Finite Group Databasebeta

← #13123714

Subgroups — #13123714

Order 1664.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88170C211yesmaximal, characteristic
2#11719279C211yesmaximal, characteristic, complemented
3#11719251C211yesmaximal, characteristic, complemented
4C4×C13×SD16C211yesmaximal, characteristic, complemented
5SD16×Dic13C211yesmaximal, characteristic, complemented
6#11718691C211yesmaximal, characteristic, complemented
7#11718675C211yesmaximal, characteristic, complemented
8D13×#106C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic, complemented
10#11718464C211yesmaximal, characteristic, complemented
11#11718450C211yesmaximal, characteristic, complemented
12#11718446C211yesmaximal, characteristic, complemented
13#11718432C211yesmaximal, characteristic, complemented
14C4×#6095C211yesmaximal, characteristic, complemented
15#11718350C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23D4×Dic13C2211yescharacteristic
24C2×#6104C2211yescharacteristic
25C4×C22⋊D13—21no—
26C2×#6101—21no—
27#88170C418yescomplemented
28C2×#6095C2211yescharacteristic
29C2×#6094C2211yescharacteristic
30C2×C8×D13C2211yescharacteristic
31#88147—21no—
32#88147C2211yescharacteristic
33C4⋊C4×D13—21no—
34C4⋊C4×D13C2211yescharacteristic
35C4⋊C4×D13C2211yescharacteristic
36#88141C2211yescharacteristic
37#88135—21no—
38#88131—21no—
39C4×D52—21no—
40C4×D52C2211yescharacteristic
41#88126—21no—
42#88126C2211yescharacteristic
43C4×Dic26C2211yescharacteristic
44C13×#106C2211yescharacteristic
45C13×#103C2211yescharacteristic
46C13×#102C2211yescharacteristic
47C4×C8×C13C2211yescharacteristic
48#88075C2211yescharacteristic
49#88072C2211yescharacteristic
50#88061C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88055C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88048C2211yescharacteristic
59#88043C2211yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66#6131—22no—
67#6131C2×C414yescomplemented
68#6129—22no—
69#6129C2×C414yescomplemented
70C2×D52—21no—
71C2×D52C2311yescharacteristic
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13C2311yescharacteristic
78C2×Dic26C2311yescharacteristic
79C13×SD16C2×C414yescomplemented
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C13×C4⋊C4—21no—
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C22⋊C4—21no—
86C42×C13—21no—
87C42×C13C2311yescharacteristic
88C22⋊Dic13—21no—
89#6107C2×C414yescomplemented
90#6104C2×C414yescomplemented
91#6103—21no—
92#6103—21no—
93#6103D411yescharacteristic
94#6103D411yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101D411yescharacteristic
103#6101D411yescharacteristic
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6095C2×C414yescomplemented
111#6094—22no—
112C8×D13C2×C414yescomplemented
113#2952—131nomaximal, Sylow
114C23×C13—21no—
115C22×D13—21no—
116C22×D13C2×D411yescharacteristic
117Q8×C13—21no—
118Q8×C13C22×C412yes—
119D4×C13—21no—
120D4×C13C22×C412yes—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—81no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2411yescharacteristic
128C22⋊D13—24no—
129C2×Dic13—21no—
130C2×Dic13—24no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—81no—
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137D52—24no—
138D52—21no—
139D52C22×C412yes—
140C4×D13—24no—
141C4×D13—81no—
142C4×D13—81no—
143C4×D13—81no—
144C4×D13—81no—
145C4×D13C22×C412yes—
146C4×D13#4112yes—
147Dic26—21no—
148Dic26C22×C412yes—
149C8×C13—21no—
150C8×C13C22×C412yes—
151#1055—21no—
152#1055C22×C412yes—
153C2×#135—131no—
154#520—131no—
155#520—131no—
156#442—131no—
157#442—131no—
158#441—131no—
159#441—131no—
160C4×SD16—131no—
161C4×SD16—131no—
162C4×SD16—131no—
163C4×SD16D1311yescharacteristic, complemented
164C2×#106—131no—
165#417—131no—
166#417—131no—
167#405—131no—
168C22×C13—22no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13C22×D411yescharacteristic
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—22no—
175C2×D13—41no—
176C2×D13—41no—
177C2×D13C4×D412yes—
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13C23×C411yescharacteristic
184C4×C13C2×#4111yescharacteristic
185Dic13—22no—
186Dic13—21no—
187Dic13—21no—
188Dic13—41no—
189Dic13—41no—
