Finite Group Databasebeta

← #13126814

Subgroups — #13126814

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#11719270C211yesmaximal, characteristic, complemented
2#11719256C211yesmaximal, characteristic, complemented
3C13×#435C211yesmaximal, characteristic, complemented
4#11718795C211yesmaximal, characteristic, complemented
5#11718794C211yesmaximal, characteristic, complemented
6#11718775C211yesmaximal, characteristic, complemented
7#11718774C211yesmaximal, characteristic, complemented
8#11718508C211yesmaximal, characteristic, complemented
9#11718502C211yesmaximal, characteristic, complemented
10#11718395C211yesmaximal, characteristic, complemented
11#11718395C211yesmaximal, characteristic, complemented
12#11718384C211yesmaximal, characteristic, complemented
13#11718382C211yesmaximal, characteristic, complemented
14#11718372C211yesmaximal, characteristic, complemented
15#11718364C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C22×C8×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21#88193—21no—
22#88192—21no—
23#88184C2211yescharacteristic
24#88184C2211yescharacteristic
25#88180C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27#88178C2211yescharacteristic
28#88178C2211yescharacteristic
29C2×D104C2211yescharacteristic
30C2×#6095C2211yescharacteristic
31C2×#6095C2211yescharacteristic
32#88152—21no—
33C4⋊C4×D13—21no—
34#88137—21no—
35#88137—21no—
36#88137—21no—
37#88135—21no—
38C4×D52C2211yescharacteristic
39C4×D52C2211yescharacteristic
40#88124C2211yescharacteristic
41#88123C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45C13×#97C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C2×D4×C13D411yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67#6127—22no—
68#6127—22no—
69#6127—41no—
70#6127—41no—
71C2×D52C2311yescharacteristic
72C2×D52C2311yescharacteristic
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×Dic26C2311yescharacteristic
78C2×Dic26C2311yescharacteristic
79C13×M16—41no—
80C2×C8×C13—41no—
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C2×C8×C13C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C13×C4⋊C4D411yescharacteristic
86C13×C22⋊C4D411yescharacteristic
87C13×C22⋊C4D411yescharacteristic
88C42×C13C2311yescharacteristic
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103#6101—21no—
104#6101—21no—
105#6101—21no—
106#6101—21no—
107C4×Dic13—21no—
108D104—22no—
109#6095—41no—
110#6095—41no—
111#3307—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13—21no—
116D4×C13—41no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2411yescharacteristic
126C22⋊D13—42no—
127C22⋊D13—42no—
128C22⋊D13—42no—
129C22⋊D13—81no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—81no—
137D52—21no—
138D52—21no—
139D52—21no—
140D52#4112yes—
141C4×D13—42no—
142C4×D13—42no—
143C4×D13—42no—
144C4×D13—81no—
145Dic26—21no—
146Dic26—21no—
147Dic26—21no—
148Dic26—21no—
149C8×C13—21no—
150C8×C13—21no—
151C8×C13—21no—
152C8×C13—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#435D1311yescharacteristic, complemented
166#417—131no—
167#416—131no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13C22×D411yescharacteristic
175C2×D13—22no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13C2×#4111yescharacteristic
186C4×C13H(5,𝔽2)11yescharacteristic
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193C2×#41—131no—
194C2×#41—131no—
195C2×SD16—131no—
196C2×SD16—131no—
197C2×D8—131no—
198C2×M16C2×D1311yescharacteristic
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—261no—
215C4×D4C2×D1311yescharacteristic
216#117—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—261no—
219#107—131no—
220#106—131no—
221#106—131no—
222C4⋊C8C2×D1311yescharacteristic
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103—131no—
228#103—131no—
229#102—131no—
230#102—131no—
231#102—131no—
232#102—131no—
233C22⋊C8C2×D1311yescharacteristic
234C22⋊C8C2×D1311yescharacteristic
235#97C2×D1311yescharacteristic
236C2×C13—41no—
237C2×C13—41no—
238C2×C13#54611yescharacteristic
239C2×C13#57511yescharacteristic
240C2×C13#57711yescharacteristic
241D13—42no—
242D13—81no—
243#41—262no—
244#41—262no—
245#41—521no—
246#41—521no—
247C2×Q8—131no—
248C2×Q8—131no—
249C2×D4—131no—
250C2×D4—131no—
251C2×D4—261no—
252C2×D4—261no—
253C2×D4—261no—
254C2×D4—261no—
255C2×D4D5211yescharacteristic
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263SD16—521no—
264SD16—521no—
265D8—262no—
266M16—41no—
267C2×C8—41no—
268C2×C8C22×D1311yescharacteristic
269C2×C8C22×D1311yescharacteristic
270C2×C8C22×D1311yescharacteristic
271C2×C8C22×D1311yescharacteristic
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—131no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4D5211yescharacteristic
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4D5211yescharacteristic
292C22⋊C4D5211yescharacteristic
293C42—261no—
294C42C22×D1311yescharacteristic
295C13#330711yescharacteristic, complemented, Sylow
296C23—261no—
297C23—261no—
298C23C2×D5211yescharacteristic
299C23C2×D5211yescharacteristic
300Q8—261no—
301Q8—261no—
302Q8—261no—
303Q8—261no—
304D4—41no—
305D4—132no—
306D4—261no—
307D4—261no—
308D4—261no—
309D4—522no—
310D4—522no—
311D4—522no—
312D4—1041no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—522no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—1041no—
327C2×C4—1041no—
328C2×C4C2×D5211yescharacteristic
329C2×C4C2×D5211yescharacteristic
330C2×C4C2×D5211yescharacteristic
331C2×C4C2×D5211yescharacteristic
332C2×C4C23×D1311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—262no—
344C22—521no—
345C22—521no—
346C22—521no—
347C22—521no—
348C22—521no—
349C22C22×D5211yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—521no—
355C4—521no—
356C4—521no—
357C4—521no—
358C4—521no—
359C4—521no—
360C4#8825111yescharacteristic
361C4#41×D1311yescharacteristic
362C2—41no—
363C2—41no—
364C2—522no—
365C2—1041no—
366C2#1171925911yescharacteristic
367C2#1171945311yescharacteristic
368C2#1171945611yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#435C2
socleC22×C13C22×D4
hypercenter#435D13
hypocenterC13#3307
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #11719270C2semidirect
2. #11719256C2semidirect
3. C13×#435C2semidirect
4. #11718795C2semidirect
5. #11718794C2semidirect
6. #11718775C2semidirect
7. #11718774C2semidirect
8. #11718508C2semidirect
9. #11718502C2semidirect
10. #11718395C2semidirect
11. #11718395C2semidirect
12. #11718384C2semidirect
13. #11718382C2semidirect
14. #11718372C2semidirect
15. #11718364C2semidirect
165. #435D13semidirect
295. C13#3307semidirect

Maximal subgroups

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

subgroupindex
#117192702
#117192562
C13×#4352
#117187952
#117187942
#117187752
#117187742
#117185082
#117185022
#117183952
#117183842
#117183822
#117183722
#117183642
#330713