Finite Group Databasebeta

← #13127067

Subgroups — #13127067

Order 1664.

448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D42×C13C211yesmaximal, characteristic
2#11719247C211yesmaximal, characteristic, complemented
3#11718879C212yesmaximal, complemented
4#11718876C212yesmaximal, complemented
5#11718736C211yesmaximal, characteristic, complemented
6#11718731C211yesmaximal, characteristic, complemented
7#11718703C212yesmaximal, complemented
8#11718696C212yesmaximal, complemented
9C4×#6105C211yesmaximal, characteristic, complemented
10#11718673C211yesmaximal, characteristic, complemented
11#11718668C211yesmaximal, characteristic, complemented
12C22×D4×C13—21no—
13C22×D4×C13C2212yes—
14C13×#127C2211yescharacteristic
15C13×#121—21no—
16C13×#121C2212yes—
17C13×#120—22no—
18C4×D4×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88190—21no—
21C2×#6105C2211yescharacteristic
22C2×#6105C2212yescomplemented
23#88180C2212yescomplemented
24#88178C2212yescomplemented
25C2×#6099C2212yescomplemented
26#88141—21no—
27#88133—22no—
28#88123C2211yescharacteristic, complemented
29C4×Dic26C2211yescharacteristic, complemented
30#88072C2212yes—
31#88072C2211yescharacteristic
32#88072C2212yescomplemented
33#88072C2212yescomplemented
34#88072C2212yescomplemented
35C22⋊#1055C2212yescomplemented
36#88050C2211yescharacteristic, complemented
37#88048C2211yescharacteristic, complemented
38#88047C2212yescomplemented
39C4⋊#1055C2211yescharacteristic, complemented
40C4×#1055C2211yescharacteristic, complemented
41C24×C13—22no—
42C2×D4×C13—24no—
43C2×D4×C13—22no—
44C2×D4×C13—22no—
45C2×D4×C13—21no—
46C2×D4×C13—21no—
47C2×D4×C13—42no—
48C2×D4×C13—44no—
49C2×D4×C13D411yescharacteristic
50C2×D4×C13C2312yes—
51C2×D4×C13C2311yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13C2312yes—
54C2×Dic26—21no—
55C2×Dic26C2311yescharacteristic
56C13×C4⋊C4D411yescharacteristic
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C13×C22⋊C4—22no—
60C13×C22⋊C4D412yes—
61C42×C13C2311yescharacteristic
62C22⋊Dic13—22no—
63C22⋊Dic13—22no—
64#6105—22no—
65#6105—42no—
66C4⋊Dic13—21no—
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2312yes—
69#6101—21no—
70#6101—22no—
71C4×Dic13—21no—
72C4×Dic13—22no—
73#6099—42no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2312yes—
76C2×#1055C2311yescharacteristic
77#3324—131nomaximal, Sylow
78C23×C13—21no—
79C23×C13—22no—
80C23×C13—44no—
81C23×C13—44no—
82C23×C13—82no—
83C23×C13C2×D412yes—
84D4×C13—22no—
85D4×C13—22no—
86D4×C13—21no—
87D4×C13—22no—
88D4×C13—44no—
89D4×C13—44no—
90D4×C13—42no—
91D4×C13—81no—
92D4×C13#4112yes—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—42no—
97C2×C4×C13C2×D412yes—
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2411yescharacteristic
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104Dic26—21no—
105Dic26—21no—
106Dic26—42no—
107#1055—21no—
108#1055—21no—
109#1055—22no—
110#556—131no—
111D42D1311yescharacteristic
112#486—131no—
113#482—132no—
114#474—131no—
115#468—132no—
116#460—131no—
117#450—132no—
118C4×SD16—131no—
119#436—131no—
120#418—132no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13—22no—
125C22×C13—41no—
126C22×C13—41no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—88no—
131C22×C13C22×D411yescharacteristic
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—41no—
135C4×C13AGL(1,ℤ/8)12yes—
136C4×C13C2×#4111yescharacteristic
