Finite Group Databasebeta

← #16831287

Subgroups — #16831287

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#14271974C212yesmaximal, complemented
2#14271973C212yesmaximal, complemented
3#14271535C211yesmaximal, characteristic, complemented
4#14271425C212yesmaximal, complemented
5#14271424C212yesmaximal, complemented
6#14271347C212yesmaximal, complemented
7#14271330C211yesmaximal, characteristic, complemented
8#14271277C212yesmaximal, complemented
9C29×#453C211yesmaximal, characteristic, complemented
10C29×H(5,𝔽2)C2211yescharacteristic, complemented
11#11745365C2212yes—
12#11745359C2211yescharacteristic, complemented
13C29×AGL(1,ℤ/8)C2212yes—
14C29×#127C2211yescharacteristic
15#11745313—22no—
16#11745313C2212yescomplemented
17#11745312—22no—
18#11745312C2212yes—
19#11745310C2212yescomplemented
20C2×#90783—22no—
21C2×#90783C2212yescomplemented
22C2×#90783C2212yescomplemented
23#11745294—22no—
24#11745294C2212yes—
25#11745277—22no—
26SD16×D29—22no—
27#11745274—22no—
28#11745273—22no—
29#11745271C2212yescomplemented
30#11745269C2212yescomplemented
31#11745231C2211yescharacteristic, complemented
32C29×#104C2212yescomplemented
33C29×#100C2211yescharacteristic, complemented
34#11745181C2211yescharacteristic, complemented
35#11745172C2212yescomplemented
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—
47Q8×D29—22no—
48#90807—22no—
49#90807—22no—
50#90807—42no—
51D4×D29—22no—
52#90805—22no—
53#90805C2312yes—
54C2×Dic58—22no—
55C2×Dic58C2312yes—
56SD16×C29—22no—
57D8×C29—22no—
58M16×C29C2312yes—
59C42×C29C2311yescharacteristic
60#90785—22no—
61#90785D412yescomplemented
62#90784D412yescomplemented
63#90783—22no—
64#90783—22no—
65#90783—22no—
66#90783—22no—
67#90783—22no—
68#90783—22no—
69#90783D412yescomplemented
70#90782—22no—
71#90782D412yescomplemented
72C4⋊Dic29—41no—
73#90777—22no—
74#90777C2312yes—
75C2×#6597—22no—
76C2×#6597C2312yes—
77Dic116—22no—
78#90773—22no—
79#90772—22no—
80C8×D29—22no—
81C23×C29—21no—
82C23×C29—21no—
83C23×C29—41no—
84C22×D29—41no—
85Q8×C29C2×D412yes—
86D4×C29—22no—
87D4×C29—22no—
88D4×C29—22no—
89D4×C29—42no—
90D4×C29—82no—
91D4×C29C2×D412yes—
92C2×C4×C29—21no—
93C2×C4×C29—22no—
94C2×C4×C29—41no—
95C2×C4×C29C2411yescharacteristic
96C22⋊D29—22no—
97C22⋊D29—42no—
98C22⋊D29—42no—
99C2×Dic29—22no—
100C2×Dic29—41no—
101C2×Dic29—42no—
102D116C2×D412yes—
103C4×D29—22no—
104C4×D29—42no—
105Dic58—22no—
106Dic58—22no—
107Dic58—42no—
108Dic58C2×D412yes—
109C8×C29—22no—
110#6597—22no—
111#6597C2×D412yes—
112#6597C2×D412yes—
113#3291—291nomaximal, Sylow
114C22×C29—22no—
115C22×C29—41no—
116C22×C29—41no—
117C22×C29—81no—
118C22×C29—81no—
119C22×C29—161no—
120C22×C29H(5,𝔽2)11yescharacteristic
121C2×D29—22no—
122C2×D29—161no—
123C4×C29—22no—
124C4×C29—22no—
125C4×C29C22×D412yes—
126Dic29—22no—
127Dic29—42no—
128#577—292no—
129#577—292no—
130#492—291no—
131#471—292no—
132#471—292no—
133#456—292no—
134#453—291no—
135#453D2911yescharacteristic, complemented
136#443—292no—
137C2×C29—21no—
138C2×C29—42no—
139C2×C29—81no—
140C2×C29—81no—
141C2×C29D4211yescharacteristic
142D29—42no—
1432−1+4—292no—
144H(5,𝔽2)—291no—
145H(5,𝔽2)C2×D2911yescharacteristic, complemented
146#137—292no—
147#137—292no—
148#137—582no—
