Finite Group Databasebeta

← #13118024

Subgroups — #13118024

Order 1664.

456 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
1C2×#88133C211yesmaximal, characteristic
2C13×#385C211yesmaximal, characteristic
3#11718871C211yesmaximal, characteristic
4#11718871C211yesmaximal, characteristic
5#11718639C211yesmaximal, characteristic, complemented
6#11718637C211yesmaximal, characteristic, complemented
7#11718634C211yesmaximal, characteristic, complemented
8#11718633C211yesmaximal, characteristic, complemented
9#11718612C211yesmaximal, characteristic
10#11718606C211yesmaximal, characteristic
11#11718605C211yesmaximal, characteristic
12#11718315C211yesmaximal, characteristic, complemented
13#11718313C211yesmaximal, characteristic, complemented
14#11718312C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, characteristic, complemented
16C23×C4×C13C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic13C2211yescharacteristic
22C2×C22⋊Dic13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39#88133C418yescomplemented
40C13×#95C2211yescharacteristic
41C13×#95C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52C24×C13C2311yescharacteristic
53C22×C4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C22⋊C4—41no—
73C13×C22⋊C4C2×C414yes—
74C22⋊Dic13—41no—
75C22⋊Dic13—41no—
76C22⋊Dic13C2×C414yes—
77C22⋊Dic13C2×C414yes—
78C4⋊Dic13—41no—
79C4⋊Dic13C2×C414yescomplemented
80#6101—41no—
81#6101—41no—
82#6101—41no—
83#6101—41no—
84#6101—41no—
85#6101—41no—
86#6101C2×C414yescomplemented
87#6101C2×C414yescomplemented
88C4×Dic13—41no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91C4×Dic13C2×C414yescomplemented
92#2383—131nomaximal, Sylow
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13C22×C412yes—
100C23×C13C2411yescharacteristic
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—44no—
118C2×C4×C13C22×C412yes—
119C2×C4×C13C22×C412yes—
120C2×Dic13—21no—
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×Dic13C22×C412yes—
141C2×Dic13C22×C412yes—
142C2×Dic13C22×C412yes—
143C2×Dic13C22×C412yes—
144C2×#126—131no—
145#389—131no—
146#389—131no—
147#389—131no—
148#388—131no—
149#388—131no—
150#388—131no—
151#387—131no—
152#387—131no—
153#387—131no—
154#385—131no—
155#385—131no—
156#385D1311yescharacteristic
157#384—131no—
158#383—131no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13C23×C411yescharacteristic
167C22×C13H(5,𝔽2)11yescharacteristic
168C22×C13H(5,𝔽2)11yescharacteristic
169C22×C13H(5,𝔽2)11yescharacteristic
170C22×C132−1+411yescharacteristic
171C22×C132−1+411yescharacteristic
172C22×C132−1+411yescharacteristic
173C4×C13—22no—
174C4×C13—22no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179Dic13—22no—
180Dic13—22no—
181Dic13—22no—
182Dic13—22no—
183Dic13—41no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187C23×C4C2×D1311yescharacteristic
188#126—138no—
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⋊C4—131no—
199C2×C4⋊C4C2×D1311yescharacteristic
200C2×C4⋊C4C2×D1311yescharacteristic
201C2×C22⋊C4—131no—
202C2×C22⋊C4—131no—
203C2×C22⋊C4—131no—
204C2×C22⋊C4—131no—
205C2×C22⋊C4C2×D1311yescharacteristic
206C2×C22⋊C4C2×D1311yescharacteristic
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211#95—131no—
212#95—131no—
213#95—131no—
214#95—131no—
215#95—131no—
216#95—131no—
217#95—131no—
218#95—131no—
219#95—131no—
220#95—131no—
221#95C2×D1311yescharacteristic
222#95C2×D1311yescharacteristic
223C2×C13—42no—
224C2×C13#52011yescharacteristic
225C2×C13#52011yescharacteristic
226C2×C13#52011yescharacteristic
227C2×C13#56011yescharacteristic
228C2×C13#56311yescharacteristic
229C2×C13#56311yescharacteristic
230C2×C13#56311yescharacteristic
231C24C22×D1311yescharacteristic
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4C22×D1311yescharacteristic
244C22×C4C22×D1311yescharacteristic
245C22×C4C22×D1311yescharacteristic
246C22×C4C22×D1311yescharacteristic
247C22×C4C22×D1311yescharacteristic
248C22×C4C22×D1311yescharacteristic
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—134no—
252C4⋊C4—134no—
253C4⋊C4—134no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C22⋊C4—41no—
262C22⋊C4—134no—
263C22⋊C4—134no—
264C22⋊C4—521no—
265C22⋊C4—521no—
266C22⋊C4C4×D1314yes—
267C42—134no—
268C42—521no—
269C42—521no—
270C42—521no—
271C13#238311yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D1312yes—
279C23C23×D1311yescharacteristic
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—44no—
297C2×C4—132no—
298C2×C4—132no—
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—261no—
321C2×C4C2×C4×D1312yes—
322C2×C4C2×C4×D1312yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D1311yescharacteristic
331C22#8825111yescharacteristic
332C22#8825111yescharacteristic
333C22#8825111yescharacteristic
334C22#8825411yescharacteristic
335C22#8825711yescharacteristic
336C22#8825711yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—262no—
344C4—262no—
345C4—262no—
346C4—262no—
347C4—521no—
348C4—521no—
349C4—521no—
350C4—521no—
351C2—42no—
352C2#1171920911yescharacteristic
353C2#1171925111yescharacteristic
354C2#1171925111yescharacteristic
355C2#1171930011yescharacteristic
356C2#1171935111yescharacteristic
357C2#1171935111yescharacteristic
358C2#1171935611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#385C2
socle, cosocleC23×C13C24
prime radicalC24×C13C23
hypercenter#385D13
hypocenterC13#2383
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
5. #11718639C2semidirect
6. #11718637C2semidirect
7. #11718634C2semidirect
8. #11718633C2semidirect
12. #11718315C2semidirect
13. #11718313C2semidirect
14. #11718312C2semidirect
15. #11718308C2semidirect
39. #88133C4semidirect
79. C4⋊Dic13C2×C4semidirect
86. #6101C2×C4semidirect
87. #6101C2×C4semidirect
91. C4×Dic13C2×C4semidirect
271. C13#2383semidirect

Maximal subgroups

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

subgroupindex
C2×#881332
C13×#3852
#117188712
#117186392
#117186372
#117186342
#117186332
#117186122
#117186062
#117186052
#117183152
#117183132
#117183122
#117183082
#238313