Finite Group Databasebeta

← #13127313

Subgroups — #13127313

Order 1664.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719431C211yesmaximal, characteristic, complemented
2#11719263C211yesmaximal, characteristic, complemented
3C13×#476C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718675C211yesmaximal, characteristic, complemented
6#11718527C211yesmaximal, characteristic, complemented
7#11718524C211yesmaximal, characteristic, complemented
8#11718522C211yesmaximal, characteristic, complemented
9D13×#106C211yesmaximal, characteristic, complemented
10#11718508C211yesmaximal, characteristic, complemented
11#11718497C211yesmaximal, characteristic, complemented
12#11718443C211yesmaximal, characteristic, complemented
13#11718438C211yesmaximal, characteristic, complemented
14#11718436C211yesmaximal, characteristic, complemented
15#11718435C211yesmaximal, characteristic, complemented
16C2×#6131—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19#88200—21no—
20#88192C2211yescharacteristic
21#88192C2211yescharacteristic
22C2×#6104C2211yescharacteristic
23#88183—21no—
24C4×C22⋊D13—21no—
25C2×#6094C2211yescharacteristic
26C2×C8×D13C2211yescharacteristic
27#88149C2211yescharacteristic
28#88149C2211yescharacteristic
29#88148—21no—
30#88148—21no—
31#88146C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34C4⋊C4×D13C2211yescharacteristic
35#88138—21no—
36#88133—21no—
37C4×D52C2211yescharacteristic
38C4×D52C2211yescharacteristic
39#88124C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic
45#88072C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88049C2211yescharacteristic
53#88048C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64#6131—44no—
65C2×D52—21no—
66C2×D52—21no—
67C2×D52D411yescharacteristic
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13C2311yescharacteristic
74C2×C4×D13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C13×C4⋊C4—21no—
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C22⋊C4—21no—
82C42×C13C2311yescharacteristic
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85#6104—22no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103D411yescharacteristic
91#6103D411yescharacteristic
92C4⋊Dic13D411yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6094—22no—
105C8×D13—22no—
106#3345—131nomaximal, Sylow
107C23×C13—21no—
108C22×D13—21no—
109C22×D13C2×D411yescharacteristic
110C22×D13C2×D411yescharacteristic
111Q8×C13—42no—
112D4×C13—21no—
113D4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—81no—
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—42no—
122C22⋊D13—81no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128D52—22no—
129D52—21no—
130D52—21no—
131D52—42no—
132D52—42no—
133C4×D13—21no—
134C4×D13—21no—
135C4×D13—21no—
136C4×D13—21no—
137C4×D13—42no—
138C4×D13—42no—
139C4×D13—42no—
140C4×D13—81no—
141C8×C13—21no—
142C8×C13—21no—
143#1055—21no—
144#1055#4112yescomplemented
145#553—131no—
146#547—131no—
147#501—131no—
148#482—131no—
149#481—131no—
150#481—131no—
151#480—131no—
152#478—131no—
153#476D1311yescharacteristic, complemented
154#469—131no—
155#466—131no—
156#442—131no—
157#435—131no—
158#428—131no—
159C2×#106—131no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C22×D411yescharacteristic
164C2×D13—21no—
165C2×D13—21no—
166C2×D13—21no—
167C2×D13—21no—
168C2×D13—21no—
169C2×D13—41no—
170C2×D13—41no—
171C2×D13—41no—
172C2×D13AGL(1,ℤ/8)12yes—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13C2×#4111yescharacteristic
179C4×C132−1+411yescharacteristic
180Dic13—21no—
181Dic13—21no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185C2×#41—261no—
186C2×D8—131no—
187C2×M16—131no—
188C22×C8—131no—
189C4⋊Q8C2×D1311yescharacteristic
190#126—261no—
191#125—131no—
192#123—261no—
193#123—261no—
194#123—261no—
195C22⋊Q8—261no—
196#121—131no—
197#121—131no—
198#121—131no—
199#121—131no—
200#121—261no—
201C4×D4—131no—
202C4×D4—131no—
203C4×D4—261no—
204C4×D4C2×D1311yescharacteristic
205#117—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209#107—131no—
210#107—131no—
211#107—131no—
212#106—131no—
213#106—131no—
214#106—131no—
215#106—131no—
216#106C2×D1311yescharacteristic
217#106C2×D1311yescharacteristic
218C4⋊C8C2×D1311yescharacteristic
219#102—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223#102C2×D1311yescharacteristic
224#102C2×D1311yescharacteristic
225C22⋊C8—131no—
226C22⋊C8—131no—
227#97—131no—
228C2×C13—81no—
229C2×C13#54711yescharacteristic
230C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
231C2×C13#57711yescharacteristic
232D13—22no—
233D13—41no—
234D13—81no—
235#41—524no—
236C2×Q8—21no—
237C2×D4—131no—
238C2×D4—131no—
239C2×D4—261no—
240C2×D4—261no—
241C2×D4—261no—
242C2×D4—261no—
243C2×D4C22×D1311yescharacteristic
244C22×C4—21no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4—261no—
251D8—262no—
252M16—262no—
253C2×C8—131no—
254C2×C8—131no—
255C2×C8—262no—
256C2×C8C22×D1311yescharacteristic
257C2×C8C22×D1311yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—131no—
260C4⋊C4—131no—
261C4⋊C4—131no—
262C4⋊C4—131no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4C22×D1311yescharacteristic
269C4⋊C4C22×D1311yescharacteristic
270C4⋊C4C22×D1311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—131no—
273C22⋊C4—131no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C42—261no—
281C42C22×D1311yescharacteristic
282C13#334511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—131no—
285C23—131no—
286C23—261no—
287Q8—42no—
288D4—21no—
289D4—21no—
290D4—262no—
291D4—261no—
292D4—261no—
293D4—522no—
294D4—522no—
295D4—522no—
296D4—1041no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—522no—
311C2×C4—522no—
312C2×C4—522no—
313C2×C4—1041no—
314C2×C4D4×D1311yescharacteristic
315C2×C4D4×D1311yescharacteristic
316C2×C4C23×D1311yescharacteristic
317C8—21no—
318C8—21no—
319C8—132no—
320C8—261no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—132no—
325C22—261no—
326C22—261no—
327C22—261no—
328C22—261no—
329C22—261no—
330C22—521no—
331C22—521no—
332C22—521no—
333C22C2×D4×D1311yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—261no—
340C4—261no—
341C4—521no—
342C4—521no—
343C4—521no—
344C4#8825411yescharacteristic
345C4#41×D1311yescharacteristic
346C2—81no—
347C2—262no—
348C2—521no—
349C2—1041no—
350C2#1171933611yescharacteristic
351C2#1171946711yescharacteristic
352C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#476C2
socleC22×C13C22×D4
hypercenter#476D13
hypocenterC13#3345
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11719431C2semidirect
2. #11719263C2semidirect
3. C13×#476C2semidirect
4. #11718741C2semidirect
5. #11718675C2semidirect
6. #11718527C2semidirect
7. #11718524C2semidirect
8. #11718522C2semidirect
9. D13×#106C2semidirect
10. #11718508C2semidirect
11. #11718497C2semidirect
12. #11718443C2semidirect
13. #11718438C2semidirect
14. #11718436C2semidirect
15. #11718435C2semidirect
144. #1055#41semidirect
153. #476D13semidirect
282. C13#3345semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117192632
C13×#4762
#117187412
#117186752
#117185272
#117185242
#117185222
D13×#1062
#117185082
#117184972
#117184432
#117184382
#117184362
#117184352
#334513