Finite Group Databasebeta

← #16835503

Subgroups — #16835503

Order 3712.

342 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 66 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
1#14272241C211yesmaximal, characteristic, complemented
2#14272150C211yesmaximal, characteristic, complemented
3#14272133C212yesmaximal, complemented
4#14272044C212yesmaximal, complemented
5#14271669C211yesmaximal, characteristic
6C23×Dic29C2211yescharacteristic
7C2×#90807C2211yescharacteristic
8C2×#90800—21no—
9C2×#90800C2212yes—
10C2×#90800C2212yes—
11#11745346—24no—
12D29⋊M16—21no—
13C29×#120C411yescharacteristic
14#11745315C411yescharacteristic
15#11745301—21no—
16#11745297C411yescharacteristic
17D4×Dic29—21no—
18#11745248C411yescharacteristic
19#11745243—21no—
20#11745240—21no—
21#11745239C2211yescharacteristic
22#11745229—21no—
23C22⋊#6599—24no—
24#11745221—21no—
25C24×C29C2×C411yescharacteristic
26C2×D4×C29—21no—
27C2×D4×C29C2×C411yescharacteristic
28C2×C22⋊D29—21no—
29C2×C22⋊D29C2×C411yescharacteristic
30C2×C22⋊D29D411yescharacteristic
31C22×Dic29—21no—
32C22×Dic29—21no—
33C22×Dic29—22no—
34C22×Dic29—22no—
35C22×Dic29C2×C411yescharacteristic
36C22×Dic29D411yescharacteristic
37C22×Dic29C2311yescharacteristic
38#90807—22no—
39#90807—22no—
40C2×C4×D29D411yescharacteristic
41C2×Dic58D411yescharacteristic
42#90800—22no—
43#90800—22no—
44#90800—22no—
45#90800—22no—
46#90800—22no—
47C2×#6599—22no—
48C2×#6599—22no—
49C2×#6599D414yescomplemented
50#90796—22no—
51D29⋊C8—22no—
52C22⋊C4×C29—21no—
53C22⋊C4×C29C2×C411yescharacteristic
54C22⋊Dic29—21no—
55C22⋊Dic29—21no—
56C22⋊Dic29C2×C411yescharacteristic
57#90781—21no—
58C4⋊Dic29—21no—
59#90779—21no—
60#90779—21no—
61C4×Dic29—21no—
62C23×C29—21no—
63C23×C29—22no—
64C23×C29—42no—
65C23×C29C22⋊C411yescharacteristic
66C23×C29C22×C411yescharacteristic
67C22×D29C22⋊C411yescharacteristic
68D4×C29—22no—
69D4×C29—42no—
70C2×C4×C29—21no—
71C2×C4×C29C22⋊C411yescharacteristic
72C22⋊D29—22no—
73C22⋊D29—22no—
74C22⋊D29—42no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—22no—
80C2×Dic29—41no—
81C2×Dic29—42no—
82C2×Dic29—41no—
83C2×Dic29C22⋊C411yescharacteristic
84C2×Dic29C2×D412yes—
85C2×Dic29C2×D411yescharacteristic
86C2×Dic29C2×D411yescharacteristic
87C2×Dic29#4112yes—
88C4×D29—21no—
89C4×D29—21no—
90Dic58—22no—
91#6599—24no—
92#6599—42no—
93#1891—291nomaximal, Sylow
94C22×C29—22no—
95C22×C29—24no—
96C22×C29—21no—
97C22×C29—41no—
98C22×C29—41no—
99C22×C29—41no—
100C22×C29—42no—
101C22×C29—41no—
102C22×C29C2×C22⋊C411yescharacteristic
103C22×C29C4×D412yes—
104C2×D29—21no—
105C2×D29—41no—
106C4×C29—21no—
107C4×C29—41no—
108Dic29—21no—
109Dic29—41no—
110Dic29—41no—
111Dic29#12011yescharacteristic
112Dic29#12112yes—
113Dic29#12311yescharacteristic
114#568—291no—
115#525—291no—
116#413—291no—
117#407—292no—
118#344—292no—
119C2×C29—21no—
120C2×C29—22no—
121C2×C29—42no—
122C2×C29—41no—
123C2×C29#38611yescharacteristic
124D29—41no—
125C2×#41—291no—
126C23×C4—291no—
127#131—584no—
128C2×M16—292no—
129C2×M16—292no—
130C2×M16—581no—
131C2×M16—581no—
132#123—291no—
133#123—291no—
134C22⋊Q8—581no—
135#121—581no—
136#120—291no—
137#120#118111yescharacteristic
138C4×D4—581no—
139C4×D4—581no—
140#117—291no—
141#101—581no—
142#100—581no—
143C22⋊C8—584no—
144C29#189111yescharacteristic, complemented, Sylow
145C24C2×#118111yescharacteristic
146#41—582no—
147#41—582no—
148C2×Q8—291no—
149C2×D4—21no—
150C2×D4—291no—
151C2×D4—291no—
152C2×D4—581no—
153C2×D4C2×#118111yescharacteristic
154C22×C4—291no—
155C22×C4—291no—
156C22×C4—291no—
157C22×C4—291no—
158C22×C4—582no—
159C22×C4—581no—
160C22×C4—581no—
161C22×C4—582no—
162M16—582no—
163M16—582no—
164M16—582no—
165M16—582no—
166M16—582no—
167M16—582no—
168C2×C8—294no—
169C2×C8—582no—
170C2×C8—582no—
171C2×C8—582no—
172C4⋊C4—581no—
173C4⋊C4—581no—
174C4⋊C4—581no—
175C22⋊C4—21no—
176C22⋊C4—291no—
177C22⋊C4—581no—
178C22⋊C4—581no—
179C22⋊C4—581no—
180C22⋊C4C2×#118111yescharacteristic
181C42—581no—
182C23—22no—
183C23—21no—
184C23—42no—
185C23—291no—
186C23C22⋊#118111yescharacteristic
187C23C22×#118111yescharacteristic
188Q8—582no—
189D4—22no—
190D4—42no—
191D4—582no—
192D4—582no—
193D4—1162no—
194C2×C4—21no—
195C2×C4—292no—
196C2×C4—292no—
197C2×C4—291no—
198C2×C4—291no—
199C2×C4—291no—
200C2×C4—581no—
201C2×C4—581no—
202C2×C4—581no—
203C2×C4—581no—
204C2×C4—582no—
205C2×C4—581no—
206C2×C4—581no—
207C2×C4—1161no—
208C2×C4—1162no—
209C2×C4—1161no—
210C2×C4C22⋊#118111yescharacteristic
211C8—584no—
212C8—1162no—
213C22—22no—
214C22—24no—
215C22—21no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—42no—
220C22—41no—
221C22—581no—
222C22—1161no—
223C22D4×#118112yes—
224C22C2×C22⋊#118111yescharacteristic
225C4—21no—
226C4—41no—
227C4—291no—
228C4—292no—
229C4—291no—
230C4—581no—
231C4—1161no—
232C4—1161no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2—41no—
237C2—1161no—
238C2#1427211111yescharacteristic
subgroupG/H
centerC2#14272111
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#120C4
socleC2×C29#386
prime radical#14271669C2
cosocleC22×Dic29C23
hypercenter#120#1181
hypocenterC29#1891
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #14272241C2semidirect
2. #14272150C2semidirect
3. #14272133C2semidirect
4. #14272044C2semidirect
49. C2×#6599D4semidirect
144. C29#1891semidirect

Maximal subgroups

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

subgroupindex
#142722412
#142721502
#142721332
#142720442
#142716692
#189129