Finite Group Databasebeta

← #16831288

Subgroups — #16831288

Order 3712.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#14271967C212yesmaximal, complemented
2#14271966C212yesmaximal, complemented
3#14271539C211yesmaximal, characteristic, complemented
4#14271432C212yesmaximal, complemented
5#14271431C212yesmaximal, complemented
6#14271332C212yesmaximal, complemented
7#14271330C211yesmaximal, characteristic, complemented
8#14271277C212yesmaximal, complemented
9C29×#453C211yesmaximal, characteristic, complemented
10C29×H(5,𝔽2)C2211yescharacteristic, complemented
11#11745364C2212yescomplemented
12#11745359C2211yescharacteristic, complemented
13C29×AGL(1,ℤ/8)C2212yescomplemented
14C29×#127C2211yescharacteristic, complemented
15#11745312—22no—
16#11745312C2212yes—
17#11745311—22no—
18#11745311C2212yescomplemented
19#11745310C2212yescomplemented
20#11745294—22no—
21#11745294C2212yescomplemented
22C2×#90782—22no—
23C2×#90782C2212yescomplemented
24C2×#90782C2212yescomplemented
25#11745278—22no—
26#11745276—22no—
27#11745273—22no—
28D8×D29—22no—
29#11745270C2212yescomplemented
30#11745269C2212yescomplemented
31#11745236C2211yescharacteristic, complemented
32C29×#104C2212yescomplemented
33C29×#100C2211yescharacteristic, complemented
34#11745181C2211yescharacteristic, complemented
35#11745171C2212yescomplemented
36#11745170C2212yescomplemented
37#11745153C2212yescomplemented
38C4×#6597C2211yescharacteristic, complemented
39#41×C29—22no—
40#41×C29C2312yes—
41C2×D4×C29—22no—
42C2×D4×C29—41no—
43C2×D4×C29—41no—
44C2×D4×C29C2311yescharacteristic
45C2×D4×C29C2311yescharacteristic
46C2×C22⋊D29—41no—
47#90809—22no—
48#90807—22no—
49D4×D29—22no—
50D4×D29—22no—
51D4×D29—42no—
52#90805—22no—
53#90805C2312yes—
54C2×D116—22no—
55C2×D116—41no—
56C2×D116C2312yes—
57SD16×C29—22no—
58D8×C29—22no—
59M16×C29C2312yes—
60C42×C29C2311yescharacteristic
61#90785D412yescomplemented
62#90784—22no—
63#90784D412yescomplemented
64#90783—22no—
65#90783D412yescomplemented
66#90782—22no—
67#90782—22no—
68#90782—22no—
69#90782—22no—
70#90782—22no—
71#90782—22no—
72#90782D412yescomplemented
73#90777—22no—
74#90777C2312yes—
75C2×#6597—22no—
76C2×#6597C2312yes—
77D232—22no—
78#90773—22no—
79#90772—22no—
80C8×D29—22no—
81C23×C29—21no—
82C23×C29—21no—
83C23×C29—41no—
84C22×D29—22no—
85C22×D29—41no—
86C22×D29—42no—
87Q8×C29C2×D412yes—
88D4×C29—22no—
89D4×C29—22no—
90D4×C29—22no—
91D4×C29—42no—
92D4×C29—82no—
93D4×C29C2×D412yes—
94C2×C4×C29—21no—
95C2×C4×C29—22no—
96C2×C4×C29—41no—
97C2×C4×C29C2411yescharacteristic
98C22⋊D29—22no—
99C22⋊D29—42no—
100C22⋊D29—42no—
101C2×Dic29—41no—
102D116—22no—
103D116—22no—
104D116—42no—
105D116—82no—
106D116C2×D412yes—
107C4×D29—22no—
108C4×D29—42no—
109Dic58C2×D412yes—
110C8×C29—22no—
111#6597—22no—
112#6597C2×D412yes—
113#6597C2×D412yes—
114#3292—291nomaximal, Sylow
115C22×C29—22no—
116C22×C29—41no—
117C22×C29—41no—
118C22×C29—81no—
119C22×C29—81no—
120C22×C29—161no—
121C22×C29H(5,𝔽2)11yescharacteristic
122C2×D29—22no—
123C2×D29—42no—
124C2×D29—82no—
125C2×D29—161no—
126C2×D29—162no—
127C4×C29—22no—
128C4×C29—22no—
129C4×C29C22×D412yes—
130Dic29—22no—
131#576—292no—
132#576—292no—
133#493—291no—
134#472—292no—
135#472—292no—
136#453—291no—
137#453—292no—
138#453D2911yescharacteristic, complemented
139#443—292no—
140C2×C29—21no—
141C2×C29—42no—
142C2×C29—81no—
143C2×C29—81no—
144C2×C29D4211yescharacteristic
145D29—42no—
146D29—82no—
147H(5,𝔽2)—292no—
148H(5,𝔽2)—291no—
149H(5,𝔽2)C2×D2911yescharacteristic, complemented
150AGL(1,ℤ/8)—292no—
