Finite Group Databasebeta

← #16829009

Subgroups — #16829009

Order 3712.

490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#11745313C211yesmaximal, characteristic, complemented
2C22×#90783C211yesmaximal, characteristic, complemented
3#14271640C211yesmaximal, characteristic, complemented
4#14271382C214yesmaximal, complemented
5#14271360C214yesmaximal, complemented
6#14271190C211yesmaximal, characteristic, complemented
7#14271168C211yesmaximal, characteristic, complemented
8#14271159C211yesmaximal, characteristic, complemented
9C29×#535C211yesmaximal, characteristic
10C2×#41×C29C2211yescharacteristic
11C22×D4×C29C2211yescharacteristic
12C22×Dic58C2211yescharacteristic
13C29×#127C2212yes—
14C29×#124C2212yes—
15C29×#121—22no—
16C29×#120—22no—
17C29×#117C2211yescharacteristic
18#11745313—24no—
19C2×#90785C2212yescomplemented
20C2×#90783—24no—
21C2×#90783C2214yes—
22C2×#90783C2212yescomplemented
23#11745288C2211yescharacteristic
24C2×#90777C2211yescharacteristic
25C22×#6597C2211yescharacteristic
26#11745249—22no—
27#11745239—22no—
28C4×Dic58C2214yescomplemented
29#11745183C2212yescomplemented
30#11745180C2214yes—
31#11745180C2212yescomplemented
32C4⋊#6597C2214yescomplemented
33C24×C29—21no—
34#41×C29—22no—
35#41×C29—22no—
36C2×Q8×C29C2311yescharacteristic
37C2×D4×C29—21no—
38C2×D4×C29—22no—
39C2×D4×C29—21no—
40C2×D4×C29—24no—
41C2×D4×C29—22no—
42C2×D4×C29C2312yes—
43C2×D4×C29C2311yescharacteristic
44C22×C4×C29—21no—
45C22×C4×C29C2311yescharacteristic
46C22×Dic29—21no—
47C2×Dic58—21no—
48C2×Dic58—22no—
49C2×Dic58D414yescomplemented
50C2×Dic58C2312yes—
51C4⋊C4×C29D412yes—
52C22⋊C4×C29—24no—
53C22⋊C4×C29D412yes—
54C42×C29C2312yes—
55C22⋊Dic29—21no—
56#90785—24no—
57#90783—28no—
58#90783—24no—
59C4⋊Dic29C2312yes—
60#90779—24no—
61C4×Dic29—21no—
62C4×Dic29—24no—
63#90777—22no—
64C2×#6597—22no—
65C2×#6597C2312yes—
66C2×#6597C2312yes—
67C23×C29—22no—
68C23×C29—21no—
69C23×C29—42no—
70C23×C29—82no—
71C23×C29C2×D411yescharacteristic
72Q8×C29—21no—
73Q8×C29—21no—
74D4×C29—22no—
75D4×C29—21no—
76D4×C29—22no—
77D4×C29—21no—
78D4×C29—42no—
79D4×C29—42no—
80D4×C29—84no—
81C2×C4×C29—21no—
82C2×C4×C29—42no—
83C2×C4×C29C2×D412yes—
84C2×C4×C29C2×D414yes—
85C2×C4×C29C2×D411yescharacteristic
86C2×C4×C29#4112yes—
87C2×C4×C29C2411yescharacteristic
88C2×Dic29—24no—
89C2×Dic29—22no—
90C2×Dic29—22no—
91Dic58—24no—
92Dic58—22no—
93Dic58C2×D414yes—
94#6597—22no—
95#6597—22no—
96#3043—291nomaximal, Sylow
97C22×C29—22no—
98C22×C29—41no—
99C22×C29—42no—
100C22×C29—42no—
101C22×C29—44no—
102C22×C29—84no—
103C22×C29#12112yes—
104C22×C29C22×D411yescharacteristic
105C4×C29—24no—
106C4×C29—41no—
107C4×C29#12112yes—
108C4×C29C22×D411yescharacteristic
109C4×C29C2×#4111yescharacteristic
110Dic29—24no—
111Dic29—42no—
112C2×#137—291no—
113C22×SD16—291no—
114#535D2911yescharacteristic
115#519—291no—
116#464—294no—
117#460—294no—
118#424—291no—
