Finite Group Databasebeta

← #13124902

Subgroups — #13124902

Order 1664.

390 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719327C211yesmaximal, characteristic, complemented
2#11719227C211yesmaximal, characteristic
3C13×#485C211yesmaximal, characteristic, complemented
4#11718708C211yesmaximal, characteristic
5#11718657C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718534C211yesmaximal, characteristic, complemented
8#11718515C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic, complemented
10#11718479C211yesmaximal, characteristic, complemented
11#11718454C211yesmaximal, characteristic, complemented
12#11718451C211yesmaximal, characteristic, complemented
13#11718449C211yesmaximal, characteristic, complemented
14#11718394C211yesmaximal, characteristic
15#11718379C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C13×C22⋊Q8C2211yescharacteristic
18C13×#117C2211yescharacteristic
19Q8×Dic13C2211yescharacteristic
20#88198C2211yescharacteristic
21C2×#6107C2211yescharacteristic
22C2×#6106C2211yescharacteristic
23#88178C2211yescharacteristic
24C2×C4×Dic13C2211yescharacteristic
25C2×Dic52C2211yescharacteristic
26C2×#6095C2211yescharacteristic
27#88147C2211yescharacteristic
28#88147C2211yescharacteristic
29#88143—21no—
30#88142C2211yescharacteristic
31#88141—21no—
32#88141C2211yescharacteristic
33#88141C2211yescharacteristic
34#88141C2211yescharacteristic
35#88135—21no—
36#88135—21no—
37#88132—21no—
38#88131—21no—
39#88126—21no—
40C42×D13—21no—
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×C22⋊C8C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
47#88061C2211yescharacteristic
48#88056C2211yescharacteristic
49#88054C2211yescharacteristic
50#88054C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13—21no—
62C22×Dic13D411yescharacteristic
63C22×Dic13D411yescharacteristic
64#6127—22no—
65#6127—22no—
66C2×D52C2311yescharacteristic
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×Dic26—21no—
71C2×Dic26C2311yescharacteristic
72C2×Dic26C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C42×C13—21no—
82C22⋊Dic13—21no—
83#6107—22no—
84#6106—22no—
85#6103—21no—
86#6103—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13C2311yescharacteristic
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13D411yescharacteristic
101C4×Dic13D411yescharacteristic
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106Dic52—22no—
107#6095—22no—
108#3107—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111Q8×C13—21no—
112Q8×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—24no—
122C2×Dic13—21no—
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131D52—21no—
132D52#4112yes—
133C4×D13—24no—
134C4×D13—42no—
135C4×D13—42no—
136Dic26—21no—
137Dic26—21no—
138Dic26—21no—
139Dic26—42no—
140Dic26#4112yes—
141C8×C13—21no—
142C8×C13—21no—
143#1055—21no—
144#1055—21no—
145#533—131no—
146C4×#41—131no—
147#485—131no—
148#485D1311yescharacteristic, complemented
149#475—131no—
150#474—131no—
151#462—131no—
152#461—131no—
153#452—131no—
154#452—131no—
155C4×Q16—131no—
156C4×Q16—131no—
157C4×SD16—131no—
158C4×SD16—131no—
159#431—131no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13C22×D411yescharacteristic
164C2×D13—22no—
165C2×D13—41no—
166C2×D13—41no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13C2×#4111yescharacteristic
173C4×C13C2×#4111yescharacteristic
174Dic13—22no—
175Dic13—21no—
176Dic13—21no—
177Dic13—41no—
178Dic13—41no—
179Dic13#13512yes—
180Dic13#13712yes—
181C2×#41—131no—
182C2×Q16—131no—
183C2×Q16—131no—
184C2×SD16—131no—
185C2×SD16—131no—
186C4⋊Q8—131no—
187C4⋊Q8—131no—
188#125—261no—
189C22⋊Q8—131no—
190C22⋊Q8—261no—
191C22⋊Q8C2×D1311yescharacteristic
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×Q8—261no—
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—261no—
200C4×D4—261no—
201#117—261no—
202#117—261no—
203#117C2×D1311yescharacteristic
204C2×C42—131no—
205C2×C42—261no—
206#107—131no—
207#107C2×D1311yescharacteristic
208#106—131no—
209#106C2×D1311yescharacteristic
210C4⋊C8—131no—
211C4⋊C8—131no—
212#103—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#103C2×D1311yescharacteristic
217#103C2×D1311yescharacteristic
218#102—131no—
219#102—131no—
220C22⋊C8—131no—
221C22⋊C8C2×D1311yescharacteristic
222C4×C8—131no—
223C4×C8—131no—
224C2×C13—41no—
225C2×C13#52511yescharacteristic
226C2×C13C2×#13511yescharacteristic
227C2×C13C2×#13711yescharacteristic
228D13—42no—
229#41—262no—
230#41—262no—
231C2×Q8—131no—
232C2×Q8—131no—
233C2×Q8—261no—
234C2×Q8C22×D1311yescharacteristic
235C2×D4—131no—
236C2×D4—261no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4C22×D1311yescharacteristic
243Q16—262no—
244Q16—262no—
245SD16—262no—
246SD16—262no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8C22×D1311yescharacteristic
250C2×C8C22×D1311yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—131no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4C22×D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C4⋊C4C22×D1311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—21no—
270C42—131no—
271C42—131no—
272C42—131no—
273C42—131no—
274C42—261no—
275C42—261no—
276C42—261no—
277C42—261no—
278C13#310711yescharacteristic, complemented, Sylow
279C23—261no—
280C23D4×D1311yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—132no—
284Q8—261no—
285Q8—261no—
286Q8—261no—
287Q8—522no—
288D4—132no—
289D4—264no—
290D4—261no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—131no—
301C2×C4—264no—
302C2×C4—262no—
303C2×C4—262no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4D4×D1311yescharacteristic
310C2×C4C23×D1311yescharacteristic
311C8—21no—
312C8—21no—
313C8—261no—
314C8—261no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—262no—
319C22—521no—
320C22—521no—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—132no—
328C4—132no—
329C4—261no—
330C4—261no—
331C4—262no—
332C4—521no—
333C4—521no—
334C4#41×D1311yescharacteristic
335C4#41×D1311yescharacteristic
336C2—41no—
337C2—522no—
338C2#1171936111yescharacteristic
339C2D13×#13511yescharacteristic
340C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#485C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenter#485D13
hypocenterC13#3107
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #11719327C2semidirect
3. C13×#485C2semidirect
5. #11718657C2semidirect
6. #11718551C2semidirect
7. #11718534C2semidirect
8. #11718515C2semidirect
9. #11718513C2semidirect
10. #11718479C2semidirect
11. #11718454C2semidirect
12. #11718451C2semidirect
13. #11718449C2semidirect
15. #11718379C2semidirect
148. #485D13semidirect
278. C13#3107semidirect

Maximal subgroups

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

subgroupindex
#117193272
#117192272
C13×#4852
#117187082
#117186572
#117185512
#117185342
#117185152
#117185132
#117184792
#117184542
#117184512
#117184492
#117183942
#117183792
#310713