Finite Group Databasebeta

← #16818478

Subgroups — #16818478

Order 3712.

280 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 57 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#14271474C212yesmaximal, complemented
2#14271088C211yesmaximal, characteristic, complemented
3#14270897C212yesmaximal, complemented
4#14270887C211yesmaximal, characteristic, complemented
5C29×#534C211yesmaximal, characteristic
6C22×D4×C29—21no—
7C29×#123—22no—
8C29×#121—21no—
9C29×#121C2212yes—
10C29×#120—22no—
11C2×C22⋊C4×C29C2211yescharacteristic
12C2×C22⋊Dic29—21no—
13C2×C4⋊Dic29C2211yescharacteristic, complemented
14#11745180—22no—
15#11745179—21no—
16#11745179C2211yescharacteristic, complemented
17C22⋊#6597C2212yescomplemented
18#11745155—22no—
19C24×C29—21no—
20C24×C29D411yescharacteristic
21C2×D4×C29—22no—
22C2×D4×C29—22no—
23C2×D4×C29—21no—
24C2×D4×C29—42no—
25C2×D4×C29—42no—
26C2×D4×C29D412yes—
27C22×C4×C29—21no—
28C22×C4×C29D411yescharacteristic
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29—21no—
32C4⋊C4×C29—21no—
33C4⋊C4×C29D412yes—
34C22⋊C4×C29—22no—
35C22⋊C4×C29—22no—
36C22⋊C4×C29—22no—
37C22⋊Dic29—42no—
38C4⋊Dic29—22no—
39C2×#6597—22no—
40C23×C29—21no—
41C23×C29—21no—
42C23×C29—22no—
43C23×C29—41no—
44C23×C29—41no—
45C23×C29—42no—
46C23×C29—81no—
47C23×C29—81no—
48C23×C29D812yes—
49C23×C29C2×D411yescharacteristic
50D4×C29—42no—
51D4×C29—44no—
52D4×C29—42no—
53D4×C29—42no—
54D4×C29—81no—
55C2×C4×C29—21no—
56C2×C4×C29—22no—
57C2×C4×C29—41no—
58C2×C4×C29—42no—
59C2×C4×C29—41no—
60C2×C4×C29C2×D412yes—
61C2×Dic29—41no—
62C2×Dic29—41no—
63C2×Dic29—41no—
64C2×Dic29—41no—
65C2×Dic29—41no—
66C2×Dic29—41no—
67#6597—42no—
68#1607—291nomaximal, Sylow
69C22×C29—21no—
70C22×C29—21no—
71C22×C29—22no—
72C22×C29—42no—
73C22×C29—41no—
74C22×C29—41no—
75C22×C29—42no—
76C22×C29—42no—
77C22×C29—42no—
78C22×C29—81no—
79C22×C29—84no—
80C22×C29#12011yescharacteristic
81C22×C29C2×D811yescharacteristic
82C22×C29AGL(1,ℤ/8)11yescharacteristic
83C4×C29—22no—
84C4×C29—42no—
85C4×C29—41no—
86Dic29—81no—
87Dic29—81no—
88#534D2911yescharacteristic
89#480—292no—
90#397—291no—
91#327—292no—
92#323—291no—
93C2×C29—21no—
94C2×C29—21no—
95C2×C29—42no—
96C2×C29—82no—
97C2×C29#44711yescharacteristic
98C2×C29#45511yescharacteristic
99C2×C29#45811yescharacteristic
100C22×D4—21no—
101#123—22no—
102#121—21no—
103#121C2×D2912yes—
104#120—22no—
105C2×C4⋊C4—291no—
106C2×C22⋊C4—581no—
107C2×C22⋊C4C2×D2911yescharacteristic
108#107—582no—
109#102—582no—
110C22⋊C8—292no—
111#95—291no—
112#95—581no—
113C29#160711yescharacteristic, complemented, Sylow
114C24—21no—
115C24C22⋊D2911yescharacteristic
116C2×D4—22no—
117C2×D4—22no—
118C2×D4—21no—
119C2×D4—42no—
120C2×D4—42no—
121C2×D4C22⋊D2912yes—
122C22×C4—21no—
123C22×C4—581no—
124C22×C4—581no—
125C22×C4C22⋊D2911yescharacteristic
126C22×C4C22×D2911yescharacteristic
127C2×C8—582no—
128C4⋊C4—21no—
129C4⋊C4—582no—
130C4⋊C4C22⋊D2912yes—
131C22⋊C4—22no—
132C22⋊C4—22no—
133C22⋊C4—22no—
134C22⋊C4—1162no—
135C23—21no—
136C23—21no—
137C23—22no—
138C23—41no—
139C23—41no—
140C23—42no—
141C23—81no—
142C23—81no—
143C23#9078212yes—
144C23C2×C22⋊D2911yescharacteristic
145D4—42no—
146D4—44no—
147D4—42no—
148D4—42no—
149D4—81no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—1161no—
156C2×C4—1161no—
157C2×C4—1161no—
158C2×C4—1161no—
159C2×C4—1161no—
160C2×C4—1161no—
161C2×C4C2×C22⋊D2912yes—
162C8—1162no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—81no—
173C22—84no—
174C22C2×#9078211yescharacteristic
175C22#1174529411yescharacteristic
176C22#1174531511yescharacteristic
177C4—22no—
178C4—42no—
179C4—41no—
180C4—2321no—
181C4—2321no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—82no—
186C2#1427129711yescharacteristic
187C2#1427134111yescharacteristic
188C2#1427135311yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#534C2
socleC22×C29#120
hypercenter#534D29
hypocenterC29#1607
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #14271474C2semidirect
2. #14271088C2semidirect
3. #14270897C2semidirect
4. #14270887C2semidirect
13. C2×C4⋊Dic29C22semidirect
16. #11745179C22semidirect
17. C22⋊#6597C22semidirect
113. C29#1607semidirect

Maximal subgroups

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

subgroupindex
#142714742
#142710882
#142708972
#142708872
C29×#5342
#160729