Finite Group Databasebeta

← #13126808

Subgroups — #13126808

Order 1664.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719529C211yesmaximal, characteristic, complemented
2#11719235C211yesmaximal, characteristic, complemented
3C13×#416C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic, complemented
5#11718775C211yesmaximal, characteristic, complemented
6#11718772C211yesmaximal, characteristic, complemented
7#11718657C211yesmaximal, characteristic, complemented
8#11718479C211yesmaximal, characteristic, complemented
9#11718473C211yesmaximal, characteristic, complemented
10#11718466C211yesmaximal, characteristic, complemented
11#11718458C211yesmaximal, characteristic, complemented
12#11718446C211yesmaximal, characteristic, complemented
13#11718442C211yesmaximal, characteristic, complemented
14#11718432C211yesmaximal, characteristic, complemented
15#11718424C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C22×C8×C13C2211yescharacteristic
19C13×#117C2211yescharacteristic
20#88200C2211yescharacteristic
21#88198C2211yescharacteristic
22C2×#6106C2211yescharacteristic
23#88193—21no—
24#88189—21no—
25D4×Dic13C2211yescharacteristic
26C2×#6104C2211yescharacteristic
27#88184C2211yescharacteristic
28#88183—21no—
29C4×C22⋊D13C2211yescharacteristic
30#88178C2211yescharacteristic
31C2×#6101—21no—
32C2×#6095C2211yescharacteristic
33C2×#6094C2211yescharacteristic
34#88149C2211yescharacteristic
35#88147C2211yescharacteristic
36C4⋊C4×D13C2211yescharacteristic
37#88144C2211yescharacteristic
38#88138—21no—
39#88137—21no—
40#88130—21no—
41C4×D52—21no—
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88061C2211yescharacteristic
50#88060C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C13×#41—22no—
60C13×#41—41no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13C2311yescharacteristic
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71#6129—22no—
72#6129—41no—
73C2×D52—21no—
74C2×D52C2311yescharacteristic
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13C2311yescharacteristic
78C2×Dic26C2311yescharacteristic
79C2×C8×C13—41no—
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C42×C13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13D411yescharacteristic
89#6106—41no—
90#6104—22no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103D411yescharacteristic
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101D411yescharacteristic
106C4×Dic13C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109#6095—41no—
110#6094—41no—
111#3307—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13—21no—
118D4×C13—21no—
119D4×C13—42no—
120D4×C13#4112yes—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—42no—
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2411yescharacteristic
129C22⋊D13—41no—
130C22⋊D13—42no—
131C22⋊D13—81no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140D52—21no—
141D52—21no—
142D52—42no—
143C4×D13—21no—
144C4×D13—21no—
145C4×D13—81no—
146C4×D13—81no—
147Dic26—21no—
148Dic26—21no—
149C8×C13—21no—
150C8×C13—21no—
151#1055—21no—
152#1055—21no—
153#553—131no—
154#547—131no—
155#491—131no—
156#485—131no—
157#483—131no—
158#478—131no—
159#468—131no—
160#465—131no—
161#461—131no—
162#449—131no—
163#449—131no—
164#442—131no—
165#435—131no—
166#417—131no—
167#416D1311yescharacteristic, complemented
168C22×C13—22no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13C22×D411yescharacteristic
175C2×D13—21no—
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C4×C13—21no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13C2×#4111yescharacteristic
186C4×C13H(5,𝔽2)11yescharacteristic
187Dic13—21no—
188Dic13—21no—
189Dic13—21no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193C2×#41—131no—
