Finite Group Databasebeta

← #13126699

Subgroups — #13126699

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719337C211yesmaximal, characteristic, complemented
2#11719212C211yesmaximal, characteristic
3C13×#483C211yesmaximal, characteristic, complemented
4#11718709C211yesmaximal, characteristic, complemented
5C2×#88050C211yesmaximal, characteristic, complemented
6#11718525C211yesmaximal, characteristic, complemented
7#11718523C211yesmaximal, characteristic, complemented
8#11718515C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic, complemented
10#11718479C211yesmaximal, characteristic, complemented
11#11718467C211yesmaximal, characteristic, complemented
12D13×#103C211yesmaximal, characteristic, complemented
13#11718453C211yesmaximal, characteristic, complemented
14#11718399C211yesmaximal, characteristic, complemented
15#11718386C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×#6127—21no—
18C22×Dic26C2211yescharacteristic
19C13×C22⋊Q8C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21#88198C2211yescharacteristic
22C2×#6106C2211yescharacteristic
23#88184C2211yescharacteristic
24#88183—21no—
25C4×C22⋊D13C2211yescharacteristic
26C22×#1055C2211yescharacteristic
27C2×#6095C2211yescharacteristic
28C2×#6095C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88151C2211yescharacteristic
31#88150—21no—
32#88150—21no—
33#88149C2211yescharacteristic
34#88148—21no—
35#88147C2211yescharacteristic
36C4⋊C4×D13C2211yescharacteristic
37#88142—21no—
38#88142C2211yescharacteristic
39#88141C2211yescharacteristic
40#88135—21no—
41#88132—21no—
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46C13×C22⋊C8C2211yescharacteristic
47#88075C2211yescharacteristic
48#88060C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88049C2211yescharacteristic
58#88048C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13D411yescharacteristic
64C22×Dic13—21no—
65Q8×D13—22no—
66Q8×D13—41no—
67#6127—44no—
68C2×D52—21no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13C2311yescharacteristic
74C2×Dic26—22no—
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26—41no—
79C2×Dic26C2311yescharacteristic
80C2×Dic26C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4C2311yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C22⋊C4—21no—
89C22⋊Dic13D411yescharacteristic
90#6106—41no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103D411yescharacteristic
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101D411yescharacteristic
104C4×Dic13—21no—
105C4×Dic13C2311yescharacteristic
106C2×#1055—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109#6095—22no—
110#6095—41no—
111C8×D13—41no—
112#3298—131nomaximal, Sylow
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—42no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C22⋊D13—42no—
128C22⋊D13SD1614yescomplemented
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—42no—
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136D52—21no—
137D52—21no—
138D52—42no—
139C4×D13—21no—
140C4×D13—21no—
141C4×D13—42no—
142C4×D13—42no—
143C4×D13—42no—
144Dic26—21no—
145Dic26—21no—
146Dic26—21no—
147Dic26—42no—
148Dic26—42no—
149Dic26—42no—
150Dic26#4112yescomplemented
151C8×C13—21no—
152C8×C13—21no—
153#1055—21no—
154#1055—21no—
155D4×Q8—131no—
156#547—131no—
157#487—131no—
158#483—131no—
159#483D1311yescharacteristic, complemented
160#475—131no—
161#465—131no—
162#465—131no—
163#461—131no—
164#448—131no—
165#448—131no—
166C4×SD16—131no—
167C8×D4—131no—
168C2×#103—131no—
169C2×#103—131no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13C2×SD1612yes—
173C22×C13C22×D411yescharacteristic
174C2×D13—21no—
175C2×D13—21no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C2×D13C2×SD1612yes—
180C4×C13—21no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13C2×#4111yescharacteristic
186C4×C13H(5,𝔽2)11yescharacteristic
187Dic13—22no—
188Dic13—21no—
189Dic13—21no—
