Finite Group Databasebeta

← #16835746

Subgroups — #16835746

Order 3712.

264 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 52 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#14272150C211yesmaximal, characteristic, complemented
2#14272143C211yesmaximal, characteristic, complemented
3#14272065C212yesmaximal, complemented
4#14272064C212yesmaximal, complemented
5#14271671C211yesmaximal, characteristic
6C2×#90807C2211yescharacteristic
7C22×C4×D29C411yescharacteristic, complemented
8C2×#90800—21no—
9#11745345—21no—
10C29×#123C411yescharacteristic, complemented
11#11745299C411yescharacteristic, complemented
12#11745291C2211yescharacteristic
13#11745258—21no—
14#11745255—21no—
15#11745246—21no—
16#11745244C2211yescharacteristic
17#11745243—21no—
18#11745239C411yescharacteristic, complemented
19#11745229C2212yes—
20#11745227—21no—
21#11745227C2212yes—
22#11745221—21no—
23C23×D29C2×C411yescharacteristic
24C2×D4×C29C2×C411yescharacteristic
25C22×C4×C29C2×C411yescharacteristic
26C2×C22⋊D29—21no—
27C2×C22⋊D29D411yescharacteristic
28C2×C22⋊D29C2311yescharacteristic
29C22×Dic29C2×C411yescharacteristic
30C22×Dic29D411yescharacteristic
31#90807—41no—
32#90807—41no—
33C2×D116—21no—
34C2×C4×D29—21no—
35C2×C4×D29—21no—
36C2×C4×D29—41no—
37C2×C4×D29—41no—
38C2×C4×D29D411yescharacteristic
39C2×Dic58D411yescharacteristic
40C22⋊#1181—22no—
41#90800—22no—
42#90800—41no—
43C2×#6599—41no—
44C4⋊#1181—41no—
45C4×#1181—41no—
46C4⋊C4×C29—21no—
47C22⋊C4×C29—21no—
48C22⋊C4×C29C2×C411yescharacteristic
49C22⋊Dic29C2×C411yescharacteristic
50#90781—21no—
51#90781—21no—
52#90781—21no—
53#90779—21no—
54#90779—21no—
55C4×Dic29—21no—
56C23×C29C22⋊C411yescharacteristic
57C23×C29C22×C411yescharacteristic
58C22×D29—21no—
59C22×D29—42no—
60C22×D29—41no—
61C22×D29C2×D411yescharacteristic
62C2×#1181—42no—
63D4×C29—41no—
64C2×C4×C29—21no—
65C2×C4×C29—21no—
66C2×C4×C29—41no—
67C2×C4×C29C22⋊C411yescharacteristic
68C22⋊D29—41no—
69C22⋊D29—41no—
70C22⋊D29—42no—
71C2×Dic29—21no—
72C2×Dic29—21no—
73C2×Dic29—21no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29C22⋊C411yescharacteristic
77C2×Dic29C22⋊C411yescharacteristic
78C2×Dic29C2×D411yescharacteristic
79D116—42no—
80C4×D29—21no—
81C4×D29—21no—
82C4×D29—42no—
83C4×D29—41no—
84C4×D29—41no—
85Dic58—41no—
86#6599—42no—
87#2120—291nomaximal, Sylow
88C22×C29—21no—
89C22×C29—21no—
90C22×C29—41no—
91C22×C29—41no—
92C22×C29C2×C22⋊C411yescharacteristic
93C2×D29—22no—
94C2×D29—21no—
95C2×D29—41no—
96C2×D29—42no—
97C2×D29—41no—
98C2×D29—41no—
99C2×D29—42no—
100#1181—82no—
101C4×C29—21no—
102C4×C29—41no—
103C4×C29—41no—
104Dic29—21no—
105Dic29—21no—
106Dic29—41no—
107Dic29#9911yescharacteristic
108Dic29#9911yescharacteristic
109#525—291no—
110#413—291no—
111#410—291no—
112#352—292no—
113AΣL(1,𝔽16)—292no—
114C2×C29—21no—
115C2×C29—41no—
116C2×C29—41no—
117C2×C29C2×#9911yescharacteristic
118D29—41no—
119D29—42no—
120C2×#41—291no—
121C23×C4—291no—
122C2×M16—581no—
123#123—291no—
124#123#118111yescharacteristic, complemented
125C22⋊Q8—581no—
126#121—581no—
127#120—291no—
128#120—291no—
129C4×D4—581no—
130C4×D4—581no—
131#117—291no—
132#117—581no—
133#101—581no—
134#100—292no—
135#99—292no—
136#99—581no—
137C29#212011yescharacteristic, complemented, Sylow
138C24—291no—
139#41—1161no—
140#41—1161no—
141C2×Q8—291no—
142C2×D4—291no—
143C2×D4—291no—
144C2×D4—581no—
145C2×D4—581no—
146C2×D4C2×#118111yescharacteristic
147C22×C4—291no—
148C22×C4—291no—
149C22×C4—291no—
150C22×C4—581no—
151C22×C4—581no—
152C22×C4—1161no—
153C22×C4—1161no—
154C22×C4C2×#118111yescharacteristic
155M16—582no—
156M16—1161no—
157C2×C8—1161no—
158C4⋊C4—21no—
159C4⋊C4—581no—
160C4⋊C4—581no—
161C4⋊C4—1161no—
162C22⋊C4—21no—
163C22⋊C4—291no—
164C22⋊C4—581no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—582no—
168C22⋊C4C2×#118111yescharacteristic
169C42—581no—
170C42—1161no—
171C23—291no—
172C23—581no—
173C23—1161no—
174C23—1162no—
175C23C22⋊#118111yescharacteristic
176C23C22×#118111yescharacteristic
177Q8—1161no—
178D4—41no—
179D4—1162no—
180D4—1161no—
181D4—1161no—
182D4—1162no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—291no—
187C2×C4—291no—
188C2×C4—291no—
189C2×C4—581no—
190C2×C4—581no—
191C2×C4—581no—
192C2×C4—581no—
193C2×C4—581no—
194C2×C4—581no—
195C2×C4—581no—
196C2×C4—1161no—
197C2×C4—1161no—
198C2×C4—1162no—
199C2×C4—1162no—
200C2×C4C22⋊#118111yescharacteristic
201C8—1162no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—582no—
207C22—581no—
208C22—1161no—
209C22—1161no—
210C22—1162no—
211C22—1162no—
212C22—1161no—
213C22C2×C22⋊#118111yescharacteristic
214C4—21no—
215C4—41no—
216C4—41no—
217C4—291no—
218C4—291no—
219C4—581no—
220C4—581no—
221C4—1161no—
222C4—2322no—
223C2—21no—
224C2—41no—
225C2—41no—
226C2—1161no—
227C2—1162no—
228C2D29⋊#9911yescharacteristic
subgroupG/H
centerC2D29⋊#99
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#123C4
socleC2×C29C2×#99
prime radical#14271671C2
cosocleC2×C22⋊D29C23
hypercenter#123#1181
hypocenterC29#2120
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #14272150C2semidirect
2. #14272143C2semidirect
3. #14272065C2semidirect
4. #14272064C2semidirect
7. C22×C4×D29C4semidirect
10. C29×#123C4semidirect
11. #11745299C4semidirect
18. #11745239C4semidirect
124. #123#1181semidirect
137. C29#2120semidirect

Maximal subgroups

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

subgroupindex
#142721502
#142721432
#142720652
#142720642
#142716712
#212029