Finite Group Databasebeta

← #16818578

Subgroups — #16818578

Order 3712.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#14271816C211yesmaximal, characteristic, complemented
2#14271355C211yesmaximal, characteristic, complemented
3#14271355C211yesmaximal, characteristic, complemented
4#14270909C211yesmaximal, characteristic, complemented
5#14270892C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic, complemented
7C29×#486C211yesmaximal, characteristic, complemented
8C2×#90809—21no—
9C29×C4⋊Q8C2211yescharacteristic
10C29×#127C2211yescharacteristic
11#11745308—21no—
12C2×#90782—21no—
13C2×#90782—21no—
14#11745257—21no—
15#11745256—22no—
16C4⋊C4×D29—21no—
17C4×D116C2211yescharacteristic
18C4×D116C2211yescharacteristic
19C29×#102—22no—
20C4×C8×C29C2211yescharacteristic
21#11745180—21no—
22#11745180—21no—
23C4⋊#6597C2211yescharacteristic
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×D4×C29—21no—
27C2×D4×C29—21no—
28C2×D4×C29—21no—
29#90809—42no—
30#90809—42no—
31C2×D116—22no—
32C2×D116D411yescharacteristic
33C2×D116D411yescharacteristic
34C2×C4×D29—22no—
35C2×C4×D29—21no—
36C2×C4×D29—21no—
37C2×C8×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29D412yes—
40C42×C29C2311yescharacteristic
41#90782—42no—
42#90782—42no—
43#90781—22no—
44#90781—21no—
45#90781—21no—
46C4⋊Dic29D411yescharacteristic
47C4⋊Dic29D411yescharacteristic
48#90779—22no—
49C2×#6597—21no—
50C2×#6597—21no—
51C23×C29—41no—
52C22×D29—21no—
53C22×D29—21no—
54Q8×C29—41no—
55Q8×C29—41no—
56D4×C29—42no—
57D4×C29—41no—
58D4×C29—41no—
59D4×C29—41no—
60D4×C29—41no—
61C2×C4×C29—22no—
62C2×C4×C29C2×D411yescharacteristic
63C2×C4×C29C2×D411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C2×Dic29—21no—
66C2×Dic29—21no—
67D116—21no—
68D116—21no—
69D116—21no—
70D116—44no—
71D116D812yescomplemented
72C4×D29—44no—
73C4×D29—41no—
74C4×D29—41no—
75C4×D29—41no—
76C4×D29—41no—
77C8×C29—41no—
78#6597—41no—
79#6597—41no—
80#1625—291nomaximal, Sylow
81C22×C29—81no—
82C22×C29—81no—
83C22×C29—81no—
84C22×C29#12011yescharacteristic
85C2×D29—22no—
86C2×D29—41no—
87C2×D29—41no—
88C2×D29—41no—
89C2×D29—41no—
90C2×D29—41no—
91C4×C29—21no—
92C4×C29—42no—
93C4×C29C2×D811yescharacteristic
94C4×C29#13511yescharacteristic
95C4×C29AGL(1,ℤ/8)11yescharacteristic
96C4×C29AGL(1,ℤ/8)11yescharacteristic
97Dic29—41no—
98Dic29—41no—
99#547—291no—
100#486D2911yescharacteristic, complemented
101#459—291no—
102#459—291no—
103#332—291no—
104D4⋊C8—291no—
105D4⋊C8—291no—
106C2×C29—161no—
107C2×C29#44711yescharacteristic
108C2×C29#44911yescharacteristic
109C2×C29#45411yescharacteristic
110D29—42no—
111D29—81no—
112C2×#41—581no—
113C2×D8—581no—
114C2×D8—581no—
115C4⋊Q8C2×D2911yescharacteristic
116#127C2×D2911yescharacteristic
117#123—582no—
118C22⋊Q8—581no—
119#121—581no—
120C4×D4—291no—
121C4×D4—291no—
122C2×C4⋊C4—581no—
123C4⋊C8—291no—
124C4⋊C8—291no—
125#102—22no—
126#102—581no—
127#102—581no—
128C4×C8C2×D2911yescharacteristic
129C29#162511yescharacteristic, complemented, Sylow
130#41—1162no—
131#41—1162no—
132C2×Q8—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—291no—
137C2×D4—291no—
138C2×D4—582no—
139C22×C4—582no—
140C22×C4—581no—
141C22×C4—581no—
142D8—1162no—
143D8—1162no—
144C2×C8—21no—
145C2×C8—581no—
146C2×C8—581no—
147C4⋊C4—21no—
148C4⋊C4—291no—
149C4⋊C4—291no—
150C4⋊C4—582no—
151C4⋊C4C22⋊D2912yes—
152C22⋊C4—582no—
153C22⋊C4—581no—
154C22⋊C4—581no—
155C42C22×D2911yescharacteristic
156C23—41no—
157C23—581no—
158C23—581no—
159Q8—41no—
160Q8—41no—
161D4—42no—
162D4—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—292no—
167D4—581no—
168D4—581no—
169D4—581no—
170D4—1164no—
171C2×C4—22no—
172C2×C4—581no—
173C2×C4—581no—
174C2×C4—1164no—
175C2×C4—1161no—
176C2×C4—1161no—
177C2×C4—1161no—
178C2×C4—1161no—
179C2×C4D4×D2911yescharacteristic
180C2×C4D4×D2911yescharacteristic
181C2×C4C2×C22⋊D2911yescharacteristic
182C8—41no—
183C8—1161no—
184C8—1161no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—582no—
189C22—1161no—
190C22—1161no—
191C22—1161no—
192C22—1161no—
193C22—1161no—
194C22#1174529911yescharacteristic
195C4—21no—
196C4—42no—
197C4—1161no—
198C4—1161no—
199C4D8×D2911yescharacteristic
200C4#1174527311yescharacteristic
201C4#1174527611yescharacteristic
202C4#1174527811yescharacteristic
203C2—161no—
204C2—1162no—
205C2—2321no—
206C2#1427129511yescharacteristic
207C2#1427130711yescharacteristic
208C2#1427133511yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#486C2
socleC22×C29#120
hypercenter#486D29
hypocenterC29#1625
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14271816C2semidirect
2. #14271355C2semidirect
3. #14271355C2semidirect
4. #14270909C2semidirect
5. #14270892C2semidirect
6. #14270892C2semidirect
7. C29×#486C2semidirect
71. D116D8semidirect
100. #486D29semidirect
129. C29#1625semidirect

Maximal subgroups

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

subgroupindex
#142718162
#142713552
#142709092
#142708922
C29×#4862
#162529