149#137—582no—
150AGL(1,ℤ/8)—292no—
151AGL(1,ℤ/8)—582no—
152AGL(1,ℤ/8)—582no—
153AGL(1,ℤ/8)C2×D2912yes—
154#135—292no—
155#135—582no—
156#135—582no—
157C2×SD16—292no—
158C2×SD16—292no—
159C2×SD16—582no—
160C2×SD16—582no—
161#131—292no—
162#131—292no—
163C4⋊Q8—291no—
164#127C2×D2911yescharacteristic
165#108—292no—
166#104—292no—
167#104C2×D2912yescomplemented
168#101—292no—
169#100—291no—
170#100C2×D2911yescharacteristic, complemented
171C4×C8—291no—
172C29#329111yescharacteristic, complemented, Sylow
173#41—22no—
174#41—292no—
175#41—582no—
176#41—582no—
177#41—582no—
178#41—1162no—
179#41C22×D2912yes—
180C2×Q8—292no—
181C2×Q8—582no—
182C2×Q8—582no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—582no—
187C2×D4—1161no—
188C2×D4C22×D2911yescharacteristic
189C2×D4C22×D2911yescharacteristic
190Q16—292no—
191Q16—582no—
192Q16—582no—
193SD16—22no—
194SD16—292no—
195SD16—292no—
196SD16—582no—
197SD16—582no—
198SD16—582no—
199SD16—582no—
200SD16—582no—
201SD16—582no—
202SD16—582no—
203D8—22no—
204D8—292no—
205D8—582no—
206M16—292no—
207M16—582no—
208M16—582no—
209M16C22×D2912yes—
210C2×C8—292no—
211C2×C8—582no—
212C2×C8—582no—
213C4⋊C4—1161no—
214C42C22×D2911yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—1161no—
219Q8—292no—
220Q8—582no—
221Q8—582no—
222Q8—1162no—
223Q8D4×D2912yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—292no—
230D4—582no—
231D4—1162no—
232D4—1162no—
233D4D4×D2912yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—582no—
238C2×C4—582no—
239C2×C4—1162no—
240C2×C4—1161no—
241C2×C4—1162no—
242C2×C4C23×D2911yescharacteristic
243C8—22no—
244C8—292no—
245C8—292no—
246C8—582no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—582no—
254C22—4641no—
255C22#1174535911yescharacteristic
256C4—22no—
257C4—22no—
258C4—582no—
259C4—1162no—
260C4C2×D4×D2912yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—1162no—
266C2#1427179511yescharacteristic
subgroupG/H
centerC2#14271795
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#453C2
socleC2×C29D42
hypercenter#453D29
hypocenterC29#3291
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. #14271974C2semidirect
2. #14271973C2semidirect
3. #14271535C2semidirect
4. #14271425C2semidirect
5. #14271424C2semidirect
6. #14271347C2semidirect
7. #14271330C2semidirect
8. #14271277C2semidirect
9. C29×#453C2semidirect
10. C29×H(5,𝔽2)C22semidirect
12. #11745359C22semidirect
16. #11745313C22semidirect
19. #11745310C22semidirect
21. C2×#90783C22semidirect
22. C2×#90783C22semidirect
29. #11745271C22semidirect
30. #11745269C22semidirect
31. #11745231C22semidirect
32. C29×#104C22semidirect
33. C29×#100C22semidirect
34. #11745181C22semidirect
35. #11745172C22semidirect
36. #11745170C22semidirect
37. #11745153C22semidirect
38. C4×#6597C22semidirect
61. #90785D4semidirect
62. #90784D4semidirect
69. #90783D4semidirect
71. #90782D4semidirect
135. #453D29semidirect
145. H(5,𝔽2)C2×D29semidirect
167. #104C2×D29semidirect
170. #100C2×D29semidirect
172. C29#3291semidirect

Maximal subgroups

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

subgroupindex
#142719742
#142719732
#142715352
#142714252
#142714242
#142713472
#142713302
#142712772
C29×#4532
#329129