151AGL(1,ℤ/8)—292no—
152AGL(1,ℤ/8)—292no—
153AGL(1,ℤ/8)—582no—
154AGL(1,ℤ/8)—582no—
155AGL(1,ℤ/8)—582no—
156AGL(1,ℤ/8)—582no—
157AGL(1,ℤ/8)C2×D2912yescomplemented
158#135—292no—
159#135—582no—
160#135—582no—
161C2×D8—292no—
162C2×D8—292no—
163C2×D8—582no—
164C2×D8—582no—
165#131—292no—
166#131—292no—
167#127—291no—
168#127C2×D2911yescharacteristic, complemented
169#108—292no—
170#104—292no—
171#104C2×D2912yescomplemented
172#100—291no—
173#100—292no—
174#100C2×D2911yescharacteristic, complemented
175C4×C8—291no—
176C29#329211yescharacteristic, complemented, Sylow
177#41—22no—
178#41—292no—
179#41—582no—
180#41—582no—
181#41—582no—
182#41C22×D2912yes—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—292no—
187C2×D4—582no—
188C2×D4—582no—
189C2×D4—582no—
190C2×D4—1161no—
191C2×D4—1162no—
192C2×D4—1161no—
193C2×D4C22×D2911yescharacteristic
194C2×D4C22×D2911yescharacteristic
195Q16—292no—
196SD16—22no—
197SD16—292no—
198SD16—292no—
199SD16—582no—
200SD16—582no—
201SD16—582no—
202D8—22no—
203D8—292no—
204D8—582no—
205D8—582no—
206D8—582no—
207D8—582no—
208D8—582no—
209D8—582no—
210D8—582no—
211M16—292no—
212M16—582no—
213M16—582no—
214M16C22×D2912yes—
215C2×C8—292no—
216C2×C8—582no—
217C2×C8—582no—
218C42C22×D2911yescharacteristic
219C23—21no—
220C23—21no—
221C23—41no—
222C23—582no—
223C23—1162no—
224C23—1161no—
225Q8—292no—
226Q8D4×D2912yes—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—82no—
232D4—292no—
233D4—582no—
234D4—582no—
235D4—582no—
236D4—1162no—
237D4—1162no—
238D4—1162no—
239D4—2322no—
240D4D4×D2912yes—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—582no—
245C2×C4—1162no—
246C2×C4—1161no—
247C2×C4C23×D2911yescharacteristic
248C8—22no—
249C8—292no—
250C8—292no—
251C8—582no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—582no—
259C22—1162no—
260C22—4642no—
261C22—4641no—
262C22—2322no—
263C22#1174535911yescharacteristic
264C4—22no—
265C4—22no—
266C4—582no—
267C4C2×D4×D2912yes—
268C2—21no—
269C2—42no—
270C2—81no—
271C2—81no—
272C2—1162no—
273C2—2322no—
274C2#1427179511yescharacteristic
subgroupG/H
centerC2#14271795
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#453C2
socleC2×C29D42
hypercenter#453D29
hypocenterC29#3292
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #14271967C2semidirect
2. #14271966C2semidirect
3. #14271539C2semidirect
4. #14271432C2semidirect
5. #14271431C2semidirect
6. #14271332C2semidirect
7. #14271330C2semidirect
8. #14271277C2semidirect
9. C29×#453C2semidirect
10. C29×H(5,𝔽2)C22semidirect
11. #11745364C22semidirect
12. #11745359C22semidirect
13. C29×AGL(1,ℤ/8)C22semidirect
14. C29×#127C22semidirect
18. #11745311C22semidirect
19. #11745310C22semidirect
21. #11745294C22semidirect
23. C2×#90782C22semidirect
24. C2×#90782C22semidirect
29. #11745270C22semidirect
30. #11745269C22semidirect
31. #11745236C22semidirect
32. C29×#104C22semidirect
33. C29×#100C22semidirect
34. #11745181C22semidirect
35. #11745171C22semidirect
36. #11745170C22semidirect
37. #11745153C22semidirect
38. C4×#6597C22semidirect
61. #90785D4semidirect
63. #90784D4semidirect
65. #90783D4semidirect
72. #90782D4semidirect
138. #453D29semidirect
149. H(5,𝔽2)C2×D29semidirect
157. AGL(1,ℤ/8)C2×D29semidirect
168. #127C2×D29semidirect
171. #104C2×D29semidirect
174. #100C2×D29semidirect
176. C29#3292semidirect

Maximal subgroups

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

subgroupindex
#142719672
#142719662
#142715392
#142714322
#142714312
#142713322
#142713302
#142712772
C29×#4532
#329229