Finite Group Databasebeta

← #13126352

Subgroups — #13126352

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
1C2×#88169C211yesmaximal, characteristic, complemented
2C2×SD16×D13C211yesmaximal, characteristic, complemented
3#11719432C211yesmaximal, characteristic, complemented
4#11719259C211yesmaximal, characteristic
5C13×#461C211yesmaximal, characteristic, complemented
6#11718834C211yesmaximal, characteristic, complemented
7#11718830C211yesmaximal, characteristic, complemented
8#11718747C211yesmaximal, characteristic, complemented
9#11718679C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718497C211yesmaximal, characteristic, complemented
12#11718474C211yesmaximal, characteristic, complemented
13#11718473C211yesmaximal, characteristic, complemented
14#11718469C211yesmaximal, characteristic, complemented
15#11718467C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic, complemented
18C2×#6129C2211yescharacteristic
19C2×D4×D13C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic
21C2×C13×SD16C2211yescharacteristic
22C13×C4⋊Q8C2211yescharacteristic, complemented
23C4×D4×C13C2211yescharacteristic
24#88200C2211yescharacteristic
25#88200C2211yescharacteristic, complemented
26C2×#6107C2211yescharacteristic, complemented
27C2×#6107C2211yescharacteristic, complemented
28C2×#6106C2211yescharacteristic
29C2×#6106C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31#88184—21no—
32C2×#6103—21no—
33#88169—24no—
34SD16×D13—24no—
35C2×Dic52C2211yescharacteristic, complemented
36C2×#6095C2211yescharacteristic
37C2×#6094C2211yescharacteristic, complemented
38C2×C8×D13C2211yescharacteristic
39#88151C2211yescharacteristic
40#88150—21no—
41#88150—21no—
42#88149C2211yescharacteristic
43#88147—21no—
44#88142—21no—
45#88140—21no—
46#88136—21no—
47#88129C2211yescharacteristic
48C4×D52C2211yescharacteristic
49C4×Dic26C2211yescharacteristic, complemented
50C13×C4⋊C8C2211yescharacteristic, complemented
51C13×#103C2211yescharacteristic, complemented
52C13×#103C2211yescharacteristic, complemented
53#88072C2211yescharacteristic
54#88061C2211yescharacteristic
55#88060C2211yescharacteristic
56#88060C2211yescharacteristic, complemented
57#88056C2211yescharacteristic, complemented
58#88050C2211yescharacteristic, complemented
59#88047C2211yescharacteristic, complemented
60#88043C2211yescharacteristic, complemented
61C23×D13—21no—
62C2×Q8×C13C2311yescharacteristic
63C2×Q8×C13C2311yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C22×Dic13—21no—
69Q8×D13—22no—
70Q8×D13—22no—
71Q8×D13—41no—
72Q8×D13—41no—
73#6129—22no—
74#6129—41no—
75D4×D13—22no—
76D4×D13—41no—
77C2×D52—21no—
78C2×D52D411yescharacteristic
79C2×D52C2311yescharacteristic
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13C2311yescharacteristic
83C2×C4×D13C2311yescharacteristic
84C2×Dic26—21no—
85C2×Dic26—21no—
86C2×Dic26C2311yescharacteristic
87C2×Dic26C2311yescharacteristic
88C13×SD16—22no—
89C13×SD16—22no—
90C2×C8×C13C2311yescharacteristic
91C2×C8×C13C2311yescharacteristic
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4C2311yescharacteristic
95C13×C22⋊C4—21no—
96C42×C13C2311yescharacteristic
97#6107—22no—
98#6107—41no—
99#6106—22no—
100#6106—41no—
101#6105D414yescomplemented
102#6103—21no—
103#6103—21no—
104#6103—21no—
105#6103—21no—
106#6103—21no—
107#6103—21no—
108#6103D411yescharacteristic
109#6103D411yescharacteristic
