Finite Group Databasebeta

← #16835519

Subgroups — #16835519

Order 3712.

338 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×#90800C211yesmaximal, characteristic
2C2×#11745221C212yesmaximal, complemented
3#14272133C211yesmaximal, characteristic
4#14272043C212yesmaximal, complemented
5C2×#11745240C211yesmaximal, characteristic
6C23×Dic29C2211yescharacteristic
7C22×Dic58C2211yescharacteristic
8C2×#90800—21no—
9C2×#90800—24no—
10C2×#90800C2212yes—
11C2×#90800C2212yes—
12C22×#6599—21no—
13C2×C22⋊C4×C29C411yescharacteristic
14C2×C22⋊Dic29C411yescharacteristic
15C2×C4⋊Dic29C411yescharacteristic
16C2×#90779C411yescharacteristic
17C2×#90779C2211yescharacteristic
18#11745240—21no—
19#11745240—21no—
20#11745240—21no—
21#11745240—21no—
22C22⋊#6599—21no—
23C22⋊#6599—21no—
24#11745221—24no—
25C24×C29C2×C411yescharacteristic
26C22×C4×C29C2×C411yescharacteristic
27C22×C4×C29C2×C411yescharacteristic
28C22×Dic29—22no—
29C22×Dic29—22no—
30C22×Dic29C2×C411yescharacteristic
31C22×Dic29C2×C411yescharacteristic
32C22×Dic29C2×C411yescharacteristic
33C22×Dic29D411yescharacteristic
34C22×Dic29D411yescharacteristic
35C22×Dic29D411yescharacteristic
36C22×Dic29D411yescharacteristic
37C22×Dic29C2311yescharacteristic
38C2×Dic58—22no—
39C2×Dic58—21no—
40C2×Dic58—21no—
41C2×Dic58—22no—
42#90800—24no—
43#90800—22no—
44#90800—22no—
45#90800—22no—
46#90800D414yes—
47C2×#6599—24no—
48C2×#6599—22no—
49C2×#6599—22no—
50C22⋊C4×C29—21no—
51C22⋊C4×C29—21no—
52C22⋊Dic29—21no—
53C22⋊Dic29—21no—
54C4⋊Dic29—21no—
55C4⋊Dic29—21no—
56#90779—21no—
57#90779—21no—
58#90779—21no—
59#90779—21no—
60C23×C29—22no—
61C23×C29—22no—
62C23×C29—41no—
63C23×C29C22⋊C411yescharacteristic
64C23×C29C22⋊C411yescharacteristic
65C23×C29C22×C411yescharacteristic
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—22no—
69C2×C4×C29—41no—
70C2×Dic29—22no—
71C2×Dic29—21no—
72C2×Dic29—21no—
73C2×Dic29—22no—
74C2×Dic29—22no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—22no—
80C2×Dic29—41no—
81C2×Dic29C22⋊C411yescharacteristic
82C2×Dic29C22⋊C411yescharacteristic
83C2×Dic29C2×D412yes—
84C2×Dic29C2×D411yescharacteristic
85C2×Dic29C2×D411yescharacteristic
86C2×Dic29#4112yes—
87Dic58—41no—
88Dic58—42no—
89Dic58—41no—
90#6599—24no—
91#6599—42no—
92#1901—291nomaximal, Sylow
93C22×C29—21no—
94C22×C29—21no—
95C22×C29—21no—
96C22×C29—21no—
97C22×C29—21no—
98C22×C29—21no—
99C22×C29—21no—
100C22×C29—44no—
101C22×C29#10112yescomplemented
102C22×C29C2×C22⋊C411yescharacteristic
103C22×C29C4×D412yes—
104C4×C29—41no—
105C4×C29—41no—
106Dic29—21no—
107Dic29—21no—
108Dic29—41no—
109Dic29—41no—
110Dic29#12011yescharacteristic
111Dic29#12112yes—
112Dic29#12311yescharacteristic
113C22×M16—291no—
114C2×C22⋊Q8—291no—
115C2×#101—292no—
116#407—291no—
117#343—292no—
118C2×C29—22no—
119C2×C29—22no—
120C2×C29—41no—
121C2×C29#38611yescharacteristic
122C2×C29C2×#10111yescharacteristic
123C2×C29#41311yescharacteristic
124C22×Q8—291no—
125C23×C4—291no—
126C2×M16—292no—
127C2×M16—292no—
128C2×M16—584no—
129C2×M16—581no—
130C22×C8—581no—
131C22⋊Q8—581no—
132C22⋊Q8—581no—
133C22⋊Q8—581no—
134C22⋊Q8—581no—
135C2×C4⋊C4—291no—
136C2×C4⋊C4—291no—
137C2×C4⋊C4—291no—
138C2×C22⋊C4—291no—
139C2×C22⋊C4#118111yescharacteristic
140#101—584no—
141C22⋊C8—581no—
142C22⋊C8—581no—
143C29#190111yescharacteristic, complemented, Sylow
144C24C2×#118111yescharacteristic
145C2×Q8—582no—
146C2×Q8—581no—
147C2×Q8—581no—
148C2×Q8—582no—
149C22×C4—291no—
150C22×C4—291no—
151C22×C4—291no—
152C22×C4—291no—
153C22×C4—291no—
154C22×C4—291no—
155C22×C4—291no—
156C22×C4—291no—
157C22×C4—582no—
158C22×C4—582no—
159C22×C4C2×#118111yescharacteristic
160C22×C4C2×#118111yescharacteristic
161M16—294no—
162M16—582no—
163M16—584no—
164M16—582no—
165M16—582no—
166C2×C8—582no—
167C2×C8—584no—
168C2×C8—582no—
169C4⋊C4—581no—
170C4⋊C4—581no—
171C4⋊C4—581no—
172C4⋊C4—581no—
173C4⋊C4—581no—
174C4⋊C4—581no—
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—581no—
178C22⋊C4—581no—
179C23—22no—
180C23—22no—
181C23—41no—
182C23C22⋊#118111yescharacteristic
183C23C22⋊#118111yescharacteristic
184C23C22×#118111yescharacteristic
185Q8—1161no—
186Q8—1162no—
187Q8—1161no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—292no—
193C2×C4—292no—
194C2×C4—291no—
195C2×C4—291no—
196C2×C4—291no—
197C2×C4—291no—
198C2×C4—581no—
199C2×C4—581no—
200C2×C4—582no—
201C2×C4—582no—
202C2×C4—581no—
203C2×C4—581no—
204C2×C4—582no—
205C2×C4—582no—
206C2×C4—581no—
207C2×C4—581no—
208C2×C4—1161no—
209C8—584no—
210C8—1162no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—44no—
219C22#1174522112yescomplemented
220C22D4×#118112yes—
221C22C2×C22⋊#118111yescharacteristic
222C4—41no—
223C4—41no—
224C4—291no—
225C4—292no—
226C4—291no—
227C4—581no—
228C4—581no—
229C4—1161no—
230C4—1161no—
231C2—22no—
232C2—22no—
233C2—41no—
234C2#1427211111yescharacteristic
235C2C2×#1174522111yescharacteristic
236C2#1427215011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C22⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC24×C29C2×C4
cosocleC22×Dic29C23
hypercenterC2×C22⋊C4#1181
hypocenterC29#1901
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11745221C2semidirect
4. #14272043C2semidirect
101. C22×C29#101semidirect
143. C29#1901semidirect
219. C22#11745221semidirect

Maximal subgroups

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

subgroupindex
C22×#908002
C2×#117452212
#142721332
#142720432
C2×#117452402
#190129