190Dic13C4×D412yes—
191C2×#41—131no—
192C2×#41—131no—
193#135—138no—
194C2×Q16—131no—
195C2×SD16—131no—
196C2×SD16C2×D1311yescharacteristic
197C2×D8—131no—
198C2×M16—131no—
199C22×C8—131no—
200C4×Q8—131no—
201C4×Q8—131no—
202C4×Q8—131no—
203C4×Q8C2×D1311yescharacteristic
204C4×D4—131no—
205C4×D4—131no—
206C4×D4—131no—
207C4×D4—261no—
208C4×D4—261no—
209C4×D4—261no—
210C4×D4—261no—
211C4×D4C2×D1311yescharacteristic
212#117—131no—
213#117—261no—
214#117—261no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219#106—131no—
220#106—131no—
221#106—131no—
222#106C2×D1311yescharacteristic
223#103—131no—
224#103—131no—
225#103—131no—
226#103C2×D1311yescharacteristic
227#102—131no—
228#102—131no—
229#102—131no—
230#102C2×D1311yescharacteristic
231#97—131no—
232#97—131no—
233C4×C8—131no—
234C4×C8C2×D1311yescharacteristic
235C2×C13—42no—
236C2×C13C2×C4×D411yescharacteristic
237C2×C13#57711yescharacteristic
238C2×C13#57711yescharacteristic
239D13—22no—
240D13—42no—
241#41—134no—
242#41—134no—
243#41—262no—
244#41—262no—
245C2×Q8—131no—
246C2×Q8C22×D1311yescharacteristic
247C2×D4—131no—
248C2×D4—261no—
249C2×D4—261no—
250C2×D4C22×D1311yescharacteristic
251C22×C4—21no—
252C22×C4—131no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260Q16—134no—
261SD16—134no—
262SD16C4×D1314yescomplemented
263D8—134no—
264M16—262no—
265C2×C8—131no—
266C2×C8—134no—
267C2×C8—131no—
268C2×C8C22×D1311yescharacteristic
269C2×C8C22×D1311yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—131no—
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4C22×D1311yescharacteristic
281C4⋊C4C22×D1311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—131no—
284C22⋊C4—131no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C42—21no—
289C42—131no—
290C42—261no—
291C42—261no—
292C42—261no—
293C42C22×D1311yescharacteristic
294C13#295211yescharacteristic, complemented, Sylow
295C23—21no—
296C23—131no—
297C23—261no—
298Q8—21no—
299Q8—132no—
300Q8—261no—
301Q8C2×C4×D1312yes—
302D4—21no—
303D4—132no—
304D4—264no—
305D4—264no—
306D4—261no—
307D4C2×C4×D1312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—131no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—131no—
316C2×C4—131no—
317C2×C4—264no—
318C2×C4—264no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—1041no—
323C2×C4—1041no—
324C2×C4—1041no—
325C2×C4—1041no—
326C2×C4—1041no—
327C2×C4D4×D1311yescharacteristic
328C2×C4D4×D1311yescharacteristic
329C2×C4C23×D1311yescharacteristic
330C8—21no—
331C8—132no—
332C8—261no—
333C8C2×C4×D1312yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—132no—
338C22—261no—
339C22—261no—
340C22—262no—
341C22—521no—
342C22—521no—
343C22C2×D4×D1311yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—132no—
350C4—261no—
351C4—261no—
352C4—262no—
353C4—521no—
354C4—521no—
355C4C22×C4×D1311yescharacteristic
356C4#41×D1311yescharacteristic
357C2—42no—
358C2—262no—
359C2—522no—
360C2C4×D4×D1311yescharacteristic
361C2#1171946711yescharacteristic
362C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutatorC4×C13C23×C4
FrattiniC2×C4C23×D13
FittingC4×C13×SD16C2
socleC22×C13C22×D4
prime radicalC2×#88170C2
cosocleC2×C4×C13C24
hypercenterC4×SD16D13
hypocenterC13#2952
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #11719279C2semidirect
3. #11719251C2semidirect
4. C4×C13×SD16C2semidirect
5. SD16×Dic13C2semidirect
6. #11718691C2semidirect
7. #11718675C2semidirect
8. D13×#106C2semidirect
9. #11718513C2semidirect
10. #11718464C2semidirect
11. #11718450C2semidirect
12. #11718446C2semidirect
13. #11718432C2semidirect
14. C4×#6095C2semidirect
15. #11718350C2semidirect
27. #88170C4semidirect
67. #6131C2×C4semidirect
69. #6129C2×C4semidirect
79. C13×SD16C2×C4semidirect
89. #6107C2×C4semidirect
90. #6104C2×C4semidirect
110. #6095C2×C4semidirect
112. C8×D13C2×C4semidirect
163. C4×SD16D13semidirect
262. SD16C4×D13semidirect
294. C13#2952semidirect

Maximal subgroups

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

subgroupindex
C2×#881702
#117192792
#117192512
C4×C13×SD162
SD16×Dic132
#117186912
#117186752
D13×#1062
#117185132
#117184642
#117184502
#117184462
#117184322
C4×#60952
#117183502
#295213