Finite Group Databasebeta

← #13124834

Subgroups — #13124834

Order 1664.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719253C211yesmaximal, characteristic, complemented
2C4×D4×D13C211yesmaximal, characteristic, complemented
3C4×C13×D8C211yesmaximal, characteristic, complemented
4#11718817C211yesmaximal, characteristic, complemented
5#11718811C211yesmaximal, characteristic, complemented
6C4×#6104C211yesmaximal, characteristic, complemented
7C4×#6104C211yesmaximal, characteristic, complemented
8#11718551C211yesmaximal, characteristic, complemented
9#11718543C211yesmaximal, characteristic, complemented
10#11718447C211yesmaximal, characteristic, complemented
11#11718435C211yesmaximal, characteristic, complemented
12#11718434C211yesmaximal, characteristic, complemented
13#11718420C211yesmaximal, characteristic, complemented
14C4×D104C211yesmaximal, characteristic, complemented
15#11718346C211yesmaximal, characteristic, complemented
16C2×D4×D13C2211yescharacteristic
17C2×#6127—21no—
18C22×C4×D13—21no—
19C2×C13×D8C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21C4×D4×C13C2211yescharacteristic, complemented
22#88194C2211yescharacteristic, complemented
23#88192C2211yescharacteristic
24D4×Dic13C2211yescharacteristic
25C2×#6104C2211yescharacteristic
26C2×#6104C2211yescharacteristic
27C4×C22⋊D13—21no—
28C4×C22⋊D13—21no—
29C2×D104C2211yescharacteristic
30#88149C2211yescharacteristic
31#88147C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33#88142C2211yescharacteristic, complemented
34#88139—21no—
35#88138—21no—
36#88135—21no—
37C22⋊C4×D13—21no—
38C4×D52C2211yescharacteristic
39C4×D52C2211yescharacteristic, complemented
40C42×D13C2211yescharacteristic
41C13×#107C2211yescharacteristic, complemented
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic, complemented
44C4×C8×C13C2211yescharacteristic, complemented
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic, complemented
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic, complemented
49#88060C2211yescharacteristic
50#88060C2211yescharacteristic
51#88058C2211yescharacteristic, complemented
52#88054C2211yescharacteristic, complemented
53#88054C2211yescharacteristic, complemented
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic, complemented
56#88047C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58C4×#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C22×Dic13—21no—
69D4×D13—22no—
70D4×D13—22no—
71#6127—44no—
72C2×D52—21no—
73C2×D52C2311yescharacteristic
74C2×D52C2311yescharacteristic
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—44no—
80C2×C4×D13D411yescharacteristic
81C2×C4×D13D411yescharacteristic
82C2×C4×D13C2311yescharacteristic
83C2×Dic26—21no—
84C13×D8—22no—
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C22⋊C4—21no—
90C13×C22⋊C4—21no—
91C42×C13C2311yescharacteristic
92C22⋊Dic13—21no—
93C22⋊Dic13—21no—
94#6104—22no—
95#6104—22no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104C4×Dic13D411yescharacteristic
105C4×Dic13D411yescharacteristic
106C4×Dic13C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109D104—22no—
110#3100—131nomaximal, Sylow
111C23×C13—21no—
112C23×C13—21no—
113C22×D13—24no—
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—42no—
117C22×D13—42no—
118C22×D13C2×D411yescharacteristic
119D4×C13—21no—
120D4×C13—21no—
121D4×C13—21no—
122D4×C13#4112yescomplemented
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2411yescharacteristic
130C22⋊D13—24no—
131C22⋊D13—42no—
132C22⋊D13—42no—
133C22⋊D13—42no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—42no—
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140D52—21no—
141D52—21no—
142D52—21no—
143D52—42no—
144D52#4112yescomplemented
145C4×D13—21no—
146C4×D13—21no—
147C4×D13—41no—
148C4×D13—42no—
149C4×D13—42no—
150C4×D13—42no—
151C4×D13—42no—
152C4×D13D814yescomplemented
153Dic26—42no—
154C8×C13—21no—
155C8×C13—21no—
156#1055—21no—
157#1055—21no—
158#532—131no—
159C2×C4×D4—131no—
160#480—131no—
161#480—131no—
162#474—131no—
163#474—131no—
164#459—131no—
165#459—131no—
166#447—131no—
167#447—131no—
168C4×D8—131no—
169C4×D8—131no—
170C4×D8—131no—
171C4×D8D1311yescharacteristic, complemented
172#431—131no—
173C22×C13—22no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13C22×D411yescharacteristic
180C2×D13—21no—
181C2×D13—21no—
182C2×D13—22no—
183C2×D13—48no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—41no—
188C2×D13—41no—
189C2×D13C2×D812yes—
190C4×C13—21no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13C2×D812yes—
194C4×C13C2×#4111yescharacteristic
195C4×C13C2×#4111yescharacteristic
