Finite Group Databasebeta

← #16818582

Subgroups — #16818582

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#14271511C211yesmaximal, characteristic, complemented
3#14271359C211yesmaximal, characteristic, complemented
4#14271359C211yesmaximal, characteristic, complemented
5#14270890C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#332C211yesmaximal, characteristic, complemented
8C2×#90809—21no—
9C29×C4⋊Q8C2211yescharacteristic
10#11745308—21no—
11C2×D232—21no—
12C2×D232—21no—
13#11745257—21no—
14#11745256—22no—
15C4⋊C4×D29—21no—
16#11745236C2211yescharacteristic
17C4×D116C2211yescharacteristic
18C4×D116C2211yescharacteristic
19C29×C4⋊C8C2211yescharacteristic
20C29×C4⋊C8C2211yescharacteristic
21#11745169—21no—
22#11745169—21no—
23#11745157—22no—
24C4×#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26#90809—42no—
27#90809—42no—
28C2×D116—22no—
29C2×D116—21no—
30C2×D116—21no—
31C2×D116—21no—
32C2×D116D411yescharacteristic
33C2×D116D411yescharacteristic
34C2×C4×D29—22no—
35C2×C4×D29—21no—
36C2×C4×D29—21no—
37C2×C8×C29—21no—
38C2×C8×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29D412yes—
41C42×C29C2311yescharacteristic
42#90781—22no—
43#90781—21no—
44#90781—21no—
45C4⋊Dic29D411yescharacteristic
46C4⋊Dic29D411yescharacteristic
47#90779—22no—
48C2×#6597—21no—
49D232—42no—
50D232—42no—
51C22×D29—21no—
52C22×D29—21no—
53C22×D29—41no—
54Q8×C29—41no—
55Q8×C29—41no—
56C2×C4×C29—22no—
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C2×C4×C29C2×D411yescharacteristic
60C2×Dic29—21no—
61C2×Dic29—21no—
62D116—21no—
63D116—21no—
64D116—21no—
65D116—42no—
66D116—44no—
67D116—41no—
68D116—41no—
69D116—41no—
70D116—41no—
71D116D812yescomplemented
72C4×D29—44no—
73C4×D29—41no—
74C4×D29—41no—
75C4×D29—41no—
76C4×D29—41no—
77C8×C29—41no—
78C8×C29—41no—
79#6597—41no—
80#1625—291nomaximal, Sylow
81C22×C29#12011yescharacteristic
82C2×D29—22no—
83C2×D29—41no—
84C2×D29—41no—
85C2×D29—41no—
86C2×D29—41no—
87C2×D29—41no—
88C2×D29—81no—
89C2×D29—81no—
90C2×D29—81no—
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#486—291no—
101#459—291no—
102#459—291no—
103#332D2911yescharacteristic, complemented
104D4⋊C8—291no—
105D4⋊C8—291no—
106C2×C29#44711yescharacteristic
107C2×C29#44911yescharacteristic
108C2×C29#45411yescharacteristic
109D29—42no—
110D29—81no—
111D29—161no—
112C2×#41—581no—
113C2×D8—581no—
114C2×D8—581no—
115C4⋊Q8C2×D2911yescharacteristic
116#127—291no—
117#123—582no—
118C22⋊Q8—581no—
119#121—581no—
120C4×D4—291no—
121C4×D4—291no—
122C2×C4⋊C4—581no—
123C4⋊C8C2×D2911yescharacteristic
124C4⋊C8C2×D2911yescharacteristic
125#102—581no—
126#102—581no—
127#102—582no—
128C4×C8—291no—
129C29#162511yescharacteristic, complemented, Sylow
130#41—1162no—
131#41—1162no—
132C2×Q8—21no—
133C2×D4—291no—
134C2×D4—291no—
135C2×D4—582no—
136C2×D4—581no—
137C2×D4—581no—
138C2×D4—581no—
139C22×C4—582no—
140C22×C4—581no—
141C22×C4—581no—
142D8—1162no—
143D8—1162no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—581no—
147C4⋊C4—21no—
148C4⋊C4—291no—
149C4⋊C4—291no—
150C4⋊C4—582no—
151C4⋊C4D11612yes—
152C22⋊C4—582no—
153C22⋊C4—581no—
154C22⋊C4—581no—
155C42C22×D2911yescharacteristic
156C23—581no—
157C23—581no—
158C23—1161no—
159Q8—41no—
160Q8—41no—
161D4—292no—
162D4—581no—
163D4—581no—
164D4—581no—
165D4—1162no—
166D4—1164no—
167D4—1161no—
168D4—1161no—
169D4—1161no—
170D4—1161no—
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×C4C2×D11611yescharacteristic
180C2×C4D4×D2911yescharacteristic
181C2×C4D4×D2911yescharacteristic
182C8—41no—
183C8—41no—
184C8—1161no—
185C22—582no—
186C22—1161no—
187C22—1161no—
188C22—1161no—
189C22—1161no—
190C22—1161no—
191C22—2321no—
192C22—2321no—
193C22—2321no—
194C22#1174524411yescharacteristic
195C4—21no—
196C4—42no—
197C4—1161no—
198C4—1161no—
199C4D8×D2911yescharacteristic
200C4#1174527611yescharacteristic
201C4#1174527611yescharacteristic
202C4#1174528111yescharacteristic
203C2—1162no—
204C2—4641no—
205C2—2321no—
206C2#1427129811yescharacteristic
207C2#1427131111yescharacteristic
208C2#1427133811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#332C2
socleC22×C29#120
hypercenter#332D29
hypocenterC29#1625
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #14271816C2semidirect
2. #14271511C2semidirect
3. #14271359C2semidirect
4. #14271359C2semidirect
5. #14270890C2semidirect
6. #14270890C2semidirect
7. C29×#332C2semidirect
71. D116D8semidirect
103. #332D29semidirect
129. C29#1625semidirect

Maximal subgroups

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

subgroupindex
#142718162
#142715112
#142713592
#142708902
C29×#3322
#162529