Finite Group Databasebeta

← #16831286

Subgroups — #16831286

Order 3712.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#14271975C212yesmaximal, complemented
2#14271970C212yesmaximal, complemented
3#14271536C211yesmaximal, characteristic, complemented
4#14271427C212yesmaximal, complemented
5#14271426C212yesmaximal, complemented
6#14271347C212yesmaximal, complemented
7#14271332C212yesmaximal, complemented
8#14271281C211yesmaximal, characteristic, complemented
9C29×#443C211yesmaximal, characteristic, complemented
10#11745365C2212yes—
11#11745364C2212yescomplemented
12C29×#135C2211yescharacteristic
13C29×#131C2212yescomplemented
14#11745313C2212yescomplemented
15#11745311C2212yes—
16#11745280—22no—
17#11745278—22no—
18SD16×D29—22no—
19#11745273—22no—
20#11745271—22no—
21#11745271C2212yescomplemented
22#11745270—22no—
23#11745270C2212yes—
24#11745266—22no—
25#11745266C2211yescharacteristic
26C2×#90773—22no—
27C2×#90773C2212yescomplemented
28C2×#90773C2212yescomplemented
29#11745263C2212yescomplemented
30#11745236C2211yescharacteristic
31#11745231C2211yescharacteristic, complemented
32C29×#108C2211yescharacteristic, complemented
33C29×#104C2212yescomplemented
34C4×C8×C29C2211yescharacteristic, complemented
35#11745172C2212yescomplemented
36#11745171C2212yescomplemented
37#11745167C2211yescharacteristic, complemented
38#11745153C2212yescomplemented
39#41×C29C2312yes—
40#90809—22no—
41Q8×D29—22no—
42#90807—22no—
43#90807—42no—
44D4×D29—22no—
45D4×D29—42no—
46#90805—22no—
47#90805—22no—
48#90805C2312yes—
49C2×D116—22no—
50C2×D116—41no—
51C2×D116C2312yes—
52C2×Dic58—22no—
53C2×Dic58C2312yes—
54Q16×C29D411yescharacteristic, complemented
55SD16×C29D412yescomplemented
56D8×C29D411yescharacteristic, complemented
57M16×C29—22no—
58M16×C29C2312yes—
59C2×C8×C29—22no—
60C2×C8×C29C2311yescharacteristic
61C2×C8×C29C2311yescharacteristic
62C42×C29C2311yescharacteristic
63#90785—22no—
64#90784—22no—
65#90783—22no—
66#90782—22no—
67C4⋊Dic29—41no—
68#90777C2312yes—
69Dic116—22no—
70Dic116D411yescharacteristic, complemented
71D232—22no—
72D232D411yescharacteristic, complemented
73#90773—22no—
74#90773—22no—
75#90773—22no—
76#90773—22no—
77#90773—22no—
78#90773—22no—
79#90773D412yescomplemented
80#90772—22no—
81C8×D29—22no—
82C22×D29—22no—
83C22×D29—42no—
84Q8×C29C2×D412yes—
85D4×C29—22no—
86D4×C29C2×D412yes—
87C2×C4×C29—21no—
88C2×C4×C29—22no—
89C2×C4×C29C2411yescharacteristic
90C22⋊D29—22no—
91C22⋊D29—42no—
92C22⋊D29—42no—
93C2×Dic29—22no—
94C2×Dic29—42no—
95D116—22no—
96D116—22no—
97D116—42no—
98D116—82no—
99D116C2×D412yes—
100C4×D29—22no—
101C4×D29—42no—
102C4×D29—42no—
103Dic58—22no—
104Dic58—22no—
105Dic58—42no—
106Dic58C2×D412yes—
107C8×C29—22no—
108C8×C29C2×D411yescharacteristic
109C8×C29C2×D411yescharacteristic
110C8×C29C2×D411yescharacteristic
111C8×C29C2×D411yescharacteristic
112#6597—22no—
113#3291—291nomaximal, Sylow
114C22×C29—22no—
115C22×C29H(5,𝔽2)11yescharacteristic
116C2×D29—22no—
117C2×D29—42no—
118C2×D29—82no—
119C2×D29—162no—
120C4×C29—22no—
121C4×C29—22no—
122C4×C29C22×D411yescharacteristic
123C4×C29C22×D411yescharacteristic
124Dic29—22no—
125Dic29—42no—
126#577—292no—
127#577—292no—
128#492—291no—
129#471—292no—
130#471—292no—
131#456—292no—
132#453—292no—
133#443—291no—
134#443D2911yescharacteristic, complemented
135C2×C29—21no—
136C2×C29—42no—
137C2×C29D4211yescharacteristic
138D29—42no—
139D29—82no—
1402−1+4—292no—
141H(5,𝔽2)—292no—
142#137—292no—
143#137—292no—
144#137—582no—
145#137—582no—
146AGL(1,ℤ/8)—292no—
147AGL(1,ℤ/8)—292no—
