4×C13C2411yescharacteristic
143C22⋊D13—42no—
144C22⋊D13—42no—
145C22⋊D13—42no—
146C22⋊D13—42no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—42no—
151C2×Dic13—42no—
152C2×Dic13—42no—
153C2×Dic13C2×D411yescharacteristic
154C2×Dic13C2×D411yescharacteristic
155D52—21no—
156D52—21no—
157D52—41no—
158D52—81no—
159C4×D13—21no—
160C4×D13—21no—
161C4×D13—21no—
162C4×D13—21no—
163Dic26—21no—
164Dic26—21no—
165Dic26—21no—
166Dic26—21no—
167Dic26—21no—
168Dic26—21no—
169C8×C13—21no—
170C8×C13C2×D412yes—
171#1055—21no—
172#1055—21no—
173C2×AGL(1,ℤ/8)—131no—
174C2×#135—131no—
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#442D1311yescharacteristic, complemented
187#435—131no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13C22×D411yescharacteristic
195C2×D13—21no—
196C2×D13—21no—
197C2×D13—21no—
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—21no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13C22×D411yescharacteristic
210C4×C13H(5,𝔽2)11yescharacteristic
211Dic13—21no—
212Dic13—21no—
213Dic13—41no—
214Dic13—41no—
215Dic13—41no—
216C2×#41—131no—
217C2×#41—131no—
218C2×#41—131no—
219C22×D4—131no—
220AGL(1,ℤ/8)—264no—
221#135—264no—
222C2×Q16—131no—
223C2×Q16—131no—
224C2×SD16—131no—
225C2×SD16—131no—
226C2×SD16—131no—
227C2×SD16—131no—
228C2×SD16—131no—
229C2×D8—131no—
230C2×D8C2×D1311yescharacteristic
231C2×M16—131no—
232C22×C8—131no—
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×D4C2×D1311yescharacteristic
247C4×D4C2×D1311yescharacteristic, complemented
248C2×C4⋊C4—261no—
249C2×C22⋊C4—261no—
250#106C2×D1311yescharacteristic, complemented
251C4⋊C8—131no—
252#103—131no—
253#103—131no—
254#103—131no—
255#102—131no—
256#102C2×D1311yescharacteristic
257#102C2×D1311yescharacteristic, complemented
258C22⋊C8—131no—
259C22⋊C8—131no—
260#97C2×D1311yescharacteristic, complemented
261C2×C13—42no—
262C2×C13—42no—
263C2×C13D4211yescharacteristic
264C2×C13#57511yescharacteristic
265C2×C13#57711yescharacteristic
266D13—41no—
267D13—41no—
268D13—81no—
269C24—261no—
270#41—262no—
271#41—262no—
272#41—262no—
273#41—521no—
274#41—521no—
275#41—521no—
276C2×Q8—131no—
277C2×Q8—131no—
278C2×Q8—131no—
279C2×D4—131no—
280C2×D4—131no—
281C2×D4—261no—
282C2×D4—261no—
283C2×D4—262no—
284C2×D4—261no—
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—131no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4—261no—
297Q16—262no—
298Q16—521no—
299SD16—262no—
300SD16—262no—
301SD16—262no—
302SD16—262no—
303SD16—521no—
304D8—262no—
305D8D5214yescomplemented
306M16—262no—
307C2×C8—131no—
308C2×C8—131no—
309C2×C8—262no—
310C2×C8C22×D1311yescharacteristic
311C2×C8C22×D1311yescharacteristic
312C4⋊C4—131no—
313C4⋊C4—261no—
314C4⋊C4—261no—
315C4⋊C4—261no—
316C4⋊C4—261no—
317C4⋊C4—261no—
318C4⋊C4C22×D1311yescharacteristic
319C4⋊C4C22×D1311yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—131no—
323C22⋊C4—131no—
324C22⋊C4—261no—
325C22⋊C4—261no—
326C22⋊C4—261no—
327C22⋊C4—261no—
328C22⋊C4—261no—
329C22⋊C4—261no—
330C42C22×D1311yescharacteristic
331C13#326711yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—131no—
335C23—131no—
336C23—261no—
337C23—522no—
338C23—522no—
339C23—1041no—
340Q8—261no—
341Q8—261no—
342Q8—261no—
343Q8—261no—
344Q8—261no—
345Q8—261no—
346D4—21no—
347D4—21no—
348D4—261no—
349D4—261no—
350D4—521no—
351D4—522no—
352D4—522no—
353D4—522no—
354D4—522no—
355D4—1041no—
356D4C2×D5212yes—
357D4C2×D5212yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—131no—
363C2×C4—131no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—522no—
372C2×C4—522no—
373C2×C4—522no—
374C2×C4D4×D1311yescharacteristic
375C2×C4D4×D1311yescharacteristic
376C2×C4C23×D1311yescharacteristic
377C8—21no—
378C8—261no—
379C8—261no—
380C8C2×D5212yes—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—261no—
388C22—261no—
389C22—261no—
390C22—261no—
391C22—261no—
392C22—261no—
393C22—521no—
394C22—521no—
395C22—521no—
396C22—1044no—
397C22C2×D4×D1311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—261no—
403C4—261no—
404C4—521no—
405C4—521no—
406C4—521no—
407C4C22×D5211yescharacteristic
408C4#8825611yescharacteristic
409C2—42no—
410C2—42no—
411C2—521no—
412C2—521no—
413C2—1041no—
414C2D4×D5211yescharacteristic
415C2#1171947811yescharacteristic
416C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#442C2
socleC22×C13C22×D4
hypercenter#442D13
hypocenterC13#3267
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#88166C2semidirect
2. C2×#88165C2semidirect
3. #11719260C2semidirect
4. #11719259C2semidirect
5. C13×#442C2semidirect
6. #11718680C2semidirect
7. #11718677C2semidirect
8. #11718529C2semidirect
9. #11718525C2semidirect
10. #11718444C2semidirect
11. #11718444C2semidirect
12. #11718442C2semidirect
13. #11718437C2semidirect
14. #11718376C2semidirect
15. #11718367C2semidirect
18. C2×#6129C22semidirect
22. C4×D4×C13C22semidirect
25. C2×#6105C22semidirect
33. C2×Dic52C22semidirect
34. C2×Dic52C22semidirect
38. C2×C8×D13C22semidirect
41. #88151C22semidirect
49. #88123C22semidirect
50. C13×#106C22semidirect
52. C13×#102C22semidirect
53. C13×#97C22semidirect
55. #88060C22semidirect
56. #88050C22semidirect
57. #88050C22semidirect
58. #88050C22semidirect
60. C4⋊#1055C22semidirect
89. C13×D8D4semidirect
186. #442D13semidirect
247. C4×D4C2×D13semidirect
250. #106C2×D13semidirect
257. #102C2×D13semidirect
260. #97C2×D13semidirect
305. D8D52semidirect
331. C13#3267semidirect

Maximal subgroups

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

subgroupindex
C2×#881662
C2×#881652
#117192602
#117192592
C13×#4422
#117186802
#117186772
#117185292
#117185252
#117184442
#117184422
#117184372
#117183762
#117183672
#326713