Finite Group Databasebeta

← #13126649

Subgroups — #13126649

Order 1664.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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, complemented
2#11719260C211yesmaximal, characteristic, complemented
3#11718878C212yesmaximal, complemented
4C2×#88072C212yesmaximal, complemented
5#11718733C211yesmaximal, characteristic, complemented
6#11718731C211yesmaximal, characteristic, complemented
7#11718699C212yesmaximal, complemented
8#11718694C212yesmaximal, complemented
9C4×#6104C211yesmaximal, characteristic, complemented
10D4×#1055C211yesmaximal, characteristic, complemented
11#11718668C211yesmaximal, characteristic, complemented
12C22×D4×C13—21no—
13C22×D4×C13C2212yes—
14C2×#6129—21no—
15C13×#127C2211yescharacteristic
16C13×#121—21no—
17C13×#121C2212yes—
18C13×#120—22no—
19C4×D4×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21C2×#6104C2211yescharacteristic
22C2×#6104C2212yescomplemented
23#88184C2212yescomplemented
24C2×C4⋊Dic13C2212yescomplemented
25C22×#1055C2212yescomplemented
26#88151—21no—
27#88140—22no—
28C4×D52C2211yescharacteristic, complemented
29#88123C2211yescharacteristic, complemented
30#88072C2212yes—
31#88072C2211yescharacteristic
32#88072C2212yescomplemented
33#88072C2212yescomplemented
34#88072C2212yescomplemented
35C22⋊#1055C2212yescomplemented
36#88049C2211yescharacteristic, complemented
37#88047C2212yescomplemented
38#88047C2211yescharacteristic, complemented
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×C22⋊D13—22no—
55C22×Dic13—22no—
56#6129—44no—
57C2×D52C2311yescharacteristic
58C2×C4×D13—21no—
59C2×Dic26—21no—
60C13×C4⋊C4D411yescharacteristic
61C13×C4⋊C4C2311yescharacteristic
62C13×C22⋊C4—21no—
63C13×C22⋊C4—22no—
64C13×C22⋊C4D412yes—
65C42×C13C2311yescharacteristic
66#6104—22no—
67#6104—42no—
68#6103—21no—
69#6103—22no—
70C4⋊Dic13—21no—
71C4⋊Dic13—22no—
72C4⋊Dic13C2312yes—
73C4⋊Dic13C2311yescharacteristic
74C2×#1055—42no—
75C2×#1055C2311yescharacteristic
76C2×#1055C2312yes—
77C2×#1055C2311yescharacteristic
78#3294—131nomaximal, Sylow
79C23×C13—21no—
80C23×C13—22no—
81C23×C13—44no—
82C23×C13—44no—
83C23×C13—82no—
84C23×C13C2×D412yes—
85C22×D13—21no—
86D4×C13—22no—
87D4×C13—21no—
88D4×C13—22no—
89D4×C13—44no—
90D4×C13—44no—
91D4×C13—42no—
92D4×C13—81no—
93D4×C13D814yescomplemented
94D4×C13#4112yescomplemented
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—42no—
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2×D412yes—
101C2×C4×C13C2×D411yescharacteristic
102C2×C4×C13C2411yescharacteristic
103C22⋊D13—44no—
104C2×Dic13—22no—
105C2×Dic13—21no—
106C2×Dic13—44no—
107D52—21no—
108D52—21no—
109C4×D13—42no—
110Dic26—42no—
111#1055—21no—
112#1055—21no—
113#1055—22no—
114#547—131no—
115D42D1311yescharacteristic, complemented
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—22no—
128C22×C13—41no—
129C22×C13—41no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—88no—
134C22×C13C2×D814yes—
135C22×C13C22×D411yescharacteristic
136C2×D13—41no—
137C2×D13—41no—
138C2×D13—41no—
139C4×C13—22no—
140C4×C13—21no—
141C4×C13—41no—
142C4×C13C2×D812yes—
143C4×C13C2×#4111yescharacteristic
144C4×C13H(5,𝔽2)11yescharacteristic
145Dic13—42no—
146Dic13—41no—
147C2×#41—261no—
148C22×D4—21no—
149C22×D4C2×D1312yes—
150C2×D8—131no—
151C2×D8—132no—
152C22×C8—132no—
153C4⋊Q8—131no—
