Finite Group Databasebeta

← #16831269

Subgroups — #16831269

Order 3712.

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

normal subgroups only

This group has 448 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#14271978C212yesmaximal, complemented
2#14271973C212yesmaximal, complemented
3#14271558C211yesmaximal, characteristic, complemented
4#14271437C212yesmaximal, complemented
5#14271424C212yesmaximal, complemented
6#14271347C212yesmaximal, complemented
7#14271340C211yesmaximal, characteristic, complemented
8#14271282C212yesmaximal, complemented
9C29×#454C211yesmaximal, characteristic, complemented
10C29×2−1+4C2211yescharacteristic, complemented
11#11745365C2212yes—
12#11745359C2211yescharacteristic
13C29×AGL(1,ℤ/8)C2212yes—
14C29×#124C2211yescharacteristic
15#11745313—22no—
16#11745313C2212yescomplemented
17#11745312—22no—
18#11745312C2212yes—
19#11745310C2212yescomplemented
20C2×#90785—22no—
21C2×#90785C2212yescomplemented
22#11745304—22no—
23#11745304C2212yes—
24C2×#90783C2212yes—
25#11745277—22no—
26SD16×D29—22no—
27#11745274—22no—
28#11745273—22no—
29#11745271C2212yes—
30#11745269C2212yes—
31#11745231C2211yescharacteristic, complemented
32C29×#104C2212yescomplemented
33C29×#101C2211yescharacteristic, complemented
34#11745181C2211yescharacteristic
35#11745172C2212yescomplemented
36#11745170C2212yescomplemented
37#11745153C2212yes—
38#11745151C2211yescharacteristic, complemented
39#41×C29—22no—
40#41×C29—41no—
41#41×C29C2312yes—
42C2×Q8×C29—22no—
43C2×Q8×C29C2311yescharacteristic
44C2×D4×C29C2311yescharacteristic
45C2×C22⋊D29—41no—
46Q8×D29—22no—
47#90807—22no—
48#90807—22no—
49#90807—42no—
50D4×D29—22no—
51#90805—22no—
52#90805C2312yes—
53C2×Dic58—22no—
54C2×Dic58C2312yes—
55SD16×C29—22no—
56D8×C29—22no—
57M16×C29C2312yes—
58C22⋊C4×C29—41no—
59C42×C29C2311yescharacteristic
60#90785—22no—
61#90785—22no—
62#90785—22no—
63#90785—22no—
64#90785D412yes—
65#90784—22no—
66#90784D412yes—
67#90783—22no—
68#90783—22no—
69#90783—22no—
70#90783D412yes—
71#90782D412yes—
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—
82C22×D29—41no—
83Q8×C29—22no—
84Q8×C29—41no—
85Q8×C29C2×D412yes—
86D4×C29—22no—
87D4×C29—22no—
88D4×C29—41no—
89D4×C29C2×D412yes—
90C2×C4×C29—22no—
91C2×C4×C29—21no—
92C2×C4×C29—21no—
93C2×C4×C29—42no—
94C2×C4×C29C2411yescharacteristic
95C22⋊D29—22no—
96C22⋊D29—42no—
97C22⋊D29—42no—
98C2×Dic29—22no—
99C2×Dic29—41no—
100C2×Dic29—42no—
101D116C2×D412yes—
102C4×D29—22no—
103C4×D29—42no—
104Dic58—22no—
105Dic58—22no—
106Dic58—42no—
107Dic58C2×D412yes—
108C8×C29—22no—
109#6597—22no—
110#6597C2×D412yes—
111#6597C2×D412yes—
112#3289—291nomaximal, Sylow
113C22×C29—22no—
114C22×C29—41no—
115C22×C29—81no—
116C22×C29H(5,𝔽2)11yescharacteristic
117C2×D29—22no—
118C2×D29—161no—
119C4×C29—22no—
120C4×C29—41no—
121C4×C29—41no—
122C4×C29C22×D412yes—
123Dic29—22no—
124Dic29—42no—
125#578—292no—
126#577—292no—
127#497—291no—
128#473—292no—
129#471—292no—
130#456—292no—
131#455—291no—
132#454D2911yescharacteristic, complemented
133#444—292no—
134C2×C29—21no—
135C2×C29—42no—
136C2×C29—81no—
