Finite Group Databasebeta

← #16831282

Subgroups — #16831282

Order 3712.

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

normal subgroups only

This group has 460 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#14271972C212yesmaximal, complemented
2#14271971C212yesmaximal, complemented
3#14271537C211yesmaximal, characteristic, complemented
4#14271429C212yesmaximal, complemented
5#14271428C212yesmaximal, complemented
6#14271345C211yesmaximal, characteristic, complemented
7#14271332C212yesmaximal, complemented
8#14271277C212yesmaximal, complemented
9C29×#456C211yesmaximal, characteristic, complemented
10C29×2−1+4C2211yescharacteristic
11#11745364C2212yescomplemented
12#11745362C2211yescharacteristic
13C29×#137C2212yescomplemented
14C29×C4⋊Q8C2211yescharacteristic, complemented
15#11745312—22no—
16#11745312C2212yes—
17#11745311—22no—
18#11745311C2212yes—
19#11745310C2212yescomplemented
20#11745304—22no—
21#11745304C2212yescomplemented
22C2×#90784—22no—
23C2×#90784C2212yescomplemented
24C2×#90784C2212yescomplemented
25#11745281—22no—
26#11745280—22no—
27#11745276—22no—
28SD16×D29—22no—
29#11745270C2212yes—
30#11745269C2212yescomplemented
31#11745236C2211yescharacteristic
32C29×#104C2212yescomplemented
33C29×#101C2211yescharacteristic, complemented
34#11745184C2211yescharacteristic, complemented
35#11745171C2212yescomplemented
36#11745170C2212yescomplemented
37#11745153C2212yescomplemented
38C4×#6597C2211yescharacteristic, complemented
39#41×C29—22no—
40#41×C29—41no—
41#41×C29C2312yes—
42C2×Q8×C29—22no—
43C2×Q8×C29C2311yescharacteristic
44C2×Q8×C29C2311yescharacteristic
45#90809—22no—
46#90809—22no—
47Q8×D29—22no—
48D4×D29—22no—
49D4×D29—42no—
50#90805—22no—
51#90805—41no—
52#90805C2312yes—
53C2×D116—22no—
54C2×D116—41no—
55C2×D116C2312yes—
56Q16×C29—22no—
57SD16×C29—22no—
58M16×C29C2312yes—
59C4⋊C4×C29—41no—
60C42×C29C2311yescharacteristic
61#90785—22no—
62#90785D412yescomplemented
63#90784—22no—
64#90784—22no—
65#90784—22no—
66#90784—22no—
67#90784—22no—
68#90784—22no—
69#90784D412yescomplemented
70#90783D412yescomplemented
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—
81C22×D29—22no—
82C22×D29—42no—
83Q8×C29—22no—
84Q8×C29—22no—
85Q8×C29—41no—
86Q8×C29C2×D412yes—
87D4×C29—22no—
88D4×C29—41no—
89D4×C29C2×D412yes—
90C2×C4×C29—21no—
91C2×C4×C29—22no—
92C2×C4×C29—21no—
93C2×C4×C29—21no—
94C2×C4×C29—42no—
95C2×C4×C29C2411yescharacteristic
96C22⋊D29—22no—
97C22⋊D29—42no—
98D116—22no—
99D116—22no—
100D116—42no—
101D116—41no—
102D116—82no—
103D116C2×D412yes—
104C4×D29—22no—
105C4×D29—42no—
106C4×D29—42no—
107Dic58—41no—
108Dic58C2×D412yes—
109C8×C29—22no—
110#6597—22no—
111#6597C2×D412yes—
112#6597C2×D412yes—
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×C29—41no—
123C4×C29—41no—
124C4×C29C22×D412yes—
125Dic29—22no—
126#577—292no—
127#577—292no—
128#492—291no—
129#471—292no—
130#471—292no—
131#456—291no—
132#456D2911yescharacteristic, complemented
133#453—292no—
134#443—292no—
135C2×C29—21no—
136C2×C29—42no—
137C2×C29D4211yescharacteristic
138D29—42no—
139D29—82no—
1402−1+4—291no—
1412−1+4C2×D2911yescharacteristic
142H(5,𝔽2)—292no—
143#137—292no—
144#137—582no—
145#137—582no—
146#137C2×D2912yescomplemented
