Finite Group Databasebeta

← #13124352

Subgroups — #13124352

Order 1664.

490 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×SD16×D13C211yesmaximal, characteristic, complemented
3#11719420C211yesmaximal, characteristic
4#11719277C211yesmaximal, characteristic, complemented
5C13×#460C211yesmaximal, characteristic, complemented
6#11718827C211yesmaximal, characteristic, complemented
7#11718824C211yesmaximal, characteristic, complemented
8#11718736C211yesmaximal, characteristic, complemented
9#11718689C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718500C211yesmaximal, characteristic, complemented
12#11718433C211yesmaximal, characteristic, complemented
13#11718431C211yesmaximal, characteristic, complemented
14#11718428C211yesmaximal, characteristic, complemented
15#11718423C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×D4×D13C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic, complemented
21C13×#127C2211yescharacteristic
22C4×Q8×C13C2211yescharacteristic, complemented
23Q8×Dic13C2211yescharacteristic, complemented
24C2×#6107C2211yescharacteristic, complemented
25C2×#6106C2211yescharacteristic
26#88194C2211yescharacteristic
27#88193—21no—
28#88193—21no—
29#88191—21no—
30#88191—21no—
31#88190C2211yescharacteristic
32C2×#6105C2211yescharacteristic
33C2×#6105C2211yescharacteristic, complemented
34#88169—24no—
35SD16×D13—24no—
36C2×Dic52C2211yescharacteristic, complemented
37C2×#6095C2211yescharacteristic
38C2×#6094C2211yescharacteristic
39C2×C8×D13C2211yescharacteristic
40#88146—21no—
41#88146C2211yescharacteristic
42#88141—21no—
43#88141C2211yescharacteristic, complemented
44#88129C2211yescharacteristic
45#88126—21no—
46#88126C2211yescharacteristic
47C4×Dic26—21no—
48C4×Dic26C2211yescharacteristic, complemented
49C13×C4⋊C8C2211yescharacteristic, complemented
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic, complemented
52#88072C2211yescharacteristic
53#88072C2211yescharacteristic, complemented
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×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C22×Dic13—21no—
72Q8×D13—22no—
73Q8×D13D414yescomplemented
74#6129—22no—
75#6129—22no—
76D4×D13—22no—
77D4×D13—22no—
78C2×D52C2311yescharacteristic
79C2×C4×D13—21no—
80C2×C4×D13C2311yescharacteristic
81C2×Dic26—21no—
82C2×Dic26C2311yescharacteristic
83C2×Dic26C2311yescharacteristic
84C13×SD16—22no—
85C13×SD16—22no—
86C2×C8×C13C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C13×C4⋊C4—21no—
89C13×C4⋊C4C2311yescharacteristic
90C42×C13—21no—
91C42×C13C2311yescharacteristic
92C22⋊Dic13—21no—
93C22⋊Dic13—21no—
94#6107—22no—
95#6106—22no—
96#6105—22no—
97#6105—22no—
98#6103—21no—
99#6103—21no—
100#6103—21no—
101#6103D411yescharacteristic
102#6103D411yescharacteristic
103C4⋊Dic13—21no—
104C4⋊Dic13C2311yescharacteristic
105#6101—21no—
106#6101—21no—
107#6101D411yescharacteristic
108#6101D411yescharacteristic
109C4×Dic13—21no—
110C4×Dic13—21no—
111C4×Dic13—21no—
112C4×Dic13—21no—
113C4×Dic13C2311yescharacteristic
114C2×#1055C2311yescharacteristic
115C2×#1055C2311yescharacteristic
116Dic52—22no—
117#6095—22no—
118#6094—22no—
119C8×D13—22no—
120#3043—131nomaximal, Sylow
121C23×C13—21no—
122C23×C13—21no—
123C22×D13—21no—
124C22×D13—42no—
125C22×D13—81no—
126C22×D13—81no—
127C22×D13C2×D411yescharacteristic
128Q8×C13—21no—
129Q8×C13C2×D412yes—
130D4×C13—21no—
131D4×C13—21no—
132D4×C13—21no—
133D4×C13—21no—
134D4×C13—81no—
135D4×C13—81no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13C2×D411yescharacteristic
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2411yescharacteristic
141C22⋊D13—42no—
142C22⋊D13—42no—
143C22⋊D13—81no—
144C22⋊D13—81no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—42no—
149C2×Dic13C2×D411yescharacteristic
150C2×Dic13C2×D411yescharacteristic
151C2×Dic13C2×D411yescharacteristic
152D52—21no—
153D52—21no—
154C4×D13—24no—
155C4×D13C2×D412yes—
156C4×D13#4112yes—
157Dic26—21no—
158Dic26—24no—
159Dic26—21no—
160Dic26—21no—
161Dic26C2×D412yes—
162C8×C13—21no—
163C8×C13—21no—
164#1055—21no—
165#1055—21no—
166C2×#137—131no—
167C22×SD16—131no—
168#535—131no—
169#519—131no—
170#464—131no—
171#464—131no—
172#464—131no—
173#464—131no—
174#460—131no—
175#460—131no—
176#460—131no—
177#460D1311yescharacteristic, complemented
178#424—131no—
179#418—131no—
180#416—131no—
181C22×C13—41no—
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—22no—
196C4×C13—21no—
197C4×C13—21no—
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—
211C2×Q16—131no—
212C2×Q16—131no—
213C2×SD16—131no—
214C2×SD16—131no—