196Dic13—21no—
197Dic13—21no—
198Dic13—41no—
199Dic13—41no—
200Dic13C2×D812yes—
201C2×#41—261no—
202C22×D4—131no—
203C23×C4—261no—
204C2×D8—131no—
205C2×D8—131no—
206C2×D8—131no—
207C2×D8C2×D1311yescharacteristic
208C4⋊Q8—131no—
209#127—131no—
210#124—261no—
211#121—131no—
212#121—131no—
213#121—261no—
214C4×D4—131no—
215C4×D4—131no—
216C4×D4—131no—
217C4×D4—131no—
218C4×D4—261no—
219C4×D4—261no—
220C4×D4—261no—
221C4×D4C2×D1311yescharacteristic
222C4×D4C2×D1311yescharacteristic, complemented
223C2×C4⋊C4—131no—
224C2×C22⋊C4—261no—
225C2×C42—131no—
226#107—131no—
227#107—131no—
228#107—131no—
229#107C2×D1311yescharacteristic, complemented
230C4⋊C8—131no—
231C4⋊C8—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236#102—131no—
237#102—131no—
238#102C2×D1311yescharacteristic
239#102C2×D1311yescharacteristic, complemented
240C22⋊C8—131no—
241C22⋊C8—131no—
242C4×C8—131no—
243C4×C8C2×D1311yescharacteristic, complemented
244C2×C13—42no—
245C2×C13—81no—
246C2×C13#52511yescharacteristic
247C2×C13C22×D811yescharacteristic
248C2×C13#57511yescharacteristic
249D13—22no—
250D13—42no—
251D13—81no—
252C24—261no—
253#41—524no—
254C2×Q8—261no—
255C2×D4—131no—
256C2×D4—131no—
257C2×D4—261no—
258C2×D4—261no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—262no—
262C2×D4—262no—
263C2×D4—261no—
264C2×D4C22×D1311yescharacteristic
265C2×D4C22×D1311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4—524no—
277D8—22no—
278D8—262no—
279D8—262no—
280D8—262no—
281C2×C8—131no—
282C2×C8—131no—
283C2×C8C22×D1311yescharacteristic
284C2×C8C22×D1311yescharacteristic
285C4⋊C4—131no—
286C4⋊C4—131no—
287C4⋊C4—261no—
288C4⋊C4—261no—
289C4⋊C4C22×D1311yescharacteristic
290C4⋊C4C22×D1311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C22⋊C4—261no—
297C22⋊C4—261no—
298C22⋊C4—261no—
299C42—131no—
300C42—131no—
301C42—131no—
302C42C22×D1311yescharacteristic
303C13#310011yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—131no—
307C23—264no—
308C23—261no—
309C23—261no—
310C23—522no—
311C23—522no—
312Q8—522no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—132no—
317D4—264no—
318D4—261no—
319D4—261no—
320D4—261no—
321D4—522no—
322D4—522no—
323D4—522no—
324D4—522no—
325D4#612712yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—131no—
331C2×C4—134no—
332C2×C4—131no—
333C2×C4—131no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—521no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4D4×D1311yescharacteristic
345C2×C4D4×D1311yescharacteristic
346C2×C4C23×D1311yescharacteristic
347C8—21no—
348C8—21no—
349C8—261no—
350C8—261no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—132no—
358C22—261no—
359C22—261no—
360C22—262no—
361C22—528no—
362C22—521no—
363C22—521no—
364C22—521no—
365C22—521no—
366C22—521no—
367C22C2×D4×D1311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—132no—
372C4—261no—
373C4—261no—
374C4—521no—
375C4—521no—
376C4D8×D1312yes—
377C4C2×#612711yescharacteristic
378C4#41×D1311yescharacteristic
379C2—42no—
380C2—81no—
381C2—262no—
382C2—522no—
383C2—1041no—
384C2#1171925211yescharacteristic
385C2C2×D8×D1311yescharacteristic
386C2#1171947311yescharacteristic
subgroupG/H
centerC2×C4D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×D8C2
socleC22×C13C22×D4
hypercenterC4×D8D13
hypocenterC13#3100
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #11719253C2semidirect
2. C4×D4×D13C2semidirect
3. C4×C13×D8C2semidirect
4. #11718817C2semidirect
5. #11718811C2semidirect
6. C4×#6104C2semidirect
7. C4×#6104C2semidirect
8. #11718551C2semidirect
9. #11718543C2semidirect
10. #11718447C2semidirect
11. #11718435C2semidirect
12. #11718434C2semidirect
13. #11718420C2semidirect
14. C4×D104C2semidirect
15. #11718346C2semidirect
21. C4×D4×C13C22semidirect
22. #88194C22semidirect
33. #88142C22semidirect
39. C4×D52C22semidirect
41. C13×#107C22semidirect
43. C13×#102C22semidirect
44. C4×C8×C13C22semidirect
46. #88072C22semidirect
48. #88061C22semidirect
51. #88058C22semidirect
52. #88054C22semidirect
53. #88054C22semidirect
55. #88049C22semidirect
56. #88047C22semidirect
57. #88047C22semidirect
58. C4×#1055C22semidirect
122. D4×C13#41semidirect
144. D52#41semidirect
152. C4×D13D8semidirect
171. C4×D8D13semidirect
222. C4×D4C2×D13semidirect
229. #107C2×D13semidirect
239. #102C2×D13semidirect
243. C4×C8C2×D13semidirect
303. C13#3100semidirect
325. D4#6127semidirect

Maximal subgroups

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

subgroupindex
#117192532
C4×D4×D132
C4×C13×D82
#117188172
#117188112
C4×#61042
#117185512
#117185432
#117184472
#117184352
#117184342
#117184202
C4×D1042
#117183462
#310013