Finite Group Databasebeta

← #13126643

Subgroups — #13126643

Order 1664.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C13×#547C211yesmaximal, characteristic, complemented
2D4×D52C211yesmaximal, characteristic, complemented
3#11718749C211yesmaximal, characteristic, complemented
4#11718748C211yesmaximal, characteristic, complemented
5#11718699C212yesmaximal, complemented
6#11718697C212yesmaximal, complemented
7#11718676C211yesmaximal, characteristic, complemented
8C4×#6104C211yesmaximal, characteristic, complemented
9D4×#1055C211yesmaximal, characteristic, complemented
10#11718628C212yesmaximal, complemented
11C2×#88049C212yesmaximal, complemented
12C2×C13×#41—21no—
13C2×D4×D13—21no—
14C22×D52C2212yes—
15C13×C4⋊Q8C2211yescharacteristic, complemented
16C13×#123—22no—
17C13×C22⋊Q8—21no—
18C13×#121C2212yescomplemented
19C4×D4×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic, complemented
21C2×C13×C4⋊C4C2212yescomplemented
22C2×#6104C2211yescharacteristic
23C2×#6104C2212yescomplemented
24#88184C2212yes—
25C22×#1055C2212yescomplemented
26#88149—21no—
27#88136—22no—
28#88128C2211yescharacteristic
29C4×D52C2211yescharacteristic
30#88072C2211yescharacteristic, complemented
31C22⋊#1055C2212yescomplemented
32#88049C2211yescharacteristic
33#88049C2212yes—
34#88049C2212yescomplemented
35#88049C2212yescomplemented
36#88049C2212yescomplemented
37#88047C2211yescharacteristic, complemented
38#88047C2212yescomplemented
39C4⋊#1055C2211yescharacteristic, complemented
40C4×#1055C2211yescharacteristic, complemented
41C23×D13—22no—
42C13×#41—44no—
43C2×Q8×C13—21no—
44C2×D4×C13—22no—
45C2×D4×C13D411yescharacteristic
46C2×D4×C13C2311yescharacteristic
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13C2312yes—
50C2×C22⋊D13—22no—
51D4×D13—44no—
52C2×D52—24no—
53C2×D52—21no—
54C2×D52—22no—
55C2×D52—21no—
56C2×D52—42no—
57C2×D52C2312yes—
58C2×D52C2311yescharacteristic
59C2×C4×D13—21no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—21no—
62C13×C4⋊C4D411yescharacteristic
63C13×C4⋊C4C2311yescharacteristic
64C13×C4⋊C4C2312yes—
65C13×C22⋊C4—21no—
66C13×C22⋊C4—22no—
67C13×C22⋊C4D412yes—
68C42×C13C2311yescharacteristic
69#6104—22no—
70#6104—42no—
71#6103—21no—
72#6103—22no—
73C4⋊Dic13C2311yescharacteristic
74C2×#1055—42no—
75C2×#1055C2311yescharacteristic
76C2×#1055C2312yes—
77C2×#1055C2311yescharacteristic
78#3294—131nomaximal, Sylow
79C23×C13—21no—
80C23×C13C2×D412yes—
81C22×D13—21no—
82C22×D13—22no—
83C22×D13—44no—
84C22×D13—44no—
85C22×D13—82no—
86Q8×C13—42no—
87D4×C13—21no—
88D4×C13—21no—
89D4×C13—44no—
90D4×C13D814yescomplemented
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—44no—
96C2×C4×C13—42no—
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2×D412yes—
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2411yescharacteristic
101C22⋊D13—44no—
102C2×Dic13—21no—
103D52—22no—
104D52—21no—
105D52—22no—
106D52—44no—
107D52—42no—
108D52—81no—
109D52#4112yescomplemented
110C4×D13—42no—
111#1055—21no—
112#1055—21no—
113#1055—22no—
114#547D1311yescharacteristic, complemented
115D42—131no—
116#486—131no—
117#480—132no—
118#474—131no—
119#466—132no—
120#459—131no—
121#447—132no—
122C4×D8—131no—
123C8×D4—131no—
124C2×#102—132no—
125C22×C13—22no—
126C22×C13—22no—
127C22×C13—41no—
128C22×C13—41no—
129C22×C13—41no—
130C22×C13C2×D814yes—
131C22×C13C22×D411yescharacteristic
132C2×D13—22no—
133C2×D13—41no—
134C2×D13—41no—
135C2×D13—42no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—88no—
139C4×C13—22no—
140C4×C13—21no—
141C4×C13—41no—
142C4×C13—42no—
143C4×C13C2×D812yes—
144C4×C13C2×#4111yescharacteristic
145C4×C13H(5,𝔽2)11yescharacteristic
146Dic13—41no—
147C2×#41—21no—
148C22×D4—132no—
149C22×D4—261no—
150C2×D8—131no—
