Finite Group Databasebeta

← #16835683

Subgroups — #16835683

Order 3712.

324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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#14272105C211yesmaximal, characteristic
2C4×C22⋊#1181C211yesmaximal, characteristic
3#14272041C212yesmaximal
4#14272041C212yesmaximal
5C2×#11745258C211yesmaximal, characteristic
6C22×C4×D29C2211yescharacteristic
7C22×Dic58C411yescharacteristic, complemented
8C2×C22⋊#1181C2212yes—
9C2×C22⋊#1181C2212yes—
10C2×C4⋊#1181—21no—
11C2×C4×#1181—21no—
12C2×C4⋊C4×C29C411yescharacteristic, complemented
13C2×#90781C2211yescharacteristic
14C2×#90781C2211yescharacteristic
15C2×#90779C411yescharacteristic, complemented
16C2×#90779C411yescharacteristic, complemented
17#11745258—21no—
18#11745258—21no—
19#11745258—21no—
20#11745258—21no—
21(C2×#1181)⋊C4—21no—
22(C2×#1181)⋊C4—21no—
23C23×D29C2311yescharacteristic
24C22×#1181—22no—
25C22×#1181—22no—
26C22×C4×C29C2×C411yescharacteristic
27C22×C4×C29C2×C411yescharacteristic
28C22×C4×C29C2×C411yescharacteristic
29C22×Dic29C2×C411yescharacteristic
30C22×Dic29C2×C411yescharacteristic
31C22×Dic29C2×C411yescharacteristic
32C2×C4×D29—42no—
33C2×C4×D29D411yescharacteristic
34C2×C4×D29D411yescharacteristic
35C2×C4×D29D411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×Dic58—21no—
38C2×Dic58—21no—
39C2×Dic58—42no—
40C22⋊#1181—22no—
41C22⋊#1181—24no—
42C22⋊#1181Q814yescomplemented
43C4⋊#1181—42no—
44C4×#1181—42no—
45C4⋊C4×C29—21no—
46C4⋊C4×C29—21no—
47#90781—21no—
48#90781—21no—
49#90781—21no—
50#90781—21no—
51#90779—21no—
52#90779—21no—
53#90779—21no—
54#90779—21no—
55C23×C29C22×C411yescharacteristic
56C22×D29—41no—
57C22×D29—41no—
58C22×D29C2×D411yescharacteristic
59C22×D29C2×D411yescharacteristic
60C22×D29C2×Q812yes—
61C22×D29#4112yes—
62C2×#1181—24no—
63C2×#1181—42no—
64C2×#1181—42no—
65C2×#1181—42no—
66C2×#1181—42no—
67C2×#1181—42no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—41no—
71C2×C4×C29—41no—
72C2×C4×C29—41no—
73C2×C4×C29C22⋊C411yescharacteristic
74C2×C4×C29C22⋊C411yescharacteristic
75C2×Dic29—22no—
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C2×Dic29C22⋊C411yescharacteristic
81C2×Dic29C22⋊C411yescharacteristic
82C4×D29—22no—
83C4×D29—22no—
84C4×D29—41no—
85C4×D29—41no—
86Dic58—42no—
87Dic58—42no—
88#1996—291nomaximal, Sylow
89C22×C29—21no—
90C22×C29—21no—
91C22×C29C2×C22⋊C411yescharacteristic
92C22×C29C4×Q812yes—
93C2×D29—21no—
94C2×D29—21no—
95C2×D29—21no—
96C2×D29—21no—
97C2×D29—42no—
98C2×D29—42no—
99C2×D29C22⋊Q812yes—
100C2×D29#12411yescharacteristic
101C2×D29C4⋊Q811yescharacteristic
102#1181—44no—
103#1181—82no—
104C4×C29—21no—
105C4×C29—21no—
106C4×C29—41no—
107C4×C29—41no—
108Dic29—21no—
109Dic29—41no—
110Dic29—41no—
111Dic29#9912yes—
112C2×C22⋊Q8—291no—