148AGL(1,ℤ/8)—582no—
149AGL(1,ℤ/8)—582no—
150#135—291no—
151#135—582no—
152#135—582no—
153#135C2×D2911yescharacteristic
154C2×SD16—292no—
155C2×SD16—292no—
156C2×SD16—582no—
157C2×SD16—582no—
158#131—292no—
159#131C2×D2912yescomplemented
160C4⋊Q8—291no—
161#127—291no—
162#108—291no—
163#108C2×D2911yescharacteristic, complemented
164#104—292no—
165#104C2×D2912yescomplemented
166#101—292no—
167#100—292no—
168C4×C8C2×D2911yescharacteristic, complemented
169C29#329111yescharacteristic, complemented, Sylow
170#41—292no—
171#41—582no—
172#41—582no—
173#41—582no—
174#41—582no—
175#41—1162no—
176#41C22×D2912yes—
177C2×Q8—292no—
178C2×Q8—582no—
179C2×Q8—582no—
180C2×D4—292no—
181C2×D4—582no—
182C2×D4—582no—
183C2×D4—1161no—
184C2×D4—1162no—
185Q16—291no—
186Q16—582no—
187Q16—582no—
188Q16D11611yescharacteristic, complemented
189SD16—292no—
190SD16—582no—
191SD16—582no—
192SD16—582no—
193SD16—582no—
194SD16—582no—
195SD16—582no—
196SD16—582no—
197SD16—582no—
198SD16D11612yescomplemented
199D8—291no—
200D8—582no—
201D8—582no—
202D8D11611yescharacteristic, complemented
203M16—22no—
204M16—292no—
205M16—582no—
206M16C22×D2912yes—
207C2×C8—22no—
208C2×C8—582no—
209C2×C8C22×D2911yescharacteristic
210C2×C8C22×D2911yescharacteristic
211C4⋊C4—1161no—
212C42C22×D2911yescharacteristic
213C23—582no—
214C23—1162no—
215Q8—292no—
216Q8—582no—
217Q8—582no—
218Q8—1162no—
219Q8C2×D11612yes—
220D4—22no—
221D4—292no—
222D4—582no—
223D4—582no—
224D4—582no—
225D4—1162no—
226D4—1162no—
227D4—1162no—
228D4—2322no—
229D4C2×D11612yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—582no—
233C2×C4—582no—
234C2×C4—1162no—
235C2×C4—1162no—
236C2×C4—1162no—
237C2×C4C23×D2911yescharacteristic
238C8—22no—
239C8—582no—
240C8C2×D11611yescharacteristic
241C8C2×D11611yescharacteristic
242C8D4×D2911yescharacteristic
243C8D4×D2911yescharacteristic
244C22—22no—
245C22—582no—
246C22—1162no—
247C22—4642no—
248C22—2322no—
249C22#1174536411yescharacteristic
250C4—22no—
251C4—22no—
252C4—582no—
253C4—1162no—
254C4C22×D11611yescharacteristic
255C4C2×D4×D2911yescharacteristic
256C2—21no—
257C2—42no—
258C2—1162no—
259C2—2322no—
260C2D4×D11611yescharacteristic
subgroupG/H
centerC2D4×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#443C2
socleC2×C29D42
hypercenter#443D29
hypocenterC29#3291
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #14271975C2semidirect
2. #14271970C2semidirect
3. #14271536C2semidirect
4. #14271427C2semidirect
5. #14271426C2semidirect
6. #14271347C2semidirect
7. #14271332C2semidirect
8. #14271281C2semidirect
9. C29×#443C2semidirect
11. #11745364C22semidirect
13. C29×#131C22semidirect
14. #11745313C22semidirect
21. #11745271C22semidirect
27. C2×#90773C22semidirect
28. C2×#90773C22semidirect
29. #11745263C22semidirect
31. #11745231C22semidirect
32. C29×#108C22semidirect
33. C29×#104C22semidirect
34. C4×C8×C29C22semidirect
35. #11745172C22semidirect
36. #11745171C22semidirect
37. #11745167C22semidirect
38. #11745153C22semidirect
54. Q16×C29D4semidirect
55. SD16×C29D4semidirect
56. D8×C29D4semidirect
70. Dic116D4semidirect
72. D232D4semidirect
79. #90773D4semidirect
134. #443D29semidirect
159. #131C2×D29semidirect
163. #108C2×D29semidirect
165. #104C2×D29semidirect
168. C4×C8C2×D29semidirect
169. C29#3291semidirect
188. Q16D116semidirect
198. SD16D116semidirect
202. D8D116semidirect

Maximal subgroups

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

subgroupindex
#142719752
#142719702
#142715362
#142714272
#142714262
#142713472
#142713322
#142712812
C29×#4432
#329129