Finite Group Databasebeta

← #13126993

Subgroups — #13126993

Order 1664.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719511C211yesmaximal, characteristic, complemented
2#11719237C211yesmaximal, characteristic, complemented
3C13×#418C211yesmaximal, characteristic, complemented
4#11718878C211yesmaximal, characteristic, complemented
5#11718795C211yesmaximal, characteristic, complemented
6#11718788C211yesmaximal, characteristic, complemented
7#11718657C211yesmaximal, characteristic, complemented
8#11718448C211yesmaximal, characteristic, complemented
9#11718446C211yesmaximal, characteristic, complemented
10#11718445C211yesmaximal, characteristic, complemented
11#11718442C211yesmaximal, characteristic, complemented
12#11718436C211yesmaximal, characteristic, complemented
13#11718433C211yesmaximal, characteristic, complemented
14#11718426C211yesmaximal, characteristic, complemented
15#11718420C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C13×#117C2211yescharacteristic
20#88207—21no—
21C2×C22⋊Dic13—21no—
22#88193—21no—
23#88192C2211yescharacteristic
24#88190C2211yescharacteristic
25#88189—21no—
26D4×Dic13C2211yescharacteristic
27C2×#6104C2211yescharacteristic
28C2×#6104C2211yescharacteristic
29#88184C2211yescharacteristic
30C4×C22⋊D13C2211yescharacteristic
31#88178C2211yescharacteristic
32C2×#6095C2211yescharacteristic, complemented
33C2×C8×D13C2211yescharacteristic, complemented
34#88149C2211yescharacteristic, complemented
35#88147C2211yescharacteristic, complemented
36#88146C2211yescharacteristic, complemented
37#88142C2211yescharacteristic, complemented
38#88139—21no—
39#88138—21no—
40#88129—21no—
41#88126—21no—
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88061C2211yescharacteristic, complemented
50#88060C2211yescharacteristic, complemented
51#88058C2211yescharacteristic, complemented
52#88056C2211yescharacteristic, complemented
53#88055C2211yescharacteristic, complemented
54#88054C2211yescharacteristic, complemented
55#88050C2211yescharacteristic, complemented
56#88050C2211yescharacteristic, complemented
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C24×C13—21no—
60C2×D4×C13—22no—
61C2×D4×C13—21no—
62C2×D4×C13—41no—
63C2×D4×C13C2311yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72#6129—22no—
73#6129—41no—
74C2×D52—21no—
75C2×D52C2311yescharacteristic
76C2×C4×D13—21no—
77C2×C4×D13C2311yescharacteristic
78C2×Dic26—21no—
79C2×Dic26C2311yescharacteristic
80C13×M16—41no—
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C22⋊C4—21no—
86C42×C13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13D411yescharacteristic
93#6104—22no—
94#6104—41no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103D411yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104#6101D411yescharacteristic
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109#6095—41no—
110C8×D13—41no—
111#3319—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—81no—
117C23×C13C2×D411yescharacteristic
118C22×D13—21no—
119C22×D13C2×D411yescharacteristic
120D4×C13—21no—
121D4×C13—21no—
122D4×C13—21no—
123D4×C13—42no—
124D4×C13#4112yes—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C22⋊D13—41no—
132C22⋊D13—42no—
133C22⋊D13—81no—
134C22⋊D13—81no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—42no—
139C2×Dic13—81no—
140C2×Dic13C2×D411yescharacteristic
141C2×Dic13C2×D411yescharacteristic
142C2×Dic13C2×D411yescharacteristic
143D52—21no—
144D52—21no—
145D52—81no—
146C4×D13—21no—
147C4×D13—21no—
148C4×D13—42no—
149Dic26—21no—
150Dic26—21no—
151Dic26—81no—
152C8×C13—21no—
153C8×C13—21no—
154#1055—21no—
155#1055—21no—
156#555—131no—
157#546—131no—
158#489—131no—
159#485—131no—
160#482—131no—
161#474—131no—
162#468—131no—
163#466—131no—
164#463—131no—
165#449—131no—
166#447—131no—
167#442—131no—
168#435—131no—
169#418D1311yescharacteristic, complemented
170#416—131no—
171C22×C13—22no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—84no—
181C22×C13C22×D411yescharacteristic
182C2×D13—21no—
183C2×D13—21no—
184C2×D13—21no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—41no—
188C4×C13—21no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13C2×#4111yescharacteristic
192C4×C13H(5,𝔽2)11yescharacteristic
193Dic13—21no—
194Dic13—21no—
195Dic13—21no—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199C2×#41—131no—
