Finite Group Databasebeta

← #16831101

Subgroups — #16831101

Order 3712.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#11745276C212yesmaximal, complemented
2#14271806C212yesmaximal, complemented
3#14271406C212yesmaximal, complemented
4#14271375C212yesmaximal, complemented
5#14271324C212yesmaximal, complemented
6#14271295C212yesmaximal, complemented
7C4×D232C211yesmaximal, characteristic, complemented
8#14271242C211yesmaximal, characteristic, complemented
9C29×#495C211yesmaximal, characteristic, complemented
10C2×#90809C2212yes—
11C2×D4×D29C2212yescomplemented
12C2×Q16×C29C2211yescharacteristic, complemented
13C2×SD16×C29C2212yescomplemented
14C2×D8×C29C2211yescharacteristic
15C29×#124C2212yescomplemented
16#11745308C2212yescomplemented
17C2×#90784C2212yescomplemented
18#11745300C2212yes—
19C2×#90782C2212yes—
20#11745276—28no—
21C2×D232C2211yescharacteristic
22C2×#90772C2212yescomplemented
23#11745246—22no—
24#11745245—22no—
25#11745244—22no—
26C22⋊C4×D29—22no—
27C4×D116C2211yescharacteristic
28C4×D116C2212yescomplemented
29C4×C8×C29C2211yescharacteristic, complemented
30#11745183C2212yescomplemented
31#11745180C2212yescomplemented
32#11745169C2212yescomplemented
33#11745168C2212yescomplemented
34#11745166C2211yescharacteristic, complemented
35C4⋊#6597C2211yescharacteristic, complemented
36C23×D29—22no—
37C2×Q8×C29C2312yes—
38C2×D4×C29C2312yes—
39C2×C22⋊D29—22no—
40C2×C22⋊D29—22no—
41#90809—24no—
42#90809—42no—
43D4×D29—24no—
44D4×D29—42no—
45C2×D116—22no—
46C2×D116D411yescharacteristic
47C2×D116C2312yes—
48C2×C4×D29—22no—
49C2×C4×D29—22no—
50C2×C4×D29C2312yes—
51Q16×C29—41no—
52SD16×C29—24no—
53D8×C29—41no—
54C2×C8×C29C2311yescharacteristic
55C2×C8×C29C2311yescharacteristic
56C22⋊C4×C29—22no—
57C22⋊C4×C29—22no—
58C42×C29C2311yescharacteristic
59C22⋊Dic29—22no—
60#90784—24no—
61#90782—24no—
62#90781—22no—
63#90781—22no—
64#90781D412yes—
65C4⋊Dic29D411yescharacteristic
66C4⋊Dic29C2312yes—
67#90779—22no—
68C2×#6597C2312yes—
69D232D414yescomplemented
70#90772—24no—
71C23×C29—22no—
72C22×D29—22no—
73C22×D29—44no—
74C22×D29—44no—
75C22×D29—82no—
76C22×D29C2×D412yes—
77Q8×C29—22no—
78Q8×C29—22no—
79D4×C29—22no—
80D4×C29—22no—
81C2×C4×C29—22no—
82C2×C4×C29C2×D411yescharacteristic
83C2×C4×C29C2×D411yescharacteristic
84C2×C4×C29C2411yescharacteristic
85C22⋊D29—44no—
86C22⋊D29—82no—
87C2×Dic29—22no—
88C2×Dic29C2×D412yes—
89D116—22no—
90D116—41no—
91D116—44no—
92D116C2×D414yes—
93C4×D29—22no—
94C4×D29—22no—
95C4×D29—44no—
96C4×D29—82no—
97C8×C29—21no—
98C8×C29C2×D412yes—
99#6597—22no—
100#3273—291nomaximal, Sylow
101C22×C29—42no—
102C22×C29—42no—
103C22×C29—42no—
104C22×C29C22×D411yescharacteristic
105C2×D29—22no—
106C2×D29—24no—
107C2×D29—22no—
108C2×D29—22no—
109C2×D29—42no—
110C2×D29—42no—
111C2×D29—88no—
112C4×C29—21no—
113C4×C29—21no—
114C4×C29—42no—
115C4×C29C22×D411yescharacteristic
116C4×C29H(5,𝔽2)11yescharacteristic
117Dic29—22no—
118Dic29—42no—
119C2×AGL(1,ℤ/8)—292no—
120#546—292no—
121#495D2911yescharacteristic, complemented
122#468—292no—
123#463—292no—
124#452—292no—
125#447—292no—
126C4×D8—291no—
127#436—291no—
128C2×C29—82no—
129C2×C29D4211yescharacteristic
130C2×C29#57511yescharacteristic
131C2×C29#57611yescharacteristic
132D29—42no—
133D29—44no—
134C2×#41—292no—
135C22×D4—292no—
