Finite Group Databasebeta

← #13126301

Subgroups — #13126301

Order 1664.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#542C211yesmaximal, characteristic, complemented
2#11719239C211yesmaximal, characteristic, complemented
3#11718755C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718718C211yesmaximal, characteristic, complemented
6#11718715C211yesmaximal, characteristic, complemented
7#11718713C211yesmaximal, characteristic, complemented
8#11718709C211yesmaximal, characteristic, complemented
9#11718702C211yesmaximal, characteristic, complemented
10#11718700C211yesmaximal, characteristic
11#11718689C211yesmaximal, characteristic, complemented
12#11718681C211yesmaximal, characteristic, complemented
13#11718677C211yesmaximal, characteristic, complemented
14#11718669C211yesmaximal, characteristic, complemented
15#11718660C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#126—21no—
18C13×#124—21no—
19C13×#124C2211yescharacteristic
20C13×#123—21no—
21C13×C22⋊Q8—21no—
22C13×C22⋊Q8C2211yescharacteristic
23C13×#121C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C13×#117C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28C2×#6106C2211yescharacteristic
29C2×#6105C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31#88184C2211yescharacteristic
32#88178C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88152—21no—
36#88150—21no—
37#88139—21no—
38#88137—21no—
39#88129C2211yescharacteristic
40C4×D52C2211yescharacteristic
41#88123C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88050C2211yescharacteristic
48#88050C2211yescharacteristic
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88048C2211yescharacteristic
54#88048C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56C4⋊#1055C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13C2311yescharacteristic
65C2×C22⋊D13—21no—
66C2×D52C2311yescharacteristic
67C2×C4×D13—21no—
68C2×Dic26—21no—
69C2×Dic26C2311yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4D411yescharacteristic
74C13×C4⋊C4D411yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C13×C22⋊C4D411yescharacteristic
83C13×C22⋊C4D411yescharacteristic
84C42×C13—21no—
85C42×C13C2311yescharacteristic
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88#6107—41no—
89#6106—41no—
90#6105—41no—
91#6104—41no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102#6099—41no—
103C2×#1055—41no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3263—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111C22×D13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—81no—
115D4×C13—21no—
116D4×C13—21no—
117D4×C13—81no—
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×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2411yescharacteristic
130C22⋊D13—81no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134D52—21no—
135D52—21no—
136C4×D13—81no—
137Dic26—21no—
138Dic26—21no—
139Dic26—81no—
140#1055—21no—
141#1055—21no—
142#1055—21no—
143#1055—21no—
144#542—131no—
145#542D1311yescharacteristic, complemented
146#476—131no—
147#476—131no—
148#475—131no—
149#475—131no—
150#470—131no—
151#469—131no—
152#465—131no—
153#465—131no—
154#464—131no—
155#464—131no—
156#463—131no—
157#463—131no—
158#424—131no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13C22×D411yescharacteristic
166C2×D13—41no—
167C2×D13—41no—
168C2×D13—41no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13H(5,𝔽2)11yescharacteristic
178C4×C132−1+411yescharacteristic
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C2×Q16—131no—
183C2×SD16—131no—
184C2×SD16—131no—
185C2×D8—131no—
186C2×M16—131no—
187C22×C8—131no—
188C4⋊Q8—131no—
189C4⋊Q8C2×D1311yescharacteristic
190#126—21no—
191#126—261no—
192#124—21no—
193#124—131no—
194#124—261no—
195#124C2×D1311yescharacteristic
196#123—21no—
197#123—261no—
198C22⋊Q8—21no—
199C22⋊Q8—131no—
200C22⋊Q8—261no—
201C22⋊Q8C2×D1311yescharacteristic
202#121—131no—
203#121C2×D1311yescharacteristic
204C4×Q8—131no—
205C4×Q8C2×D1311yescharacteristic
206C4×D4—131no—
207C4×D4C2×D1311yescharacteristic
208#117C2×D1311yescharacteristic
209#106—131no—
210#106—131no—
211#106—131no—
212#106—131no—
213C4⋊C8—131no—
214C4⋊C8—131no—
215C4⋊C8—131no—
216C4⋊C8—131no—
217#103—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#102—131no—
222#102—131no—
223#102—131no—
224#102—131no—
225C2×C13—41no—
226C2×C13—81no—
227C2×C13#53711yescharacteristic
228C2×C13#57711yescharacteristic
229C2×C13#57711yescharacteristic
230D13—81no—
231C2×Q8—21no—
232C2×Q8—131no—
233C2×Q8—261no—
234C2×Q8C22×D1311yescharacteristic
235C2×D4—21no—
236C2×D4—131no—
237C2×D4—261no—
238C2×D4C22×D1311yescharacteristic
239C22×C4—21no—
240C22×C4—261no—
241C22×C4C22×D1311yescharacteristic
242Q16—521no—
243SD16—521no—
244SD16—521no—
245D8—521no—
246M16—521no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8—131no—
250C2×C8—131no—
251C2×C8—521no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4C22⋊D1311yescharacteristic
261C4⋊C4C22⋊D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C4⋊C4C22×D1311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
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⋊C4C22⋊D1311yescharacteristic
275C22⋊C4C22⋊D1311yescharacteristic
276C42—21no—
277C42—261no—
278C42C22×D1311yescharacteristic
279C42C22×D1311yescharacteristic
280C13#326311yescharacteristic, complemented, Sylow
281C23—21no—
282C23—261no—
283C23C2×C22⋊D1311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—261no—
288Q8—261no—
289Q8—1041no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—261no—
294D4—261no—
295D4—1041no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—1041no—
306C2×C4C2×C22⋊D1311yescharacteristic
307C2×C4C2×C22⋊D1311yescharacteristic
308C2×C4C2×C22⋊D1311yescharacteristic
309C2×C4C2×C22⋊D1311yescharacteristic
310C2×C4C2×C22⋊D1311yescharacteristic
311C2×C4C23×D1311yescharacteristic
312C8—261no—
313C8—261no—
314C8—261no—
315C8—261no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—521no—
323C22—521no—
324C22—521no—
325C22C22×C22⋊D1311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4#8825611yescharacteristic
338C4#8825711yescharacteristic
339C2—41no—
340C2—81no—
341C2—1041no—
342C2#1171953811yescharacteristic
343C2#1171954111yescharacteristic
344C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#542C2
socleC22×C13C22×D4
prime radical#11718700C2
hypercenter#542D13
hypocenterC13#3263
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. C13×#542C2semidirect
2. #11719239C2semidirect
3. #11718755C2semidirect
4. #11718745C2semidirect
5. #11718718C2semidirect
6. #11718715C2semidirect
7. #11718713C2semidirect
8. #11718709C2semidirect
9. #11718702C2semidirect
11. #11718689C2semidirect
12. #11718681C2semidirect
13. #11718677C2semidirect
14. #11718669C2semidirect
15. #11718660C2semidirect
145. #542D13semidirect
280. C13#3263semidirect

Maximal subgroups

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

subgroupindex
C13×#5422
#117192392
#117187552
#117187452
#117187182
#117187152
#117187132
#117187092
#117187022
#117187002
#117186892
#117186812
#117186772
#117186692
#117186602
#326313