Finite Group Databasebeta

← #16835328

Subgroups — #16835328

Order 3712.

584 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 86 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×#11745221C212yesmaximal, complemented
2C2×#11745229C212yesmaximal, complemented
3#14272135C212yesmaximal, complemented
4C22×#90805C211yesmaximal, characteristic
5C23×C4×C29C411yescharacteristic
6C22×C22⋊D29C411yescharacteristic
7C22×C22⋊D29C2211yescharacteristic
8C2×#90805—24no—
9C2×#90805—24no—
10C2×#90805—24no—
11C22×D116C411yescharacteristic
12C22×C4×D29C411yescharacteristic
13C22×C4×D29C2211yescharacteristic
14C22×Dic58C2211yescharacteristic
15C2×#90800C2214yes—
16#11745229—24no—
17#11745221—24no—
18#11745219—24no—
19C24×C29C2×C411yescharacteristic
20C23×D29C2×C411yescharacteristic
21C23×D29C2×C411yescharacteristic
22C22×C4×C29—22no—
23C22×C4×C29—22no—
24C22×C4×C29—22no—
25C22×C4×C29C2×C411yescharacteristic
26C22×C4×C29C2×C411yescharacteristic
27C2×C22⋊D29—22no—
28C2×C22⋊D29—22no—
29C2×C22⋊D29—22no—
30C2×C22⋊D29—22no—
31C2×C22⋊D29—22no—
32C2×C22⋊D29D414yes—
33C22×Dic29C2×C411yescharacteristic
34C22×Dic29C2311yescharacteristic
35#90805—232no—
36C2×D116—22no—
37C2×D116—22no—
38C2×D116—22no—
39C2×C4×D29—22no—
40C2×C4×D29—22no—
41C2×C4×D29—22no—
42C2×C4×D29—22no—
43C2×C4×D29—22no—
44C2×C4×D29D414yes—
45C2×Dic58—22no—
46C2×Dic58—22no—
47C2×Dic58D414yes—
48#90800—24no—
49#90800—24no—
50C2×#6599—24no—
51C23×C29—21no—
52C23×C29—21no—
53C23×C29—42no—
54C23×C29C22⋊C412yes—
55C23×C29C22×C411yescharacteristic
56C22×D29—21no—
57C22×D29—21no—
58C22×D29—21no—
59C22×D29—21no—
60C22×D29—42no—
61C22×D29—42no—
62C22×D29C22⋊C412yes—
63C22×D29C22⋊C412yes—
64C2×C4×C29—28no—
65C2×C4×C29—21no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—21no—
69C2×C4×C29C22⋊C412yes—
70C2×C4×C29C22⋊C412yes—
71C22⋊D29—28no—
72C22⋊D29—28no—
73C2×Dic29—21no—
74C2×Dic29—21no—
75C2×Dic29C22⋊C412yes—
76C2×Dic29C2×D412yes—
77C2×Dic29C2×D412yes—
78C2×Dic29C2×D412yes—
79D116—28no—
80C4×D29—28no—
81C4×D29—28no—
82Dic58—28no—
83#6599—44no—
84#1785—291nomaximal, Sylow
85C22×C29—22no—
86C22×C29—22no—
87C22×C29—42no—
88C22×C29—42no—
89C22×C29—42no—
90C22×C29C2×C22⋊C411yescharacteristic
91C22×C29C2×C22⋊C411yescharacteristic
92C22×C29C2×C22⋊C411yescharacteristic
93C2×D29—22no—
94C2×D29—22no—
95C2×D29—24no—
96C2×D29—42no—
97C2×D29—42no—
98C2×D29—42no—
99C2×D29—42no—
100C2×D29—42no—
101C4×C29—22no—
102C4×C29—22no—
103Dic29—22no—
104Dic29#12014yes—
105C22×#41—291no—
106C2×#101—292no—
107C2×#100—292no—
108#407—292no—
109C2×C29—21no—
110C2×C29—21no—
111C2×C29—42no—
112C2×C29#37911yescharacteristic
113C2×C29#41312yes—
114D29—42no—
115D29—42no—
116C2×#41—584no—
117C2×#41—584no—
118C2×#41—584no—
119C22×Q8—291no—
120C22×D4—291no—
121C22×D4—291no—
122C22×D4—291no—
123C23×C4—291no—
124C23×C4—291no—
125C23×C4#118111yescharacteristic
126C2×M16—294no—
127#101—584no—
128#100—584no—
129C22⋊C8—584no—
130C29#178511yescharacteristic, complemented, Sylow
131C24—291no—
132C24—291no—
133C24C2×#118111yescharacteristic
134#41—5832no—
135C2×Q8—294no—
136C2×Q8—582no—
137C2×Q8—582no—
138C2×D4—294no—
139C2×D4—582no—
140C2×D4—582no—
141C2×D4—582no—
142C2×D4—582no—
143C2×D4—582no—
144C2×D4—582no—
145C2×D4—582no—
146C2×D4—582no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—291no—
151C22×C4—291no—
152C22×C4—294no—
153C22×C4—582no—
154C22×C4—582no—
155C22×C4—582no—
156C22×C4—582no—
157C22×C4—582no—
158C22×C4C2×#118111yescharacteristic
159C22×C4C2×#118111yescharacteristic
160M16—584no—
161M16—584no—
162C2×C8—584no—
163C23—21no—
164C23—21no—
165C23—42no—
166C23—292no—
167C23—292no—
168C23—581no—
169C23—581no—
170C23—581no—
171C23—581no—
172C23—1162no—
173C23—1162no—
174C23C22⋊#118112yes—
175C23C22×#118111yescharacteristic
176Q8—588no—
177D4—588no—
178D4—588no—
179D4—588no—
180C2×C4—28no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—292no—
186C2×C4—292no—
187C2×C4—292no—
188C2×C4—292no—
189C2×C4—588no—
190C2×C4—588no—
191C2×C4—581no—
192C2×C4—581no—
193C2×C4C22⋊#118112yes—
194C2×C4C22⋊#118112yes—
195C8—1164no—
196C22—22no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—582no—
202C22—582no—
203C22—584no—
204C22—1162no—
205C22—1162no—
206C22—1162no—
207C22—1162no—
208C22—1162no—
209C22C2×C22⋊#118111yescharacteristic
210C22C2×C22⋊#118111yescharacteristic
211C22C2×C22⋊#118111yescharacteristic
212C4—22no—
213C4—22no—
214C4—294no—
215C4—582no—
216C2—21no—
217C2—21no—
218C2—42no—
219C2—1162no—
220C2—1162no—
221C2#1427210411yescharacteristic
222C2#1427214912yes—
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC23×C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC22×#90805C2
cosocleC22×Dic29C23
hypercenterC23×C4#1181
hypocenterC29#1785
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#11745221C2semidirect
2. C2×#11745229C2semidirect
3. #14272135C2semidirect
130. C29#1785semidirect

Maximal subgroups

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

subgroupindex
C2×#117452212
C2×#117452292
#142721352
C22×#908052
#178529