Finite Group Databasebeta

← #16827847

Subgroups — #16827847

Order 3712.

752 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 181 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×#11745306C211yesmaximal, characteristic, complemented
2C2×#11745302C211yesmaximal, characteristic
3C2×#11745309C211yesmaximal, characteristic, complemented
4C2×#11745237C211yesmaximal, characteristic, complemented
5C2×#11745298C211yesmaximal, characteristic, complemented
6#14271063C218yesmaximal, complemented
7C42×Dic29C211yesmaximal, characteristic, complemented
8C2×C29×#124C211yesmaximal, characteristic, complemented
9C22×Q8×C29C2211yescharacteristic
10C22×D4×C29C2211yescharacteristic
11C22×C22⋊D29C2214yes—
12C22×D116C2211yescharacteristic
13C22×Dic58C2211yescharacteristic
14C29×#124—24no—
15C2×C22⋊C4×C29C2214yes—
16C2×C42×C29C2211yescharacteristic
17C2×C22⋊Dic29C2214yes—
18#11745309—24no—
19#11745306—24no—
20#11745302—24no—
21#11745298—24no—
22C2×#90781C2214yes—
23C2×#90781C2214yes—
24C2×#90779C2214yes—
25C2×C4×Dic29C2214yes—
26C2×C4×Dic29C2211yescharacteristic
27C2×C4×Dic29C2211yescharacteristic
28#11745237—24no—
29C24×C29C2312yes—
30C23×D29C2312yes—
31C2×Q8×C29—22no—
32C2×Q8×C29—22no—
33C2×Q8×C29—22no—
34C2×D4×C29—22no—
35C2×D4×C29—22no—
36C2×D4×C29—22no—
37C22×C4×C29C2312yes—
38C22×C4×C29C2312yes—
39C22×C4×C29C2311yescharacteristic
40C2×C22⋊D29—28no—
41C2×C22⋊D29—216no—
42C22×Dic29C2312yes—
43C22×Dic29C2312yes—
44C22×Dic29C2312yes—
45C2×D116—22no—
46C2×D116—22no—
47C2×D116—22no—
48C2×Dic58—22no—
49C2×Dic58—22no—
50C2×Dic58—22no—
51C22⋊C4×C29—28no—
52C42×C29D414yescomplemented
53C22⋊Dic29—28no—
54#90781—28no—
55#90781—28no—
56#90779—28no—
57C4×Dic29—28no—
58C4×Dic29D414yes—
59C4×Dic29D414yescomplemented
60C23×C29—22no—
61C23×C29—22no—
62C23×C29—22no—
63C23×C29—28no—
64C23×C29C2411yescharacteristic
65C22×D29—22no—
66C22×D29—22no—
67C22×D29—22no—
68C22×D29—28no—
69Q8×C29—44no—
70D4×C29—44no—
71C2×C4×C29—24no—
72C2×C4×C29—22no—
73C2×C4×C29—22no—
74C2×C4×C29—22no—
75C2×C4×C29C2×D412yes—
76C2×C4×C29C2×D412yes—
77C2×C4×C29C2×D414yes—
78C2×C4×C29C2×D412yes—
79C22⋊D29—416no—
80C2×Dic29—24no—
81C2×Dic29—22no—
82C2×Dic29—22no—
83C2×Dic29—22no—
84C2×Dic29C2×D414yes—
85C2×Dic29C2×D414yes—
86C2×Dic29#4118yes—
87D116—44no—
88Dic58—44no—
89#2858—291nomaximal, Sylow
90C22×C29—44no—
91C22×C29—42no—
92C22×C29—44no—
93C22×C29—44no—
94C22×C29C22×D411yescharacteristic
95C22×C29C22×D411yescharacteristic
96C22×C29C22×D411yescharacteristic
97C22×C29C2×#4114yes—
98C2×D29—44no—
99C2×D29—42no—
100C2×D29—44no—
101C2×D29—44no—
102C4×C29—24no—
103C4×C29—42no—
104C4×C29#12714yes—
105Dic29—24no—
106Dic29—42no—
107Dic29#12418yescomplemented
108C2×C4⋊Q8—291no—
109C2×#127—291no—
110C2×#124—291no—
111C2×#124—291no—
112C2×#124—291no—
