Finite Group Databasebeta

← #13124695

Subgroups — #13124695

Order 1664.

376 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719434C211yesmaximal, characteristic, complemented
2#11719279C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718683C211yesmaximal, characteristic, complemented
6#11718532C211yesmaximal, characteristic, complemented
7#11718531C211yesmaximal, characteristic, complemented
8#11718522C211yesmaximal, characteristic, complemented
9D13×#106C211yesmaximal, characteristic, complemented
10#11718508C211yesmaximal, characteristic, complemented
11#11718500C211yesmaximal, characteristic, complemented
12#11718465C211yesmaximal, characteristic
13#11718464C211yesmaximal, characteristic
14#11718457C211yesmaximal, characteristic, complemented
15#11718452C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C13×C4⋊Q8C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19#88200—21no—
20Q8×Dic13C2211yescharacteristic
21#88198—21no—
22C2×#6094C2211yescharacteristic
23C2×C8×D13C2211yescharacteristic
24#88150—21no—
25#88147—21no—
26#88147C2211yescharacteristic
27#88146C2211yescharacteristic
28C4⋊C4×D13—21no—
29C4⋊C4×D13C2211yescharacteristic
30C4⋊C4×D13C2211yescharacteristic
31#88144C2211yescharacteristic
32#88143—21no—
33#88142C2211yescharacteristic
34C4×D52—21no—
35C4×D52C2211yescharacteristic
36#88126—21no—
37#88126C2211yescharacteristic
38#88124C2211yescharacteristic
39C13×#106C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88058C2211yescharacteristic
49#88057C2211yescharacteristic
50#88054C2211yescharacteristic
51#88054C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61#6131—22no—
62#6131Q814yescomplemented
63C2×D52—21no—
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13C2311yescharacteristic
71C2×Dic26—21no—
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C42×C13—21no—
80C42×C13C2311yescharacteristic
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103D411yescharacteristic
85#6103D411yescharacteristic
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98#6101D411yescharacteristic
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6094—22no—
105C8×D13—22no—
106#3084—131nomaximal, Sylow
107C22×D13—21no—
108C22×D13C2×D411yescharacteristic
109Q8×C13—21no—
110Q8×C13—81no—
111Q8×C13C2×Q812yes—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125D52—24no—
126D52—21no—
127D52C2×Q812yes—
128C4×D13—24no—
129C4×D13—81no—
130C4×D13—81no—
131C4×D13—81no—
132C4×D13—81no—
133C4×D13C2×Q812yes—
134C4×D13#4112yes—
135Dic26—81no—
136C8×C13—21no—
137C8×C13—21no—
138#1055—21no—
139#1055—21no—
140#544—131no—
141#520—131no—
142#479—131no—
143#479—131no—
144#478—131no—
145#478—131no—
146#476—131no—
147#476—131no—
148#475—131no—
149#475D1311yescharacteristic, complemented
150#428—131no—
151C2×#106—131no—
152#424—131no—
153#417—131no—
154#416—131no—
155C22×C13C22×D411yescharacteristic
156C2×D13—21no—
157C2×D13—21no—
158C2×D13—22no—
159C2×D13—41no—
160C2×D13—41no—
161C2×D13C22⋊Q812yes—
162C4×C13—22no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13C22×Q811yescharacteristic
169C4×C13C2×#4111yescharacteristic
170Dic13—21no—
171Dic13—21no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175Dic13C22⋊Q812yes—
176C2×#41—131no—
177C2×M16—131no—
178C22×C8—131no—
179C4⋊Q8—131no—
180C4⋊Q8—261no—
181C4⋊Q8C2×D1311yescharacteristic
182#125—131no—
183#125—131no—
184#125—261no—
185C22⋊Q8—261no—
186C22⋊Q8—261no—
187C4×Q8—131no—
188C4×Q8C2×D1311yescharacteristic
189C4×D4—131no—
190C4×D4—131no—
191C4×D4—261no—
192C4×D4—261no—
193#117—131no—
194#117—131no—
195#117—261no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—261no—
199#107—131no—
200#107—131no—
201#106—131no—
202#106—131no—
203#106—131no—
204#106—131no—
205#106C2×D1311yescharacteristic
206#106C2×D1311yescharacteristic
207C4⋊C8—131no—
208C4⋊C8—131no—
209C4⋊C8—131no—
210C4⋊C8C2×D1311yescharacteristic
211#103—131no—
212#103—131no—
213#103C2×D1311yescharacteristic
214#103C2×D1311yescharacteristic
215#102—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219C2×C13C2×C22⋊Q811yescharacteristic
220C2×C13#57711yescharacteristic
221C2×C13#57711yescharacteristic
222D13—22no—
223D13—42no—
224#41—134no—
225#41—262no—
226C2×Q8—21no—
227C2×Q8—261no—
228C2×Q8C22×D1311yescharacteristic
229C2×D4—131no—
230C2×D4—261no—
231C22×C4—131no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—261no—
237M16—262no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—262no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
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⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C4⋊C4C22×D1311yescharacteristic
261C22⋊C4—131no—
262C22⋊C4—131no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C42—21no—
267C42—131no—
268C42—261no—
269C42—261no—
270C42C22×D1311yescharacteristic
271C13#308411yescharacteristic, complemented, Sylow
272C23—131no—
273C23—261no—
274Q8—21no—
275Q8—81no—
276Q8—1041no—
277Q8Q8×D1312yes—
278D4—132no—
279D4—264no—
280D4—261no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—131no—
286C2×C4—132no—
287C2×C4—132no—
288C2×C4—131no—
289C2×C4—131no—
290C2×C4—264no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—1041no—
295C2×C4—1041no—
296C2×C4—1041no—
297C2×C4—1041no—
298C2×C4D4×D1311yescharacteristic
299C2×C4D4×D1311yescharacteristic
300C2×C4C23×D1311yescharacteristic
301C8—21no—
302C8—21no—
303C8—261no—
304C8—261no—
305C22—132no—
306C22—261no—
307C22—261no—
308C22—262no—
309C22—521no—
310C22—521no—
311C22C2×D4×D1311yescharacteristic
312C4—21no—
313C4—21no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—132no—
319C4—261no—
320C4—261no—
321C4—521no—
322C4—521no—
323C4—521no—
324C4C2×Q8×D1311yescharacteristic
325C4#41×D1311yescharacteristic
326C2—262no—
327C2—522no—
328C2D13×C22⋊Q811yescharacteristic
329C2#1171946711yescharacteristic
330C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radicalC2×#6131C22
hypercenter#475D13
hypocenterC13#3084
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #11719434C2semidirect
3. C13×#475C2semidirect
4. #11718745C2semidirect
5. #11718683C2semidirect
6. #11718532C2semidirect
7. #11718531C2semidirect
8. #11718522C2semidirect
9. D13×#106C2semidirect
10. #11718508C2semidirect
11. #11718500C2semidirect
14. #11718457C2semidirect
15. #11718452C2semidirect
62. #6131Q8semidirect
149. #475D13semidirect
271. C13#3084semidirect

Maximal subgroups

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

subgroupindex
#117194342
#117192792
C13×#4752
#117187452
#117186832
#117185322
#117185312
#117185222
D13×#1062
#117185082
#117185002
#117184652
#117184642
#117184572
#117184522
#308413