Finite Group Databasebeta

← #13127568

Subgroups — #13127568

Order 1664.

382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719390C211yesmaximal, characteristic, complemented
2#11719258C211yesmaximal, characteristic
3C13×#478C211yesmaximal, characteristic, complemented
4#11718728C211yesmaximal, characteristic, complemented
5#11718679C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718550C211yesmaximal, characteristic, complemented
8#11718532C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic, complemented
10#11718509C211yesmaximal, characteristic, complemented
11#11718489C211yesmaximal, characteristic, complemented
12#11718425C211yesmaximal, characteristic, complemented
13#11718423C211yesmaximal, characteristic, complemented
14#11718423C211yesmaximal, characteristic, complemented
15#11718421C211yesmaximal, characteristic, complemented
16C2×#6127—21no—
17C13×#125C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19#88194C2211yescharacteristic
20#88194C2211yescharacteristic
21C2×#6105C2211yescharacteristic
22#88184—21no—
23C2×#6095C2211yescharacteristic
24C2×#6095C2211yescharacteristic
25#88147C2211yescharacteristic
26#88147C2211yescharacteristic
27#88144C2211yescharacteristic
28#88143—21no—
29#88143—21no—
30#88142—21no—
31#88142C2211yescharacteristic
32#88141—21no—
33#88141C2211yescharacteristic
34#88141C2211yescharacteristic
35#88138—21no—
36#88138—21no—
37#88128C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic
45#88072C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88055C2211yescharacteristic
49#88054C2211yescharacteristic
50#88054C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88050C2211yescharacteristic
53#88049C2211yescharacteristic
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×D4×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C2×C22⋊D13—21no—
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65#6127—44no—
66C2×D52—21no—
67C2×D52—21no—
68C2×D52C2311yescharacteristic
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×Dic26—21no—
73C2×Dic26D411yescharacteristic
74C2×Dic26C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C42×C13C2311yescharacteristic
84#6105—22no—
85#6103—21no—
86#6103—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13D411yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101D411yescharacteristic
96#6101D411yescharacteristic
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6095—22no—
105#6095—22no—
106#3368—131nomaximal, Sylow
107C23×C13—21no—
108C22×D13—21no—
109C22×D13—21no—
110D4×C13—21no—
111D4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—42no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C22⋊D13—42no—
120C22⋊D13—42no—
121C22⋊D13—81no—
122C22⋊D13—81no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129D52—21no—
130D52—21no—
131D52—21no—
132D52—21no—
133D52—42no—
134D52—81no—
135C4×D13—42no—
136C4×D13—42no—
137Dic26—21no—
138Dic26—22no—
139Dic26—42no—
140Dic26#4112yescomplemented
141C8×C13—21no—
142C8×C13—21no—
143#1055—21no—
144#1055—21no—
145#557—131no—
146#550—131no—
147#490—131no—
148#490—131no—
149#486—131no—
150#478—131no—
151#478D1311yescharacteristic, complemented
152#474—131no—
153#460—131no—
154#460—131no—
155#460—131no—
156#446—131no—
157#440—131no—
158#440—131no—
159C4×SD16—131no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C22×D411yescharacteristic
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—41no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13C2×#4111yescharacteristic
176C4×C132−1+411yescharacteristic
177Dic13—22no—
178Dic13—21no—
179Dic13—21no—
180Dic13—21no—
181Dic13—41no—
182Dic13AGL(1,ℤ/8)12yes—