137C4×C13H(5,𝔽2)11yescharacteristic
138Dic13—41no—
139Dic13—42no—
140Dic13—41no—
141C22×D4—21no—
142C22×D4C2×D1312yes—
143C2×SD16—131no—
144C2×SD16—132no—
145C2×M16—132no—
146C4⋊Q8—131no—
147#127C2×D1311yescharacteristic
148#126—262no—
149#124—261no—
150C22⋊Q8—132no—
151#121—21no—
152#121C2×D1312yes—
153#120—22no—
154C4×Q8—131no—
155C4×Q8—261no—
156C4×D4C2×D1311yescharacteristic
157C4×D4C2×D1311yescharacteristic
158#117—132no—
159#107—132no—
160#106—131no—
161C4⋊C8—131no—
162#103—131no—
163#102—131no—
164#102—132no—
165#102—132no—
166#102—132no—
167#102—132no—
168C22⋊C8—132no—
169C4×C8—131no—
170C2×C13—42no—
171C2×C13—42no—
172C2×C13—82no—
173C2×C13#54611yescharacteristic
174C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C13#57711yescharacteristic
176C24—22no—
177C2×Q8—131no—
178C2×Q8—261no—
179C2×D4—24no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—42no—
185C2×D4—44no—
186C2×D4C22⋊D1311yescharacteristic
187C2×D4C22×D1312yes—
188C2×D4C22×D1311yescharacteristic
189C22×C4—21no—
190C22×C4C22×D1312yes—
191SD16—262no—
192SD16—522no—
193M16—522no—
194C2×C8—131no—
195C2×C8—131no—
196C2×C8—132no—
197C4⋊C4—131no—
198C4⋊C4—132no—
199C4⋊C4—261no—
200C4⋊C4—262no—
201C4⋊C4—261no—
202C4⋊C4C22⋊D1311yescharacteristic
203C4⋊C4C22×D1311yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—22no—
206C22⋊C4—262no—
207C22⋊C4—262no—
208C22⋊C4C22⋊D1312yes—
209C42—262no—
210C42—261no—
211C42C22×D1311yescharacteristic
212C13#332411yescharacteristic, complemented, Sylow
213C23—21no—
214C23—22no—
215C23—44no—
216C23—44no—
217C23—82no—
218C23C2×C22⋊D1312yes—
219Q8—261no—
220Q8—261no—
221Q8—522no—
222D4—22no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#612912yes—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—261no—
236C2×C4—262no—
237C2×C4—261no—
238C2×C4C2×C22⋊D1312yes—
239C2×C4C2×C22⋊D1311yescharacteristic
240C2×C4C2×C22⋊D1311yescharacteristic
241C2×C4C23×D1311yescharacteristic
242C8—261no—
243C8—261no—
244C8—262no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—88no—
255C22C22×C22⋊D1311yescharacteristic
256C4—22no—
257C4—21no—
258C4—41no—
259C4—522no—
260C4—521no—
261C4—521no—
262C4#8818612yes—
263C4C2×#612911yescharacteristic
264C4#8825111yescharacteristic
265C2—42no—
266C2—42no—
267C2—82no—
268C2C2×#8818611yescharacteristic
269C2#1171951111yescharacteristic
270C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalD42×C13C2
socleC22×C13C22×D4
hypercenterD42D13
hypocenterC13#3324
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
2. #11719247C2semidirect
3. #11718879C2semidirect
4. #11718876C2semidirect
5. #11718736C2semidirect
6. #11718731C2semidirect
7. #11718703C2semidirect
8. #11718696C2semidirect
9. C4×#6105C2semidirect
10. #11718673C2semidirect
11. #11718668C2semidirect
22. C2×#6105C22semidirect
23. #88180C22semidirect
24. #88178C22semidirect
25. C2×#6099C22semidirect
28. #88123C22semidirect
29. C4×Dic26C22semidirect
32. #88072C22semidirect
33. #88072C22semidirect
34. #88072C22semidirect
35. C22⋊#1055C22semidirect
36. #88050C22semidirect
37. #88048C22semidirect
38. #88047C22semidirect
39. C4⋊#1055C22semidirect
40. C4×#1055C22semidirect
212. C13#3324semidirect

Maximal subgroups

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

subgroupindex
D42×C132
#117192472
#117188792
#117188762
#117187362
#117187312
#117187032
#117186962
C4×#61052
#117186732
#117186682
#332413