Finite Group Databasebeta

← #13125520

Subgroups — #13125520

Order 1664.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719324C211yesmaximal, characteristic, complemented
2#11719308C211yesmaximal, characteristic, complemented
3C13×#469C211yesmaximal, characteristic, complemented
4#11718815C211yesmaximal, characteristic, complemented
5D8×Dic13C211yesmaximal, characteristic, complemented
6#11718795C211yesmaximal, characteristic, complemented
7#11718783C211yesmaximal, characteristic, complemented
8#11718702C211yesmaximal, characteristic, complemented
9#11718699C211yesmaximal, characteristic, complemented
10#11718517C211yesmaximal, characteristic, complemented
11#11718513C211yesmaximal, characteristic, complemented
12#11718446C211yesmaximal, characteristic, complemented
13#11718429C211yesmaximal, characteristic, complemented
14#11718421C211yesmaximal, characteristic, complemented
15#11718418C211yesmaximal, characteristic, complemented
16C2×C13×D8C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C13×#121C2211yescharacteristic
19C13×#121C2211yescharacteristic
20#88194C2211yescharacteristic
21#88193—21no—
22#88192—21no—
23#88190—21no—
24#88190C2211yescharacteristic
25#88189—21no—
26D4×Dic13C2211yescharacteristic
27D4×Dic13C2211yescharacteristic
28C2×#6105C2211yescharacteristic
29C2×#6104C2211yescharacteristic
30#88184C2211yescharacteristic
31#88180C2211yescharacteristic
32#88178C2211yescharacteristic
33C22×#1055C2211yescharacteristic
34C2×#6095C2211yescharacteristic
35#88147C2211yescharacteristic
36#88144C2211yescharacteristic
37#88142C2211yescharacteristic
38#88141C2211yescharacteristic
39#88140—21no—
40#88137—21no—
41#88133—21no—
42#88132—21no—
43C13×#106C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88061C2211yescharacteristic
49#88058C2211yescharacteristic
50#88056C2211yescharacteristic
51#88055C2211yescharacteristic
52#88055C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×Dic26—21no—
72C2×Dic26C2311yescharacteristic
73C13×D8—22no—
74C13×M16—22no—
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13D411yescharacteristic
87C22⋊Dic13D411yescharacteristic
88#6105—22no—
89#6104—22no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13D411yescharacteristic
94C4⋊Dic13D411yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104C2×#1055—22no—
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107#6095—22no—
108#3179—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13—21no—
111C23×C13C2×D411yescharacteristic
112C22×D13—21no—
113D4×C13—21no—
114D4×C13—21no—
115D4×C13—21no—
116D4×C13—21no—
117D4×C13—81no—
118D4×C13—81no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C22⋊D13—81no—
126C22⋊D13—81no—
127C22⋊D13—81no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—81no—
132C2×Dic13—81no—
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137D52—21no—
138D52—21no—
139C4×D13—81no—
140Dic26—21no—
141Dic26—21no—
142Dic26—81no—
143C8×C13—21no—
144C8×C13#4112yes—
145#1055—21no—
146#1055#4112yes—
147#542—131no—
148#540—131no—
149#501—131no—
150#496—131no—
151#488—131no—
152#486—131no—
153#469D1311yescharacteristic, complemented
154#468—131no—
155#466—131no—
156#465—131no—
157#442—131no—
158#440—131no—
159C4×SD16—131no—
160C4×D8—131no—
161#405—131no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13C22×D411yescharacteristic
172C2×D13—41no—
173C2×D13—41no—
174C2×D13—41no—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13C2×#4111yescharacteristic
179C4×C13C2×#4111yescharacteristic
180Dic13—21no—
181Dic13—21no—
182Dic13—21no—
