Finite Group Databasebeta

← #16835632

Subgroups — #16835632

Order 3712.

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

normal subgroups only

This group has 408 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
1C2×#11745215C214yesmaximal, complemented
2#14272105C211yesmaximal, characteristic, complemented
3C4×C22⋊#1181C211yesmaximal, characteristic, complemented
4C2×#11745257C211yesmaximal, characteristic
5C22×D116C411yescharacteristic, complemented
6C22×D116C2212yes—
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181C2212yes—
9C2×C22⋊#1181C2212yes—
10C2×C4⋊#1181—21no—
11C2×C4×#1181—21no—
12C2×C4⋊C4×C29C411yescharacteristic, complemented
13C2×#90781C412yescomplemented
14#11745257—21no—
15#11745257—21no—
16#11745257—21no—
17#11745257—21no—
18(C2×#1181)⋊C4—21no—
19(C2×#1181)⋊C4—21no—
20#11745215—28no—
21C23×D29C2×C412yes—
22C23×D29C2311yescharacteristic
23C22×#1181—22no—
24C22×#1181—22no—
25C22×C4×C29C2×C412yes—
26C22×C4×C29C2×C411yescharacteristic
27C22×Dic29C2×C411yescharacteristic
28C2×D116—24no—
29C2×D116—22no—
30C2×D116—22no—
31C2×D116—24no—
32C2×D116—21no—
33C2×D116—21no—
34C2×D116—42no—
35C2×C4×D29—42no—
36C2×C4×D29D411yescharacteristic
37C2×C4×D29D411yescharacteristic
38C2×C4×D29D411yescharacteristic
39C2×C4×D29D411yescharacteristic
40C22⋊#1181—22no—
41C22⋊#1181—24no—
42C22⋊#1181D414yescomplemented
43C4⋊#1181—42no—
44C4×#1181—42no—
45C4⋊C4×C29—21no—
46C4⋊C4×C29—21no—
47#90781—22no—
48#90781—22no—
49C23×C29C22×C411yescharacteristic
50C22×D29—22no—
51C22×D29—24no—
52C22×D29—41no—
53C22×D29—41no—
54C22×D29—42no—
55C22×D29—42no—
56C22×D29C2×D411yescharacteristic
57C22×D29C2×D411yescharacteristic
58C22×D29C2×D412yes—
59C22×D29#4112yes—
60C2×#1181—24no—
61C2×#1181—42no—
62C2×#1181—42no—
63C2×#1181—42no—
64C2×#1181—42no—
65C2×#1181—42no—
66C2×C4×C29—22no—
67C2×C4×C29—22no—
68C2×C4×C29—24no—
69C2×C4×C29C22⋊C411yescharacteristic
70C2×C4×C29C22⋊C411yescharacteristic
71C2×Dic29—41no—
72C2×Dic29C22⋊C411yescharacteristic
73C2×Dic29C22⋊C411yescharacteristic
74D116—42no—
75D116—44no—
76D116—42no—
77D116—42no—
78D116—42no—
79C4×D29—22no—
80C4×D29—22no—
81C4×D29—41no—
82C4×D29—41no—
83#1964—291nomaximal, Sylow
84C22×C29—21no—
85C22×C29—21no—
86C22×C29C2×C22⋊C411yescharacteristic
87C22×C29C4×D412yes—
88C2×D29—21no—
89C2×D29—21no—
90C2×D29—21no—
91C2×D29—21no—
92C2×D29—42no—
93C2×D29—42no—
94C2×D29—42no—
95C2×D29—42no—
96C2×D29—42no—
97C2×D29—84no—
98C2×D29#12112yes—
99C2×D29#12411yescharacteristic
100C2×D29#12711yescharacteristic
101#1181—44no—
102#1181—82no—
103C4×C29—21no—
104C4×C29—42no—
105C4×C29#9912yescomplemented
106Dic29—21no—
107Dic29—21no—
108C2×#121—291no—
109C2×#99—294no—
110#380—291no—
111C4×C22⋊C4—291no—
112C2×C29—22no—
113C2×C29#39011yescharacteristic