136AGL(1,ℤ/8)—588no—
137C2×Q16C2×D2911yescharacteristic, complemented
138C2×SD16—292no—
139C2×SD16C2×D2912yescomplemented
140C2×D8—292no—
141C2×D8—291no—
142C2×D8C2×D2911yescharacteristic
143C2×M16—292no—
144#124C2×D2912yescomplemented
145#123—582no—
146C22⋊Q8—292no—
147#121—292no—
148#121—582no—
149#120—582no—
150C4×D4—291no—
151C4×D4—292no—
152C2×C22⋊C4—582no—
153#107—291no—
154C4⋊C8—291no—
155#103—292no—
156#102—292no—
157#102—292no—
158C22⋊C8—292no—
159C4×C8C2×D2911yescharacteristic, complemented
160C29#327311yescharacteristic, complemented, Sylow
161C24—582no—
162#41—584no—
163#41—1162no—
164C2×Q8C22×D2912yes—
165C2×D4—291no—
166C2×D4—292no—
167C2×D4—582no—
168C2×D4—582no—
169C2×D4—584no—
170C2×D4—582no—
171C2×D4—1162no—
172C2×D4C22×D2912yes—
173C22×C4—292no—
174C22×C4—582no—
175C22×C4—582no—
176Q16—41no—
177SD16—24no—
178SD16—584no—
179D8—41no—
180D8—294no—
181D8—584no—
182M16—584no—
183C2×C8—292no—
184C2×C8C22×D2911yescharacteristic
185C2×C8C22×D2911yescharacteristic
186C4⋊C4—291no—
187C4⋊C4—292no—
188C4⋊C4—582no—
189C22⋊C4—22no—
190C22⋊C4—22no—
191C22⋊C4—292no—
192C22⋊C4—582no—
193C22⋊C4—582no—
194C22⋊C4—582no—
195C42C22×D2911yescharacteristic
196C23—22no—
197C23—292no—
198C23—582no—
199C23—1164no—
200C23—1164no—
201C23—2322no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—22no—
206D4—294no—
207D4—582no—
208D4—1161no—
209D4—1164no—
210D4—1164no—
211D4—2322no—
212C2×C4—22no—
213C2×C4—292no—
214C2×C4—582no—
215C2×C4—582no—
216C2×C4—582no—
217C2×C4—1164no—
218C2×C4—2322no—
219C2×C4D4×D2911yescharacteristic
220C2×C4D4×D2911yescharacteristic
221C2×C4C23×D2911yescharacteristic
222C8—21no—
223C8—582no—
224C8D4×D2912yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—582no—
229C22—584no—
230C22—582no—
231C22—582no—
232C22—1162no—
233C22—1162no—
234C22—2328no—
235C22C2×D4×D2911yescharacteristic
236C4—21no—
237C4—21no—
238C4—42no—
239C4—582no—
240C4—1162no—
241C4C2×D4×D2911yescharacteristic
242C4#1174535911yescharacteristic
243C2—82no—
244C2—1162no—
245C2—1164no—
246C2#1427179811yescharacteristic
247C2#1427196011yescharacteristic
248C2#1427196511yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#495C2
socleC22×C29C22×D4
hypercenter#495D29
hypocenterC29#3273
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#11745276C2semidirect
2. #14271806C2semidirect
3. #14271406C2semidirect
4. #14271375C2semidirect
5. #14271324C2semidirect
6. #14271295C2semidirect
7. C4×D232C2semidirect
8. #14271242C2semidirect
9. C29×#495C2semidirect
11. C2×D4×D29C22semidirect
12. C2×Q16×C29C22semidirect
13. C2×SD16×C29C22semidirect
15. C29×#124C22semidirect
16. #11745308C22semidirect
17. C2×#90784C22semidirect
22. C2×#90772C22semidirect
28. C4×D116C22semidirect
29. C4×C8×C29C22semidirect
30. #11745183C22semidirect
31. #11745180C22semidirect
32. #11745169C22semidirect
33. #11745168C22semidirect
34. #11745166C22semidirect
35. C4⋊#6597C22semidirect
69. D232D4semidirect
121. #495D29semidirect
137. C2×Q16C2×D29semidirect
139. C2×SD16C2×D29semidirect
144. #124C2×D29semidirect
159. C4×C8C2×D29semidirect
160. C29#3273semidirect

Maximal subgroups

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

subgroupindex
C2×#117452762
#142718062
#142714062
#142713752
#142713242
#142712952
C4×D2322
#142712422
C29×#4952
#327329