Finite Group Databasebeta

← #16835395

Subgroups — #16835395

Order 3712.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D29⋊(C22⋊C8)C211yesmaximal, characteristic
2#14272105C211yesmaximal, characteristic
3#14272036C214yesmaximal, complemented
4C2×C4⋊C4×D29C211yesmaximal, characteristic
5C22×C4×D29—21no—
6C22×C4×D29C2211yescharacteristic
7C2×C22⋊#1181—21no—
8C2×C4⋊#1181C2212yes—
9C2×D29⋊C8C2212yes—
10C2×C4⋊C4×C29C411yescharacteristic, complemented
11C2×C4⋊Dic29C411yescharacteristic, complemented
12C2×#90779—21no—
13C4⋊C4×D29—21no—
14C4⋊C4×D29—21no—
15C4⋊C4×D29C412yescomplemented
16C4⋊C4×D29C2212yes—
17C22⋊#6599—21no—
18(C2×#1181)⋊C4—21no—
19#11745219—21no—
20C23×D29D411yescharacteristic
21C22×#1181—22no—
22C22×C4×C29—21no—
23C22×C4×C29C2×C411yescharacteristic
24C22×Dic29—21no—
25C22×Dic29D411yescharacteristic
26C2×C4×D29—24no—
27C2×C4×D29—22no—
28C2×C4×D29—22no—
29C2×C4×D29—42no—
30C2×C4×D29—42no—
31C2×C4×D29C2×C411yescharacteristic
32C2×C4×D29D411yescharacteristic
33C2×C4×D29D411yescharacteristic
34C2×C4×D29C2311yescharacteristic
35C22⋊#1181—42no—
36C2×#6599—22no—
37C4⋊#1181—24no—
38D29⋊C8—24no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29C2×C412yes—
41C4⋊Dic29—21no—
42C4⋊Dic29C2×C412yes—
43#90779—22no—
44#90779—22no—
45C23×C29C22⋊C411yescharacteristic
46C22×D29—22no—
47C22×D29—22no—
48C22×D29C22⋊C411yescharacteristic
49C22×D29D812yes—
50C22×D29SD1612yes—
51C22×D29C2×D411yescharacteristic
52C2×#1181—42no—
53C2×#1181—42no—
54C2×#1181—42no—
55C2×C4×C29—22no—
56C2×C4×C29—22no—
57C2×C4×C29—42no—
58C2×C4×C29C22⋊C411yescharacteristic
59C2×C4×C29C22×C411yescharacteristic
60C2×Dic29—22no—
61C2×Dic29—22no—
62C2×Dic29—42no—
63C2×Dic29C22⋊C411yescharacteristic
64C2×Dic29C2×D411yescharacteristic
65C4×D29—22no—
66C4×D29—22no—
67C4×D29—22no—
68C4×D29—44no—
69C4×D29—42no—
70C4×D29—42no—
71C4×D29#4114yes—
72#6599—42no—
73#1823—291nomaximal, Sylow
74C22×C29—21no—
75C22×C29—21no—
76C22×C29#10212yes—
77C22×C29C2×C22⋊C411yescharacteristic
78C2×D29—21no—
79C2×D29—21no—
80C2×D29—24no—
81C2×D29—24no—
82C2×D29#10212yes—
83C2×D29#12312yes—
84C2×D29C2×D811yescharacteristic
85C2×D29C2×SD1611yescharacteristic
86C2×D29#13712yes—
87#1181—82no—
88C4×C29—21no—
89C4×C29—42no—
90C4×C29#11712yes—
91Dic29—21no—
92Dic29—42no—
93Dic29#12312yes—
94C22×C4⋊C4—291no—
95C2×C22⋊C8—291no—
96#380—291no—
97#340—294no—
98C2×C29—22no—
99C2×C29#38111yescharacteristic
100C2×C29C2×#10211yescharacteristic
101C2×C29#41911yescharacteristic
102D29—22no—
103D29#48012yes—
104D29#48312yes—
105C23×C4—291no—
106C23×C4—581no—
107C22×C8—292no—
108C2×C4⋊C4—291no—
109C2×C4⋊C4—292no—
110C2×C4⋊C4—292no—
111C2×C4⋊C4—292no—
112C2×C4⋊C4—581no—
113C2×C4⋊C4—581no—
114C2×C4⋊C4—581no—
115C2×C4⋊C4#118111yescharacteristic, complemented
116C2×C22⋊C4—581no—
117C22⋊C8—581no—
118C22⋊C8—581no—
119#95—581no—
120C29#182311yescharacteristic, complemented, Sylow
121C24—291no—
122C22×C4—21no—
123C22×C4—291no—
124C22×C4—291no—
125C22×C4—291no—
126C22×C4—291no—
127C22×C4—291no—
128C22×C4—584no—
129C22×C4—582no—
130C22×C4—582no—
131C22×C4—581no—
132C22×C4—582no—
133C22×C4—1162no—
134C22×C4—1162no—
135C22×C4C2×#118111yescharacteristic
136C2×C8—582no—
137C2×C8—584no—
138C4⋊C4—21no—
139C4⋊C4—292no—
140C4⋊C4—582no—
141C4⋊C4—582no—
142C4⋊C4—584no—
143C4⋊C4—581no—
144C4⋊C4C2×#118112yes—
145C22⋊C4—1162no—
146C23—291no—
147C23—291no—
148C23—292no—
149C23—292no—
150C23—582no—
151C23—582no—
152C23C22⋊#118111yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—291no—
157C2×C4—294no—
158C2×C4—291no—
159C2×C4—582no—
160C2×C4—582no—
161C2×C4—582no—
162C2×C4—582no—
163C2×C4—582no—
164C2×C4—1162no—
165C2×C4—1162no—
166C2×C4—1164no—
167C2×C4—1162no—
168C2×C4—1162no—
169C2×C4—1162no—
170C2×C4—1162no—
171C2×C4C22⋊#118111yescharacteristic
172C2×C4C22×#118111yescharacteristic
173C8—1162no—
174C22—21no—
175C22—21no—
176C22—292no—
177C22—291no—
178C22—291no—
179C22—292no—
180C22—292no—
181C22—584no—
182C22—584no—
183C22—581no—
184C22—581no—
185C22#1174522312yes—
186C22C2×C22⋊#118111yescharacteristic
187C4—21no—
188C4—42no—
189C4—292no—
190C4—581no—
191C4—1162no—
192C4—2322no—
193C4#1174534512yes—
194C2—22no—
195C2—292no—
196C2—292no—
197C2—582no—
198C2#1427210611yescharacteristic
199C2C2×#1174522311yescharacteristic
200C2#1427215611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC23×D29D4
cosocleC2×C4×D29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1823
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14272036C2semidirect
10. C2×C4⋊C4×C29C4semidirect
11. C2×C4⋊Dic29C4semidirect
15. C4⋊C4×D29C4semidirect
115. C2×C4⋊C4#1181semidirect
120. C29#1823semidirect

Maximal subgroups

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

subgroupindex
D29⋊(C22⋊C8)2
#142721052
#142720362
C2×C4⋊C4×D292
#182329