154#127C2×D1311yescharacteristic
155#123—262no—
156C22⋊Q8—261no—
157#121—21no—
158#121—132no—
159#121C2×D1312yes—
160#120—22no—
161C4×D4—131no—
162C4×D4C2×D1311yescharacteristic
163C4×D4C2×D1311yescharacteristic
164C2×C4⋊C4—132no—
165#107—131no—
166#107—132no—
167C4⋊C8—131no—
168#102—131no—
169#102—132no—
170#102—132no—
171#102—132no—
172#102—132no—
173#102—131no—
174C22⋊C8—132no—
175C4×C8—131no—
176C2×C13—24no—
177C2×C13—42no—
178C2×C13—82no—
179C2×C13#54611yescharacteristic
180C2×C13C22×D811yescharacteristic
181C2×C13#57711yescharacteristic
182D13—81no—
183C24—22no—
184#41—524no—
185C2×Q8—261no—
186C2×D4—24no—
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—42no—
192C2×D4—44no—
193C2×D4—131no—
194C2×D4—262no—
195C2×D4C22⋊D1311yescharacteristic
196C2×D4C22×D1312yes—
197C2×D4C22×D1311yescharacteristic
198C22×C4—21no—
199C22×C4—262no—
200C22×C4—261no—
201C22×C4C22×D1312yes—
202D8—262no—
203D8—522no—
204C2×C8—131no—
205C2×C8—131no—
206C2×C8—132no—
207C2×C8—522no—
208C4⋊C4—131no—
209C4⋊C4—132no—
210C4⋊C4—262no—
211C4⋊C4—261no—
212C4⋊C4C22⋊D1311yescharacteristic
213C4⋊C4C22×D1311yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—22no—
216C22⋊C4—261no—
217C22⋊C4—262no—
218C22⋊C4C22⋊D1312yes—
219C42C22×D1311yescharacteristic
220C13#329411yescharacteristic, complemented, Sylow
221C23—21no—
222C23—22no—
223C23—44no—
224C23—44no—
225C23—82no—
226C23—261no—
227C23C2×C22⋊D1312yes—
228Q8—522no—
229D4—22no—
230D4—21no—
231D4—22no—
232D4—44no—
233D4—44no—
234D4—42no—
235D4—81no—
236D4—261no—
237D4—261no—
238D4—524no—
239D4#610414yescomplemented
240D4#612912yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—261no—
246C2×C4—262no—
247C2×C4—524no—
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—22no—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—88no—
265C22—521no—
266C22—521no—
267C22—521no—
268C22C2×#610414yes—
269C22C22×C22⋊D1311yescharacteristic
270C4—22no—
271C4—21no—
272C4—41no—
273C4—521no—
274C4—522no—
275C4C2×#610412yes—
276C4C2×#612911yescharacteristic
277C4#8825111yescharacteristic
278C2—24no—
279C2—42no—
280C2—82no—
281C2—1041no—
282C2C22×#610411yescharacteristic
283C2#1171951111yescharacteristic
284C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingD42×C13C2
socleC22×C13C22×D4
hypercenterD42D13
hypocenterC13#3294
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
1. D42×C13C2semidirect
2. #11719260C2semidirect
3. #11718878C2semidirect
4. C2×#88072C2semidirect
5. #11718733C2semidirect
6. #11718731C2semidirect
7. #11718699C2semidirect
8. #11718694C2semidirect
9. C4×#6104C2semidirect
10. D4×#1055C2semidirect
11. #11718668C2semidirect
22. C2×#6104C22semidirect
23. #88184C22semidirect
24. C2×C4⋊Dic13C22semidirect
25. C22×#1055C22semidirect
28. C4×D52C22semidirect
29. #88123C22semidirect
32. #88072C22semidirect
33. #88072C22semidirect
34. #88072C22semidirect
35. C22⋊#1055C22semidirect
36. #88049C22semidirect
37. #88047C22semidirect
38. #88047C22semidirect
39. C4⋊#1055C22semidirect
40. C4×#1055C22semidirect
93. D4×C13D8semidirect
94. D4×C13#41semidirect
115. D42D13semidirect
220. C13#3294semidirect
239. D4#6104semidirect
240. D4#6129semidirect

Maximal subgroups

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

subgroupindex
D42×C132
#117192602
#117188782
C2×#880722
#117187332
#117187312
#117186992
#117186942
C4×#61042
D4×#10552
#117186682
#329413