Finite Group Databasebeta

← #16829816

Subgroups — #16829816

Order 3712.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#14271718C211yesmaximal, characteristic, complemented
2#14271714C211yesmaximal, characteristic
3#14271519C214yesmaximal, complemented
4#14271513C211yesmaximal, characteristic, complemented
5#14271511C211yesmaximal, characteristic, complemented
6#14271510C211yesmaximal, characteristic, complemented
7#14271158C214yesmaximal, complemented
8C4×C8×D29C211yesmaximal, characteristic, complemented
9C29×#487C211yesmaximal, characteristic, complemented
10C2×#90809C2212yes—
11C29×C4⋊Q8C2211yescharacteristic
12C29×C4⋊Q8C2211yescharacteristic
13#11745309C2212yes—
14#11745308—21no—
15Q8×Dic29—21no—
16C2×C8×D29C2212yes—
17#11745259—21no—
18#11745257—21no—
19#11745257—21no—
20#11745255—21no—
21#11745255—21no—
22#11745254C2212yes—
23#11745252C2212yes—
24#11745249—21no—
25#11745236C2211yescharacteristic
26C42×D29C2211yescharacteristic
27#11745231C2211yescharacteristic
28C29×#103C2214yes—
29C4×C8×C29C2211yescharacteristic
30#11745183C2214yes—
31#11745169C2214yes—
32C8×Dic29C2212yes—
33#11745157C2214yes—
34C4×#6597C2211yescharacteristic
35C2×Q8×C29—21no—
36C2×Q8×C29C2312yes—
37#90809—28no—
38C2×D116—22no—
39C2×D116—21no—
40C2×D116—21no—
41C2×D116C2312yes—
42C2×C4×D29—22no—
43C2×C4×D29D411yescharacteristic
44C2×C4×D29D411yescharacteristic
45C2×C4×D29C2311yescharacteristic
46C2×Dic58—21no—
47C2×C8×C29C2312yes—
48C4⋊C4×C29—21no—
49C4⋊C4×C29—21no—
50C4⋊C4×C29—21no—
51C4⋊C4×C29C2312yes—
52C42×C29C2311yescharacteristic
53#90781—22no—
54#90781—22no—
55#90781—22no—
56C4⋊Dic29—21no—
57C4⋊Dic29—22no—
58C4⋊Dic29C2312yes—
59#90779—22no—
60C4×Dic29—22no—
61C4×Dic29D411yescharacteristic
62C4×Dic29D411yescharacteristic
63C4×Dic29C2311yescharacteristic
64C2×#6597C2312yes—
65C8×D29—24no—
66C22×D29—22no—
67C22×D29C2×D411yescharacteristic
68Q8×C29—24no—
69Q8×C29—42no—
70C2×C4×C29—22no—
71C2×C4×C29—22no—
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2×D411yescharacteristic
74C2×C4×C29C2411yescharacteristic
75C2×Dic29—22no—
76C2×Dic29C2×D411yescharacteristic
77C2×Dic29C2×D411yescharacteristic
78C2×Dic29C2×D411yescharacteristic
79D116—24no—
80D116—44no—
81D116—42no—
82D116—42no—
83C4×D29—22no—
84C4×D29—22no—
85C4×D29—44no—
86C4×D29#4114yes—
87Dic58—42no—
88C8×C29—22no—
89#6597—22no—
90#3131—291nomaximal, Sylow
91C22×C29C22×D411yescharacteristic
92C2×D29—21no—
93C2×D29—21no—
94C2×D29—42no—
95C2×D29—42no—
96C2×D29—42no—
97C2×D29#12412yes—
98C4×C29—42no—
99C4×C29—42no—
100C4×C29#13512yes—
101C4×C29#13512yes—
102C4×C29C2×#4112yes—
103Dic29—21no—
104Dic29—21no—
105Dic29—42no—
106Dic29#12412yes—
107#533—291no—
108#532—291no—
109#488—294no—
110#487—291no—
111#487D2911yescharacteristic, complemented
112#486—291no—
113#486—291no—
114#416—294no—
115C2×C4×C8—291no—
116C2×C29C2×#12411yescharacteristic
117C2×C29C2×#13511yescharacteristic
118C2×C29C2×#13511yescharacteristic
119D29—22no—
120D29—82no—
121C2×#41—292no—
122C22×C8—292no—
123C4⋊Q8—291no—
124C4⋊Q8C2×D2911yescharacteristic
125C4⋊Q8C2×D2911yescharacteristic
126#127—291no—
127#125—292no—
128#124—292no—
129C22⋊Q8—581no—
130C22⋊Q8—581no—
131#121—581no—
132#121—581no—
133C4×Q8—581no—
134C4×Q8—581no—
135C4×D4—581no—
136C4×D4—581no—
137#117—292no—
138C2×C42—291no—
139#103—294no—
140#103C2×D2914yes—
141#102—294no—
142#102—294no—
143C4×C8—292no—
144C4×C8—291no—
145C4×C8C2×D2911yescharacteristic
146C29#313111yescharacteristic, complemented, Sylow
147#41—588no—
148C2×Q8—21no—
149C2×Q8—581no—
150C2×Q8C22×D2912yes—
151C2×D4—292no—
152C2×D4—582no—
153C2×D4—581no—
154C2×D4—581no—
155C22×C4—291no—
156C22×C4—291no—
157C22×C4—291no—
158C22×C4—582no—
159C2×C8—292no—
160C2×C8—584no—
161C2×C8C22×D2912yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—292no—
166C4⋊C4—582no—
167C4⋊C4—582no—
168C4⋊C4—581no—
169C4⋊C4C22×D2912yes—
170C22⋊C4—582no—
171C22⋊C4—582no—
172C22⋊C4—582no—
173C42—291no—
174C42—291no—
175C42—291no—
176C42—582no—
177C42C22×D2911yescharacteristic
178C23—291no—
179C23—582no—
180Q8—24no—
181Q8—42no—
182Q8—1162no—
183D4—584no—
184D4—1164no—
185D4—1162no—
186D4—1162no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—291no—
190C2×C4—294no—
191C2×C4—291no—
192C2×C4—291no—
193C2×C4—582no—
194C2×C4—582no—
195C2×C4—582no—
196C2×C4—1164no—
197C2×C4D4×D2911yescharacteristic
198C2×C4D4×D2911yescharacteristic
199C2×C4C23×D2911yescharacteristic
200C8—22no—
201C8—582no—
202C22—292no—
203C22—581no—
204C22—581no—
205C22—1162no—
206C22—1162no—
207C22—1162no—
208C22C2×D4×D2911yescharacteristic
209C4—42no—
210C4—42no—
211C4—292no—
212C4—581no—
213C4—581no—
214C4—1162no—
215C4#1174527812yes—
216C4#1174528112yes—
217C4#41×D2912yes—
218C2—582no—
219C2—2322no—
220C2#124×D2911yescharacteristic
221C2C2×#1174527811yescharacteristic
222C2C2×#1174528111yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#487C2
socleC22×C29C22×D4
prime radical#14271714C2
hypercenter#487D29
hypocenterC29#3131
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #14271718C2semidirect
3. #14271519C2semidirect
4. #14271513C2semidirect
5. #14271511C2semidirect
6. #14271510C2semidirect
7. #14271158C2semidirect
8. C4×C8×D29C2semidirect
9. C29×#487C2semidirect
111. #487D29semidirect
146. C29#3131semidirect

Maximal subgroups

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

subgroupindex
#142717182
#142717142
#142715192
#142715132
#142715112
#142715102
#142711582
C4×C8×D292
C29×#4872
#313129