Finite Group Databasebeta

← #13127732

Subgroups — #13127732

Order 1664.

374 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719432C211yesmaximal, characteristic, complemented
2#11719395C211yesmaximal, characteristic, complemented
3C13×#501C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718727C211yesmaximal, characteristic, complemented
6#11718552C211yesmaximal, characteristic, complemented
7#11718551C211yesmaximal, characteristic, complemented
8#11718537C211yesmaximal, characteristic, complemented
9#11718533C211yesmaximal, characteristic
10#11718531C211yesmaximal, characteristic, complemented
11#11718531C211yesmaximal, characteristic, complemented
12#11718530C211yesmaximal, characteristic
13#11718516C211yesmaximal, characteristic, complemented
14#11718372C211yesmaximal, characteristic
15#11718362C211yesmaximal, characteristic, complemented
16C2×Q8×D13—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C13×#125C2211yescharacteristic
19#88200—21no—
20C2×D104C2211yescharacteristic
21#88151—21no—
22#88150—21no—
23#88150—21no—
24#88150—21no—
25#88150—21no—
26#88147C2211yescharacteristic
27#88147C2211yescharacteristic
28#88147C2211yescharacteristic
29#88147C2211yescharacteristic
30C4⋊C4×D13—21no—
31#88144C2211yescharacteristic
32#88142C2211yescharacteristic
33#88142C2211yescharacteristic
34#88142C2211yescharacteristic
35C4×D52C2211yescharacteristic
36C4×D52C2211yescharacteristic
37C4×Dic26C2211yescharacteristic
38C13×#107C2211yescharacteristic
39C13×#107C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#97C2211yescharacteristic
43#88061C2211yescharacteristic
44#88061C2211yescharacteristic
45#88057C2211yescharacteristic
46#88055C2211yescharacteristic
47#88054C2211yescharacteristic
48#88054C2211yescharacteristic
49C8×Dic13C2211yescharacteristic
50#88049C2211yescharacteristic
51#88049C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60Q8×D13—44no—
61C2×D52C2311yescharacteristic
62C2×D52C2311yescharacteristic
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26D411yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C42×C13C2311yescharacteristic
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13D411yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98#6101D411yescharacteristic
99C4×Dic13C2311yescharacteristic
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103D104Q814yescomplemented
104#3384—131nomaximal, Sylow
105C22×D13—21no—
106C22×D13—21no—
107Q8×C13—42no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2411yescharacteristic
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13C2×D411yescharacteristic
118C2×Dic13C2×D411yescharacteristic
119C2×Dic13C2×D411yescharacteristic
120C2×Dic13C2×D411yescharacteristic
121D52—21no—
122D52—21no—
123D52C2×Q812yes—
124D52C2×Q812yescomplemented
125C4×D13—42no—
126C4×D13—42no—
127C4×D13—42no—
128C4×D13—42no—
129C4×D13—81no—
130C4×D13—81no—
131Dic26—22no—
132Dic26—42no—
133Dic26—42no—
134Dic26—81no—
135C8×C13—21no—
136C8×C13C2×Q812yescomplemented
137#1055—21no—
138#1055—21no—
139#554—131no—
140D4×Q8—131no—
141#501—131no—
142#501D1311yescharacteristic, complemented
143#498—131no—
144#478—131no—
145#478—131no—
146#476—131no—
147#476—131no—
148#476—131no—
149#474—131no—
150#446—131no—
151#442—131no—
152#442—131no—
153C4×D8—131no—
154C22×C13C22×D411yescharacteristic
155C2×D13—22no—
156C2×D13—22no—
157C2×D13—41no—
