Finite Group Databasebeta

← #16829784

Subgroups — #16829784

Order 3712.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#14271768C211yesmaximal, characteristic
2#14271640C211yesmaximal, characteristic, complemented
3#14271488C212yesmaximal, complemented
4#14271471C212yesmaximal, complemented
5#14271364C212yesmaximal, complemented
6#14271304C212yesmaximal, complemented
7#14271265C212yesmaximal, complemented
8C4×#90773C212yesmaximal, complemented
9C29×#433C211yesmaximal, characteristic, complemented
10C22×Dic58C2211yescharacteristic
11C29×#117C2211yescharacteristic
12#11745292C2212yes—
13#11745288C2211yescharacteristic
14C2×#90773C2212yes—
15C2×#90773C2212yes—
16#11745256—22no—
17#11745249—22no—
18#11745246—22no—
19#11745239—22no—
20#11745236C2211yescharacteristic
21C4×D116C2212yes—
22#11745232C2211yescharacteristic
23C4×Dic58C2212yes—
24C4×Dic58C2212yes—
25C29×C4⋊C8C2212yes—
26C29×C22⋊C8C2212yes—
27C29×#97C2211yescharacteristic
28C4×C8×C29C2211yescharacteristic
29#11745169C2212yes—
30#11745169C2212yes—
31#11745166C2212yes—
32#11745165C2212yes—
33#11745164C2212yes—
34#11745164C2212yes—
35C22×C4×C29C2311yescharacteristic
36C2×C22⋊D29—22no—
37C22×Dic29—21no—
38C2×D116—22no—
39C2×D116C2312yes—
40C2×C4×D29—22no—
41C2×Dic58—21no—
42C2×Dic58—24no—
43C2×Dic58C2312yes—
44C2×C8×C29C2312yes—
45C2×C8×C29C2312yes—
46C4⋊C4×C29D412yes—
47C22⋊C4×C29D412yes—
48C42×C29C2311yescharacteristic
49C42×C29C2311yescharacteristic
50C22⋊Dic29—21no—
51#90781—22no—
52#90781—22no—
53C4⋊Dic29C2312yes—
54C4⋊Dic29C2312yes—
55#90779—22no—
56#90779—22no—
57#90779—22no—
58C4×Dic29—21no—
59C4×Dic29—22no—
60C4×Dic29—22no—
61#90773—24no—
62#90773—24no—
63C23×C29C2×D411yescharacteristic
64C22×D29—22no—
65C2×C4×C29—22no—
66C2×C4×C29C2×D412yes—
67C2×C4×C29C2×D412yes—
68C2×C4×C29C2×D411yescharacteristic
69C2×C4×C29C2411yescharacteristic
70C22⋊D29—82no—
71C2×Dic29—24no—
72C2×Dic29—22no—
73C2×Dic29—22no—
74C2×Dic29—22no—
75D116—22no—
76D116—22no—
77D116—82no—
78C4×D29—82no—
79Dic58—24no—
80Dic58—22no—
81Dic58#4114yes—
82C8×C29—22no—
83C8×C29—22no—
84#3126—291nomaximal, Sylow
85C22×C29—21no—
86C22×C29—22no—
87C22×C29C22×D411yescharacteristic
88C2×D29—42no—
89C2×D29—42no—
90C2×D29—42no—
91C4×C29—21no—
92C4×C29—22no—
93C4×C29—22no—
94C4×C29C2×#4112yes—
95Dic29—24no—
96Dic29—42no—
97Dic29—42no—
98#540—291no—
99#519—291no—
100#482—292no—
101#479—292no—
102#460—292no—
103#448—292no—
104#440—292no—
105C4×SD16—292no—
106#433D2911yescharacteristic, complemented
107C2×C29—41no—
108C2×C29#52511yescharacteristic
109C2×C29#57712yes—
110D29—82no—
111C22×Q8—291no—
112C2×SD16—292no—
113C2×SD16—292no—
114#127—291no—
115#125—291no—
116#123—582no—
117#121—292no—
118#121—582no—
119C4×Q8—292no—
120C4×Q8—292no—
121C4×Q8—582no—
122C4×D4—292no—
123#117—291no—
124#117—582no—
125#117C2×D2911yescharacteristic
126#107—292no—
127#106—292no—
128C4⋊C8C2×D2912yes—
129#103—292no—
130#103—292no—
131#102—292no—
132#102—292no—
133C22⋊C8C2×D2912yes—
134#97C2×D2911yescharacteristic
135C4×C8C2×D2911yescharacteristic
136C29#312611yescharacteristic, complemented, Sylow
137C2×Q8—292no—
138C2×Q8—584no—
139C2×Q8—581no—
140C2×D4—292no—
141C2×D4—582no—
142C2×D4—582no—
143C22×C4—581no—
144C22×C4—582no—
145C22×C4C22×D2911yescharacteristic
146SD16—584no—
147SD16—584no—
148C2×C8C22×D2912yes—
149C2×C8C22×D2912yes—
150C4⋊C4—292no—
151C4⋊C4—292no—
152C4⋊C4—582no—
153C4⋊C4—582no—
154C4⋊C4—582no—
155C4⋊C4D11612yes—
156C22⋊C4—581no—
157C22⋊C4—582no—
158C22⋊C4—582no—
159C22⋊C4D11612yes—
160C42—581no—
161C42—582no—
162C42—582no—
163C42C22×D2911yescharacteristic
164C42C22×D2911yescharacteristic
165C23—582no—
166C23C2×D11611yescharacteristic
167Q8—294no—
168Q8—584no—
169Q8—582no—
170D4—582no—
171D4—582no—
172D4—2322no—
173D4—2322no—
174C2×C4—22no—
175C2×C4—584no—
176C2×C4—582no—
177C2×C4—582no—
178C2×C4—582no—
179C2×C4—2322no—
180C2×C4C2×D11612yes—
181C2×C4C2×D11612yes—
182C2×C4C2×D11611yescharacteristic
183C2×C4C23×D2911yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—1162no—
189C22—1162no—
190C22—1162no—
191C22C22×D11611yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—584no—
196C4—1162no—
197C4—1162no—
198C4#41×D2912yes—
199C2—41no—
200C2—2322no—
201C2#1427167511yescharacteristic
202C2#1427197512yes—
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#433C2
socleC22×C29C22×D4
prime radical#14271768C2
hypercenter#433D29
hypocenterC29#3126
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #14271640C2semidirect
3. #14271488C2semidirect
4. #14271471C2semidirect
5. #14271364C2semidirect
6. #14271304C2semidirect
7. #14271265C2semidirect
8. C4×#90773C2semidirect
9. C29×#433C2semidirect
106. #433D29semidirect
136. C29#3126semidirect

Maximal subgroups

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

subgroupindex
#142717682
#142716402
#142714882
#142714712
#142713642
#142713042
#142712652
C4×#907732
C29×#4332
#312629