183Dic13—21no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187C2×SD16—131no—
188C2×SD16—131no—
189C2×D8—131no—
190C2×D8C2×D1311yescharacteristic
191C2×M16C2×D1311yescharacteristic
192C22×C8—131no—
193C4⋊Q8—131no—
194#127—131no—
195#126—261no—
196#125—131no—
197#124—131no—
198#124—261no—
199#123—261no—
200#123—261no—
201#123—261no—
202C22⋊Q8—131no—
203C22⋊Q8—261no—
204#121—131no—
205#121—261no—
206#121—261no—
207#121C2×D1311yescharacteristic
208#121C2×D1311yescharacteristic
209C4×Q8—131no—
210C4×D4—131no—
211C4×D4—131no—
212C4×D4—131no—
213#117—131no—
214#107—131no—
215#107—131no—
216#106—131no—
217#106C2×D1311yescharacteristic
218#103—131no—
219#103—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223#102—131no—
224#102C2×D1311yescharacteristic
225#102C2×D1311yescharacteristic
226#97—131no—
227#97—131no—
228C4×C8—131no—
229C4×C8—131no—
230C2×C13—41no—
231C2×C13—81no—
232C2×C13—81no—
233C2×C13#53211yescharacteristic
234C2×C13#57611yescharacteristic
235C2×C13#57711yescharacteristic
236D13—81no—
237C2×Q8—131no—
238C2×Q8—261no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—131no—
242C2×D4—261no—
243C2×D4—261no—
244C2×D4—261no—
245C2×D4C22×D1311yescharacteristic
246C2×D4C22×D1311yescharacteristic
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4C22×D1311yescharacteristic
251SD16—262no—
252SD16—262no—
253D8—22no—
254D8—262no—
255M16—22no—
256C2×C8—131no—
257C2×C8—131no—
258C2×C8—262no—
259C2×C8C22×D1311yescharacteristic
260C2×C8C22×D1311yescharacteristic
261C4⋊C4—131no—
262C4⋊C4—131no—
263C4⋊C4—131no—
264C4⋊C4—131no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4C22×D1311yescharacteristic
271C4⋊C4C22×D1311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—131no—
275C22⋊C4—131no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C42—131no—
284C42—131no—
285C42—261no—
286C13#317911yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—261no—
290C23D4×D1311yescharacteristic
291Q8—261no—
292Q8—261no—
293Q8—1041no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—261no—
301D4—261no—
302D4—1041no—
303D4—1041no—
304D4—1041no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—1041no—
317C2×C4—1041no—
318C2×C4—1041no—
319C2×C4D4×D1311yescharacteristic
320C2×C4C23×D1311yescharacteristic
321C8—21no—
322C8—132no—
323C8—261no—
324C8#612912yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—521no—
335C22—521no—
336C22—521no—
337C22C2×D4×D1311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—261no—
342C4—261no—
343C4—261no—
344C4—261no—
345C4—521no—
346C4—521no—
347C4—521no—
348C4C2×#612911yescharacteristic
349C4#41×D1311yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—1041no—
354C2#1171930111yescharacteristic
355C2#1171947911yescharacteristic
356C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#469C2
socleC22×C13C22×D4
hypercenter#469D13
hypocenterC13#3179
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #11719324C2semidirect
2. #11719308C2semidirect
3. C13×#469C2semidirect
4. #11718815C2semidirect
5. D8×Dic13C2semidirect
6. #11718795C2semidirect
7. #11718783C2semidirect
8. #11718702C2semidirect
9. #11718699C2semidirect
10. #11718517C2semidirect
11. #11718513C2semidirect
12. #11718446C2semidirect
13. #11718429C2semidirect
14. #11718421C2semidirect
15. #11718418C2semidirect
153. #469D13semidirect
286. C13#3179semidirect

Maximal subgroups

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

subgroupindex
#117193242
#117193082
C13×#4692
#117188152
D8×Dic132
#117187952
#117187832
#117187022
#117186992
#117185172
#117185132
#117184462
#117184292
#117184212
#117184182
#317913