Finite Group Databasebeta

← #16822655

Subgroups — #16822655

Order 3712.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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×#11745286C211yesmaximal, characteristic
2#14271067C212yesmaximal, complemented
3#14271058C212yesmaximal, complemented
4#14271057C212yesmaximal
5#14271051C212yesmaximal
6#14271046C212yesmaximal, complemented
7#14271044C212yesmaximal, complemented
8#14271026C211yesmaximal, characteristic
9C29×#380C211yesmaximal, characteristic
10C23×C4×C29C2211yescharacteristic
11C22×Dic58C2211yescharacteristic
12C2×C4⋊C4×C29C2212yes—
13C2×C22⋊C4×C29C2211yescharacteristic
14C2×C22⋊C4×C29C2211yescharacteristic
15C2×C22⋊Dic29C2212yes—
16C2×C22⋊Dic29C2212yes—
17C2×C4⋊Dic29C2211yescharacteristic
18#11745286C418yescomplemented
19C2×#90779C2212yes—
20C2×#90779C2212yes—
21C2×#90779C2212yes—
22C2×C4×Dic29C2212yes—
23C2×C4×Dic29C2212yes—
24C29×#95C2212yes—
25#11745179C2211yescharacteristic
26#11745179C2212yes—
27#11745179C2211yescharacteristic
28#11745179C2212yes—
29#11745179C2212yes—
30#11745179C2212yes—
31#11745179C2212yes—
32C24×C29C2311yescharacteristic
33C22×C4×C29—42no—
34C22×C4×C29C2×C414yes—
35C22×C4×C29C2312yes—
36C22×C4×C29C2312yes—
37C22×C4×C29C2311yescharacteristic
38C22×C4×C29C2311yescharacteristic
39C22×Dic29C2312yes—
40C22×Dic29C2312yes—
41C22×Dic29C2312yes—
42C22×Dic29C2312yes—
43C2×Dic58—42no—
44C2×Dic58C2×C414yes—
45C4⋊C4×C29—42no—
46C22⋊C4×C29—41no—
47C22⋊C4×C29—41no—
48C22⋊Dic29—42no—
49C22⋊Dic29C2×C418yes—
50C4⋊Dic29C2×C414yes—
51#90779—42no—
52#90779—42no—
53#90779C2×C418yes—
54C4×Dic29—42no—
55C4×Dic29—42no—
56C23×C29—22no—
57C23×C29—21no—
58C23×C29—21no—
59C23×C29—22no—
60C23×C29C22×C412yes—
61C23×C29C2411yescharacteristic
62C2×C4×C29—22no—
63C2×C4×C29—22no—
64C2×C4×C29—22no—
65C2×C4×C29—22no—
66C2×C4×C29—22no—
67C2×C4×C29—22no—
68C2×C4×C29—22no—
69C2×C4×C29—22no—
70C2×C4×C29—44no—
71C2×C4×C29C22×C412yes—
72C2×C4×C29C22×C412yes—
73C2×Dic29—22no—
74C2×Dic29—22no—
75C2×Dic29—22no—
76C2×Dic29—22no—
77C2×Dic29—22no—
78C2×Dic29—22no—
79C2×Dic29—22no—
80C2×Dic29—22no—
81C2×Dic29—22no—
82C2×Dic29—22no—
83C2×Dic29C22×C414yes—
84C2×Dic29C22×C414yes—
85Dic58—44no—
86#2378—291nomaximal, Sylow
87C22×C29—22no—
88C22×C29—22no—
89C22×C29—22no—
90C22×C29—42no—
91C22×C29—42no—
92C22×C29C23×C411yescharacteristic
93C22×C29H(5,𝔽2)12yes—
94C22×C29H(5,𝔽2)11yescharacteristic
95C22×C292−1+411yescharacteristic
96C22×C292−1+412yes—
97C4×C29—22no—
98C4×C29—22no—
99C4×C29—42no—
100C4×C29—42no—
101Dic29—24no—
102Dic29—24no—
103Dic29—42no—
104Dic29—42no—
105C2×C22⋊Q8—291no—
106#391—292no—
107#389—292no—
108#388—292no—
109#388—292no—
110#387—292no—
111#387—292no—
112#381—291no—
113#380D2911yescharacteristic
114C2×C29—42no—
115C2×C29#51811yescharacteristic
116C2×C29#51911yescharacteristic
117C2×C29#52011yescharacteristic
118C2×C29#56212yes—
119C2×C29#56312yes—
120C22×Q8—291no—
121C23×C4C2×D2911yescharacteristic
122C22⋊Q8—298no—
123C2×C4⋊C4—292no—
124C2×C4⋊C4—291no—
125C2×C4⋊C4—292no—
126C2×C4⋊C4—292no—
127C2×C4⋊C4C2×D2912yes—
128C2×C22⋊C4—292no—
129C2×C22⋊C4—292no—
130C2×C22⋊C4C2×D2911yescharacteristic
131C2×C22⋊C4C2×D2911yescharacteristic
132C2×C42—292no—
133C2×C42—292no—
134#95—291no—
135#95—292no—
136#95—291no—
137#95—292no—
138#95—292no—
139#95—292no—
140#95—292no—
141#95C2×D2912yes—
142C29#237811yescharacteristic, complemented, Sylow
143C24C22×D2911yescharacteristic
144C2×Q8—294no—
145C2×Q8—1162no—
146C22×C4—42no—
147C22×C4—292no—
148C22×C4—292no—
149C22×C4—292no—
150C22×C4—292no—
151C22×C4C4×D2914yes—
152C22×C4C22×D2912yes—
153C22×C4C22×D2912yes—
154C22×C4C22×D2911yescharacteristic
155C22×C4C22×D2911yescharacteristic
156C4⋊C4—42no—
157C4⋊C4—298no—
158C4⋊C4—294no—
159C4⋊C4—1162no—
160C4⋊C4—1162no—
161C22⋊C4—41no—
162C22⋊C4—41no—
163C22⋊C4—298no—
164C22⋊C4—1162no—
165C42—1162no—
166C42—1162no—
167C23—21no—
168C23—22no—
169C23—21no—
170C23—22no—
171C23C2×C4×D2912yes—
172C23C23×D2911yescharacteristic
173Q8—1164no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—294no—
184C2×C4—294no—
185C2×C4—582no—
186C2×C4—582no—
187C2×C4—582no—
188C2×C4—582no—
189C2×C4—582no—
190C2×C4—582no—
191C2×C4—582no—
192C2×C4—582no—
193C2×C4—582no—
194C2×C4—582no—
195C2×C4C2×C4×D2912yes—
196C2×C4C2×C4×D2912yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D2911yescharacteristic
203C22#1174535912yes—
204C22#1174535911yescharacteristic
205C22#1174536211yescharacteristic
206C22#1174536512yes—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—584no—
212C4—584no—
213C4—1162no—
214C4—1162no—
215C2—42no—
216C2#1427163611yescharacteristic
217C2#1427164011yescharacteristic
218C2#1427164411yescharacteristic
219C2#1427190812yes—
220C2#1427191412yes—
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#380C2
socle, cosocleC23×C29C24
prime radicalC24×C29C23
hypercenter#380D29
hypocenterC29#2378
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #14271067C2semidirect
3. #14271058C2semidirect
6. #14271046C2semidirect
7. #14271044C2semidirect
18. #11745286C4semidirect
142. C29#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#117452862
#142710672
#142710582
#142710572
#142710512
#142710462
#142710442
#142710262
C29×#3802
#237829