Finite Group Databasebeta

← #16820740

Subgroups — #16820740

Order 3712.

382 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 71 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×#11745182C212yesmaximal, complemented
2#14271043C212yesmaximal, complemented
3#14271035C211yesmaximal, characteristic, complemented
4#14270930C211yesmaximal, characteristic, complemented
5C29×#534C211yesmaximal, characteristic
6C22×D4×C29C2212yes—
7C23×Dic29C2211yescharacteristic
8C29×#123—22no—
9C29×#121—21no—
10C29×#121—21no—
11C29×#120—22no—
12C2×C22⋊C4×C29C2211yescharacteristic
13C2×C22⋊Dic29—22no—
14C2×C22⋊Dic29C2212yes—
15C2×C22⋊Dic29C2211yescharacteristic
16C2×#90779—21no—
17#11745182—24no—
18#11745179—21no—
19#11745179—22no—
20C24×C29D412yes—
21C24×C29C2311yescharacteristic
22C2×D4×C29—22no—
23C2×D4×C29—22no—
24C2×D4×C29—22no—
25C2×D4×C29—22no—
26C2×D4×C29—22no—
27C2×D4×C29—22no—
28C2×D4×C29—21no—
29C2×D4×C29—21no—
30C22×C4×C29D412yes—
31C22×C4×C29D411yescharacteristic
32C22×C4×C29D411yescharacteristic
33C22×Dic29—21no—
34C22×Dic29—21no—
35C22×Dic29—22no—
36C22×Dic29—22no—
37C22×Dic29—42no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29—21no—
40C22⋊C4×C29—22no—
41C22⋊C4×C29—22no—
42C22⋊C4×C29—22no—
43C22⋊Dic29—21no—
44C22⋊Dic29—22no—
45C22⋊Dic29—22no—
46C22⋊Dic29—44no—
47C22⋊Dic29D412yescomplemented
48#90779—42no—
49C23×C29—22no—
50C23×C29—22no—
51C23×C29—22no—
52C23×C29—41no—
53C23×C29—41no—
54C23×C29—42no—
55C23×C29—42no—
56C23×C29C2×D411yescharacteristic
57C23×C29C2×D412yes—
58C23×C29C2×D411yescharacteristic
59C23×C29#4111yescharacteristic
60C23×C29#4112yes—
61D4×C29—42no—
62D4×C29—42no—
63D4×C29—42no—
64D4×C29—42no—
65D4×C29—81no—
66D4×C29—81no—
67C2×C4×C29—21no—
68C2×C4×C29—21no—
69C2×C4×C29—22no—
70C2×C4×C29—22no—
71C2×C4×C29—22no—
72C2×C4×C29—41no—
73C2×C4×C29—41no—
74C2×Dic29—22no—
75C2×Dic29—24no—
76C2×Dic29—22no—
77C2×Dic29—41no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C2×Dic29—42no—
81C2×Dic29—41no—
82C2×Dic29—42no—
83C2×Dic29—42no—
84C2×Dic29—42no—
85#2044—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—22no—
88C22×C29—21no—
89C22×C29—22no—
90C22×C29—41no—
91C22×C29—41no—
92C22×C29—42no—
93C22×C29—44no—
94C22×C29—42no—
95C22×C29—42no—
96C22×C29—42no—
97C22×C29—82no—
98C22×C29#12011yescharacteristic
99C22×C29#12111yescharacteristic
100C22×C29#12112yes—
101C22×C29#12312yes—
102C22×C29#12411yescharacteristic
103C4×C29—42no—
104C4×C29—41no—
105C4×C29—41no—
106Dic29—42no—
107Dic29—42no—
108Dic29—82no—
109#534D2911yescharacteristic
110C2×#99—292no—
111#386—292no—
112#385—291no—
113#342—291no—
114C2×C29—21no—
115C2×C29—22no—
116C2×C29—22no—
117C2×C29—21no—
118C2×C29—82no—
119C2×C29#39411yescharacteristic
120C2×C29B(4,𝔽2)11yescharacteristic
121C2×C29#45811yescharacteristic
122C22×D4C2×D2912yes—
123C23×C4—291no—
124#123—22no—
125#121—21no—
126#121—21no—
127#120—22no—
128C2×C4⋊C4—581no—
129C2×C22⋊C4—291no—
130C2×C22⋊C4—292no—
131C2×C22⋊C4—582no—
132C2×C22⋊C4C2×D2911yescharacteristic
133#99—584no—
134#95—581no—
135#95—582no—
136C29#204411yescharacteristic, complemented, Sylow
137C24C22⋊D2912yes—
138C24C22×D2911yescharacteristic
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4—21no—
146C2×D4—21no—
147C22×C4—581no—
148C22×C4—582no—
149C22×C4—581no—
150C22×C4—582no—
151C22×C4—1162no—
152C22×C4C22⋊D2912yes—
153C22×C4C22⋊D2911yescharacteristic
154C22×C4C22⋊D2911yescharacteristic
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—1162no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—292no—
162C22⋊C4—581no—
163C22⋊C4—582no—
164C22⋊C4—582no—
165C22⋊C4—1164no—
166C23—22no—
167C23—22no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—42no—
172C23—42no—
173C23D4×D2911yescharacteristic
174C23#9080711yescharacteristic
175C23#9080712yes—
176C23C2×C22⋊D2912yes—
177C23C2×C22⋊D2911yescharacteristic
178D4—42no—
179D4—42no—
180D4—42no—
181D4—42no—
182D4—81no—
183D4—81no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—584no—
192C2×C4—582no—
193C2×C4—582no—
194C2×C4—1161no—
195C2×C4—1161no—
196C2×C4—1162no—
197C2×C4—1161no—
198C2×C4—1161no—
199C2×C4—1162no—
200C2×C4—1162no—
201C2×C4—1162no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—44no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—82no—
214C22#1174529712yes—
215C22#1174529811yescharacteristic
216C22#1174530011yescharacteristic
217C22#1174530112yes—
218C22#1174531511yescharacteristic
219C4—42no—
220C4—41no—
221C4—41no—
222C4—1162no—
223C4—1162no—
224C4—2322no—
225C2—21no—
226C2—22no—
227C2—22no—
228C2—21no—
229C2—82no—
230C2#1427107711yescharacteristic
231C2#1427135011yescharacteristic
232C2#1427135311yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC24×C29C23
FrattiniC24C22×D29
Fitting, prime radicalC29×#534C2
socleC22×C29#120
hypercenter#534D29
hypocenterC29#2044
LCSG ▷ C24×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#11745182C2semidirect
2. #14271043C2semidirect
3. #14271035C2semidirect
4. #14270930C2semidirect
47. C22⋊Dic29D4semidirect
136. C29#2044semidirect

Maximal subgroups

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

subgroupindex
C2×#117451822
#142710432
#142710352
#142709302
C29×#5342
#204429