194C2×#41C2×D1311yescharacteristic
195C2×SD16—131no—
196C2×SD16—131no—
197C2×D8—131no—
198C2×M16—131no—
199C22×C8C2×D1311yescharacteristic
200C4⋊Q8—131no—
201#126—261no—
202#125—131no—
203#123—261no—
204#123—261no—
205#123—261no—
206C22⋊Q8—131no—
207C22⋊Q8—131no—
208#121—131no—
209#121—131no—
210#121—261no—
211#121—261no—
212C4×D4—131no—
213C4×D4—131no—
214C4×D4—131no—
215C4×D4—261no—
216#117C2×D1311yescharacteristic
217C2×C4⋊C4—131no—
218C2×C4⋊C4—261no—
219#107—131no—
220#106—131no—
221#106—131no—
222C4⋊C8—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103C2×D1311yescharacteristic
228#103C2×D1311yescharacteristic
229#102—131no—
230#102—131no—
231#102C2×D1311yescharacteristic
232#102C2×D1311yescharacteristic
233C22⋊C8—131no—
234C22⋊C8—131no—
235#97—131no—
236C2×C13—41no—
237C2×C13—42no—
238C2×C13#54611yescharacteristic
239C2×C13#57511yescharacteristic
240C2×C13#57711yescharacteristic
241D13—41no—
242D13—81no—
243#41—22no—
244#41—41no—
245#41—262no—
246#41—521no—
247C2×Q8—131no—
248C2×Q8C22×D1311yescharacteristic
249C2×D4—21no—
250C2×D4—131no—
251C2×D4—131no—
252C2×D4—261no—
253C2×D4—261no—
254C2×D4—261no—
255C2×D4C22×D1311yescharacteristic
256C22×C4—21no—
257C22×C4—131no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4C22×D1311yescharacteristic
263SD16—521no—
264SD16—521no—
265D8—262no—
266M16—521no—
267C2×C8—41no—
268C2×C8—131no—
269C2×C8—131no—
270C2×C8C22×D1311yescharacteristic
271C2×C8C22×D1311yescharacteristic
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⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4C22×D1311yescharacteristic
283C4⋊C4C22×D1311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—131no—
286C22⋊C4—131no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C42—21no—
294C42—131no—
295C13#330711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—131no—
298C23—261no—
299C23D4×D1311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—261no—
303Q8—261no—
304D4—21no—
305D4—42no—
306D4—261no—
307D4—261no—
308D4—522no—
309D4—521no—
310D4—522no—
311D4—1041no—
312D4#612712yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—131no—
320C2×C4—131no—
321C2×C4—131no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—522no—
328C2×C4—522no—
329C2×C4—1041no—
330C2×C4—1041no—
331C2×C4D4×D1311yescharacteristic
332C2×C4C23×D1311yescharacteristic
333C8—21no—
334C8—21no—
335C8—261no—
336C8—261no—
337C22—21no—
338C22—22no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—261no—
344C22—261no—
345C22—261no—
346C22—521no—
347C22—521no—
348C22—521no—
349C22C2×D4×D1311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—261no—
355C4—261no—
356C4—261no—
357C4—521no—
358C4—521no—
359C4—521no—
360C4C2×#612711yescharacteristic
361C4#8825111yescharacteristic
362C2—41no—
363C2—42no—
364C2—521no—
365C2—1041no—
366C2#1171919511yescharacteristic
367C2#1171947311yescharacteristic
368C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#416C2
socleC22×C13C22×D4
hypercenter#416D13
hypocenterC13#3307
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #11719529C2semidirect
2. #11719235C2semidirect
3. C13×#416C2semidirect
4. #11718899C2semidirect
5. #11718775C2semidirect
6. #11718772C2semidirect
7. #11718657C2semidirect
8. #11718479C2semidirect
9. #11718473C2semidirect
10. #11718466C2semidirect
11. #11718458C2semidirect
12. #11718446C2semidirect
13. #11718442C2semidirect
14. #11718432C2semidirect
15. #11718424C2semidirect
167. #416D13semidirect
295. C13#3307semidirect

Maximal subgroups

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

subgroupindex
#117195292
#117192352
C13×#4162
#117188992
#117187752
#117187722
#117186572
#117184792
#117184732
#117184662
#117184582
#117184462
#117184422
#117184322
#117184242
#330713