Finite Group Databasebeta

← #16822677

Subgroups — #16822677

Order 3712.

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

normal subgroups only

This group has 408 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×#11745232C211yesmaximal, characteristic
2#14271060C212yesmaximal
3#14271058C212yesmaximal
4#14271050C212yesmaximal
5#14271048C212yesmaximal
6#14271046C212yesmaximal
7#14271044C212yesmaximal
8#14271029C211yesmaximal, characteristic
9C29×#382C211yesmaximal, characteristic
10C2×C4⋊C4×C29C2211yescharacteristic
11C2×C4⋊C4×C29C2211yescharacteristic
12C2×C42×C29C2211yescharacteristic
13C2×C4⋊Dic29C2211yescharacteristic
14C2×C4⋊Dic29C2211yescharacteristic
15C2×C4⋊Dic29C2211yescharacteristic
16C2×C4⋊Dic29C2211yescharacteristic
17C2×#90779C2212yes—
18C2×#90779C2212yes—
19C2×#90779C2212yes—
20C2×#90779C2212yes—
21C2×C4×Dic29C2212yes—
22C2×C4×Dic29C2212yes—
23#11745232C418yescomplemented
24C29×#95C2212yes—
25C29×#95C2212yes—
26#11745179C2212yes—
27#11745179C2212yes—
28#11745179C2212yes—
29#11745179C2212yes—
30#11745179C2212yes—
31#11745179C2212yes—
32C22×C4×C29C2312yes—
33C22×C4×C29C2312yes—
34C22×C4×C29C2311yescharacteristic
35C22×C4×C29C2311yescharacteristic
36C22×C4×C29C2311yescharacteristic
37C22×Dic29C2312yes—
38C22×Dic29C2312yes—
39C22×Dic29C2312yes—
40C22×Dic29C2312yes—
41C4⋊C4×C29—41no—
42C4⋊C4×C29—41no—
43C42×C29C2×C414yes—
44C4⋊Dic29—41no—
45C4⋊Dic29—41no—
46C4⋊Dic29C2×C414yes—
47C4⋊Dic29C2×C414yes—
48#90779—42no—
49#90779—42no—
50#90779C2×C418yes—
51#90779C2×C418yes—
52C4×Dic29—42no—
53C4×Dic29—42no—
54C23×C29C2411yescharacteristic
55C2×C4×C29—21no—
56C2×C4×C29—21no—
57C2×C4×C29—21no—
58C2×C4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—22no—
62C2×C4×C29—22no—
63C2×C4×C29—22no—
64C2×C4×C29—22no—
65C2×C4×C29—22no—
66C2×C4×C29—22no—
67C2×C4×C29C22×C412yes—
68C2×C4×C29C22×C412yes—
69C2×C4×C29C22×C412yes—
70C2×Dic29—22no—
71C2×Dic29—22no—
72C2×Dic29—22no—
73C2×Dic29—22no—
74C2×Dic29—22no—
75C2×Dic29—22no—
76C2×Dic29—22no—
77C2×Dic29—22no—
78C2×Dic29—22no—
79C2×Dic29—22no—
80C2×Dic29C22×C414yes—
81C2×Dic29C22×C414yes—
82#2382—291nomaximal, Sylow
83C22×C29C23×C411yescharacteristic
84C22×C29H(5,𝔽2)11yescharacteristic
85C22×C29H(5,𝔽2)11yescharacteristic
86C22×C292−1+411yescharacteristic
87C22×C292−1+411yescharacteristic
88C22×C292−1+411yescharacteristic
89C22×C292−1+411yescharacteristic
90C4×C29—22no—
91C4×C29—22no—
92C4×C29—22no—
93C4×C29—42no—
94C4×C29—42no—
95Dic29—24no—
96Dic29—24no—
97Dic29—42no—
98Dic29—42no—
99C2×#125—291no—
100#389—292no—
101#389—292no—
102#387—292no—
103#387—292no—
104#387—292no—
105#387—292no—
106#382—291no—
107#382D2911yescharacteristic
108C2×C29#51911yescharacteristic
109C2×C29#52011yescharacteristic
110C2×C29#52011yescharacteristic
111C2×C29#56211yescharacteristic
112C2×C29#56311yescharacteristic
113C2×C29#56311yescharacteristic
114C2×C29#56411yescharacteristic
115#125—298no—
116C2×C4⋊C4—292no—
117C2×C4⋊C4—292no—
118C2×C4⋊C4—291no—
119C2×C4⋊C4—291no—
120C2×C4⋊C4—292no—
121C2×C4⋊C4—292no—
122C2×C4⋊C4—291no—
123C2×C4⋊C4—291no—
124C2×C4⋊C4C2×D2911yescharacteristic
125C2×C4⋊C4C2×D2911yescharacteristic
126C2×C42—292no—
127C2×C42—292no—
128C2×C42C2×D2911yescharacteristic
129#95—292no—
130#95—292no—
131#95—292no—
132#95—292no—
133#95—292no—
134#95—292no—
135#95C2×D2912yes—
136#95C2×D2912yes—
137C29#238211yescharacteristic, complemented, Sylow
138C22×C4—292no—
139C22×C4—292no—
140C22×C4—292no—
141C22×C4—292no—
142C22×C4C22×D2912yes—
143C22×C4C22×D2912yes—
144C22×C4C22×D2911yescharacteristic
145C22×C4C22×D2911yescharacteristic
146C22×C4C22×D2911yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—298no—
150C4⋊C4—298no—
151C4⋊C4—294no—
152C4⋊C4—294no—
153C4⋊C4—1162no—
154C4⋊C4—1162no—
155C4⋊C4—1161no—
156C4⋊C4—1161no—
157C42—1162no—
158C42—1162no—
159C42C4×D2914yes—
160C23C23×D2911yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—294no—
174C2×C4—294no—
175C2×C4—582no—
176C2×C4—582no—
177C2×C4—582no—
178C2×C4—582no—
179C2×C4—582no—
180C2×C4—582no—
181C2×C4—582no—
182C2×C4—582no—
183C2×C4—582no—
184C2×C4—582no—
185C2×C4C2×C4×D2912yes—
186C2×C4C2×C4×D2912yes—
187C2×C4C2×C4×D2912yes—
188C22C22×C4×D2911yescharacteristic
189C22#1174535911yescharacteristic
190C22#1174536211yescharacteristic
191C22#1174536411yescharacteristic
192C22#1174536511yescharacteristic
193C22#1174536511yescharacteristic
194C22#1174536511yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—584no—
201C4—584no—
202C4—1162no—
203C4—1162no—
204C2#1427164011yescharacteristic
205C2#1427164311yescharacteristic
206C2#1427164411yescharacteristic
207C2#1427190711yescharacteristic
208C2#1427191311yescharacteristic
209C2#1427191711yescharacteristic
210C2C29⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#382C2
socle, prime radical, cosocleC23×C29C24
hypercenter#382D29
hypocenterC29#2382
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
23. #11745232C4semidirect
137. C29#2382semidirect

Maximal subgroups

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

subgroupindex
C2×#117452322
#142710602
#142710582
#142710502
#142710482
#142710462
#142710442
#142710292
C29×#3822
#238229