190Dic13—41no—
191Dic13—41no—
192Dic13C2×SD1612yes—
193C2×#41—261no—
194C22×Q8—131no—
195C22×Q8—131no—
196C2×SD16—131no—
197C2×SD16—131no—
198C2×SD16—131no—
199C22×C8—131no—
200C22×C8—131no—
201C4⋊Q8—131no—
202C4⋊Q8—131no—
203C4⋊Q8—261no—
204#123—261no—
205#123—261no—
206C22⋊Q8—131no—
207C22⋊Q8—261no—
208C22⋊Q8—261no—
209C22⋊Q8—261no—
210C22⋊Q8C2×D1311yescharacteristic
211#121—131no—
212#121—131no—
213C4×Q8—131no—
214C4×D4—131no—
215C4×D4—131no—
216C4×D4—261no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4C2×D1311yescharacteristic
219#106—131no—
220#106C2×D1311yescharacteristic
221#106C2×D1311yescharacteristic
222C4⋊C8—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103—131no—
228#103—131no—
229#103—131no—
230#103C2×D1311yescharacteristic
231#103C2×D1311yescharacteristic
232#102—131no—
233C22⋊C8—131no—
234C22⋊C8C2×D1311yescharacteristic
235C4×C8—131no—
236C2×C13—22no—
237C2×C13#54611yescharacteristic
238C2×C13C22×SD1611yescharacteristic
239C2×C13#57811yescharacteristic
240D13—22no—
241D13—81no—
242#41—524no—
243C2×Q8—131no—
244C2×Q8—131no—
245C2×Q8—261no—
246C2×Q8—261no—
247C2×Q8—262no—
248C2×Q8—261no—
249C2×Q8—262no—
250C2×Q8—521no—
251C2×Q8—521no—
252C2×Q8C22×D1311yescharacteristic
253C2×D4—131no—
254C2×D4—131no—
255C2×D4—261no—
256C2×D4—261no—
257C22×C4—21no—
258C22×C4—131no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4C22×D1311yescharacteristic
264SD16—262no—
265SD16—521no—
266SD16—521no—
267C2×C8—131no—
268C2×C8—131no—
269C2×C8—521no—
270C2×C8—521no—
271C2×C8C22×D1311yescharacteristic
272C2×C8C22×D1311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—131no—
276C4⋊C4—131no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4C22×D1311yescharacteristic
284C4⋊C4C22×D1311yescharacteristic
285C4⋊C4C22×D1311yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—131no—
288C22⋊C4—131no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C42—131no—
294C42—261no—
295C13#329811yescharacteristic, complemented, Sylow
296C23—131no—
297C23—261no—
298C23D4×D1311yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—132no—
302Q8—261no—
303Q8—261no—
304Q8—261no—
305Q8—522no—
306Q8—522no—
307Q8—522no—
308D4—134no—
309D4—261no—
310D4—261no—
311D4—522no—
312D4—522no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—131no—
321C2×C4—131no—
322C2×C4—131no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—522no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4D4×D1311yescharacteristic
333C2×C4C23×D1311yescharacteristic
334C8—21no—
335C8—21no—
336C8—261no—
337C8—261no—
338C22—21no—
339C22—21no—
340C22—132no—
341C22—261no—
342C22—261no—
343C22—521no—
344C22—521no—
345C22—521no—
346C22SD16×D1312yes—
347C22C2×D4×D1311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—132no—
354C4—261no—
355C4—261no—
356C4—262no—
357C4—521no—
358C4—521no—
359C4#41×D1311yescharacteristic
360C4#8825611yescharacteristic
361C2—22no—
362C2—262no—
363C2—1041no—
364C2#1171935911yescharacteristic
365C2C2×SD16×D1311yescharacteristic
366C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#483C2
socleC22×C13C22×D4
prime radical#11719212C2
hypercenter#483D13
hypocenterC13#3298
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #11719337C2semidirect
3. C13×#483C2semidirect
4. #11718709C2semidirect
5. C2×#88050C2semidirect
6. #11718525C2semidirect
7. #11718523C2semidirect
8. #11718515C2semidirect
9. #11718513C2semidirect
10. #11718479C2semidirect
11. #11718467C2semidirect
12. D13×#103C2semidirect
13. #11718453C2semidirect
14. #11718399C2semidirect
15. #11718386C2semidirect
128. C22⋊D13SD16semidirect
150. Dic26#41semidirect
159. #483D13semidirect
295. C13#3298semidirect

Maximal subgroups

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

subgroupindex
#117193372
#117192122
C13×#4832
#117187092
C2×#880502
#117185252
#117185232
#117185152
#117185132
#117184792
#117184672
D13×#1032
#117184532
#117183992
#117183862
#329813