Finite Group Databasebeta

← #16827866

Subgroups — #16827866

Order 3712.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11745252C211yesmaximal, characteristic, complemented
2C2×#11745309C211yesmaximal, characteristic
3#14271070C211yesmaximal, characteristic, complemented
4#14271065C211yesmaximal, characteristic
5#14271064C211yesmaximal, characteristic
6#14271055C214yesmaximal, complemented
7#14271052C214yesmaximal, complemented
8C42×Dic29C211yesmaximal, characteristic, complemented
9C29×#391C211yesmaximal, characteristic, complemented
10C22×Q8×C29C2211yescharacteristic
11C22×D116C2211yescharacteristic
12C2×C4⋊C4×C29C2211yescharacteristic
13C2×C42×C29C2211yescharacteristic
14#11745309—24no—
15C2×#90781C2212yes—
16C2×#90781C2214yes—
17C2×#90781C2214yes—
18C2×#90781C2212yes—
19C2×C4⋊Dic29C2212yes—
20C2×C4⋊Dic29C2211yescharacteristic
21C2×#90779C2212yes—
22C2×C4×Dic29C2212yes—
23C2×C4×Dic29C2212yes—
24C2×C4×Dic29C2211yescharacteristic
25C2×C4×Dic29C2211yescharacteristic
26#11745252—24no—
27C29×#95C2214yes—
28#11745179C2214yes—
29C23×D29C2312yes—
30C2×Q8×C29—22no—
31C2×Q8×C29—22no—
32C2×Q8×C29—22no—
33C22×C4×C29C2312yes—
34C22×C4×C29C2312yes—
35C22×C4×C29C2312yes—
36C22×C4×C29C2311yescharacteristic
37C22×Dic29C2312yes—
38C22×Dic29C2311yescharacteristic
39C22×Dic29C2311yescharacteristic
40C22×Dic29C2312yes—
41C2×D116—22no—
42C2×D116—22no—
43C2×D116—22no—
44C4⋊C4×C29—22no—
45C42×C29—22no—
46#90781—28no—
47#90781—24no—
48#90781—24no—
49#90781—28no—
50C4⋊Dic29—22no—
51C4⋊Dic29—24no—
52#90779—24no—
53C4×Dic29—22no—
54C4×Dic29—24no—
55C4×Dic29—24no—
56C4×Dic29D414yes—
57C23×C29C2411yescharacteristic
58C22×D29—22no—
59C22×D29—24no—
60C22×D29—24no—
61C22×D29—22no—
62C22×D29—22no—
63Q8×C29—44no—
64C2×C4×C29—22no—
65C2×C4×C29—22no—
66C2×C4×C29—22no—
67C2×C4×C29—22no—
68C2×C4×C29—24no—
69C2×C4×C29—22no—
70C2×C4×C29—22no—
71C2×C4×C29C2×D412yes—
72C2×C4×C29#4112yes—
73C2×C4×C29#4112yes—
74C2×C4×C29#4114yes—
75C2×Dic29—22no—
76C2×Dic29—22no—
77C2×Dic29—22no—
78C2×Dic29—22no—
79C2×Dic29—22no—
80C2×Dic29—24no—
81C2×Dic29C2×D412yes—
82C2×Dic29C2×D412yes—
83C2×Dic29#4114yes—
84D116—44no—
85#2861—291nomaximal, Sylow
86C22×C29C22×D411yescharacteristic
87C22×C29C2×#4111yescharacteristic
88C22×C29C2×#4111yescharacteristic
89C22×C29C2×#4112yes—
90C22×C29C2×#4112yes—
91C2×D29—42no—
92C2×D29—44no—
93C2×D29—44no—
94C2×D29—42no—
95C2×D29—42no—
96C4×C29—24no—
97C4×C29—42no—
98C4×C29—42no—
99C4×C29#12414yes—
100Dic29—24no—
101Dic29—22no—
102Dic29—22no—
103Dic29—42no—
104C2×#125—291no—
105C2×#124—291no—
106#391—291no—
107#391D2911yescharacteristic, complemented
108#390—291no—
109#390—291no—
110#388—294no—
111#388—294no—
112C43—291no—
113C2×C29C2×#12411yescharacteristic
114C2×C29#52912yes—
115C2×C29#52912yes—
116C2×C29#53211yescharacteristic
117C2×C29#53211yescharacteristic
118D29—82no—
119C22×Q8C2×D2911yescharacteristic
120C22×D4—291no—
121#125—584no—
122#124—584no—
123C2×C4⋊C4—292no—
124C2×C4⋊C4—292no—
125C2×C4⋊C4—291no—
126C2×C4⋊C4C2×D2911yescharacteristic
127C2×C22⋊C4—292no—
128C2×C22⋊C4—292no—
129C2×C22⋊C4—294no—
130C2×C22⋊C4—294no—
131C2×C42—291no—
132C2×C42—292no—
133C2×C42—292no—
134C2×C42—291no—
135C2×C42C2×D2911yescharacteristic
136#95—294no—
137#95C2×D2914yes—
138C29#286111yescharacteristic, complemented, Sylow
139C24—292no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×D4—582no—
144C2×D4—582no—
145C2×D4—582no—
146C22×C4—292no—
147C22×C4—291no—
148C22×C4—291no—
149C22×C4—292no—
150C22×C4C22×D2912yes—
151C22×C4C22×D2912yes—
152C22×C4C22×D2912yes—
153C22×C4C22×D2911yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—584no—
156C4⋊C4—584no—
157C4⋊C4—582no—
158C22⋊C4—584no—
159C22⋊C4—584no—
160C22⋊C4—588no—
161C22⋊C4—588no—
162C42—22no—
163C42—294no—
164C42—584no—
165C42—582no—
166C42—584no—
167C23—582no—
168C23—582no—
169C23—582no—
170C23—584no—
171C23—584no—
172C23C23×D2911yescharacteristic
173Q8—44no—
174D4—1164no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—292no—
183C2×C4—292no—
184C2×C4—294no—
185C2×C4—582no—
186C2×C4—582no—
187C2×C4—582no—
188C2×C4—582no—
189C2×C4—582no—
190C2×C4—584no—
191C2×C4#9080512yes—
192C2×C4D4×D2912yes—
193C2×C4#9080712yes—
194C2×C4#9080914yes—
195C22—1162no—
196C22—1164no—
197C22—1164no—
198C22—1162no—
199C22—1162no—
200C22C2×#9080511yescharacteristic
201C22C2×D4×D2911yescharacteristic
202C22C2×#9080711yescharacteristic
203C22C2×#9080912yes—
204C22#41×D2912yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—584no—
209C4—582no—
210C4—582no—
211C4—1162no—
212C4#1174524714yes—
213C2—2322no—
214C2C2×#1174524711yescharacteristic
215C2#1427169912yes—
216C2#1427170012yes—
217C2#1427171211yescharacteristic
218C2#1427171411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#391C2
prime radicalC22×D116C22
hypercenter#391D29
hypocenterC29#2861
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#11745252C2semidirect
3. #14271070C2semidirect
6. #14271055C2semidirect
7. #14271052C2semidirect
8. C42×Dic29C2semidirect
9. C29×#391C2semidirect
107. #391D29semidirect
138. C29#2861semidirect

Maximal subgroups

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

subgroupindex
C2×#117452522
C2×#117453092
#142710702
#142710652
#142710642
#142710552
#142710522
C42×Dic292
C29×#3912
#286129