119#418—291no—
120#416—291no—
121C2×C29—22no—
122C2×C29—81no—
123C2×C29—82no—
124C2×C29C2×#12111yescharacteristic
125C2×C29#57712yes—
126C2×#41C2×D2911yescharacteristic
127C22×Q8—291no—
128C22×D4C2×D2911yescharacteristic
129#137—584no—
130C2×Q16—292no—
131C2×SD16—294no—
132C2×SD16—292no—
133C2×SD16—584no—
134C2×M16—291no—
135C22×C8—291no—
136#127C2×D2912yes—
137#124C2×D2912yes—
138#121—22no—
139#120—22no—
140C4×Q8—294no—
141C4×Q8—582no—
142#117—291no—
143#117—582no—
144#117C2×D2911yescharacteristic
145C4⋊C8—294no—
146#103—292no—
147#102—294no—
148#102—292no—
149C29#304311yescharacteristic, complemented, Sylow
150C24—21no—
151#41—22no—
152#41—22no—
153C2×Q8—294no—
154C2×Q8—292no—
155C2×Q8—582no—
156C2×Q8—581no—
157C2×Q8C22×D2911yescharacteristic
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—24no—
163C2×D4C22×D2912yes—
164C2×D4C22×D2911yescharacteristic
165C22×C4—21no—
166C22×C4—581no—
167C22×C4C22×D2911yescharacteristic
168Q16—584no—
169SD16—588no—
170SD16—584no—
171M16—582no—
172C2×C8—292no—
173C2×C8—292no—
174C2×C8—582no—
175C4⋊C4—292no—
176C4⋊C4—584no—
177C4⋊C4C22⋊D2912yes—
178C22⋊C4—24no—
179C22⋊C4—581no—
180C22⋊C4C22⋊D2912yes—
181C42—581no—
182C42—584no—
183C42C22×D2912yes—
184C23—22no—
185C23—21no—
186C23—42no—
187C23—82no—
188C23C2×C22⋊D2911yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—294no—
192Q8—584no—
193Q8—582no—
194D4—22no—
195D4—21no—
196D4—22no—
197D4—21no—
198D4—42no—
199D4—42no—
200D4—84no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—584no—
204C2×C4—582no—
205C2×C4—582no—
206C2×C4D4×D2912yes—
207C2×C4#9080712yes—
208C2×C4C2×C22⋊D2914yes—
209C2×C4C2×C22⋊D2911yescharacteristic
210C2×C4C23×D2911yescharacteristic
211C8—582no—
212C8—582no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—42no—
217C22—44no—
218C22—84no—
219C22#1174530012yes—
220C22C22×C22⋊D2911yescharacteristic
221C4—24no—
222C4—41no—
223C4—584no—
224C4—1162no—
225C4#1174530012yes—
226C4C2×D4×D2911yescharacteristic
227C4C2×#9080711yescharacteristic
228C2—22no—
229C2—82no—
230C2—81no—
231C2C2×#1174530011yescharacteristic
232C2#1427197412yes—
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#535C2
socleC22×C29C22×D4
hypercenter#535D29
hypocenterC29#3043
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#11745313C2semidirect
2. C22×#90783C2semidirect
3. #14271640C2semidirect
4. #14271382C2semidirect
5. #14271360C2semidirect
6. #14271190C2semidirect
7. #14271168C2semidirect
8. #14271159C2semidirect
19. C2×#90785C22semidirect
22. C2×#90783C22semidirect
28. C4×Dic58C22semidirect
29. #11745183C22semidirect
31. #11745180C22semidirect
32. C4⋊#6597C22semidirect
49. C2×Dic58D4semidirect
149. C29#3043semidirect

Maximal subgroups

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

subgroupindex
C2×#117453132
C22×#907832
#142716402
#142713822
#142713602
#142711902
#142711682
#142711592
C29×#5352
#304329