Finite Group Databasebeta

← #16821155

Subgroups — #16821155

Order 3712.

258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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#14271709C211yesmaximal, characteristic
2#14271137C211yesmaximal, characteristic, complemented
3#14270957C212yesmaximal, complemented
4#14270955C212yesmaximal, complemented
5C29×#410C211yesmaximal, characteristic, complemented
6C2×#41×C29C2211yescharacteristic
7C2×#90805C411yescharacteristic, complemented
8C29×#117—21no—
9#11745309C411yescharacteristic, complemented
10#11745306C411yescharacteristic, complemented
11#11745302C2211yescharacteristic
12#11745301—21no—
13#11745301—21no—
14#11745298C2211yescharacteristic
15C4×C22⋊D29—21no—
16C4×C22⋊D29—21no—
17#11745288—21no—
18C2×C4×Dic29C411yescharacteristic, complemented
19C29×#99—21no—
20C29×#99C2212yes—
21#11745182—21no—
22#11745182C2212yes—
23#41×C29—41no—
24#41×C29—41no—
25C2×Q8×C29C2×C411yescharacteristic
26C2×D4×C29D411yescharacteristic
27C2×D4×C29D411yescharacteristic
28C2×D4×C29C2311yescharacteristic
29C22×C4×C29C2×C411yescharacteristic
30C22×C4×C29D411yescharacteristic
31C22×C4×C29D411yescharacteristic
32C2×C22⋊D29—21no—
33C2×C22⋊D29—21no—
34C2×C22⋊D29—21no—
35C22×Dic29—21no—
36#90805—41no—
37#90805—41no—
38C2×D116C2×C411yescharacteristic
39C2×C4×D29—21no—
40C2×Dic58C2×C411yescharacteristic
41C4⋊C4×C29—41no—
42C22⋊C4×C29—22no—
43C42×C29—41no—
44C22⋊Dic29—21no—
45C22⋊Dic29—21no—
46C22⋊Dic29—22no—
47#90781—21no—
48#90781—21no—
49C4⋊Dic29—41no—
50#90779—21no—
51#90779—21no—
52C4×Dic29—21no—
53C4×Dic29—41no—
54C4×Dic29C2×C411yescharacteristic
55C4×Dic29C2×C411yescharacteristic
56C23×C29C22⋊C411yescharacteristic
57C23×C29C2×D411yescharacteristic
58C23×C29C2×D411yescharacteristic
59C22×D29—21no—
60Q8×C29—41no—
61D4×C29—41no—
62D4×C29—41no—
63D4×C29—41no—
64C2×C4×C29—21no—
65C2×C4×C29—21no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—42no—
71C2×C4×C29C22⋊C411yescharacteristic
72C2×C4×C29C22⋊C411yescharacteristic
73C2×C4×C29C22⋊C411yescharacteristic
74C2×C4×C29C22×C411yescharacteristic
75C22⋊D29—42no—
76C22⋊D29—42no—
77C22⋊D29—42no—
78C2×Dic29—21no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29—42no—
82C2×Dic29—42no—
83D116—41no—
84C4×D29—41no—
85C4×D29—41no—
86Dic58—41no—
87#2126—291nomaximal, Sylow
88C22×C29—21no—
89C22×C29—21no—
90C22×C29—21no—
91C22×C29—41no—
92C22×C29—41no—
93C22×C29—41no—
94C22×C29C2×C22⋊C411yescharacteristic
95C2×D29—41no—
96C2×D29—41no—
97C2×D29—41no—
98C4×C29—21no—
99C4×C29—21no—
100C4×C29—21no—
101C4×C29—82no—
102C4×C29#9911yescharacteristic
103C4×C29#9911yescharacteristic
104Dic29—22no—
105Dic29—41no—
106Dic29—41no—
107Dic29—82no—
108#532—291no—
109#410—291no—
110#410D2911yescharacteristic, complemented
111#354—292no—
112#353—292no—
113C2×C29—21no—
114C2×C29—41no—
115C2×C29—41no—
116C2×C29—41no—
117C2×C29C2×#9911yescharacteristic
118D29—81no—
119C2×#41—291no—
120C2×#41C2×D2911yescharacteristic
121C4⋊Q8—291no—
122#127—291no—
123#124—291no—
124#124—291no—
125#121—581no—
126#121—581no—
127C4×D4—581no—
128C4×D4—581no—
129#117—21no—
130#117—581no—
131C2×C42—291no—
132#99—21no—
133#99—292no—
134#99—581no—
135#99C2×D2912yes—
136C29#212611yescharacteristic, complemented, Sylow
137#41—41no—
138#41—41no—
139#41—1161no—
140#41—1161no—
141C2×Q8—291no—
142C2×Q8C4×D2911yescharacteristic
143C2×D4—291no—
144C2×D4—581no—
145C2×D4—581no—
146C2×D4—581no—
147C2×D4D11611yescharacteristic
148C2×D4C22⋊D2911yescharacteristic
149C2×D4C22×D2911yescharacteristic
150C22×C4—581no—
151C22×C4—581no—
152C22×C4C4×D2911yescharacteristic
153C22×C4D11611yescharacteristic
154C22×C4C22⋊D2911yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C4⋊C4—1161no—
159C22⋊C4—22no—
160C22⋊C4—581no—
161C22⋊C4—581no—
162C22⋊C4—581no—
163C22⋊C4—581no—
164C22⋊C4—582no—
165C42—41no—
166C42—291no—
167C42—291no—
168C42—581no—
169C42—1161no—
170C23—581no—
171C23#9078111yescharacteristic
172C23C2×D11611yescharacteristic
173C23C2×C22⋊D2911yescharacteristic
174Q8—41no—
175Q8—1161no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—1161no—
180D4—1162no—
181D4—1162no—
182D4—1162no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—581no—
191C2×C4—581no—
192C2×C4—581no—
193C2×C4—1162no—
194C2×C4—1161no—
195C2×C4—1161no—
196C2×C4—1162no—
197C2×C4#9078111yescharacteristic
198C2×C4#9078111yescharacteristic
199C2×C4#9078111yescharacteristic
200C2×C4C2×C4×D2911yescharacteristic
201C22—21no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—1161no—
208C22—1161no—
209C22—1161no—
210C22C2×#9078111yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—582no—
216C4—1161no—
217C4—1161no—
218C4—2322no—
219C4#1174515411yescharacteristic
220C4#1174515411yescharacteristic
221C2—21no—
222C2—41no—
223C2—41no—
224C2—41no—
225C2—2321no—
226C2C2×#1174515411yescharacteristic
subgroupG/H
centerC4#11745154
commutatorC2×C4×C29C22×C4
FrattiniC2×D4C22×D29
FittingC29×#410C2
socleC2×C29C2×#99
prime radical#14271709C2
cosocleC2×D4×C29C23
hypercenter#410D29
hypocenterC29#2126
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14271137C2semidirect
3. #14270957C2semidirect
4. #14270955C2semidirect
5. C29×#410C2semidirect
7. C2×#90805C4semidirect
9. #11745309C4semidirect
10. #11745306C4semidirect
18. C2×C4×Dic29C4semidirect
110. #410D29semidirect
136. C29#2126semidirect

Maximal subgroups

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

subgroupindex
#142717092
#142711372
#142709572
#142709552
C29×#4102
#212629