Finite Group Databasebeta

← #13124930

Subgroups — #13124930

Order 1664.

444 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C2×D4×Dic13C211yesmaximal, characteristic
2#11719327C211yesmaximal, characteristic, complemented
3C13×#450C211yesmaximal, characteristic
4#11718879C211yesmaximal, characteristic
5#11718825C212yesmaximal, complemented
6#11718823C212yesmaximal, complemented
7#11718705C211yesmaximal, characteristic, complemented
8#11718420C212yesmaximal, complemented
9#11718418C212yesmaximal, complemented
10#11718383C211yesmaximal, characteristic, complemented
11#11718380C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C23×Dic13—21no—
14C2×C13×SD16C2212yes—
15C13×C22⋊Q8C2211yescharacteristic
16C2×C22⋊Dic13—21no—
17Q8×Dic13C2211yescharacteristic, complemented
18#88198C2211yescharacteristic, complemented
19D4×Dic13—21no—
20D4×Dic13—21no—
21D4×Dic13C2212yes—
22D4×Dic13C2212yes—
23C2×#6105C2212yes—
24C2×C4⋊Dic13C2211yescharacteristic
25#88178C2211yescharacteristic
26C2×C4×Dic13C2211yescharacteristic
27#88143—21no—
28#88142C2211yescharacteristic, complemented
29#88141—21no—
30#88141C2211yescharacteristic, complemented
31#88132—21no—
32#88131—21no—
33C13×#102C2212yes—
34C13×C22⋊C8C2211yescharacteristic
35#88075C2212yescomplemented
36#88072C2212yes—
37C22⋊#1055C2211yescharacteristic
38#88058C2212yescomplemented
39#88056C2212yescomplemented
40#88055C2212yescomplemented
41#88054C2212yescomplemented
42#88047C2212yescomplemented
43C24×C13—21no—
44C2×Q8×C13C2311yescharacteristic
45C2×D4×C13—24no—
46C2×D4×C13—21no—
47C2×D4×C13C2312yes—
48C22×C4×C13C2311yescharacteristic
49C22×Dic13—21no—
50C22×Dic13—22no—
51C22×Dic13—22no—
52C22×Dic13—44no—
53C22×Dic13D411yescharacteristic
54C22×Dic13D411yescharacteristic
55C2×Dic26—21no—
56C2×Dic26C2311yescharacteristic
57C13×SD16—24no—
58C2×C8×C13C2312yes—
59C13×C4⋊C4—21no—
60C13×C4⋊C4C2311yescharacteristic
61C13×C22⋊C4—21no—
62C22⋊Dic13—21no—
63C22⋊Dic13—22no—
64C22⋊Dic13—22no—
65#6105—24no—
66C4⋊Dic13—21no—
67C4⋊Dic13—21no—
68C4⋊Dic13C2311yescharacteristic
69C4⋊Dic13C2312yes—
70#6101—21no—
71#6101—21no—
72#6101—21no—
73#6101—21no—
74#6101—21no—
75C4×Dic13—21no—
76C4×Dic13—21no—
77C4×Dic13D411yescharacteristic
78C4×Dic13D411yescharacteristic
79C4×Dic13C2311yescharacteristic
80C4×Dic13C2311yescharacteristic
81C2×#1055C2312yes—
82#3110—131nomaximal, Sylow
83C23×C13—24no—
84C23×C13—22no—
85C23×C13—42no—
86C23×C13—42no—
87C23×C13C2×D411yescharacteristic
88Q8×C13—22no—
89D4×C13—24no—
90D4×C13—22no—
91D4×C13#4114yes—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2411yescharacteristic
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13—44no—
103C2×Dic13—42no—
104C2×Dic13—44no—
105C2×Dic13C2×D411yescharacteristic
106C2×Dic13C2×D411yescharacteristic
107C2×Dic13C2×D411yescharacteristic
108C2×Dic13C2×D411yescharacteristic
109Dic26—22no—
110Dic26—42no—
111C8×C13—22no—
112#1055—22no—
113#533—131no—
114C2×C4×D4—131no—
115#484—131no—
116#484—131no—
117#474—132no—
118#461—132no—
119#450—131no—
120#450D1311yescharacteristic
121#440—132no—
122#440—132no—
123#432—131no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13—24no—
127C22×C13—48no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13#13712yes—
131C22×C13C22×D411yescharacteristic
132C4×C13—21no—
133C4×C13—41no—
134C4×C13—41no—
135C4×C13C2×#4112yes—
