Finite Group Databasebeta

← #13127300

Subgroups — #13127300

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
1C13×#553C211yesmaximal, characteristic, complemented
2#11719260C211yesmaximal, characteristic, complemented
3#11718727C211yesmaximal, characteristic, complemented
4#11718726C211yesmaximal, characteristic, complemented
5#11718700C211yesmaximal, characteristic, complemented
6#11718699C211yesmaximal, characteristic, complemented
7#11718695C211yesmaximal, characteristic, complemented
8#11718694C211yesmaximal, characteristic, complemented
9#11718675C211yesmaximal, characteristic, complemented
10#11718672C211yesmaximal, characteristic, complemented
11#11718669C211yesmaximal, characteristic, complemented
12#11718664C211yesmaximal, characteristic, complemented
13#11718656C211yesmaximal, characteristic, complemented
14#11718629C211yesmaximal, characteristic, complemented
15C2×#88048C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C13×#126—21no—
18C13×#125C2211yescharacteristic
19C13×#123—21no—
20C13×#121—21no—
21C13×#121C2211yescharacteristic
22C13×#121C2211yescharacteristic
23C4×D4×C13—21no—
24C4×D4×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C13×#117C2211yescharacteristic
27C2×C13×C4⋊C4C2211yescharacteristic
28C2×#6104C2211yescharacteristic
29#88184C2211yescharacteristic
30#88184C2211yescharacteristic
31C2×C4⋊Dic13C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88151—21no—
36#88140—21no—
37#88140—21no—
38C4×D52C2211yescharacteristic
39#88123C2211yescharacteristic
40#88072C2211yescharacteristic
41#88072C2211yescharacteristic
42#88072C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88049C2211yescharacteristic
46#88049C2211yescharacteristic
47#88049C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88048C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13D411yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71#6129—44no—
72C2×D52C2311yescharacteristic
73C2×C4×D13—21no—
74C2×Dic26—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4D411yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C13×C22⋊C4D411yescharacteristic
87C13×C22⋊C4D411yescharacteristic
88C42×C13—21no—
89C42×C13C2311yescharacteristic
90#6104—22no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100#6099—22no—
101C2×#1055—22no—
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#3345—131nomaximal, Sylow
107C23×C13—21no—
108C23×C13C2×D411yescharacteristic
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111D4×C13—22no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—42no—
115D4×C13—81no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—81no—
124C2×C4×C13—81no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2411yescharacteristic
130C22⋊D13—42no—
131C22⋊D13—42no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137D52—21no—
138D52—21no—
139C4×D13—42no—
140Dic26—42no—
141#1055—21no—
142#1055—21no—
143#1055—21no—
144#1055#4112yescomplemented
145#553D1311yescharacteristic, complemented
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#435—131no—
158#428—131no—
159C2×#106—131no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13AGL(1,ℤ/8)12yes—
169C22×C13C22×D411yescharacteristic
170C2×D13—41no—
171C2×D13—41no—
172C2×D13—41no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13C2×#4111yescharacteristic
181C4×C132−1+411yescharacteristic
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185C2×#41—261no—
186C2×D8—131no—
187C2×M16—131no—
188C22×C8—131no—
189C4⋊Q8—131no—
190#126—21no—
191#125C2×D1311yescharacteristic
192#123—21no—
193#123—261no—
194#123—261no—
195C22⋊Q8—261no—
196#121—21no—
197#121—131no—
198#121—131no—
199#121C2×D1311yescharacteristic
200#121C2×D1311yescharacteristic
201C4×D4—21no—
202C4×D4—131no—
203C4×D4C2×D1311yescharacteristic
204C4×D4C2×D1311yescharacteristic
205#117C2×D1311yescharacteristic
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4C2×D1311yescharacteristic
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⋊C8—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223#102—131no—
224#102—131no—
225C22⋊C8—131no—
226C22⋊C8—131no—
227#97—131no—
228C2×C13—22no—
229C2×C13—41no—
230C2×C13—81no—
231C2×C13#54711yescharacteristic
232C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
233C2×C13#57711yescharacteristic
234D13—81no—
235#41—524no—
236C2×Q8—261no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—131no—
240C2×D4—261no—
241C2×D4—261no—
242C2×D4C22⋊D1311yescharacteristic
243C2×D4C22×D1311yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4C22×D1311yescharacteristic
250C22×C4C22×D1311yescharacteristic
251D8—262no—
252M16—262no—
253C2×C8—131no—
254C2×C8—131no—
255C2×C8—131no—
256C2×C8—131no—
257C2×C8—262no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—131no—
262C4⋊C4—131no—
263C4⋊C4—131no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4C22⋊D1311yescharacteristic
268C4⋊C4C22×D1311yescharacteristic
269C4⋊C4C22×D1311yescharacteristic
270C4⋊C4C22×D1311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4C22⋊D1311yescharacteristic
279C22⋊C4C22⋊D1311yescharacteristic
280C42—21no—
281C42C22×D1311yescharacteristic
282C13#334511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—261no—
285C23C2×C22⋊D1311yescharacteristic
286C23C2×C22⋊D1311yescharacteristic
287Q8—522no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—261no—
294D4—261no—
295D4—522no—
296D4—522no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—522no—
310C2×C4—522no—
311C2×C4—522no—
312C2×C4C2×C22⋊D1311yescharacteristic
313C2×C4C2×C22⋊D1311yescharacteristic
314C2×C4C2×C22⋊D1311yescharacteristic
315C2×C4C2×C22⋊D1311yescharacteristic
316C2×C4C23×D1311yescharacteristic
317C8—132no—
318C8—261no—
319C8—261no—
320C8—261no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—521no—
330C22—521no—
331C22—521no—
332C22#8820312yes—
333C22C22×C22⋊D1311yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—521no—
342C4—521no—
343C4—521no—
344C4#41×D1311yescharacteristic
345C4#8825711yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—1041no—
350C2C2×#8820311yescharacteristic
351C2#1171952911yescharacteristic
352C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#553C2
socleC22×C13C22×D4
hypercenter#553D13
hypocenterC13#3345
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. C13×#553C2semidirect
2. #11719260C2semidirect
3. #11718727C2semidirect
4. #11718726C2semidirect
5. #11718700C2semidirect
6. #11718699C2semidirect
7. #11718695C2semidirect
8. #11718694C2semidirect
9. #11718675C2semidirect
10. #11718672C2semidirect
11. #11718669C2semidirect
12. #11718664C2semidirect
13. #11718656C2semidirect
14. #11718629C2semidirect
15. C2×#88048C2semidirect
144. #1055#41semidirect
145. #553D13semidirect
282. C13#3345semidirect

Maximal subgroups

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

subgroupindex
C13×#5532
#117192602
#117187272
#117187262
#117187002
#117186992
#117186952
#117186942
#117186752
#117186722
#117186692
#117186642
#117186562
#117186292
C2×#880482
#334513