137C2×C29D4211yescharacteristic
138D29—42no—
1392−1+4—292no—
1402−1+4C2×D2911yescharacteristic, complemented
141H(5,𝔽2)—291no—
142#137—292no—
143#137—292no—
144#137—292no—
145#137—582no—
146#137—582no—
147#137—582no—
148AGL(1,ℤ/8)—582no—
149AGL(1,ℤ/8)C2×D2912yes—
150#135—292no—
151#135—582no—
152#135—582no—
153C2×Q16—292no—
154C2×Q16—582no—
155C2×SD16—292no—
156C2×SD16—582no—
157#131—292no—
158#131—292no—
159C4⋊Q8—291no—
160#124C2×D2911yescharacteristic
161#108—292no—
162#104—292no—
163#104C2×D2912yescomplemented
164#101—292no—
165#101C2×D2911yescharacteristic, complemented
166#100—291no—
167#97—291no—
168C29#328911yescharacteristic, complemented, Sylow
169#41—22no—
170#41—41no—
171#41—292no—
172#41—582no—
173#41—582no—
174#41—582no—
175#41—1162no—
176#41C22×D2912yes—
177C2×Q8—22no—
178C2×Q8—292no—
179C2×Q8—582no—
180C2×Q8—582no—
181C2×Q8C22×D2911yescharacteristic
182C2×D4—582no—
183C2×D4—1161no—
184C2×D4C22×D2911yescharacteristic
185Q16—292no—
186Q16—582no—
187Q16—582no—
188Q16—582no—
189Q16—582no—
190Q16—582no—
191SD16—22no—
192SD16—292no—
193SD16—292no—
194SD16—582no—
195SD16—582no—
196SD16—582no—
197SD16—582no—
198SD16—582no—
199D8—22no—
200D8—292no—
201M16—292no—
202M16—582no—
203M16—582no—
204M16C22×D2912yes—
205C2×C8—292no—
206C2×C8—582no—
207C2×C8—582no—
208C4⋊C4—1161no—
209C22⋊C4—41no—
210C42C22×D2911yescharacteristic
211C23—21no—
212C23—1161no—
213Q8—22no—
214Q8—41no—
215Q8—292no—
216Q8—582no—
217Q8—582no—
218Q8—1162no—
219Q8D4×D2912yes—
220D4—22no—
221D4—22no—
222D4—41no—
223D4—292no—
224D4—582no—
225D4—1162no—
226D4—1162no—
227D4D4×D2912yes—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—42no—
232C2×C4—582no—
233C2×C4—582no—
234C2×C4—1162no—
235C2×C4—1161no—
236C2×C4—1162no—
237C2×C4C23×D2911yescharacteristic
238C8—22no—
239C8—292no—
240C8—292no—
241C8—582no—
242C22—22no—
243C22—41no—
244C22—81no—
245C22—582no—
246C22—4641no—
247C22#1174535911yescharacteristic
248C4—22no—
249C4—41no—
250C4—41no—
251C4—582no—
252C4—1162no—
253C4C2×D4×D2912yes—
254C2—21no—
255C2—42no—
256C2—81no—
257C2—1162no—
258C2#1427179511yescharacteristic
subgroupG/H
centerC2#14271795
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#454C2
socleC2×C29D42
hypercenter#454D29
hypocenterC29#3289
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #14271978C2semidirect
2. #14271973C2semidirect
3. #14271558C2semidirect
4. #14271437C2semidirect
5. #14271424C2semidirect
6. #14271347C2semidirect
7. #14271340C2semidirect
8. #14271282C2semidirect
9. C29×#454C2semidirect
10. C29×2−1+4C22semidirect
16. #11745313C22semidirect
19. #11745310C22semidirect
21. C2×#90785C22semidirect
31. #11745231C22semidirect
32. C29×#104C22semidirect
33. C29×#101C22semidirect
35. #11745172C22semidirect
36. #11745170C22semidirect
38. #11745151C22semidirect
132. #454D29semidirect
140. 2−1+4C2×D29semidirect
163. #104C2×D29semidirect
165. #101C2×D29semidirect
168. C29#3289semidirect

Maximal subgroups

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

subgroupindex
#142719782
#142719732
#142715582
#142714372
#142714242
#142713472
#142713402
#142712822
C29×#4542
#328929