Finite Group Databasebeta

← #13126642

Subgroups — #13126642

Order 1664.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C22⋊D13C211yesmaximal, characteristic, complemented
2#11719316C211yesmaximal, characteristic, complemented
3C13×#447C211yesmaximal, characteristic, complemented
4C2×#88072C211yesmaximal, characteristic, complemented
5#11718818C211yesmaximal, characteristic, complemented
6#11718817C211yesmaximal, characteristic, complemented
7#11718811C211yesmaximal, characteristic, complemented
8D8×Dic13C211yesmaximal, characteristic, complemented
9#11718699C211yesmaximal, characteristic, complemented
10#11718435C211yesmaximal, characteristic, complemented
11D13×#102C211yesmaximal, characteristic, complemented
12#11718421C211yesmaximal, characteristic, complemented
13#11718420C211yesmaximal, characteristic, complemented
14#11718397C211yesmaximal, characteristic, complemented
15#11718386C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C22×C22⋊D13—21no—
18C2×#6129—21no—
19C2×D4×D13C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic
21C2×C13×D8C2211yescharacteristic, complemented
22C13×#121C2211yescharacteristic, complemented
23#88207—21no—
24#88194C2211yescharacteristic
25#88193—21no—
26#88192C2211yescharacteristic
27#88192C2211yescharacteristic, complemented
28#88191—21no—
29#88189—21no—
30D4×Dic13C2211yescharacteristic
31D4×Dic13C2211yescharacteristic, complemented
32C2×#6104C2211yescharacteristic, complemented
33#88184C2211yescharacteristic
34C4×C22⋊D13C2211yescharacteristic
35C2×C4⋊Dic13C2211yescharacteristic, complemented
36C22×#1055C2211yescharacteristic, complemented
37C2×C8×D13C2211yescharacteristic, complemented
38C4⋊C4×D13C2211yescharacteristic, complemented
39#88142C2211yescharacteristic, complemented
40#88137—21no—
41#88132—21no—
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic, complemented
44C13×C22⋊C8C2211yescharacteristic, complemented
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic, complemented
48#88072C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50#88061C2211yescharacteristic, complemented
51#88061C2211yescharacteristic, complemented
52#88060C2211yescharacteristic, complemented
53#88058C2211yescharacteristic, complemented
54#88058C2211yescharacteristic, complemented
55#88054C2211yescharacteristic, complemented
56C8×Dic13C2211yescharacteristic, complemented
57#88049C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C24×C13—21no—
60C23×D13—21no—
61C2×D4×C13—22no—
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13—41no—
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C2×D4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13—21no—
73C2×C22⋊D13—21no—
74C2×C22⋊D13—21no—
75C2×C22⋊D13—44no—
76C2×C22⋊D13D411yescharacteristic
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80#6129—44no—
81D4×D13—22no—
82D4×D13—41no—
83C2×D52C2311yescharacteristic
84C2×C4×D13—21no—
85C2×C4×D13C2311yescharacteristic
86C2×Dic26—21no—
87C13×D8—22no—
88C13×D8—41no—
89C2×C8×C13C2311yescharacteristic
90C2×C8×C13C2311yescharacteristic
91C13×C4⋊C4C2311yescharacteristic
92C13×C22⋊C4—21no—
93C22⋊Dic13—21no—
94C22⋊Dic13—21no—
95C22⋊Dic13—21no—
96C22⋊Dic13—21no—
97C22⋊Dic13D411yescharacteristic
98#6104—41no—
99#6103—21no—
100#6103D411yescharacteristic
101C4⋊Dic13—21no—
102C4⋊Dic13C2311yescharacteristic
103C4⋊Dic13C2311yescharacteristic
104C4⋊Dic13C2311yescharacteristic
