Finite Group Databasebeta

← #13124325

Subgroups — #13124325

Order 1664.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88169C211yesmaximal, characteristic, complemented
2C2×#88165C211yesmaximal, characteristic
3D13×#124C211yesmaximal, characteristic, complemented
4C4×#6129C211yesmaximal, characteristic, complemented
5C13×#463C211yesmaximal, characteristic, complemented
6#11718826C211yesmaximal, characteristic, complemented
7#11718814C211yesmaximal, characteristic, complemented
8#11718715C211yesmaximal, characteristic, complemented
9#11718677C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718498C211yesmaximal, characteristic, complemented
12#11718463C211yesmaximal, characteristic, complemented
13#11718459C211yesmaximal, characteristic, complemented
14#11718431C211yesmaximal, characteristic, complemented
15#11718428C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×D4×D13C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic, complemented
20C2×C13×D8C2211yescharacteristic
21C13×#124C2211yescharacteristic
22C4×D4×C13C2211yescharacteristic, complemented
23#88201C2211yescharacteristic
24C2×#6107C2211yescharacteristic, complemented
25#88190C2211yescharacteristic
26D4×Dic13C2211yescharacteristic, complemented
27C2×#6105C2211yescharacteristic
28C2×#6105C2211yescharacteristic, complemented
29C2×#6104C2211yescharacteristic
30C4×C22⋊D13—21no—
31C2×C4×Dic13—21no—
32#88169—24no—
33#88165—24no—
34C2×Dic52C2211yescharacteristic, complemented
35C2×#6095C2211yescharacteristic
36C2×#6094C2211yescharacteristic
37C2×#6094C2211yescharacteristic
38#88146C2211yescharacteristic
39#88141C2211yescharacteristic, complemented
40#88139—21no—
41#88139—21no—
42#88135—21no—
43C22⋊C4×D13—21no—
44C22⋊C4×D13—21no—
45#88131—21no—
46#88129C2211yescharacteristic
47C42×D13C2211yescharacteristic
48C4×Dic26C2211yescharacteristic, complemented
49C13×C4⋊C8C2211yescharacteristic, complemented
50C13×#103C2211yescharacteristic, complemented
51C13×#102C2211yescharacteristic
52#88075C2211yescharacteristic, complemented
53#88072C2211yescharacteristic
54#88061C2211yescharacteristic
55#88056C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88054C2211yescharacteristic, complemented
58#88050C2211yescharacteristic, complemented
59#88049C2211yescharacteristic
60C4⋊#1055C2211yescharacteristic, complemented
61C23×D13—21no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13C2311yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70Q8×D13—22no—
71Q8×D13—22no—
72#6129—22no—
73#6129D414yes—
74D4×D13—22no—
75D4×D13—22no—
76C2×D52C2311yescharacteristic
77C2×C4×D13—21no—
78C2×C4×D13D411yescharacteristic
79C2×C4×D13D411yescharacteristic
80C2×C4×D13C2311yescharacteristic
81C2×Dic26—21no—
82C2×Dic26C2311yescharacteristic
83C2×Dic26C2311yescharacteristic
84C13×SD16—22no—
85C13×D8—22no—
86C2×C8×C13C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C22⋊C4—21no—
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C42×C13C2311yescharacteristic
93C22⋊Dic13—21no—
94C22⋊Dic13—21no—
95C22⋊Dic13—21no—
96#6107—22no—
97#6105—22no—
98#6105—22no—
99#6104—22no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103#6103—21no—
104#6103—21no—
105C4⋊Dic13C2311yescharacteristic
106#6101—21no—
107#6101—21no—
108C4×Dic13—21no—