151C2×D8—132no—
152C22×C8—132no—
153C4⋊Q8C2×D1311yescharacteristic, complemented
154#127—131no—
155#123—22no—
156C22⋊Q8—21no—
157#121—132no—
158#121—261no—
159#121C2×D1312yescomplemented
160#120—262no—
161C4×D4—131no—
162C4×D4C2×D1311yescharacteristic
163C4×D4C2×D1311yescharacteristic, complemented
164C2×C4⋊C4C2×D1312yescomplemented
165#107—131no—
166#107—132no—
167C4⋊C8—131no—
168#102—131no—
169#102—131no—
170#102—132no—
171#102—132no—
172#102—132no—
173#102—132no—
174C22⋊C8—132no—
175C4×C8—131no—
176C2×C13—24no—
177C2×C13—81no—
178C2×C13#54611yescharacteristic
179C2×C13C22×D811yescharacteristic
180C2×C13#57711yescharacteristic
181D13—42no—
182D13—82no—
183C24—262no—
184#41—44no—
185C2×Q8—21no—
186C2×D4—22no—
187C2×D4—131no—
188C2×D4—132no—
189C2×D4—264no—
190C2×D4—262no—
191C2×D4—262no—
192C2×D4—261no—
193C2×D4—261no—
194C2×D4—522no—
195C2×D4—524no—
196C2×D4C22⋊D1311yescharacteristic
197C2×D4C22×D1311yescharacteristic
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—261no—
201C22×C4C22×D1312yes—
202D8—262no—
203D8—522no—
204C2×C8—131no—
205C2×C8—131no—
206C2×C8—132no—
207C2×C8—522no—
208C4⋊C4—22no—
209C4⋊C4—21no—
210C4⋊C4—131no—
211C4⋊C4C22⋊D1311yescharacteristic
212C4⋊C4C22×D1311yescharacteristic
213C4⋊C4C22×D1312yes—
214C22⋊C4—21no—
215C22⋊C4—22no—
216C22⋊C4—261no—
217C22⋊C4—262no—
218C22⋊C4C22⋊D1312yes—
219C42C22×D1311yescharacteristic
220C13#329411yescharacteristic, complemented, Sylow
221C23—21no—
222C23—261no—
223C23—262no—
224C23—524no—
225C23—524no—
226C23—1042no—
227C23C2×C22⋊D1312yes—
228Q8—42no—
229D4—21no—
230D4—21no—
231D4—44no—
232D4—132no—
233D4—262no—
234D4—261no—
235D4—262no—
236D4—524no—
237D4—524no—
238D4—522no—
239D4—1041no—
240D4#610414yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—261no—
248C2×C4—522no—
249C2×C4C2×C22⋊D1311yescharacteristic
250C2×C4C2×C22⋊D1312yes—
251C2×C4C2×C22⋊D1311yescharacteristic
252C2×C4C23×D1311yescharacteristic
253C8—261no—
254C8—261no—
255C8—262no—
256C22—22no—
257C22—22no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—262no—
262C22—521no—
263C22—521no—
264C22—522no—
265C22—522no—
266C22—522no—
267C22—1048no—
268C22C2×#610414yes—
269C22C22×C22⋊D1311yescharacteristic
270C4—22no—
271C4—21no—
272C4—41no—
273C4—42no—
274C4—521no—
275C4C2×#610412yes—
276C4#41×D1311yescharacteristic
277C4#8825611yescharacteristic
278C2—24no—
279C2—81no—
280C2—522no—
281C2—1042no—
282C2C22×#610411yescharacteristic
283C2#1171953411yescharacteristic
284C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#547C2
socleC22×C13C22×D4
hypercenter#547D13
hypocenterC13#3294
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C13×#547C2semidirect
2. D4×D52C2semidirect
3. #11718749C2semidirect
4. #11718748C2semidirect
5. #11718699C2semidirect
6. #11718697C2semidirect
7. #11718676C2semidirect
8. C4×#6104C2semidirect
9. D4×#1055C2semidirect
10. #11718628C2semidirect
11. C2×#88049C2semidirect
15. C13×C4⋊Q8C22semidirect
18. C13×#121C22semidirect
20. C4×D4×C13C22semidirect
21. C2×C13×C4⋊C4C22semidirect
23. C2×#6104C22semidirect
25. C22×#1055C22semidirect
30. #88072C22semidirect
31. C22⋊#1055C22semidirect
34. #88049C22semidirect
35. #88049C22semidirect
36. #88049C22semidirect
37. #88047C22semidirect
38. #88047C22semidirect
39. C4⋊#1055C22semidirect
40. C4×#1055C22semidirect
90. D4×C13D8semidirect
109. D52#41semidirect
114. #547D13semidirect
153. C4⋊Q8C2×D13semidirect
159. #121C2×D13semidirect
163. C4×D4C2×D13semidirect
164. C2×C4⋊C4C2×D13semidirect
220. C13#3294semidirect
240. D4#6104semidirect

Maximal subgroups

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

subgroupindex
C13×#5472
D4×D522
#117187492
#117187482
#117186992
#117186972
#117186762
C4×#61042
D4×#10552
#117186282
C2×#880492
#329413