Finite Group Databasebeta

← #16829783

Subgroups — #16829783

Order 3712.

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

normal subgroups only

This group has 382 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#14271768C211yesmaximal, characteristic
2#14271487C212yesmaximal, complemented
3#14271470C212yesmaximal, complemented
4#14271363C212yesmaximal, complemented
5#14271302C212yesmaximal, complemented
6#14271261C212yesmaximal, complemented
7C4×#90784C212yesmaximal, complemented
8#14271224C211yesmaximal, characteristic, complemented
9C29×#519C211yesmaximal, characteristic, complemented
10C22×Q8×C29C2211yescharacteristic
11C4×Q8×C29—22no—
12C4×Q8×C29C2212yes—
13C4×Q8×C29C2212yes—
14C29×#117—22no—
15C29×#117C2211yescharacteristic
16C29×#117C2211yescharacteristic
17C2×#90784C2212yes—
18C2×#90784C2212yes—
19#11745292C2212yes—
20#11745256—22no—
21#11745246—22no—
22#11745236C2211yescharacteristic
23C4×D116C2212yes—
24#11745232C2211yescharacteristic
25#11745183C2212yes—
26#11745183C2212yes—
27C22⋊#6597C2212yes—
28#11745157C2212yes—
29#11745157C2212yes—
30#11745156C2212yes—
31#11745155C2212yes—
32C4⋊#6597C2212yes—
33#11745151C2211yescharacteristic
34C4×#6597C2211yescharacteristic
35C2×Q8×C29—24no—
36C2×Q8×C29—21no—
37C2×Q8×C29C2312yes—
38C22×C4×C29—21no—
39C22×C4×C29C2311yescharacteristic
40C2×C22⋊D29—22no—
41C2×D116—22no—
42C2×D116C2312yes—
43C2×C4×D29—22no—
44C4⋊C4×C29—22no—
45C4⋊C4×C29—22no—
46C4⋊C4×C29D412yes—
47C4⋊C4×C29C2312yes—
48C22⋊C4×C29—21no—
49C22⋊C4×C29D412yes—
50C42×C29—22no—
51C42×C29—22no—
52C42×C29—21no—
53C42×C29C2311yescharacteristic
54C42×C29C2311yescharacteristic
55#90784—24no—
56#90784—24no—
57#90781—22no—
58#90781—22no—
59C4⋊Dic29C2312yes—
60#90779—22no—
61C2×#6597C2312yes—
62C2×#6597C2312yes—
63C23×C29C2×D411yescharacteristic
64C22×D29—22no—
65Q8×C29—24no—
66Q8×C29—22no—
67Q8×C29#4114yes—
68C2×C4×C29—24no—
69C2×C4×C29—22no—
70C2×C4×C29—22no—
71C2×C4×C29—22no—
72C2×C4×C29C2×D412yes—
73C2×C4×C29C2×D411yescharacteristic
74C2×C4×C29C2×D412yes—
75C2×C4×C29C2411yescharacteristic
76C22⋊D29—82no—
77C2×Dic29—22no—
78D116—22no—
79D116—22no—
80D116—82no—
81C4×D29—82no—
82#6597—22no—
83#6597—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—24no—
92C4×C29—21no—
93C4×C29—22no—
94C4×C29—22no—
95C4×C29—42no—
96C4×C29C2×#4112yes—
97Dic29—42no—
98#540—291no—
99#519D2911yescharacteristic, complemented
100#482—292no—
101#479—292no—
102#460—292no—
103#448—292no—
104#440—292no—
105C4×SD16—292no—
106#433—291no—
107C2×C29—41no—
108C2×C29#52511yescharacteristic
109C2×C29#57712yes—
110D29—82no—
111C22×Q8C2×D2911yescharacteristic
112C2×SD16—292no—
113C2×SD16—292no—
114#127—291no—
115#125—291no—
116#123—582no—
117#121—292no—
118#121—582no—
119C4×Q8—22no—
120C4×Q8C2×D2912yes—
121C4×Q8C2×D2912yes—
122C4×D4—292no—
123#117—22no—
124#117C2×D2911yescharacteristic
125#117C2×D2911yescharacteristic
126#107—292no—
127#106—292no—
128C4⋊C8—292no—
129#103—292no—
130#103—292no—
131#102—292no—
132#102—292no—
133C22⋊C8—292no—
134#97—291no—
135C4×C8—291no—
136C29#312611yescharacteristic, complemented, Sylow
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8C22×D2912yes—
140C2×D4—292no—
141C2×D4—582no—
142C2×D4—582no—
143C22×C4—21no—
144C22×C4—582no—
145C22×C4C22×D2911yescharacteristic
146SD16—584no—
147SD16—584no—
148C2×C8—292no—
149C2×C8—292no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—292no—
153C4⋊C4—582no—
154C4⋊C4C22⋊D2912yes—
155C4⋊C4C22×D2912yes—
156C22⋊C4—21no—
157C22⋊C4—582no—
158C22⋊C4—582no—
159C22⋊C4C22⋊D2912yes—
160C42—22no—
161C42—22no—
162C42—21no—
163C42C22×D2911yescharacteristic
164C42C22×D2911yescharacteristic
165C23—582no—
166C23C2×C22⋊D2911yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#9080514yes—
170D4—582no—
171D4—582no—
172D4—2322no—
173D4—2322no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—582no—
179C2×C4—2322no—
180C2×C4C2×C22⋊D2912yes—
181C2×C4C2×C22⋊D2912yes—
182C2×C4C2×C22⋊D2911yescharacteristic
183C2×C4C23×D2911yescharacteristic
184C8—582no—
185C8—582no—
186C22—21no—
187C22—22no—
188C22—1162no—
189C22—1162no—
190C22—1162no—
191C22C22×C22⋊D2911yescharacteristic
192C4—24no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—1162no—
198C4C2×#9080512yes—
199C2—41no—
200C2—2322no—
201C2#1427167411yescharacteristic
202C2#1427197112yes—
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#519C2
socleC22×C29C22×D4
prime radical#14271768C2
hypercenter#519D29
hypocenterC29#3126
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #14271487C2semidirect
3. #14271470C2semidirect
4. #14271363C2semidirect
5. #14271302C2semidirect
6. #14271261C2semidirect
7. C4×#90784C2semidirect
8. #14271224C2semidirect
9. C29×#519C2semidirect
99. #519D29semidirect
136. C29#3126semidirect

Maximal subgroups

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

subgroupindex
#142717682
#142714872
#142714702
#142713632
#142713022
#142712612
C4×#907842
#142712242
C29×#5192
#312629