Finite Group Databasebeta

← #16820657

Subgroups — #16820657

Order 3712.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#14271789C211yesmaximal, characteristic, complemented
2#14271018C211yesmaximal, characteristic
3#14271018C212yesmaximal
4#14270929C212yesmaximal, complemented
5C29×#342C211yesmaximal, characteristic, complemented
6C24×D29C2211yescharacteristic
7C2×C22⋊C4×C29C2212yes—
8C2×C22⋊C4×C29C2211yescharacteristic
9C2×C22⋊Dic29C2211yescharacteristic
10C2×C22⋊Dic29C2212yes—
11C2×#90781—22no—
12C2×#90781—24no—
13#11745286—22no—
14#11745240—24no—
15C24×C29C2311yescharacteristic
16C23×D29—21no—
17C23×D29—22no—
18C23×D29—22no—
19C23×D29—21no—
20C23×D29—44no—
21C23×D29Q812yescomplemented
22C22×C4×C29—22no—
23C22×C4×C29D412yes—
24C22×Dic29—21no—
25C22×Dic29D414yes—
26C2×Dic58—22no—
27C22⋊C4×C29—22no—
28C22⋊C4×C29—22no—
29C22⋊C4×C29—22no—
30C22⋊Dic29—22no—
31C22⋊Dic29—22no—
32C22⋊Dic29—22no—
33#90781—48no—
34#90781—44no—
35C4⋊Dic29—22no—
36#90779—24no—
37C23×C29—42no—
38C23×C29C2×D411yescharacteristic
39C23×C29C2×D412yes—
40C23×C29C2×Q811yescharacteristic
41C23×C29#4112yes—
42C23×C29#4111yescharacteristic
43C22×D29—24no—
44C22×D29—28no—
45C22×D29—24no—
46C22×D29—22no—
47C22×D29—44no—
48C22×D29—48no—
49C22×D29—44no—
50C22×D29—42no—
51C22×D29—44no—
52C22×D29—41no—
53C22×D29—41no—
54C22×D29—42no—
55C2×C4×C29—22no—
56C2×C4×C29—42no—
57C2×C4×C29—44no—
58C2×C4×C29—42no—
59C2×Dic29—24no—
60C2×Dic29—44no—
61C2×Dic29—42no—
62C2×Dic29—41no—
63Dic58—82no—
64#2029—291nomaximal, Sylow
65C22×C29—22no—
66C22×C29—24no—
67C22×C29—41no—
68C22×C29—42no—
69C22×C29—41no—
70C22×C29#12011yescharacteristic
71C22×C29C22⋊Q812yes—
72C22×C29C22⋊Q811yescharacteristic
73C22×C29#12411yescharacteristic
74C22×C29#12412yes—
75C2×D29—28no—
76C2×D29—24no—
77C2×D29—44no—
78C2×D29—48no—
79C2×D29—44no—
80C2×D29—42no—
81C2×D29—42no—
82C2×D29—44no—
83C4×C29—42no—
84C4×C29—82no—
85Dic29—44no—
86Dic29—81no—
87#543—291no—
88#379—292no—
89#379—291no—
90#342—292no—
91#342D2911yescharacteristic, complemented
92C2×C29—21no—
93C2×C29—22no—
94C2×C29—22no—
95C2×C29—21no—
96C2×C29#39311yescharacteristic
97C2×C29B(4,𝔽2)12yes—
98D29—44no—
99C25—291no—
100C22⋊Q8—584no—
101C22⋊Q8—582no—
102C2×C22⋊C4—292no—
103C2×C22⋊C4—291no—
104C2×C22⋊C4—584no—
105C2×C22⋊C4—582no—
106C2×C22⋊C4C2×D2912yes—
107C2×C22⋊C4C2×D2911yescharacteristic
108C29#202911yescharacteristic, complemented, Sylow
109C24—292no—
110C24—581no—
111C24—582no—
112C24—582no—
113C24—581no—
114C24—1164no—
115C24C22×D2911yescharacteristic
116C2×Q8—582no—
117C22×C4—22no—
118C22×C4—294no—
119C22×C4—581no—
120C22×C4D11612yes—
121C4⋊C4—584no—
122C4⋊C4—582no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—582no—
127C22⋊C4—582no—
128C22⋊C4—582no—
129C22⋊C4—1164no—
130C22⋊C4—1168no—
131C23—42no—
132C23—584no—
133C23—588no—
134C23—584no—
135C23—582no—
136C23—1162no—
137C23—1164no—
138C23—1164no—
139C23—1168no—
140C23—1164no—
141C23—1161no—
142C23—1161no—
143C23—1162no—
144C23C2×D11611yescharacteristic
145C23#9080512yes—
146C23D4×D2912yes—
147C23#9080711yescharacteristic
148C23Q8×D2911yescharacteristic
149Q8—2322no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—584no—
155C2×C4—1164no—
156C2×C4—1162no—
157C2×C4—1161no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22—588no—
164C22—584no—
165C22—1168no—
166C22—1164no—
167C22—1164no—
168C22—1162no—
169C22—1162no—
170C22—1164no—
171C22#1174523711yescharacteristic
172C22#1174524411yescharacteristic
173C22#1174524712yes—
174C22#1174525812yes—
175C22#1174525911yescharacteristic
176C4—42no—
177C4—82no—
178C4—1164no—
179C4—2321no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—1164no—
185C2#1427107611yescharacteristic
186C2#1427135112yes—
subgroupG/H
centerC22#11745244
commutator, cosocleC24×C29C23
FrattiniC24C22×D29
FittingC29×#342C2
socleC22×C29#120
prime radicalC24×D29C22
hypercenter#342D29
hypocenterC29#2029
LCSG ▷ C24×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #14271789C2semidirect
4. #14270929C2semidirect
5. C29×#342C2semidirect
21. C23×D29Q8semidirect
91. #342D29semidirect
108. C29#2029semidirect

Maximal subgroups

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

subgroupindex
#142717892
#142710182
#142709292
C29×#3422
#202929