Finite Group Databasebeta

← #16830963

Subgroups — #16830963

Order 3712.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 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#14271784C212yesmaximal, complemented
2#14271454C212yesmaximal, complemented
3#14271449C212yesmaximal, complemented
4#14271421C211yesmaximal, characteristic, complemented
5#14271416C211yesmaximal, characteristic
6#14271392C212yesmaximal, complemented
7#14271386C212yesmaximal, complemented
8#14271379C212yesmaximal, complemented
9C29×#424C211yesmaximal, characteristic, complemented
10C2×M16×C29C2211yescharacteristic
11C22×C8×C29C2211yescharacteristic
12C29×#117C2211yescharacteristic
13#11745292C2212yes—
14#11745286C2212yes—
15C2×Dic116C2211yescharacteristic
16C2×D232C2211yescharacteristic
17C2×#90773C2212yes—
18#11745260—22no—
19#11745258—22no—
20#11745247—22no—
21#11745245—22no—
22#11745237C2212yes—
23C4×D116C2212yes—
24#11745231C2212yes—
25C4×Dic58C2212yes—
26C29×C4⋊C8C2212yes—
27C29×C4⋊C8C2212yes—
28#11745169C2212yes—
29#11745169C2212yes—
30#11745165C2212yes—
31#11745165C2211yescharacteristic
32#11745165C2211yescharacteristic
33#11745164C2212yes—
34#11745164C2212yes—
35C22×C4×C29C2311yescharacteristic
36C2×C22⋊D29—22no—
37C2×D116C2312yes—
38C2×C4×D29—22no—
39C2×Dic58—22no—
40C2×Dic58C2312yes—
41M16×C29—41no—
42C2×C8×C29—41no—
43C2×C8×C29C2312yes—
44C2×C8×C29C2311yescharacteristic
45C2×C8×C29C2311yescharacteristic
46C4⋊C4×C29D412yes—
47C22⋊C4×C29D411yescharacteristic
48C22⋊C4×C29D411yescharacteristic
49C42×C29C2312yes—
50C22⋊Dic29—22no—
51#90781—22no—
52#90781—22no—
53#90781—22no—
54#90781—22no—
55C4⋊Dic29—22no—
56C4⋊Dic29C2312yes—
57C4⋊Dic29C2312yes—
58#90779—22no—
59#90779—22no—
60C4×Dic29—22no—
61Dic116—41no—
62D232—41no—
63#90773—42no—
64C23×C29C2×D411yescharacteristic
65C22×D29—22no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29C2×D412yes—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2×D412yes—
71C2×C4×C29C2411yescharacteristic
72C22⋊D29—82no—
73C2×Dic29—22no—
74C2×Dic29—22no—
75C2×Dic29—22no—
76D116—22no—
77D116—22no—
78C4×D29—82no—
79Dic58—22no—
80Dic58—22no—
81Dic58—82no—
82C8×C29—22no—
83C8×C29—21no—
84C8×C29—21no—
85#3263—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—22no—
88C22×C29C22×D411yescharacteristic
89C2×D29—42no—
90C2×D29—42no—
91C2×D29—42no—
92C4×C29—21no—
93C4×C29—22no—
94C4×C29—22no—
95C4×C29H(5,𝔽2)11yescharacteristic
96C4×C292−1+411yescharacteristic
97Dic29—42no—
98Dic29—42no—
99Dic29—42no—
100#542—292no—
101#476—292no—
102#475—292no—
103#470—291no—
104#469—291no—
105#465—292no—
106#464—292no—
107#463—292no—
108#424D2911yescharacteristic, complemented
109C2×C29—41no—
110C2×C29#53711yescharacteristic
111C2×C29#57712yes—
112D29—82no—
113C2×Q16—291no—
114C2×SD16—292no—
115C2×D8—291no—
116C2×M16C2×D2911yescharacteristic
117C22×C8C2×D2911yescharacteristic
118C4⋊Q8—292no—
119#126—582no—
120#124—292no—
121#124—582no—
122#123—582no—
123C22⋊Q8—292no—
124C22⋊Q8—582no—
125#121—292no—
126C4×Q8—292no—
127C4×D4—292no—
128#117C2×D2911yescharacteristic
129#106—292no—
130#106—291no—
131#106—291no—
132C4⋊C8C2×D2912yes—
133C4⋊C8C2×D2912yes—
134#103—292no—
135#103—292no—
136#102—292no—
137#102—292no—
138C29#326311yescharacteristic, complemented, Sylow
139C2×Q8—292no—
140C2×Q8—582no—
141C2×D4—292no—
142C2×D4—582no—
143C22×C4—582no—
144C22×C4C22×D2911yescharacteristic
145Q16—1161no—
146SD16—1162no—
147D8—1161no—
148M16—41no—
149C2×C8—41no—
150C2×C8C22×D2911yescharacteristic
151C2×C8C22×D2912yes—
152C2×C8C22×D2911yescharacteristic
153C4⋊C4—292no—
154C4⋊C4—292no—
155C4⋊C4—582no—
156C4⋊C4—582no—
157C4⋊C4—582no—
158C4⋊C4D11612yes—
159C22⋊C4—582no—
160C22⋊C4—582no—
161C22⋊C4—582no—
162C22⋊C4—582no—
163C22⋊C4—582no—
164C22⋊C4D11611yescharacteristic
165C22⋊C4D11611yescharacteristic
166C42—582no—
167C42C22×D2912yes—
168C23—582no—
169C23C2×D11611yescharacteristic
170Q8—582no—
171Q8—582no—
172Q8—2322no—
173D4—582no—
174D4—582no—
175D4—2322no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—582no—
179C2×C4—582no—
180C2×C4—582no—
181C2×C4—2322no—
182C2×C4C2×D11612yes—
183C2×C4C2×D11612yes—
184C2×C4C2×D11611yescharacteristic
185C2×C4C23×D2911yescharacteristic
186C8—22no—
187C8—21no—
188C8—21no—
189C22—21no—
190C22—22no—
191C22—1162no—
192C22—1162no—
193C22—1162no—
194C22C22×D11611yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—1162no—
199C4—1162no—
200C4—1162no—
201C4#1174535911yescharacteristic
202C4#1174536211yescharacteristic
203C2—41no—
204C2—2322no—
205C2#1427174411yescharacteristic
206C2#1427197512yes—
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#424C2
socleC22×C29C22×D4
prime radical#14271416C2
hypercenter#424D29
hypocenterC29#3263
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #14271784C2semidirect
2. #14271454C2semidirect
3. #14271449C2semidirect
4. #14271421C2semidirect
6. #14271392C2semidirect
7. #14271386C2semidirect
8. #14271379C2semidirect
9. C29×#424C2semidirect
108. #424D29semidirect
138. C29#3263semidirect

Maximal subgroups

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

subgroupindex
#142717842
#142714542
#142714492
#142714212
#142714162
#142713922
#142713862
#142713792
C29×#4242
#326329