Finite Group Databasebeta

← #13121964

Subgroups — #13121964

Order 1664.

416 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#400C211yesmaximal, characteristic, complemented
2#11718650C211yesmaximal, characteristic
3#11718648C211yesmaximal, characteristic
4#11718646C211yesmaximal, characteristic, complemented
5#11718642C211yesmaximal, characteristic, complemented
6#11718338C211yesmaximal, characteristic
7#11718334C211yesmaximal, characteristic
8#11718331C211yesmaximal, characteristic
9#11718330C211yesmaximal, characteristic
10#11718328C211yesmaximal, characteristic
11#11718319C211yesmaximal, characteristic, complemented
12#11718317C211yesmaximal, characteristic, complemented
13#11718317C211yesmaximal, characteristic, complemented
14#11718316C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, characteristic, complemented
16C22×C4×D13C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×#6103C2211yescharacteristic
21C2×#6103C2211yescharacteristic
22C2×#6103C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C13×#95C2211yescharacteristic
38C13×#95C2211yescharacteristic
39C13×#95C2211yescharacteristic
40C13×#95C2211yescharacteristic
41C13×#95C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C23×D13C2311yescharacteristic
52C22×C4×C13C2311yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×Dic13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C2×C4×D13—22no—
67C2×C4×D13—22no—
68C2×C4×D13—41no—
69C2×Dic26—41no—
70C2×Dic26—41no—
71C2×Dic26—41no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74#6103—41no—
75#6103—41no—
76#6103—41no—
77#6103—41no—
78#6103—41no—
79#6103Q814yescomplemented
80C4⋊Dic13—41no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85#6101—22no—
86#6101—22no—
87#6101—41no—
88#6101—41no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91#2742—131nomaximal, Sylow
92C23×C13C2411yescharacteristic
93C22×D13—21no—
94C22×D13—21no—
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—21no—
98C22×D13—21no—
99C22×D13C2×Q812yes—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13C2×Q812yes—
120C2×C4×C13#4112yes—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13C2×Q812yes—
141C2×Dic13#4112yes—
142C4×D13—44no—
143Dic26—44no—
144#400—131no—
145#400D1311yescharacteristic, complemented
146#399—131no—
147#395—131no—
148#395—131no—
149#393—131no—
150#389—131no—
151#389—131no—
152#388—131no—
153#388—131no—
154#387—131no—
155#387—131no—
156#385—131no—
157#380—131no—
158#380—131no—
159C22×C13C22×Q811yescharacteristic
160C22×C13C2×#4111yescharacteristic
161C22×C13C2×#4111yescharacteristic
162C22×C13H(5,𝔽2)11yescharacteristic
163C22×C13H(5,𝔽2)11yescharacteristic
164C22×C13H(5,𝔽2)11yescharacteristic
165C22×C132−1+411yescharacteristic
166C2×D13—22no—
167C2×D13—22no—
168C2×D13—22no—
169C2×D13—41no—
170C2×D13—41no—
171C2×D13—41no—
172C2×D13—41no—
173C4×C13—22no—
174C4×C13—22no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180Dic13—22no—
181Dic13—22no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187C22×Q8—131no—
188C23×C4—131no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—131no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4C2×D1311yescharacteristic
199C2×C4⋊C4C2×D1311yescharacteristic
200C2×C22⋊C4—131no—
201C2×C22⋊C4—131no—
202C2×C22⋊C4—131no—
203C2×C22⋊C4—131no—
204C2×C22⋊C4—131no—
205C2×C22⋊C4—131no—
206C2×C42—131no—
207C2×C42—131no—
208#95—131no—
209#95—131no—
210#95—131no—
211#95—131no—
212#95—131no—
213#95—131no—
214#95—131no—
215#95—131no—
216#95—131no—
217#95C2×D1311yescharacteristic
218#95C2×D1311yescharacteristic
219#95C2×D1311yescharacteristic
220#95C2×D1311yescharacteristic
221#95C2×D1311yescharacteristic
222C2×C13#54211yescharacteristic
223C2×C13#54211yescharacteristic
224C2×C13#54411yescharacteristic
225C2×C13#55111yescharacteristic
226C2×C13#55411yescharacteristic
227C2×C13#55411yescharacteristic
228C2×C13#56011yescharacteristic
229D13—42no—
230C24—131no—
231C2×Q8—521no—
232C2×Q8—521no—
233C2×Q8—521no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—262no—
242C22×C4—262no—
243C22×C4—521no—
244C22×C4C22×D1311yescharacteristic
245C22×C4C22×D1311yescharacteristic
246C22×C4C22×D1311yescharacteristic
247C22×C4C22×D1311yescharacteristic
248C22×C4C22×D1311yescharacteristic
249C22×C4C22×D1311yescharacteristic
250C22×C4C22×D1311yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—262no—
254C4⋊C4—262no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C22⋊C4—134no—
263C22⋊C4—521no—
264C22⋊C4—521no—
265C22⋊C4—521no—
266C22⋊C4—521no—
267C22⋊C4—521no—
268C42—521no—
269C42—521no—
270C13#274211yescharacteristic, complemented, Sylow
271C23—132no—
272C23—261no—
273C23—261no—
274C23—261no—
275C23—261no—
276C23—261no—
277C23—261no—
278C23C23×D1311yescharacteristic
279Q8—524no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—132no—
300C2×C4—132no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—524no—
321C2×C4#612912yes—
322C2×C4Q8×D1312yes—
323C22—262no—
324C22—262no—
325C22—262no—
326C22—521no—
327C22—521no—
328C22—521no—
329C22—521no—
330C22C2×#612911yescharacteristic
331C22C2×Q8×D1311yescharacteristic
332C22#41×D1311yescharacteristic
333C22#8825611yescharacteristic
334C22#8825611yescharacteristic
335C22#8825611yescharacteristic
336C22#8825711yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—262no—
345C4—262no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4—521no—
350C4—521no—
351C2—522no—
352C2#1171934011yescharacteristic
353C2#1171936311yescharacteristic
354C2#1171938711yescharacteristic
355C2#1171939411yescharacteristic
356C2#1171939511yescharacteristic
357C2#1171941511yescharacteristic
358C2#1171941611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#400C2
prime radicalC23×D13C23
hypercenter#400D13
hypocenterC13#2742
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C13×#400C2semidirect
4. #11718646C2semidirect
5. #11718642C2semidirect
11. #11718319C2semidirect
12. #11718317C2semidirect
13. #11718317C2semidirect
14. #11718316C2semidirect
15. #11718308C2semidirect
79. #6103Q8semidirect
145. #400D13semidirect
270. C13#2742semidirect

Maximal subgroups

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

subgroupindex
C13×#4002
#117186502
#117186482
#117186462
#117186422
#117183382
#117183342
#117183312
#117183302
#117183282
#117183192
#117183172
#117183162
#117183082
#274213