Finite Group Databasebeta

← #13125437

Subgroups — #13125437

Order 1664.

364 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719329C211yesmaximal, characteristic
2#11719327C211yesmaximal, characteristic, complemented
3C13×#470C211yesmaximal, characteristic, complemented
4#11718851C211yesmaximal, characteristic, complemented
5Q16×Dic13C211yesmaximal, characteristic, complemented
6#11718795C211yesmaximal, characteristic
7M16×Dic13C211yesmaximal, characteristic, complemented
8#11718713C211yesmaximal, characteristic, complemented
9#11718710C211yesmaximal, characteristic
10#11718517C211yesmaximal, characteristic, complemented
11#11718513C211yesmaximal, characteristic, complemented
12#11718458C211yesmaximal, characteristic, complemented
13#11718456C211yesmaximal, characteristic, complemented
14#11718451C211yesmaximal, characteristic, complemented
15#11718449C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×C22⋊Q8C2211yescharacteristic
20#88201C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23#88198C2211yescharacteristic
24C2×#6107C2211yescharacteristic
25C2×#6106C2211yescharacteristic
26#88184C2211yescharacteristic
27#88178C2211yescharacteristic
28C2×C4×Dic13C2211yescharacteristic
29C2×#6099C2211yescharacteristic
30C2×#6095C2211yescharacteristic
31#88152—21no—
32#88147C2211yescharacteristic
33#88146—21no—
34#88144C2211yescharacteristic
35#88143—21no—
36#88142C2211yescharacteristic
37#88141—21no—
38#88141C2211yescharacteristic
39#88140—21no—
40#88135—21no—
41#88132—21no—
42#88131—21no—
43C13×#106C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88061C2211yescharacteristic
49#88058C2211yescharacteristic
50#88056C2211yescharacteristic
51#88055C2211yescharacteristic
52#88055C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C22×Dic13D411yescharacteristic
64C22×Dic13D411yescharacteristic
65C2×D52C2311yescharacteristic
66C2×C4×D13—21no—
67C2×Dic26—21no—
68C2×Dic26C2311yescharacteristic
69C13×Q16—22no—
70C13×M16—22no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C22⋊Dic13—21no—
80#6107—22no—
81#6106—22no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13D411yescharacteristic
101C4×Dic13D411yescharacteristic
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104#6099—22no—
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107#6095—22no—
108#3172—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C22⋊D13—42no—
124C2×Dic13—22no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—41no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133D52—21no—
134D52—21no—
135C4×D13—42no—
136Dic26—21no—
137Dic26—21no—
138Dic26—42no—
139C8×C13—21no—
140C8×C13#4112yes—
141#1055—21no—
142#1055#4112yes—
143#533—131no—
144#529—131no—
145#501—131no—
146#497—131no—
147#491—131no—
148#489—131no—
149#470—131no—
150#470D1311yescharacteristic, complemented
151#468—131no—
152#468—131no—
153C4×Q16—131no—
154C4×Q16—131no—
155C4×SD16—131no—
156C4×SD16—131no—
157C4×M16—131no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13C22×D411yescharacteristic
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—41no—
165C4×C13—21no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13C2×#4111yescharacteristic
171C4×C13C2×#4111yescharacteristic
172Dic13—21no—
173Dic13—21no—
174Dic13—21no—
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13#13712yes—
179C2×Q16—131no—
180C2×Q16C2×D1311yescharacteristic
181C2×SD16—131no—
182C2×SD16—131no—
183C2×M16—131no—
184C2×M16C2×D1311yescharacteristic
185C4⋊Q8—131no—
186C4⋊Q8—131no—
187#126—261no—
188#125—131no—
189#125—261no—
190#124—131no—
191#123—261no—
192C22⋊Q8—131no—
193C22⋊Q8—261no—
194C22⋊Q8C2×D1311yescharacteristic
195C22⋊Q8C2×D1311yescharacteristic
196#121—131no—
197C4×Q8—131no—
198C4×Q8—131no—
199C4×Q8—131no—
200C4×Q8—261no—
201C4×D4—131no—
202C4×D4—261no—
203#117—261no—
204#117—261no—
205C2×C42—131no—
206#107—131no—
207#107—131no—
208#106—131no—
209#106C2×D1311yescharacteristic
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#103C2×D1311yescharacteristic
215#103C2×D1311yescharacteristic
216#102—131no—
217#102—131no—
218#97—131no—
219#97—131no—
220C4×C8—131no—
221C4×C8—131no—
222C2×C13—41no—
223C2×C13#53211yescharacteristic
224C2×C13C2×#13711yescharacteristic
225C2×C13#57511yescharacteristic
226D13—81no—
227C2×Q8—131no—
228C2×Q8—261no—
229C2×Q8C22×D1311yescharacteristic
230C2×Q8C22×D1311yescharacteristic
231C2×D4—131no—
232C2×D4—261no—
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—261no—
236C22×C4C22×D1311yescharacteristic
237Q16—22no—
238Q16—262no—
239SD16—262no—
240SD16—262no—
241M16—22no—
242M16—262no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4C22×D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—131no—
270C42—131no—
271C42—131no—
272C42—131no—
273C42—261no—
274C42—261no—
275C42—261no—
276C13#317211yescharacteristic, complemented, Sylow
277C23—261no—
278C23D4×D1311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—261no—
284Q8—261no—
285Q8—522no—
286D4—261no—
287D4—261no—
288D4—522no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—262no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—522no—
304C2×C4—521no—
305C2×C4D4×D1311yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—21no—
308C8—132no—
309C8—261no—
310C8#612912yes—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—521no—
315C22—521no—
316C22—521no—
317C22C2×D4×D1311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—132no—
324C4—261no—
325C4—261no—
326C4—261no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4C2×#612911yescharacteristic
331C4#41×D1311yescharacteristic
332C2—41no—
333C2—1041no—
334C2#1171930111yescharacteristic
335C2D13×#13711yescharacteristic
336C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#470C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#470D13
hypocenterC13#3172
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #11719327C2semidirect
3. C13×#470C2semidirect
4. #11718851C2semidirect
5. Q16×Dic13C2semidirect
7. M16×Dic13C2semidirect
8. #11718713C2semidirect
10. #11718517C2semidirect
11. #11718513C2semidirect
12. #11718458C2semidirect
13. #11718456C2semidirect
14. #11718451C2semidirect
15. #11718449C2semidirect
150. #470D13semidirect
276. C13#3172semidirect

Maximal subgroups

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

subgroupindex
#117193292
#117193272
C13×#4702
#117188512
Q16×Dic132
#117187952
M16×Dic132
#117187132
#117187102
#117185172
#117185132
#117184582
#117184562
#117184512
#117184492
#317213