147AGL(1,ℤ/8)—292no—
148AGL(1,ℤ/8)—292no—
149AGL(1,ℤ/8)—582no—
150AGL(1,ℤ/8)—582no—
151#135—292no—
152#135—582no—
153#135—582no—
154C2×SD16—292no—
155C2×SD16—292no—
156C2×SD16—582no—
157C2×SD16—582no—
158#131—292no—
159#131—292no—
160C4⋊Q8C2×D2911yescharacteristic, complemented
161#127—291no—
162#108—292no—
163#104—292no—
164#104C2×D2912yescomplemented
165#101—291no—
166#101C2×D2911yescharacteristic, complemented
167#100—292no—
168C4×C8—291no—
169C29#329111yescharacteristic, complemented, Sylow
170#41—22no—
171#41—41no—
172#41—292no—
173#41—582no—
174#41—582no—
175#41—582no—
176#41—1161no—
177#41C22×D2912yes—
178C2×Q8—22no—
179C2×Q8—582no—
180C2×Q8C22×D2911yescharacteristic
181C2×Q8C22×D2911yescharacteristic
182C2×D4—292no—
183C2×D4—582no—
184C2×D4—582no—
185C2×D4—1161no—
186C2×D4—1162no—
187Q16—22no—
188Q16—292no—
189Q16—582no—
190SD16—22no—
191SD16—292no—
192SD16—292no—
193SD16—582no—
194SD16—582no—
195SD16—582no—
196SD16—582no—
197SD16—582no—
198SD16—582no—
199SD16—582no—
200D8—292no—
201D8—582no—
202D8—582no—
203M16—292no—
204M16—582no—
205M16—582no—
206M16C22×D2912yes—
207C2×C8—292no—
208C2×C8—582no—
209C2×C8—582no—
210C4⋊C4—41no—
211C42C22×D2911yescharacteristic
212C23—582no—
213C23—1162no—
214Q8—22no—
215Q8—22no—
216Q8—41no—
217Q8—292no—
218Q8—1161no—
219Q8D4×D2912yes—
220D4—22no—
221D4—41no—
222D4—292no—
223D4—582no—
224D4—582no—
225D4—582no—
226D4—1162no—
227D4—1161no—
228D4—1162no—
229D4—2322no—
230D4D4×D2912yes—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—582no—
237C2×C4—1162no—
238C2×C4—1162no—
239C2×C4C23×D2911yescharacteristic
240C8—22no—
241C8—292no—
242C8—292no—
243C8—582no—
244C22—22no—
245C22—582no—
246C22—1162no—
247C22—4642no—
248C22—2322no—
249C22#1174535911yescharacteristic
250C4—22no—
251C4—22no—
252C4—41no—
253C4—41no—
254C4—582no—
255C4C2×D4×D2912yes—
256C2—21no—
257C2—42no—
258C2—1162no—
259C2—2322no—
260C2#1427179511yescharacteristic
subgroupG/H
centerC2#14271795
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#456C2
socleC2×C29D42
hypercenter#456D29
hypocenterC29#3291
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14271972C2semidirect
2. #14271971C2semidirect
3. #14271537C2semidirect
4. #14271429C2semidirect
5. #14271428C2semidirect
6. #14271345C2semidirect
7. #14271332C2semidirect
8. #14271277C2semidirect
9. C29×#456C2semidirect
11. #11745364C22semidirect
13. C29×#137C22semidirect
14. C29×C4⋊Q8C22semidirect
19. #11745310C22semidirect
21. #11745304C22semidirect
23. C2×#90784C22semidirect
24. C2×#90784C22semidirect
30. #11745269C22semidirect
32. C29×#104C22semidirect
33. C29×#101C22semidirect
34. #11745184C22semidirect
35. #11745171C22semidirect
36. #11745170C22semidirect
37. #11745153C22semidirect
38. C4×#6597C22semidirect
62. #90785D4semidirect
69. #90784D4semidirect
70. #90783D4semidirect
72. #90782D4semidirect
132. #456D29semidirect
146. #137C2×D29semidirect
160. C4⋊Q8C2×D29semidirect
164. #104C2×D29semidirect
166. #101C2×D29semidirect
169. C29#3291semidirect

Maximal subgroups

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

subgroupindex
#142719722
#142719712
#142715372
#142714292
#142714282
#142713452
#142713322
#142712772
C29×#4562
#329129