Finite Group Databasebeta

← #16819571

Subgroups — #16819571

Order 3712.

316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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×C4⋊C4×D29C211yesmaximal, characteristic
2#14271126C212yesmaximal
3#14270932C211yesmaximal, characteristic, complemented
4#14270931C212yesmaximal, complemented
5C29×#343C211yesmaximal, characteristic, complemented
6C22×C4×D29C412yes—
7C22×C4×D29C2211yescharacteristic
8C2×M16×C29C2212yes—
9C2×C4⋊C4×C29C2211yescharacteristic
10C2×C4⋊Dic29C2211yescharacteristic
11C2×#90779C412yes—
12C2×#90777C2212yes—
13C4⋊C4×D29—22no—
14C4⋊C4×D29—22no—
15#11745168—22no—
16#11745168—22no—
17C23×D29C2×C411yescharacteristic
18C22×C4×C29C2×C412yes—
19C22×C4×C29C2311yescharacteristic
20C22×Dic29C2×C411yescharacteristic
21C22×Dic29C2×C412yes—
22C2×C4×D29—22no—
23C2×C4×D29—21no—
24C2×C4×D29—21no—
25C2×C4×D29—22no—
26C2×C4×D29—22no—
27C2×C4×D29—44no—
28C2×C4×D29D412yes—
29C2×C4×D29D412yes—
30M16×C29—22no—
31M16×C29—22no—
32C2×C8×C29—22no—
33C4⋊C4×C29—22no—
34C4⋊Dic29—22no—
35#90779—24no—
36#90777—22no—
37#90777—22no—
38C2×#6597—22no—
39C23×C29C22×C411yescharacteristic
40C22×D29—21no—
41C22×D29—21no—
42C22×D29—22no—
43C22×D29—22no—
44C22×D29C22⋊C411yescharacteristic
45C22×D29C22⋊C411yescharacteristic
46C2×C4×C29—22no—
47C2×C4×C29—42no—
48C2×C4×C29C2×D412yes—
49C2×C4×C29#4112yes—
50C2×C4×C29#4111yescharacteristic
51C2×C4×C29#4111yescharacteristic
52C2×Dic29—21no—
53C2×Dic29—21no—
54C2×Dic29—22no—
55C2×Dic29—42no—
56C2×Dic29C22⋊C412yes—
57C4×D29—22no—
58C4×D29—22no—
59C4×D29—22no—
60C4×D29—22no—
61C4×D29—44no—
62C4×D29—44no—
63C8×C29—42no—
64#6597—42no—
65#1821—291nomaximal, Sylow
66C22×C29—21no—
67C22×C29—21no—
68C22×C29C2×C22⋊C411yescharacteristic
69C22×C29#11711yescharacteristic
70C22×C29#11711yescharacteristic
71C2×D29—24no—
72C2×D29—24no—
73C2×D29—21no—
74C2×D29—21no—
75C2×D29—21no—
76C2×D29—21no—
77C2×D29#10012yes—
78C2×D29#10112yes—
79C4×C29—42no—
80C4×C29#12312yes—
81C4×C29#12312yes—
82Dic29—22no—
83Dic29—42no—
84C22×C4⋊C4—291no—
85#407—292no—
86#343—292no—
87#343—291no—
88#343D2911yescharacteristic, complemented
89C2×C29—21no—
90C2×C29—21no—
91C2×C29#38111yescharacteristic
92C2×C29C2×#10011yescharacteristic
93C2×C29C2×#10111yescharacteristic
94D29—22no—
95D29—22no—
96C23×C4—291no—
97C23×C4—292no—
98C2×M16—292no—
99C2×M16C2×D2912yes—
100C2×C4⋊C4—292no—
101C2×C4⋊C4—291no—
102C2×C4⋊C4—582no—
103C2×C4⋊C4—582no—
104C2×C4⋊C4C2×D2911yescharacteristic
105C22⋊C8—582no—
106C22⋊C8—582no—
107C29#182111yescharacteristic, complemented, Sylow
108C24—291no—
109C22×C4—291no—
110C22×C4—292no—
111C22×C4—292no—
112C22×C4—292no—
113C22×C4—582no—
114C22×C4—582no—
115C22×C4—582no—
116C22×C4—581no—
117C22×C4—581no—
118C22×C4—1164no—
119C22×C4C4×D2912yes—
120C22×C4C22×D2911yescharacteristic
121M16—22no—
122M16—22no—
123M16—582no—
124M16—582no—
125C2×C8—22no—
126C2×C8—582no—
127C4⋊C4—22no—
128C4⋊C4—584no—
129C4⋊C4—582no—
130C23—291no—
131C23—291no—
132C23—582no—
133C23—582no—
134C23—581no—
135C23—581no—
136C23C2×C4×D2911yescharacteristic
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—292no—
140C2×C4—581no—
141C2×C4—581no—
142C2×C4—582no—
143C2×C4—582no—
144C2×C4—582no—
145C2×C4—582no—
146C2×C4—582no—
147C2×C4—1164no—
148C2×C4—1164no—
149C2×C4—1162no—
150C2×C4#9080512yes—
151C2×C4D4×D2912yes—
152C2×C4#9080711yescharacteristic
153C2×C4#9080911yescharacteristic
154C8—42no—
155C8—1162no—
156C22—21no—
157C22—21no—
158C22—292no—
159C22—292no—
160C22—584no—
161C22—584no—
162C22—581no—
163C22—581no—
164C22—581no—
165C22—581no—
166C22#1174523411yescharacteristic
167C22C22⋊C4×D2911yescharacteristic
168C22#1174525411yescharacteristic
169C4—42no—
170C4—582no—
171C4—1162no—
172C4#1174524512yes—
173C4#1174525612yes—
174C2—21no—
175C2—21no—
176C2—582no—
177C2—582no—
178C2#1427102511yescharacteristic
179C2#100×D2911yescharacteristic
180C2#101×D2911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC23×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#343C2
socleC22×C29C2×C22⋊C4
prime radicalC23×D29C2×C4
cosocleC22×C4×C29C23
hypercenter#343D29
hypocenterC29#1821
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #14270932C2semidirect
4. #14270931C2semidirect
5. C29×#343C2semidirect
88. #343D29semidirect
107. C29#1821semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D292
#142711262
#142709322
#142709312
C29×#3432
#182129