Finite Group Databasebeta

← #13127623

Subgroups — #13127623

Order 1664.

384 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719386C211yesmaximal, characteristic, complemented
2D4×Dic26C211yesmaximal, characteristic, complemented
3C13×#463C211yesmaximal, characteristic, complemented
4#11718826C211yesmaximal, characteristic, complemented
5SD16×Dic13C211yesmaximal, characteristic, complemented
6#11718813C211yesmaximal, characteristic, complemented
7#11718811C211yesmaximal, characteristic
8#11718716C211yesmaximal, characteristic, complemented
9#11718675C211yesmaximal, characteristic, complemented
10#11718503C211yesmaximal, characteristic, complemented
11#11718489C211yesmaximal, characteristic, complemented
12#11718456C211yesmaximal, characteristic, complemented
13#11718452C211yesmaximal, characteristic, complemented
14#11718422C211yesmaximal, characteristic, complemented
15#11718421C211yesmaximal, characteristic, complemented
16C22×Dic26—21no—
17C2×C13×SD16C2211yescharacteristic
18C2×C13×D8C2211yescharacteristic
19C13×#124C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21#88201C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23#88194C2211yescharacteristic
24D4×Dic13C2211yescharacteristic
25D4×Dic13C2211yescharacteristic
26D4×Dic13C2211yescharacteristic
27C2×#6104C2211yescharacteristic
28#88178—21no—
29#88142C2211yescharacteristic
30#88142C2211yescharacteristic
31#88140—21no—
32#88139—21no—
33#88137—21no—
34#88135—21no—
35#88132—21no—
36#88132—21no—
37C4×D52C2211yescharacteristic
38#88123C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88057C2211yescharacteristic
51#88057C2211yescharacteristic
52#88055C2211yescharacteristic
53#88054C2211yescharacteristic
54#88054C2211yescharacteristic
55C8×Dic13C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26—44no—
74C2×Dic26D411yescharacteristic
75C13×SD16—22no—
76C13×D8—22no—
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C13×C22⋊C4—21no—
83C42×C13C2311yescharacteristic
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87#6104—22no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13D411yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101D411yescharacteristic
100#6101D411yescharacteristic
101C4×Dic13—21no—
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#3373—131nomaximal, Sylow
107C23×C13—21no—
108C23×C13—21no—
109C22×D13—21no—
110Q8×C13—21no—
111Q8×C13—21no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—21no—
115D4×C13#4112yes—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C22⋊D13—42no—
123C22⋊D13—81no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—81no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134D52—21no—
135D52—21no—
136C4×D13—81no—
137Dic26—22no—
138Dic26—42no—
139Dic26—42no—
140Dic26—42no—
141C8×C13—21no—
142C8×C13—21no—
143#1055—21no—
144#1055—21no—
145#559—131no—
146D4×Q8—131no—
147#489—131no—
148#489—131no—
149#486—131no—
150#476—131no—
151#476—131no—
152#475—131no—
153#463—131no—
154#463D1311yescharacteristic, complemented
155#459—131no—
156#446—131no—
157#442—131no—
158#442—131no—
159C4×SD16—131no—
160C22×C13—22no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13C22×D411yescharacteristic
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—41no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13C2×#4111yescharacteristic
175C4×C132−1+411yescharacteristic
176Dic13—21no—
177Dic13—21no—
178Dic13—21no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182Dic13AGL(1,ℤ/8)12yes—
183C22×Q8—261no—
184C2×SD16C2×D1311yescharacteristic
185C2×D8—131no—
186C2×D8C2×D1311yescharacteristic
187C4⋊Q8—131no—
188C4⋊Q8—131no—
189C4⋊Q8—131no—
190#127—131no—
191#124—131no—
192#124—261no—
193#124C2×D1311yescharacteristic
194#123—261no—
195#123—261no—
196C22⋊Q8—261no—
197C22⋊Q8—261no—
198C22⋊Q8—261no—
199C4×Q8—131no—
200C4×Q8—131no—
201C4×D4—131no—
202C4×D4—131no—
203C4×D4—131no—
204C4×D4—131no—
205C4×D4—261no—
206C4×D4C2×D1311yescharacteristic
207#106—131no—
208#106—131no—
209#106—131no—
210C4⋊C8—131no—
211C4⋊C8—131no—
212C4⋊C8C2×D1311yescharacteristic
213#103—131no—
214#103—131no—
215#103C2×D1311yescharacteristic
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222#102C2×D1311yescharacteristic
223#97—131no—
224#97—131no—
225C4×C8—131no—
226C2×C13—42no—
227C2×C13—81no—
228C2×C13#54811yescharacteristic
229C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
230C2×C13#57711yescharacteristic
231D13—81no—
232C2×Q8—131no—
233C2×Q8—261no—
234C2×Q8—261no—
235C2×Q8—261no—
236C2×Q8—524no—
237C2×Q8C22×D1311yescharacteristic
238C2×D4—131no—
239C2×D4—261no—
240C2×D4—261no—
241C2×D4C22×D1311yescharacteristic
242C2×D4C22×D1311yescharacteristic
243C22×C4—21no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248SD16—22no—
249D8—22no—
250D8—262no—
251C2×C8—131no—
252C2×C8—131no—
253C2×C8C22×D1311yescharacteristic
254C2×C8C22×D1311yescharacteristic
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—131no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4C22×D1311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C42—131no—
276C42—131no—
277C42—261no—
278C42C22×D1311yescharacteristic
279C13#337311yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—261no—
283Q8—21no—
284Q8—21no—
285Q8—262no—
286Q8—522no—
287Q8—522no—
288Q8—522no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—261no—
293D4—261no—
294D4—522no—
295D4—1041no—
296D4#612912yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—131no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4—1041no—
310C2×C4—1041no—
311C2×C4D4×D1311yescharacteristic
312C2×C4D4×D1311yescharacteristic
313C2×C4C23×D1311yescharacteristic
314C8—21no—
315C8—21no—
316C8—261no—
317C8—261no—
318C22—22no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—521no—
325C22—521no—
326C22—521no—
327C22C2×D4×D1311yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—132no—
333C4—261no—
334C4—261no—
335C4—261no—
336C4—521no—
337C4—521no—
338C4—521no—
339C4C2×#612911yescharacteristic
340C4#8825711yescharacteristic
341C2—42no—
342C2—81no—
343C2—1041no—
344C2#1171930311yescharacteristic
345C2#1171947511yescharacteristic
346C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#463C2
socleC22×C13C22×D4
prime radical#11718811C2
hypercenter#463D13
hypocenterC13#3373
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. #11719386C2semidirect
2. D4×Dic26C2semidirect
3. C13×#463C2semidirect
4. #11718826C2semidirect
5. SD16×Dic13C2semidirect
6. #11718813C2semidirect
8. #11718716C2semidirect
9. #11718675C2semidirect
10. #11718503C2semidirect
11. #11718489C2semidirect
12. #11718456C2semidirect
13. #11718452C2semidirect
14. #11718422C2semidirect
15. #11718421C2semidirect
154. #463D13semidirect
279. C13#3373semidirect

Maximal subgroups

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

subgroupindex
#117193862
D4×Dic262
C13×#4632
#117188262
SD16×Dic132
#117188132
#117188112
#117187162
#117186752
#117185032
#117184892
#117184562
#117184522
#117184222
#117184212
#337313