105#6101—21no—
106#6101—21no—
107#6101D411yescharacteristic
108C4×Dic13C2311yescharacteristic
109C2×#1055—41no—
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112C8×D13—41no—
113#3294—131nomaximal, Sylow
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—81no—
120C23×C13C2×D411yescharacteristic
121C22×D13—21no—
122C22×D13—42no—
123C22×D13—42no—
124C22×D13—81no—
125C22×D13C2×D411yescharacteristic
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—21no—
130D4×C13—21no—
131D4×C13—42no—
132D4×C13—42no—
133D4×C13#4112yescomplemented
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2411yescharacteristic
139C22⋊D13—42no—
140C22⋊D13—42no—
141C22⋊D13—42no—
142C22⋊D13—42no—
143C22⋊D13—42no—
144C22⋊D13—81no—
145C22⋊D13D814yescomplemented
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—42no—
150C2×Dic13—42no—
151C2×Dic13—42no—
152C2×Dic13C2×D411yescharacteristic
153C2×Dic13C2×D411yescharacteristic
154C2×Dic13C2×D411yescharacteristic
155D52—21no—
156D52—21no—
157C4×D13—21no—
158C4×D13—21no—
159C4×D13—42no—
160Dic26—42no—
161C8×C13—21no—
162C8×C13—21no—
163#1055—21no—
164#1055—21no—
165#547—131no—
166D42—131no—
167#486—131no—
168#480—131no—
169#480—131no—
170#474—131no—
171#466—131no—
172#466—131no—
173#459—131no—
174#447—131no—
175#447D1311yescharacteristic, complemented
176C4×D8—131no—
177C8×D4—131no—
178C2×#102—131no—
179C2×#102—131no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—22no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—84no—
192C22×C13C2×D812yes—
193C22×C13C22×D411yescharacteristic
194C2×D13—21no—
195C2×D13—21no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C2×D13—84no—
200C2×D13C2×D812yes—
201C4×C13—21no—
202C4×C13—41no—
203C4×C13C2×#4111yescharacteristic
204C4×C13H(5,𝔽2)11yescharacteristic
205Dic13—21no—
206Dic13—21no—
207Dic13—41no—
208Dic13—41no—
209Dic13—41no—
210Dic13C2×D812yes—
211C2×#41—261no—
212C22×D4—131no—
213C22×D4—261no—
214C22×D4C2×D1311yescharacteristic
215C2×D8—131no—
216C2×D8C2×D1311yescharacteristic
217C2×D8C2×D1311yescharacteristic, complemented
218C22×C8—131no—
219C22×C8—131no—
220C4⋊Q8—131no—
221#127—131no—
222#123—261no—
223#123—261no—
224C22⋊Q8—261no—
225#121—131no—
226#121—131no—
227#121—131no—
228#121—261no—
229#121C2×D1311yescharacteristic, complemented
230#120—261no—
231#120—261no—
232C4×D4—131no—
233C4×D4—131no—
234C4×D4—131no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—131no—
237#107—131no—
238#107—131no—
239#107—131no—
240C4⋊C8—131no—
241#102—131no—
242#102—131no—
243#102—131no—
244#102—131no—
245#102—131no—
246#102—131no—
247#102—131no—
248#102—131no—
249#102C2×D1311yescharacteristic
250#102C2×D1311yescharacteristic, complemented
251C22⋊C8—131no—
252C22⋊C8C2×D1311yescharacteristic, complemented
253C4×C8—131no—
254C2×C13—22no—
255C2×C13—42no—
256C2×C13—81no—
257C2×C13—81no—
258C2×C13#54611yescharacteristic
259C2×C13C22×D811yescharacteristic
260C2×C13#57711yescharacteristic
261D13—22no—
262D13—81no—
263C24—21no—
264C24—261no—
265#41—524no—
266C2×Q8—261no—
267C2×D4—22no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—131no—
272C2×D4—131no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—262no—
277C2×D4—261no—
278C2×D4—261no—
279C2×D4—261no—
280C2×D4—521no—
281C2×D4—524no—
282C2×D4C22×D1311yescharacteristic
283C2×D4C22×D1311yescharacteristic
284C2×D4C22×D1311yescharacteristic