113#380—291no—
114C4×C22⋊C4—291no—
115#342—292no—
116#342—292no—
117C2×C29—22no—
118C2×C29#39111yescharacteristic
119C2×C29C2×#9911yescharacteristic
120C2×C29#41011yescharacteristic
121D29—22no—
122D29—21no—
123D29—21no—
124C22×Q8—291no—
125C23×C4—291no—
126C22⋊Q8—581no—
127C22⋊Q8—581no—
128C22⋊Q8—581no—
129C22⋊Q8—581no—
130C2×C4⋊C4—291no—
131C2×C4⋊C4—291no—
132C2×C4⋊C4—581no—
133C2×C4⋊C4#118111yescharacteristic, complemented
134C2×C22⋊C4—292no—
135C2×C22⋊C4—291no—
136C2×C22⋊C4—291no—
137C2×C22⋊C4—292no—
138C2×C42—581no—
139#95—581no—
140#95—581no—
141C29#199611yescharacteristic, complemented, Sylow
142C24—291no—
143C2×Q8—581no—
144C2×Q8—581no—
145C2×Q8—1162no—
146C22×C4—291no—
147C22×C4—291no—
148C22×C4—291no—
149C22×C4—291no—
150C22×C4—291no—
151C22×C4—291no—
152C22×C4—291no—
153C22×C4—582no—
154C22×C4—582no—
155C22×C4—1162no—
156C22×C4C2×#118111yescharacteristic
157C22×C4C2×#118111yescharacteristic
158C22×C4C2×#118111yescharacteristic
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—581no—
162C4⋊C4—581no—
163C4⋊C4—581no—
164C4⋊C4—581no—
165C4⋊C4—1162no—
166C22⋊C4—294no—
167C22⋊C4—581no—
168C22⋊C4—581no—
169C22⋊C4—581no—
170C22⋊C4—581no—
171C22⋊C4—582no—
172C22⋊C4—584no—
173C42—1162no—
174C23—291no—
175C23—291no—
176C23—292no—
177C23—292no—
178C23—1161no—
179C23—1161no—
180C23C22×#118111yescharacteristic
181Q8—1162no—
182Q8—1162no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—291no—
189C2×C4—291no—
190C2×C4—582no—
191C2×C4—582no—
192C2×C4—582no—
193C2×C4—584no—
194C2×C4—581no—
195C2×C4—581no—
196C2×C4—1161no—
197C2×C4—1161no—
198C2×C4—1162no—
199C2×C4—1162no—
200C2×C4—1161no—
201C2×C4—1161no—
202C2×C4—1162no—
203C2×C4—1162no—
204C2×C4—1162no—
205C2×C4C22⋊#118111yescharacteristic
206C2×C4C22⋊#118111yescharacteristic
207C22—21no—
208C22—21no—
209C22—292no—
210C22—291no—
211C22—291no—
212C22—581no—
213C22—581no—
214C22—581no—
215C22—581no—
216C22—1162no—
217C22—1162no—
218C22Q8×#118112yes—
219C22C2×C22⋊#118111yescharacteristic
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—292no—
225C4—581no—
226C4—1164no—
227C4—1161no—
228C4—1161no—
229C4—2322no—
230C2—22no—
231C2—582no—
232C2—581no—
233C2—581no—
234C2(C2×#1181)⋊Q811yescharacteristic
235C2D29⋊#9911yescharacteristic
236C2#1427214211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radical, cosocleC23×D29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1996
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
7. C22×Dic58C4semidirect
12. C2×C4⋊C4×C29C4semidirect
15. C2×#90779C4semidirect
16. C2×#90779C4semidirect
42. C22⋊#1181Q8semidirect
133. C2×C4⋊C4#1181semidirect
141. C29#1996semidirect

Maximal subgroups

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

subgroupindex
#142721052
C4×C22⋊#11812
#142720412
C2×#117452582
#199629