Finite Group Databasebeta

← #16831267

Subgroups — #16831267

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#14271976C212yesmaximal, complemented
2#14271969C212yesmaximal, complemented
3#14271435C212yesmaximal, complemented
4#14271423C212yesmaximal, complemented
5#14271345C212yesmaximal, complemented
6#14271340C211yesmaximal, characteristic, complemented
7#14271335C211yesmaximal, characteristic, complemented
8#14271286C212yesmaximal, complemented
9C29×#497C211yesmaximal, characteristic, complemented
10#11745362C2212yes—
11#11745362C2211yescharacteristic, complemented
12#11745359C2211yescharacteristic
13C2×Q16×C29C2212yescomplemented
14C2×SD16×C29C2212yes—
15C29×C4⋊Q8C2211yescharacteristic, complemented
16C29×#124C2211yescharacteristic
17#11745304C2212yes—
18#11745304C2212yes—
19#11745304C2212yescomplemented
20#11745294C2212yes—
21#11745281—22no—
22#11745280—22no—
23#11745280—22no—
24Q16×D29—22no—
25#11745278—22no—
26#11745277—22no—
27#11745276—22no—
28SD16×D29—22no—
29#11745266C2212yes—
30#11745263C2212yes—
31#11745263C2212yescomplemented
32C29×#97C2211yescharacteristic, complemented
33#11745184C2211yescharacteristic, complemented
34#11745184C2212yescomplemented
35#11745181C2211yescharacteristic
36#11745167C2212yescomplemented
37#11745153C2212yes—
38#11745153C2212yescomplemented
39C2×Q8×C29C2311yescharacteristic
40C2×Q8×C29C2312yes—
41C2×D4×C29C2311yescharacteristic
42C2×C22⋊D29—41no—
43#90809—22no—
44#90809—22no—
45#90809—22no—
46Q8×D29—22no—
47Q8×D29—22no—
48Q8×D29—22no—
49#90807—22no—
50D4×D29—22no—
51#90805—42no—
52#90805—41no—
53#90805C2312yes—
54#90805C2312yes—
55Q16×C29—22no—
56Q16×C29—22no—
57SD16×C29—22no—
58SD16×C29—22no—
59C2×C8×C29C2312yes—
60C4⋊C4×C29—41no—
61C22⋊C4×C29—41no—
62C42×C29C2311yescharacteristic
63#90785—22no—
64#90785—22no—
65#90785—22no—
66#90784—22no—
67#90784—22no—
68#90784—22no—
69#90783—22no—
70#90782—22no—
71#90777C2312yes—
72#90777C2312yes—
73Dic116D412yes—
74D232D412yes—
75#90773D412yes—
76#90773D412yes—
77#90772—22no—
78#90772—22no—
79C8×D29—22no—
80C8×D29—22no—
81C23×C29—21no—
82C22×D29—41no—
83Q8×C29—22no—
84Q8×C29—22no—
85Q8×C29—22no—
86D4×C29—22no—
87C2×C4×C29—21no—
88C2×C4×C29—21no—
89C2×C4×C29—22no—
90C2×C4×C29C2411yescharacteristic
91C22⋊D29—22no—
92C22⋊D29—22no—
93C22⋊D29—42no—
94C2×Dic29—41no—
95D116—41no—
96D116—42no—
97D116C2×D412yes—
98D116C2×D412yes—
99C4×D29—22no—
100C4×D29—22no—
101C4×D29—42no—
102C4×D29—42no—
103C4×D29—42no—
104Dic58—41no—
105Dic58—42no—
106Dic58C2×D412yes—
107Dic58C2×D412yes—
108C8×C29C2×D412yes—
109C8×C29C2×D412yes—
110#6597—22no—
111#6597—22no—
112#3289—291nomaximal, Sylow
113C22×C29—41no—
114C22×C29—81no—
115C22×C29H(5,𝔽2)11yescharacteristic
116C2×D29—22no—
117C2×D29—22no—
118C2×D29—161no—
119C4×C29—41no—
120C4×C29—41no—
121C4×C29—42no—
122C4×C29C22×D412yes—
123Dic29—22no—
124Dic29—22no—
125#578—292no—
126#577—292no—
127#497D2911yescharacteristic, complemented
128#473—292no—
129#471—292no—
130#456—292no—
131#455—291no—
132#454—291no—
133#444—292no—
134C2×C29—21no—
135C2×C29—81no—
136C2×C29D4211yescharacteristic