109C4×Dic13—21no—
110C4×Dic13—21no—
111C4×Dic13D411yescharacteristic
112C4×Dic13D411yescharacteristic
113C4×Dic13C2311yescharacteristic
114C2×#1055C2311yescharacteristic
115C2×#1055C2311yescharacteristic
116Dic52—22no—
117#6095—22no—
118#6094—22no—
119#6094—22no—
120#3040—131nomaximal, Sylow
121C23×C13—21no—
122C23×C13—21no—
123C22×D13—21no—
124C22×D13—42no—
125C22×D13—42no—
126C22×D13—42no—
127C22×D13C2×D411yescharacteristic
128Q8×C13—21no—
129Q8×C13—21no—
130D4×C13—21no—
131D4×C13—21no—
132D4×C13—21no—
133D4×C13C2×D412yes—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—42no—
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2×D411yescharacteristic
139C2×C4×C13C2411yescharacteristic
140C22⋊D13—24no—
141C22⋊D13—42no—
142C2×Dic13—21no—
143C2×Dic13—24no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—42no—
147C2×Dic13C2×D411yescharacteristic
148C2×Dic13C2×D411yescharacteristic
149C2×Dic13C2×D411yescharacteristic
150D52—21no—
151D52—21no—
152C4×D13—41no—
153C4×D13—41no—
154C4×D13—42no—
155C4×D13C2×D412yes—
156C4×D13#4112yes—
157Dic26—21no—
158Dic26—21no—
159Dic26—21no—
160Dic26—42no—
161Dic26C2×D412yes—
162C8×C13—21no—
163C8×C13—21no—
164#1055—21no—
165#1055—21no—
166C2×#137—131no—
167C2×AGL(1,ℤ/8)—131no—
168C2×#124—131no—
169C4×#41—131no—
170#464—131no—
171#464—131no—
172#464—131no—
173#464—131no—
174#463—131no—
175#463—131no—
176#463—131no—
177#463D1311yescharacteristic, complemented
178#423—131no—
179#419—131no—
180#418—131no—
181C22×C13—22no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13C22×D411yescharacteristic
188C2×D13—21no—
189C2×D13—21no—
190C2×D13—41no—
191C2×D13—41no—
192C2×D13—41no—
193C2×D13—84no—
194C2×D13#12112yes—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13C22×D411yescharacteristic
200C4×C13C2×#4111yescharacteristic
201Dic13—22no—
202Dic13—21no—
203Dic13—21no—
204Dic13—41no—
205Dic13—41no—
206Dic13#12112yes—
207C2×#41—131no—
208C22×Q8—131no—
209C22×D4—131no—
210#137—264no—
211AGL(1,ℤ/8)—264no—
212C2×Q16—131no—
213C2×Q16—131no—
214C2×SD16—131no—
215C2×SD16—131no—
216C2×SD16—131no—
217C2×SD16C2×D1311yescharacteristic, complemented
218C2×D8—131no—
219C2×D8C2×D1311yescharacteristic
220C2×M16—131no—
221C2×M16—131no—
222#124—131no—
223#124—131no—
224#124—131no—
225#124—261no—
226#124—261no—
227#124C2×D1311yescharacteristic
228C4×Q8—131no—
229C4×Q8—131no—
230C4×D4—131no—
231C4×D4—261no—
232C4×D4—261no—
233C4×D4C2×D1311yescharacteristic, complemented
234#117—131no—
235#117—261no—
236C2×C22⋊C4—261no—
237C2×C22⋊C4—261no—
238C2×C42—131no—
239C2×C42—261no—
240C4⋊C8—131no—
241C4⋊C8—131no—
242C4⋊C8—131no—
243C4⋊C8C2×D1311yescharacteristic, complemented
244#103—131no—
245#103—131no—
246#103—131no—
247#103C2×D1311yescharacteristic, complemented
248#102—131no—
249#102—131no—
250#102—131no—
251#102C2×D1311yescharacteristic
252C2×C13—42no—
253C2×C13—81no—
254C2×C13C2×#12111yescharacteristic
255C2×C13#57511yescharacteristic
256C2×C13#57511yescharacteristic
257D13—22no—
258D13—81no—
259C24—261no—
260#41—134no—
261#41—262no—
262C2×Q8—131no—
263C2×Q8—131no—
264C2×Q8—261no—
265C2×Q8—262no—
266C2×Q8—262no—
267C2×Q8C22×D1311yescharacteristic
268C2×D4—131no—
269C2×D4—262no—
270C2×D4—262no—
271C2×D4—261no—
272C2×D4—261no—
273C2×D4C22×D1311yescharacteristic
