Finite Group Databasebeta

← #13125440

Subgroups — #13125440

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#11719285C211yesmaximal, characteristic
2#11719283C211yesmaximal, characteristic, complemented
3C4×C13×Q16C211yesmaximal, characteristic, complemented
4#11718851C211yesmaximal, characteristic, complemented
5#11718850C211yesmaximal, characteristic, complemented
6C4×#6107C211yesmaximal, characteristic, complemented
7C4×#6106C211yesmaximal, characteristic, complemented
8#11718547C211yesmaximal, characteristic
9#11718537C211yesmaximal, characteristic, complemented
10#11718477C211yesmaximal, characteristic, complemented
11#11718473C211yesmaximal, characteristic
12#11718458C211yesmaximal, characteristic, complemented
13#11718456C211yesmaximal, characteristic, complemented
14C4×#6095C211yesmaximal, characteristic, complemented
15C4×#6094C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C4×Q8×C13C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19#88201C2211yescharacteristic
20#88200C2211yescharacteristic
21#88200C2211yescharacteristic
22#88198C2211yescharacteristic
23C2×#6107C2211yescharacteristic
24C2×#6106C2211yescharacteristic
25C2×#6095C2211yescharacteristic
26C2×#6094C2211yescharacteristic
27C2×#6094C2211yescharacteristic
28#88152—21no—
29#88151C2211yescharacteristic
30#88150—21no—
31#88149C2211yescharacteristic
32#88148—21no—
33#88144C2211yescharacteristic
34#88143—21no—
35#88142C2211yescharacteristic
36C4×D52—21no—
37C4×D52C2211yescharacteristic
38#88126—21no—
39#88126—21no—
40C42×D13C2211yescharacteristic
41C4×Dic26—21no—
42C4×Dic26C2211yescharacteristic
43C13×#107C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46C4×C8×C13C2211yescharacteristic
47#88075C2211yescharacteristic
48#88075C2211yescharacteristic
49#88061C2211yescharacteristic
50#88057C2211yescharacteristic
51#88056C2211yescharacteristic
52#88055C2211yescharacteristic
53#88055C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D52—21no—
62C2×D52C2311yescharacteristic
63C2×C4×D13—21no—
64C2×C4×D13D411yescharacteristic
65C2×C4×D13D411yescharacteristic
66C2×C4×D13C2311yescharacteristic
67C2×Dic26—21no—
68C2×Dic26C2311yescharacteristic
69C13×Q16—22no—
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C42×C13—21no—
77C42×C13—21no—
78C42×C13C2311yescharacteristic
79#6107—22no—
80#6106—22no—
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13D411yescharacteristic
101C4×Dic13D411yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#6095—22no—
106#6094—22no—
107#6094—22no—
108#3172—131nomaximal, Sylow
109C22×D13—21no—
110C22×D13C2×D411yescharacteristic
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×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128D52—21no—
129D52—21no—
130D52—42no—
131C4×D13—22no—
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—41no—
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#470—131no—
151#468—131no—
152#468—131no—
153C4×Q16—131no—
154C4×Q16D1311yescharacteristic, complemented
155C4×SD16—131no—
156C4×SD16—131no—
157C4×M16—131no—
158C22×C13C22×D411yescharacteristic
159C2×D13—21no—
160C2×D13—21no—
161C2×D13—21no—
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×C13#13712yes—
171C4×C13C2×#4111yescharacteristic
172C4×C13C2×#4111yescharacteristic
173Dic13—21no—
174Dic13—21no—
175Dic13—21no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×Q16—131no—
180C2×Q16C2×D1311yescharacteristic
181C2×SD16—131no—
182C2×SD16—131no—
183C2×M16—131no—
184C2×M16—131no—
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—131no—
194C22⋊Q8—131no—
195C22⋊Q8—261no—
196#121—131no—
197C4×Q8—131no—
198C4×Q8—261no—
199C4×Q8C2×D1311yescharacteristic
200C4×Q8C2×D1311yescharacteristic
201C4×D4—131no—
202C4×D4—261no—
203#117—261no—
204#117—261no—
205C2×C42—131no—
206#107—131no—
207#107C2×D1311yescharacteristic
208#106—131no—
209#106—131no—
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×C8C2×D1311yescharacteristic
222C2×C13#53211yescharacteristic
223C2×C13C2×#13711yescharacteristic
224C2×C13#57511yescharacteristic
225D13—41no—
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—131no—
236C22×C4—261no—
237Q16—22no—
238Q16—262no—
239SD16—262no—
240SD16—262no—
241M16—262no—
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—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—21no—
270C42—21no—
271C42—131no—
272C42—131no—
273C42—131no—
274C42—261no—
275C42C22×D1311yescharacteristic
276C13#317211yescharacteristic, complemented, Sylow
277C23—131no—
278C23—261no—
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—131no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—262no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—521no—
303C2×C4—522no—
304C2×C4D4×D1311yescharacteristic
305C2×C4D4×D1311yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—21no—
308C8—132no—
309C8—261no—
310C8#612712yes—
311C22—261no—
312C22—261no—
313C22—261no—
314C22—521no—
315C22—521no—
316C22—521no—
317C22C2×D4×D1311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—261no—
324C4—261no—
325C4—261no—
326C4—521no—
327C4—521no—
328C4—521no—
329C4#8817212yes—
330C4C2×#612711yescharacteristic
331C4#41×D1311yescharacteristic
332C2—521no—
333C2—1041no—
334C2#1171925311yescharacteristic
335C2C2×#8817211yescharacteristic
336C2#1171947311yescharacteristic
subgroupG/H
centerC2×C4D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×Q16C2
socleC22×C13C22×D4
prime radical#88149C22
hypercenterC4×Q16D13
hypocenterC13#3172
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #11719283C2semidirect
3. C4×C13×Q16C2semidirect
4. #11718851C2semidirect
5. #11718850C2semidirect
6. C4×#6107C2semidirect
7. C4×#6106C2semidirect
9. #11718537C2semidirect
10. #11718477C2semidirect
12. #11718458C2semidirect
13. #11718456C2semidirect
14. C4×#6095C2semidirect
15. C4×#6094C2semidirect
154. C4×Q16D13semidirect
276. C13#3172semidirect

Maximal subgroups

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

subgroupindex
#117192852
#117192832
C4×C13×Q162
#117188512
#117188502
C4×#61072
C4×#61062
#117185472
#117185372
#117184772
#117184732
#117184582
#117184562
C4×#60952
C4×#60942
#317213