Finite Group Databasebeta

← #16820656

Subgroups — #16820656

Order 3712.

466 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 69 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#14271019C212yesmaximal
3#14270930C211yesmaximal, characteristic, complemented
4#14270929C212yesmaximal, complemented
5C29×#379C211yesmaximal, characteristic
6C25×C29C2211yescharacteristic
7C2×C22⋊C4×C29—22no—
8C2×C22⋊C4×C29C2211yescharacteristic
9C2×C22⋊C4×C29C2211yescharacteristic
10C2×C22⋊Dic29—24no—
11C2×C22⋊Dic29C2212yes—
12C2×C22⋊Dic29C2212yes—
13#11745286—22no—
14#11745240—24no—
15C24×C29—22no—
16C24×C29—21no—
17C24×C29—21no—
18C24×C29—22no—
19C24×C29—44no—
20C24×C29Q812yescomplemented
21C24×C29C2311yescharacteristic
22C22×C4×C29—21no—
23C22×C4×C29D412yes—
24C22×Dic29—22no—
25C22×Dic29D414yes—
26C2×Dic58—22no—
27C22⋊C4×C29—22no—
28C22⋊C4×C29—22no—
29C22⋊C4×C29—44no—
30C22⋊Dic29—22no—
31C22⋊Dic29—22no—
32C22⋊Dic29—22no—
33C22⋊Dic29—22no—
34C22⋊Dic29—48no—
35C4⋊Dic29—22no—
36#90779—24no—
37C23×C29—28no—
38C23×C29—24no—
39C23×C29—22no—
40C23×C29—24no—
41C23×C29—44no—
42C23×C29—42no—
43C23×C29—44no—
44C23×C29—42no—
45C23×C29—44no—
46C23×C29—48no—
47C23×C29—41no—
48C23×C29—41no—
49C23×C29—42no—
50C23×C29C2×D412yes—
51C23×C29C2×D411yescharacteristic
52C23×C29C2×Q811yescharacteristic
53C23×C29#4111yescharacteristic
54C23×C29#4112yes—
55C2×C4×C29—22no—
56C2×C4×C29—42no—
57C2×C4×C29—42no—
58C2×C4×C29—41no—
59C2×Dic29—24no—
60C2×Dic29—44no—
61C2×Dic29—44no—
62C2×Dic29—42no—
63Dic58—82no—
64#2029—291nomaximal, Sylow
65C22×C29—24no—
66C22×C29—22no—
67C22×C29—28no—
68C22×C29—24no—
69C22×C29—41no—
70C22×C29—41no—
71C22×C29—42no—
72C22×C29—48no—
73C22×C29—44no—
74C22×C29—42no—
75C22×C29—44no—
76C22×C29—42no—
77C22×C29—44no—
78C22×C29#12011yescharacteristic
79C22×C29C22⋊Q811yescharacteristic
80C22×C29C22⋊Q812yes—
81C22×C29#12411yescharacteristic
82C22×C29#12412yes—
83C4×C29—42no—
84C4×C29—81no—
85Dic29—44no—
86Dic29—82no—
87#543—291no—
88#379—292no—
89#379D2911yescharacteristic
90#342—292no—
91#342—291no—
92C2×C29—22no—
93C2×C29—21no—
94C2×C29—21no—
95C2×C29—22no—
96C2×C29—44no—
97C2×C29#39311yescharacteristic
98C2×C29B(4,𝔽2)12yes—
99C25C2×D2911yescharacteristic
100C22⋊Q8—584no—
101C22⋊Q8—582no—
102C2×C22⋊C4—22no—
103C2×C22⋊C4—292no—
104C2×C22⋊C4—292no—
105C2×C22⋊C4—584no—
106C2×C22⋊C4C2×D2911yescharacteristic
107C2×C22⋊C4C2×D2911yescharacteristic
108C29#202911yescharacteristic, complemented, Sylow
109C24—22no—
110C24—21no—
111C24—21no—
112C24—22no—
113C24—44no—
114C24Dic5812yescomplemented
115C24C22×D2911yescharacteristic
116C2×Q8—582no—
117C22×C4—21no—
118C22×C4—294no—
119C22×C4—582no—
120C22×C4C22⋊D2912yes—
121C4⋊C4—584no—
122C4⋊C4—582no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—44no—
126C22⋊C4—582no—
127C22⋊C4—582no—
128C22⋊C4—582no—
129C22⋊C4—582no—
130C22⋊C4—1168no—
131C23—24no—
132C23—28no—
133C23—22no—
134C23—24no—
135C23—44no—
136C23—42no—
137C23—42no—
138C23—44no—
139C23—44no—
140C23—48no—
141C23—41no—
142C23—41no—
143C23—42no—
144C23C2×Dic5811yescharacteristic
145C23#9080511yescharacteristic
146C23D4×D2912yes—
147C23#9080712yes—
148C23C2×C22⋊D2911yescharacteristic
149Q8—2322no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—584no—
155C2×C4—1164no—
156C2×C4—1164no—
157C2×C4—1162no—
158C22—22no—
159C22—24no—
160C22—24no—
161C22—28no—
162C22—41no—
163C22—41no—
164C22—42no—
165C22—44no—
166C22—48no—
167C22—42no—
168C22—44no—
169C22—42no—
170C22—44no—
171C22#1174524012yes—
172C22#1174524712yes—
173C22#1174528611yescharacteristic
174C22#1174529811yescharacteristic
175C22#1174529911yescharacteristic
176C4—42no—
177C4—81no—
178C4—1164no—
179C4—2322no—
180C2—21no—
181C2—22no—
182C2—21no—
183C2—22no—
184C2—44no—
185C2#1427107511yescharacteristic
186C2#1427134912yes—
subgroupG/H
centerC22#11745299
commutator, cosocleC24×C29C23
FrattiniC24C22×D29
FittingC29×#379C2
socleC22×C29#120
prime radicalC25×C29C22
hypercenter#379D29
hypocenterC29#2029
LCSG ▷ C24×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #14271789C2semidirect
3. #14270930C2semidirect
4. #14270929C2semidirect
20. C24×C29Q8semidirect
108. C29#2029semidirect
114. C24Dic58semidirect

Maximal subgroups

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

subgroupindex
#142717892
#142710192
#142709302
#142709292
C29×#3792
#202929