Finite Group Databasebeta

← #16818426

Subgroups — #16818426

Order 3712.

310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271744C211yesmaximal, characteristic, complemented
2#14271297C212yesmaximal, complemented
3#14270896C212yesmaximal, complemented
4#14270889C211yesmaximal, characteristic, complemented
5C29×#394C211yesmaximal, characteristic, complemented
6C22×D4×C29C2211yescharacteristic
7C2×#90805—21no—
8C2×C4⋊C4×C29C2211yescharacteristic
9C2×C22⋊C4×C29—21no—
10C2×C22⋊C4×C29—21no—
11C2×#90782—22no—
12#11745292—21no—
13#11745292C2212yes—
14#11745259—22no—
15#11745257—22no—
16C29×#95C2211yescharacteristic
17#11745180—22no—
18C22⋊#6597C2212yes—
19C24×C29—21no—
20C2×D4×C29—22no—
21C2×D4×C29—42no—
22C22×C4×C29—21no—
23C22×C4×C29D411yescharacteristic
24C22×C4×C29D411yescharacteristic
25C22×C4×C29C2311yescharacteristic
26C2×C22⋊D29—22no—
27#90805—42no—
28#90805—42no—
29C2×D116—21no—
30C2×D116—21no—
31C2×D116D412yes—
32C2×C4×D29—22no—
33C2×Dic58—21no—
34C4⋊C4×C29—22no—
35C22⋊C4×C29—42no—
36C22⋊C4×C29—42no—
37#90782—44no—
38#90781—22no—
39#90781—22no—
40C4⋊Dic29—21no—
41C4⋊Dic29D412yes—
42C2×#6597—22no—
43C23×C29—22no—
44C23×C29—41no—
45C23×C29—41no—
46C23×C29—41no—
47C23×C29—41no—
48C23×C29—41no—
49C23×C29—41no—
50C23×C29C2×D411yescharacteristic
51C22×D29—22no—
52D4×C29—24no—
53D4×C29—42no—
54C2×C4×C29—21no—
55C2×C4×C29—21no—
56C2×C4×C29—21no—
57C2×C4×C29—41no—
58C2×C4×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29—41no—
61C2×C4×C29—41no—
62C2×C4×C29D812yescomplemented
63C2×C4×C29C2×D412yes—
64C22⋊D29—42no—
65C22⋊D29—42no—
66C2×Dic29—22no—
67D116—42no—
68D116—42no—
69D116—81no—
70C4×D29—44no—
71Dic58—42no—
72#6597—42no—
73#1598—291nomaximal, Sylow
74C22×C29—21no—
75C22×C29—21no—
76C22×C29—42no—
77C22×C29—42no—
78C22×C29—42no—
79C22×C29—81no—
80C22×C29—81no—
81C22×C29—81no—
82C22×C29—81no—
83C22×C29#12011yescharacteristic
84C22×C29C2×D811yescharacteristic
85C22×C29AGL(1,ℤ/8)11yescharacteristic
86C2×D29—42no—
87C2×D29—42no—
88C2×D29—42no—
89C4×C29—22no—
90C4×C29—22no—
91C4×C29—41no—
92C4×C29—81no—
93Dic29—42no—
94#537—291no—
95#447—292no—
96#394D2911yescharacteristic, complemented
97#327—292no—
98#324—291no—
99C2×C29—21no—
100C2×C29—21no—
101C2×C29—82no—
102C2×C29#44711yescharacteristic
103C2×C29#45411yescharacteristic
104C2×C29B(4,𝔽2)11yescharacteristic
105D29—82no—
106C2×#41—581no—
107C22×D4C2×D2911yescharacteristic
108C2×D8—582no—
109C22⋊Q8—582no—
110#121—292no—
111#121—582no—
112#121—581no—
113C2×C4⋊C4C2×D2911yescharacteristic
114C2×C22⋊C4—21no—
115C2×C22⋊C4—21no—
116#102—582no—
117C22⋊C8—292no—
118#95C2×D2911yescharacteristic
119C29#159811yescharacteristic, complemented, Sylow
120C24—21no—
121#41—1162no—
122#41—1162no—
123C2×Q8—581no—
124C2×D4—22no—
125C2×D4—42no—
126C2×D4—292no—
127C2×D4—581no—
128C2×D4—581no—
129C2×D4—582no—
130C22×C4—21no—
131C22×C4—582no—
132C22×C4C22⋊D2911yescharacteristic
133C22×C4C22⋊D2911yescharacteristic
134C22×C4C22×D2911yescharacteristic
135D8—1164no—
136C2×C8—582no—
137C4⋊C4—22no—
138C4⋊C4—292no—
139C4⋊C4—581no—
140C22⋊C4—42no—
141C22⋊C4—42no—
142C22⋊C4—582no—
143C22⋊C4—582no—
144C23—22no—
145C23—41no—
146C23—41no—
147C23—41no—
148C23—41no—
149C23—41no—
150C23—41no—
151C23—582no—
152C23C2×C22⋊D2911yescharacteristic
153Q8—1162no—
154D4—24no—
155D4—42no—
156D4—1162no—
157D4—1162no—
158D4—1162no—
159D4—1162no—
160D4—2321no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—582no—
170C2×C4—1164no—
171C2×C4#9078212yescomplemented
172C2×C4D4×D2912yes—
173C8—1162no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—1162no—
184C22—1162no—
185C22—1162no—
186C22C2×#9078211yescharacteristic
187C22#1174529911yescharacteristic
188C22#1174531111yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—81no—
193C4—1162no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—2322no—
198C2#1427129611yescharacteristic
199C2#1427133511yescharacteristic
200C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#394C2
socleC22×C29#120
hypercenter#394D29
hypocenterC29#1598
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #14271744C2semidirect
2. #14271297C2semidirect
3. #14270896C2semidirect
4. #14270889C2semidirect
5. C29×#394C2semidirect
62. C2×C4×C29D8semidirect
96. #394D29semidirect
119. C29#1598semidirect
171. C2×C4#90782semidirect

Maximal subgroups

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

subgroupindex
#142717442
#142712972
#142708962
#142708892
C29×#3942
#159829