285C22×C4—131no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4C22×D1311yescharacteristic
291D8—22no—
292D8—41no—
293D8—521no—
294C2×C8—131no—
295C2×C8—131no—
296C2×C8—521no—
297C2×C8—521no—
298C2×C8C22×D1311yescharacteristic
299C2×C8C22×D1311yescharacteristic
300C4⋊C4—131no—
301C4⋊C4—131no—
302C4⋊C4—131no—
303C4⋊C4—131no—
304C4⋊C4—261no—
305C4⋊C4—261no—
306C4⋊C4—261no—
307C4⋊C4C22×D1311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—131no—
310C22⋊C4—131no—
311C22⋊C4—261no—
312C22⋊C4—261no—
313C22⋊C4—261no—
314C22⋊C4—261no—
315C22⋊C4—261no—
316C42—131no—
317C13#329411yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—131no—
325C23—261no—
326C23—522no—
327C23—522no—
328C23—1041no—
329C23D4×D1311yescharacteristic
330Q8—522no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—134no—
339D4—261no—
340D4—261no—
341D4—522no—
342D4—522no—
343D4—522no—
344D4—522no—
345D4—522no—
346D4—1041no—
347D4#612912yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—131no—
352C2×C4—131no—
353C2×C4—131no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—522no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4D4×D1311yescharacteristic
364C2×C4C23×D1311yescharacteristic
365C8—21no—
366C8—21no—
367C8—261no—
368C8—261no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—132no—
382C22—261no—
383C22—261no—
384C22—521no—
385C22—521no—
386C22—521no—
387C22—1044no—
388C22D8×D1312yes—
389C22C2×D4×D1311yescharacteristic
390C4—21no—
391C4—41no—
392C4—132no—
393C4—261no—
394C4—261no—
395C4—521no—
396C4—521no—
397C4—521no—
398C4C2×#612911yescharacteristic
399C4#8825111yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—262no—
405C2—1041no—
406C2#1171929611yescharacteristic
407C2C2×D8×D1311yescharacteristic
408C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#447C2
socleC22×C13C22×D4
hypercenter#447D13
hypocenterC13#3294
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. D4×C22⋊D13C2semidirect
2. #11719316C2semidirect
3. C13×#447C2semidirect
4. C2×#88072C2semidirect
5. #11718818C2semidirect
6. #11718817C2semidirect
7. #11718811C2semidirect
8. D8×Dic13C2semidirect
9. #11718699C2semidirect
10. #11718435C2semidirect
11. D13×#102C2semidirect
12. #11718421C2semidirect
13. #11718420C2semidirect
14. #11718397C2semidirect
15. #11718386C2semidirect
21. C2×C13×D8C22semidirect
22. C13×#121C22semidirect
27. #88192C22semidirect
31. D4×Dic13C22semidirect
32. C2×#6104C22semidirect
35. C2×C4⋊Dic13C22semidirect
36. C22×#1055C22semidirect
37. C2×C8×D13C22semidirect
38. C4⋊C4×D13C22semidirect
39. #88142C22semidirect
43. C13×#102C22semidirect
44. C13×C22⋊C8C22semidirect
47. #88072C22semidirect
48. #88072C22semidirect
49. #88072C22semidirect
50. #88061C22semidirect
51. #88061C22semidirect
52. #88060C22semidirect
53. #88058C22semidirect
54. #88058C22semidirect
55. #88054C22semidirect
56. C8×Dic13C22semidirect
57. #88049C22semidirect
58. #88047C22semidirect
133. D4×C13#41semidirect
145. C22⋊D13D8semidirect
175. #447D13semidirect
217. C2×D8C2×D13semidirect
229. #121C2×D13semidirect
250. #102C2×D13semidirect
252. C22⋊C8C2×D13semidirect
317. C13#3294semidirect
347. D4#6129semidirect

Maximal subgroups

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

subgroupindex
D4×C22⋊D132
#117193162
C13×#4472
C2×#880722
#117188182
#117188172
#117188112
D8×Dic132
#117186992
#117184352
D13×#1022
#117184212
#117184202
#117183972
#117183862
#329413