Finite Group Databasebeta

← #13127308

Subgroups — #13127308

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#11719270C211yesmaximal, characteristic, complemented
2#11719260C211yesmaximal, characteristic, complemented
3C13×#435C211yesmaximal, characteristic, complemented
4#11718796C211yesmaximal, characteristic, complemented
5#11718782C211yesmaximal, characteristic, complemented
6#11718776C211yesmaximal, characteristic, complemented
7C2×#88057C211yesmaximal, characteristic, complemented
8#11718508C211yesmaximal, characteristic, complemented
9#11718503C211yesmaximal, characteristic, complemented
10#11718398C211yesmaximal, characteristic, complemented
11#11718397C211yesmaximal, characteristic, complemented
12#11718396C211yesmaximal, characteristic, complemented
13#11718396C211yesmaximal, characteristic, complemented
14#11718372C211yesmaximal, characteristic, complemented
15#11718363C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C2×C13×M16C2211yescharacteristic
18C22×C8×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88193—21no—
21#88184C2211yescharacteristic
22#88184C2211yescharacteristic
23#88184C2211yescharacteristic
24#88184C2211yescharacteristic
25#88180C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×D104C2211yescharacteristic
30#88152—21no—
31#88151—21no—
32#88140—21no—
33#88140—21no—
34#88137—21no—
35#88135—21no—
36C4×D52C2211yescharacteristic
37C4×D52C2211yescharacteristic
38#88124C2211yescharacteristic
39#88123C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42C13×C22⋊C8C2211yescharacteristic
43C13×#97C2211yescharacteristic
44#88061C2211yescharacteristic
45#88061C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88058C2211yescharacteristic
51#88058C2211yescharacteristic
52#88058C2211yescharacteristic
53#88057C2211yescharacteristic
54#88057C2211yescharacteristic
55#88057C2211yescharacteristic
56#88057C2211yescharacteristic
57#88057C2211yescharacteristic
58#88057C2211yescharacteristic
59C2×D4×C13D411yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69#6129—44no—
70C2×D52C2311yescharacteristic
71C2×D52C2311yescharacteristic
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×Dic26—21no—
75C13×M16—22no—
76C2×C8×C13—22no—
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4D411yescharacteristic
82C13×C22⋊C4D411yescharacteristic
83C13×C22⋊C4D411yescharacteristic
84C42×C13C2311yescharacteristic
85C22⋊Dic13—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105D104—22no—
106#3345—131nomaximal, Sylow
107C23×C13C2×D411yescharacteristic
108C23×C13C2×D411yescharacteristic
109C22×D13—21no—
110C22×D13—21no—
111D4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—42no—
122C22⋊D13—42no—
123C22⋊D13—42no—
124C22⋊D13—81no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—81no—
134D52—21no—
135D52—21no—
136D52—21no—
137D52—21no—
138C4×D13—42no—
139C4×D13—81no—
140Dic26—42no—
141C8×C13—21no—
142C8×C13—21no—
143C8×C13—21no—
144C8×C13#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#476—131no—
154#469—131no—
155#466—131no—
156#442—131no—
157#435D1311yescharacteristic, complemented
158#428—131no—
159C2×#106—131no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13AGL(1,ℤ/8)12yes—
166C22×C13C22×D411yescharacteristic
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—41no—
170C2×D13—41no—
171C2×D13—41no—
172C2×D13—41no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13C2×#4111yescharacteristic
178C4×C132−1+411yescharacteristic
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185C2×#41—261no—
186C2×D8—131no—
187C2×M16C2×D1311yescharacteristic
188C22×C8C2×D1311yescharacteristic
189C4⋊Q8—131no—
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#106—131no—
217#106—131no—
218C4⋊C8C2×D1311yescharacteristic
219#102—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223#102—131no—
224#102—131no—
225C22⋊C8C2×D1311yescharacteristic
226C22⋊C8C2×D1311yescharacteristic
227#97C2×D1311yescharacteristic
228C2×C13—22no—
229C2×C13—41no—
230C2×C13#54711yescharacteristic
231C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
232C2×C13#57711yescharacteristic
233D13—81no—
234D13—81no—
235#41—524no—
236C2×Q8—261no—
237C2×D4—131no—
238C2×D4—131no—
239C2×D4—261no—
240C2×D4—261no—
241C2×D4—261no—
242C2×D4—261no—
243C2×D4D5211yescharacteristic
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4C22×D1311yescharacteristic
250C22×C4C22×D1311yescharacteristic
251D8—262no—
252M16—22no—
253C2×C8—22no—
254C2×C8C22×D1311yescharacteristic
255C2×C8C22×D1311yescharacteristic
256C2×C8C22×D1311yescharacteristic
257C2×C8C22×D1311yescharacteristic
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—131no—
261C4⋊C4—131no—
262C4⋊C4—131no—
263C4⋊C4—131no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4D5211yescharacteristic
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4D5211yescharacteristic
279C22⋊C4D5211yescharacteristic
280C42—261no—
281C42C22×D1311yescharacteristic
282C13#334511yescharacteristic, complemented, Sylow
283C23—261no—
284C23—261no—
285C23C2×D5211yescharacteristic
286C23C2×D5211yescharacteristic
287Q8—522no—
288D4—22no—
289D4—261no—
290D4—261no—
291D4—261no—
292D4—261no—
293D4—522no—
294D4—522no—
295D4—522no—
296D4—1041no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4—522no—
310C2×C4—1041no—
311C2×C4—1041no—
312C2×C4C2×D5211yescharacteristic
313C2×C4C2×D5211yescharacteristic
314C2×C4C2×D5211yescharacteristic
315C2×C4C2×D5211yescharacteristic
316C2×C4C23×D1311yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8#612912yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—521no—
327C22—521no—
328C22—521no—
329C22—521no—
330C22—521no—
331C22—521no—
332C22#8816212yes—
333C22C22×D5211yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4—521no—
342C4—521no—
343C4—521no—
344C4C2×#612911yescharacteristic
345C4#8825711yescharacteristic
346C2—22no—
347C2—41no—
348C2—1041no—
349C2—1041no—
350C2#1171926011yescharacteristic
351C2C2×#8816211yescharacteristic
352C2#1171945611yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#435C2
socleC22×C13C22×D4
hypercenter#435D13
hypocenterC13#3345
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #11719270C2semidirect
2. #11719260C2semidirect
3. C13×#435C2semidirect
4. #11718796C2semidirect
5. #11718782C2semidirect
6. #11718776C2semidirect
7. C2×#88057C2semidirect
8. #11718508C2semidirect
9. #11718503C2semidirect
10. #11718398C2semidirect
11. #11718397C2semidirect
12. #11718396C2semidirect
13. #11718396C2semidirect
14. #11718372C2semidirect
15. #11718363C2semidirect
144. C8×C13#41semidirect
157. #435D13semidirect
282. C13#3345semidirect
320. C8#6129semidirect

Maximal subgroups

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

subgroupindex
#117192702
#117192602
C13×#4352
#117187962
#117187822
#117187762
C2×#880572
#117185082
#117185032
#117183982
#117183972
#117183962
#117183722
#117183632
#334513