Finite Group Databasebeta

← #16829423

Subgroups — #16829423

Order 3712.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#14271674C211yesmaximal, characteristic
2#14271504C214yesmaximal, complemented
3#14271487C214yesmaximal, complemented
4#14271203C212yesmaximal, complemented
5#14271162C212yesmaximal, complemented
6#14271127C211yesmaximal, characteristic, complemented
7C2×C29×#117C211yesmaximal, characteristic, complemented
8C23×C4×C29C2211yescharacteristic
9C2×#90805C2211yescharacteristic
10C29×#117—22no—
11C29×#117C2214yes—
12C2×C4⋊C4×C29C2212yes—
13C2×C22⋊C4×C29—21no—
14C2×C42×C29—21no—
15#11745315—21no—
16#11745292C2212yes—
17#11745291—21no—
18C4×C22⋊D29—22no—
19#11745288C2211yescharacteristic
20#11745286C2212yes—
21C2×#90777C2212yes—
22C22⋊#6597C2214yes—
23#11745158C2214yescomplemented
24#11745157C2214yescomplemented
25#11745156C2214yescomplemented
26#11745155C2214yescomplemented
27C24×C29D411yescharacteristic
28C22×C4×C29—24no—
29C22×C4×C29—22no—
30C22×C4×C29D412yes—
31C22×C4×C29D411yescharacteristic
32C22×C4×C29C2312yes—
33C22×C4×C29C2311yescharacteristic
34C2×C22⋊D29—22no—
35C2×C22⋊D29—21no—
36#90805—24no—
37C2×D116C2311yescharacteristic
38C2×C4×D29—21no—
39C2×Dic58C2311yescharacteristic
40C4⋊C4×C29—22no—
41C4⋊C4×C29C2314yes—
42C22⋊C4×C29—24no—
43C42×C29—24no—
44C22⋊Dic29—22no—
45C22⋊Dic29—21no—
46#90781—22no—
47C4⋊Dic29C2312yes—
48#90779—22no—
49C4×Dic29—21no—
50#90777—24no—
51C2×#6597C2314yes—
52C23×C29—22no—
53C23×C29—42no—
54C23×C29C2×D412yes—
55C23×C29C2×D411yescharacteristic
56C22×D29—21no—
57C2×C4×C29—22no—
58C2×C4×C29—24no—
59C2×C4×C29—24no—
60C2×C4×C29—24no—
61C2×C4×C29—44no—
62C2×C4×C29C2×D412yes—
63C2×C4×C29C2×D411yescharacteristic
64C2×C4×C29#4114yes—
65C2×C4×C29C2411yescharacteristic
66C22⋊D29—44no—
67C22⋊D29—42no—
68C2×Dic29—22no—
69C2×Dic29—21no—
70D116—22no—
71C4×D29—42no—
72Dic58—22no—
73#6597—24no—
74#3093—291nomaximal, Sylow
75C22×C29—22no—
76C22×C29—22no—
77C22×C29—22no—
78C22×C29—22no—
79C22×C29—44no—
80C22×C29#12312yes—
81C22×C29C22×D411yescharacteristic
82C2×D29—41no—
83C2×D29—42no—
84C4×C29—22no—
85C4×C29—44no—
86C4×C29#12312yes—
87C4×C29C2×#4112yes—
88Dic29—41no—
89Dic29—42no—
90#525—291no—
91C2×#117D2911yescharacteristic, complemented
92#485—294no—
93#482—294no—
94#428—292no—
95#417—292no—
96#407—291no—
97C2×C29—22no—
98C2×C29—42no—
99C2×C29C2×#12311yescharacteristic
100C2×C29#57512yes—
101D29—81no—
102C2×#41—291no—
103C23×C4C2×D2911yescharacteristic
104C2×M16—292no—
105#123—581no—
106C22⋊Q8—292no—
107#121—292no—
108#120—581no—
109C4×D4—582no—
110#117—22no—
111#117—291no—
112#117C2×D2914yes—
113C2×C4⋊C4C2×D2912yes—
114C2×C22⋊C4—21no—
115C2×C42—21no—
116#107—294no—
117#106—294no—
118#103—294no—
119#102—294no—
120C22⋊C8—294no—
121C29#309311yescharacteristic, complemented, Sylow
122C24C22⋊D2911yescharacteristic
123#41—584no—
124C2×Q8—291no—
125C2×D4—291no—
126C2×D4—582no—
127C2×D4—581no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—581no—
131C22×C4C22⋊D2911yescharacteristic
132C22×C4C22⋊D2912yes—
133C22×C4C22×D2912yes—
134C22×C4C22×D2911yescharacteristic
135M16—584no—
136C2×C8—294no—
137C4⋊C4—22no—
138C4⋊C4—292no—
139C4⋊C4—582no—
140C4⋊C4C22×D2914yes—
141C22⋊C4—24no—
142C22⋊C4—581no—
143C22⋊C4—582no—
144C22⋊C4—582no—
145C42—24no—
146C42—581no—
147C23—22no—
148C23—42no—
149C23—581no—
150C23C2×C22⋊D2912yes—
151C23C2×C22⋊D2911yescharacteristic
152Q8—582no—
153D4—582no—
154D4—1164no—
155D4—1162no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—582no—
162C2×C4—581no—
163C2×C4—1162no—
164C2×C4#9080514yes—
165C2×C4C2×C22⋊D2912yes—
166C2×C4C2×C22⋊D2911yescharacteristic
167C2×C4C23×D2911yescharacteristic
168C8—584no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—1161no—
175C22—1162no—
176C22#1174529112yes—
177C22C22×C22⋊D2911yescharacteristic
178C4—22no—
179C4—44no—
180C4—1161no—
181C4—1162no—
182C4#1174529112yes—
183C4C2×#9080512yes—
184C2—22no—
185C2—42no—
186C2—2321no—
187C2C2×#1174529111yescharacteristic
188C2#1427196112yes—
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#117C2
socleC22×C29C22×D4
prime radical#14271674C2
hypercenterC2×#117D29
hypocenterC29#3093
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14271504C2semidirect
3. #14271487C2semidirect
4. #14271203C2semidirect
5. #14271162C2semidirect
6. #14271127C2semidirect
7. C2×C29×#117C2semidirect
23. #11745158C22semidirect
24. #11745157C22semidirect
25. #11745156C22semidirect
26. #11745155C22semidirect
91. C2×#117D29semidirect
121. C29#3093semidirect

Maximal subgroups

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

subgroupindex
#142716742
#142715042
#142714872
#142712032
#142711622
#142711272
C2×C29×#1172
#309329