Finite Group Databasebeta

← #13127337

Subgroups — #13127337

Order 1664.

360 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#11719237C211yesmaximal, characteristic, complemented
2#11719219C211yesmaximal, characteristic, complemented
3C13×#428C211yesmaximal, characteristic, complemented
4#11718796C211yesmaximal, characteristic, complemented
5#11718788C211yesmaximal, characteristic, complemented
6#11718664C211yesmaximal, characteristic, complemented
7#11718628C211yesmaximal, characteristic, complemented
8#11718551C211yesmaximal, characteristic, complemented
9#11718546C211yesmaximal, characteristic, complemented
10#11718544C211yesmaximal, characteristic, complemented
11#11718537C211yesmaximal, characteristic, complemented
12#11718532C211yesmaximal, characteristic, complemented
13#11718530C211yesmaximal, characteristic, complemented
14#11718527C211yesmaximal, characteristic, complemented
15#11718521C211yesmaximal, characteristic, complemented
16C2×C13×M16C2211yescharacteristic
17C13×#117C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19#88184—21no—
20#88184C2211yescharacteristic
21#88184C2211yescharacteristic
22C4×C22⋊D13—21no—
23C4×C22⋊D13C2211yescharacteristic
24C2×D104C2211yescharacteristic
25C2×C8×D13C2211yescharacteristic
26#88152—21no—
27#88149C2211yescharacteristic
28#88149C2211yescharacteristic
29#88148—21no—
30#88147C2211yescharacteristic
31#88147C2211yescharacteristic
32#88146C2211yescharacteristic
33#88146C2211yescharacteristic
34#88144C2211yescharacteristic
35#88142C2211yescharacteristic
36#88139—21no—
37#88138—21no—
38#88129—21no—
39#88126—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88061C2211yescharacteristic
46#88061C2211yescharacteristic
47#88060C2211yescharacteristic
48#88057C2211yescharacteristic
49#88055C2211yescharacteristic
50#88054C2211yescharacteristic
51#88049C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88049C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13—21no—
62C2×C22⋊D13—21no—
63C2×C22⋊D13D411yescharacteristic
64C2×D52—21no—
65C2×D52—21no—
66C2×D52C2311yescharacteristic
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13C2311yescharacteristic
71C2×Dic26—21no—
72C13×M16—22no—
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C42×C13—21no—
82C22⋊Dic13D411yescharacteristic
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103D411yescharacteristic
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103D104—22no—
104C8×D13—22no—
105#3347—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C22×D13—21no—
108C22×D13—21no—
109C22×D13C2×D411yescharacteristic
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—81no—
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C22⋊D13—41no—
120C22⋊D13—42no—
121C22⋊D13—81no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127D52—21no—
128D52—21no—
129D52—21no—
130D52—21no—
131D52—81no—
132D52—81no—
133C4×D13—21no—
134C4×D13—21no—
135C4×D13—42no—
136C4×D13—81no—
137Dic26—81no—
138C8×C13—21no—
139C8×C13#4112yes—
140#1055—21no—
141#1055—21no—
142#555—131no—
143#553—131no—
144#501—131no—
145#482—131no—
146#482—131no—
147#482—131no—
148#480—131no—
149#478—131no—
150#474—131no—
151#469—131no—
152#466—131no—
153#442—131no—
154#435—131no—
155#428D1311yescharacteristic, complemented
156#427—131no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13C22×D411yescharacteristic
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—21no—
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—41no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13C2×#4111yescharacteristic
176C4×C132−1+411yescharacteristic
177Dic13—21no—
178Dic13—21no—
179Dic13—21no—
180Dic13—41no—
181Dic13—41no—
182C2×D8—131no—
183C2×M16C2×D1311yescharacteristic
184C22×C8—131no—
185C4⋊Q8—131no—
186#126—261no—
187#125—131no—
188#124—261no—
189#124—261no—
190#123—261no—
191#121—131no—
192#121—131no—
193#121—131no—
194#121—131no—
195#121—261no—
196#121—261no—
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—261no—
201#117—131no—
202#117—131no—
203#117—261no—
204#117C2×D1311yescharacteristic
205C2×C4⋊C4C2×D1311yescharacteristic
206#107—131no—
207#107—131no—
208#107—131no—
209#107C2×D1311yescharacteristic
210#107C2×D1311yescharacteristic
211#106—131no—
212#106—131no—
213#106C2×D1311yescharacteristic
214#106C2×D1311yescharacteristic
215C4⋊C8—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222C22⋊C8—131no—
223C22⋊C8—131no—
224#97—131no—
225C2×C13—41no—
226C2×C13#54711yescharacteristic
227C2×C13#57511yescharacteristic
228C2×C13#57611yescharacteristic
229D13—41no—
230D13—81no—
231D13—81no—
232C2×Q8—261no—
233C2×D4—131no—
234C2×D4—131no—
235C2×D4—131no—
236C2×D4—261no—
237C2×D4—261no—
238C2×D4—261no—
239C2×D4—261no—
240C22×C4—21no—
241C22×C4—131no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4C22×D1311yescharacteristic
245D8—262no—
246M16—22no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8—262no—
250C2×C8C22×D1311yescharacteristic
251C2×C8C22×D1311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4C22×D1311yescharacteristic
260C4⋊C4C22×D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—131no—
265C22⋊C4—131no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C42—21no—
275C42—131no—
276C42—261no—
277C42—261no—
278C13#334711yescharacteristic, complemented, Sylow
279C23—131no—
280C23—261no—
281C23—261no—
282C23D4×D1311yescharacteristic
283Q8—1041no—
284D4—261no—
285D4—261no—
286D4—261no—
287D4—261no—
288D4—521no—
289D4—522no—
290D4—1041no—
291D4—1041no—
292D4—1041no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—131no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—522no—
308C2×C4—1041no—
309C2×C4D4×D1311yescharacteristic
310C2×C4C23×D1311yescharacteristic
311C8—21no—
312C8—261no—
313C8—261no—
314C8#612712yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—261no—
319C22—261no—
320C22—261no—
321C22—521no—
322C22—521no—
323C22—521no—
324C22—521no—
325C22—521no—
326C22—521no—
327C22C2×D4×D1311yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—261no—
334C4—261no—
335C4—261no—
336C4—521no—
337C4—521no—
338C4C2×#612711yescharacteristic
339C4#8825411yescharacteristic
340C2—41no—
341C2—521no—
342C2—1041no—
343C2—1041no—
344C2#1171921211yescharacteristic
345C2#1171947911yescharacteristic
346C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
hypercenter#428D13
hypocenterC13#3347
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #11719237C2semidirect
2. #11719219C2semidirect
3. C13×#428C2semidirect
4. #11718796C2semidirect
5. #11718788C2semidirect
6. #11718664C2semidirect
7. #11718628C2semidirect
8. #11718551C2semidirect
9. #11718546C2semidirect
10. #11718544C2semidirect
11. #11718537C2semidirect
12. #11718532C2semidirect
13. #11718530C2semidirect
14. #11718527C2semidirect
15. #11718521C2semidirect
155. #428D13semidirect
278. C13#3347semidirect

Maximal subgroups

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

subgroupindex
#117192372
#117192192
C13×#4282
#117187962
#117187882
#117186642
#117186282
#117185512
#117185462
#117185442
#117185372
#117185322
#117185302
#117185272
#117185212
#334713