110C4⋊Dic13—21no—
111C4⋊Dic13D411yescharacteristic
112C4⋊Dic13C2311yescharacteristic
113#6101—21no—
114#6101—21no—
115#6101—21no—
116C4×Dic13—21no—
117C2×#1055C2311yescharacteristic
118C2×#1055C2311yescharacteristic
119Dic52—22no—
120#6095—22no—
121#6094—22no—
122C8×D13—22no—
123#3266—131nomaximal, Sylow
124C23×C13—21no—
125C22×D13—21no—
126C22×D13—42no—
127C22×D13—42no—
128C22×D13—81no—
129C22×D13C2×D411yescharacteristic
130C22×D13C2×D411yescharacteristic
131Q8×C13—21no—
132Q8×C13—21no—
133Q8×C13—21no—
134Q8×C13—21no—
135D4×C13—21no—
136D4×C13C2×D412yes—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—81no—
141C2×C4×C13C2×D411yescharacteristic
142C2×C4×C13C2×D411yescharacteristic
143C2×C4×C13C2411yescharacteristic
144C22⋊D13—42no—
145C22⋊D13—42no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—42no—
150C2×Dic13C2×D411yescharacteristic
151C2×Dic13C2×D411yescharacteristic
152D52—22no—
153D52—21no—
154D52—21no—
155D52—81no—
156C4×D13—21no—
157C4×D13—21no—
158C4×D13—21no—
159C4×D13—21no—
160C4×D13—42no—
161C4×D13—42no—
162Dic26—21no—
163Dic26—21no—
164Dic26—21no—
165Dic26—42no—
166Dic26—42no—
167Dic26C2×D412yes—
168C8×C13—21no—
169C8×C13—21no—
170#1055—21no—
171#1055C2×D412yes—
172C2×#137—131no—
173C22×SD16—131no—
174D4×Q8—131no—
175#546—131no—
176#497—131no—
177#468—131no—
178#467—131no—
179#464—131no—
180#461D1311yescharacteristic, complemented
181#452—131no—
182#451—131no—
183#450—131no—
184#448—131no—
185#440—131no—
186#435—131no—
187C22×C13—22no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13C22×D411yescharacteristic
191C2×D13—21no—
192C2×D13—21no—
193C2×D13—21no—
194C2×D13—21no—
195C2×D13—21no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C2×D13—84no—
200C2×D13#13712yescomplemented
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13C22×D411yescharacteristic
207C4×C13H(5,𝔽2)11yescharacteristic
208Dic13—22no—
209Dic13—21no—
210Dic13—21no—
211Dic13—41no—
212Dic13—41no—
213C2×#41—131no—
214C22×Q8—131no—
215C22×Q8—131no—
216C22×D4—131no—
217#137—264no—
218C2×Q16—131no—
219C2×Q16—131no—
220C2×Q16—131no—
221C2×SD16—131no—
222C2×SD16—131no—
223C2×SD16—131no—
224C2×SD16—131no—
225C2×SD16—264no—
226C2×SD16C2×D1311yescharacteristic
227C2×SD16C2×D1311yescharacteristic
228C2×M16—131no—
229C22×C8—131no—
230C4⋊Q8—261no—
231C4⋊Q8C2×D1311yescharacteristic, complemented
232#124—131no—
233#123—261no—
234C22⋊Q8—131no—
235C22⋊Q8—131no—
236C22⋊Q8—131no—
237C22⋊Q8—261no—
238C22⋊Q8—261no—
239#121—131no—
240#121—261no—
241#120—261no—
242C4×Q8—131no—
243C4×D4—131no—
244C4×D4—261no—
245C4×D4C2×D1311yescharacteristic
246C2×C22⋊C4—261no—
247#107—131no—
248C4⋊C8C2×D1311yescharacteristic, complemented
249#103—131no—
250#103—131no—
251#103C2×D1311yescharacteristic, complemented
252#103C2×D1311yescharacteristic, complemented
253#102—131no—
254#102—131no—
255C22⋊C8—131no—
256C22⋊C8—131no—
257#97—131no—
258C2×C13—42no—
259C2×C13D4211yescharacteristic
260C2×C13C2×#13711yescharacteristic
261C2×C13#57711yescharacteristic
262D13—22no—
263D13—41no—
264D13—81no—
265C24—261no—
266#41—262no—
267#41—521no—
268C2×Q8—131no—
269C2×Q8—131no—
270C2×Q8—261no—
271C2×Q8—261no—
272C2×Q8—262no—
273C2×Q8—262no—
274C2×Q8—521no—
275C2×Q8—521no—
276C2×Q8C22×D1311yescharacteristic
277C2×Q8C22×D1311yescharacteristic
278C2×D4—131no—
279C2×D4—131no—
280C2×D4—261no—
281C2×D4—261no—
282C2×D4—262no—
283C2×D4—261no—