113C2×#124D2911yescharacteristic, complemented
114#390—298no—
115C43—291no—
116C2×C29—82no—
117C2×C29C2×#12412yes—
118C2×C29C2×#12711yescharacteristic
119C2×C29#53212yes—
120C2×C29#53212yes—
121D29—82no—
122C22×Q8—291no—
123C22×Q8C2×D2911yescharacteristic
124C22×D4—294no—
125C22×D4—291no—
126C22×D4C2×D2911yescharacteristic
127C4⋊Q8—584no—
128#127—584no—
129#124—24no—
130#124—584no—
131#124—584no—
132#124—584no—
133C2×C4⋊C4—294no—
134C2×C22⋊C4—294no—
135C2×C22⋊C4—294no—
136C2×C22⋊C4—294no—
137C2×C22⋊C4C2×D2914yes—
138C2×C42—291no—
139C2×C42—291no—
140C2×C42—294no—
141C2×C42C2×D2911yescharacteristic
142C29#285811yescharacteristic, complemented, Sylow
143C24—292no—
144C24C22×D2912yes—
145C2×Q8—22no—
146C2×Q8—22no—
147C2×Q8—22no—
148C2×Q8—582no—
149C2×Q8—582no—
150C2×Q8—582no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—588no—
155C2×D4—5816no—
156C2×D4—582no—
157C2×D4—582no—
158C2×D4—582no—
159C22×C4—292no—
160C22×C4—292no—
161C22×C4—292no—
162C22×C4C22×D2912yes—
163C22×C4C22×D2912yes—
164C22×C4C22×D2911yescharacteristic
165C4⋊C4—588no—
166C22⋊C4—28no—
167C22⋊C4—588no—
168C22⋊C4—588no—
169C22⋊C4—588no—
170C42—294no—
171C42—294no—
172C42—588no—
173C42C22⋊D2914yescomplemented
174C23—22no—
175C23—22no—
176C23—28no—
177C23—22no—
178C23—582no—
179C23—582no—
180C23—588no—
181C23—582no—
182C23C23×D2911yescharacteristic
183Q8—44no—
184Q8—1164no—
185D4—44no—
186D4—11616no—
187D4—1164no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—294no—
193C2×C4—298no—
194C2×C4—294no—
195C2×C4—584no—
196C2×C4—582no—
197C2×C4—582no—
198C2×C4—582no—
199C2×C4D4×D2912yes—
200C2×C4D4×D2912yes—
201C2×C4C2×C22⋊D2914yes—
202C2×C4C2×C22⋊D2912yes—
203C22—44no—
204C22—42no—
205C22—44no—
206C22—44no—
207C22—1164no—
208C22—1162no—
209C22—1164no—
210C22—1164no—
211C22C2×D4×D2911yescharacteristic
212C22C2×D4×D2911yescharacteristic
213C22#41×D2914yes—
214C22C22×C22⋊D2911yescharacteristic
215C4—24no—
216C4—42no—
217C4—298no—
218C4—584no—
219C4—1162no—
220C4#1174530214yes—
221C2—82no—
222C2—2322no—
223C2#124×D2912yes—
224C2C2×#1174530211yescharacteristic
225C2#1427170912yes—
226C2#1427171212yes—
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC2×C29×#124C2
prime radicalC2×#11745302C2
hypercenterC2×#124D29
hypocenterC29#2858
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#11745306C2semidirect
3. C2×#11745309C2semidirect
4. C2×#11745237C2semidirect
5. C2×#11745298C2semidirect
6. #14271063C2semidirect
7. C42×Dic29C2semidirect
8. C2×C29×#124C2semidirect
52. C42×C29D4semidirect
59. C4×Dic29D4semidirect
107. Dic29#124semidirect
113. C2×#124D29semidirect
142. C29#2858semidirect
173. C42C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117453062
C2×#117453022
C2×#117453092
C2×#117452372
C2×#117452982
#142710632
C42×Dic292
C2×C29×#1242
#285829