Finite Group Databasebeta

← #13125796

Subgroups — #13125796

Order 1664.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719385C211yesmaximal, characteristic, complemented
2D13×#124C211yesmaximal, characteristic, complemented
3C13×#495C211yesmaximal, characteristic, complemented
4#11718847C211yesmaximal, characteristic, complemented
5#11718846C211yesmaximal, characteristic, complemented
6#11718831C211yesmaximal, characteristic, complemented
7#11718830C211yesmaximal, characteristic, complemented
8#11718827C211yesmaximal, characteristic, complemented
9#11718826C211yesmaximal, characteristic, complemented
10#11718817C211yesmaximal, characteristic
11#11718814C211yesmaximal, characteristic, complemented
12#11718720C211yesmaximal, characteristic, complemented
13#11718717C211yesmaximal, characteristic, complemented
14#11718358C211yesmaximal, characteristic, complemented
15#11718346C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic, complemented
19C2×C13×SD16C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic, complemented
21C2×C13×D8C2211yescharacteristic
22C13×#124C2211yescharacteristic
23C13×#124C2211yescharacteristic, complemented
24#88201C2211yescharacteristic
25#88200C2211yescharacteristic
26Q8×Dic13C2211yescharacteristic, complemented
27C2×#6107C2211yescharacteristic, complemented
28C2×#6106C2211yescharacteristic
29#88192C2211yescharacteristic
30#88190C2211yescharacteristic
31D4×Dic13C2211yescharacteristic, complemented
32C2×#6105C2211yescharacteristic, complemented
33C2×#6104C2211yescharacteristic
34#88139—21no—
35#88139—21no—
36#88137—21no—
37#88135—21no—
38C22⋊C4×D13—21no—
39C22⋊C4×D13—21no—
40#88133—21no—
41#88131—21no—
42#88129C2211yescharacteristic
43C42×D13C2211yescharacteristic
44#88124C2211yescharacteristic, complemented
45C4×C8×C13C2211yescharacteristic, complemented
46#88075C2211yescharacteristic, complemented
47#88075C2211yescharacteristic, complemented
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88060C2211yescharacteristic
53#88060C2211yescharacteristic
54#88056C2211yescharacteristic, complemented
55#88056C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88054C2211yescharacteristic, complemented
58C4×#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C2×D4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67Q8×D13—41no—
68Q8×D13—41no—
69D4×D13—41no—
70D4×D13—41no—
71C2×D52C2311yescharacteristic
72C2×C4×D13—21no—
73C2×C4×D13D411yescharacteristic
74C2×C4×D13D411yescharacteristic
75C2×C4×D13C2311yescharacteristic
76C2×Dic26—21no—
77C2×Dic26C2311yescharacteristic
78C13×Q16—41no—
79C13×SD16—41no—
80C13×SD16—41no—
81C13×D8—41no—
82C2×C8×C13C2311yescharacteristic
83C2×C8×C13C2311yescharacteristic
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C13×C22⋊C4—21no—
87C13×C22⋊C4—21no—
88C42×C13C2311yescharacteristic
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13—21no—
93#6107—41no—
94#6106—41no—
95#6105—41no—
96#6104—41no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100#6103—21no—
101#6103—21no—
102C4⋊Dic13—21no—
103C4⋊Dic13C2311yescharacteristic
104C4⋊Dic13C2311yescharacteristic
105#6101—21no—
106#6101—21no—
107#6101—21no—
108C4×Dic13—21no—
109C4×Dic13D411yescharacteristic
110C4×Dic13D411yescharacteristic
111C4×Dic13C2311yescharacteristic
112C2×#1055C2311yescharacteristic
113C2×#1055C2311yescharacteristic
114#3211—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13—21no—
117C22×D13—21no—
118C22×D13—42no—
119C22×D13—42no—
120C22×D13—42no—
121C22×D13C2×D411yescharacteristic
122Q8×C13—21no—
123Q8×C13—21no—
124Q8×C13—21no—
125Q8×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13C2×D411yescharacteristic
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2411yescharacteristic
135C22⋊D13—42no—
136C22⋊D13—42no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—42no—
141C2×Dic13C2×D411yescharacteristic
142C2×Dic13C2×D411yescharacteristic
143C2×Dic13C2×D411yescharacteristic
144D52—21no—
145D52—21no—
146C4×D13—22no—
147C4×D13—21no—
148C4×D13—21no—
149C4×D13—41no—
150C4×D13—42no—
151Dic26—21no—
152Dic26—21no—
153Dic26—42no—
154C8×C13—21no—
155C8×C13—21no—
156#1055—21no—
157#1055—21no—
158#529—131no—
159C2×#124—131no—
160#495—131no—
161#495D1311yescharacteristic, complemented
162#488—131no—
163#488—131no—
164#464—131no—
165#464—131no—
166#463—131no—
167#463—131no—
168#451—131no—
169#450—131no—
170#448—131no—
171#447—131no—
172#431—131no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13C22×D411yescharacteristic
180C2×D13—21no—
181C2×D13—21no—
182C2×D13—41no—
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—84no—