114C2×C29C2×#9911yescharacteristic
115C2×C29#41011yescharacteristic
116D29—22no—
117D29—21no—
118D29—21no—
119D29—82no—
120C22×D4—292no—
121C22×D4—291no—
122C23×C4—291no—
123#121—581no—
124#121—581no—
125#121—581no—
126#121—581no—
127C2×C4⋊C4—581no—
128C2×C4⋊C4#118111yescharacteristic, complemented
129C2×C22⋊C4—292no—
130C2×C22⋊C4—292no—
131C2×C22⋊C4—292no—
132C2×C42—581no—
133#99—588no—
134#95—581no—
135#95—581no—
136C29#196411yescharacteristic, complemented, Sylow
137C24—291no—
138C24—292no—
139C2×D4—584no—
140C2×D4—582no—
141C2×D4—582no—
142C2×D4—584no—
143C2×D4—581no—
144C2×D4—581no—
145C2×D4—1162no—
146C22×C4—291no—
147C22×C4—291no—
148C22×C4—291no—
149C22×C4—291no—
150C22×C4—291no—
151C22×C4—582no—
152C22×C4—582no—
153C22×C4—1162no—
154C22×C4C2×#118112yes—
155C22×C4C2×#118111yescharacteristic
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—1162no—
159C22⋊C4—294no—
160C22⋊C4—582no—
161C22⋊C4—582no—
162C22⋊C4—582no—
163C22⋊C4—584no—
164C42—1162no—
165C23—291no—
166C23—291no—
167C23—292no—
168C23—292no—
169C23—582no—
170C23—584no—
171C23—1161no—
172C23—1161no—
173C23—1162no—
174C23—1162no—
175C23C22×#118111yescharacteristic
176D4—1162no—
177D4—1164no—
178D4—1162no—
179D4—1162no—
180D4—1162no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—22no—
184C2×C4—291no—
185C2×C4—291no—
186C2×C4—582no—
187C2×C4—582no—
188C2×C4—584no—
189C2×C4—1161no—
190C2×C4—1161no—
191C2×C4—1161no—
192C2×C4—1162no—
193C2×C4—1162no—
194C2×C4—1162no—
195C2×C4—1162no—
196C2×C4—1162no—
197C2×C4C22⋊#118111yescharacteristic
198C2×C4C22⋊#118111yescharacteristic
199C22—21no—
200C22—21no—
201C22—292no—
202C22—291no—
203C22—291no—
204C22—581no—
205C22—581no—
206C22—581no—
207C22—581no—
208C22—1162no—
209C22—1162no—
210C22—1162no—
211C22—1162no—
212C22—1162no—
213C22—2324no—
214C22D4×#118112yes—
215C22C2×C22⋊#118111yescharacteristic
216C4—21no—
217C4—42no—
218C4—581no—
219C4—581no—
220C4—1164no—
221C4—2322no—
222C4#1174521512yescomplemented
223C2—22no—
224C2—582no—
225C2—581no—
226C2—581no—
227C2—2322no—
228C2#1427211511yescharacteristic
229C2C2×#1174521511yescharacteristic
230C2#1427214411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×#11745257C2
cosocleC23×D29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1964
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11745215C2semidirect
2. #14272105C2semidirect
3. C4×C22⋊#1181C2semidirect
5. C22×D116C4semidirect
12. C2×C4⋊C4×C29C4semidirect
13. C2×#90781C4semidirect
42. C22⋊#1181D4semidirect
105. C4×C29#99semidirect
128. C2×C4⋊C4#1181semidirect
136. C29#1964semidirect
222. C4#11745215semidirect

Maximal subgroups

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

subgroupindex
C2×#117452152
#142721052
C4×C22⋊#11812
C2×#117452572
#196429