274C2×D4C22×D1311yescharacteristic
275C22×C4—21no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282Q16—262no—
283Q16—262no—
284SD16—22no—
285SD16—262no—
286SD16—262no—
287SD16—262no—
288D8—22no—
289D8—262no—
290M16—262no—
291M16—262no—
292C2×C8—131no—
293C2×C8—131no—
294C2×C8C22×D1311yescharacteristic
295C2×C8C22×D1311yescharacteristic
296C4⋊C4—131no—
297C4⋊C4—261no—
298C4⋊C4—261no—
299C4⋊C4C22×D1311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—261no—
304C22⋊C4—261no—
305C22⋊C4—261no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C22⋊C4—261no—
310C22⋊C4—261no—
311C42—131no—
312C42—131no—
313C42—131no—
314C42—261no—
315C42—261no—
316C42—261no—
317C42C22×D1311yescharacteristic
318C13#304011yescharacteristic, complemented, Sylow
319C23—21no—
320C23—21no—
321C23—131no—
322C23—261no—
323C23—522no—
324C23—522no—
325C23—522no—
326Q8—21no—
327Q8—21no—
328Q8—132no—
329Q8—261no—
330Q8—261no—
331Q8—261no—
332Q8—522no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—264no—
337D4—261no—
338D4—261no—
339D4—522no—
340D4D4×D1312yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—131no—
345C2×C4—132no—
346C2×C4—132no—
347C2×C4—131no—
348C2×C4—131no—
349C2×C4—264no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4D4×D1311yescharacteristic
358C2×C4D4×D1311yescharacteristic
359C2×C4C23×D1311yescharacteristic
360C8—21no—
361C8—21no—
362C8—261no—
363C8—261no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—132no—
371C22—261no—
372C22—261no—
373C22—521no—
374C22—521no—
375C22—521no—
376C22—1044no—
377C22C2×D4×D1311yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—132no—
383C4—261no—
384C4—261no—
385C4—262no—
386C4—521no—
387C4—521no—
388C4C2×D4×D1311yescharacteristic
389C4#41×D1311yescharacteristic
390C2—42no—
391C2—81no—
392C2—262no—
393C2—1041no—
394C2D13×#12111yescharacteristic
395C2#1171947311yescharacteristic
396C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#463C2
socleC22×C13C22×D4
prime radicalC2×#88165C2
hypercenter#463D13
hypocenterC13#3040
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#88169C2semidirect
3. D13×#124C2semidirect
4. C4×#6129C2semidirect
5. C13×#463C2semidirect
6. #11718826C2semidirect
7. #11718814C2semidirect
8. #11718715C2semidirect
9. #11718677C2semidirect
10. #11718506C2semidirect
11. #11718498C2semidirect
12. #11718463C2semidirect
13. #11718459C2semidirect
14. #11718431C2semidirect
15. #11718428C2semidirect
19. C2×C13×SD16C22semidirect
22. C4×D4×C13C22semidirect
24. C2×#6107C22semidirect
26. D4×Dic13C22semidirect
28. C2×#6105C22semidirect
34. C2×Dic52C22semidirect
39. #88141C22semidirect
48. C4×Dic26C22semidirect
49. C13×C4⋊C8C22semidirect
50. C13×#103C22semidirect
52. #88075C22semidirect
55. #88056C22semidirect
56. #88054C22semidirect
57. #88054C22semidirect
58. #88050C22semidirect
60. C4⋊#1055C22semidirect
177. #463D13semidirect
217. C2×SD16C2×D13semidirect
233. C4×D4C2×D13semidirect
243. C4⋊C8C2×D13semidirect
247. #103C2×D13semidirect
318. C13#3040semidirect

Maximal subgroups

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

subgroupindex
C2×#881692
C2×#881652
D13×#1242
C4×#61292
C13×#4632
#117188262
#117188142
#117187152
#117186772
#117185062
#117184982
#117184632
#117184592
#117184312
#117184282
#304013