186C2×D13#13512yes—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13H(5,𝔽2)11yescharacteristic
192C4×C13H(5,𝔽2)11yescharacteristic
193Dic13—21no—
194Dic13—21no—
195Dic13—21no—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199C22×Q8—131no—
200C22×D4—131no—
201C2×Q16—131no—
202C2×Q16C2×D1311yescharacteristic, complemented
203C2×SD16—131no—
204C2×SD16—131no—
205C2×SD16C2×D1311yescharacteristic
206C2×SD16C2×D1311yescharacteristic, complemented
207C2×D8—131no—
208C2×D8C2×D1311yescharacteristic
209#126—261no—
210#125—131no—
211#124—131no—
212#124—131no—
213#124—131no—
214#124—261no—
215#124—261no—
216#124C2×D1311yescharacteristic
217#124C2×D1311yescharacteristic, complemented
218#123—261no—
219C22⋊Q8—131no—
220#121—131no—
221C4×Q8—131no—
222C4×D4—131no—
223C4×D4—261no—
224#117—261no—
225C2×C22⋊C4—261no—
226C2×C22⋊C4—261no—
227C2×C42—131no—
228C4⋊C8—131no—
229C4⋊C8—131no—
230#103—131no—
231#103—131no—
232#103—131no—
233#103—131no—
234#102—131no—
235#102—131no—
236#102—131no—
237#102—131no—
238C22⋊C8—131no—
239C22⋊C8—131no—
240C4×C8—131no—
241C4×C8C2×D1311yescharacteristic, complemented
242C2×C13—81no—
243C2×C13—81no—
244C2×C13#53511yescharacteristic
245C2×C13C2×#13511yescharacteristic
246C2×C13#57511yescharacteristic
247D13—22no—
248D13—81no—
249C24—261no—
250C2×Q8—131no—
251C2×Q8—261no—
252C2×Q8—521no—
253C2×Q8—521no—
254C2×Q8C22×D1311yescharacteristic
255C2×Q8C22×D1311yescharacteristic
256C2×D4—131no—
257C2×D4—261no—
258C2×D4—261no—
259C2×D4—521no—
260C2×D4—521no—
261C2×D4C22×D1311yescharacteristic
262C2×D4C22×D1311yescharacteristic
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—261no—
267C22×C4—261no—
268Q16—41no—
269Q16—521no—
270SD16—41no—
271SD16—41no—
272SD16—521no—
273SD16—521no—
274D8—41no—
275D8—521no—
276C2×C8—131no—
277C2×C8—131no—
278C2×C8C22×D1311yescharacteristic
279C2×C8C22×D1311yescharacteristic
280C4⋊C4—131no—
281C4⋊C4—131no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
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—131no—
300C42—131no—
301C42—131no—
302C42—261no—
303C42C22×D1311yescharacteristic
304C13#321111yescharacteristic, complemented, Sylow
305C23—21no—
306C23—21no—
307C23—131no—
308C23—261no—
309C23—522no—
310C23—522no—
311C23—522no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—261no—
317Q8—261no—
318Q8—522no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—261no—
324D4—261no—
325D4—522no—
326D4—522no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—131no—
330C2×C4—131no—
331C2×C4—131no—
332C2×C4—262no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—521no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4D4×D1311yescharacteristic
342C2×C4D4×D1311yescharacteristic
343C2×C4C23×D1311yescharacteristic
344C8—21no—
345C8—21no—
346C8—261no—
347C8—261no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—132no—
355C22—261no—
356C22—261no—
357C22—521no—
358C22—521no—
359C22—521no—
360C22—1044no—
361C22C2×D4×D1311yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—261no—
367C4—261no—
368C4—261no—
369C4—521no—
370C4—521no—
371C4—521no—
372C4#8825111yescharacteristic
373C4#8825111yescharacteristic
374C2—81no—
375C2—81no—
376C2—262no—
377C2—1041no—
378C2#1171942011yescharacteristic
379C2D13×#13511yescharacteristic
380C2#1171947311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#495C2
socleC22×C13C22×D4
prime radical#11718817C2
hypercenter#495D13
hypocenterC13#3211
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #11719385C2semidirect
2. D13×#124C2semidirect
3. C13×#495C2semidirect
4. #11718847C2semidirect
5. #11718846C2semidirect
6. #11718831C2semidirect
7. #11718830C2semidirect
8. #11718827C2semidirect
9. #11718826C2semidirect
11. #11718814C2semidirect
12. #11718720C2semidirect
13. #11718717C2semidirect
14. #11718358C2semidirect
15. #11718346C2semidirect
18. C2×C13×Q16C22semidirect
20. C2×C13×SD16C22semidirect
23. C13×#124C22semidirect
26. Q8×Dic13C22semidirect
27. C2×#6107C22semidirect
31. D4×Dic13C22semidirect
32. C2×#6105C22semidirect
44. #88124C22semidirect
45. C4×C8×C13C22semidirect
46. #88075C22semidirect
47. #88075C22semidirect
54. #88056C22semidirect
55. #88056C22semidirect
56. #88054C22semidirect
57. #88054C22semidirect
58. C4×#1055C22semidirect
161. #495D13semidirect
202. C2×Q16C2×D13semidirect
206. C2×SD16C2×D13semidirect
217. #124C2×D13semidirect
241. C4×C8C2×D13semidirect
304. C13#3211semidirect

Maximal subgroups

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

subgroupindex
#117193852
D13×#1242
C13×#4952
#117188472
#117188462
#117188312
#117188302
#117188272
#117188262
#117188172
#117188142
#117187202
#117187172
#117183582
#117183462
#321113