200C22×D4C2×D1311yescharacteristic
201C2×SD16—131no—
202C2×D8—131no—
203C2×D8—131no—
204C2×M16C2×D1311yescharacteristic
205C22×C8—131no—
206C4⋊Q8—131no—
207#124—131no—
208#124—261no—
209#124—261no—
210#123—261no—
211C22⋊Q8—131no—
212#121—131no—
213#121—131no—
214#121—131no—
215#121—261no—
216#121—261no—
217#120—261no—
218C4×D4—131no—
219C4×D4—131no—
220C4×D4—131no—
221#117—131no—
222#117—261no—
223#117C2×D1311yescharacteristic
224C2×C22⋊C4—261no—
225#107—131no—
226#107—131no—
227#106—131no—
228C4⋊C8—131no—
229#103—131no—
230#103—131no—
231#103—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102C2×D1311yescharacteristic
236#102C2×D1311yescharacteristic
237#102C2×D1311yescharacteristic
238#102C2×D1311yescharacteristic
239C22⋊C8—131no—
240C22⋊C8—131no—
241#97—131no—
242C2×C13—41no—
243C2×C13—42no—
244C2×C13—81no—
245C2×C13#54611yescharacteristic
246C2×C13#57511yescharacteristic
247C2×C13#57611yescharacteristic
248D13—41no—
249D13—81no—
250C24—21no—
251#41—262no—
252#41—521no—
253C2×Q8—131no—
254C2×Q8—261no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—131no—
259C2×D4—131no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4—261no—
263C2×D4—261no—
264C2×D4C22×D1311yescharacteristic
265C2×D4C22×D1311yescharacteristic
266C22×C4—131no—
267C22×C4—261no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4C22×D1311yescharacteristic
271SD16—521no—
272D8—262no—
273D8—521no—
274M16—41no—
275C2×C8—131no—
276C2×C8—131no—
277C2×C8—521no—
278C2×C8C22×D1311yescharacteristic
279C2×C8C22×D1311yescharacteristic
280C4⋊C4—131no—
281C4⋊C4—131no—
282C4⋊C4—131no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4C22×D1311yescharacteristic
286C4⋊C4C22×D1311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—131no—
289C22⋊C4—131no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C22⋊C4—261no—
297C22⋊C4—261no—
298C22⋊C4—261no—
299C42—21no—
300C42—131no—
301C42—261no—
302C13#331911yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—131no—
309C23—261no—
310C23D4×D1311yescharacteristic
311Q8—261no—
312Q8—261no—
313Q8—1041no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—261no—
319D4—261no—
320D4—521no—
321D4—522no—
322D4—1041no—
323D4—1041no—
324D4—1041no—
325D4#612712yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—131no—
331C2×C4—131no—
332C2×C4—131no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—522no—
339C2×C4—522no—
340C2×C4—1041no—
341C2×C4D4×D1311yescharacteristic
342C2×C4C23×D1311yescharacteristic
343C8—21no—
344C8—21no—
345C8—261no—
346C8—261no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—84no—
357C22—261no—
358C22—261no—
359C22—261no—
360C22—521no—
361C22—521no—
362C22—521no—
363C22C2×D4×D1311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—261no—
368C4—261no—
369C4—261no—
370C4—521no—
371C4—521no—
372C4—521no—
373C4C2×#612711yescharacteristic
374C4#8825111yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—521no—
379C2—1041no—
380C2#1171919511yescharacteristic
381C2#1171947811yescharacteristic
382C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#418C2
socleC22×C13C22×D4
hypercenter#418D13
hypocenterC13#3319
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #11719511C2semidirect
2. #11719237C2semidirect
3. C13×#418C2semidirect
4. #11718878C2semidirect
5. #11718795C2semidirect
6. #11718788C2semidirect
7. #11718657C2semidirect
8. #11718448C2semidirect
9. #11718446C2semidirect
10. #11718445C2semidirect
11. #11718442C2semidirect
12. #11718436C2semidirect
13. #11718433C2semidirect
14. #11718426C2semidirect
15. #11718420C2semidirect
32. C2×#6095C22semidirect
33. C2×C8×D13C22semidirect
34. #88149C22semidirect
35. #88147C22semidirect
36. #88146C22semidirect
37. #88142C22semidirect
49. #88061C22semidirect
50. #88060C22semidirect
51. #88058C22semidirect
52. #88056C22semidirect
53. #88055C22semidirect
54. #88054C22semidirect
55. #88050C22semidirect
56. #88050C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
169. #418D13semidirect
302. C13#3319semidirect

Maximal subgroups

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

subgroupindex
#117195112
#117192372
C13×#4182
#117188782
#117187952
#117187882
#117186572
#117184482
#117184462
#117184452
#117184422
#117184362
#117184332
#117184262
#117184202
#331913