136Dic13—21no—
137Dic13—21no—
138Dic13—21no—
139Dic13—41no—
140Dic13—41no—
141Dic13—42no—
142Dic13AGL(1,ℤ/8)12yes—
143C22×D4C2×D1311yescharacteristic
144C23×C4—261no—
145C2×SD16—132no—
146C2×SD16C2×D1312yes—
147C4⋊Q8—131no—
148C4⋊Q8—131no—
149#125—261no—
150C22⋊Q8—131no—
151C22⋊Q8—261no—
152C22⋊Q8C2×D1311yescharacteristic
153C4×Q8—131no—
154C4×Q8—131no—
155C4×Q8—261no—
156C4×D4—132no—
157C4×D4—132no—
158C4×D4—261no—
159C4×D4—261no—
160#117—261no—
161C2×C4⋊C4—131no—
162C2×C22⋊C4—261no—
163C2×C42—131no—
164#107—132no—
165#107—132no—
166C4⋊C8—132no—
167#103—132no—
168#103—132no—
169#102—132no—
170#102C2×D1312yes—
171C22⋊C8—131no—
172C22⋊C8C2×D1311yescharacteristic
173#97—132no—
174C2×C13—22no—
175C2×C13—44no—
176C2×C13#52511yescharacteristic
177C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C13C2×#13711yescharacteristic
179C24—21no—
180C2×Q8—131no—
181C2×Q8—261no—
182C2×Q8C22×D1311yescharacteristic
183C2×D4—24no—
184C2×D4—21no—
185C2×D4C22×D1312yes—
186C22×C4—131no—
187C22×C4—131no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4—261no—
191C22×C4—524no—
192C22×C4C22×D1311yescharacteristic
193SD16—24no—
194SD16—264no—
195C2×C8—132no—
196C2×C8C22×D1312yes—
197C4⋊C4—21no—
198C4⋊C4—131no—
199C4⋊C4—132no—
200C4⋊C4—261no—
201C4⋊C4—261no—
202C4⋊C4—261no—
203C4⋊C4—261no—
204C4⋊C4—261no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C4⋊C4C22×D1311yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—262no—
210C22⋊C4—262no—
211C22⋊C4—261no—
212C42—131no—
213C42—131no—
214C42—131no—
215C42—131no—
216C42—261no—
217C42—261no—
218C13#311011yescharacteristic, complemented, Sylow
219C23—24no—
220C23—22no—
221C23—42no—
222C23—42no—
223C23D4×D1311yescharacteristic
224Q8—22no—
225Q8—262no—
226Q8—522no—
227D4—24no—
228D4—22no—
229D4#612914yes—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—131no—
234C2×C4—131no—
235C2×C4—131no—
236C2×C4—131no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—261no—
240C2×C4—261no—
241C2×C4—262no—
242C2×C4—524no—
243C2×C4—524no—
244C2×C4—522no—
245C2×C4D4×D1311yescharacteristic
246C2×C4C23×D1311yescharacteristic
247C8—22no—
248C8—262no—
249C22—21no—
250C22—21no—
251C22—24no—
252C22—48no—
253C22—42no—
254C22—42no—
255C22#8816912yes—
256C22C2×D4×D1311yescharacteristic
257C4—21no—
258C4—41no—
259C4—41no—
260C4—132no—
261C4—261no—
262C4—261no—
263C4—261no—
264C4—522no—
265C4—521no—
266C4—521no—
267C4C2×#612912yes—
268C2—22no—
269C2—44no—
270C2#1171929111yescharacteristic
271C2C2×#8816911yescharacteristic
272C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#450C2
socleC22×C13C22×D4
prime radicalC22×D4×C13C22
hypercenter#450D13
hypocenterC13#3110
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. #11719327C2semidirect
5. #11718825C2semidirect
6. #11718823C2semidirect
7. #11718705C2semidirect
8. #11718420C2semidirect
9. #11718418C2semidirect
10. #11718383C2semidirect
11. #11718380C2semidirect
17. Q8×Dic13C22semidirect
18. #88198C22semidirect
28. #88142C22semidirect
30. #88141C22semidirect
35. #88075C22semidirect
38. #88058C22semidirect
39. #88056C22semidirect
40. #88055C22semidirect
41. #88054C22semidirect
42. #88047C22semidirect
218. C13#3110semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
#117193272
C13×#4502
#117188792
#117188252
#117188232
#117187052
#117184202
#117184182
#117183832
#117183802
#311013