Finite Group Databasebeta

← #16819950

Subgroups — #16819950

Order 3712.

378 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 93 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×#11745291C211yesmaximal, characteristic
2C2×#11745154C212yesmaximal
3#14271026C211yesmaximal, characteristic, complemented
4#14270929C212yesmaximal, complemented
5C2×C29×#117C211yesmaximal, characteristic, complemented
6C23×C4×C29C2211yescharacteristic
7C22×C22⋊D29C2211yescharacteristic
8C29×#117—24no—
9C2×C4⋊C4×C29—21no—
10C2×C22⋊C4×C29C2212yes—
11C2×C42×C29—21no—
12C2×C22⋊Dic29C2212yes—
13C2×C22⋊Dic29C2211yescharacteristic
14#11745291—22no—
15#11745291—21no—
16#11745291—21no—
17C2×#90781C412yescomplemented
18C2×#90779C412yescomplemented
19#11745179—22no—
20#11745154—24no—
21C24×C29C2311yescharacteristic
22C23×D29C2×C411yescharacteristic
23C22×C4×C29—22no—
24C22×C4×C29—22no—
25C22×C4×C29—22no—
26C22×C4×C29C2×C412yes—
27C22×C4×C29D412yes—
28C22×C4×C29D411yescharacteristic
29C22×C4×C29D411yescharacteristic
30C2×C22⋊D29—21no—
31C2×C22⋊D29—21no—
32C2×C22⋊D29—22no—
33C2×C22⋊D29—22no—
34C22×Dic29—22no—
35C22×Dic29C2×C411yescharacteristic
36C22×Dic29C2×C412yes—
37C4⋊C4×C29—24no—
38C22⋊C4×C29—22no—
39C22⋊C4×C29D414yes—
40C42×C29—24no—
41C22⋊Dic29—21no—
42C22⋊Dic29—21no—
43C22⋊Dic29—22no—
44C22⋊Dic29—22no—
45#90781—22no—
46#90781—22no—
47#90779—22no—
48#90779—22no—
49C23×C29—42no—
50C23×C29C22×C411yescharacteristic
51C23×C29C2×D411yescharacteristic
52C23×C29C2×D411yescharacteristic
53C23×C29C2×D412yes—
54C23×C29#4112yes—
55C22×D29—21no—
56C22×D29—22no—
57C22×D29—42no—
58C2×C4×C29—24no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—24no—
62C2×C4×C29—21no—
63C2×C4×C29—21no—
64C2×C4×C29—24no—
65C2×C4×C29—44no—
66C2×C4×C29C22⋊C412yes—
67C2×C4×C29C22⋊C412yes—
68C22⋊D29—41no—
69C22⋊D29—42no—
70C22⋊D29—41no—
71C2×Dic29—21no—
72C2×Dic29—22no—
73C2×Dic29—22no—
74C2×Dic29—42no—
75C2×Dic29—44no—
76C2×Dic29—42no—
77#1899—291nomaximal, Sylow
78C22×C29—22no—
79C22×C29—22no—
80C22×C29—22no—
81C22×C29—42no—
82C22×C29—42no—
83C22×C29C2×C22⋊C411yescharacteristic
84C22×C29C4×D412yes—
85C22×C29#12011yescharacteristic
86C22×C29#12112yes—
87C22×C29#12311yescharacteristic
88C2×D29—41no—
89C2×D29—42no—
90C2×D29—82no—
91C4×C29—22no—
92C4×C29—22no—
93C4×C29—44no—
94Dic29—41no—
95Dic29—42no—
96Dic29—82no—
97C2×#123—291no—
98C2×#117D2911yescharacteristic, complemented
99C2×#99—292no—
100#381—291no—
101#342—292no—
102C2×C29—22no—
103C2×C29—21no—
104C2×C29—22no—
105C2×C29—21no—
106C2×C29#38611yescharacteristic
107C2×C29#41012yes—
108D29—81no—
109C22×D4—291no—
110C23×C4C2×D2911yescharacteristic
111#123—582no—
112#123—581no—
113#123—581no—
114#117—24no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—292no—
117C2×C22⋊C4—291no—
118C2×C22⋊C4—292no—
119C2×C22⋊C4—292no—
120C2×C22⋊C4C2×D2912yes—
121C2×C42—21no—
122#99—584no—
123#95—582no—
124C29#189911yescharacteristic, complemented, Sylow
125C24—291no—
126C24C22×D2911yescharacteristic
127C2×D4—581no—
128C2×D4—582no—
129C2×D4—582no—
130C2×D4—581no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—291no—
135C22×C4—292no—
136C22×C4—582no—
137C22×C4C4×D2912yes—
138C22×C4D11612yes—
139C22×C4C22⋊D2911yescharacteristic
140C22×C4C22⋊D2911yescharacteristic
141C4⋊C4—24no—
142C4⋊C4—582no—
143C4⋊C4—582no—
144C22⋊C4—22no—
145C22⋊C4—581no—
146C22⋊C4—581no—
147C22⋊C4—582no—
148C22⋊C4—582no—
149C22⋊C4—582no—
150C22⋊C4—582no—
151C22⋊C4C22⋊D2914yes—
152C42—24no—
153C23—42no—
154C23—581no—
155C23—582no—
156C23—1162no—
157C23C2×C4×D2911yescharacteristic
158C23C2×D11611yescharacteristic
159C23#9080512yes—
160C23C2×C22⋊D2911yescharacteristic
161C23C2×C22⋊D2912yes—
162D4—1161no—
163D4—1162no—
164D4—1161no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—24no—
172C2×C4—44no—
173C2×C4—582no—
174C2×C4—581no—
175C2×C4—582no—
176C2×C4—1162no—
177C2×C4—1164no—
178C2×C4—1162no—
179C2×C4#9078112yes—
180C2×C4#9078112yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—1161no—
187C22—1162no—
188C22—2322no—
189C22C2×#9078111yescharacteristic
190C22C4×C22⋊D2912yes—
191C22#1174529111yescharacteristic
192C22#1174529212yes—
193C22#1174531511yescharacteristic
194C4—22no—
195C4—22no—
196C4—44no—
197C4—1161no—
198C4—1162no—
199C4—2322no—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2—2321no—
205C2#1427104211yescharacteristic
206C2#1427113612yes—
subgroupG/H
centerC22C2×#90781
commutatorC23×C29C22×C4
FrattiniC24C22×D29
FittingC2×C29×#117C2
socleC22×C29C2×C22⋊C4
prime radicalC22×C22⋊D29C22
cosocleC24×C29C23
hypercenterC2×#117D29
hypocenterC29#1899
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #14271026C2semidirect
4. #14270929C2semidirect
5. C2×C29×#117C2semidirect
17. C2×#90781C4semidirect
18. C2×#90779C4semidirect
98. C2×#117D29semidirect
124. C29#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#117452912
C2×#117451542
#142710262
#142709292
C2×C29×#1172
#189929