183C2×#41—261no—
184C2×SD16—131no—
185C2×SD16—131no—
186C2×SD16—131no—
187C4⋊Q8—131no—
188C4⋊Q8—261no—
189#127—131no—
190#127—131no—
191#127—131no—
192#125—131no—
193#125—261no—
194#125—261no—
195#125C2×D1311yescharacteristic
196#121—261no—
197#121—261no—
198#121—261no—
199C4×Q8—131no—
200C4×Q8—131no—
201C4×Q8—131no—
202C4×Q8—131no—
203C4×Q8—261no—
204C4×D4—131no—
205C4×D4—131no—
206C4×D4C2×D1311yescharacteristic
207#107—131no—
208#107C2×D1311yescharacteristic
209#106C2×D1311yescharacteristic
210C4⋊C8—131no—
211C4⋊C8—131no—
212C4⋊C8C2×D1311yescharacteristic
213#103—131no—
214#102—131no—
215#102—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#102—131no—
221#102C2×D1311yescharacteristic
222#102C2×D1311yescharacteristic
223#97—131no—
224#97—131no—
225C4×C8—131no—
226C2×C13—81no—
227C2×C13#54811yescharacteristic
228C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
229C2×C13#57711yescharacteristic
230D13—81no—
231D13—81no—
232#41—524no—
233C2×Q8—131no—
234C2×Q8—131no—
235C2×Q8—261no—
236C2×D4—131no—
237C2×D4—131no—
238C2×D4—261no—
239C2×D4—261no—
240C2×D4—261no—
241C2×D4—261no—
242C2×D4—261no—
243C2×D4—261no—
244C2×D4C22×D1311yescharacteristic
245C22×C4—21no—
246C22×C4—261no—
247C22×C4—261no—
248SD16—262no—
249SD16—262no—
250SD16—262no—
251C2×C8—131no—
252C2×C8—131no—
253C2×C8C22×D1311yescharacteristic
254C2×C8C22×D1311yescharacteristic
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—131no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4C22×D1311yescharacteristic
268C4⋊C4C22×D1311yescharacteristic
269C4⋊C4C22×D1311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C42—131no—
274C42—131no—
275C42—261no—
276C42—261no—
277C42—261no—
278C42C22×D1311yescharacteristic
279C13#336811yescharacteristic, complemented, Sylow
280C23—21no—
281C23—261no—
282C23—261no—
283Q8—132no—
284Q8—262no—
285Q8—261no—
286Q8—522no—
287D4—21no—
288D4—21no—
289D4—261no—
290D4—261no—
291D4—261no—
292D4—261no—
293D4—522no—
294D4—522no—
295D4—522no—
296D4—1041no—
297D4—1041no—
298D4—1041no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—131no—
306C2×C4—131no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—522no—
310C2×C4—522no—
311C2×C4D4×D1311yescharacteristic
312C2×C4D4×D1311yescharacteristic
313C2×C4C23×D1311yescharacteristic
314C8—21no—
315C8—21no—
316C8—261no—
317C8—261no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—521no—
322C22—521no—
323C22—521no—
324C22—521no—
325C22—521no—
326C22—521no—
327C22C2×D4×D1311yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—132no—
334C4—261no—
335C4—261no—
336C4—261no—
337C4—262no—
338C4—521no—
339C4#8825411yescharacteristic
340C4#41×D1311yescharacteristic
341C2—81no—
342C2—1041no—
343C2—1041no—
344C2#1171933811yescharacteristic
345C2#1171947511yescharacteristic
346C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#478C2
socleC22×C13C22×D4
prime radical#11719258C2
hypercenter#478D13
hypocenterC13#3368
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #11719390C2semidirect
3. C13×#478C2semidirect
4. #11718728C2semidirect
5. #11718679C2semidirect
6. #11718551C2semidirect
7. #11718550C2semidirect
8. #11718532C2semidirect
9. #11718513C2semidirect
10. #11718509C2semidirect
11. #11718489C2semidirect
12. #11718425C2semidirect
13. #11718423C2semidirect
14. #11718423C2semidirect
15. #11718421C2semidirect
140. Dic26#41semidirect
151. #478D13semidirect
279. C13#3368semidirect

Maximal subgroups

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

subgroupindex
#117193902
#117192582
C13×#4782
#117187282
#117186792
#117185512
#117185502
#117185322
#117185132
#117185092
#117184892
#117184252
#117184232
#117184212
#336813