Finite Group Databasebeta

← #13124789

Subgroups — #13124789

Order 1664.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719312C211yesmaximal, characteristic
2#11719228C211yesmaximal, characteristic, complemented
3C13×#482C211yesmaximal, characteristic, complemented
4#11718694C211yesmaximal, characteristic, complemented
5#11718664C211yesmaximal, characteristic, complemented
6#11718543C211yesmaximal, characteristic, complemented
7#11718542C211yesmaximal, characteristic, complemented
8#11718527C211yesmaximal, characteristic, complemented
9#11718521C211yesmaximal, characteristic, complemented
10#11718440C211yesmaximal, characteristic, complemented
11#11718438C211yesmaximal, characteristic, complemented
12#11718431C211yesmaximal, characteristic, complemented
13D13×#102C211yesmaximal, characteristic, complemented
14#11718396C211yesmaximal, characteristic, complemented
15#11718388C211yesmaximal, characteristic, complemented
16C2×D4×D13C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C13×#121C2211yescharacteristic
19C13×#117C2211yescharacteristic, complemented
20#88194—21no—
21#88192C2211yescharacteristic
22#88191—21no—
23#88184C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic, complemented
25C2×#6094C2211yescharacteristic
26C2×C8×D13C2211yescharacteristic
27#88149C2211yescharacteristic
28#88146C2211yescharacteristic
29#88146C2211yescharacteristic
30#88146C2211yescharacteristic, complemented
31C4⋊C4×D13C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic, complemented
33#88139—21no—
34#88136—21no—
35#88135—21no—
36#88135—21no—
37C4×D52—21no—
38C4×Dic26—21no—
39C13×#107C2211yescharacteristic, complemented
40C13×#106C2211yescharacteristic, complemented
41C13×#102C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic, complemented
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic, complemented
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88060C2211yescharacteristic, complemented
50#88060C2211yescharacteristic, complemented
51#88057C2211yescharacteristic, complemented
52#88057C2211yescharacteristic, complemented
53#88049C2211yescharacteristic
54#88049C2211yescharacteristic
55#88048C2211yescharacteristic, complemented
56#88047C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13D411yescharacteristic
67C2×C22⋊D13D411yescharacteristic
68C22×Dic13—21no—
69D4×D13—22no—
70D4×D13—22no—
71#6127—22no—
72#6127—22no—
73C2×D52—21no—
74C2×D52D411yescharacteristic
75C2×D52C2311yescharacteristic
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13C2311yescharacteristic
79C2×C4×D13C2311yescharacteristic
80C2×Dic26D411yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C22⋊C4—21no—
87C13×C22⋊C4—21no—
88C42×C13—21no—
89C22⋊Dic13—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—22no—
107C8×D13—22no—
108#3096—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111C22×D13—21no—
112C22×D13—42no—
113C22×D13—81no—
114C22×D13—81no—
115C22×D13C2×D411yescharacteristic
116C22×D13C2×D411yescharacteristic
117D4×C13—21no—
118D4×C13—21no—
119D4×C13—81no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C22⋊D13—22no—
128C22⋊D13—22no—
129C22⋊D13—42no—
130C22⋊D13—81no—
131C22⋊D13—81no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—81no—
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138D52—22no—
139D52—21no—
140D52—21no—
141D52—81no—
142C4×D13—21no—
143C4×D13—21no—
144C4×D13—81no—
145C4×D13—81no—
146C4×D13#4112yes—
147C4×D13#4112yes—
148Dic26—22no—
149C8×C13—21no—
150C8×C13—21no—
151#1055—21no—
152#1055—21no—
153#535—131no—
154#520—131no—
155#482—131no—
156#482—131no—
157#482—131no—
158#482D1311yescharacteristic, complemented
159#481—131no—
160#481—131no—
161#480—131no—
162#480—131no—
163#428—131no—
164#427—131no—
165#418—131no—
166C2×#102—131no—
167#408—131no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13C22×D411yescharacteristic
175C2×D13—21no—
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—21no—
179C2×D13—21no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—84no—
184C2×D13#12312yes—
185C4×C13—21no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13C2×#4111yescharacteristic
190C4×C13C2×#4111yescharacteristic
191Dic13—21no—
192Dic13—41no—
193Dic13—41no—
194Dic13—41no—
195Dic13#12312yes—
196C2×#41—131no—
197C22×D4—131no—
198C2×M16—131no—
199C22×C8—131no—
200#127—261no—