137D29—42no—
138D29—42no—
1392−1+4—292no—
1402−1+4—291no—
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)—292no—
149AGL(1,ℤ/8)—582no—
150#135—292no—
151#135—582no—
152#135—582no—
153C2×Q16—582no—
154C2×Q16C2×D2912yescomplemented
155C2×SD16—582no—
156C2×SD16C2×D2912yes—
157#131—292no—
158#131—292no—
159C4⋊Q8C2×D2911yescharacteristic, complemented
160#124C2×D2911yescharacteristic
161#108—292no—
162#104—292no—
163#104—292no—
164#101—291no—
165#101—292no—
166#100—291no—
167#97C2×D2911yescharacteristic, complemented
168C29#328911yescharacteristic, complemented, Sylow
169#41—292no—
170#41—292no—
171#41—582no—
172#41—582no—
173#41—582no—
174#41—582no—
175#41—1161no—
176#41—1162no—
177C2×Q8—582no—
178C2×Q8—582no—
179C2×Q8—582no—
180C2×Q8C22×D2911yescharacteristic
181C2×Q8C22×D2912yes—
182C2×D4—582no—
183C2×D4—1161no—
184C2×D4C22×D2911yescharacteristic
185Q16—22no—
186Q16—22no—
187Q16—292no—
188Q16—582no—
189Q16—582no—
190Q16—582no—
191SD16—22no—
192SD16—22no—
193SD16—292no—
194SD16—292no—
195SD16—582no—
196SD16—582no—
197SD16—582no—
198SD16—582no—
199D8—292no—
200D8—582no—
201M16—292no—
202M16—292no—
203M16—582no—
204M16—582no—
205C2×C8—582no—
206C2×C8—582no—
207C2×C8C22×D2912yes—
208C4⋊C4—41no—
209C22⋊C4—41no—
210C42C22×D2911yescharacteristic
211C23—21no—
212C23—1161no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—292no—
217Q8—292no—
218Q8—1162no—
219Q8—1161no—
220D4—22no—
221D4—292no—
222D4—292no—
223D4—582no—
224D4—582no—
225D4—1161no—
226D4—1162no—
227D4—1162no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—582no—
232C2×C4—582no—
233C2×C4—1162no—
234C2×C4—1162no—
235C2×C4—1162no—
236C2×C4—1161no—
237C2×C4C23×D2911yescharacteristic
238C8—582no—
239C8—582no—
240C8D4×D2912yes—
241C8D4×D2912yes—
242C22—41no—
243C22—81no—
244C22—582no—
245C22—582no—
246C22—4641no—
247C22#1174535911yescharacteristic
248C4—41no—
249C4—41no—
250C4—42no—
251C4—582no—
252C4—582no—
253C4C2×D4×D2912yes—
254C2—21no—
255C2—81no—
256C2—1162no—
257C2—1162no—
258C2#1427179811yescharacteristic
subgroupG/H
centerC2#14271798
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#497C2
socleC2×C29D42
hypercenter#497D29
hypocenterC29#3289
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #14271976C2semidirect
2. #14271969C2semidirect
3. #14271435C2semidirect
4. #14271423C2semidirect
5. #14271345C2semidirect
6. #14271340C2semidirect
7. #14271335C2semidirect
8. #14271286C2semidirect
9. C29×#497C2semidirect
11. #11745362C22semidirect
13. C2×Q16×C29C22semidirect
15. C29×C4⋊Q8C22semidirect
19. #11745304C22semidirect
31. #11745263C22semidirect
32. C29×#97C22semidirect
33. #11745184C22semidirect
34. #11745184C22semidirect
36. #11745167C22semidirect
38. #11745153C22semidirect
127. #497D29semidirect
154. C2×Q16C2×D29semidirect
159. C4⋊Q8C2×D29semidirect
167. #97C2×D29semidirect
168. C29#3289semidirect

Maximal subgroups

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

subgroupindex
#142719762
#142719692
#142714352
#142714232
#142713452
#142713402
#142713352
#142712862
C29×#4972
#328929