215C2×SD16—131no—
216C2×SD16—131no—
217C2×SD16—264no—
218C2×SD16C2×D1311yescharacteristic
219C2×SD16C2×D1311yescharacteristic, complemented
220C2×M16—131no—
221C22×C8—131no—
222#127—131no—
223#127C2×D1311yescharacteristic
224#124—131no—
225#124—131no—
226#121—261no—
227#121—261no—
228#120—261no—
229#120—261no—
230C4×Q8—131no—
231C4×Q8—131no—
232C4×Q8—131no—
233C4×Q8—261no—
234C4×Q8—261no—
235C4×Q8C2×D1311yescharacteristic, complemented
236#117—131no—
237#117—131no—
238#117—261no—
239#117—261no—
240C4⋊C8—131no—
241C4⋊C8—131no—
242C4⋊C8—131no—
243C4⋊C8C2×D1311yescharacteristic, complemented
244#103—131no—
245#103—131no—
246#102—131no—
247#102—131no—
248#102—131no—
249#102—131no—
250#102C2×D1311yescharacteristic
251#102C2×D1311yescharacteristic, complemented
252C2×C13—81no—
253C2×C13—81no—
254C2×C13C2×#12111yescharacteristic
255C2×C13#57711yescharacteristic
256C2×C13#57711yescharacteristic
257D13—22no—
258D13—81no—
259C24—261no—
260#41—262no—
261#41—262no—
262C2×Q8—134no—
263C2×Q8—131no—
264C2×Q8—131no—
265C2×Q8—261no—
266C2×Q8—262no—
267C2×Q8C22×D1311yescharacteristic
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—131no—
271C2×D4—262no—
272C2×D4—262no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—261no—
277C2×D4C22×D1311yescharacteristic
278C2×D4C22×D1311yescharacteristic
279C22×C4—131no—
280C22×C4—261no—
281C22×C4—261no—
282Q16—262no—
283Q16—262no—
284SD16—22no—
285SD16—22no—
286SD16—262no—
287SD16—262no—
288SD16—262no—
289SD16—262no—
290M16—262no—
291C2×C8—131no—
292C2×C8—131no—
293C2×C8—262no—
294C2×C8C22×D1311yescharacteristic
295C2×C8C22×D1311yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—131no—
298C4⋊C4—131no—
299C4⋊C4—131no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4—261no—
303C4⋊C4C22×D1311yescharacteristic
304C22⋊C4—131no—
305C22⋊C4—131no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C22⋊C4—261no—
310C22⋊C4—261no—
311C42—21no—
312C42—131no—
313C42—261no—
314C42—261no—
315C42—261no—
316C42—261no—
317C42C22×D1311yescharacteristic
318C13#304311yescharacteristic, complemented, Sylow
319C23—21no—
320C23—21no—
321C23—131no—
322C23—261no—
323C23—522no—
324C23—1041no—
325C23—1041no—
326Q8—21no—
327Q8—132no—
328Q8—264no—
329Q8—261no—
330Q8—261no—
331Q8—261no—
332Q8D4×D1312yes—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—21no—
337D4—81no—
338D4—81no—
339D4—261no—
340D4—261no—
341D4—522no—
342D4—522no—
343D4—1041no—
344D4—1041no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—131no—
348C2×C4—132no—
349C2×C4—132no—
350C2×C4—131no—
351C2×C4—131no—
352C2×C4—264no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—522no—
357C2×C4D4×D1311yescharacteristic
358C2×C4D4×D1311yescharacteristic
359C2×C4C23×D1311yescharacteristic
360C8—21no—
361C8—21no—
362C8—261no—
363C8—261no—
364C22—41no—
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—22no—
381C4—41no—
382C4—132no—
383C4—261no—
384C4—261no—
385C4—262no—
386C4—521no—
387C4—521no—
388C4C2×D4×D1311yescharacteristic
389C4#41×D1311yescharacteristic
390C2—81no—
391C2—81no—
392C2—262no—
393C2—1041no—
394C2D13×#12111yescharacteristic
395C2#1171946711yescharacteristic
396C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#460C2
socleC22×C13C22×D4
prime radical#11719420C2
hypercenter#460D13
hypocenterC13#3043
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#88169C2semidirect
2. C2×SD16×D13C2semidirect
4. #11719277C2semidirect
5. C13×#460C2semidirect
6. #11718827C2semidirect
7. #11718824C2semidirect
8. #11718736C2semidirect
9. #11718689C2semidirect
10. #11718506C2semidirect
11. #11718500C2semidirect
12. #11718433C2semidirect
13. #11718431C2semidirect
14. #11718428C2semidirect
15. #11718423C2semidirect
20. C2×C13×SD16C22semidirect
22. C4×Q8×C13C22semidirect
23. Q8×Dic13C22semidirect
24. C2×#6107C22semidirect
33. C2×#6105C22semidirect
36. C2×Dic52C22semidirect
43. #88141C22semidirect
48. C4×Dic26C22semidirect
49. C13×C4⋊C8C22semidirect
51. C13×#102C22semidirect
53. #88072C22semidirect
55. #88056C22semidirect
56. #88054C22semidirect
57. #88054C22semidirect
58. #88050C22semidirect
60. C4⋊#1055C22semidirect
73. Q8×D13D4semidirect
177. #460D13semidirect
219. C2×SD16C2×D13semidirect
235. C4×Q8C2×D13semidirect
243. C4⋊C8C2×D13semidirect
251. #102C2×D13semidirect
318. C13#3043semidirect

Maximal subgroups

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

subgroupindex
C2×#881692
C2×SD16×D132
#117194202
#117192772
C13×#4602
#117188272
#117188242
#117187362
#117186892
#117185062
#117185002
#117184332
#117184312
#117184282
#117184232
#304313