201#124—261no—
202#121—131no—
203#121—131no—
204#121—131no—
205#121C2×D1311yescharacteristic
206#120—261no—
207#120—261no—
208C4×Q8—261no—
209C4×D4—261no—
210C4×D4—261no—
211C4×D4—261no—
212#117—131no—
213#117—131no—
214#117—131no—
215#117C2×D1311yescharacteristic, complemented
216C2×C4⋊C4—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—131no—
219#107—131no—
220#107—131no—
221#107—131no—
222#107C2×D1311yescharacteristic, complemented
223#106—131no—
224#106—131no—
225#106—131no—
226#106C2×D1311yescharacteristic, complemented
227#102—131no—
228#102—131no—
229#102—131no—
230#102—131no—
231#102—131no—
232#102—131no—
233#102C2×D1311yescharacteristic
234#102C2×D1311yescharacteristic
235C22⋊C8—131no—
236C22⋊C8—131no—
237C22⋊C8—131no—
238C22⋊C8C2×D1311yescharacteristic, complemented
239C2×C13—41no—
240C2×C13—81no—
241C2×C13C2×#12311yescharacteristic
242C2×C13#57611yescharacteristic
243C2×C13#57711yescharacteristic
244D13—22no—
245D13—41no—
246D13—81no—
247C24—261no—
248#41—262no—
249#41—262no—
250C2×Q8—131no—
251C2×D4—21no—
252C2×D4—131no—
253C2×D4—131no—
254C2×D4—131no—
255C2×D4—131no—
256C2×D4—261no—
257C2×D4—262no—
258C2×D4—262no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4C22×D1311yescharacteristic
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4C22×D1311yescharacteristic
269M16—262no—
270C2×C8—131no—
271C2×C8—131no—
272C2×C8—262no—
273C2×C8C22×D1311yescharacteristic
274C2×C8C22×D1311yescharacteristic
275C4⋊C4—131no—
276C4⋊C4—131no—
277C4⋊C4—131no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4C22×D1311yescharacteristic
282C4⋊C4C22×D1311yescharacteristic
283C4⋊C4C22×D1311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C42—21no—
293C42—261no—
294C42—261no—
295C42—261no—
296C13#309611yescharacteristic, complemented, Sylow
297C23—21no—
298C23—131no—
299C23—131no—
300C23—261no—
301C23—522no—
302C23—1041no—
303C23—1041no—
304C23D4×D1311yescharacteristic
305Q8—262no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—262no—
310D4—262no—
311D4—262no—
312D4—261no—
313D4—261no—
314D4—522no—
315D4—1041no—
316D4—1041no—
317D4—1041no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—131no—
324C2×C4—132no—
325C2×C4—132no—
326C2×C4—131no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—1041no—
333C2×C4—1041no—
334C2×C4—1041no—
335C2×C4D4×D1311yescharacteristic
336C2×C4C23×D1311yescharacteristic
337C8—21no—
338C8—21no—
339C8—261no—
340C8—261no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—132no—
348C22—261no—
349C22—261no—
350C22—261no—
351C22—261no—
352C22—261no—
353C22—521no—
354C22—521no—
355C22—521no—
356C22—1044no—
357C22C2×D4×D1311yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—132no—
363C4—261no—
364C4—521no—
365C4—521no—
366C4—521no—
367C4#41×D1311yescharacteristic
368C4#41×D1311yescharacteristic
369C2—41no—
370C2—81no—
371C2—262no—
372C2—521no—
373C2—1041no—
374C2D13×#12311yescharacteristic
375C2#1171947511yescharacteristic
376C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#482C2
socleC22×C13C22×D4
prime radical#11719312C2
hypercenter#482D13
hypocenterC13#3096
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #11719228C2semidirect
3. C13×#482C2semidirect
4. #11718694C2semidirect
5. #11718664C2semidirect
6. #11718543C2semidirect
7. #11718542C2semidirect
8. #11718527C2semidirect
9. #11718521C2semidirect
10. #11718440C2semidirect
11. #11718438C2semidirect
12. #11718431C2semidirect
13. D13×#102C2semidirect
14. #11718396C2semidirect
15. #11718388C2semidirect
19. C13×#117C22semidirect
24. C2×C4⋊Dic13C22semidirect
30. #88146C22semidirect
32. C4⋊C4×D13C22semidirect
39. C13×#107C22semidirect
40. C13×#106C22semidirect
43. C13×C22⋊C8C22semidirect
46. C22⋊#1055C22semidirect
49. #88060C22semidirect
50. #88060C22semidirect
51. #88057C22semidirect
52. #88057C22semidirect
55. #88048C22semidirect
56. #88047C22semidirect
57. #88047C22semidirect
58. #88047C22semidirect
158. #482D13semidirect
215. #117C2×D13semidirect
222. #107C2×D13semidirect
226. #106C2×D13semidirect
238. C22⋊C8C2×D13semidirect
296. C13#3096semidirect

Maximal subgroups

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

subgroupindex
#117193122
#117192282
C13×#4822
#117186942
#117186642
#117185432
#117185422
#117185272
#117185212
#117184402
#117184382
#117184312
D13×#1022
#117183962
#117183882
#309613