284C2×D4—521no—
285C2×D4C22×D1311yescharacteristic
286C22×C4—21no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—261no—
290C22×C4—261no—
291C22×C4—261no—
292Q16—262no—
293Q16—262no—
294Q16—521no—
295SD16—22no—
296SD16—22no—
297SD16—134no—
298SD16—262no—
299SD16—262no—
300SD16—521no—
301M16—262no—
302C2×C8—131no—
303C2×C8—131no—
304C2×C8—262no—
305C2×C8C22×D1311yescharacteristic
306C2×C8C22×D1311yescharacteristic
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—131no—
310C4⋊C4—131no—
311C4⋊C4—261no—
312C4⋊C4—261no—
313C4⋊C4—261no—
314C4⋊C4—261no—
315C4⋊C4C22×D1311yescharacteristic
316C22⋊C4—21no—
317C22⋊C4—131no—
318C22⋊C4—131no—
319C22⋊C4—261no—
320C22⋊C4—261no—
321C22⋊C4—261no—
322C22⋊C4—261no—
323C22⋊C4—261no—
324C22⋊C4—261no—
325C42—261no—
326C42C22×D1311yescharacteristic
327C13#326611yescharacteristic, complemented, Sylow
328C23—21no—
329C23—131no—
330C23—131no—
331C23—261no—
332C23—522no—
333C23—522no—
334C23—1041no—
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—132no—
340Q8—261no—
341Q8—261no—
342Q8—261no—
343Q8—522no—
344Q8—522no—
345D4—21no—
346D4—262no—
347D4—261no—
348D4—261no—
349D4—522no—
350D4—522no—
351D4—1041no—
352D4D4×D1312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—81no—
357C2×C4—131no—
358C2×C4—131no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—522no—
367C2×C4—522no—
368C2×C4—522no—
369C2×C4D4×D1311yescharacteristic
370C2×C4D4×D1311yescharacteristic
371C2×C4C23×D1311yescharacteristic
372C8—21no—
373C8—21no—
374C8—132no—
375C8—261no—
376C22—22no—
377C22—41no—
378C22—41no—
379C22—132no—
380C22—261no—
381C22—261no—
382C22—261no—
383C22—261no—
384C22—261no—
385C22—521no—
386C22—521no—
387C22—521no—
388C22—1044no—
389C22C2×D4×D1311yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—261no—
396C4—261no—
397C4—262no—
398C4—521no—
399C4—521no—
400C4C2×D4×D1311yescharacteristic
401C4#8825611yescharacteristic
402C2—42no—
403C2—262no—
404C2—521no—
405C2—1041no—
406C2#1171931411yescharacteristic
407C2#1171946711yescharacteristic
408C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radical#11719259C2
hypercenter#461D13
hypocenterC13#3266
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#88169C2semidirect
2. C2×SD16×D13C2semidirect
3. #11719432C2semidirect
5. C13×#461C2semidirect
6. #11718834C2semidirect
7. #11718830C2semidirect
8. #11718747C2semidirect
9. #11718679C2semidirect
10. #11718506C2semidirect
11. #11718497C2semidirect
12. #11718474C2semidirect
13. #11718473C2semidirect
14. #11718469C2semidirect
15. #11718467C2semidirect
17. C2×Q8×D13C22semidirect
22. C13×C4⋊Q8C22semidirect
25. #88200C22semidirect
26. C2×#6107C22semidirect
27. C2×#6107C22semidirect
35. C2×Dic52C22semidirect
37. C2×#6094C22semidirect
49. C4×Dic26C22semidirect
50. C13×C4⋊C8C22semidirect
51. C13×#103C22semidirect
52. C13×#103C22semidirect
56. #88060C22semidirect
57. #88056C22semidirect
58. #88050C22semidirect
59. #88047C22semidirect
60. #88043C22semidirect
101. #6105D4semidirect
180. #461D13semidirect
200. C2×D13#137semidirect
231. C4⋊Q8C2×D13semidirect
248. C4⋊C8C2×D13semidirect
251. #103C2×D13semidirect
252. #103C2×D13semidirect
327. C13#3266semidirect

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
#117194322
#117192592
C13×#4612
#117188342
#117188302
#117187472
#117186792
#117185062
#117184972
#117184742
#117184732
#117184692
#117184672
#326613