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—41no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13C22×Q811yescharacteristic
168C4×C132−1+411yescharacteristic
169Dic13—21no—
170Dic13—21no—
171Dic13—21no—
172Dic13—41no—
173Dic13—41no—
174Dic13AGL(1,ℤ/8)12yes—
175C22×Q8—261no—
176C2×D8—131no—
177C4⋊Q8—131no—
178C4⋊Q8—131no—
179C4⋊Q8—131no—
180C4⋊Q8C2×D1311yescharacteristic
181#125—131no—
182#125C2×D1311yescharacteristic
183C22⋊Q8—261no—
184C22⋊Q8—261no—
185C22⋊Q8—261no—
186C22⋊Q8—261no—
187C22⋊Q8—261no—
188C22⋊Q8—261no—
189C4×Q8—131no—
190C4×D4—131no—
191C4×D4—131no—
192C4×D4—131no—
193C4×D4—131no—
194C4×D4—131no—
195C4×D4—131no—
196C2×C4⋊C4—261no—
197#107—131no—
198#107C2×D1311yescharacteristic
199#107C2×D1311yescharacteristic
200#106—131no—
201#106—131no—
202#106—131no—
203#106—131no—
204#106C2×D1311yescharacteristic
205#106C2×D1311yescharacteristic
206C4⋊C8—131no—
207C4⋊C8—131no—
208C4⋊C8—131no—
209#102—131no—
210#102—131no—
211#102—131no—
212#102—131no—
213#102—131no—
214#102—131no—
215#97—131no—
216#97C2×D1311yescharacteristic
217C4×C8—131no—
218C2×C13D4×Q811yescharacteristic
219C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C13#57711yescharacteristic
221D13—42no—
222D13—42no—
223C2×Q8—21no—
224C2×Q8—131no—
225C2×Q8—261no—
226C2×Q8—261no—
227C2×Q8—261no—
228C2×Q8—524no—
229C2×D4—131no—
230C2×D4—131no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—261no—
237D8—134no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8C22×D1311yescharacteristic
241C2×C8C22×D1311yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C4⋊C4C22×D1311yescharacteristic
258C4⋊C4C22×D1311yescharacteristic
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C42—131no—
266C42—131no—
267C42C22×D1311yescharacteristic
268C13#338411yescharacteristic, complemented, Sylow
269C23—261no—
270C23—261no—
271Q8—42no—
272Q8—262no—
273Q8—522no—
274Q8—522no—
275Q8—1041no—
276D4—132no—
277D4—132no—
278D4—261no—
279D4—261no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—522no—
293C2×C4—522no—
294C2×C4—1041no—
295C2×C4—1041no—
296C2×C4D4×D1311yescharacteristic
297C2×C4D4×D1311yescharacteristic
298C2×C4C23×D1311yescharacteristic
299C8—21no—
300C8—261no—
301C8—261no—
302C8Q8×D1312yescomplemented
303C22—262no—
304C22—262no—
305C22—521no—
306C22—521no—
307C22—521no—
308C22—521no—
309C22C2×D4×D1311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—132no—
317C4—261no—
318C4—261no—
319C4—261no—
320C4—521no—
321C4—521no—
322C4C2×Q8×D1311yescharacteristic
323C4#8825411yescharacteristic
324C2—522no—
325C2—522no—
326C2#1171943211yescharacteristic
327C2D13×AGL(1,ℤ/8)11yescharacteristic
328C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radicalC2×D104C22
hypercenter#501D13
hypocenterC13#3384
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #11719432C2semidirect
2. #11719395C2semidirect
3. C13×#501C2semidirect
4. #11718745C2semidirect
5. #11718727C2semidirect
6. #11718552C2semidirect
7. #11718551C2semidirect
8. #11718537C2semidirect
10. #11718531C2semidirect
11. #11718531C2semidirect
13. #11718516C2semidirect
15. #11718362C2semidirect
103. D104Q8semidirect
124. D52C2×Q8semidirect
136. C8×C13C2×Q8semidirect
142. #501D13semidirect
268. C13#3384semidirect
302. C8Q8×D13semidirect

Maximal subgroups

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

subgroupindex
#117194322
#117193952
C13×#5012
#117187452
#117187272
#117185522
#117185512
#117185372
#117185332
#117185312
#117185302
#117185162
#117183722
#117183622
#338413